dynamic modeling and control characteristics of the two...

Research ArticleDynamic Modeling and Control Characteristics ofthe Two-Modular HTR-PM Nuclear Plant

Zhe Dong Yifei Pan Maoxuan Song Xiaojing Huang Yujie Dong and Zuoyi Zhang

Institute of Nuclear and New Energy Technology Collaborative Innovation Centre of Advanced Nuclear Energy TechnologyKey Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education Tsinghua University Beijing 100084 China

Correspondence should be addressed to Zhe Dong dongzhemailtsinghuaeducn

Received 5 December 2016 Revised 2 March 2017 Accepted 5 March 2017 Published 22 May 2017

Academic Editor Enrico Zio

Copyright copy 2017 Zhe Dong et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Themodular high temperature gas-cooled reactor (MHTGR) is a typical small modular reactor (SMR) with inherent safety featureDue to its high reactor outlet coolant temperature the MHTGR can be applied not only for electricity production but also as aheat source for industrial complexes Through multimodular scheme that is the superheated steam flows produced by multipleMHTGR-based nuclear supplying system (NSSS) modules combined together to drive a common thermal load the inherent safetyfeature of MHTGR is applicable to large-scale nuclear plants at any desired power ratings Since the plant power control techniqueof traditional single-modular nuclear plants cannot be directly applied to the multimodular plants it is necessary to develop thepower control method of multimodular plants where dynamical modeling control design and performance verification are threemain aspects of developing plant control method In this paper the study in the power control for two-modular HTR-PM plantis summarized and the verification results based on numerical simulation are given The simulation results in the cases of plantpower step and ramp show that the plant control characteristics are satisfactory

1 Introduction

With comparison to burning fossil fuels there is nearly nogreenhouse gas emission in nuclear fission reaction Thusnuclear fission energy is a crucial clean energy for giving basisproducts such as electricity fresh water and process heat andfor addressing the challenges associated with global climateand environmental impact [1 2] Actually nuclear energymay substitute the fossil in a centralized way and in a greatamount with commercial availability and economic compet-itiveness [3] After the successful development of small (tensof megawatts) light water reactors (LWRs) for propulsion bythe US Navy the commercial nuclear reactors began to becommissioned since the late 1950s These early-stage nuclearreactors were the simply scaled up versions of the naval reac-tor with high power density [4] Although the increase of thereactor size induced the economic competitiveness withthose fossil plants the complicated operational issues beganto moderate the industryrsquos confidence in the plant safetyMore stringent safety requirements were then imposed

which induced a complex layering of redundant safety andauxiliary systems to the original simple LWRsThe escalationof plant complexity contributed to the rapidly increasingcosts licensing periods and construction delays Howeverthe plant safety still cannot be guaranteed satisfactorilyAfter the severe nuclear accidents that is Three Mile IslandChernobyl and Fukushima the safety issues of nuclearreactors have become much more significant than beforeThus there should be a novel reactor technology providing asatisfactory tradeoff between safety and economics

Small modular reactors (SMRs) are those nuclear fissionreactors whose electrical output power is less than 300MWe[4ndash6] Due to the low power density and large heat capacitysome SMRs even have the inherent safety feature whichprevents SMRs from the hazards of core-melting radiologicalrelease and LOCA (Loss of Coolant Accident) With load-following function SMRs can be incorporated with renew-able energy sources to build hybrid energy systems (HESs)having the virtues such as persistent power supply and freerefueling [1 2] By adopting multimodular operation strategy

HindawiScience and Technology of Nuclear InstallationsVolume 2017 Article ID 6298037 19 pageshttpsdoiorg10115520176298037

2 Science and Technology of Nuclear Installations

Control rod driving mechanism

Pebble-Bed of fuel elements

Cold helium riser

Helium blower

OTSG

Reflector

Hot helium chamber

Coaxial pipe

Figure 1 Composition of the MHTGR-based NSSS module

[7] that is multiple nuclear steam supplying system (NSSS)modules feeding steam to common thermal load equipmentsuch as the turbinegenerator set the inherent safety featureof a SMR can be applicable to large-scale nuclear plantsat any desired power ratings which could be beneficial inproviding electricity to remote areas without transmission ordistribution infrastructure in generating local power for alarge population center and in being viable for specificapplications such as heat sources for the industrial complexesFurthermore the SMRs can offer simpler safer and standard-izedmodular design by being factory-built requiring smallerinitial capital investment and having shorter constructionperiod and have been regarded by International AtomicEnergy Agency (IAEA) as one of the active developing trendsof nuclear energy

Due to its inherent safety feature the modular high tem-perature gas-cooled reactor (MHTGR such as HTR-Moduledesigned in Germany and MHTGR designed in US) hasbeen seen as one of the best candidates for the next-generation nuclear plants The MHTGR is a typical SMRwhich uses helium as coolant and graphite as moderator andstructural material and its inherent safety is determined bythe low power density strong negative temperature feedbackeffect and slim reactor shape [8ndash10] China began to study theMHTGR at the end of 1970s and a 10MWth pebble-bed hightemperature gas-cooled reactor HTR-10 which was designedby the Institute of Nuclear and New Energy Technology(INET) of Tsinghua University achieved its criticality inDecember 2000 and full power in January 2003 [11]Then sixsafety demonstration tests were done on the HTR-10 whichmanifested its inherent safety and self-stabilizing features[12] Based on the experience of the HTR-10 project a hightemperature gas-cooled reactor pebble-bed module (HTR-PM) plant was then proposed which consists of two pebble-bed one-zoneMHTGRs with combined 2 times 250MWth powerand adopts the operation scheme of two NSSS modulesdriving one steam turbine [13 14] Figure 1 shows that a NSSSmodule of the HTR-PM plant is composed of an MHTGRa helically coiled once-through steam generator (OTSG) a

primary helium blower and some connecting pipes Figure 2illustrates a simplified flow diagram of the entire two-modular HTR-PM plant The HTR-PM plant is now in thestage of plant construction and commissioning By incorpo-rating more MHTGR-based NSSS modules more large-scalemultimodular high temperature gas-cooled nuclear plant canbe realized

Satisfactory plant dynamic behavior is important forrealizing load-following function and for further formingHESs with fossil or renewable energy sources which is givenby not only the open-loop dynamics but also the controlstrategy There have been some promising results in dynami-cal modeling and control design for entire nuclear plants Inthe field of plant modeling Han gave a mathematical modelof pressurized water reactors for thermal-hydraulic analysis[15] Fazekas et al proposed a simple dynamic model for theprimary circuit in VVER plants for controller design pur-poses [16] Dong et al presented a lumped parameterdynamic model for control design and verification for theNSSS of the nuclear heating reactors (NHRs) [17] Withcomparison to the abundant results in reactor power-levelregulation such as the linear control nonlinear control andintelligent method [18ndash20] there are still less results in thefield of entire nuclear plant control Shtessel proposed asliding-mode plant control and state-observation strategy forspace nuclear energy system TOPAZ II [21] Huang et al gavea multi-input-multioutput (MIMO) fuzzy-adapted recursivesliding-mode plant controller for an advanced boiling waterreactor (ABWR) nuclear power plant [22] In order to achievesafe stable and efficient operation of the HTR-PM plant it isnecessary to give the lumped parameter model of the mainplant dynamics and to propose proper plant control strategyIt is worth noting that due to the two-modular schemethere is much difference between themodeling and control ofthe HTR-PM plant and that of those single-modular nuclearplant

In this paper both the dynamical modeling and controldesign method for HTR-PM plant are first summarizedor reviewed the realization of feedback loops and control

Science and Technology of Nuclear Installations 3

1 helium blower

1 OTSG

1 MHTGR

2 feedwater pump2 helium blower

2 OTSG

2 MHTGR

Deaerator

Main condenser

Turbine generator

Main steam valve

Bypass valve

1 feedwater pump1 high pressure heater

2 high pressure heater 3 LPH2 LPH1 LPH

1 NSSS

2 NSSS

LPH low pressure heater

Gland heater

Figure 2 Simplified flow diagram for the HTR-PM plant

laws are proposed and then the verification results basedupon numerical simulation are given which shows the maintransient performance of the HTR-PM plant is satisfactoryfor building HESs with the renewables

2 Dynamical Modeling

In this section the main parts of dynamic model of the HTR-PM plant that is the pebble-bed one-zone MHTGR OTSGfluid flownetwork (FFN) of the common secondary-loop sys-tem and turbinegenerator unit are summarized from [23ndash26] This model is proposed for control system design andverification whose parameters are determined by the datacollected from physical and thermal-hydraulic design

21 MHTGR From Figure 1 the cold helium enters theprimary blower where it is pressurized before flowing into thecold gas duct Then the cold helium gets into the channels(called riser) inside the side reflector from bottom to top andpasses through the pebble-bed (called downcomer) from topto bottom where it is heated to a high temperature about750∘C The hot helium leaves the hot gas chamber inside thebottom reflector and flows into theOTSGprimary side whereit transfers the heat to the secondary feedwater To guaranteethe inherent safety feature theMHTGRof theHTR-PMplanthas a slim core shape Relative to using a single node [23] it ismore proper to divide the reactor core intoN nodes along theaxial direction [24] The nodalization is shown in Figure 3where the riser is some tubes in the side reflector throughwhich helium can flow upward to the upper entry of thepebble-bed and the downcomer is the volume gap among the

fuel elements inside the pebble-bed through which heliumcan flow down Moreover the pressure loss of the primaryhelium flow is very small with comparison to the primarypressure and is omitted here

211 NeutronKinetics Thenodalized neutron kinetics can bewritten as [24]

d119899r1d119905 = 1205881 minus 120573 minus 12057211Λ 1 119899r1 + 1Λ 112057212119899r2 +

6sum119896=1

120573119896Λ 1119862r1119896d119899r119894d119905 = 120588119894 minus 120573 minus 120572119894119894Λ 119894 119899r119894

+ 1Λ 119894 (120572119894119894minus1119899r119894minus1 + 120572119894119894+1119899r119894+1)+ 6sum119896=1

120573119896Λ 119894119862r119894119896 119894 = 2 119873 minus 1d119899r119873d119905 = 120588119873 minus 120573 minus 120572119873119873Λ119873 119899r119873 + 1Λ119873120572119873119873minus1119899r119873minus1

+ 6sum119896=1

120573119896Λ119873119862r119873119896d119862r119894119896

d119905 = 120582119896 (119899r119894 minus 119862r119894119896) 119894 = 1 119873 119896 = 1 2 6

(1)


