Research ArticleStudy on Multiobjective Modeling and Optimization of OffshoreMicro Integrated Energy System considering Uncertainty ofLoad and Wind Power

Jun Wu 1 Baolin Li 1 Jun Chen2 Qinghui Lou2 Xiangyu Xing1 and Xuedong Zhu 1

1School of Electrical Engineering amp Automation Wuhan University Wuhan China2Research Institute Nanjing NARI-Relays Engineering Technology Co Ltd Nanjing China

Correspondence should be addressed to Baolin Li baolin-liwhueducn

Received 21 August 2020 Revised 23 November 2020 Accepted 8 December 2020 Published 24 December 2020

Academic Editor Xin Li

Copyright copy 2020 JunWu et al+is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Offshore micro integrated energy systems (OMIESs) are the basis of offshore oil and gas engineering and play an important role indeveloping and utilizing marine resources By introducing offshore wind power generation the carbon emissions of offshoremicro integrated energy systems can be effectively reduced however greater challenges have been posted to the reliable operationdue to the uncertainty To reduce the influence brought by the uncertainty a multiobjective optimization model was proposedbased on the chance-constrained programming (CCP) the operating cost and penalty cost of natural gas emission were selected asobjectives +en the improved hybrid constraints handling strategy based on nondominated sorting genetic algorithm II(IHCHS-NSGAII) was introduced to solve the model efficiently Finally the numerical studies verified the efficiency of theproposed algorithm as well as the validity and feasibility of the proposed model in improving the economy of OMIESunder uncertainty

1 Introduction

Currently there are 6500 offshore oil and gas platformsworldwide [1] which is expected to become an importantway to solve energy and environmental problems worldwideby developing and utilizing marine oil and gas resources[2ndash4]+ese offshore oil and gas platforms are far away fromthe land and can be categorized as an offshore micro in-tegrated energy system [5] It contains a variety of energysuch as electricity gas and heat and coordinates and op-timizes the economy and energy utilization efficiencythrough energy coupling equipment (such as the power togas (P2G) and direct-fired boilers (GB)) Traditionally thatpower is provided by gas turbines (GTs) coupled to electricgenerators installed on the platforms and operating bycombustion of natural gas however for safety consider-ations redundant GTs generally run with lower operatingefficiency and higher pollution emissions [6 7] By intro-ducing offshore wind power the carbon emissions of

offshore micro integrated energy systems (OMIESs) can beeffectively reduced However affected by the complex off-shore environment greater challenges have been posted tothe reliable operation due to the uncertainty of load andoffshore wind power [8] +erefore it is of great significanceto carry out economic optimization dispatch considering theuncertain factors in the OMIES

At present scholars have conducted many studies on theoptimal operation model of the IES (integrated energysystem) [9ndash12] In [9] the photovoltaic uncertainty wasdescribed by a series of scenarios then the model wasproposed based on demand response to realizing coordi-nated optimization for the multiple energy systems In [10]the modeling of all equipment in the IES was presented tospecify the physical operational constraints and an opti-mization model was set up to minimize the total costconsidering the heat energy with different grades Reference[11] studied the influence on the operational costs and thestability of the regional IES when the controllable loads

HindawiComplexityVolume 2020 Article ID 8820332 13 pageshttpsdoiorg10115520208820332

including electric vehicles and air conditioning loads wereconsidered a virtual energy storage system (ESS) Reference[12] proposed a two-stage stochastic scheduling scheme ofan integrated multienergy system which considers the windpower uncertainty to achieve the optimal economic oper-ation with the minimum curtailment of wind power +eliterature listed above proposed different models of IESoptimization scheduling taking into consideration the in-termittency of renewable energy the different grades of heatenergy and the flexibility brought by ESS However few ofthem focus on the optimization of offshore oil and gasplatforms and combine the OMIES with offshore windpower as well as considering the effect of uncertainty

Generally there are mainly three different ways tohandle the uncertainty of offshore wind power namelyrobust optimization [13 14] interval optimization [15] andstochastic optimization [16 17] Among them stochasticoptimal scheduling uses more accurate probability distri-bution information of uncertain variables to participate inthe modeling and solving of scheduling models +e chance-constrained programming (CCP) model allows someconstraints containing uncertain variables to fail in theoptimization process but the probability level of itsestablishment must meet the confidence level requirementsReference [18] explored the low-carbon and economicplanning of OMIES considering the effect of the productionprocess or the uncertainty of the external environmentWiththe development of offshore wind power it is necessary tostudy the economic operation of the system underuncertainty

In this paper the improved hybrid constraints handlingstrategy based on nondominated sorting genetic algorithm II(IHCHS-NSGAII) was introduced to solve the biobjectiveoptimization model based on CCP to minimize the oper-ating cost and natural gas emission +e paper mainly hasthe following contributions

(i) A biobjective optimization model based on CCPwas proposed to handle the uncertainty of load andwind power To maximize wind power penetrationthe wind curtailment penalty item was added to thecost objective function Besides the natural gasemission was selected as the other objective con-sidering the current situation that there exists a largeamount of natural gas emission in actual OMIES

(ii) Based on NSGAII the hybrid constraints handlingstrategy was introduced and modified through threeaspects namely dimensionality reduction indi-vidual repair and normalization to improve theperformance of NSGAII when dealing with complexconstraints

(iii) +e relationship between natural gas emission andwind power utilization was analyzed by imple-menting an OMIES example in the Bohai Sea toprovide schemes or suggestions for offshore oil andgas platforms

+e rest of this paper is organized as follows Section 2introduces the OMIES Section 3 formulates the CCP

biobjective optimization problem Section 4 presentsIHCHS-NSGAII Section 5 shows the numerical results andanalysis and the conclusion is drawn in Section 6

2 Introduction of OMIES

+e energy flow of OMIES is shown in Figure 1 whichmainlyincludes electricity gas and thermal Also different energy iscoupled with conversion equipment for instance the GTsburn the exploited natural gas to supply electricity to theentire system and simultaneously utilize the high-temperatureflue gas generated by the combustion to heat the system [19]OMIES is formed by multiple offshore oil and gas centerplatforms interconnected by submarine cables and trans-mission pipelines

Generally the OMIES is different from a general IESFirst of all for the limitation of the capacity of the offshoreplatform energy equipment is placed relatively concentratedon the offshore platforms the physical distance betweenldquosourcerdquo and ldquoloadrdquo is relatively short Also the transmissionnetwork is not as complicated as that of a land-based powersystem Secondly ensuring steady and safe production is themost thing for offshore oil and gas engineering thus leadingto the redundant configuration of GTs Besides the exploitednatural gas that cannot be transmitted will be burned by thetorch on the platform due to the limitation of the pipelinesrsquotransmission capacity which is known as natural gasemission So it is necessary to do some research based on thecharacteristics of OMIES

3 CCP Optimization Model

Challenges have been posted to the operation of OMIES dueto the uncertainty of load and offshore wind power on theone hand in order to reduce pollution emissions and energywaste the staff hope to reduce the output of GTs and utilizeas much wind power as possible on the other hand to tackleuncertainty and ensure the safe and stable operation of thesystem the power system needs to reserve a certain amountof spare capacity to try to avoid production shutdown due toload shedding but it will also increase the operating cost ofthe system +erefore it is necessary to establish a multi-objective operation optimization model that takes into ac-count system operating costs and the consumption of windpower

31 Objective Functions

311 Objective Function 1 Five parts are included in theoperating cost namely the pollution cost of GTs and GBsthe cost of gas well production the penalty cost of naturalgas emission and wind curtailment

minF1 1113944T

t1

1113944iisinΩgt

αgt1i + αgt

2iPgtit + αgt

3i Pgtit1113872 1113873

21113876 1113877 + 1113944

jisinΩgb

αgbj G

gbjt

+ 1113944kisinΩcp

αwellk Gwellkt + 1113944

kisinΩcp

αgaskΔGgas

kt+ 1113944 αwindi ΔP

Wit

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(1)

2 Complexity

312 Objective Function 2 +e natural gas emission notonly causes energy waste but also pollutes the environmentso objective function 2 aims to minimize the natural gasemission

minF2 1113944T

t11113944ΔGgas

ki (2)

32 Operation Constraints +e OMIESs contain variouskinds of energy and equipment and the following four typesof constraints shall be met for safe operation

321 Decision Variable Constraints Generally the solutionfor a practical optimal scheduling problem includes theoutputs of all kinds of devices in the whole system so thatthe operators can make adjustments at appropriate times toachieve goals In the OMIES scheduling problem proposedin this paper the decision variable constraints can beexpressed as follows

Pgtmini leP

gtit leP

gtmaxi (3)

0lePWit leP

Wpreit (4)

Gwellmink leG

wellkt leG

wellmaxk (5)

0leHgbjt leH

gbmaxj (6)

0leHebet leH

ebmaxe (7)

0leGtP2G leG

tmaxP2G (8)

minusπ2le θht le

π2

(9)

pminn lepnt lep

maxn (10)

minusRdowni leP

gtit minus P

gtitminus1 leR

upi (11)

Equations (3)ndash(8) describe the upper and lower boundsof GTs offshore wind power gas well GBs EBs and P2Grespectively Equations (9) and (10) are the node angel andnode pressure limits Equation (11) describes the ramp limitsof GTs

322 System Balance Constraints For each system theenergy flow in and out at each bus shall be equal

1113944iisinh

Pgtit + 1113944

iisinWG

Pwit minus 1113944

gisinhPght minus E

loadht minus 1113944

eisinhP

ebet minus P

p2g 0

(12)

1113944kisinn

Gwellkt + G

p2g

kt + 1113944misinn

Gmnt minus 1113944iisinn

Ggt

it minus Gloadnt minus 1113944

jisinnG

gb

jt minus 1113944kisinnΔGgas

kt 0

(13)

1113944iisinΩgt

Hgtit + 1113944

jisinΩgb

Hgbjt + 1113944

eisinΩeb

Hebet minus H

loadt 0

(14)

