modeling of coal-fired power units with thermopower ... · modeling of coal-fired power units with...

Modeling of Coal-Fired Power Units with ThermoPowerFocussing on Start-Up Process

Sebastian Meinke1 Friedrich Gottelt2 Martin Müller1 Egon Hassel11 University of Rostock, Chair of Thechnical Thermodynamics

A.-Einstein-Str. 2, 18059 Rostock, Germany2XRG Simulation, Harburger Schlossstr. 6-12, 21079 Hamburg, Germany

[email protected] [email protected]

Abstract

Governmental encouragement of renewable energieslike wind energy led to an extensive increase of in-stalled wind energy capacity worldwide. In order toallow a complete integration of this continuously fluc-tuating energy source, it is necessary to have a highlyflexible operation management as well as power sta-tions which are able to follow the high dynamics ofthe wind power production.

In this context the component fatigue and opera-tional limitations of current and future power stationshave to be investigated under the influence of en-hanced plant dynamics.

For this purpose a detailed Modelica model of thehard coal fired steam power plant of Rostock, Ger-many is presented and extensively validated. Themodel makes use of the well-known non-commerciallibrary ThermoPower. This Modelica Library is ex-tended by models for common solid fuel burners andradiation-dominated firing zones. In addition to this,different approaches for modeling two-phase contain-ers like the feed water tank are discussed. The derivedmodel is used to compare different operation modeswith respect to the occurring component wear.

Keywords: ThermoPower, coal fired power plants,firing modeling, two phase tank, power unit start up

1 Introduction

In a future power grid with high renewable power feed,especially from wind power, it becomes more impor-tant as well as economically beneficial for conven-tional power plants to be able to adjust the productionin order to balance the renewable energies. But due tothe long life time, the majority of current power plantshave been designed decades ago mainly for steady

state operation. Consequently, the focus was put moreon reliability and preservative operation than on highdynamics.

The recent and ongoing changes in the energy mar-ket in Germany will lead to an increased number ofstart-ups and load changes, which cause additional lifetime consumption. Improvements of the existing tech-nologies are required to enable higher dynamics at lim-ited additional stress during transient operation.

This is especially true for coal fired power plantsbecause of the fuel pulverization in coal mills. Thesemills have a slow and often unknown dynamic andlimit the load gradient of coal fired units. Addition-ally, the boiler itself shows a slow transient responsedue to its big metal and water masses as well as uncer-tainties like degradation of the heat transfer due to ashbuild up on the heating surfaces. To overcome this, theload change rates are made sufficiently slow. Improve-ments to this conservative approach could be achievedby the use of advanced control systems, e.g. state ob-servers and model based control systems or additionalsensors, like for example coal dust measurement [1].

For the evaluation of such optimizations of the pro-cess and the control system, computer aided simula-tion of the power plant process could be a powerfultool.

2 Scope of Investigations and Ther-modynamical Model

In order to judge the expected impacts of a moredynamic power plant operation a detailed, transientmodel consisting of one-dimensional or lumped inter-linked sub models, based on thermodynamic funda-mental equations, is presented. The 550 MW hard coalpower plant Rostock, that started its operation in 1994,has been used as a reference. The power plant repre-

Proceedings 8th Modelica Conference, Dresden, Germany, March 20-22, 2011

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sents the state of the art and is due to its long rest lifetime heavily effected by future changes of the energymarket.

2.1 Object of Investigation

The power plant Rostock has a conventional, hard coalfired steam generator. This is a single direction once-through forced-flow boiler in Benson design, which isrun in modified sliding pressure operation. The boileris equipped with four superheater and two reheaterheating surfaces. The fuel supply is carried out by acoal dust firing with direct injection. The combustionitself takes place in 16 NOx-lean vortex staged burn-ers, which are distributed on 4 burner levels with each2 burners on the front and back side.

The main characteristics are provided in the follow-ing table (1):

Table 1: Key data of power unit Rostock, Germany [2]

power unit data gross electric power 550 MWnet efficiancy rate 43.2 %district heating 300 MJ/smax. degree of utilization 62 %

boiler manufacturer Babcockdesign once-through forced-flow boiler

single direction designsingle reheating

life steam production 417 kg/sSH-pressure/ -temperature 262 bar/545 ◦CRH-pressure/ -temperature 53 bar/562 ◦Cfiring opposed firing, 4 levels

combined coal dust/oilcoal mills 4 roll wheel coal mill MPS 225,

hard coalturbo gen set manufacturer ABB

design without regulating wheelnumber of housings 1 HP, 1 IP, 2 LPoperation mode natural/modified sliding pres-

sure

2.2 Overview of the Power Plant Model

Base for this power plant model is the non-commercialModelica library ThermoPower [3]. Many of the com-prised sub models in the ThermoPower library, likepipes, valves, metal walls, mixers, etc. have been usedin this work or have been taken as a starting point forself-developed models. One of the newly added mod-els is a generic two phase tank, that can be used fora feed water tank, preheaters, a start bottle or a con-denser. Furthermore, models for cyclone separators, acombustion chambers and segments of a flue gas ducthave been developed . Two of these new sub modelsare presented in the following section 3.