Ree

ctor

Rise

r

Lower header

Output headerLeakage

Inner ductOuter duct

MHTGR

Neutron kinetics

1 2Control rods

Heat exchangeHelium ow

Reactivity

OTSG primary side

12

Dow

ncom

er

Pebb

le-b

ed12

N

N

N

Figure 3 Nodalization of the MHTGR

where 119894 = 1 119873 119899r119894 is the relative neutron flux of the 119894thnode 119862r119894119896 is the relative concentration of the 119896th delayedneutron group of the 119894th node 120572119894119894 and 120572119894119894 (119895 = 1 119873119894) arethe coupling coefficients corresponding to the 119894th node 119873119894is the number of adjacent nodes of the 119894th node Λ 119894 is theprompt neutron lifetime in the 119894th node 120588119894 is the reactivityof the 119894th node 120573 is the fraction of all the delayed neutrons inall the nodes and 120573119896 is the fraction of the kth delayed neutrongroup in every node

The nodal reactivity feedback is expressed as function ofthe nodal fuel temperature119879c119894 (119894 = 1 119873) and temperatureof the reflector 119879r The total nodal reactivity is given as [24]

120588119894 = 120588r119894 + (120572f 119894 + 120572m119894) (119879c119894 minus 119879c0119894) + 120572r (119879r minus 119879r0) (2)

where 120588r119894 is the nodal reactivity provided by the control rods120572f 119894 and 120572m119894 are respectively the reactivity coefficients ofthe fuel and moderator inside node i 120572r is the reactivitycoefficient of the average reflector temperature and 119879c0119894 and119879r0 are respectively the initial temperature of the fuel insidenode 119894 and that of the reflector Since the reflector is verythick and since the metal core support structure is cooled bythe cold heliumwith its temperature nomore than 250∘C the

reactivity feedback induced by the support structure is omit-ted here which has been verified by theMHTGRphysical andthermal-hydraulic design

Moreover it can be derived that [24]

120572119894119895 = (11989911989501198991198940 )119863119860120592Σf 119894119881119889

119895 = 2 119894 = 1119894 minus 1 119894 + 1 119894 = 2 119873 minus 1119873 minus 1 119894 = 119873

120572119894119894 =

119863119860120592Σf 2119881119889 119894 = 1119863119860120592119881119889 ( 1Σf 119894minus1

+ 1Σf 119894+1) 119894 = 2 119873 minus 1

119863119860120592Σf 119873minus1119881119889 119894 = 119873

(3)

where A is the cross-sectional area of the active core region119881 is the volume of every node 119889 is the height of every node120592 is the fission number Σa119894 and Σf 119894 (119894 = 1 119873) are


respectively the macroabsorption and fission cross sectionsin the 119894th node

212 Thermal Hydraulics

(1) Pebble-Bed The thermal dynamics of 119894th node of thepebble-bed can be written as [24]

(1 minus 120576) 120588c119894119881119862c119894d119879c119894

d119905 = 1198750119894119899r119894 minus 119870d119894119860d119894 (119879c119894 minus 119879d119894) minus 119870cr119894119860cr119894 (119879c119894 minus 119879r)

+

minus119870c1119860 (119879c1 minus 119879c2) 119894 = 1minus119870c119894119860 (119879c119894 minus 119879c119894+1) + 119870c119894minus1119860 (119879c119894minus1 minus 119879c119894) 119894 = 2 119873 minus 1119870c119873minus1119860 (119879c119873minus1 minus 119879c119873) 119894 = 119873

(4)

where 120588c119894 119862c119894 119879c119894 and 1198750119894 are respectively the densityspecific heat temperature and rated power of fuel pile insidenode 119894 119870d119894 and 119860d119894 are respectively the heat transfercoefficient and heat transfer area between the fuel pile andhelium inside node 119894 119879d119894 is the temperature of the heliuminside node i119870cr119894 and119860cr119894 are respectively the heat transfercoefficient and heat transfer area between the fuel pile in node119894 and the reflector 119879r is the temperature of the reflector 119870c119894(119894 = 1 119873 minus 1) is the heat transfer coefficient between thefuel pile inside node 119894 and that inside node 119894 + 1 and 120576 is theporosity of the pebble-bed

(2) Reflector To improve the heat capacity and to weakenthe neutron leakage the reflector of the MHTGR is verythick which means that the thermal inertial of the reflectoris so large that the dynamic response of the reflector is indifferent scale with that of the fuel elements and helium flowMoreover the side reflector is cooled by the cold helium flowinjected into the reactor with a high speed Therefore for thesimplicity of dynamic model it is reasonable to regard thereflector as one nodal

From Figure 3 there are two heat transfer processes withthe reflector This first one is the fission heat conducted fromthe fuel pile inside every node which heats up the reflectorThe second one is that the cold helium inside the riser coolsdown the reflector The heat transfer about the reflector canbe written as [24]

120588r119881r119862rd119879rd119905 = 119873sum

119894=1

119870cr119894119860cr119894 (119879c119894 minus 119879r)minus 119870ur119860ur (119879r minus 119879u)

(5)

where 120588r119881r and119862r are respectively the density volume andspecific heat of the reflector119870ur and119860ur are the heat transfercoefficient and heat transfer area between the reflector andthe coolant in the riser and 119879u is the average coolanttemperature inside the riser

(3) DowncomerThe cold helium enters the downcomer fromits upper entry and flows downward to cool the pebble-bed The heat is mainly transferred to the helium inside thedowncomer which can be described as [24]

119881119894 d120588d119894d119905 = 119882u minus 119882d1 119894 = 1119882d119894minus1 minus 119882d119894 119894 = 2 119873

120576119881119894119862pd (120588d119894119879d119894)

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)

+ 119862p (119882u119879u minus 119882d1119879d1) 119894 = 1119862p (119882d119894minus1119879d119894minus1 minus 119882d119894119879d119894) 119894 = 2 119873

(6)

where 120588d119894 and 119882d119894 are respectively the density and flowrateof the helium inside node 119894 of the downcomer and 119862p is thehelium specific heat at constant pressureThen substitute (6)the thermodynamics of the helium in the downcomer can bewritten as [24]

120576119881119894120588d119894119862pd119879d119894

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)

+ 119862p119882u (119879u minus 119879d1) 119894 = 1119862p119882d119894minus1 (119879d119894minus1 minus 119879d119894) 119894 = 2 119873

(7)

(4) Riser In the channels of the riser the cold helium flowsupward to cool the reflector and the heat transfer process canbe described by [23 24]

119881ud120588ud119905 = (1 minus 120581)119882lh minus 119882u

119881u119862pd (120588u119879u)

d119905 = 119862p [(1 minus 120581)119882lh119879lh minus 119882u119879u]+ 119870ur119860ur (119879r minus 119879u)

(8)

where 120588u 119882u and 119879u are respectively the density flowrateand temperature of the helium inside the riser 119882lh and119879lh are respectively the flowrate and temperature of thehelium inside the lower header and 120581 is the leakage ration ofthe lower header Substitute (8) the thermodynamics of thehelium inside the riser can be written as

119881u120588u119862pd119879ud119905 = 119862p (1 minus 120581)119882lh (119879lh minus 119879u)

+ 119870ur119860ur (119879r minus 119879u) (9)


Subcooled section Boiling section

1 2 3 4 5Secondary side

Primary sideCold helium Hot helium

Water Steam

Figure 4 Nodalization scheme of the OTSG

(5) Lower Header The lower header is assumed to be awell-mixed chamber which has no heat exchange with theenvironment and the thermodynamics corresponding to thelower header can be expressed as [23 24]

119881lh120588lh d119879lhd119905 = 119882lh (119879in minus 119879lh) (10)

where 119879in is the temperature of the inlet cold helium 120588lh119882lh and 119879lh are respectively the density flowrate andtemperature of the helium inside the lower header and 119881lhis the volume of the low header

(6) Outlet Header The output header is assumed to be a well-mixed chamber and its dynamics can be given as [23 24]

119881oh120588oh d119879ohd119905 = 120581119882lh (119879lh minus 119879oh) + 119882d119873 (119879d10 minus 119879oh) (11)

where 120588oh119882lh and119879oh are respectively the density flowrateand temperature of the helium inside the outlet header and119881oh is the volume of the outlet header

213 MHTGR Dynamics The dynamic model of MHTGRis composed of neutron kinetics determined by (1)ndash(3)as well as thermal hydraulics given by (4) (5) (7) and(9)ndash(11) The dynamic behavior of this MHTGR model canbe influenced by nodal number N and an improper nodalnumber leads to the fluctuation of the responses Actuallythis model is only utilized for control design and verificationand is not for physical and thermal-hydraulic design Thenodal numbers are determined by comparing the response

of this model with that of the model for physical andthermal-hydraulic designWhen the error between responsesis satisfactorily small the corresponding nodal number issuitable Here the nodal number N is chosen to be 10Based on the simulation results to be given in Section 4 itwill be seen that there is no numerical fluctuation in theresponses and all the transience is determined by power-levelmaneuverwhich show that the nodal number is properlyselected

Since the dynamic model in this paper is tuned basedupon the comparison with the model for reactor physicaland thermal-hydraulic design the stability of this model isalso guaranteed by the model for reactor design Moreoverit was shown in [27] that the MHTGR is open-loop globallyasymptotically stable and by the use of the shifted-ectropy-based self-stability analysis method given in [27] it canbe shown that the model coupled by neutron kinetics andthermal hydraulics are open-loop globally asymptoticallystable

22 OTSG Since the OTSG can provide superheated steamwhich does not satisfy the one-to-one map from pressure totemperature the OTSG is more proper for building multi-SMR-based nuclear plants Therefore the dynamic modelof the OTSG is very crucial for studying behavior of theSMR-based plant and also for verifying the operation andcontrol strategies In this section a moving-boundary model[25] is introduced for describing OTSG dynamics in thecases of generating saturated and superheated steam [26]Thenodalization of the OTSG is given in Figure 4

221 Secondary Side The dynamics of the OTSG secondaryside is given by both the thermodynamics and pressure dropsof the secondary fluid flow

(1) Thermodynamics The thermodynamics of the secondaryside can be given by the following vector-valued nonlineardifferential equation [26]

Es (xs) dxsd119905 = fs (xs us) (12)

where

xs = [11989713 ℎs5 ℎs1 119866s3]T us = [119866s1 ℎfw 119876s2 119876s4]T

Es (xs) =[[[[[[[[

119864s11 (xs) 0 12120588s211989713 119864s14 (xs)119864s21 (xs) 12120588s411989735 0 119864s24 (xs)0 0 120591H 0

0 0 0 120591G

]]]]]]]]

119864s11 (xs) = 12 [120588s3 (ℎs1 minus ℎs3) + (119875s3 minus 119875s1) + 11989713 (1 minus 120588s2 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)(120588s2119892 sin 120579 + 119865s2 1198662s21198602s2)]


119864s14 (xs) = 119865s21198662s211989721321198602s2 (1 minus 120588s2 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119864s21 (xs)= 12 120588s3 (ℎs3 minus ℎs5) + (119875s5 minus 119875s3) + 11989735 [(2 minus 120588s4 120597ℎs3120597119875s3

