Finding Optimal Load Dispatch Solutions by Using a

Research ArticleFinding Optimal Load Dispatch Solutions by Using a ProposedCuckoo Search Algorithm

Thang Trung Nguyen 1 Cong-Trang Nguyen1 Le Van Dai 2 and Nguyen Vu Quynh 3

1Power System Optimization Research Group Faculty of Electrical and Electronics Engineering Ton DucThang UniversityHo Chi Minh City Vietnam2Institute of Research and Development Duy Tan University Da Nang Vietnam3Department of Electromechanical and Electronic Faculty of Mechatronics and Electronics Lac Hong University Dong Nai Vietnam

Correspondence should be addressed to Le Van Dai levandaiduytaneduvn

Received 22 January 2019 Revised 16 April 2019 Accepted 16 May 2019 Published 28 May 2019

Academic Editor Changzhi Wu

Copyright copy 2019 Thang Trung Nguyen et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Optimal load dispatch (OLD) is an important engineering problem in power system optimization field due to its significance ofreducing the amount of electric generation fuel and increasing benefit In the paper an improved cuckoo search algorithm (ICSA) isproposed for determining optimal generation of all available thermal generation units so that all constraints consisting of prohibitedpower zone (PPZ) real power balance (RPB) power generation limitations (PGL) ramp rate limits (RRL) and real power reserve(RPR) are completely satisfiedTheproposed ICSAmethodperformance ismore robust than conventional Cuckoo search algorithm(CCSA) by applying new modifications Compared to CCSA the proposed ICSA approach can obtain high quality solutionsand speed up the solution search ability The ICSA robustness is verified on different systems with diversification of objectivefunctions as well as the considered constraint set The results from the proposed ICSA method are compared to other algorithmsfor comparison The result comparison analysis indicates that the proposed ICSA approach is more robust than CCSA and otherexisting optimization approaches in finding solutions with significant quality and shortening simulation time Consequently itshould lead to a conclusion that the proposed ICSA approach deserves to be applied for finding solutions of OLD problem inpower system optimization field

1 Introduction

Over the past decades an enormous number of studieshave concerned and solved different optimization operationproblems in regard to electric grids by utilizing potentialsearch ability of optimization approaches Many concernedoperation problems regarding distribution power networktransmission network and different types of power plantas well as electric components in the network have beensuccessfully solved This study focuses on optimal loaddispatch (OLD) problem with the task of allocating thegenerated power of all considered thermal generation unitsto reduce the cost of burnt fossil fuels All physical andoperational constraints are required to be exactly satisfied Ifall generation units in each power plant and all power plants

are working under the most appropriate schedule total fuelcost of all units can be the smallest and consumers can getsignificant amount of revenue [1] The achievement is thanksto the meaning of OLD problem

A huge number of optimization approaches using math-ematical programming have been widely applied so farfor solving the considered OLD problem such as dynamicprogramming (DP) [2] lambda iterationmethod [3]NewtonRaphson and Lagrangian multiplier (NRLM) method [4]and linear programming (LP) [5 6] Conventional methodsfocused on the systems with simple constraints and convexobjective functionwhere nonlinear constraints and the effectsof valve loading process were not considered The complexlevel of the constraints and objective has been mentioned inmany articles For example the authors in [3] could only solve

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 1564693 29 pageshttpsdoiorg10115520191564693

2 Mathematical Problems in Engineering

the OLD problem successfully by separating three-curveobjective function into three different single curve objectivefunctions In [7] amore realistic representation of the electricgeneration fuel function corresponding to multi fossil fuelsources was introduced in which the authors considered adiscontinuous cost function and the effects of valve loadingprocess (EoVLP) of thermal units More complicated modelswere also introduced For example some thermal generationunits were driven by burning multi fossil fuel sources (MFS)to generate electricity [8] or some operating conditions ofgenerators including upper generation boundary lower gen-eration boundary and prohibited power zones were added[9] However these methods have been only applied to thesystems where the generation power-fuel cost characteristicof thermal generation units was mathematically modelled asthe second order function and the effects of valve loadingprocess were ignored [10]

Other artificial intelligence-based advanced methodshave been recently applied for solving OLD problem Evolu-tionary programming-based approaches (EP) [1 11 12] andgenetic algorithm (GA) [13ndash15] were considered as fast algo-rithms because of their parallel search ability In addition GAand EP possessed good properties such as finding solutionsnearby global optimum capability of effectively handlingnonlinear constraints reliable search ability and not manyadjustment parameters [10] Thus it could become a suitablechoice for successfully solving OLD problem However GAwas prematurely convergent to local optimum solutions[16] In this regard simulated annealing approach (SA)[17] was a better probabilistic approach in finding solutionswith appropriate fitness but there was a high possibility ofeasily converging to local optimal zones when coping withcomplicatedly constrained problem It converges slower thanGA and EP though Differential evolution algorithm (DE)[10 18] also belongs to the same class as GA and EP Howeverit is more popular thanks to simple structure with severaladjustment parameters and high rate of success DE has beenmore widely and successfully applied than SA and GA [19]But its faster convergence manner led to the same drawbackas GA like high rate of falling into local optimum andhardly ever toward promising zones quickly In fact theseshortcomings could be tackled by setting population size tohigher value But high population size could suffer from longsimulation time to calculate fitness function and evaluatequality of solutions [20] Hopfield neural network (HNN)[21 22] focused on optimizing energy function and wasonly successfully applied for optimization problems whereobjective functions were differentiable HNN could be anappropriatemethod for large-scale systemswith highnumberof generation units but it needed long simulation time andmay also converge to local optimum solution zones [23]Particle swam optimization (PSO) [16 24] is a random searchapproach developed by behavior of a swarm or flock duringfood search process In comparison with GA PSO ownedmore advantages such as simpler implementation and fewparameters with easy selection However the success rateof PSO was highly influenced by adjustment parametersand it copes with high rate to be trapped in many zoneswith local optimum solutions [25] Harmony search (HS)

[26] is a metaheuristic-based method inspired from musicInstead of using gradient search HS has employed stochasticrandom search to exploit its potential ability Thus it tendedto converge to local optimal zones rather than global optimalzones [27] Biogeography-based optimization (BBO) [28]could compete with PSO and DE since its solutions weredirectly updated by migration from other existing solutionsand its solutions directly shared their attributes with othersolutions [29]