The focus of the investigation has been put on thewater-/steam circuit, the combustion chamber of thesteam generator and the fresh air passage within thecoal mills, as well as their dynamics and the influence

of different operation modes on distinct devices e.g.thick-walled headers and turbine shafts.

A simplified schematic of the model is shown in fig-ure 1. Indicated are the feed water pumps, high pres-sure preheaters (HPP), the steam generator, the differ-ent turbine stages, as well as the forced draft and millfan, the air preheater and the coal mills. The low pres-sure preheaters (LPP) are not part of the power plantmodel, since they are not highly stressed, due to theirlow temperature level.

firing

exhaust gas

coal

fresh air

forced draft fan

steam air preheater

mill fan

air preheater

coal mills

economizer

reheater 1

superheater 3

reheater 2

superheater 4superheater 2superheater 1

HP IP LP

feed water pump

HPP

HPB

IPBevaporator

circula-tion

pump

cyclone

start bottle

to condensor

fromfeed water tank

to LPP

air preheater

Figure 1: structure of power plant model

For making simulation-based statements about theinfluence of different power plant operation modes thethermodynamical model is coupled to a reduced copyof the power plant control system, which is imple-mented using the Modelica Standard Library compo-nents.

The implemented control system uses the currentlycalculated physical values (i.e. live steam parameter,generated power at a specific coal input) and in a con-sequence adjusts set values (e.g. life steam pressure)and manipulated variables (e.g. rotational speed of thefeed water pump) of the water-steam cycle. Becauseof this feedback the grade of details as well as the ac-curacy of the modelled steam cycle and its interfacesto the control system needs to be reasonably high.

In detail the power plant control system sets the ma-nipulated values using a map based pilot control. Theexpected control variable is predicted by a transferfunction based model of the process. The differencebetween this predictive value and the correspondingmeasurement is adjusted via a corrective control loop,as described in the VDI/VDE guideline 3508 [7].

2.3 Level of Detail

In the following the degree of detail is explained by us-ing the detailed reproduced boiler as an example. Theboiler model differentiates eight separate heating sur-faces: economizer, evaporator, four superheaters and


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two reheaters. Between the superheaters SH1 and SH2as well as SH3 and SH4 plus in between the reheatersRH1 and RH2, spray atemperators are located for livesteam temperature control.

In compliance with the modular approach of Mod-elica any of the boiler’s eight different heat exchang-ers is composed of different base models, see figure 2.Starting from highest temperature components the fol-lowing modules can be found: The flue channel seg-ment which models the energy storage as well as thegas side heat transfer due to convection and radiation, asub model, that calculates the conductive heat transferinside the metal wall of the pipes and a third modulefor the convective heat transfer occurring at the innerwall as well as a one-dimensional pipe flow model.The heat flow at the system boundary between thesemodules is implemented using connectors. On the gasside very complex heat and mass transfer conditionsoccur defined by a large range of temperature and avariety of geometric characteristics. To cope with thiscomplexity semi-empirical heat transfer correlationsfor the different stages of the combustion chamber canbe distiguished while the three-dimensional flow fieldis reduced to one dimension. The latter reduction ne-glects any deviations from the perfect symmetric tem-perature and flow field but is in congruence with the"one-pipe"-approach of the water and steam side of theboiler.

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Figure 2: Dymola view of a generic superheater,which distinguishes inlet and outlet header and heat-ing surface

Before and after each of the bundle heat exchang-ers a thick-walled header is located to allow a mixing

of several legs connected in parallel. Again, we findmodels for convective and conductive heat transfer andenergy storage in the metal masses of the surroundingwalls. In addition, there are adapter modules to couplecomponents of different dimensionality. This is nec-essary because the headers are discretisized in flow di-rection while the thick header walls are discretisized inheat flow direction which is perpendicular to the firstmentioned.

3 Addidtional Components

In the following chapter a selection of the developedcomponents are presented, section 3.1 explains the submodels for the reproduction of the firing process andgas side heat transfer. In section 3.2 the modeling of atwo phase tank is discussed.

3.1 Modelling of the steam generators gasside

Due to the complex, unsteady and 3-dimenstional na-ture of a real firing process, a model of the combus-tion process, which is a part of an overall power plantmodel, needs to be strongly simplified. For that rea-son instant combustion is assumed and subsequently alumped gas volume model is used for the reproductionof the combustion chamber, which works according tothe principle of a homogeneous agitating tub [6] withuniform flue gas conditions (see figure 3).

The main input values for combustion calculationare fuel and fresh air properties. The description ofthe fuel is conducted by a raw coal composition andthe coal mass flow, which is delivered by a coal millmodel. The modeling of the coal mills has been doneaccording to work of Niemczyk et al., 2009 [4].