10038161003816100381610038161003816100381610038161003816119875s3)(120588s2119892 sin 120579 + 119865s2 1198662s21198602s2) minus (120588s4119892 sin 120579 + 119865s4 1198662s41198602s4)]

119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1

+ 119866s3119860 s3) (ℎs1 minus ℎs3) 119876s4 + 119866s4 (ℎs3 minus ℎs5)119860 s4

ℎfw minus ℎs1120591H119866s1 minus 119866s3120591G ]T

(13)

119892 is the gravitational acceleration (Nsdotms2) both 120591G and 120591Hare given positive constants denoting inertial effect ℎfw isthe enthalpy per unit mass (Jkg) of the feedwater flow 119897119894119895(119894 119895 = 1 5 and 119894 lt 119895) is the length between points 119894 and119895 in Figure 4 and 120588s119894 119866s119894 ℎs119894 119876s119894 and 119860 s119894 are respectivelythe flow density (kgm3) flowrate (kgs) enthalpy per unitmass (Jkg) heat flux from the primary side and crosssection (m2) of node 119894 of the secondary side Here 11989713 isthe length of the subcooled section 11989735 is that of the boilingsection and ℎ1s is specific enthalpy of the feedwater Dueto the high speed of the steam flow it is assumed that119866s3 = 119866s4 = 119866s5

(2) Pressure Drops The pressure drop of the fluid flow in theOTSG secondary side cannot be omitted and the pressure ofeach node is given by [26]

119875s3 = 119875s1 minus 120588s211989211989713 sin 120579 minus 119865s2119897131198662s2119875s5 = 119875s3 minus 120588s411989211989735 sin 120579 minus 119865s4119897351198662s4119875s4 = (119875s3 + 119875s5)2 119875s2 = (119875s1 + 119875s3)2

(14)

where 120579 is the helically coiled angle of the tubes119865s119894 (119894 = 2 4) isthe friction factor of the two sections and 119875s1 is the feedwaterpressure

222 Tube Wall There is no flow inside the metal tube wallbetween the primary and secondary sides and the dynamicsof the tubewall are determined by its thermodynamics whichcan be expressed as [26]

d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)

where 119876p2 and 119876p4 are respectively the heat flux from theprimary heliumflow to tubewall in the subcooled and boilingsections

223 Primary Side Since velocity of the primary heliumflow is much higher than that of the two-phase flow insidethe secondary side the energy and temperature relationshipof the primary side can be given by the following algebraicequation [26]

Ap (xs) xp = bp (xm xp) (16)

where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[

1 minus2 1 00 11989735 minus11989715 11989713minus119862p119866p minus119870p211989713 119862p119866p 00 0 minus119862p119866p minus119870p411989735

]]]]]]

bp (xm xp)= [0 0 minus119870p211989713119879m2 minus119870p411989735119879m4 minus 119862p119866p119879p5]T

(17)

where 119866p is the primary helium flowrate 119862p is the heliumspecific heat 119879p119894 is the helium temperature at point 119894 (119894 =1 5) 119870p2 and 119870p4 are the heat transfer coefficientsbetween the primary side and tube wall of the subcooledand boiling sections respectively and 119870s2 and 119870s4 arerespectively the heat transfer coefficients between the tubewall and secondary side of the subcooled and boiling sections

23 Secondary-Loop FFN After the hot helium leaves thereactor it flows into theOTSG primary side where it transfersthe heat to the secondary feedwater By absorbing the heatof the primary loop the feedwater is converted to thesuperheated steam in 571∘C and about 139MPa or so The


1 2

f1 f2

31 2

3

4

Figure 5 Fluid flow network of the secondary loop of the HTR-PMplant

main steam flow at 1324MPa combined from the two NSSSmodules then enters the steam turbine for producing elec-tricity The condensed flow is fed into the OTSG secondaryside again after it goes through the grand heater low pressureheaters (LPHs) deaerator and high pressure heaters (HPHs)Thus the hydraulics of the secondary-loop system can bemodeled as the FFN shown in Figure 5 where branches f1and f2 are the fan branches of which everyone has a feedwaterpump branches 1 and 2 denote the secondary side of theOTSGs corresponding to the first and second NSSS modulerespectively and branch 3 contains the equipment of the plantsecondary loop such as the steam turbine condenser lowpressure heaters and deaerator

The flowrate dynamics of branches 1 2 and 3 can be givenas [28 29]

dQd119905 + KQ2DR = KH (18)

where Q = [1198761 1198762 1198763]T Q2D = [diag(Q)]2 K = diag(11987011198702 1198703) R = [1198771 1198772 1198773]T H = [1198671 1198672 1198673]T and 119876119895119877119895 119867119895 and 119870119895 are the flowrate resistance pressure dropand inertia coefficient of branch 119895 (119895 = 1 2 3) re-spectively

Every FFN can be divided into a tree containing thefan branches and its complement that is the cotree whosebranches are referred to as the links From Figure 5 thebranches with solid line that is branches 3 f1 and f2 consti-tute the tree of this FFN and the branches with dashed linethat is branches 1 and 2 are the links which constitute thecotree Based on the network property the pressure drops andthe flowrates of the tree branches are not independent andobey the following algebraic equations given by Kirchhoff rsquosvoltage law (KVL) and Kirchhoff rsquos current law (KCL) [28]

[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)

where 119867f119895 is the pressure drop of fan branch 119895 (119895 = 1 2) andcan be further expressed as

119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)

Then based on (18) and (19) the hydraulics of the FFNshown in Figure 4 can be given by differential-algebraicsystem [29]

dQcd119905 = minusKc (RfQc +Q2cDRc) + Kc (Hd minus 1198673120578)

1198701198673 = kTcHd minus kTfcQc minus kTcQ2cDRc + 1198703119876231198773

(21)

where Qc = [1198761 1198762]T Q2cD = [diag(1198761 1198762)]2 kc = [11987011198702]T kfc = [1198701119877f1 1198702119877f2]T119870 = 1198701+1198702+1198703Kc = diag(11987011198702) Rf = diag(119877f1 119877f2) and 120578 = [1 1]T24 Model Integration The above dynamic models of theMHTGR OTSG and secondary-loop FFN can be integratedtogether with other commonly utilized models such as theturbine and the synchronous generator to form the dynamicmodel for the whole plant Based upon this model a simu-lation code for the dynamic behavior and control character-istics of the HTR-PM plant is developed under MATLABSimulink platform and the composition of this Simulinkmodel is shown in Figure 6 This model can incorporate theplant control laws proposed in the next section for givingthe simulations of the operational and control characteristicsof the HTR-PM plant where the program modules namedas ldquo1 NSSSrdquo and ldquo2 NSSSrdquo are used to simulate thedynamic behavior of the two NSSS modules the programmodule named as ldquosecondary-loop FFNrdquo is used to simulatethe thermal hydraulics for the secondary-loop FFN themodule ldquoSecondary Thermal Featurerdquo is used to simulate thethermodynamics of secondary-loop systems and moduleldquoGeneratorrdquo is used to simulate the electric generator dynam-ics Furthermore some important model parameters are giv-en in Table 1

3 Plant Power Control

Plant control is a key technique to provide safe stable andefficient operation for every nuclear plant and to balancethe power supply and demand Since the two NSSS modulesof the HTR-PM plant are coupled together by the com-mon secondary loop including the turbinegenerator setand since the side-by-side arranged MHTGR and OTSG ofa NSSS module are tightly coupled with each other throughthe connecting pipes it is more difficult to design a powercontrol strategy for the two-modular HTR-PM plant than forthose traditional single-modular traditional nuclear plantsFurthermore the HTR-PM plant is essentially a large-scale and multi-input-multioutput (MIMO) nonlinear sys-tem whose complexity in its dynamics certainly leads to thecomplexity in its plant control strategy while in the practicalengineering a single control loop is usually utilized toregulate a single process parameter such as the nuclear powerprimary flow feedwater flow helium temperature and steam


To Workspace1

SimuTime

Secondary thermal point

Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2

Main Steam Pressure_SetPoint

1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++

Figure 6 Composition of the SIMULINK code

temperature Since the combination of all these single controlloops deeply affects the plant dynamic behavior it is neces-sary to coordinate these control loops for satisfactory closed-loop stability as well as transient performance In this sectionthe control design method is first reviewed and the controlrealization including feedback loops and control laws is thengiven

31 Control Design Method The control design mainly liesin two aspects that is feedback loop design and control lawdesign which are tightly related to each other There havebeen many process control system design approaches such asthe relative gain analysis- (RGA-) based method In thispaper both the feedback loops and control laws of HTR-PM control system are designed by the use of the physics-basedNSSS controlmethod proposed in [30ndash36] andmodulecoordination control method proposed in [28 29] whichprovide the globally asymptotic closed-loop stability throughguaranteeing the convergence of Lyapunov functions deter-mined by the shifted-ectropies of neutron kinetics andthermodynamics as well as the kinetic energy stored insecondary-loop FFN

311 NSSS Module Control Both the MHTGR and OTSGare complex nonlinear dynamic systems and their dynamicsare tightly coupled with each other due to their side-by-side arrangement To improve both the steady and transient

performance it is necessary to give proper control laws for theNSSS module composed of the MHTGR and OTSG by con-sidering the nonlinear dynamics The physics-based control(PBC) method is an effective way to design nonlinear reactorcontrol laws by retaining or strengthening stable subdynam-ics and by cancelling or suppressing unstable subdynamicswhich has been applied to the load-following control designfor the PWR [30 31] MHTGR [32ndash34] and OTSG [35] Veryrecently based upon the PBC method a novel model-freeMHTGR-based NSSS module control strategy was proposedin [36] which provides globally asymptotic stability (GAS)for the NSSS module if the feedwater temperature is constantand both the helium and feedwater flowrate are well regu-lated This NSSS module control strategy can be realized byfeedback loops given in Section 321 and simple control lawsgiven in Section 331

312 Coordination Control of Multiple NSSS ModulesThrough the multimodular scheme the inherent safety of theMHTGR is applicable to the large-scale plants with anydesired power ratings Module coordination control is oneof the most important characteristics of the multimodularnuclear plants such as the HTR-PM with comparison to thecontrol of those traditional single module nuclear plants Ithas been revealed in [29] that the module coordination prob-lem is essentially a flowrate-pressure regulation problem ofthe secondary-loop FFN Moreover based on the dissipation