It is clear that each method has advantages as well asdisadvantages for different applications for finding OLDproblem solutions Hence another natural approach is tocombine different methods to exploit the advantages of eachmethod and enhance the overall searching capability Severalhybrid methods have been developed in such way includ-ing hybrid Genetic algorithm Pattern Search and Sequen-tial Quadratic Programming (GAndashPSndashSQP) method [30]hybrid Artificial Cooperative Search algorithm (HACSA)[31] hybrid PSO-SQP [32] and hybrid GA (HGA) [33]Basically these hybrid methods could deal with OLD prob-lem more effectively than each member method On theother hand they could suffer from the difficulty of selectingmany controllable parameters In addition to such popularoriginal algorithms and hybrid methods there are manyother original and improved methods that have been appliedfor solving the considered OLD problem These methods areSymbiotic organisms search algorithm (SOS) [34] and itsmodified version (MSOS) [34] teaching activity and learningactivity-based optimization (TLBO) [35] chemical reaction-based approach (CRBA) [36] enhanced particle swarmoptimization (EPSO) [37] sequential quadratic technique-based cross entropy approach (CEA-SQT) [38] traversesearch-based optimization approach (TSBO) [39] invasiveweed approach (IWA) [40] Improved Differential evolu-tion (IDE) [41] immune algorithm using power redistribu-tion IAPR [42] Colonial competitive differential evolution(CCDE) [43] Chaotic Bat algorithm (CBA) [44] Exchangemarket algorithm (EMA) [45] adaptive search techniquealgorithm and differential evolution (GRASP-DE) [46] 120579-Modified Bat Algorithm (120579-MBA) [47] Tournament-basedharmony search algorithm (TBHSA) [48] New Modified 120573-Hill Climbing Local Search Algorithm (M120573-HCLSA) [49]improved version of artificial bee colony algorithm (IABCA)[50] artificial cooperative search algorithm (ACSA) [51]and ameliorated greywolf optimization algorithm (AGWOA)[52] Among these methods ACSA and AGWOA werethe two latest methods which were applied for OLD andpublished in early 2019 However the demonstration of realperformance of the two methods is still questionable In factACSA has been tested only on systemswith small scale singlefuel and simple constraints such as generation limits andpower balance The largest scale system was considered in[51] to be 40-unit system Unlike [51] different types of fuelcost function complicated constraints and large scale systemwith 140 units have been taken into account in [52] Viacomparisons withmany existing methods AGWOAhas beenstated to be the best one with many surprising results Thusthe validation of reported solutions from the methodmust beverified and its strong search ability must be reevaluated In

Mathematical Problems in Engineering 3

the numerical results section we will report the verificationof the two questionable issues

In this paper we have proposed an improved cuckoosearch algorithm (ICSA) for dealing with large scale OLDproblem with the consideration of complicated constraintstogether with nondifferentiable fuel cost function In theproposed ICSA approach some newmodifications have beenperformed on conventional cuckoo search algorithm (CCSA)to improve the quality of CCSA The CCSA method wasfirst developed in 2009 [53] for solving a set of popularbenchmark functions and its highly superior performanceover PSO and GA has attracted a huge number of researchersin learning and applying for different optimization problemsin different fields Furthermore its improved variants are alsoan extremely vast number In relation toOLDproblemCCSAhas been applied and presented in [23 54ndash57] meanwhileits improved methods consisting of modified cuckoo searchalgorithm (MCSA) and improved cuckoo search algorithmwith one solution evaluation (OSE-CSA) have been respec-tively presented in [58 59] In [55] Basu has applied CCSAfor solving OLD problem with 40-unit system with singlefuel option and the effective of valve loading process 20-unitsystem with single fuel and quadratic fuel cost function and10-unit system with multiple fuel sources and without theeffects of valve loading process The author has made a bigeffort in demonstrating the high potential search of CCSAby comparing with many popular metaheuristic algorithmsbut the shortcoming of the study was neglecting complicatedconstraints and large scale systems

Studies in [56 57] have dealt with OLD problem withtwo power systems considering simple constraints and smallnumber of units Only three simplest constraints such aspower balance limitations of generation and prohibitedpower zones have been taken into account meanwhilethe largest system was solved to be 6-unit system Thusthere were few methods compared to CCSA and the realperformance of CCSA was not shown persuasively in thestudies In [23] authors have applied CCSA for solving differ-ent systems with very complicated constraints complicatedcharacteristics of thermal generating units and high numberof units Among the mentioned studies regarding CCSA forOLD problem authors in [23] could show the best view inevaluating the real performance of CCSA since there were sixcases that were carried out and a huge number of methodswere compared to CCSA In spite of the real potential searchability CCSA has been commented to be low convergence toglobal optimum and significantly improved better [58 59]MCSA in [58] has been proposed by using a new strategyfor the second generation technique Themutation operationin CCSA has been replaced with current-to-best1 model ofDE in [60] MCSA has been applied for solving four systemswith 3 6 15 and 40 units in which the most complicatedconstraint considered was prohibited power zone and onlysingle fuel source was taken into account MCSA methodhas been compared to other popular methods such as PSOGA and EP But the comparisons with CCSA have notbeen carried out Thus the improvement of such proposed

method in [58] was not proved persuasively OSE-CSA in[59] has canceled one evaluation time in case that OSE-CSAhas continued to improve solution quality The improvementseemed to be appropriate for CCSA in dealing with OLDproblem with complicated systems CCSA in [23 55] havebeen considered for comparison in [59] and they have beenproved to be less effective than OSE-CSA However OSE-CSA has used one more control parameter called one rankparameter and it needed to be tuned thoroughly for obtaininghigh performance In the proposed ICSA approach we havefocused on a new strategy of the second new solutiongeneration in CCSA method As shown in [58 59] CCSAhas become a strong search method thanks to the first newsolution generation which was performed by Levy flighttechnique while the second new solution generation couldnot take on local search function well In the second updateprogress via mutation operator two random old solutions areused to generate an increased step size However the mannercan lead to new low quality solutions because the increasedstep will be very small when iterative algorithm is carryingout at the last iterations In fact current solutions at finalseveral iterations tend to be close together and the differentvalues between each two ones are very small leading to a verysmall increased step In order to tackle the disadvantage of theCCSA we apply a new adaptive technique for improvementof solution quality Firstly we propose twoways for producingthe increased step including two-solution-based increasedstep and four-solution-based increased step The decisionwhen which step size will be used is dependent on theresult of comparison between fitness function ratio (FFR)and a predetermined parameter 119879119900119897 FFR is defined as aratio of deviation between fitness functions of the consideredsolution and the most promising solution to the fitness valueof the best one meanwhile 119879119900119897 is a boundary to give the finaldecision for the selection of a used step size At the beginning119879119900119897 is a fixed value for all solutions and then it will be adaptivebased on the comparison between it and FFR When FFR of asolution is less than 119879119900119897 119879119900119897 of the solution will be decreasedequally to ninety percent of the previous valueOtherwise thevalue of 119879119900119897 remains unchanged in case the FFR is equal toor higher than 119879119900119897 The adaptive technique has a significantlyimportant role in enhancing the potential search ability of theproposed method This proposed method is investigated onsix cases with different considered constraints different typesof fuel cost function and large scale systemsThe detail of thesix cases is as follows

Case 1 Four systems with single fuel source (SFS) and powerloss (PL) constraint

Case 2 A 110-unit system with SFS

Case 3 Four systems with SFS and the effects of valve loadingprocess (EoVLP)

Case 4 Two systems with SFS and PPZ and RPR constraints

Case 5 A 15-unit system with SFS and RRL PPZ and PLconstraints


Case 6 Three systems with multiple fuel sources (MFS) andEoVLP

The achieved results in terms of minimum fuel costaverage fuel cost maximum fuel cost and standard deviationfound by the proposed method compared to those obtainedby others reveal that the method is very efficient for theOLD problem In addition the performance improvementof the proposed method over CCSA is also investigatedvia the comparison of the best solution and all trial runsIn summary the main advantages of the proposed ICSAapproach over CCSA as well as the main contribution of thestudy are as follows

(i) Based on fitness function of each considered solutionlocal search or global search is decided to be appliedmore effectively

(ii) Find better solutions with smaller number of itera-tions and shorter execution time for each run