The raw coal composition can be obtained by an el-ementary analysis and integrates a single ash and em-bedded water fraction (equation 1). On the gas sidethe ThermoPower component SourceW was used forgenerating a combustion air mass flow. To indicate thepreheated air conditions the moist air media of Mod-elica.Media has been applied. The air properties arefunctions of the boiler load.

The essential of this model is a simple combustioncalculation without pollutants. Also implemented arefunctions for lower heating value according (see equa-tion 2 [5]) and air ratio in dependency of desired firingpower.

Other parameters are the ash fraction, which is sus-pended in the flue gas and the unburnt carbon fraction


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Hout = Hin

Qpipes

Hout

Qwall

pipe bundle

supporting tubes

duct wall

Qsupp

Hout = Hin

Qwallhomogeneoustemperature

duct wall

flue gas

coal composition and mass flow

preheated moisted air

xcoal , mcoalHair

Hslag

hot bottom ashfl

ue

ga

s d

uct

com

bu

stio

nch

am

ber

Sou

rcew

air

Figure 3: scheme of the combustion chamber and fluegas duct

that remains in the solid ash. This data is importantfor the particle radiation and is set to default values of0.90 and 0.02, respectively. In result of the known en-ergy balance the combustion model creates a flue gaswith its adiabatic combustion temperature. Thereforethe "simple flue gas" media model was introduced andits properties can be transfered to an output flow con-nector. (see equation 3).

xC + xH + xS + xO + xN + xW + xA = 1 (1)

Hu = 34.8(xC − xCu)+93.8xH +10.46xS

+6.28xN −10.8xO −2.45xW (2)

xi,RG =m̂i,RG

m̂RG(3)

The heat transfer from the flue gas to the differentsurface areas is caused by two physical mechanisms,radiation and convection. Convection is heat transfervia particle transport and works on all overflowed sur-faces. The formula 4 uses a heat transfer coefficient,which depends on the fluid properties, the flow ve-locity and the geometry of the surface (see equation5). Every vertical surface (membrane duct wall and

the supporting tubes, which are carrying the pipe bun-dles) is handled like an overflowed plate. The Nusselt-number is calculated according to [6].

The streaming around the pipe bundle surface is aforced flow across a tube. In this case the Nusselt-number calculation is extended by a geometrical align-ment factor [6]. The used flue gas properties are av-eraged values between two nodes. For ribbed tubes(economizer) an effective heat transfer coefficient willbe computed according to [5], which takes the rib ef-fects into consideration.

Q̇conv = αconv ·Awall · (Tgas −TWall) (4)

αkonv =Nu ·λ

l(5)

Especially in higher temperature regions above1000 ◦C (combustion chamber) the heat radiation isthe dominant heat transfer mechanism (see equation6). The radiation sources are the flue gas, the con-tained solid particles (dust) and the surfaces. The in-fluences of these three sources are expressed in dif-ferent dimension free emission (ε) and absorption (a)coefficients.

In the flue gas only the components H2O and CO2are relevant emitters. The combined emission coef-ficient of both is calculated using equation 7 [6]. Thecalculation of the emission coefficients for dust (in factunburnt carbon and flying ash) is also described in [6].The implemented functions also consider the back ra-diation from the wall to the flue gas represented by theabsorption coefficients.

Q̇rad = εgas/wall ·σ ·A ·(εgas/dust ·T 4gas−agas/dust ·T 4

wall)(6)

εgas/wall =εwall

1− (1−agas/dust) · (1− εwall)(7)

Considering the discharged heat flow to the mem-brane wall the homogeneous temperature in the com-bustion chamber is calculated by the energy balance.The main parameter for adjustment is the introducedfouling correction factor. This factor is implementedinto the energy balance and represents the fouling ofthe heat surfaces. The fouling decreases with lowerflue gas temperatures.

Subsequently the exhaust gas is flowing to the fluegas duct, which is the second part of the steam gener-ator and located above the combustion chamber. Foreffective modeling it is divided in segments - one for


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every pipe bundle heat exchanger. Each sub modelis based on the 1-dimensional gas flow model of theThermoPower library. The modified models havethree heat transfer ports - one for the flue gas duct wall(evaporator), the supporting tubes (superheater SH 1)and the pipe bundle itself (superheaters, reheater andeconomizer) - shown in figure 4.