Table 1 Main parameters of the dynamic model

Parameter Name Unit ValueΛ 119894 (119894 = 1 10) Prompt neutron lifetime s 766119890 minus 4120573 Fraction of all the delayed neutrons 0671205731 Fraction of 1st group delayed neutrons 002561205732 Fraction of 2nd group delayed neutrons 0141205733 Fraction of 3rd group delayed neutrons 0131205734 Fraction of 4th group delayed neutrons 0271205735 Fraction of 5th group delayed neutrons 00861205736 Fraction of 6th group delayed neutrons 00171205821 Decay constant of 1st group precursor sminus1 002561205822 Decay constant of 2nd group precursor sminus1 0141205823 Decay constant of 3rd group precursor sminus1 0131205824 Decay constant of 4th group precursor sminus1 0271205825 Decay constant of 5th group precursor sminus1 00861205826 Decay constant of 6th group precursor sminus1 0017

A = [120572119894119895]10times10 Coupling coefficients

[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3

120572f 119894 (119894 = 1 10) Reactivity coefficient of fuel temperature ΔKK∘C minus436119890 minus 5120572m119894 (119894 = 1 10) Reactivity coefficient of moderator temperature ΔKK∘C minus094119890 minus 5120572r Reactivity coefficient of reflector temperature ΔKK∘C 149119890 minus 5120576 Porosity of the pebble-bed 039

structure of the FFNs it has also been proved in [29] thatfeedback loops given in Section 322 and control laws givenin Section 332 can provide globally input-to-state stability(ISS) and satisfactory transient performance for the cotreeflowrates and tree branch pressure drops for the secondary-loop FFN

32 Feedback Loops and Controller Functions All the feed-back loops of the plant control system of the HTR-PM plantare shown in Figure 7 Since the feedback loops of the twoNSSS modules are the same with each other only thoseof the first NSSS module are illustrated From Figure 2we can see that the plant control system is constituted bythe controllers for regulating the reactor nuclear powerprimary helium flowrate secondary feedwater flowrate out-let helium temperature steam temperature reactor thermalpower and main steam pressure as well as the controller

for discharge and bypass Based on their functions thesecontrollers can be classified to the layers of module controlmodule coordination and supervisory as well as bypass anddischarge

321 Module Control The layer of module control is com-posed of the controllers for regulating the nuclear powerhelium flowrate reactor outlet helium temperature steamtemperature and NSSS output thermal power The functionsof these five controllers are given as follows

(1) Nuclear Power Controller It regulates the neutron fluxby generating both the given direction and velocity signalsthat determine the control rod movement These signalsare utilized to drive the stepping motors belonging tothe reactor control rod mechanism for realizing the givenmovement The movement of the control rods inducessatisfactory reactivity to the reactor which guarantees the


Plant control system

Set p

oint

s of p

lant

po

wer

Turbine controller

Discharge and bypass controller

Feed water ow controller

ermal power controller

Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re

Steam temperature controller

Set p

oint

s of h

eliu

m

ow

-rat

e

Helium ow controller

Set p

oint

s of h

eliu

m

tem

pera

ture

Helium temperature controller

Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor

Nuclear power controller

+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG

1 primary helium blower1 feedwater pump1 HPH

1 LPH 2 LPH 3 LPH

2 HPH 2 feedwater pump1 primary helium blower

Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator

Turbinegenerator set

T T

T

T T

T

P

P

P

P P

N

N

GG

GG

Figure 7 Composition of HTR-PM plant control system

stability and transient performance of the reactor neutronflux

(2) Helium Flow Controller Satisfactory primary helium cir-culation is the precondition of transferring the heat producedby the fission reaction to the secondary loop for steamgeneration In order to provide enough pressure header forthe primary helium circulation the helium flow controllergives the referenced frequency for the variable frequencydriver (VFD) of the induction motor that drives the primaryhelium blower

(3) Feedwater FlowController It regulates the secondary feed-water flowrates of theOTSGs through adjusting the rotationalspeed of the feedwater pumps by their hydraulic couplingsIt is worth noting that the feedwater flowrate controller is

responsible for the stability and transient performance of notonly the NSSS modules but also the secondary-loop FFN ofthe HTR-PM plant

(4) Helium Temperature Controller It regulates the reactoroutlet helium temperature by properly adjusting the set-points of the nuclear power controller and (or) helium flowcontroller Specifically if there is only modification of thereferenced relative nuclear power then the helium temper-ature controller and the nuclear power controller constitute acascaded feedback loop where the former one is in the outerloop as the major controller and the latter one is in the innerloop as minor controller

(5) Steam Temperature Controller It regulates the outletsteam temperature of the OTSG by properly adjusting the


setpoints of the helium flowrate controller and (or) feedwaterflowrate controller Specifically if its output is only therevision of the setpoints of the primary helium flowrate thenthe steam temperature controller serves as the major reg-ulator of the cascaded loop formed with the helium flowcontroller Moreover if its output is only the revision for thereferenced feedwater flowrate then the steam temperaturecontroller and feedwater flow controller form a cascaded loopwhere the former one is the major regulator In the poweroperation stage of the HTR-PM plant the OTSG outlet steamtemperature should be kept to be 571∘C constantly

(6) Thermal Power Controller It is essentially a feedforwardcontroller that gives the referenced feedwater flowrate basedon both the setpoint ofNSSS thermal power and themeasure-ment of the temperatures and pressures of the feedwater andoutlet superheated steam of each OTSG

322 Module Coordination The two NSSS modules of theHTR-PM plant are tightly coupled with each other throughthe common secondary-loop FFN To regulate the feedwaterflowrate of 1 NSSS module it is necessary to adjust 119867d1 byrevising the rotating speed of the pump However frommodel (21) the variation of 119867d1 influences not only thefeedwater flowrate of 1 NSSS module but also pressure dropH3 which can be utilized tomeasure themain steam pressureThen from (21) the variation in H3 influences the dynamicbehavior of the feedwater flowrate of 2 NSSS module whichinduces the need of adjusting 119867d2 for keeping this feedwaterflowrate Therefore regulating the feedwater flowrate of oneNSSS module needs to adjust the rotating speeds of the twopumps and each NSSS feedwater flowrate can influence themain steam pressure The module coordination is just theflowrate-pressure control of the secondary-loop FFN

It has been proved theoretically in [29] that the FFNflowrate regulation can be realized by distributed controllersofwhich each one only needs themeasurement of the flowrateto be regulatedThus theNSSS feedwater flowrate controllerscan well guarantee the stability and transient performance ofthe flowrates of the HTR-PM secondary-loop FFN shownin Figure 7 Moreover in the power operation stage of theHTR-PM plant the main steam pressure should be kept to be1324MPa constantlyThe stability of themain steam pressureis a basic operation requirement of the OTSG and alsoindicates the power balance between NSSS modules and theturbinegenerator Here themain steampressure of theHTR-PM plant is regulated by the turbine controller which pro-vides the main steam pressure stability through adjusting theopening of the main steam valve Thus the collaboration ofthe NSSS feedwater flowrate controllers and the turbinecontroller realizes the flowrate-pressure regulation of thesecondary-loop FFN which achieves the function of NSSSmodule coordination and keeps the power balance betweenthe NSSS modules and turbine

323 Supervisor The supervisor gives the setpoint of thethermal power for every NSSS module according to therequirement of the power grid and has no feedback regulation

function Moreover it also contains the map from the refer-enced NSSS thermal power to the referenced values of theNSSS process variables including the reactor nuclear powerprimary helium flowrate secondary feedwater flowrate reac-tor outlet helium temperature OTSG outlet steam temper-ature and main steam pressure which gives the setpointsof all the controllers The supervisor can be viewed asan input-output (IO) interface between the power plant andthe power grid so as to improve the power balance qualitybetween the grid and plant

324 Bypass and Discharge The function bypass and dis-charge guarantee the operationability of the HTR-PM plantin some tough cases The bypass controller opens the bypassvalve so that the OTSG outlet steam flows into the con-denser in the cases of load rejection reactor startup turbinebypass and so forth The function of the bypass controller isessentially providing a virtual load to compensate the largedifference between the thermal inertias of the NSSS andturbine The discharge controller opens the discharge valve ifthe pressure of the outlet steam is larger than its maximalvalue and closes the valve when the steam pressure is lowerthan a given value

33 Control Laws The control laws for the nuclear powerprimary helium flowrate feedwater flowrate MHTGR outlethelium temperature OTSG outlet steam temperature andmain steam pressure which have the feedback regulationfunction are all given in this subsection These control lawscan be classified into control laws forNSSSmodules and thosefor module coordination

331 Module Control Laws Themodule control laws includethe feedback regulation algorithms of the nuclear powerprimary helium flowrate feedwater flowrate MHTGR outlethelium temperature and OTSG outlet steam temperaturewhich are designed based on the physics-based NSSS controlmethod proposed in [30ndash36]

(1) Nuclear Power Control Law The nuclear power controllaws is designed to be proportional-differential (PD) feedbackregulation algorithm with the transfer function given by

119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)

where positive scalars 119896np and 120591nd are respectively the pro-portional and differential feedback gains 120591nd is a small inertiatime constant 119906N is the setpoint of the control rod speedsignal used to drive steppingmotors of the control rod drivingmechanism and 119899re is themismatch of the referenced relativenuclear power 119899rr from its actual value 119899r that is 119899re =119899rr minus 119899r It is necessary to note that relative nuclear power isthe normalized reactor neutron concentration and the totalthermal power is the outlet thermal power of the NSSSmodule The steady values of the relative nuclear power iscalibrated by that of total thermal power through experiment


(2) Helium Flow Control Law The feedback control of theprimary helium flowrate adopts the proportional-integral(PI) law with its transfer function given by

119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)

where positive constants 119896hf p and 119896hf i are respectivelythe proportional and integral feedback gains 119906HF is thereferenced rotating speed of the primary helium blower and119882He is the error between the referenced and actual values ofthe primary helium flowrate

(3) Feedwater Flow Control Law The NSSS module feedwaterflowrate is also regulated by PI control law which is given by

119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)

where positive scalars 119896fwp and 119896fwi are respectively thecorresponding proportional and integral gains 119906FW is thedriving signal of the hydraulic coupling and119882fwe is the errorbetween the referenced and actual values of the feedwaterflowrate

(4) MHTGR Outlet Helium Temperature Control Law Thereactor outlet helium temperature is regulated by the lead-lagfeedback law that is given by transfer functions

119866HT1 (119904) = 119906HT1 (119904)119879HOe (119904) = 119896ht1p + 119896htd119904119896np + 119896nd119904 119866HT2 (119904) = 119906HT2 (119904)119879HOe (119904) = minus(119896ht2p + 119896hti119904 )

(25)

where 119896np and 119896nd are respectively the proportional anddifferential gains of the nuclear power control law gains 119896ht119895p(119895 = 1 2) 119896htd and 119896hti are positive constants determin-ing the lead-lag performance 119906HT1 is the revision to thesetpoint of the relative nuclear power 119906HT2 is the revision tothe referenced primary helium flowrate 119879HOe is the errorbetween the setpoint and measurement of the reactor outlethelium temperature

(5) OTSG Outlet Steam Temperature Control Law The OTSGoutlet steam temperature of every NSSS module is regulatedby PI feedback laws