323 Equipment Operation Constraints Equipment in theOMIES is constrained by energy conservation constraints

Gas load

P2G

Gas turbine

Git Pit

Hit

Pit

Gkt

Het

PetPp2g

Gjt

Gki

Hjt

Waste heat

recovery boilerG

as-fi

red

boile

r

Offshore

wind power

Electri

cboil

er

Nat

ural

gas w

ellElectric

load

Heatload

gt gt

gt

well

eb

ebp2g

w

gb

gb

Figure 1 Energy flow of OMIES

Complexity 3

PWpreit minus P

Wit ΔPW

it (15)

Ggtit

Pgtit

η middot HVgas (16)

Hgtit

Pgtit middot 1 minus ηgt minus ηl1113872 1113873 middot ηwhb

ηgt

(17)

Hgbjt ηgb middot HVgas middot G

gbjt (18)

Hebet ηeb middot P

ebet (19)

GtP2G

ηP2GPtP2G

Hg

(20)

Equation (15) describes the relationship between actualwind power and forecasted value Equations (16)ndash(20) arethe relationships between the input and output of eachequipment +e power flow constraints of OMIES can befound in [20] +e relationship between the flow of naturalgas flowing through a pipeline and the pressure at both endsof the pipeline can be found in [21]

324 Chance Constraints Offshore oil and gas platformsface a complex and changeable environment In this paperthe uncertainty of power load and offshore wind power ismodeled by stochastic variables +e forecast error of off-shore wind power and power load can be expressed bynormal distribution as follows

εwtt sim N 0 σwt( 1113857

σwt ρwttPwtt + ρwtinsPwtins

εloadt sim N 0 σ load( 1113857

σ load ρloadtEloadt

(21)

+erefore the power balance constraint shall be con-verted as (22) considering the uncertainty

Pr 1113944iisinh

Pgt

it + 1113944iisinWG

Pwit minus 1113944

gisinhPght minus 1113944

eisinhP

ebet minus P

p2gminus E

loadht

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ge η1

(22)

Equation (22) indicates that the power flow shall be metunder a certain confidence coefficient

To ensure the safe operation of the system and preventthe uncertainty of wind power and load from affecting thepower balance the reserve capacity should meet the up- anddown-reserve capacity constraints

Pr 1113944

N

i1Pimax minus Pi( 1113857geUSR + wuPW

⎧⎨

⎩

⎫⎬

⎭ ge η2 (23)

Pr 1113944

N

i1Pi minus Pimin( 1113857gewd PWmax minus PW( 1113857

⎧⎨

⎩

⎫⎬

⎭ ge η3 (24)

33 Transformation of Chance Constraints Chance con-straints in equations (22)ndash(24) are difficult to handle And itcan be solved by converting into their equivalence type [22]

1113944iisinh

Pgt

it + 1113944iisinWG

Pwit minus 1113944

gisinhPght minus 1113944

eisinhP

ebet minus P

p2g

minusEloadht ge inf K|K ϕminus1

1 η1( 11138571113966 1113967

1wu

1113944

N

i1Pimax minus Pi( 1113857 minus USR

⎛⎝ ⎞⎠ minus Pwit ge inf K|K ϕminus1

2 η2( 11138571113966 1113967

1wd

1113944

N

i1Pi minus Pimin( 1113857⎛⎝ ⎞⎠ minus Pwtins + P

wit ge inf K|K ϕminus1

3 η3( 11138571113966 1113967

(25)

4 IHCHS-NSGAII

Although NSGAII [23] is recognized as one of the mosteffective ways to deal with such multiconstrained problemsthe proposed model in Section 3 is still difficult to solve dueto the complexity of the variable vectors and different kindsof constraints especially when there might be coupling andnonlinearity +erefore a high efficient optimizationmethod was needed to handle the complex multiconstrainedmultiobjective optimization problem In this section ahybrid constraint processing strategy (HCHS) [24] is in-troduced and modified to improve the performance ofNSGAII when dealing with complex constraints

41 Dimensionality Reduction Method Generally theequality constraints such as electric power and gas balanceconstraints are not easy to handle for NSGAII so it isnecessary to transfer equality constraints into inequalityones with their own limitations in the meantime the vectordimension can be reduced and the solving efficiency of thealgorithm would be improved Taking the power balanceconstraint as an example the specific conversion process isas follows

Equation (12) can be equivalently converted as

Pgt

it Pght + Eloadht + P

ebet + P

p2gminus P

wit (26)

On the other hand equation (26) shall be met byconstraints described in equation (3) +ereby the equalityconstraint is equivalently transformed into an inequalityone And the other equality constraints can be converted inthe same way

42 Repair Process after Generation of a New IndividualViolation of some constraints that are related to the variablesgeneration process such as the ramp rate constraints cannotalways be reduced for the individuals Since the individualsare generated using some heuristic-based stochasticmethods in NSGAII the constraint handling method in [23]cannot reduce the violation of some constraints such as the

4 Complexity

ramp rate constraints and the rated power constraints re-lated to the variables generation process +us a repairprocess is needed to convert the infeasible individuals intofeasible ones In this paper the repair process is utilized torepair the variables corresponding to the active poweroutput of GT which violates the ramp rate constraints Sincethe ramp rate constraint violations appear between thevariables with close time intervals which have strongcoupling it is difficult for the optimization algorithm toreduce them during the evolutionary process +erefore it isnecessary to ldquorepairrdquo the variables when the population isgenerated When a ramp rate constraint is violated all of thevariables P

gtit in a scheduling period should be repaired from

the beginning time interval for the related GT so that theramp rate limit and the rated power requirement can be metsimultaneously It is obvious that the repair process mayneed much computing resources and time Besides con-sidering the proportion of infeasible individuals is dynamicduring the whole computation period the repair probabilityon the infeasible potential solutions is designed to beupdated based on the current stage of the algorithm asshown as follows

Pre Gc( 1113857

Gc

Gs

1113888 1113889

2

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)

It can be seen from equation (27) that the value of Pre issmall at the beginning of optimization to accept more po-tential infeasible individuals so that the diversity of thepopulation can be ensured And when Gc is large enough allof the individuals which violate the ramp rate constraintshould be repaired But comparing with the microgriddispatch problem in [24] the OMIES scheduling problem ismore complex and the main target is to find feasible so-lutions +erefore to solve the constrained multiobjectiveproblem of OMIES scheduling in this paper equation (27) ismodified as follows

Pre Gc( 1113857

Gc

Gs

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(28)

where Gs 025Gmax In this way the average value of Pre isincreased compared with that in equation (27) and most ofthe individuals in the population can be repaired during theoptimization process

43 Normalization Process in Selection Considering thetypes and amounts of constraints in the proposed model it isefficient to normalize each of the constraint violation beforeadding up and the specific details could be found in [24] Itcan be seen from Section 2 that in the proposed OMIESscheduling problem there are various types of constraintsand different types of constraint violations cannot becompared or added directly +us in this paper the numberof violated constraints of different types is also considered as

a factor to evaluate the infeasible level of the individuals +enormalization method is modified in this paper as

vlknorm 1nk

1113944

nk

i1

vlki minus vkmin

vkmax minus vkmin (29)

It can be seen from equation (29) that by introducing nk

the normalization process can be more reasonable and thenumber of violated constraints can be taken into account inthe constraintsrsquo handling process Hence the algorithmwould find potential solutions with a lower sum of nor-malized violations and the ones with a lower number ofviolated constraints are preferred during the evolutionaryprocess +erefore the average number of violated con-straints in the population would drop rapidly and thefeasible regions can be found efficiently

5 Simulation

In this section the results of the numerical studies arepresented and analyzed which are conducted based on amodified OMIES located in the Bohai Sea of China in [25] asshown in Figure 2 +e optimization models are solvedunder the MATLAB environment In addition a computerwith Intel i5-8700 CPU320 GHz and 8GBmemory is usedto run the optimization models

51 Parameters of the OMIES +is case is composed of a 6-node power system a 6-node natural gas system and athermal system EBs are located in nodes 1 4 and 5 in thepower system with capacities of 12MW 095MW and11MW respectively Parameters related to GTs are listedin Table 1 +e natural gas system consists of 3 gas wellnodes and 3 gas load nodes GBs are located in nodes 1 and2 with maximum thermal powers of 3MW and 4MWrespectively Parameters related to the gas well are listed inTable 2 And the natural gas caloricity is 97 kWhm3 +eoffshore wind turbine is located in node 5 in the powersystem with a capacity of 9MW And the penalty costcoefficient of offshore wind power is 50 $MW Node 2 inthe natural gas system and node 4 in the power system areconnected by a P2G with a capacity of 06MW +econfidence coefficients are all set to 095 in this paper +eother parameters could be found in Table 3 By the way thedata used in this paper are collected from an actual off-shore oil and gas engineering and the parameters men-tioned above are obtained by fitting or calculating thesedata

+e forecast curve of electricity gas and heat load wasshown in Figure 3

52 Results and Discussions +e parameters such as thenumber of population individuals mutation rate and cal-culation accuracy used in IHCHS-NSGAII are selected re-ferring to [24] +e maximum generation number is set to20000 generations and the population size is 50

Besides in this section the penalty function method(PFM) constraint domination principle (CDP) and the

Complexity 5

original HCHS are introduced to compare the performancewith the improved HCHS +e parameter settings of PFMandHCHS can be found in [24] Each algorithm is combinedwith NSGAII and run 10 times +e average feasible solu-tions using different constraint handling methods arerecorded during the evolutionary process

It can be seen from Table 4 that before 1000 generationsthe numbers of feasible solutions obtained are low by all theconstraint handling methods which indicates that theOMIES scheduling problem is very complex with varioustypes of constraintsWith the increase of the generations thefeasible solutions become more by CDP HCHS and im-proved HCHS However by using PFM NSGAII cannotfind enough feasible solutions Even after 20000 iterationsNSGAII only finds 15 feasible solutions As for CDP thesituation is better with 27 solutions which means that CDP

is more effective in dealing with multiconstrained multi-objective optimization problems than PFM However nearlyhalf of the obtained solutions are still infeasible HCHS isbased on CDP but by the hybrid constraints handlingmethods it can find more feasible solutions When HCHS ismodified by the method proposed in this paper it can beseen that it can find a similar amount of feasible solutionswith 10000 generations with those by original HCHS after20000 generations Moreover within 18000 iterations all thesolutions in the population are feasible by the proposedimproved HCHS +e results indicate that comparing withthe existing constraints handling methods the proposedimproved HCHS is more adaptable to the complexity of themulticonstrained OMIES scheduling problem which canmake NSGAII reduce the overall violations consideringdifferent constraint types and converge to the feasible