An exception is the superheater SH 1, its pipe bun-dle is at the lower end of the supporting tubes and theheat transfer will be computed by empiric equations[5]. For every flue section following parameters canbe defined: number of nodes, geometry and foulingfactor. In cooperation with the other models of theThermoPower library it is easy to construct direct- orcounter-current heat exchangers.

flue gas duct models with different heating surfaces

cross section of flue gas duct (top view)

pipebundle

support-ingtubes

duct wall

Figure 4: overview of the heating surfaces of the fluegas duct

3.2 Two-Phase Tank

In order to decouple the low pressure part from thehigh pressure part of the water-steam cycle a largestorage tank is located between the low pressurepreheaters and the feed water pump. This tanktypically contains both, steam and liquid water. Thetwo phases interlink to each other by heat and masstransfer. During slow load changes and steady stateoperation water and steam will be in an equilibrium,i.e. the phases will be near the dew and boiling curve,respectively. Due to limited heat transfer betweenboth phases a constant temperature difference betweenthe phases will arise. In contrast to this, during faststate changes, as they may occur during condensatehold-up, a significant fraction of steam may be presentin liquid phase and vice versa. To cope with thiseffects a model solving energy and mass balance forboth phases separately was implemented, using thecentral equations below. Herein the generic inlet andoutlet ports in and out are defined as ThermoPowercomponents flange :

//mass balance: Index v = vapor// Index l = liquidder(Mv) = in.w*x_in + out.w*x_out + w_ev- w_con;der(Ml) = in.w*(1-x_in) +out.w*(1-x_out)- w_ev + w_con;// energy balance vapor phaseder(Hv) - der(p*Vv) =(in.w*x_in+wzero)*h_in_v +(out.w*x_out+wzero)*h_out_v - Qflow +(w_ev+wzero)*hvs - (w_con+wzero)*hls;// energy balance liquid phaseder(Hl) - der(p*Vl) =(in.w*(1-x_in)+wzero)*h_in_l +(out.w*(1-x_out)+wzero)*h_out_l + Qflow -(w_ev+wzero)*hvs + (w_con+wzero)*hls;Thereby linking the two phases via the evaporationand condensation mass flow rates and the heat ex-change via the common surface:w_ev = max(0,tau*(hl-hls)/(hvs-hls)*Ml);w_con = max(0,tau*(hvs-hv)/(hvs-hls)*Mv);Qflow = Asup*alpha*(Tv - Tl); The codeomits the heat exchange with the surrounding wallsfor the sake of simplicity. However, the model makesuse of some unknown parameters, namely tau asthe time constant for phase change processes andalpha as the heat transfer coefficient (HTC) at phaseinterface. For this reason a parameter variation wasdone to gain information about the influence of theseparameters.

For evaluation a temporary reduction of the conden-sate mass flow entering the feed water tank is con-sidered. Usually the condensate flow is controlled tokeep the feed water tank level at a defined set valuebut when short-term generator power is needed thecondensate mass flow is reduced thus increasing theturbine mass flow in an indirect manner. This con-densate holdup is the state-of-the-art method for pri-mary regulation. The scenario comprehends a reducedcondensate mass flow rate over approximately 13 minstarting at t = 60 min while a constant mass flow isextruded by the feed water pumps. In consequencethe water level decreases, see figure 5. After finish-ing the condensate holdup the controller starts fillingthe container again by massively increasing the con-densate inflow into the tank. Considering the varia-tion of the heat transfer between the phase interfacewe find that the time response of the level is not af-fected by differing interface heat transfer coefficients.In contrast to this the tank pressure is qualitatively andquantitatively influenced by this parameter, see figure


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0 10 20 30 40 50 60 70 80 90 100 110 1200

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alpha=1.5e4alpha=1.5e5alpha=1.5e6alpha=1.5e7

Figure 5: Tank Pressure development during conden-sate hold-up

6. The stationary tank pressure is lower for cases withnear-ideal heat transfer indicated by high heat transfercoefficients α ≥ 1.5 · 107 W/(m2K). The scenario withheavily reduced heat transfer leads to decreasing pres-sures during condensate holdup because the effect ofthe reduced cooling by the cold condensate is over-compensated by the decompressing effect of the emp-tying process. For the cases with a high energetic cou-pling of the two phases we find the cooling effect ofthe condensate to outweigh the emptying process. Thetime constants for phase change have a similar phase-coupling impact as the heat transfer but turns out to bequantitatively of minor influence and is therefore notdiscussed in detail.

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alpha=1.5e4alpha=1.5e5alpha=1.5e6alpha=1.5e7

Figure 6: Tank Pressure development during conden-sate hold-up varying the HTC

The question arising from figure 6 is how intensethe heat transfer between the liquid and gaseous phaseis. Analysis of continuous measurement data providedby the power plant operator revealed a fairly constanttemperature difference between the liquid temperatureand the saturation temperature gathered from the tank

pressure ∆T ≈ 3.7K. This suggests a good heat trans-fer between the phases referring to a heat transfer coef-ficient of α = 1.5 ·105 W/(m2K). This high heat transfercoefficient, typical for good inter-phase mixing, is en-sured by the applied Stork spray injector.