119866S1 (119904) = 119906S1 (119904)119879Se (119904) = 119896s1p + 119896s1i119904 119866S2 (119904) = 119906S2 (119904)119879Se (119904) = minus(119896s2p + 119896s2i119904 )

(26)

where positive constants 119896s119895p and 119896s119895i (119895 = 1 2) are respec-tively the proportional and integral feedback gains 119906S1 isthe revision of the setpoint of the primary helium flowrate119906S2 is the revision of the setpoint of the secondary feedwaterflowrate and 119879se is the error between the setpoint andmeasurement of the OTSG outlet steam temperature

332 Module Coordination Laws The NSSS module coordi-nation laws are just the flowrate-pressure feedback controllaws for the secondary-loop FFN flowrates and pressuredrop which are designed based on the module coordinationcontrol method proposed in [28 29]

(1) FFN Flowrate Control Law As discussed in Section 312and [28 29] the flowrates of a FFN can be well regulated bycontrolling the flowrates of its cotree branches in a distributedway From the structure of HTR-PM secondary-loop FFNshown in Figure 5 the OTSG secondary sides of the first andthe second NSSS modules form branches 1 and 2 of this FFNwhich are just the cotree branches Thus from the graphproperties of the FFN all the branch flowrates can be wellcontrolled or stabilized by regulating the feedwater flowratesof the OTSGs Then it is clear that OTSG feedwater flowratecontrol law (24) can realize the FFNflowrate control functionwhich means that flowrate control law (24) belongs to boththe layers of module control and module coordination

(2) FFN Pressure Drop Control Law The pressure drop of theFFN tree branches (excluding the brancheswith pump) is alsoa crucial issue to guarantee the stability and operationabilityThe pressure drop 1198673 of the HTR-PM secondary-loop FFNshown in Figure 5 can be measured by the main steampressure which is regulated by the turbine control law withtransfer function given by

119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)

Here in (27) positive scalars 119896pp and 119896pi are respectivelythe proportional and integral gains 119906SP is the setpoint ofthe steam valve opening and 119875Se is the mismatch of thereferenced main steam pressure from its actual value

333 Parameters of Control Laws The plant control perfor-mance relies on the two aspects that is the performances ofboth the module control and module coordination Theformer one is guaranteed by the physics-based NSSS controlapproach and the latter one is provided by the FFN flowrate-pressure controlmethod All the control laws take the form asPI or PD feedback laws For PI control laws the proportionalgain is larger and the response is faster but if it is too largethe control action will hit the saturation margin which leadsto the deterioration of closed-loop stability Moreover theintegral gain is larger and the transition period to the steadystate is shorter but the overshoot is larger Usually propor-tional gain is chosen not larger than 10 and the integralgain is chosen not larger than 01 For the PD law for nuclearpower regulation the proportional gain is chosen not largerthan 05 and the differential gain is chosen not larger than30

4 Simulation Results with Discussions

In this section the dynamic behavior of the HTR-PM plantin both the cases of power step and ramp are studied throughthe numerical simulation This study is performed based on


10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Figure 8 Responses of 1 and 2 NSSS in the case of power step-down 119899r119894 119879cout119894 119879s119894 and 119875th119894 are respectively the relative nuclear powerMHTGR outlet helium temperature OTSG outlet steam temperature and total thermal power of the 119894th NSSS 119894 = 1 2

the MATLABSimulink simulation code shown in Figure 6that integrates both the plant model introduced in Section 2and control strategy given in Section 3 Moreover necessarydiscussions are also given in this section

41 Simulation Results

411 Power Step The dynamic responses of the power stepbetween 100 and 95 plant full power (PFP) are obtainedthrough numerical simulation

(1) Power Step-Down Initially the HTR-PM plant remainsat the steady state of 100 PFP which means that the twoNSSS modules are running at the 100 reactor full power(RFP) At 5000 s the thermal power setpoint of the first (ie1) NSSS module steps down from 100 to 95 RFP andthen at 10000 s the referenced thermal power of the second(ie 2)NSSSmodule steps down from 100 to 95RFPThedynamic responses of the relative nuclear powers reactor out-let helium temperatures OTSG outlet steam temperaturesand thermal powers of 1 and 2 NSSS modules are given inFigure 8The responses of flowrates119876119894 (119894 = 1 2 3) feedwaterpressures -119867f119896 (119896 = 1 2) and main steam pressure 1198673 areillustrated in Figure 9

(2) Power Step-Up Initially the HTR-PM plant remains atthe steady state of 95 PFP that is the two NSSS modulesoperate at 95 RFPThe thermal power setpoints of 1 and 2NSSS modules step up from 95 to 100 RFP at 5000 s and10000 s respectively The dynamic responses of the relativenuclear powers reactor outlet helium temperatures OTSGoutlet steam temperatures and thermal powers of 1 and 2NSSS modules are given in Figure 10 The responses of 119876119894(119894 = 1 2 3) -119867f119896 (119896 = 1 2) and H3 are shown in Figure 11

412 Power Ramp The responses of the steady power rampbetween 100 and 50 plant full power (PFP) are given bythe simulation study

(1) Power Ramp-Down Initially the HTR-PM plant remainsat the steady state of 100 PFP that is the twoNSSSmodulesoperate at 100 RFP At 5000 s 1 NSSS module maneuversfrom 100 to 50 RFP steadily in 10 minutes and then at10000 s the referenced thermal power of 2 NSSS modulechanges steadily from 100 to 50 RFP in 10 minutes whichis just the power decrease process from 100 to 50 PFP oftheHTR-PMplantThe responses of the relative nuclear pow-ers reactor outlet helium temperatures OTSG outlet steamtemperatures and thermal powers of 1 and 2NSSSmodulesare given in Figure 12 The responses of flowrates 119876119894 (119894 =1 2 3) feedwater headers -119867f119896 (119896 = 1 2) and main steampressure H3 are illustrated in Figure 13

(2) Power Ramp-Up Initially the HTR-PM plant remains atthe steady state of 95 PFP that is the two NSSS modulesoperate at 95 RFP At 5000 s and 10000 s 1 and 2 NSSSmodules respectively maneuver steadily from 50 to 100RFP in 10 minutes which is the process of HTR-PM powerincrease from 50 to 100 PFPThe responses of the relativenuclear powers reactor outlet helium temperatures OTSGoutlet steam temperatures and thermal powers of 1 and2 NSSS modules are given in Figure 14 The responses offlowrates119876119894 (119894 = 1 2 3) -119867f119896 (119896 = 1 2) andH3 are illustratedin Figure 15

42 Discussions The variation of the plant power is realizedby the successive power maneuver of 1 and 2 NSSSmodules and at most one NSSS module can be in the state of


10000 10500 11000 115009500

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13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

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17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

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89895

90905

91

16

17

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19

minusH

f2(M

Pa)

10000 10500 11000 115009500

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185

186

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188

minusH

f2(M

Pa)

10000 10500 11000 115009500

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889092949698

Q2 (k

gs)

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184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)

Figure 9 Responses of secondary-loop FFN flowrates and pressure drops in the case of power step-down

10000 10500 11000 115009500

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0951

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nr2

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570572574

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240245250255

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W)

094

095

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nr2

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7465

747

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570

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0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Figure 10 Responses of 1 and 2 NSSS in the case of power step-up 119899r119894 119879cout119894 119879s119894 and 119875th119894 are respectively the relative nuclear powerMHTGR outlet helium temperature OTSG outlet steam temperature and total thermal power of the 119894th NSSS 119894 = 1 2

power maneuver at any time Generally from Figures 8ndash15the control laws for the modules and those for the modulecoordination guarantee satisfactory closed-loop stability andtransient performance of the process variables of the NSSSmodules as well as the secondary-loop FFN

The variation of a NSSS power-level setpoint directlyinduces the variations of the setpoints of nuclear powerreactor outlet helium temperature primary helium flowrateand secondary feedwater flowrate of this NSSS which enlargethe errors between the practical values and setpoints of thesevariablesThese errors drive the nuclear power controller andhelium temperature controller to insert or withdraw thecontrol rods and drive the flowrate controllers to slow downor speed up the helium blower and feedwater pump Due to

the negative feedback laws the movement of control rodshelium blower and feedwater pump can suppress the errorsMoreover the variations of the flowrates and helium tem-perature induce the variations of steam temperature andmain steam pressure which drive the steam temperaturecontroller to revise the setpoints of helium or feedwaterflowrates for maintaining the steam temperature and drivethe pressure controller to change the steam valve openingfor keeping the main steam pressure The variation of thesteam valve opening can also reduce the feedwater flowrateof the other NSSS which leads to the successive variationsof steam temperature helium temperature fuel temperatureand nuclear power of the other NSSSThen the controllers ofthe other NSSS are active to suppress the errors of process


10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)

Figure 11 Responses of secondary-loop FFN flowrates and pressure drops in the case of power step-up

10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Figure 12 Responses of 1 and 2 NSSS in the case of power ramp-down 119899r119894 119879cout119894 119879s119894 and 119875th119894 are respectively the relative nuclear powerMHTGR outlet helium temperature OTSG outlet steam temperature and total thermal power of the 119894th NSSS 119894 = 1 2

variables caused by the variation of steam valve openingFurthermore since the steam flow extracted from the turbineis equally distributed to the two HPHs the power maneuverof one module changes feedwater temperatures of both twomodules To maintain the thermal powers the setpoints offeedwater flowrates of the two modules should be adjustedby the thermal power controllers

Specifically to the NSSS module control performancewe can clearly see from the simulations results illustrated inFigures 8ndash15 that simple module control laws (22)ndash(26) canguarantee satisfactory stability and transient performance forthe NSSS modules in the cases of power-level maneuver andmaintenance Here the expressions of these module controllaws are given by guaranteeing proper dissipation featurefor the NSSS module with its shifted-ectropy as the storage

function which is the key idea of physics-based nuclear plantcontrol method with the ability of giving simple control lawsThese simulation results effectively show the feasibility ofthese module control laws which can be implemented andcommissioned easily in the practical engineering

Furthermore the key difference between the HTR-PMplant and those single-modular nuclear plants is the modulecoordination controlThere is a tight hydraulic coupling effectof the two NSSS modules that is induced by the commonsecondary-loop FFN There is also coupling effect betweenthe feedwater temperatures of the two NSSS modules whichis induced by the equal distribution of the steam flowextracted from the turbine to the two HPHs belonging tothe two modules respectively Because of the existence ofthe hydraulic and thermal module coupling effects when


10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)

Figure 13 Responses of secondary-loop FFN flowrates and pressure drops in the case of power ramp-down