G-W G

L

L

L

L

2

3

4 5

6

Natural gas system

1

2

3

4

5

6

L

Gas turbine generator unit

L Electric load

Electric boiler Gas load

Gas-fired boiler

Power system

GB

GB

GB

Gas turbine generator unit withwaste heat recovery boiler

Gas well

G

G-W G

1

P2G

W

P2G Power to gas

W Offshore wind power

Figure 2 A case of OMIES

6 Complexity

regions faster +erefore more computational resources canbe applied to find better Pareto solutions

+e optimal solution set is shown in Figure 4From the perspective of the distribution of the Pareto set

the operating cost and the natural gas emission cannot beperfectly optimized at the same time +e staff need to weighenvironmental protection economy and stability accordingto actual needs And the final Pareto optimal solution is notcontinuous For solutions at discontinuities one objectivefunction may have a small difference but the other objectivefunction can be greatly optimized +erefore particularattention should be paid to the choice of solutions atdiscontinuities

What is more the optimal solutions in the Pareto set ofthe two objective functions are selected as the two schemes

Scheme One +e optimal solution for operating cost(operating cost 8094448 $ and natural gas emission40000m3)Scheme Two +e optimal solution for natural gasemission (operating cost 877844 $ and natural gasemission 2100m3)

+e operating cost comparison of the two schemes isshown in Figure 5 and the specific operating cost values areshown in Table 4

It can be seen from Figure 5 and Table 5 that the pol-lution cost of GBs in the two schemes is basically the same+e pollution cost of GTs and GBs cost of the gas well andthe penalty cost of wind curtailment in scheme one are lowerthan those in scheme two while the penalty cost of gas

Table 3 Other parameters

Parameters ValueEfficiency of GT 04Heat loss coefficient of GT 03Heat recovery efficiency of WHRB 047Combustion efficiency of GB 085Pollution coefficient of GB 024$MWElectrothermal conversion efficiency of EB 099Reserve capacity factor 012Error coefficient of offshore wind power capacity 002Error coefficient of offshore wind power output 02Error coefficient of power load 02

Table 2 Parameters related to the gas well

Number of gas well 1 2 3Location of gas well 1 2 5Minimum output of gas well106m3 01000 00113 00050Maximum output of gas well106m3 01313 00158 00071Minimum gas emission106m3 0 0 0Maximum gas emission106m3 01000 00113 00050Cost coefficients of gas production $106m3 20 15 25Penalty cost coefficients of gas emission $106m3 200 150 250

Table 1 Parameters related to GTs [25]

Number of units 1 2 3Location of units 1 1 4Maximum output (MW) 0 0 0Minimum output (MW) 12 9 12Maximum ramp up rate (MWh) 3 2 3Maximum ramp down rate (MWh) 3 2 3Whether equipped with WHRB Yes No NoQuadratic pollution coefficient 00047 00052 00074Linear pollution coefficient 00940 00730 01180Constant coefficient 04900 02855 05320

Complexity 7

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

312 Objective Function 2 +e natural gas emission notonly causes energy waste but also pollutes the environmentso objective function 2 aims to minimize the natural gasemission

minF2 1113944T

t11113944ΔGgas

ki (2)

32 Operation Constraints +e OMIESs contain variouskinds of energy and equipment and the following four typesof constraints shall be met for safe operation

321 Decision Variable Constraints Generally the solutionfor a practical optimal scheduling problem includes theoutputs of all kinds of devices in the whole system so thatthe operators can make adjustments at appropriate times toachieve goals In the OMIES scheduling problem proposedin this paper the decision variable constraints can beexpressed as follows

Pgtmini leP

gtit leP

gtmaxi (3)

0lePWit leP

Wpreit (4)

Gwellmink leG

wellkt leG

wellmaxk (5)

0leHgbjt leH

gbmaxj (6)

0leHebet leH

ebmaxe (7)

0leGtP2G leG

tmaxP2G (8)

minusπ2le θht le

π2

(9)

pminn lepnt lep

maxn (10)

minusRdowni leP

gtit minus P

gtitminus1 leR

upi (11)

Equations (3)ndash(8) describe the upper and lower boundsof GTs offshore wind power gas well GBs EBs and P2Grespectively Equations (9) and (10) are the node angel andnode pressure limits Equation (11) describes the ramp limitsof GTs

322 System Balance Constraints For each system theenergy flow in and out at each bus shall be equal

1113944iisinh

Pgtit + 1113944

iisinWG

Pwit minus 1113944

gisinhPght minus E

loadht minus 1113944

eisinhP

ebet minus P

p2g 0

(12)

1113944kisinn

Gwellkt + G

p2g

kt + 1113944misinn

Gmnt minus 1113944iisinn

Ggt

it minus Gloadnt minus 1113944

jisinnG

gb

jt minus 1113944kisinnΔGgas

kt 0

(13)

1113944iisinΩgt

Hgtit + 1113944

jisinΩgb

Hgbjt + 1113944

eisinΩeb

Hebet minus H

loadt 0

(14)

323 Equipment Operation Constraints Equipment in theOMIES is constrained by energy conservation constraints

Gas load

P2G

Gas turbine

Git Pit

Hit

Pit

Gkt

Het

PetPp2g

Gjt

Gki

Hjt

Waste heat

recovery boilerG

as-fi

red

boile

r

Offshore

wind power

Electri

cboil

er

Nat

ural

gas w

ellElectric

load

Heatload

gt gt

gt

well

eb

ebp2g

w

gb

gb

Figure 1 Energy flow of OMIES

Complexity 3

PWpreit minus P

Wit ΔPW

it (15)

Ggtit

Pgtit

η middot HVgas (16)

Hgtit

Pgtit middot 1 minus ηgt minus ηl1113872 1113873 middot ηwhb

ηgt

(17)

Hgbjt ηgb middot HVgas middot G

gbjt (18)

Hebet ηeb middot P

ebet (19)

GtP2G

ηP2GPtP2G

Hg

(20)

Equation (15) describes the relationship between actualwind power and forecasted value Equations (16)ndash(20) arethe relationships between the input and output of eachequipment +e power flow constraints of OMIES can befound in [20] +e relationship between the flow of naturalgas flowing through a pipeline and the pressure at both endsof the pipeline can be found in [21]

324 Chance Constraints Offshore oil and gas platformsface a complex and changeable environment In this paperthe uncertainty of power load and offshore wind power ismodeled by stochastic variables +e forecast error of off-shore wind power and power load can be expressed bynormal distribution as follows

εwtt sim N 0 σwt( 1113857

σwt ρwttPwtt + ρwtinsPwtins

εloadt sim N 0 σ load( 1113857

σ load ρloadtEloadt

(21)

+erefore the power balance constraint shall be con-verted as (22) considering the uncertainty

Pr 1113944iisinh

Pgt

it + 1113944iisinWG

Pwit minus 1113944

gisinhPght minus 1113944

eisinhP

ebet minus P

p2gminus E

loadht

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ge η1

(22)

Equation (22) indicates that the power flow shall be metunder a certain confidence coefficient

To ensure the safe operation of the system and preventthe uncertainty of wind power and load from affecting thepower balance the reserve capacity should meet the up- anddown-reserve capacity constraints

Pr 1113944

N

i1Pimax minus Pi( 1113857geUSR + wuPW

⎧⎨

⎩

⎫⎬

⎭ ge η2 (23)

Pr 1113944

N

i1Pi minus Pimin( 1113857gewd PWmax minus PW( 1113857

⎧⎨

⎩

⎫⎬

⎭ ge η3 (24)

33 Transformation of Chance Constraints Chance con-straints in equations (22)ndash(24) are difficult to handle And itcan be solved by converting into their equivalence type [22]

1113944iisinh

Pgt

it + 1113944iisinWG

Pwit minus 1113944

gisinhPght minus 1113944

eisinhP

ebet minus P

p2g

minusEloadht ge inf K|K ϕminus1

1 η1( 11138571113966 1113967

1wu

1113944

N

i1Pimax minus Pi( 1113857 minus USR

⎛⎝ ⎞⎠ minus Pwit ge inf K|K ϕminus1

2 η2( 11138571113966 1113967

1wd

1113944

N

i1Pi minus Pimin( 1113857⎛⎝ ⎞⎠ minus Pwtins + P

wit ge inf K|K ϕminus1

3 η3( 11138571113966 1113967

(25)

4 IHCHS-NSGAII

Although NSGAII [23] is recognized as one of the mosteffective ways to deal with such multiconstrained problemsthe proposed model in Section 3 is still difficult to solve dueto the complexity of the variable vectors and different kindsof constraints especially when there might be coupling andnonlinearity +erefore a high efficient optimizationmethod was needed to handle the complex multiconstrainedmultiobjective optimization problem In this section ahybrid constraint processing strategy (HCHS) [24] is in-troduced and modified to improve the performance ofNSGAII when dealing with complex constraints

41 Dimensionality Reduction Method Generally theequality constraints such as electric power and gas balanceconstraints are not easy to handle for NSGAII so it isnecessary to transfer equality constraints into inequalityones with their own limitations in the meantime the vectordimension can be reduced and the solving efficiency of thealgorithm would be improved Taking the power balanceconstraint as an example the specific conversion process isas follows

Equation (12) can be equivalently converted as

Pgt

it Pght + Eloadht + P

ebet + P

p2gminus P

wit (26)

On the other hand equation (26) shall be met byconstraints described in equation (3) +ereby the equalityconstraint is equivalently transformed into an inequalityone And the other equality constraints can be converted inthe same way

42 Repair Process after Generation of a New IndividualViolation of some constraints that are related to the variablesgeneration process such as the ramp rate constraints cannotalways be reduced for the individuals Since the individualsare generated using some heuristic-based stochasticmethods in NSGAII the constraint handling method in [23]cannot reduce the violation of some constraints such as the