When considering the pressure development andthe subcooling of the liquid water in the tank itbecomes clear that the implementation of separatephase balancing has only minor influence on theglobal behavior of the component. Therefore, themodel might be reduced using only one lumpedstate into account. This state will be in the wetsteam region during proper operation of the tank, i.e.0 ≤ level ≤ levelmax:Mass balance for both phases:der(M) = in.m+out.m;Energy balance for both phases:der(H) - V*der(p) = in.w*h_in +out.w*h_out ;With boiling vapor at the outlet of the liquid phaseinterface:h_out=hls

The reduced model shows - as stated - similar tran-sient behavior concerning mass storage, see figure 7.In contrast to this, a different time development of thetank pressure has to be stated. The steady-state value isslightly lower for the simplified model and differs dur-ing transients. However, the deviation is below 1 %relative error for both transient time period and steadystate and the pressure time derivatives show the samesign.

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Simplified ModelDetailed Model

Figure 7: Filling level development during condensatehold-up applying different levels of detail

The effect of model simplification on the requiredcondensate mass flow is shown in figure 9 and onlysmall deviations must be stated. Thus, for controllerdesign of the condensate pump the simplified modelmay be sufficient.


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Figure 8: Tank pressure development during conden-sate hold-up applying different levels of detail

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Figure 9: Condensate mass flow devepment duringcondensate hold-up applying different levels of detail

The mentioned deviations of the tank pressure forthe detailed and simplified model may induce differ-ing tapping mass flows. Tappings are controlled orfixed steam extractions providing steam from the tur-bines for heating of the low pressure preheaters andthe feedwater tank. If the tapping valve is not con-trolled the corresponding mass flow rate is defined bythe pressure states in the turbine and the low pres-sure path. Thus, the heating mass input may differbetween both models requiring different condensatemass flows. In the consequence the effective turbinemass flow in the low pressure turbine stages is dif-ferent when integrating the tank models in a completesteam cycle. Considering a conservative estimation ina scenario of 80 % relative load this results in approx.2 % relative error of the generator power.

Comparing the models presented both, advantagesand drawbacks, apply to each of the model approaches.The detailed model considering two different phases

promises better numerical stability and more realisticresults, especially during short-term transients whilethe simplified model is easier to initialize and will needless computational effort. Testing the convenience ofthe models under different usage conditions with re-spect to initialization and simulation progress will bea subject item of future investigations.

4 Validation of the Model

In order to check the created model on correctness,comparative measurements have been recorded in thepower plant Rostock, which are shown below in con-trast to the results of the simulation.

In the investigated period of time the power plantbegins operation after 37 hour shutdown period withtwo subsequent positive load changes up to 95 per-cent. The development of the desired net power shownin figure 10 is the input to the model and is processedby the control system to a desired firing power signaland subsequently transfered to the coal mills and oilburners. Despite the simplifications in the reproducedcontrol system of the power plant model a good re-production could be achieved, differences between themodel and measurement could be caused by parame-ter changes of the process, especially during a start,like a drifting heating value, uncertainties in the milldynamic or degradation of the heating surfaces.

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desired Net powerdes.firing power − simulationdes.firing power − measurement

Figure 10: Definition of validation setup - power re-quest from the load dispatcher and corresponding de-sired firing power

Beneath the power request the plant model needstwo additional inputs, the state of the condensate wa-ter, which is provided by a load dependent table andthe composition of the used coal. Since coal is not anhomogeneous fuel the mass fraction of containing ashand water of the modeled coal are fluctuating in ran-dom intervals by +/- 1%. All other boundary condi-tions for the model, like furnace outlet and condenser


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pressure as well as air inlet temperature have constantvalues.

Since the dynamic behavior of the overall process ismainly dominated by the fuel pulverization in the coalmills and the transient response of the boiler, it wouldbe beneficial to validate the sub models for those twosystems independently. But this is not possible, be-cause the measurement of the system response of thecoal mills, the coal dust mass flow rate upstream of theburners, is only possible with high efforts and low ac-curacy. Thus, such a measurement system is not stan-dard and is not available. In a consequence, validationof the overall model is conducted by the use of thesteam properties in the boiler and the generator out-put.

The live steam pressure and mass flow arise fromthe current heating by the furnace and the cooling fromthe working medium due to the feed by the feedwaterpump. In figure 11 simulated and measured pressuresat outlet of the boiler are compared. After 50 min thepower plant is in sliding pressure operation and thelife steam pressure is changing proportional with theload. In general a good conformity of both graphs canbe stated. Variations (e.g. between 40 and 70 min)could be explained with differences in the firing power.Considering this, a good reproduction of the hydrauliccharacteristic can be stated.

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Figure 11: Comparison of calculated and measuredlife steam pressure at the boiler outlet

In figure 12 the development of the boiler inflow(Eco in) and outflow (life steam) mass flow rate isshown. In the first 50 min the boiler is in circulationmode and a minimum amount of 143 kg/s of feedwateris entering the economizer and the unevaporated waterfraction is separated after the evaporator and loopedback to the boiler inlet. Then the power plant switchesto Benson operation and the feed water as well as thelife steam mass flow rate is proportional to the load.