(iii) Shorten simulation time for the whole search of eachstudy case

However the proposed method also copes with the sameshortcomings as CSA Although the shortcomings do notcause bad results for the proposed method they make theproposed method be time consuming in tuning optimalparameter The shortcomings are analyzed as follows

(i) Control parameter probability of replacing controlvariables in each old solution must be tuned in rangebetween 0 and 1 There is no proper theory for deter-mining the most effective values of the parameterThus the performance of the proposed method mustbe tried by setting the parameter to values from 01 to1

(ii) The method uses more computation steps for searchprocessThus the proposedmethod uses higher num-ber of computation steps for each iteration Howeverdue to more effective search ability for each iterationthe proposed method can use smaller number ofiterations but it finds more effective solutions

The remaining parts of the paper are arranged as fol-lows Section 2 shows the objective and constraints of theconsidered OLD problem CCSA and the proposed methodare clearly explained in Section 3 Section 4 is in charge ofpresenting the implementation of ICSA method for the stud-ied problem The simulation results together with analysisand discussions are given in Section 5 Finally conclusion issummarized in Section 6 In addition appendix is also addedfor showing found solutions by the proposed ICSA approachfor test cases

2 Optimal Load DispatchProblem Description

21 Fuel Cost Function Forms with Single Fuel Source In theconsidered OLD problem the optimal operation of a set of

thermal generation units is concerned as the duty of reducingtotal cost of all the units which can be seen by the followingmodel

Reduce 119865 = 119873sum119894=1

119865119894 (119875119894) (1)

In traditional OLD problem fuel cost function of the119894119905ℎ generation unit 119865119894(119875119894) is represented as the second orderfunction with respect to real power output and coefficients asthe model below [2]

119865119894 (119875119894) = 1205721198941198752119894 + 120582119894119875119894 + 120575119894 (2)

In addition for the case considering the effects ofvalve loading process on thermal generation units fuel costbecomes more complicated by adding sinusoidal term asbelow [12]

119865119894 (119875119894) = 1205721198941198752119894 + 120582119894119875119894 + 120575119894+ 1003816100381610038161003816120573119894 times sin (120574119894 times (119875119894min minus 119875119894))1003816100381610038161003816 (3)

Real Power Balance Constraint Total real power demand ofall loads in power system together with real power loss in allconductors must be equal to the generation from all availablethermal generation units The requirement is constrained bythe following equality

119873sum119894=1

119875119894 = 119875119863 + 119875119871 (4)

where total real power loss 119875119871 is determined by Kronrsquosequation below

119875119871 = 11986100 + 119873sum119895=1

1198610119895119875119895 + 119873sum119895=1

119873sum119894=1

119875119895119861119895119894119875119894 (5)

GenerationBoundaryConstraint For the purpose of economyand safe operation each thermal generation unit is con-strained by the lower generation bound and upper generationbound as the following model

119875119894min le 119875119894 le 119875119894max (6)

22 Fuel Cost Function Forms with Multi-Fuel Sources Inthis section fuel cost function of thermal generation units ismathematicallymodeled in terms of different forms from thatin the section above due to the consideration of multi-fuelsources Each type of fuel source is formed as each secondorder function and the fuel cost function form is the sumof different second order functions for the case of neglectingthe effects of valve loading progress But for the considerationcase of the effects the form ismore complexwith the presenceof sinusoidal terms [15] As a result the forms of cost functioncan be expressed in Equation (7) [21] and Equation (8) [15]


119865119894 (119875119894) =

1205751198941 + 1205821198941119875119894 + 12057211989411198752119894 fuel 1 119875119894min le 119875119894 le 11987511989411198981198861199091205751198942 + 1205821198942119875119894 + 12057211989421198752119894 fuel 2 1198751198942min le 119875119894 le 1198751198942max120575119894119895 + 120582119894119895119875119894 + 1205721198941198951198752119894 fuel 119895 119875119894119895min le 119875119894 le 119875119894119895max

(7)

119865119894 (119875119894) =

1205751198941 + 1205821198941119875119894 + 12057211989411198752119894 + 10038161003816100381610038161205731198941 times sin (1205741198941 times (119875119894min minus 119875119894))1003816100381610038161003816 for fuel 1 119875119894min le 119875119894 le 11987511989411198981198861199091205751198942 + 1205821198942119875119894 + 12057211989421198752119894 + 10038161003816100381610038161205731198942 times sin (1205741198942 times (119875119894min minus 119875119894))1003816100381610038161003816 for fuel 2 1198751198942min le 119875119894 le 1198751198942119898119886119909 119895 = 1 119898119894120575119894119895 + 120582119894119895119875119894 + 1205721198941198951198752119894 + 10038161003816100381610038161003816120573119894119895 times sin (120574119894119895 times (119875119894min minus 119875119894))10038161003816100381610038161003816 for fuel 119895 119875119894119895min le 119875119894 le 119875119894119895max

(8)

Cost function forms in Equations (7) and (8) are onlyincluded in objective function (1) meanwhile main con-straints in formulas (4) and (6) must be always satisfied

23 Prohibited Power Zone Real Power Reserve and RampRate Limit Constraints Prohibited power zones (PPZ) aredifferent ranges of power in fuel cost function that thermalgeneration units are not allowed to work due to operationprocess of steam or gas valves in their shaft bearing Thepower generation of units in the violated zones is harmfulto gas or steam turbines even destroyed shaft bearing Thusthe constraint is strictly observed In the fuel-power charac-teristic curve of generation units PPZ causes small violationzones and such curves become discontinuous As consideringPPZ constraint the determination of power generation ofunits is more complex and equal to either lower bound orupper bound Unlike PPZ constraint RPR constraint is notrelated to fuel-power feature curve but it causes difficulty foroptimization approaches in satisfying one more inequalityconstraint Each generation unit among the set of availablegeneration units must reserve real power so that the sumof real power from all generation units can be higher orequal to the requirement of power system for the purposeof stabilizing power system in case that there are some unitsstopping producing electricity On the contrary to PPZ con-straint ramp rate limit (RRL) constraint does not allowpoweroutput of thermal generating units outside a predeterminedrange The constraint considers maximum power change ofeach thermal generating unit as compared to the previouspower value Thus optimal generation must satisfy the RRLconstraint The PPZ constraint RPR constraint and RRLconstraint can be presented as follows

Prohibited Power Zones As considering PPZ constraint validworking zones of each thermal generating unit are notcontinuous and its generation must be outside the violatedzones as the following mathematical description

119875119894 isin

119875119894min le 119875119894 le 1198751198971198941119875119906119894119896minus1 le 119875119894 le 119875119897119894119896 k = 2 ni forall119894 isin Ω119875119906119894119899119894 le 119875119894 le 119875119894max

(9)

As observing Equation (9) generation units cannotbe operated within the violated zones except for startingpoint and end point Consequently the verification of PPZconstraint violation should be carried out first and thenthe correction should be done before dealing with otherconstraints such as real power reserve constraint and realpower balance Besides if power output of all units can satisfythe PPZ constraint generation limits in Equation (6) are alsoexactly met

Real Power Reserve Constraint Real power reserve in powersystem aims to enhance the ability of stability recovery ofpower system and avoid blackout In order to get high enoughpower for requirement all available units are constrained bythe following inequality