4 Complexity

ramp rate constraints and the rated power constraints re-lated to the variables generation process +us a repairprocess is needed to convert the infeasible individuals intofeasible ones In this paper the repair process is utilized torepair the variables corresponding to the active poweroutput of GT which violates the ramp rate constraints Sincethe ramp rate constraint violations appear between thevariables with close time intervals which have strongcoupling it is difficult for the optimization algorithm toreduce them during the evolutionary process +erefore it isnecessary to ldquorepairrdquo the variables when the population isgenerated When a ramp rate constraint is violated all of thevariables P

gtit in a scheduling period should be repaired from

the beginning time interval for the related GT so that theramp rate limit and the rated power requirement can be metsimultaneously It is obvious that the repair process mayneed much computing resources and time Besides con-sidering the proportion of infeasible individuals is dynamicduring the whole computation period the repair probabilityon the infeasible potential solutions is designed to beupdated based on the current stage of the algorithm asshown as follows

Pre Gc( 1113857

Gc

Gs

1113888 1113889

2

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)

It can be seen from equation (27) that the value of Pre issmall at the beginning of optimization to accept more po-tential infeasible individuals so that the diversity of thepopulation can be ensured And when Gc is large enough allof the individuals which violate the ramp rate constraintshould be repaired But comparing with the microgriddispatch problem in [24] the OMIES scheduling problem ismore complex and the main target is to find feasible so-lutions +erefore to solve the constrained multiobjectiveproblem of OMIES scheduling in this paper equation (27) ismodified as follows

Pre Gc( 1113857

Gc

Gs

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(28)

where Gs 025Gmax In this way the average value of Pre isincreased compared with that in equation (27) and most ofthe individuals in the population can be repaired during theoptimization process

43 Normalization Process in Selection Considering thetypes and amounts of constraints in the proposed model it isefficient to normalize each of the constraint violation beforeadding up and the specific details could be found in [24] Itcan be seen from Section 2 that in the proposed OMIESscheduling problem there are various types of constraintsand different types of constraint violations cannot becompared or added directly +us in this paper the numberof violated constraints of different types is also considered as

a factor to evaluate the infeasible level of the individuals +enormalization method is modified in this paper as

vlknorm 1nk

1113944

nk

i1

vlki minus vkmin

vkmax minus vkmin (29)

It can be seen from equation (29) that by introducing nk

the normalization process can be more reasonable and thenumber of violated constraints can be taken into account inthe constraintsrsquo handling process Hence the algorithmwould find potential solutions with a lower sum of nor-malized violations and the ones with a lower number ofviolated constraints are preferred during the evolutionaryprocess +erefore the average number of violated con-straints in the population would drop rapidly and thefeasible regions can be found efficiently

5 Simulation

In this section the results of the numerical studies arepresented and analyzed which are conducted based on amodified OMIES located in the Bohai Sea of China in [25] asshown in Figure 2 +e optimization models are solvedunder the MATLAB environment In addition a computerwith Intel i5-8700 CPU320 GHz and 8GBmemory is usedto run the optimization models

51 Parameters of the OMIES +is case is composed of a 6-node power system a 6-node natural gas system and athermal system EBs are located in nodes 1 4 and 5 in thepower system with capacities of 12MW 095MW and11MW respectively Parameters related to GTs are listedin Table 1 +e natural gas system consists of 3 gas wellnodes and 3 gas load nodes GBs are located in nodes 1 and2 with maximum thermal powers of 3MW and 4MWrespectively Parameters related to the gas well are listed inTable 2 And the natural gas caloricity is 97 kWhm3 +eoffshore wind turbine is located in node 5 in the powersystem with a capacity of 9MW And the penalty costcoefficient of offshore wind power is 50 $MW Node 2 inthe natural gas system and node 4 in the power system areconnected by a P2G with a capacity of 06MW +econfidence coefficients are all set to 095 in this paper +eother parameters could be found in Table 3 By the way thedata used in this paper are collected from an actual off-shore oil and gas engineering and the parameters men-tioned above are obtained by fitting or calculating thesedata

+e forecast curve of electricity gas and heat load wasshown in Figure 3

52 Results and Discussions +e parameters such as thenumber of population individuals mutation rate and cal-culation accuracy used in IHCHS-NSGAII are selected re-ferring to [24] +e maximum generation number is set to20000 generations and the population size is 50

Besides in this section the penalty function method(PFM) constraint domination principle (CDP) and the

Complexity 5

original HCHS are introduced to compare the performancewith the improved HCHS +e parameter settings of PFMandHCHS can be found in [24] Each algorithm is combinedwith NSGAII and run 10 times +e average feasible solu-tions using different constraint handling methods arerecorded during the evolutionary process

It can be seen from Table 4 that before 1000 generationsthe numbers of feasible solutions obtained are low by all theconstraint handling methods which indicates that theOMIES scheduling problem is very complex with varioustypes of constraintsWith the increase of the generations thefeasible solutions become more by CDP HCHS and im-proved HCHS However by using PFM NSGAII cannotfind enough feasible solutions Even after 20000 iterationsNSGAII only finds 15 feasible solutions As for CDP thesituation is better with 27 solutions which means that CDP

is more effective in dealing with multiconstrained multi-objective optimization problems than PFM However nearlyhalf of the obtained solutions are still infeasible HCHS isbased on CDP but by the hybrid constraints handlingmethods it can find more feasible solutions When HCHS ismodified by the method proposed in this paper it can beseen that it can find a similar amount of feasible solutionswith 10000 generations with those by original HCHS after20000 generations Moreover within 18000 iterations all thesolutions in the population are feasible by the proposedimproved HCHS +e results indicate that comparing withthe existing constraints handling methods the proposedimproved HCHS is more adaptable to the complexity of themulticonstrained OMIES scheduling problem which canmake NSGAII reduce the overall violations consideringdifferent constraint types and converge to the feasible

G-W G

L

L

L

L

2

3

4 5

6

Natural gas system

1

2

3

4

5

6

L

Gas turbine generator unit

L Electric load

Electric boiler Gas load

Gas-fired boiler

Power system

GB

GB

GB

Gas turbine generator unit withwaste heat recovery boiler

Gas well

G

G-W G

1

P2G

W

P2G Power to gas

W Offshore wind power

Figure 2 A case of OMIES

6 Complexity

regions faster +erefore more computational resources canbe applied to find better Pareto solutions

+e optimal solution set is shown in Figure 4From the perspective of the distribution of the Pareto set

the operating cost and the natural gas emission cannot beperfectly optimized at the same time +e staff need to weighenvironmental protection economy and stability accordingto actual needs And the final Pareto optimal solution is notcontinuous For solutions at discontinuities one objectivefunction may have a small difference but the other objectivefunction can be greatly optimized +erefore particularattention should be paid to the choice of solutions atdiscontinuities

What is more the optimal solutions in the Pareto set ofthe two objective functions are selected as the two schemes

Scheme One +e optimal solution for operating cost(operating cost 8094448 $ and natural gas emission40000m3)Scheme Two +e optimal solution for natural gasemission (operating cost 877844 $ and natural gasemission 2100m3)

+e operating cost comparison of the two schemes isshown in Figure 5 and the specific operating cost values areshown in Table 4

It can be seen from Figure 5 and Table 5 that the pol-lution cost of GBs in the two schemes is basically the same+e pollution cost of GTs and GBs cost of the gas well andthe penalty cost of wind curtailment in scheme one are lowerthan those in scheme two while the penalty cost of gas

Table 3 Other parameters

Parameters ValueEfficiency of GT 04Heat loss coefficient of GT 03Heat recovery efficiency of WHRB 047Combustion efficiency of GB 085Pollution coefficient of GB 024$MWElectrothermal conversion efficiency of EB 099Reserve capacity factor 012Error coefficient of offshore wind power capacity 002Error coefficient of offshore wind power output 02Error coefficient of power load 02

Table 2 Parameters related to the gas well

Number of gas well 1 2 3Location of gas well 1 2 5Minimum output of gas well106m3 01000 00113 00050Maximum output of gas well106m3 01313 00158 00071Minimum gas emission106m3 0 0 0Maximum gas emission106m3 01000 00113 00050Cost coefficients of gas production $106m3 20 15 25Penalty cost coefficients of gas emission $106m3 200 150 250

Table 1 Parameters related to GTs [25]

Number of units 1 2 3Location of units 1 1 4Maximum output (MW) 0 0 0Minimum output (MW) 12 9 12Maximum ramp up rate (MWh) 3 2 3Maximum ramp down rate (MWh) 3 2 3Whether equipped with WHRB Yes No NoQuadratic pollution coefficient 00047 00052 00074Linear pollution coefficient 00940 00730 01180Constant coefficient 04900 02855 05320

Complexity 7

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

PWpreit minus P

Wit ΔPW

it (15)

Ggtit

Pgtit

η middot HVgas (16)

Hgtit

Pgtit middot 1 minus ηgt minus ηl1113872 1113873 middot ηwhb

ηgt

(17)

Hgbjt ηgb middot HVgas middot G

gbjt (18)

Hebet ηeb middot P

ebet (19)

GtP2G

ηP2GPtP2G

Hg

(20)

Equation (15) describes the relationship between actualwind power and forecasted value Equations (16)ndash(20) arethe relationships between the input and output of eachequipment +e power flow constraints of OMIES can befound in [20] +e relationship between the flow of naturalgas flowing through a pipeline and the pressure at both endsof the pipeline can be found in [21]

324 Chance Constraints Offshore oil and gas platformsface a complex and changeable environment In this paperthe uncertainty of power load and offshore wind power ismodeled by stochastic variables +e forecast error of off-shore wind power and power load can be expressed bynormal distribution as follows

εwtt sim N 0 σwt( 1113857

σwt ρwttPwtt + ρwtinsPwtins

εloadt sim N 0 σ load( 1113857

σ load ρloadtEloadt

(21)

+erefore the power balance constraint shall be con-verted as (22) considering the uncertainty

Pr 1113944iisinh

Pgt

it + 1113944iisinWG

Pwit minus 1113944

gisinhPght minus 1113944

eisinhP

ebet minus P

p2gminus E

loadht

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ge η1

(22)

Equation (22) indicates that the power flow shall be metunder a certain confidence coefficient

To ensure the safe operation of the system and preventthe uncertainty of wind power and load from affecting thepower balance the reserve capacity should meet the up- anddown-reserve capacity constraints

Pr 1113944

N

i1Pimax minus Pi( 1113857geUSR + wuPW

⎧⎨

⎩

⎫⎬

⎭ ge η2 (23)