In order to verify the proper representation of the

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mas

s flo

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ate

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simulation Eco inmeasurement Eco insimulation life steammeasurement life steam

Figure 12: Comparison of calculated and measuredeconomizer in and superheater out mass flow rate

heat transfer from the exhaust gas to the different heat-ing surfaces by the model, the calculated steam tem-peratures at the outlet header of each heating deviceare compared to the corresponding measurement. Inthe following some representative plots are discussed.In figure 13 the water temperature entering the boilerat the economizer inlet and the steam temperature afterthe evaporator is brought out with respect to time.

40 80 120 160 200100

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simulation Eco inmeasurement Eco insimulation evaporator outmeasurement evaporator out

Figure 13: Comparison of calculated and measuredfluid temperature at inlet of the economizer and afterevaporator

Whereas the simulated evaporator outlet tempera-ture shows a good agreement with the measurement -the mean relative error is about 3.3 %, the economizerinlet temperature shows a deviation between 10 and 30min with a maximum error of 28 %. This is caused bya difference in the circulation rate: in the simulationa large quantity of cold feed water is lowering the ecoinlet temperature in contrast to the measurement. Thismeans that a higher amount of almost boiling circu-lated water, as can be seen in figure 12 as the differenceof the eco in and life steam flow, is leading to a higheco inlet temperature. In Benson operation the error isless than 5.2 % and shows a very good correlation.

The trend of the temperature after superheater SH 1


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shows analogue results, hence the furnace and heattransfer model is capable to reproduce the heat trans-fer of the boiler and its temporal behaviour (see figure14).

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simulation SH 1 outmeasurement SH 1 outsimulation life steamsimulation HP−Turbine inmeasurement life steam

Figure 14: Comparison of calculated and measuredsteam temperatures after the first and the last super-heater

In the same diagram the simulated and measuredlive steam temperatures are plotted. During the firstphase of a start with low flow through the life steampipes to the turbines, an inhomogeneous tempera-ture distribution and the unknown location of the sen-sor complicates a validation, but the measurement iswithin the model temperatures at the in- and outlet ofthe life steam pipe.

During sliding pressure operation again a very highcorrelation between simulation and measurement canbe stated. This can only be achieved by copying thecascaded PI-controller of the spray attemperators, thatensures the right tempering of the live steam.

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ate

in k

g/s


Figure 15: Comparison of calculated and measured in-jection mass flow rates at the first HP-injector (afterfirst superheater)

Figure 15 shows the comparability of the imple-mented temperature control by comparing the simu-lated and measured injection mass flow rates. Bothmeasured and simulated injection flow rates agree

qualitatively very well and show similar dynamics.The figure shows that the attemperator is operated

at its limits which leads to quite extreme changes ofvalve opening between fully opened and fully closed.This behavior is uncritical, since the task of the first in-jector is it to keep the second injector within its properoperation limits.

As can be seen in figure 16 the net generator power,whose behavior is effected by the dynamics of the en-tire power plant process, shows a good correlation.Thus, it can be stated, that the dominating and relevanteffects are reproduced by the model and the validationshown above approves the accuracy and the validity ofthe model assumptions.

40 80 120 160 2000

20

40

60

80

100

time in min

net g

ener

ator

pow

er in

%


Figure 16: Comparison of the simulated net generatorpower and corresponding measurement

5 Evaluation of Component Strain

With this existing model it is possible to predict tem-peratures and temperature gradients at points whichare inaccessible to measurements like wall tempera-tures of highly stressed components.

For the first 90 min of the presented soft start theoccurring wall temperatures of the superheater outletheader are displayed in figure 17. Obviously the metaltemperature at the outside of the wall follows the in-ner temperature with a certain delay and its amplitudesare considerably smaller. This effect can be explainedwith time specifics of the heat conduction and energystorage. The noticeable phase shift of the temperaturesleads to relative high temperature differences betweenthe inner and outer fiber in case of sharp edged changesin evaporator heating or cooling.

The evaluation of metal temperatures offers the pos-sibility to benchmark different controller parametersets with a view to preserving operation at concur-rently high load dynamics.


361

10 20 30 40 50 60 70 80 90200

250

300

350

400

time in min

tem

pera

ture

in °

C

inner wallouter wall

Figure 17: Metal temperatures in the superheater SH 2outlet header

Quantification of the effects of thermal stress on thedifferent components of a plant is a challenging taskas the processes of fatigue are complex and highly sta-tistical. For this reason the results of a fatigue predic-tion in this context can only be of qualitative natureand should be understood as a trend indicator that iscapable of identifying the most stressed componentsand predict possible side effects of innovative con-trol strategies on this complex system. For a detailedinvestigation of certain components a FEM-analysisshould be carried out considering the installation sit-uation (and with it possible pretensions in the compo-nent) and the exact geometry.