4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Figure 14 Responses of 1 and 2 NSSS in the case of power ramp-up 119899r119894 119879cout119894 119879s119894 and 119875th119894 are respectively the relative nuclear powerMHTGR outlet helium temperature OTSG outlet steam temperature and total thermal power of the 119894th NSSS 119894 = 1 2

one NSSS module is in the state of power maneuveringboth the feedwater flowrate and output thermal power ofthe other NSSS module must vary simultaneously if thereis no control input Due to the proper referenced feedwaterflowrates given by thermal power controllers and due tothe effectiveness of the feedwater flowrate control law boththe secondary flowrates and thermal power of the two NSSSmodules are statically decoupled with each other whichmeans that the steady values of the feedwater flowrates (outletthermal power) of the two NSSS modules are decoupledwith each other For example from columns 1 and 3 ofFigures 8 and 10 the power step of 1 NSSS module doesnot influence the steady values of the feedwater flowrate andoutlet thermal power of 2 NSSSmoduleThanks to the plant

control strategy proposed in this paper we can see fromthe simulation results that the power step and ramp of oneNSSS module only induce small transient disturbance to theother module and do not induce steady-point perturbationsof the secondary flowrate and thermal power The feedbacklaws of the module coordinated control given by (24) and(27) are also simple for engineering implementation andconditioning

In summary the power maneuver of the HTR-PM plantcan be realized by the plant control strategy given in Section 3which has already been applied to the HTR-PM powercontrol project The numerical simulation results show thatthe HTR-PM plant is flexible enough for constituting HESswith those renewable energy sources such as the wind and


9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)

Figure 15 Responses of secondary-loop FFN flowrates and pressure drops in the case of power ramp-up

solarMoreover the technical issues of integratingmoreNSSSmodules are nearly the same with integrating two modulesby allocating a pump to each NSSS module implementingmodule control laws in Section 322 to each NSSS moduleand applyingmodule coordination laws in Section 323 to thesecondary FFN

5 Conclusions

Due to its inherent safety feature and potential economiccompetitiveness the modular high temperature gas-cooledreactor (MHTGR) has already been seen as one of the bestcandidates in building the next generation nuclear plantsThrough the multimodular scheme the inherent safety fea-ture of the MHTGR can be applicable to the large-scalenuclear plants at any desired power ratings Plant powercontrol is the one of the crucial techniques for guaranteeingthe safe stable and efficient operation of every nuclearplant and the plant power control strategy of the traditionalsingle-modular nuclear plants cannot be directly applied tomultimodular plants Thus it is very necessary to study theplant power control of multimodular nuclear plants Heredynamicmodeling control strategy design and performanceverification are the three main aspects of plant power controlstudying where the former one is the basis for the lattertwo In this paper the dynamical modeling of the main partsof the HTR-PM plant is first given and the correspondingplant control strategy including the feedback loops andcontrol laws is then proposed By integrating the dynamicmodel and power control strategy for a simulation code inMATLABSimulink environment numerical verification isperformed Simulation results in the cases of plant powerstep and ramp show that the plant control strategy providessatisfactory closed-loop stability and transient performancefor the HTR-PM plant The future work mainly lies incommissioning the power control system of the HTR-PMplant which is implemented based on the control strategygiven in this paper practically for a practical verification

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

Thiswork is jointly supported byNational SampTMajor Projectof China and Natural Science Foundation of China (NSFC)(Grant no 61374045)

References

[1] H E Garcia J Chen J S Kim et al ldquoDynamic performanceanalysis of two regional nuclear hybrid energy systemsrdquo Energyvol 107 pp 234ndash258 2016

[2] M Lykidi and P Gourdel ldquoHow to manage flexible nuclearpower plants in a deregulated electricity market from the pointof view of social welfarerdquo Energy vol 85 pp 167ndash180 2015

[3] W Dazhong and L Yingyun ldquoRoles and prospect of nuclearpower in Chinarsquos energy supply strategyrdquo Nuclear Engineeringand Design vol 218 no 1ndashndash3 pp 3ndash12 2002

[4] D T Ingersoll ldquoDeliberately small reactors and the secondnuclear erardquo Progress in Nuclear Energy vol 51 no 4-5 pp 589ndash603 2009

[5] J Vujic R M Bergmann R Skoda and M Miletic ldquoSmallmodular reactors simpler safer cheaperrdquo Energy vol 45 no1 pp 288ndash295 2012

[6] M K Rowinski T J White and J Zhao ldquoSmall and mediumsized reactors (SMR) a review of technologyrdquo Renewable andSustainable Energy Reviews vol 44 pp 643ndash656 2015

[7] D D Lanning ldquoModularized high-temperature gas-cooledreactor systemsrdquoNuclear Technology vol 88 no 2 pp 139ndash1561989

[8] H Reutler and G H Lohnert ldquoThe modular high-temperaturereactorrdquo Nuclear Technology vol 62 no 1 pp 22ndash30 1983

[9] H Reutler and G H Lohnert ldquoAdvantages of going modular inHTRsrdquo Nuclear Engineering and Design vol 78 no 2 pp 129ndash136 1984


[10] G H Lohnert ldquoTechnical design features and essential safety-related properties of theHTR-modulerdquoNuclear Engineering andDesign vol 121 no 2 pp 259ndash275 1990

[11] Z Wu D Lin and D Zhong ldquoThe design features of the HTR-10rdquo Nuclear Engineering and Design vol 218 pp 25ndash32 2002

[12] S Hu X Liang and L Wei ldquoCommissioning and operationexperience and safety experiments on HTR-10rdquo in Proceedingsof the 3rd International Topical Meeting on High TemperatureReactor Technology Johannesburg SouthAfricaOctober 2006

[13] Z Zhang and Y Sun ldquoEconomic potential of modular reactornuclear power plants based on the Chinese HTR-PM projectrdquoNuclear Engineering and Design vol 237 no 23 pp 2265ndash22742007

[14] Z Zhang Z Wu D Wang et al ldquoCurrent status and technicaldescription of Chinese 2 times 250 MW119905ℎ HTR-PM demonstrationplantrdquo Nuclear Engineering and Design vol 239 no 7 pp 1212ndash1219 2009

[15] G Y Han ldquoA mathematical model for the thermal-hydraulicanalysis of nuclear power plantsrdquo International Communica-tions inHeat andMass Transfer vol 27 no 6 pp 795ndash805 2000

[16] C Fazekas G Szederkenyi and K M Hangos ldquoA simpledynamic model of the primary circuit in VVER plants forcontroller design purposesrdquo Nuclear Engineering and Designvol 237 no 10 pp 1071ndash1087 2007

[17] Z Dong X Huang J Feng and L Zhang ldquoDynamic modelfor control system design and simulation of a low temperaturenuclear reactorrdquo Nuclear Engineering and Design vol 239 no10 pp 2141ndash2151 2009

[18] R M Edwards K Y Lee and M A Schultz ldquoState feedbackassisted classical control an incremental approach to controlmodernization of existing and future nuclear reactors andpower plantsrdquo Nuclear Technology vol 92 no 2 pp 167ndash1851990

[19] M G Na I J Hwang and Y J Lee ldquoDesign of a fuzzy modelpredictive power controller for pressurized water reactorsrdquoIEEE Transactions on Nuclear Science vol 53 no 3 pp 1504ndash1514 2006

[20] G R Ansarifar and H R Akhavan ldquoSliding mode controldesign for a PWR nuclear reactor using sliding mode observerduring load following operationrdquoAnnals of Nuclear Energy vol75 pp 611ndash619 2015

[21] Y B Shtessel ldquoSlidingmode control of the space nuclear reactorsystemrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 34 no 2 pp 579ndash589 1998

[22] Z Huang R M Edwards and K Y Lee ldquoFuzzy-adaptedrecursive sliding-mode controller design for a nuclear powerplant controlrdquo IEEE Transactions on Nuclear Science vol 51 no1 pp 256ndash266 2004

[23] H Li X Huang and L Zhang ldquoA simplified mathematicaldynamic model of the HTR-10 high temperature gas-cooledreactor with control system design purposesrdquoAnnals of NuclearEnergy vol 35 no 9 pp 1642ndash1651 2008

[24] Z Dong X Huang and L Zhang ldquoA nodal dynamic modelfor control system design and simulation of an MHTGR corerdquoNuclear Engineering and Design vol 240 no 5 pp 1251ndash12612010

[25] H Li X Huang and L Zhang ldquoA lumped parameter dynamicmodel of the helical coiled once-through steam generator withmovable boundariesrdquo Nuclear Engineering and Design vol 238no 7 pp 1657ndash1663 2008

[26] Z Dong ldquoA differential-algebraic model for the once-throughsteam generator of MHTGR-based multimodular nuclearplantsrdquoMathematical Problems in Engineering vol 2015 ArticleID 370101 12 pages 2015

[27] Z Dong ldquoSelf-stability analysis of MHTGRs a shifted-ectropybased approachrdquo Nuclear Engineering and Design vol 248 pp137ndash148 2012

[28] Z Dong ldquoDissipation analysis and adaptive control of fluidnetworksrdquo in Proceedings of the American Control Conference(ACC rsquo15) pp 671ndash676 Chicago Ill USA July 2015

[29] Z Dong M Song X Huang Z Zhang and Z Wu ldquoModulecoordination control of MHTGR-based multi-modular nuclearplantsrdquo IEEE Transactions on Nuclear Science vol 63 no 3 pp1889ndash1900 2016

[30] Z Dong J Feng X Huang and L Zhang ldquoPower-levelcontrol of nuclear reactors based on feedback dissipation andbacksteppingrdquo IEEE Transactions onNuclear Science vol 57 no3 pp 1577ndash1588 2010

[31] Z Dong ldquoNonlinear state-feedback dissipation power levelcontrol for nuclear reactorsrdquo IEEE Transactions on NuclearScience vol 58 no 1 pp 241ndash257 2011

[32] Z Dong ldquoPhysically-based power-level control for modularhigh temperature gas-cooled reactorsrdquo IEEE Transactions onNuclear Science vol 59 no 5 pp 2531ndash2549 2012

[33] Z Dong ldquoPower-level control for MHTGRs with time-delayin helium temperature measurementrdquo IEEE Transactions onNuclear Science vol 61 no 3 pp 1349ndash1359 2014

[34] Z Dong ldquoModel-free power-level control of MHTGRs againstinput saturation and dead-zonerdquo IEEE Transactions on NuclearScience vol 62 no 6 pp 3297ndash3310 2015

[35] Z Dong X Huang and L Zhang ldquoSaturated output feedbackdissipation steam temperature control for the OTSG of MHT-GRsrdquo IEEE Transactions on Nuclear Science vol 58 no 3 pp1277ndash1289 2011

[36] Z Dong ldquoModel-free coordinated control for MHTGR-basednuclear steam supply systemsrdquo Energies vol 9 no 1 article 372016

TribologyAdvances in

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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Submit your manuscripts athttpswwwhindawicom