119873sum119894=1

119878119894 ge 119878119877 (10)

where 119878119894 is the real power reserve contribution of the 119894119905ℎthermal generation unit and the determination of 119878119894 can bedone by employing the two models below

119878119894 = 119875119894max minus 119875119894 119894119891 119878119894max gt (119875119894max minus 119875119894)119878119894max else

forall119894 notin Ω (11)

119878119894 = 0 forall119894 isin Ω (12)

Equation (10) shows that the constraint of prohibitedpower zones is not included in the real power reserveconstraints however prohibited power zones are alwaysstrictly considered and must be exactly satisfied

Ramp Rate Limit (RRL) Constraint In OLD problem allconsidered thermal generating units are supposed to be underworking status but previous active power of each thermalgenerating unit is not taken into account Thus increased ordecreased power is not constrained This assumption seemsto be not practical until RRL constraint is considered RRLconstraint considers initial power output and the power


change is supervised Regulated power can be higher or lowerthan the initial value as long as it is within a predeterminedrange Increased step size (ISS) and decreased step size (DSS)are given as input data and they are used to limit the change ofpower output of each thermal generating unit The constraintcan bemathematically expressed as the following formula [7]

1198751198940 minus 119863119878119878119894 le 119875119894 le 1198751198940 + 119868119878119878119894 (13)

where 1198751198940 is the initial power output of the 119894119905ℎ thermalgenerating unit before its power output is regulated 119868119878119878119894 and119863119878119878119894 are respectively maximum increased and decreasedstep sizes of the 119894119905ℎ thermal generating unit

3 The Proposed Cuckoo Search Algorithm

31 Classical Cuckoo Search Algorithm In search techniqueof CCSA [53] a set of solutions is randomly generated withina predetermined range in the first step and then the quality ofeach one is ranked by computing value of fitness functionThemost effective solution corresponding to the smallest valueof fitness function is determined and then search procedurecomes into a loop algorithm until the maximum iterationis reached In the loop algorithm two techniques updatingnew solutions two times (corresponding to two generations)are Levy flights and mutation technique which is calledstrange eggs identification technique The two generationscan produce promising quality solutions for CCSA Aftereach generation CCSA will carry out comparing fitness ofnewly updated solutions and initial solutions for keepingbetter ones and abandoning worse ones The most effectivesolution at last step of the loop search algorithm is determinedand it is restored as one candidate solution for a study caseThe detail of the two stages is as follows

311 Levy Flights Stage This is the first calculation step in theloop algorithm and it also produces new solutions in the firstgeneration for CCSA New solution 119878119900119897119899119890119908119909 is created by thefollowing model

119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572 (119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy (120573) (14)

where 120572 is the positive scaling factor and it is nearly set todifferent values for different problems in the studies [53 62]In the work the most appropriate values for such factor canbe chosen to be 02505 for different systems

312 Discovery of Alien Eggs Stage The step plays a veryimportant role for updating new solutions 119878119900119897119899119890119908119909 of thewhole population However not every control variable ineach old solution is newly updated and the decision ofreplacement is dependent on comparison criteria as thefollowing equation

119878119900119897119899119890119908119909=

119878119900119897119909 + 1205761 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) if 1205762 lt 119875119886119878119900119897119909 119900119905ℎ119890119903119908119894119904119890

(15)

32 Proposed Algorithm In the part a new variant of CCSA(ICSA) is constructed by applying three effective changes onthe main functions of CCSA in order to shorten simula-tion time corresponding to reduction of iterations and findmore promising solutions The proposed amendments areexplained in detail as follows

(i) Suggest one more equation producing updated stepsize in addition to existing one in CCSA

(ii) Create a new selection standard by computing fitnessfunction ratio 119865119865119877119909 and comparing 119865119865119877119909 with apredetermined parameter 119879119900119897119909 Thus thanks to thestandard the existing updated step size and additionalupdate step size will be chosen more effectively

(iii) Automatically change value of 119879119900119897119909 for the xth solu-tion based on the result of comparing 119865119865119877119909 with theprevious 119879119900119897119909

Such three points are clarified by observing the followingsections

321 Strange Eggs Identification Technique (Mutation Tech-nique) The first proposed improvement in our proposedICSA approach is to select a more suitable formula forproducing new solutions with better fitness function valueIn CCSA Equation (16) below is used to produce a changingstep nearby old solutions for all current solutions

Δ1198781199001198971198991198901199081199091 = 1205763 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) (16)

The use of Equation (16) aims to produce a random walkaround old solutions in search zones with intent to findout promising solutions In order to reduce the possibilityof suffering the local trap and approach to other favorablezones for searching we propose a new Equation (17) Theformula is built by the idea of enlarging search zone withthe use of two more available solutions Obviously the largerchanging step can own higher performance in moving toother search spaces that the classical approach used in CCSAThe suggestion is mathematically expressed by the formulabelow

Δ1198781199001198971198991198901199081199092= 1205764 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894) (17)

The changing step obtained by using Eq (17) is namedfour-point changing step Now two solutions which arenewly formed by using two different changing steps shownin formulas (16) and (17) are found by the two followingmethods

1198781199001198971198991198901199081199091 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199091 (18)

1198781199001198971198991198901199081199092 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199092 (19)

It can be clearly observed that the distance between 119878119900119897119909(old solution) and 1198781199001198971198991198901199081199091 (new solution) is lower than thatbetween 119878119900119897119909 and 1198781199001198971198991198901199081199092 This difference can contribute ahighly efficient improvement to the proposed ICSA approachsearch ability


ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2

Figure 1 Simulation of solutions corresponding to the first itera-tions of the loop algorithm

For the CCSA case if two solutions 1198781199001198971199031198861198991198891 and 1198781199001198971199031198861198991198892are either slightly different or completely coincident suchnewly updated solution 1198781199001198971198991198901199081199091 does not have good chanceto leave the current zone and approach to more promisingzones In another word the new one is approximately coin-cident with the old one As the search task is taking place atsome last iterations this phenomenon becomes much worsebecause all current solutions are lumped in a small zone andthe capability of moving to other zones is impossible As aresult the CCSA approach will work ineffectively and searchstrategy is time consuming until other runs are started

Contrary to the two-point step size the new proposedformula may produce a large enough length to escape thelocal optimum zone and reach new favorable zones Itexplainswhy the four-point changing step has positive impacton the considered random walk rather than the two-pointchanging step

322 New Standard forChoosing theMostAppropriate Chang-ing Step In this section we extend our analysis to answer thequestionwhen to use the four-point step size FromEquations(18) and (19) two new solutions which are represented asthe results of the two-point-based factor and the four-pointstep size can be illustrated by using Figure 1 corresponding tothe search process at the first some iterations and Figure 2corresponding to the last some iterations For the sake ofsimplicity we rewrite the two equations as follows

1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)

Here we suppose that 1198781199001198971 and 1198781199001198972 are obtained byfour exact solutions 1198781199001198971 1198781199001198972 1198781199001198973 and 1198781199001198974 and calculatedas follows

ΔSol2

ΔSol1

Solx

Solnew1

Solnew2

Figure 2 Simulation of solutions corresponding to the last itera-tions of the loop algorithm

Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)