However, for a first estimation of the effects of moredynamic plant operation in the future two different ap-proaches are used and should be discussed in the fol-lowing:

The guidelines of the Deutsche Dampfkesselauss-chuss (2000) TRD 301 [8] and 508 [9] give directivesfor the estimation of fatigue of thick-walled boilercomponents under smouldering pressure and temper-ature due to start-up processes. For this purpose aneffective stress range is evaluated with a Wöhler dia-gram for crack initiation. The following equation givesthe law for calculating the stress range ∆σ .

∆σi =

(αm

dm

2sb

)∆p+

(αϑ

βLϑ Eϑ

1−ν

)∆Θ (8)

Herein αm, αϑ , dm, βLϑ , Eϑ , ν , ∆p and ∆Θ denotefor mechanical and thermal correction factor for stresssuperelevation at branches, mean diameter, mean wallthickness, linear expansion coefficient, Young’s modu-lus, Poisson’s ratio and the range of pressure and tem-perature difference during load change, respectively.Figure 18 shows qualitatively the evaluation of theworking stress during load change. The maximumnumber of load changes comparable to the actual one

is generated from the Wöhler-curve. The percentilefatigue of the actual load change is then:

e =1N

100 (9)

This estimation leads to conservative results in orderto handle the numerous uncertainties in calculation ofworking stresses at complex components and materialproperties.

Kapitel 2 Grundlagen der Lebensdauerberechnung in der Kraftwerkstechnik

Abbildung 2.4: Qualitativer Verlauf einer Wöhlerlinie [LLW90]

Bereich der Kraftwerkstechnik be�ndet man sich häu�g in diesem Ermüdungsbereich. Auf-grund der hohen Belastungen müssen bei der Auslegung plastische Verformungen akzeptiertwerden.

• Z ist der Bereich der Zeitfestigkeit bzw. Zeitschwingfestigkeit. Meistens wird hier ein Bereichin etwa zwischen 5 ·10

4 und 2 ·106 Lastwechseln angegeben. Die Wöhlerkurve ist in diesem

Bereich bei doppeltlogarithmischer Auftragung nahezu eine Gerade.

• D ist der Bereich der so genannten Dauerfestigkeit. Liegt die Spannungsamplitude unter-halb der Dauerfestigkeit kann das Bauteil theoretisch unendlich viele Lastwechsel ertragenohne das ein Versagen auftreten wird.

Für die Lebensdauervorhersage liefert die Wöhlerlinie die bei einer vorgegeben Bauteilbelas-tung maximal mögliche Lastwechselzahl. Zur Ermittlung der Anrisszahl bei einem bestimmtenLastfall i geht man ausgehend vom zu untersuchenden Spannungswert σi auf der Ordinate waag-recht bis zur Wöhlerlinie und liest die maximale Lastwechselzahl bis zum Anriss NA auf derAbszisse ab. Umgekehrt kann entsprechend nach Vorgabe einer bestimmten Anzahl an Lastwech-seln die dafür maximal zulässige Betriebsbelastung ermittelt werden. Der Lebensdauerverbrauchnach einem Lastzyklus beträgt dann in Prozent:

ew,i =1

NA

· 100 (2.10)

Aufgrund der Ableitung der Wöhlerlinien aus Versuchsreihen besitzen die Werte folglich nureine statistische Genauigkeit. Man kann den aus Wöhlerlinien ermittelten Lebensdauerverbrauchsomit als groben Richtwert verwenden, der für die Auslegung noch mit den nötigen Sicherheitenbeaufschlagt werden muss. Die Realität kann dadurch aber natürlich nicht völlig exakt wieder-geben werden. [Kla80], [LLW90]

10

Figure 18: Principle of evaluation of component stressfor cyclic loading [11].

This method allows to benchmark different opera-tion modes in terms of their level of deterioration todifferent components. In figure 19 the fatigue of a softstart and several load changes is plotted for the inletand outlet headers of the superheaters and reheaters.Please note that currently normal operation is between50 % and 100 % load, so the shown load change of60 % could be considered as an unconventional oper-ation.

SH1i SH1o SH2i SH2o SH3i SH3o SH4i SH4o RH1i RH1o RH2i RH2o0

1

2

3

4

5

6x 10

−3

fatig

ue in

%

warmstartload change > 60%load change > 40%load change > 20%

Figure 19: Fatigue of heating surface in- and outletheaders for different base stress situations


362

It can be obtained, that the outlet header of super-heater SH 4 is effected the most, whereas the headersof the reheaters are not or lowly stressed. Furthermoreit can be derived, that load changes less than 40 %barely cause any fatigue, because the stress levels arebelow the endurance strength.

Considering the flaw growth of predamaged compo-nent gives a far more sensitive view on the operationmode. The German Forschungskuratorium Maschi-nenbau [10] gives guidelines for the calculation ofcrack progress. Figure 20 gives a general overviewon crack propagation rate as function of the range ofstress intensity factor ∆K.