Pr 1113944

N

i1Pi minus Pimin( 1113857gewd PWmax minus PW( 1113857

⎧⎨

⎩

⎫⎬

⎭ ge η3 (24)

33 Transformation of Chance Constraints Chance con-straints in equations (22)ndash(24) are difficult to handle And itcan be solved by converting into their equivalence type [22]

1113944iisinh

Pgt

it + 1113944iisinWG

Pwit minus 1113944

gisinhPght minus 1113944

eisinhP

ebet minus P

p2g

minusEloadht ge inf K|K ϕminus1

1 η1( 11138571113966 1113967

1wu

1113944

N

i1Pimax minus Pi( 1113857 minus USR

⎛⎝ ⎞⎠ minus Pwit ge inf K|K ϕminus1

2 η2( 11138571113966 1113967

1wd

1113944

N

i1Pi minus Pimin( 1113857⎛⎝ ⎞⎠ minus Pwtins + P

wit ge inf K|K ϕminus1

3 η3( 11138571113966 1113967

(25)

4 IHCHS-NSGAII

Although NSGAII [23] is recognized as one of the mosteffective ways to deal with such multiconstrained problemsthe proposed model in Section 3 is still difficult to solve dueto the complexity of the variable vectors and different kindsof constraints especially when there might be coupling andnonlinearity +erefore a high efficient optimizationmethod was needed to handle the complex multiconstrainedmultiobjective optimization problem In this section ahybrid constraint processing strategy (HCHS) [24] is in-troduced and modified to improve the performance ofNSGAII when dealing with complex constraints

41 Dimensionality Reduction Method Generally theequality constraints such as electric power and gas balanceconstraints are not easy to handle for NSGAII so it isnecessary to transfer equality constraints into inequalityones with their own limitations in the meantime the vectordimension can be reduced and the solving efficiency of thealgorithm would be improved Taking the power balanceconstraint as an example the specific conversion process isas follows

Equation (12) can be equivalently converted as

Pgt

it Pght + Eloadht + P

ebet + P

p2gminus P

wit (26)

On the other hand equation (26) shall be met byconstraints described in equation (3) +ereby the equalityconstraint is equivalently transformed into an inequalityone And the other equality constraints can be converted inthe same way

42 Repair Process after Generation of a New IndividualViolation of some constraints that are related to the variablesgeneration process such as the ramp rate constraints cannotalways be reduced for the individuals Since the individualsare generated using some heuristic-based stochasticmethods in NSGAII the constraint handling method in [23]cannot reduce the violation of some constraints such as the

4 Complexity

ramp rate constraints and the rated power constraints re-lated to the variables generation process +us a repairprocess is needed to convert the infeasible individuals intofeasible ones In this paper the repair process is utilized torepair the variables corresponding to the active poweroutput of GT which violates the ramp rate constraints Sincethe ramp rate constraint violations appear between thevariables with close time intervals which have strongcoupling it is difficult for the optimization algorithm toreduce them during the evolutionary process +erefore it isnecessary to ldquorepairrdquo the variables when the population isgenerated When a ramp rate constraint is violated all of thevariables P

gtit in a scheduling period should be repaired from

the beginning time interval for the related GT so that theramp rate limit and the rated power requirement can be metsimultaneously It is obvious that the repair process mayneed much computing resources and time Besides con-sidering the proportion of infeasible individuals is dynamicduring the whole computation period the repair probabilityon the infeasible potential solutions is designed to beupdated based on the current stage of the algorithm asshown as follows

Pre Gc( 1113857

Gc

Gs

1113888 1113889

2

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)

It can be seen from equation (27) that the value of Pre issmall at the beginning of optimization to accept more po-tential infeasible individuals so that the diversity of thepopulation can be ensured And when Gc is large enough allof the individuals which violate the ramp rate constraintshould be repaired But comparing with the microgriddispatch problem in [24] the OMIES scheduling problem ismore complex and the main target is to find feasible so-lutions +erefore to solve the constrained multiobjectiveproblem of OMIES scheduling in this paper equation (27) ismodified as follows

Pre Gc( 1113857

Gc

Gs

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(28)

where Gs 025Gmax In this way the average value of Pre isincreased compared with that in equation (27) and most ofthe individuals in the population can be repaired during theoptimization process

43 Normalization Process in Selection Considering thetypes and amounts of constraints in the proposed model it isefficient to normalize each of the constraint violation beforeadding up and the specific details could be found in [24] Itcan be seen from Section 2 that in the proposed OMIESscheduling problem there are various types of constraintsand different types of constraint violations cannot becompared or added directly +us in this paper the numberof violated constraints of different types is also considered as

a factor to evaluate the infeasible level of the individuals +enormalization method is modified in this paper as

vlknorm 1nk

1113944

nk

i1

vlki minus vkmin

vkmax minus vkmin (29)

It can be seen from equation (29) that by introducing nk

the normalization process can be more reasonable and thenumber of violated constraints can be taken into account inthe constraintsrsquo handling process Hence the algorithmwould find potential solutions with a lower sum of nor-malized violations and the ones with a lower number ofviolated constraints are preferred during the evolutionaryprocess +erefore the average number of violated con-straints in the population would drop rapidly and thefeasible regions can be found efficiently

5 Simulation

In this section the results of the numerical studies arepresented and analyzed which are conducted based on amodified OMIES located in the Bohai Sea of China in [25] asshown in Figure 2 +e optimization models are solvedunder the MATLAB environment In addition a computerwith Intel i5-8700 CPU320 GHz and 8GBmemory is usedto run the optimization models

51 Parameters of the OMIES +is case is composed of a 6-node power system a 6-node natural gas system and athermal system EBs are located in nodes 1 4 and 5 in thepower system with capacities of 12MW 095MW and11MW respectively Parameters related to GTs are listedin Table 1 +e natural gas system consists of 3 gas wellnodes and 3 gas load nodes GBs are located in nodes 1 and2 with maximum thermal powers of 3MW and 4MWrespectively Parameters related to the gas well are listed inTable 2 And the natural gas caloricity is 97 kWhm3 +eoffshore wind turbine is located in node 5 in the powersystem with a capacity of 9MW And the penalty costcoefficient of offshore wind power is 50 $MW Node 2 inthe natural gas system and node 4 in the power system areconnected by a P2G with a capacity of 06MW +econfidence coefficients are all set to 095 in this paper +eother parameters could be found in Table 3 By the way thedata used in this paper are collected from an actual off-shore oil and gas engineering and the parameters men-tioned above are obtained by fitting or calculating thesedata

+e forecast curve of electricity gas and heat load wasshown in Figure 3

52 Results and Discussions +e parameters such as thenumber of population individuals mutation rate and cal-culation accuracy used in IHCHS-NSGAII are selected re-ferring to [24] +e maximum generation number is set to20000 generations and the population size is 50

Besides in this section the penalty function method(PFM) constraint domination principle (CDP) and the

Complexity 5

original HCHS are introduced to compare the performancewith the improved HCHS +e parameter settings of PFMandHCHS can be found in [24] Each algorithm is combinedwith NSGAII and run 10 times +e average feasible solu-tions using different constraint handling methods arerecorded during the evolutionary process

It can be seen from Table 4 that before 1000 generationsthe numbers of feasible solutions obtained are low by all theconstraint handling methods which indicates that theOMIES scheduling problem is very complex with varioustypes of constraintsWith the increase of the generations thefeasible solutions become more by CDP HCHS and im-proved HCHS However by using PFM NSGAII cannotfind enough feasible solutions Even after 20000 iterationsNSGAII only finds 15 feasible solutions As for CDP thesituation is better with 27 solutions which means that CDP

is more effective in dealing with multiconstrained multi-objective optimization problems than PFM However nearlyhalf of the obtained solutions are still infeasible HCHS isbased on CDP but by the hybrid constraints handlingmethods it can find more feasible solutions When HCHS ismodified by the method proposed in this paper it can beseen that it can find a similar amount of feasible solutionswith 10000 generations with those by original HCHS after20000 generations Moreover within 18000 iterations all thesolutions in the population are feasible by the proposedimproved HCHS +e results indicate that comparing withthe existing constraints handling methods the proposedimproved HCHS is more adaptable to the complexity of themulticonstrained OMIES scheduling problem which canmake NSGAII reduce the overall violations consideringdifferent constraint types and converge to the feasible

G-W G

L

L

L

L

2

3

4 5

6

Natural gas system

1

2

3

4

5

6

L

Gas turbine generator unit

L Electric load

Electric boiler Gas load

Gas-fired boiler

Power system

GB

GB

GB

Gas turbine generator unit withwaste heat recovery boiler

Gas well

G

G-W G

1

P2G

W

P2G Power to gas

W Offshore wind power

Figure 2 A case of OMIES

6 Complexity

regions faster +erefore more computational resources canbe applied to find better Pareto solutions

+e optimal solution set is shown in Figure 4From the perspective of the distribution of the Pareto set

the operating cost and the natural gas emission cannot beperfectly optimized at the same time +e staff need to weighenvironmental protection economy and stability accordingto actual needs And the final Pareto optimal solution is notcontinuous For solutions at discontinuities one objectivefunction may have a small difference but the other objectivefunction can be greatly optimized +erefore particularattention should be paid to the choice of solutions atdiscontinuities

What is more the optimal solutions in the Pareto set ofthe two objective functions are selected as the two schemes

Scheme One +e optimal solution for operating cost(operating cost 8094448 $ and natural gas emission40000m3)Scheme Two +e optimal solution for natural gasemission (operating cost 877844 $ and natural gasemission 2100m3)

+e operating cost comparison of the two schemes isshown in Figure 5 and the specific operating cost values areshown in Table 4

It can be seen from Figure 5 and Table 5 that the pol-lution cost of GBs in the two schemes is basically the same+e pollution cost of GTs and GBs cost of the gas well andthe penalty cost of wind curtailment in scheme one are lowerthan those in scheme two while the penalty cost of gas

Table 3 Other parameters

Parameters ValueEfficiency of GT 04Heat loss coefficient of GT 03Heat recovery efficiency of WHRB 047Combustion efficiency of GB 085Pollution coefficient of GB 024$MWElectrothermal conversion efficiency of EB 099Reserve capacity factor 012Error coefficient of offshore wind power capacity 002Error coefficient of offshore wind power output 02Error coefficient of power load 02