Asmentioned above the high changing step between newsolution and old solution can help to explore new favorablezones However in optimization algorithms searching stepscannot be arbitrarily large otherwise the algorithm maydiverge in particular for the cases that the consideredsolutions 119878119900119897119909 are not close together in solution search spaceFor example at the beginning of loop algorithm with thefirst iterations in Figure 1 1198781199001198971198991198901199081 is a better choice than1198781199001198971198991198901199082 because it is kept in a sufficient limit and does notlead to a risk of divergence In contrast as many of currentsolutions are in different positions but their distance is notvery short or approximately coincident such as at the lastiterations in Figure 2 1198781199001198971198991198901199081 and 119878119900119897119909 have a very shortdistance but 1198781199001198971198991198901199082 and 119878119900119897119909 have higher distance Accordingto the phenomenon in Figure 2 the proposed ICSA approachneeds to produce a high changing step to move solutions toother search zones without local optimum Hence 1198781199001198971198991198901199082would be preferred to 1198781199001198971198991198901199081

Based on the argument above the determination of thecondition for using either two-point changing step or four-point changing step is really crucial to the performance ofthe proposed ICSA approach in searching solutions of OLDproblem Here the ratio of 119865119865119877119909 which can be found byEquation (24) is suggested to be a suitable measurement forthe selection of two options

Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)

For a particular set of the current solutions each individ-ual depending on its 119865119865119877119909 will create a corresponding newsolution by using either Equation (18) or (19) If the valueof one current solution is smaller than the predeterminedparameter 119879119900119897 Equation (19) is applied for updating suchconsidered solution 119909 Otherwise Equation (18) is a betteroption The steps of the modified algorithm are similar to the


If 1205765 lt 119875119886If FFRx lt Tolx119878119900119897119899119890119908119909 = 119878119900119897119909 + 1205764(1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894)else119878119900119897119899119890119908119909 = 119878119900119897119909 + 1205764(1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892)end

else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End

Algorithm 1 New mutation technique applied in the proposed ICSA approach

conventional CSA except that an additional step should beadded at each iteration In this step the119865119865119889 of all individualsolutions should be calculated by utilizing Equation (24) andthen the result of comparing the ratio with 119879119900119897will be used todecidewhich updating formula should be selectedThewholedescription of the proposed standard and new mutationtechnique can be coded inMatlab program language by usingAlgorithm 1

323 Adjustment of Tolerance for Each Solution As pointedout above the proposed method needs assistances to deter-mine the most appropriate step size for finding out favorablesolution zones The given aim can be reached if the selectionof 119879119900119897119909 is reasonable however the range of this parameteris infinite and hard to select Thus the adaptation of tuningthe parameter is really necessary First of all the compari-son between 119879119900119897119909 and 119865119865119877119909 is carried out and then theadaptation will be determined based on the obtained resultfrom the comparison Results of comparison between the twoparameters can be either 119865119865119877119909 is less than 119879119900119897119909 or 119865119865119877119909is higher than 119879119900119897119909 The case that two parameters are equalhardly ever occurs

As the comer assumptionhappens (ie119865119865119877119909 is less than119879119900119897119909) at the considered time the four-point step size will beemployed for the 119909119905ℎ solution If 119879119900119897119909 remains unchanged atthe previous value the identification of improvement fromsuch four-point step size or two-point step size is vagueConsequently value of 119879119900119897119909 must be automatically reducedto a lower value in case that it has significant contribution tofound promising solution of previous iteration Clearly thedecrease of119879119900119897119909 can enable the proposedmethod to jump outlocal optimal zone and approachmore effective zones By trialand error method 119879119900119897119909 is selected to be a function of itselfthat is 09 of the previous value Finally the implementationof the proposed ICSA approach is presented in Algorithm 2

4 The Application of the ProposedICSA for OLD Problem

Thewhole computation steps of the proposed ICSA approachfor solving OLD problem are explained as follows

41 Handling Constraints and Randomly Producing InitialPopulation As shown in Section 2 the considered OLDproblem takes five following constraints into account

(i) Power balance constraint is shown in Equation (4)

(ii) Power output limitation constraint is shown in Equa-tion (6)

(iii) Prohibited power zone constraint is shown in Equa-tion (9)

(iv) Real power reserve constraint is shown in Equation(10)

(v) Ramp rate limit constraint is shown in Equation (13)

Among the five constraints ramp rate limit generationlimit and prohibited power zone seem to be more com-plicated than power balance and power reserve constraintsHowever the three constraints can be solved more easilybecause each unit is constrained independently in the threeconstraints whereas power balance constraint and powerreserve constraint consider all the thermal generating unitssimultaneously Power reserve constraint can be handledby penalizing the total generation of all units while powerbalance constraint can be solved by penalizing one violatedthermal generating unit The whole computation procedurefor solving all constraints and calculating fitness function ofsolutions is described in detail as follows

Step 1 Redefine maximum and minimum power output ofeach thermal generating unit as considering PPZ and RRLconstraints by using the following formulas

119875119894max = 119875119894max if 119875119894max le 119875i0 + 119868119878119878119894119875i0 + 119868119878119878119894 if 119875119894max gt 119875i0 + 119868119878119878119894

119894 = 1 119873(25)

119875119894min = 119875119894min if 119875119894min ge 119875i0 minus 119863119878119878119894119875i0 minus 119863119878119878119894 119890119897119904119890

119894 = 1 119873(26)


Produce initial population with119873119901119904 solutions (1198781199001198971 1198781199001198972 119878119900119897119909 119878119900119897119873119901119904)Calculate fitness function (1198651198651 1198651198652 119865119865119909 119865119865119873119901)Go to the loop algorithm by setting 119866 = 1

While (119866119898119886119909 gt 119866) (i) The first newly produced solutions119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572(119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy(120573) (ii) Perform selection approach

119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904

(iii) The second newly produced solutionsIf 1205766 lt 119875119886

If Δ119865119865119877119909 lt 119879119900119897119909119879119900119897119909 = 11987911990011989711990909119878119900119897119899119890119908119909 = 119878119900119897119909 + 1205764(1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894)Else 119879119900119897119909 = 119879119900119897119909 amp 119878119900119897119899119890119908119909 = 119878119900119897119909 + 1205764(1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892)End

Else 119878119900119897119899119890119908119909 = 119878119900119897119909End

(iv) Perform selection approach

119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904

(v) Determine the most effective solution and its fitnessDetermine 119865119865119909 with the smallest value and assign 119878119900119897119909 to 119878119900119897119866119887119890119904119905If 119866119898119886119909 gt 119866 perform step (i) and increase 119866 to 119866 + 1 Otherwise stop the loop algorithm and report boththe smallest fitness together with 119878119900119897119866119887119890119904119905End while

Algorithm 2The proposed ICSA approach

119875119894max

= 119875119897119894119896 if 119875119897119894119896 lt 119875119894max lt 119875119906119894119896 amp 119875119894max lt 119875119906119894119896119875119894max 119890119897119904119890

119894 = 1 119873(27)

119875119894min

= 119875119906119894119896 if 119875119897119894119896 lt 119875119894max lt 119875119906119894119896 amp 119875119894max gt 119875119897119894119896119875119894min 119890119897119904119890

119894 = 1 119873(28)

Among the four Equations (25) and (26) are used firstin order to redefine upper bound and lower bound for allthermal generating units as considering RRL constraint Thethe redefined bounds continue to be redefined for the secondtime by using (27) and (28) as considering PPZ constraints