StructuresJournal of

International Journal of

RotatingMachinery


EnergyJournal of


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Volume 201Hindawi Publishing Corporation httpwwwhindawicom Volume 201

International Journal ofInternational Journal of


Nuclear InstallationsScience and Technology of


Solar EnergyJournal of


Wind EnergyJournal of


Nuclear EnergyInternational Journal of


High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Control rod driving mechanism

Pebble-Bed of fuel elements

Cold helium riser

Helium blower

OTSG

Reflector

Hot helium chamber

Coaxial pipe

Figure 1 Composition of the MHTGR-based NSSS module

[7] that is multiple nuclear steam supplying system (NSSS)modules feeding steam to common thermal load equipmentsuch as the turbinegenerator set the inherent safety featureof a SMR can be applicable to large-scale nuclear plantsat any desired power ratings which could be beneficial inproviding electricity to remote areas without transmission ordistribution infrastructure in generating local power for alarge population center and in being viable for specificapplications such as heat sources for the industrial complexesFurthermore the SMRs can offer simpler safer and standard-izedmodular design by being factory-built requiring smallerinitial capital investment and having shorter constructionperiod and have been regarded by International AtomicEnergy Agency (IAEA) as one of the active developing trendsof nuclear energy

Due to its inherent safety feature the modular high tem-perature gas-cooled reactor (MHTGR such as HTR-Moduledesigned in Germany and MHTGR designed in US) hasbeen seen as one of the best candidates for the next-generation nuclear plants The MHTGR is a typical SMRwhich uses helium as coolant and graphite as moderator andstructural material and its inherent safety is determined bythe low power density strong negative temperature feedbackeffect and slim reactor shape [8ndash10] China began to study theMHTGR at the end of 1970s and a 10MWth pebble-bed hightemperature gas-cooled reactor HTR-10 which was designedby the Institute of Nuclear and New Energy Technology(INET) of Tsinghua University achieved its criticality inDecember 2000 and full power in January 2003 [11]Then sixsafety demonstration tests were done on the HTR-10 whichmanifested its inherent safety and self-stabilizing features[12] Based on the experience of the HTR-10 project a hightemperature gas-cooled reactor pebble-bed module (HTR-PM) plant was then proposed which consists of two pebble-bed one-zoneMHTGRs with combined 2 times 250MWth powerand adopts the operation scheme of two NSSS modulesdriving one steam turbine [13 14] Figure 1 shows that a NSSSmodule of the HTR-PM plant is composed of an MHTGRa helically coiled once-through steam generator (OTSG) a

primary helium blower and some connecting pipes Figure 2illustrates a simplified flow diagram of the entire two-modular HTR-PM plant The HTR-PM plant is now in thestage of plant construction and commissioning By incorpo-rating more MHTGR-based NSSS modules more large-scalemultimodular high temperature gas-cooled nuclear plant canbe realized

Satisfactory plant dynamic behavior is important forrealizing load-following function and for further formingHESs with fossil or renewable energy sources which is givenby not only the open-loop dynamics but also the controlstrategy There have been some promising results in dynami-cal modeling and control design for entire nuclear plants Inthe field of plant modeling Han gave a mathematical modelof pressurized water reactors for thermal-hydraulic analysis[15] Fazekas et al proposed a simple dynamic model for theprimary circuit in VVER plants for controller design pur-poses [16] Dong et al presented a lumped parameterdynamic model for control design and verification for theNSSS of the nuclear heating reactors (NHRs) [17] Withcomparison to the abundant results in reactor power-levelregulation such as the linear control nonlinear control andintelligent method [18ndash20] there are still less results in thefield of entire nuclear plant control Shtessel proposed asliding-mode plant control and state-observation strategy forspace nuclear energy system TOPAZ II [21] Huang et al gavea multi-input-multioutput (MIMO) fuzzy-adapted recursivesliding-mode plant controller for an advanced boiling waterreactor (ABWR) nuclear power plant [22] In order to achievesafe stable and efficient operation of the HTR-PM plant it isnecessary to give the lumped parameter model of the mainplant dynamics and to propose proper plant control strategyIt is worth noting that due to the two-modular schemethere is much difference between themodeling and control ofthe HTR-PM plant and that of those single-modular nuclearplant

In this paper both the dynamical modeling and controldesign method for HTR-PM plant are first summarizedor reviewed the realization of feedback loops and control


1 helium blower

1 OTSG

1 MHTGR


2 OTSG

2 MHTGR

Deaerator

Main condenser

Turbine generator

Main steam valve

Bypass valve



1 NSSS

2 NSSS


Gland heater









6sum119896=1




+ 6sum119896=1

120573119896Λ119873119862r119873119896d119862r119894119896

d119905 = 120582119896 (119899r119894 minus 119862r119894119896) 119894 = 1 119873 119896 = 1 2 6

(1)


Ree

ctor

Rise

r

Lower header



MHTGR

Neutron kinetics

1 2Control rods


Reactivity

OTSG primary side

12

Dow

ncom

er

Pebb

le-b

ed12

N

N

N








120572119894119895 = (11989911989501198991198940 )119863119860120592Σf 119894119881119889


120572119894119894 =

119863119860120592Σf 2119881119889 119894 = 1119863119860120592119881119889 ( 1Σf 119894minus1

+ 1Σf 119894+1) 119894 = 2 119873 minus 1

119863119860120592Σf 119873minus1119881119889 119894 = 119873

(3)






(1 minus 120576) 120588c119894119881119862c119894d119879c119894


+


(4)




120588r119881r119862rd119879rd119905 = 119873sum

119894=1


(5)




120576119881119894119862pd (120588d119894119879d119894)

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(6)


120576119881119894120588d119894119862pd119879d119894

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(7)



119881u119862pd (120588u119879u)


(8)



+ 119870ur119860ur (119879r minus 119879u) (9)





Water Steam














Es (xs) dxsd119905 = fs (xs us) (12)

where


Es (xs) =[[[[[[[[


0 0 0 120591G

]]]]]]]]






119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1



(13)




(14)



d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)




where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[


]]]]]]


(17)




1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















1 helium blower

1 OTSG

1 MHTGR


2 OTSG

2 MHTGR

Deaerator

Main condenser

Turbine generator

Main steam valve

Bypass valve



1 NSSS

2 NSSS


Gland heater









6sum119896=1




+ 6sum119896=1

120573119896Λ119873119862r119873119896d119862r119894119896

d119905 = 120582119896 (119899r119894 minus 119862r119894119896) 119894 = 1 119873 119896 = 1 2 6

(1)


Ree

ctor

Rise

r

Lower header



MHTGR

Neutron kinetics

1 2Control rods


Reactivity

OTSG primary side

12

Dow

ncom

er

Pebb

le-b

ed12

N

N

N








120572119894119895 = (11989911989501198991198940 )119863119860120592Σf 119894119881119889


120572119894119894 =

119863119860120592Σf 2119881119889 119894 = 1119863119860120592119881119889 ( 1Σf 119894minus1

+ 1Σf 119894+1) 119894 = 2 119873 minus 1

119863119860120592Σf 119873minus1119881119889 119894 = 119873

(3)






(1 minus 120576) 120588c119894119881119862c119894d119879c119894


+


(4)




120588r119881r119862rd119879rd119905 = 119873sum

119894=1


(5)




120576119881119894119862pd (120588d119894119879d119894)

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(6)


120576119881119894120588d119894119862pd119879d119894

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(7)



119881u119862pd (120588u119879u)


(8)



+ 119870ur119860ur (119879r minus 119879u) (9)





Water Steam














Es (xs) dxsd119905 = fs (xs us) (12)

where


Es (xs) =[[[[[[[[


0 0 0 120591G

]]]]]]]]






119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1



(13)




(14)



d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)




where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[


]]]]]]


(17)




1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















Ree

ctor

Rise

r

Lower header



MHTGR

Neutron kinetics

1 2Control rods


Reactivity

OTSG primary side

12

Dow

ncom

er

Pebb

le-b

ed12

N

N

N








120572119894119895 = (11989911989501198991198940 )119863119860120592Σf 119894119881119889


120572119894119894 =

119863119860120592Σf 2119881119889 119894 = 1119863119860120592119881119889 ( 1Σf 119894minus1

+ 1Σf 119894+1) 119894 = 2 119873 minus 1

119863119860120592Σf 119873minus1119881119889 119894 = 119873

(3)






(1 minus 120576) 120588c119894119881119862c119894d119879c119894


+


(4)




120588r119881r119862rd119879rd119905 = 119873sum

119894=1


(5)




120576119881119894119862pd (120588d119894119879d119894)

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(6)


120576119881119894120588d119894119862pd119879d119894

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(7)



119881u119862pd (120588u119879u)


(8)



+ 119870ur119860ur (119879r minus 119879u) (9)





Water Steam














Es (xs) dxsd119905 = fs (xs us) (12)

where


Es (xs) =[[[[[[[[


0 0 0 120591G

]]]]]]]]






119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1



(13)




(14)



d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)




where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[


]]]]]]


(17)




1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of


















(1 minus 120576) 120588c119894119881119862c119894d119879c119894


+


(4)




120588r119881r119862rd119879rd119905 = 119873sum

119894=1


(5)




120576119881119894119862pd (120588d119894119879d119894)

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(6)


120576119881119894120588d119894119862pd119879d119894

d119905= 119870d119894119860d119894 (119879c119894 minus 119879d119894)


(7)



119881u119862pd (120588u119879u)


(8)



+ 119870ur119860ur (119879r minus 119879u) (9)





Water Steam














Es (xs) dxsd119905 = fs (xs us) (12)

where


Es (xs) =[[[[[[[[


0 0 0 120591G

]]]]]]]]






119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1



(13)




(14)



d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)




where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[


]]]]]]


(17)




1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of


















Water Steam














Es (xs) dxsd119905 = fs (xs us) (12)

where


Es (xs) =[[[[[[[[


0 0 0 120591G

]]]]]]]]






119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1



(13)




(14)



d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)




where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[


]]]]]]


(17)




1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of


















119864s24 (xs) = 11989735 [(1 minus 12120588s4 120597ℎs3120597119875s310038161003816100381610038161003816100381610038161003816119875s3)

119865s2119866s2119897131198602s2 + 2119865s4119866s4119897131198602s2 ]

fs (xs us) = [119876s2119860 s2+ 12 (119866s1119860 s1



(13)




(14)



d119879m2d119905 = 119876p2 minus 119876s2119862m120588m119860m211989713 +

119879m4 minus 119879m211989715d11989713d119905

d119879m4d119905 = 119876p4 minus 119876s4119862m120588m119860m411989735 +

119879m4 minus 119879m211989715d11989713d119905

(15)




where

xp = [119879p1 119879p2 119879p3 119879p4]T

Ap (xm) = [[[[[[


]]]]]]


(17)