Table 2 Parameters related to the gas well

Number of gas well 1 2 3Location of gas well 1 2 5Minimum output of gas well106m3 01000 00113 00050Maximum output of gas well106m3 01313 00158 00071Minimum gas emission106m3 0 0 0Maximum gas emission106m3 01000 00113 00050Cost coefficients of gas production $106m3 20 15 25Penalty cost coefficients of gas emission $106m3 200 150 250

Table 1 Parameters related to GTs [25]

Number of units 1 2 3Location of units 1 1 4Maximum output (MW) 0 0 0Minimum output (MW) 12 9 12Maximum ramp up rate (MWh) 3 2 3Maximum ramp down rate (MWh) 3 2 3Whether equipped with WHRB Yes No NoQuadratic pollution coefficient 00047 00052 00074Linear pollution coefficient 00940 00730 01180Constant coefficient 04900 02855 05320

Complexity 7

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

ramp rate constraints and the rated power constraints re-lated to the variables generation process +us a repairprocess is needed to convert the infeasible individuals intofeasible ones In this paper the repair process is utilized torepair the variables corresponding to the active poweroutput of GT which violates the ramp rate constraints Sincethe ramp rate constraint violations appear between thevariables with close time intervals which have strongcoupling it is difficult for the optimization algorithm toreduce them during the evolutionary process +erefore it isnecessary to ldquorepairrdquo the variables when the population isgenerated When a ramp rate constraint is violated all of thevariables P

gtit in a scheduling period should be repaired from

the beginning time interval for the related GT so that theramp rate limit and the rated power requirement can be metsimultaneously It is obvious that the repair process mayneed much computing resources and time Besides con-sidering the proportion of infeasible individuals is dynamicduring the whole computation period the repair probabilityon the infeasible potential solutions is designed to beupdated based on the current stage of the algorithm asshown as follows

Pre Gc( 1113857

Gc

Gs

1113888 1113889

2

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(27)

It can be seen from equation (27) that the value of Pre issmall at the beginning of optimization to accept more po-tential infeasible individuals so that the diversity of thepopulation can be ensured And when Gc is large enough allof the individuals which violate the ramp rate constraintshould be repaired But comparing with the microgriddispatch problem in [24] the OMIES scheduling problem ismore complex and the main target is to find feasible so-lutions +erefore to solve the constrained multiobjectiveproblem of OMIES scheduling in this paper equation (27) ismodified as follows

Pre Gc( 1113857

Gc

Gs

Gc leGs

1 Gc gtGs

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

(28)

where Gs 025Gmax In this way the average value of Pre isincreased compared with that in equation (27) and most ofthe individuals in the population can be repaired during theoptimization process

43 Normalization Process in Selection Considering thetypes and amounts of constraints in the proposed model it isefficient to normalize each of the constraint violation beforeadding up and the specific details could be found in [24] Itcan be seen from Section 2 that in the proposed OMIESscheduling problem there are various types of constraintsand different types of constraint violations cannot becompared or added directly +us in this paper the numberof violated constraints of different types is also considered as

a factor to evaluate the infeasible level of the individuals +enormalization method is modified in this paper as

vlknorm 1nk

1113944

nk

i1

vlki minus vkmin

vkmax minus vkmin (29)

It can be seen from equation (29) that by introducing nk

the normalization process can be more reasonable and thenumber of violated constraints can be taken into account inthe constraintsrsquo handling process Hence the algorithmwould find potential solutions with a lower sum of nor-malized violations and the ones with a lower number ofviolated constraints are preferred during the evolutionaryprocess +erefore the average number of violated con-straints in the population would drop rapidly and thefeasible regions can be found efficiently

5 Simulation

In this section the results of the numerical studies arepresented and analyzed which are conducted based on amodified OMIES located in the Bohai Sea of China in [25] asshown in Figure 2 +e optimization models are solvedunder the MATLAB environment In addition a computerwith Intel i5-8700 CPU320 GHz and 8GBmemory is usedto run the optimization models

51 Parameters of the OMIES +is case is composed of a 6-node power system a 6-node natural gas system and athermal system EBs are located in nodes 1 4 and 5 in thepower system with capacities of 12MW 095MW and11MW respectively Parameters related to GTs are listedin Table 1 +e natural gas system consists of 3 gas wellnodes and 3 gas load nodes GBs are located in nodes 1 and2 with maximum thermal powers of 3MW and 4MWrespectively Parameters related to the gas well are listed inTable 2 And the natural gas caloricity is 97 kWhm3 +eoffshore wind turbine is located in node 5 in the powersystem with a capacity of 9MW And the penalty costcoefficient of offshore wind power is 50 $MW Node 2 inthe natural gas system and node 4 in the power system areconnected by a P2G with a capacity of 06MW +econfidence coefficients are all set to 095 in this paper +eother parameters could be found in Table 3 By the way thedata used in this paper are collected from an actual off-shore oil and gas engineering and the parameters men-tioned above are obtained by fitting or calculating thesedata

+e forecast curve of electricity gas and heat load wasshown in Figure 3

52 Results and Discussions +e parameters such as thenumber of population individuals mutation rate and cal-culation accuracy used in IHCHS-NSGAII are selected re-ferring to [24] +e maximum generation number is set to20000 generations and the population size is 50

Besides in this section the penalty function method(PFM) constraint domination principle (CDP) and the

Complexity 5

original HCHS are introduced to compare the performancewith the improved HCHS +e parameter settings of PFMandHCHS can be found in [24] Each algorithm is combinedwith NSGAII and run 10 times +e average feasible solu-tions using different constraint handling methods arerecorded during the evolutionary process

It can be seen from Table 4 that before 1000 generationsthe numbers of feasible solutions obtained are low by all theconstraint handling methods which indicates that theOMIES scheduling problem is very complex with varioustypes of constraintsWith the increase of the generations thefeasible solutions become more by CDP HCHS and im-proved HCHS However by using PFM NSGAII cannotfind enough feasible solutions Even after 20000 iterationsNSGAII only finds 15 feasible solutions As for CDP thesituation is better with 27 solutions which means that CDP

is more effective in dealing with multiconstrained multi-objective optimization problems than PFM However nearlyhalf of the obtained solutions are still infeasible HCHS isbased on CDP but by the hybrid constraints handlingmethods it can find more feasible solutions When HCHS ismodified by the method proposed in this paper it can beseen that it can find a similar amount of feasible solutionswith 10000 generations with those by original HCHS after20000 generations Moreover within 18000 iterations all thesolutions in the population are feasible by the proposedimproved HCHS +e results indicate that comparing withthe existing constraints handling methods the proposedimproved HCHS is more adaptable to the complexity of themulticonstrained OMIES scheduling problem which canmake NSGAII reduce the overall violations consideringdifferent constraint types and converge to the feasible

G-W G

L

L

L

L

2

3

4 5

6

Natural gas system

1

2

3

4

5

6

L

Gas turbine generator unit

L Electric load

Electric boiler Gas load

Gas-fired boiler

Power system

GB

GB

GB

Gas turbine generator unit withwaste heat recovery boiler

Gas well

G

G-W G

1

P2G

W

P2G Power to gas

W Offshore wind power

Figure 2 A case of OMIES

6 Complexity

regions faster +erefore more computational resources canbe applied to find better Pareto solutions

+e optimal solution set is shown in Figure 4From the perspective of the distribution of the Pareto set

the operating cost and the natural gas emission cannot beperfectly optimized at the same time +e staff need to weighenvironmental protection economy and stability accordingto actual needs And the final Pareto optimal solution is notcontinuous For solutions at discontinuities one objectivefunction may have a small difference but the other objectivefunction can be greatly optimized +erefore particularattention should be paid to the choice of solutions atdiscontinuities

What is more the optimal solutions in the Pareto set ofthe two objective functions are selected as the two schemes

Scheme One +e optimal solution for operating cost(operating cost 8094448 $ and natural gas emission40000m3)Scheme Two +e optimal solution for natural gasemission (operating cost 877844 $ and natural gasemission 2100m3)

+e operating cost comparison of the two schemes isshown in Figure 5 and the specific operating cost values areshown in Table 4

It can be seen from Figure 5 and Table 5 that the pol-lution cost of GBs in the two schemes is basically the same+e pollution cost of GTs and GBs cost of the gas well andthe penalty cost of wind curtailment in scheme one are lowerthan those in scheme two while the penalty cost of gas

Table 3 Other parameters

Parameters ValueEfficiency of GT 04Heat loss coefficient of GT 03Heat recovery efficiency of WHRB 047Combustion efficiency of GB 085Pollution coefficient of GB 024$MWElectrothermal conversion efficiency of EB 099Reserve capacity factor 012Error coefficient of offshore wind power capacity 002Error coefficient of offshore wind power output 02Error coefficient of power load 02

Table 2 Parameters related to the gas well

Number of gas well 1 2 3Location of gas well 1 2 5Minimum output of gas well106m3 01000 00113 00050Maximum output of gas well106m3 01313 00158 00071Minimum gas emission106m3 0 0 0Maximum gas emission106m3 01000 00113 00050Cost coefficients of gas production $106m3 20 15 25Penalty cost coefficients of gas emission $106m3 200 150 250

Table 1 Parameters related to GTs [25]

Number of units 1 2 3Location of units 1 1 4Maximum output (MW) 0 0 0Minimum output (MW) 12 9 12Maximum ramp up rate (MWh) 3 2 3Maximum ramp down rate (MWh) 3 2 3Whether equipped with WHRB Yes No NoQuadratic pollution coefficient 00047 00052 00074Linear pollution coefficient 00940 00730 01180Constant coefficient 04900 02855 05320

Complexity 7

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

original HCHS are introduced to compare the performancewith the improved HCHS +e parameter settings of PFMandHCHS can be found in [24] Each algorithm is combinedwith NSGAII and run 10 times +e average feasible solu-tions using different constraint handling methods arerecorded during the evolutionary process