Step 2 (randomly produce initial population) For dealingwith the power balance constraint all available units areseparated into two groups in which the first group withdecision variables consists of the power output from thesecond unit to the last unit (P2 P3 PN) meanwhile onlythe power output of the first unit (1198751) belongs to the secondgroup with dependent variable So upper bound solution119878119900119897119898119886119909 and lower bound solution 119878119900119897119898119894119899 must be defined asfollows

119878119900119897min = [1198752min 1198753min 119875119873min]119878119900119897max = [1198752max 1198753max 119875119873max] (29)

Based on the upper bound solution and lower boundsolution each solution 119878119900119897119909 is initially produced by thefollowing model

119878119900119897119909 = 119878119900119897min + rand (119878119900119897max minus 119878119900119897min) 119909 = 1 119873119901119904 (30)


Step 3 Handle prohibited power zone constraint for decisionvariables P2 P3 PN

After being randomly produced there is a high possi-bility that decision variables fall into PPZ and they violatePPZ constraint So the verification of falling into PPZ andcorrection of the violation should be accomplished by usingthe following formula

119875119894 =

119875119897119894119896 if 119875119897119894119896 lt 119875119894 le 119875119897119894119896 + 1198751198961198941198962119875119906119894119896 if (119875119894 gt 119875119897119894119896 + 1198751198961198941198962 ) amp (119875119894 lt 119875119906119894119896)119875119894 119890119897119904119890

119894 = 2 119873 amp 119896 = 1 119899119894

(31)

Step 4 Handle RPB constraint by calculating 1198751 and penaliz-ing 1198751 if it violates constraints

In this step power balance constraint is exactly handledby calculating and penalizing dependent variable (1198751) 1198751 isobtained by using formulas (4) and (5) as follows

1198751 = minus (11986101 minus 1 + 2sum119873119894=2 1198611119894119875119894) plusmn radicΔ211986111 (32)

where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)

In Equation (32) 1198751 has been determined for the purposeof dealing with real power balance constraint However it isnot sure that 1198751 can satisfy upper bound and lower boundconstraints and prohibited power zone constraints So 1198751must be checked and penalized

Firstly 1198751 is checked and penalized for upper and lowerbound constraints by the following model

Δ1198751x =

0 if 1198751min le 1198751x le 1198751max

1198751min minus 1198751x if 1198751min gt 1198751x1198751x minus 1198751max if 1198751max lt 1198751x

(34)

In Equation (34) if the second case or the third caseoccurs it means P1 has violated either lower bound or upperbound and it would be penalized by using either (P1x= P1min-P1x) or (P1x =P1x -P1max) Otherwise ifP1 has not violatedthe bound constraints (ie the first case in (34) happened)

P1 would continue to be checked for PPZ constraint by thefollowing model

Δ1198751x

=

1198751 minus 1198751198971119896 if 1198751198971119896 lt 1198751 le 1198751198971119896 + 119875119896111989621198751199061119896 minus 1198751 if (1198751 gt 1198751198971119896 + 11987511989611198962 ) amp (1198751 lt 1198751199061119896)0 119890119897119904119890

(35)

Step 5 Handle real power reserve constraint (10)First of all 119878119894 is determined by using (11) and (12) and

then the 119909119905ℎ solution will be checked and penalized if poweroutput of all thermal generating units cannot satisfy RPRconstraint The penalty for violation of the constraint can becalculated by using equation (36)

Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)

As a result real power reserve constraint can be solved byusing the penalty method

42 Calculate Fitness Function for Solutions Fitness functionof each solution is used to evaluate quality of solutionNormally the function is the sum of objective function andpenalty of violating constraints and is obtained by

119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)

43 The First Newly Updated Solutions by Levy Flights Tech-nique In this section the first newly updated solutionsare performed by employing Levy flights technique usingEquation (14) However each new solution can be out oftheir feasible operating zone such as PPZ and upper andlower limitations When the power output violates its PPZconstraints Equation (31) will be applied to tackle theconstraint Besides the following equation will be employedwhen power output is higher or lower than their limitations

119878119900119897119909 =

119878119900119897max if 119878119900119897max lt 119878119900119897119909119878119900119897min if 119878119900119897min gt 119878119900119897119909119878119900119897119909 Otherwise

119909 = 1 119873119901 (38)

After that Equations (32)-(37) are performed for deter-mining all variables and penalty terms Finally Equation (38)is employed to calculate fitness function

44 The Second Newly Updated Solutions by Using Muta-tion Technique The second newly updated solutions areaccomplished as presented in Section 3 above Similar to


the task after doing the first update each solution in thenew population must satisfy PPZ constraint and upper andlower boundaries by considering Equations (31) and (38)Then Equations (32)-(37) are performed for determiningall variables and penalty terms Finally Equation (38) isemployed to calculate fitness function and the solution withthe best value is assigned to the best one 11987811990011989711986611988711989011990411990545 Criterion of Stopping the Loop Algorithm In the loopalgorithm of using the proposed ICSA approach the solutionsearch work is stopped in case that the predeterminedmaximum iterations 119866119898119886119909 is reached For each search ter-mination the most effective solution is stored and anotherrun continues to be accomplished until the predeterminednumber of runs is reached After finishing the runs thebest one is found and reported In addition other valuessuch as the fitness of the worst solution and average fitnessof all solutions are also reported for comparing with othermethods

46 The Whole Iterative Process The whole iterative algo-rithm for implementing the proposed ICSA approach forcoping with OLD problem is described in detail in Figure 3

5 Results and Discussions

The proposed ICSA approach performance has been investi-gated on six cases with different fuel options different fuelcharacteristics and complicated constraints The details ofthe studied cases are presented as follows


Subcase 11 A 3-unit system [57]Subcase 12 A 6-unit system [57]Subcase 13 A 3-unit system [56]Subcase 14 A 6-unit system [56]

Case 2 A 110-unit system with SFS [57]


Subcase 31 A 3-unit system supplying to a load of850MW [58]Subcase 32 A 13-unit system supplying to a load of1800MW [1]Subcase 33 A 13-unit system supplying to a load of2520MW [1]Subcase 34 A 40-unit system supplying to a load of2500MW [1]Subcase 35 An 80-unit system supplying to a load of4100MW [49]


Subcase 41 A 60-unit system supplying to a10600MW load [9]


Case 5 A 15-unit system with SFS and RRL PPZ and PLconstraints [61]


Subcase 61 An 80-unit system supplying to a21600MW load [15]Subcase 62 A 160-unit system supplying to a43200MW load [15]Subcase 63 A 320-unit system supplying to an86400MW load [54]

For each considered case with each load case the pro-posed ICSA approach is run 50 times on the programlanguage of Matlab and a PC with 4 GB of RAM and 24GHzprocessor The selection of adjustment parameters including119875119886 and 119879119900119897119909 is carefully considered to obtain the best optimalsolutions meanwhile two others such as 119873119901119904 and 119866119898119886119909 arechosen corresponding to the scale of particular test system9 values with the change of 01 in the range [01 09] are inturn selected for 119875119886 while 119879119900119897119909 is 001 at the beginning Theinformation including load demand119873119901119904 119866119898119886119909 and the best119875119886 is reported in Table 1