Figure 20: Overview on crack propagation undercyclic load [10].

According to figure 20 there is a certain load thatdoes not leads to crack propagation (∆K ≤ ∆Kth). Inregion I to III there is a stable propagation to be ex-pected (∆Kth ≤ ∆K ≤ ∆Kc) which can be conserva-tively estimated by the law of Paris and Erdogan:

dadN

=C∆Km (10)

Where a, N, C, m denotes for crack length, num-ber of cycles, a case-specific factor and a load specificexponent, respectively. The stress intensity factor hasto be calculated depending on the flaw’s geometry andsize and its position within the component. With thistool it is possible to detect the most strained compo-nents by comparing the crack growth over a certainreference time period.

In an analogue manner as in figure 19 the flaw prop-agation is shown for thick-walled headers in figure 21.

SH1i SH1o SH2i SH2o SH3i SH3o SH4i SH4o RH1i RH1o RH2i RH2o0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

flaw

gro

wth

in m

m

warmstartload change > 60%load change > 40%load change > 20%

Figure 21: Flaw growth in potentially pre-damagedthick-walled in- and outlet headers for different basestress situations

In contrast to the fatigue also low stress levelsof small load changes cause impairment and conse-quently with this estimation a method is given to eval-uate the deterioration potential of normal operation.

6 Conclusion and Outlook

A detailed model of a coal-fired power unit has beenimplemented and extensively validated. The modelmakes use of the open-source Modelica library Ther-moPower. A number of components especially formodeling of start-up-specific components, like the cy-clone separator and the start-up bottle as well as mod-els for the description of the fuel conversion and heattransfer in the firing of the plant have been imple-mented.

As an example for an application of the devel-oped model some base operation scenarios, like loadchanges and a soft start, have been evaluated in termsof life time consumption. In a next step the influenceof increased load gradients will be investigated.

The modular structure of the model allows the easyreplacement of single components, e.g. life steamtemperature control, which enables the benchmark ofadvanced control systems or the implementation ofdifferent or additional hardware for different opera-tion scenarios. In this way, future demands on powerplants, which might become necessary in order to real-ize wind integration successfully at controllable costs,can be benchmarked. This aspect of power plant oper-ation management will probably become more impor-tant due to highly increasing wind power production


363

and its fluctuating characteristic.The detailed manner of the plant model does not al-

low long term simulation over years or even weeks dueto high computing time at this actual state of develop-ment. Therefore the fatigue has to be extrapolated in afirst step assuming a constant or a repetitive operationmode for a long time period. Future work could covera model reduction to increase its efficiency.

References

[1] Dahl-Soerensen, M.J./ Solberg, B. PulverizedFuel Control using Biased Flow Measurements.In: IFAC Symposium on Power Plants and PowerSystems Control, Tampere, 2009.

[2] Hojczyk,B./ Hühne,W./ Thierfelder,H.G.Das Steinkohlekraftwerk Rostock. In: VGBKraftwerkstechnik 77, 1997.

[3] Casella,C./ Leva,A. Open Library for PowerPlant Simulation: Design and Experimental Val-idation. In: proceedings of 3rd. InternationalModelica Conference, Linköping, 2003.

[4] Niemczyk,P./ Andersen,P./ Bendtsen,J.D. /Soen-dergaard Pedersen,T. /Ravn,A.P. Derivation andvalidation of a coal mill model for control. In:IFAC Symposium on Power Plants and PowerSystems Control, Tampere, 2009.

[5] Effenberger Dampferzeugung. Berlin, Springer-Verlag, 2000.

[6] Verein Deutscher Ingenieure VDI-Wärmeatlas,10. Auflage. Berlin, Springer-Verlag, 2006.

[7] VDI/VDE-Gesellschaft Mess- und Automa-tisierungstechnik VDI/VDE - Richtlinie3508: Block-Führung/-Regelung vonWärmekraftwerken, 2002.

[8] Deutscher Dampfkesselausschuss TechnischeRegeln für Dampfkessel (TRD) 301 Berechnungauf Wechselbeanpruchung durch schwellendenInnendruck bzw. durch kombinierte Innendruck-und Temperaturänderungen. Carl Heymanns Ver-lag KG, 2000.

[9] Deutscher Dampfkesselausschuss TechnischeRegeln für Dampfkessel (TRD) 508 ZusätzlichePrüfungen an Bauteilen berechnet mit zeitab-hängigen Festigkeitswerten. Carl Heymanns Ver-lag KG, 2000.

[10] Forschungskuratorium Maschinenbau Bruch-mechanischer Festigkeitsnachweis für Maschi-nenbauteile. VDMA-Verlag, 2001.

[11] Lewin,G./ Lässig, G./ Woywode,N. Apparateund Behälter: Grundlagen Festigkeitsrechung.Berlin, Verlag Technik, 1990.


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