It can be seen from Table 4 that before 1000 generationsthe numbers of feasible solutions obtained are low by all theconstraint handling methods which indicates that theOMIES scheduling problem is very complex with varioustypes of constraintsWith the increase of the generations thefeasible solutions become more by CDP HCHS and im-proved HCHS However by using PFM NSGAII cannotfind enough feasible solutions Even after 20000 iterationsNSGAII only finds 15 feasible solutions As for CDP thesituation is better with 27 solutions which means that CDP

is more effective in dealing with multiconstrained multi-objective optimization problems than PFM However nearlyhalf of the obtained solutions are still infeasible HCHS isbased on CDP but by the hybrid constraints handlingmethods it can find more feasible solutions When HCHS ismodified by the method proposed in this paper it can beseen that it can find a similar amount of feasible solutionswith 10000 generations with those by original HCHS after20000 generations Moreover within 18000 iterations all thesolutions in the population are feasible by the proposedimproved HCHS +e results indicate that comparing withthe existing constraints handling methods the proposedimproved HCHS is more adaptable to the complexity of themulticonstrained OMIES scheduling problem which canmake NSGAII reduce the overall violations consideringdifferent constraint types and converge to the feasible

G-W G

L

L

L

L

2

3

4 5

6

Natural gas system

1

2

3

4

5

6

L

Gas turbine generator unit

L Electric load

Electric boiler Gas load

Gas-fired boiler

Power system

GB

GB

GB

Gas turbine generator unit withwaste heat recovery boiler

Gas well

G

G-W G

1

P2G

W

P2G Power to gas

W Offshore wind power

Figure 2 A case of OMIES

6 Complexity

regions faster +erefore more computational resources canbe applied to find better Pareto solutions

+e optimal solution set is shown in Figure 4From the perspective of the distribution of the Pareto set

the operating cost and the natural gas emission cannot beperfectly optimized at the same time +e staff need to weighenvironmental protection economy and stability accordingto actual needs And the final Pareto optimal solution is notcontinuous For solutions at discontinuities one objectivefunction may have a small difference but the other objectivefunction can be greatly optimized +erefore particularattention should be paid to the choice of solutions atdiscontinuities

What is more the optimal solutions in the Pareto set ofthe two objective functions are selected as the two schemes

Scheme One +e optimal solution for operating cost(operating cost 8094448 $ and natural gas emission40000m3)Scheme Two +e optimal solution for natural gasemission (operating cost 877844 $ and natural gasemission 2100m3)

+e operating cost comparison of the two schemes isshown in Figure 5 and the specific operating cost values areshown in Table 4

It can be seen from Figure 5 and Table 5 that the pol-lution cost of GBs in the two schemes is basically the same+e pollution cost of GTs and GBs cost of the gas well andthe penalty cost of wind curtailment in scheme one are lowerthan those in scheme two while the penalty cost of gas

Table 3 Other parameters

Parameters ValueEfficiency of GT 04Heat loss coefficient of GT 03Heat recovery efficiency of WHRB 047Combustion efficiency of GB 085Pollution coefficient of GB 024$MWElectrothermal conversion efficiency of EB 099Reserve capacity factor 012Error coefficient of offshore wind power capacity 002Error coefficient of offshore wind power output 02Error coefficient of power load 02

Table 2 Parameters related to the gas well

Number of gas well 1 2 3Location of gas well 1 2 5Minimum output of gas well106m3 01000 00113 00050Maximum output of gas well106m3 01313 00158 00071Minimum gas emission106m3 0 0 0Maximum gas emission106m3 01000 00113 00050Cost coefficients of gas production $106m3 20 15 25Penalty cost coefficients of gas emission $106m3 200 150 250

Table 1 Parameters related to GTs [25]

Number of units 1 2 3Location of units 1 1 4Maximum output (MW) 0 0 0Minimum output (MW) 12 9 12Maximum ramp up rate (MWh) 3 2 3Maximum ramp down rate (MWh) 3 2 3Whether equipped with WHRB Yes No NoQuadratic pollution coefficient 00047 00052 00074Linear pollution coefficient 00940 00730 01180Constant coefficient 04900 02855 05320

Complexity 7

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

regions faster +erefore more computational resources canbe applied to find better Pareto solutions

+e optimal solution set is shown in Figure 4From the perspective of the distribution of the Pareto set

the operating cost and the natural gas emission cannot beperfectly optimized at the same time +e staff need to weighenvironmental protection economy and stability accordingto actual needs And the final Pareto optimal solution is notcontinuous For solutions at discontinuities one objectivefunction may have a small difference but the other objectivefunction can be greatly optimized +erefore particularattention should be paid to the choice of solutions atdiscontinuities

What is more the optimal solutions in the Pareto set ofthe two objective functions are selected as the two schemes

Scheme One +e optimal solution for operating cost(operating cost 8094448 $ and natural gas emission40000m3)Scheme Two +e optimal solution for natural gasemission (operating cost 877844 $ and natural gasemission 2100m3)

+e operating cost comparison of the two schemes isshown in Figure 5 and the specific operating cost values areshown in Table 4

It can be seen from Figure 5 and Table 5 that the pol-lution cost of GBs in the two schemes is basically the same+e pollution cost of GTs and GBs cost of the gas well andthe penalty cost of wind curtailment in scheme one are lowerthan those in scheme two while the penalty cost of gas

Table 3 Other parameters

Parameters ValueEfficiency of GT 04Heat loss coefficient of GT 03Heat recovery efficiency of WHRB 047Combustion efficiency of GB 085Pollution coefficient of GB 024$MWElectrothermal conversion efficiency of EB 099Reserve capacity factor 012Error coefficient of offshore wind power capacity 002Error coefficient of offshore wind power output 02Error coefficient of power load 02

Table 2 Parameters related to the gas well

Number of gas well 1 2 3Location of gas well 1 2 5Minimum output of gas well106m3 01000 00113 00050Maximum output of gas well106m3 01313 00158 00071Minimum gas emission106m3 0 0 0Maximum gas emission106m3 01000 00113 00050Cost coefficients of gas production $106m3 20 15 25Penalty cost coefficients of gas emission $106m3 200 150 250

Table 1 Parameters related to GTs [25]

Number of units 1 2 3Location of units 1 1 4Maximum output (MW) 0 0 0Minimum output (MW) 12 9 12Maximum ramp up rate (MWh) 3 2 3Maximum ramp down rate (MWh) 3 2 3Whether equipped with WHRB Yes No NoQuadratic pollution coefficient 00047 00052 00074Linear pollution coefficient 00940 00730 01180Constant coefficient 04900 02855 05320

Complexity 7

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

emission is opposite since the objective functions of the twoschemes are different +e operating cost in scheme one islower than that in scheme two about 105 lower It can beseen that when more offshore wind power is consumedoperating costs can be effectively reduced in terms of pol-lution cost and gas production cost however this will alsoincrease natural gas emission

It can be seen from Figures 6 and 7 that in the actualutilization of offshore wind power scheme one is slightlybetter than scheme two Both schemes show that the opti-mization strategy used in this paper keeps the curtailedoffshore wind power at a very low level for most of thescheduling cycle and the peak of the curtailed power occursonly around 12ndash15 hours

Table 4 Average feasible solutions using different constraint handling methods during the evolutionary process

Generations 100 500 1000 3000 5000 10000 15000 18000 20000PFM 0 2 6 5 8 7 11 13 15CDP 0 4 9 13 18 24 27 25 27HCHS 1 5 11 20 22 29 35 39 38Improved HCHS 3 7 12 22 27 36 47 50 50

10 15 20Time (h)

00 5Po

wer

load

(MW

)

Node 2Node 1

Node 3

Node 4Node 5Node 6

2468

1012

(a)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

01234

Gas

load

(m3 )

times104

Gas node 3Gas node 4Gas node 6

(b)

0 2 4 6 8 10 12 14 16 18 20 22 24Time (h)

6

7

8

9

Hea

t loa

d (M

W)

(c)

Figure 3 Different load forecast curves

8 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

Table 5 Specific operating cost values

Schemes Pollution cost of GTs$ Pollution cost of GBs$ Penalty cost of gas emission$ Cost of gas well$ Penalty cost of windcurtailment$

One 2385283 63072 00142 167387 2897100Two 2429183 67028 00008 191436 3474900

800 810 820 830 840 850 860 870 880Operating cost ($)

0

50

100

150

200

250

300

350

400

Nat

ural

gas

emiss

ion

(m3 )

The last population

The feasible solutions

Figure 4 +e Pareto set obtained by IHCHS-NSGAII

Scheme one

Scheme two

5513

616264

Pollution cost of GTsPenalty cost of gas emissionPenalty cost of wind curtailment

Pollution cost of GBsCost of gas well productionCost of P2G

100 200 300 400 500 600 7000Cost ($)

Figure 5 Operating cost structure under different schemes

Complexity 9

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Forecasted offshore wind powerActual offshore wind power

(a)

0

05

1

15

2

25

Curt

aile

d of

fshor

e win

d po

wer

(MW

)

0 6 12 18 24Time (h)

Curtailed offshore wind power

(b)

Figure 7 Forecasted and actual offshore wind power in scheme two

0 6 12 18 24Time (h)

1

2

3

4

5

6

7

8

9

10

11

Offs

hore

win

d po

wer

(MW

)

Forecasted offshore wind powerActual offshore wind power

(a)

0 6 12 18 24Time (h)

Curt

aile

d of

fshor

e win

d po

wer

(MW

)Curtailed offshore wind power

2

18

16

14

12

1

08

06

04

02

0

(b)

Figure 6 Forecasted and actual offshore wind power in scheme one

10 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

6 Conclusion

While offshore wind power reduces environmental pollu-tion it also has an impact on the safe and stable operation ofOMIES In this paper a biobjective optimization modelbased on the CCP was proposed to improve the economy ofOMIES and reduce the natural gas emission therefore thenatural gas emission and the operating cost containing thepollution cost and wind curtailment penalty cost are se-lected respectively as objective functions Besides theIHCHS-NSGAII was proposed to solve the multiconstrainedbiobjective model fast and efficiently from three aspectsnamely dimensionality reduction individual repair processand normalization and weighted sum process in selection+en it was applied to an OMIES problem and the resultsshow that the proposed method can make NSGAII convergeto the feasible regions faster thus more computationalresources can be applied to find better Pareto solutionsBesides the operating cost and the natural gas emissioncannot be perfectly optimized at the same time since thePareto set is discontinuous Also the utilization of offshorewind power improves the economy of OMIES but increasesnatural gas emissions Further studies are needed on theinfluence of the energy storage systems such as battery andgasheat storage facilities