51 Obtained Results on Case 1 considering Four Systems withSFS and PL Constraint In this section we have implementedthe proposed ICSA approach for solving four systems dividedinto four subcases Tables 2 and 3 show the comparisons ofobtained results from Subcases 11 and 12 and Subcases 13and 14 respectively As listed in Table 2 the proposed ICSAmethod and CCSA can find equal fuel cost for Subcases 11whereas the reduction of fuel cost from the proposed ICSAmethod as compared to CCSA is clearer for Subcase 12 Asshown in Table 3 for comparing the proposed ICSA and threemethods consisting of CCSA ABC and FA the minimumfuel cost of the proposed ICSA is approximately equal to thatof these methods for Subcases 13 but much less than that ofthese methods for Subcase 14 Furthermore the proposedICSA has been run by setting 119873119901119904 and 119866119898119886119909 to 5 and 20but these values were much higher for CCSA ABC and FAThey are 20 and 5000 for CCSA 40 and 100 for ABC and 20and 5000 for FA Consequently the proposed method is veryefficient for Case 1 with four subcases

Optimal solutions obtained by ICSA for Case 1 are shownin Tables 16ndash18

52 Obtained Results on Case 2 considering 110-Unit Systemwith SFS In this section we have employed a very largescale system with 110 units but there were not challenges forobjective function and complex constraints since EoVLP andconstraints were not taken into account Both CCSA andthe proposed ICSA methods have been run for comparingwith BBO hybrid BBO and DE (DEBBO) and Opposi-tional real coded chemical reaction optimization algorithm(ORCCROA) in [36] IWA in [40] and AGWO in [52] As


Select parameters

- Correct solutions if violating PPZ constraint using Eq (31)- Determine using Eq (32)- Penalize for violating upper and lower bounds constraint using Eq (34)- Penalize for violating PPZ constraint using Eq (35)- Penalize the xth solution for violating RPR constraint using Eq (36)

- Determine quality of solutions employing Eq (37) - Select the most effective solution - Start the loop algorithm by selecting

- Perform the first solution update using Section 32 - Correct boundaries of solutions by using Eq (38)

- Correct solutions if violating PPZ constraint using Eq (31)- Determine using Eq (32)- Penalize for violating upper and lower bounds constraint using Eq (34)- Penalize for violating PPZ constraint using Eq (35)- Penalize the xth solution for violating RPR constraint using Eq(36)

- Determine fitness function using Eq (37)- Compare old solutions and new solutions to keep better ones

- Perform the second solution update using Algorithm 1 - Correct boundaries of solutions by using (38)


- Determine fitness function using Eq (37)- Compare old solutions and new solutions to keep better ones- Select the most effective solution

Stop

Start

- Redefine upper and lower bounds using Eqs (25)-(28)- Randomly generate initial population using Eq (30)

Nps Pa Gmax Ｈ＞ Tolx

P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1

Figure 3 All computation steps for solving OLD problem by employing the proposed ICSA approach

shown in Table 4 AGWO [52] has reached less fuel cost thanICSA however the exact fuel cost which was recalculatedby using reported solution pointed out that the method hasreached a very high fuel cost of $2157404250 For comparisonwith other methods ICSA has found less fuel cost thanall these methods Particularly the reduction of generationfuel cost is significant as compared to BBO DEBBO andCCSA Execution time comparisons are also useful evidence

for indicating the high performance of ICSA Thus it canconclude that ICSA is a strong method for Case 2

Optimal solution obtained by ICSA for the case is shownin Table 19

53 Obtained Results on Case 3 considering Four Systems withSFS and EoVLP In this section the real performance of theproposed ICSA approach has been investigated based on five


Table 1 Information of considered cases and adjustment parameters

Case Fuel cost function Constraint Subcase No of units 119875119863 (MW) Nps Gmax Best 1198751198861 SFS PL

11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01

Table 2 Comparison of minimum cost ($) obtained by different methods for Subcases 11 and 12

Subcase 11 Subcase 12119875119863 (MW) CCSA [57] ICSA 119875119863 (MW) CCSA [57] ICSA350 185645 18564484 600 320947 320903906400 208123 208122936 650 344826 344788747450 231124 231123635 700 369122 369087027500 254655 254654692 750 39384 393784477550 278724 278724051 800 418969 418895633600 30334 303339858 850 444503 44442193650 32851 328510461 900 470453 470361336700 354244 35424442 950 496821 496715358


Subcase 13 14Method Cost ($) 119873119901119904 119866119898119886119909 Cost ($) 119873119901119904 119866119898119886119909CCSA [56] 160046 20 5000 835606 20 5000ABC [56] 160051 40 100 837227 40 100FA [56] 160047 20 5000 838845 20 5000ICSA 1599984 5 20 8313221 5 20

Table 4 Comparison of results obtained by different methods for Case 2

Method Minimum cost ($) Mean cost ($) Maximum cost ($) Time (s) 119873119901119904 119866119898119886119909 Recalculated cost ($)BBO [36] 1982412 1972135 1991026 208 - 400 lowastDEBBO [36] 1982311 1983267 1988286 184 - 400 lowastORCCROA [36] 1980163 1980163 1980169 60 - 400 1998814OIWO [40] 1979891 1979894 1979899 31 - 250 1979891AGWO [52] 197988lowast 197988 197988 - - - 21574042CCSA 19800742 1981501 1983100 72 10 1000 198007423ICSA 19798893 1980119 1983370 76 10 1000 197988938lowastDenote that recalculated cost cannot be obtained because solutions were not reported


Table 5 Comparisons of obtained results for Subcase 31

Method Minimum cost ($) Recalculated cost ($) Nps Gmax

MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20

Table 6 Result comparisons for Subcases 32 and 33

Approach Subcase 32 Subcase 33 Computer (Processor-Ram)Min cost ($h) Time (s) Min cost ($h) Time (s)

CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -

IFEP [1] 1799407 15743 - -DE [10] 1796383 - 2416992 - -GA-MU[15] 17963985 828 - - 07GHzQPSO[16] 1796901 - - - -GA-PS-SQP [30] 1796425 1106 - - 256MB-1GHzPSO-SQP[32] 1796993 3397 2426105 - -SOS [34] 179638292 085 24169917 071 22GHz- 4GBMSOS [34] 179638292 081 24169917 065 22GHz- 4GBCEA-SQT [38] 1796385 3433 2416994 3425 3GHz-2-GBTSBO [39] 179638292 - - - -IWA [40] 1796383 53 - - 306GHz-1 GBCBA [44] 1796383 097 - - 33GHz -4GBM120573-HCLSA [49] 1796097lowast 8034 2416418lowastlowast 74671 24 Ghz- 2GBIABCA [50] 1797296 - - - -CCSA [59] 1796383 37 24169917 38 2GHz- 2GBOSE-CSA [59] 1796383 385 24169917 28 2GHz- 2GBProposed method 1796383 095 24169917 095 24GHz- 4GBlowast Recalculated cost is $179691 lowastlowast recalculated cost is $2417388

subcases with the gradual increase of number of units Thesmallest scale system considers 3 units but the largest scalesystem takes 80 units In addition to the implementation ofthe proposed ICSA we have also implemented CCSA forSubcase 31 and Subcase 35 for further comparison becauseCCSA has not been run for the two subcases so far

Comparison of obtained results from Subcase 31 shownin Table 5 indicates that the proposed ICSA is superior toCCSAwith lower fuel cost but it seems to be less effective thanMCSA [58] The minimum cost of MCSA reported in [58] isthe smallest fuel cost but the recalculated cost is much higherthan that of the proposed method Furthermore MCSA hasbeen implemented by setting very high values to 119873119901119904 and119866119898119886119909