1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















1 2

f1 f2

31 2

3

4




dQd119905 + KQ2DR = KH (18)



[1198671 1198672]T = minus [1198673 + 119867f1 1198673 + 119867f2]T [1198763 119876f1 119876f2]T = [1198761 + 1198762 1198761 1198762]T (19)


119867f119895 = minus119867d119895 + 119877f119895119876f119895 119895 = 1 2 (20)




(21)





To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















To Workspace1

SimuTime


Psc

Ts1

Gs1

Ts2

Gs2

Pwin1

Pwin2

TurbinPower

Gfw1

Tfw1

Gfw2

Tfw2


1324

Load2

Out_Load

Load1

Out_Load

Gsin2

Gsin1

Generator

TurbinePower

Omiga

W

Eq1

Pe

Fluid ow network

Gsr1

Pr

Gsr2

Gs1

Ps

Hf1

Hf2

Gs2

Display_dGs2

Display_dGs1

Display_W

Display_Tst2

Display_Tst1

Display_Tfw2

Display_Tfw1

Display_SimuTime

Display_Pm

Display_Pe

Display_Omiga

Display_Gfw2

Display_Gfw1

Display_Eq1

Clock

2 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

1 NSSS

Load

Gsin

Psin

Tsin

Psout

Tst

dGs

++

++











[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of


















[[[[[[[[[[[[[[[[[[[[[[[[[[[[

35 7018 71 55

22 69 3931 70 33

37 70 2942 70 28

45 70 2647 70 24

50 70 2256 35

]]]]]]]]]]]]]]]]]]]]]]]]]]]]

times 10minus3









Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of
















Set p

oint

s of p

lant

po

wer

Turbine controller




Set p

oint

s of r

eact

orth

erm

al p

ower

Set p

oint

s of s

team

te

mpe

ratu

re


Set p

oint

s of h

eliu

m

ow

-rat

e


Set p

oint

s of h

eliu

m

tem

pera

ture


Set p

oint

s of r

eact

or

nucle

ar p

ower

Supervisor


+

minus

+

+

+

+++

+

+

+

+

+

+

minus

minusminus

minus

1 MHTGR

1 MHTGR

1 NSSS

2 NSSS

1 OTSG

1 OTSG


1 LPH 2 LPH 3 LPH


Control rods

Control rods

Steam valve

Bypass valve

Generator

Condenser

Glandheater

Deaerator


T T

T

T T

T

P

P

P

P P

N

N

GG

GG



















119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of

























119866N (119904) = 119906N (119904)nre (119904) = 119896np + 119896nd119904120591nd119904 + 1 (22)




119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of
















119866HF (119904) = 119906HF (119904)119882He (119904) = 119896hf p + 119896hf i119904 (23)



119866FW (119904) = 119906FW (119904)119882fwe (119904) = 119896fwp + 119896fwi119904 (24)




(25)




(26)





119866SP (119904) = 119906SP (119904)119875S (119904) = 119896pp + 119896pi119904 (27)






10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















10000 10500 11000 115009500

Time (s)

08509

0951

nr2

5000 5500 6000 6500 7000 75004500Time (s)

099

1

101

nr2

5000 5500 6000 65004500Time (s)

08509

0951

nr1

0940945

0950955

1200

0

1050

0

1100

0

1150

0

1250

0

1000

0

9500

Time (s)

nr1

10000 10500 11000 11500Time (s)

9500

748750

7465000 5500 6000 6500 7000 75004500

Time (s)

7495

750

7505

5000 5500 6000 65004500Time (s)

746748750

7465

747

7475

1050

0

1150

0

1200

0

1000

0

1250

0

1100

0

9500

Time (s)

10000 10500 11000 115009500Time (s)

568570572

570

571

572

5000 5500 6000 65004500Time (s)

5000 5500 6000 65004500Time (s)

568570572

10000 10500 11000 115009500Time (s)

570

571

572

10000 10500 11000 115009500Time (s)

240245250255

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

252

253

254

Pth

2(M

W)

5000 5500 6000 65004500Time (s)

240245250255

Pth

1(M

W)

10000 10500 11000 115009500Time (s)

240

2405

241

Pth

1(M

W)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)

Ts1

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)












10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

178180182184186

Q3 (k

gs)

10000 10500 11000 115009500

Time (s)

17918

181182183

minusH

f1(M

Pa)

16

17

18

19

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

89895

90905

91

16

17

18

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

185

186

187

188

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

889092949698

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

184186188190192

Q3 (k

gs)

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

94945

95955

96

Q2 (k

gs)

4500 5500 6000 65005000

Time (s)


10000 10500 11000 115009500

Time (s)

0951

105

nr2

10000 10500 11000 115009500

Time (s)

746748750

10000 10500 11000 115009500

Time (s)

570572574

10000 10500 11000 115009500

Time (s)

240245250255

Pth

2(M

W)

094

095

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

7465

747

7475

5000 5500 6000 65004500

Time (s)

570

571

572

5000 5500 6000 65004500

Time (s)

239

240

241

Pth

2(M

W)

7495

750

7505

9500

1050

0

1100

0

1200

0

1150

0

1000

0

1250

0

Time (s)

1100

0

1050

0

1200

0

1250

0

1000

0

1150

0

9500

Time (s)

099

1

101

nr1

10000 10500 11000 115009500

Time (s)

570

571

572

10000 10500 11000 115009500

Time (s)

252

253

254

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

0951

105

nr1

5000 5500 6000 65004500

Time (s)

746748750

5000 5500 6000 65004500

Time (s)

570572574

5000 5500 6000 65004500

Time (s)

240245250255

Pth

1(M

W)

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















10000 10500 11000 115009500

Time (s)

184

186

188

19

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

18

19

20

21

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

18

19

20

21

minusH

f1(M

Pa)

5000 5500 6000 65004500

Time (s)

18

182

184

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

9500 10500 11000 1150010000

Time (s)

94945

95955

96

Q1 (k

gs)

9500 10500 11000 1150010000

Time (s)

889092949698

Q2 (k

gs)

9500 10500 11000 1150010000

Time (s)

184186188190192

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

889092949698

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

8889909192

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

178180182184186188

Q3 (k

gs)


10000 10500 11000 115009500

Time (s)

569570571572

5000 5500 6000 65004500

Time (s)

571

5715

572

10000 10500 11000 115009500

Time (s)

571

5715

572

5000 5500 6000 65004500

Time (s)

569570571572

10000 10500 11000 115009500

Time (s)

150200250

Pth

2(M

W)

5000 5500 6000 65004500

Time (s)

252253254255

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

126

127

128

Pth

1(M

W)

5000 5500 6000 65004500

Time (s)

150200250

Pth

1(M

W)

9500 10000 10500 11000 11500

Time (s)

720730740750751

5000 5500 6000 6500 7000 75004500

Time (s)

749

750

7185

719

7195

1000

0

1050

0

1100

0

1150

0

1200

0

1250

0

9500

Time (s)

5000 5500 6000 65004500

Time (s)

720730740750

10000 10500 11000 115009500

Time (s)

0608

1

nr2

095

1

105

5000 5500 6000 6500 7000 75004500

Time (s)

nr2

045

05

055

9500

1050

0

1100

0

1150

0

1200

0

1250

0

1000

0

Time (s)

nr1

5000 5500 6000 65004500

Time (s)

0608

1

nr1

Ts2

(∘C)

Tco

ut2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)







10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















10000 10500 11000 115009500

Time (s)

14

145

15

minusH

f1(M

Pa)

1214161820

5000 5500 6000 65004500

Time (s)

minusH

f1(M

Pa)

10000 10500 11000 115009500

Time (s)

4445464748

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

1214161820

minusH

f2(M

Pa)

5000 5500 6000 65004500

Time (s)

18

185

19

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

90

92

94

96

Q2 (k

gs)

10000 10500 11000 115009500

Time (s)

13235

1324

13245

H3

(MPa

)

5000 5500 6000 65004500

Time (s)

13235

1324

13245

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

100

120

140

Q3 (k

gs)

4500 5000 5500 6000 6500140160180200

Time (s)

Q3 (k

gs)


4500 5000 5500 6000 6500

150200250

Time (s)

Pth

1(M

W)

150200250

Pth

2(M

W)

10000 10500 11000 115009500

Time (s)

5000 5500 6000 65004500

Time (s)

125126127128

Pth

2(M

W)

9500 10000 10500 11000 11500252

253

254

Time (s)

Pth

1(M

W)

4500 5000 5500 6000 6500

0608

1

Time (s)

nr1

nr2

10000 10500 11000 115009500

Time (s)

0608

1

nr2

5000 5500 6000 6500 7000 75004500

Time (s)

045

05

055

nr1

9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

095

1

105

4500 5000 5500 6000 6500720730740750

Time (s)

9500 10000 10500 11000 11500

Time (s)

720730740750

716718720

5000 5500 6000 6500 7000 75004500

Time (s)9500

1250

0

1000

0

1200

0

1050

0

1100

0

1150

0

Time (s)

749750751

4500 5000 5500 6000 6500570571572573

Time (s)

10000 10500 11000 115009500

Time (s)

570571572573

5000 5500 6000 65004500

Time (s)

5705705

5715715

10000 10500 11000 115009500

Time (s)

5705705

5715715

Tco

ut2

(∘C)

Ts2

(∘C)

Ts2

(∘C)

Tco

ut2

(∘C)

Ts1

(∘C)

Tco

ut1

(∘C)

Tco

ut1

(∘C)

Ts1

(∘C)






9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of















9500 10000 10500 11000 1150018

185

19

Time (s)

minusH

f1(M

Pa)

4500 5000 5500 6000 650014

16

18

20

Time (s)

minusH

f1(M

Pa)

Q1 (k

gs)

10000 10500 11000 115009500

Time (s)

90

92

94

96

Q1 (k

gs)

5000 5500 6000 65004500

Time (s)

40

60

80

100

9500 10000 10500 11000 1150014

16

18

20

Time (s)

minusH

f2(M

Pa)

4500 5000 5500 6000 650014

145

15

Time (s)

minusH

f2(M

Pa)

10000 10500 11000 115009500

Time (s)

40

60

80

100

Q2 (k

gs)

5000 5500 6000 65004500

Time (s)

4445464748

Q2 (k

gs)

9500 10000 10500 11000 1150013235

1324

13245

Time (s)

H3

(MPa

)

4500 5000 5500 6000 650013235

1324

13245

Time (s)

H3

(MPa

)

10000 10500 11000 115009500

Time (s)

140160180200

Q3 (k

gs)

5000 5500 6000 65004500

Time (s)

100

120

140

Q3 (k

gs)



5 Conclusions




Acknowledgments


References








































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of












































FuelsJournal of







Advances in



Journal of


Renewable Energy





RotatingMachinery


EnergyJournal of



Journal of














dynamic modeling and control characteristics of the two...

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