Abbreviations

OMIES Offshore micro integrated energy systemIES Integrated energy systemCCP Chance-constrained programmingGT Gas turbineGB Gas-fired boilerEB Electric boilerESS Energy storage systemNSGA II Nondominated sorting genetic algorithm IIPFM Penalty function methodCDP Constraint domination principleHCHS-NSGAII

Hybrid constraints handling strategyNSGAII

IHCHS-NSGAII

+e improved hybrid constraints handlingstrategy based on nondominated sortinggenetic algorithm II

Mathematical Symbols

t Index for hoursi Index for GTsj Index for GBsk Index for central platforms(g h) Index for power system nodes(m n) Index for gas system nodese Index for EBs

Sets

Ωgt Set of GTsΩcp Set of central platformsΩgb Set of GBs

Ωeb Set of EBs

Variables

Pgtit Active power output of GT i in period t

Ggbjt Gas consumed by GB j in period tΔGgas

kt Gas emission of central platform k inperiod t

θgt Voltage angel of the power system atnode g in period t

Pebet Power consumed by EB e in period t

pnt Pressure of gas system at node n inperiod t

Gwellkt Gas generated by gas well k in period t

Ggtit Gas consumed by GT i in period tΔPW

it Curtailed offshore wind power in periodt

PWit Actual offshore wind power in period t

PWpreit Forecasted offshore wind power in

period tαwindi Penalty cost of curtailed offshore wind

powerP

gtmaxi P

gtmini Maximum and minimum output of GT i

αgt1i α

gt2i α

gt3i Pollution coefficients of GT i

αgbj Emission coefficient of GB j

αwellk Gas production coefficient of centralplatform k

αgask Gas emission coefficient of centralplatform k

xgh Reactance of transmission line (g h)

Pmaxgh Capacity of transmission line (g h)

Rupi Rdown

i Ramp up and ramp down limit of GT iEload

ht Power load at node h in period tCmn Constants related to temperature

length diameter friction etc of pipe (mn)

Gwellmaxk Gwellmin

k Maximum and minimum production ofgas well k

pmaxn pmin

n Maximum and minimum pressure ofnode n

Gloadnt Gas load at node n in period t

Hloadt Heat load in period t

Hgbmaxj Maximum output thermal power of GB j

ηgt Efficiency of GTηl +ermal loss coefficient of GTηwhb Heat recovery efficiency of WHRBHVgas Natural gas caloricityηeb Efficiency of EBPght Power transmitted between line gand h

in period tGmnt Gas transmitted between pipem and n in

period tH

gtit Heat power provided by WHRB

connected with GT i in period tH

gb

jt Heat power provided by GB j in period tHeb

et Heat power provided by EB k in period t

Complexity 11

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

GtP2G Gas converted by P2G in period t

GtmaxP2G Maximum output of P2G

ηP2G Conversion efficiency of P2Gεwtt εloadt Stochastic variables that describe the

forecast error of offshore wind powerand power load

σwt σload Variance of forecast error of offshorewind power and power load

ρwtt ρwtins Error coefficient of offshore wind poweroutput and capacity

ρloadt Error coefficient of power loadη1 η2 η3 Confidence coefficient of power balance

constraint up-reserve capacityconstraint and down-reserve capacityconstraint

USR Coefficient of the reserve requirementwu wd Offshore wind power output demand

coefficient for up- and down-reserveϕminus11 (η1) ϕ

minus12 (η1)

ϕminus13 (η1)

Inverse function of the normaldistribution function

Gc Gs Current and switch generationPre Repair probabilityvkmin vkmax Minimum and maximum violationvlki i-th constraint violation of the l-th

individualnk Number of violated k-th type of

constraints

Data Availability

+e table data and modeling data used to support the findingof this study are included within the article

Conflicts of Interest

+e authors declare that they have no known competingfinancial interests or personal relationships that could haveappeared to influence the work reported in this paper

Acknowledgments

+is work was supported by the National Key Research andDevelopment Program of China China (No2018YFB0904800)

References

[1] M Leporini B Marchetti F Corvaro and F PolonaraldquoReconversion of offshore oil and gas platforms into re-newable energy sites production assessment of differentscenariosrdquo Renewable Energy vol 135 pp 1121ndash1132 2019

[2] S D Musa T Zhonghua A O Ibrahim and M HabibldquoChinarsquos energy status a critical look at fossils and renewableoptionsrdquo Renewable and Sustainable Energy Reviews vol 81pp 2281ndash2290 2018

[3] Maribus gGmbHgteWorld Ocean Review-Marine ResourcesOpportunities and Risks Maribus Gemeinnutzige GmbHHamburg Germany httpsworldoceanreviewcomwp-contentdownloadswor3WOR3_enpdf

[4] S Van Elden J Meeuwig J M Hemmi and R HobbsldquoOffshore oil and gas platforms as novel ecosystems a globalperspectiverdquo Frontiers in Marine Science vol 6 p 548 2019

[5] A Zhang G Peng W Yang G Qu and H Huang ldquoRiskassessment of offshore micro integrated energy system basedon fluid mosaic modelrdquo IEEE Access vol 8 pp 76715ndash767252020

[6] W He K Uhlen M Hadiya Z Chen G Shi and E del RioldquoCase study of integrating an offshore wind farmwith offshoreoil and gas platforms and with an onshore electrical gridrdquoJournal of Renewable Energy vol 2013 Article ID 60716510 pages 2013

[7] S Oliveira-Pinto P Rosa-Santos and F Taveira-PintoldquoElectricity supply to offshore oil and gas platforms fromrenewable ocean wave energy overview and case studyanalysisrdquo Energy Conversion and Management vol 186pp 556ndash569 2019

[8] M L Kolstad A R Ardal K Sharifabadi andT M Undeland ldquoIntegrating offshore wind power andmultiple oil and gas platforms to the onshore power grid usingVSC-HVDC technologyrdquo Marine Technology Society Journalvol 48 no 2 pp 31ndash44 2014

[9] J Zhai X Wu S Zhu B Yang and H Liu ldquoOptimization ofintegrated energy system considering photovoltaic uncer-tainty and multi-energy networkrdquo IEEE Access vol 8pp 141558ndash141568 2020

[10] J Zheng Y Kou M Li and Q Wu ldquoStochastic optimizationof cost-risk for integrated energy system considering windand solar power correlatedrdquo Journal of Modern Power Systemsand Clean Energy vol 7 no 6 pp 1472ndash1483 2019

[11] L Bigarelli A Lidozzi M Di Benedetto L Solero andS Bifaretti ldquoModel predictive energy management for sus-tainable off-shore oil and gas platformsrdquo in Proceedings of the2019 21st European Conference on Power Electronics andApplications (EPErsquo19 ECCE Europe) Genova Italy September2019

[12] A Turk Q Wu M Zhang and J Oslashstergaard ldquoDay-aheadstochastic scheduling of integrated multi-energy system forflexibility synergy and uncertainty balancingrdquo Energyvol 196 pp 117ndash130 2020

[13] C Zhao J Wang J-P Watson and Y Guan ldquoMulti-stagerobust unit commitment considering wind and demand re-sponse uncertaintiesrdquo IEEE Transactions on Power Systemsvol 28 no 3 pp 2708ndash2717 2013

[14] R Jiang J Wang and Y Guan ldquoRobust unit commitmentwith wind power and pumped storage hydrordquo IEEE Trans-actions on Power Systems vol 27 no 2 pp 800ndash810 2011

[15] H Pandzic Y Dvorkin T Qiu Y Wang and D S KirschenldquoToward cost-efficient and reliable unit commitment underuncertaintyrdquo IEEE Transactions on Power Systems vol 31no 2 pp 970ndash982 2015

[16] H Wu M Shahidehpour Z Li and W Tian ldquoChance-constrained day-ahead scheduling in stochastic power systemoperationrdquo IEEE Transactions on Power Systems vol 29 no 4pp 1583ndash1591 2014

[17] Q Wang Y Guan and J Wang ldquoA chance-constrained two-stage stochastic program for unit commitment with uncertainwind power outputrdquo IEEE Transactions on Power Systemsvol 27 no 1 pp 206ndash215 2011

[18] A Zhang H Zhang J Wu M Qadrdan and Q Li ldquoMulti-objective stochastic planning for offshore micro integratedenergy systemsrdquo Automation of Electric Power Systemsvol 43 no 7 pp 129ndash135 2019

12 Complexity

[19] D V Singh and E Pedersen ldquoA review of waste heat recoverytechnologies for maritime applicationsrdquo Energy Conversionand Management vol 111 pp 315ndash328 2016

[20] D Sun X Xie J Wang Q Li and C Wei ldquoIntegratedgeneration-transmission expansion planning for offshoreoilfield power systems based on genetic Tabu hybrid algo-rithmrdquo Journal of Modern Power Systems and Clean Energyvol 5 no 1 pp 117ndash125 2017

[21] C M Correa-Posada and P Sanchez-Martın ldquoIntegratedpower and natural gas model for energy adequacy in short-term operationrdquo IEEE Transactions on Power Systems vol 30no 6 pp 3347ndash3355 2014

[22] J Wu B Zhang Y Jiang P Bie and H Li ldquoChance-constrainedstochastic congestionmanagement of power systems consideringuncertainty of wind power and demand side responserdquo Inter-national Journal of Electrical Power amp Energy Systems vol 107pp 703ndash714 2019

[23] K Deb A Pratap S Agarwal and T Meyarivan ldquoA fast andelitist multiobjective genetic algorithm NSGA-IIrdquo IEEETransactions on Evolutionary Computation vol 6 no 2pp 182ndash197 2002

[24] X Li J Lai and R Tang ldquoA hybrid constraints handlingstrategy for multiconstrained multiobjective optimizationproblem of microgrid economicalenvironmental dispatchrdquoComplexity vol 2017 Article ID 6249432 12 pages 2017

[25] JWu B Li J Chen et al ldquoMulti-objective optimal schedulingof offshore micro integrated energy system consideringnatural gas emissionrdquo International Journal of ElectricalPower amp Energy Systems vol 125 Article ID 106535 2021

Complexity 13