Reports for Subcases 32 and 33 shown in Table 6are the comparisons of the proposed ICSA approach andother methods such as conventional Evolution programming(CEP) [1] Fast EP (FEP) [1] improved FEP (IFEP) [1] DE[12] multiplier Lagrange-based genetic algorithm with (GA-MU) [15] QPSO [16] GA-PS-SQP [30] PSO-SQP [32] M120573-HCLSA [49] IABCA [50] CCSA [59] OSE-CSA [59] SOS[34] MSOS [34] CEA-SQT [38] TSBO [39] IWA [40] andCBA [44] As observed from the table ICSAapproach obtainsbetter solutions than mostmethods excluding DE [10] CCSA

[59] OSE-CSA [59] SOS [34] MSOS [34] CEA-SQT [38]TSBO [39] IWA [40] and CBA [44] especially M120573-HCLSA[49] with lower cost $1796097 However recalculated costfrom reported solution of M120573-HCLSA is $179691 BesidesICSA is very fast as compared to most methods where twoother versions of Cuckoo search algorithm CCSA and OSE-CSA are also included except two methods in [34] Theprocessor of computer that all the methods run on is alsoreported in the final column Clearly ICSA approach is veryefficient for the case with the 13-unit system where effects ofvalve loading process are considered

In Subcase 34 the number of units is much larger thanthat of three subcases above up to 40 units [1] The obtainedresult comparisons with others are indicated in Table 7Clearly the minimum cost comparisons reveal that the pro-posedmethod is one of the leading methods due to the lowestcost except the comparison with CCSA [23] OSE-CSA [59]SOS [34] MSOS [34] EMA [45] 120579-MBA [47] and AGWOA[52] It is noted that AGWOA [52] has reported the bestminimum cost with $12140430 but recalculated minimumcost which was obtained by substituting reported optimalgeneration of all thermal generating units is $12141331 Theaverage and the maximum costs from the proposed methoddo not belong to the leading method group however the


Table 7 Result comparisons for Subcase 34

Approach Best cost Average cost Worst cost CPU time Computer($h) ($h) ($h) (s) (Processor-Ram)

IFEP [1] 12262435 12338200 12574063 116735 035Ghz - 0128 GBQPSO[16] 12144821 12222507 - - -CCSA [23] 1214125355 12152041 12181025 303 21 Ghz-2GBBBO [28] 1214269530 121 50803 121688 66 11749 23Ghz-512-MBGA-PS-SQP [30] 12145800 12203900 - 4698 31Ghz-256MBPSOndashSQP [32] 12209467 12224525 73397 -SOS [34] 1214125355 1214149546 1214355918 - 22Ghz - 4GBMSOS [34] 1214125355 1214125355 1214125355 1813 22Ghz - 4GBEPSO [37] 1214125702 1214557003 1217095582 50 4724 25 GhzIWA [40] 12141254 - - - 306Ghz - 1GBIDE [41] 1214422682 1214488196 1214572746 796 30 GhzIAPR [42] 1214369729 1216484401 1224927018 1092 283 Ghz - 4GBCCDE [43] 1214126858 1214128507 1214136302 - -CBA [44] 1214125468 1214189826 12143615 155 33 Ghz - 4GBEMA [45] 1214125355 1214171328 1214261548 - -GRASP-DE [46] 121414621 121736025 122245696 - -120579-MBA [47] 1214125355 121412948 121412786 - 24Ghz -1GBTBHSA [48] 12142515 12152865 - - 266Ghz- 4GBM120573-HCLSA [49] 12141468 12149684 - 95194 266Ghz- 4GBAGWOA [52] 12140430lowast 12141230 12144670 - 24Ghz- 2GBOSE-CSA [59] 1214125355 12147245 12159618 302 2 Ghz - 2GBProposed method 1214125355 1216010759 1225022623 146 24Ghz- 4GBlowastRecalculated minimum cost is $12141331


Method Best cost Average cost Worst cost CPU time Computer($h) ($h) ($h) (s) (Processor-Ram)

M120573-HCLSA [49] 24285452 24299269 - 127970 266Ghz- 4GBAGWOA [52] 24282450 24291940 2429868 - 24Ghz- 2 GBCCSA 24282450 24336514 24403675 32 24Ghz- 4GBICSA 2428204 24301865 24387617 33 24Ghz- 4GB

execution time that ICSA approach takes is smaller thanmostones except IAPR [42] and 120579-MBA [47] which have been runon stronger computers Note that MSOS [34] has been fasterthan the proposed method for Subcases 31 and 32 abovebut it is too slower than the proposed method for the casenamely 1813 seconds compared to 146 seconds Comparedto two other versions of Cuckoo search CCSA [23] and OSE-CSA [59] the proposed method is also faster about threetimes although the processors are slightly different For thiscase 120579-MBA [47] shows a very good performance howeverthe method has not been tested onmore complicated systemsand larger scale and therefore more comparisons with themethod must end Clearly the proposed method is stillefficient for the case where large scale and effects of valveloading process are included

Subcase 35 is the largest scale system with 80 units Inaddition to the implementation of ICSA CCSA has beenalso run for the Subcase 35 for further investigation ofefficiency improvement of the proposed ICSA approach The

comparisons of minimum cost in Table 8 show that theproposed ICSA can find more optimal solution than M120573-HCLSA [49] AGWOA [52] and CCSA The proposed ICSAis also superior to CCSA in terms ofmore stable search abilityand lower fluctuation since its average cost and maximumcost are less than those of CCSA The outstanding figurecannot be reached as compared to AGWOA [52] howeverit is hard to conclude AGWOA [52] is superior to theproposed ICSA approach about more stable search abilityand lower fluctuation Actually comparison of the values ofpopulation and iterations as well as execution time cannot beaccomplished because the information was not reported in[52]Thus it can conclude that the proposed ICSA is effectivefor the subcase

Optimal solutions obtained by ICSA for the case areshown in Tables 20ndash23

54 Obtained Results on Case 4 with Two Systems consideringSFS and PPZ and RPR Constraints In this section two



Subcase Approach Best cost ($h) Mean cost ($h) Worst cost ($h) Std dev ($h) CPU time (s) Computer (Processor-Ram)

41

GA [9] - 131992310 - - 56381 07GhzIGA-MU [9] - 130180030 - - 16258 07GhzCCSA [23] 1301703949 1301715986 1301740722 07531 2028 210GHz-20 GB

OSE-CSA [59] 1301699367 1301708301 130175178 085519 34412 20GHz- 20GBICSA 130169962 1301739 1302335 86509 09153

42

GA [9] - 198831690 - - 94093 07GhzIGA-MUM [9] - 195274060 - - 25545 07GhzCCSA [23] 1952587847 1952643818 1952717057 24857 3036 210Ghz-20 GB

OSE-CSA [59] 1952559077 1952575392 1952623724 14674 53352 20 Ghz- 20GBICSA 195255762 1952602 1952694 28002 15892 240Ghz- 40 GB

Table 10 Comparisons of result obtained by different methods for Case 5

Method Minimum Cost ($) CPU time (s) Nps Gmax Computer (Processor-Ram)MCSA [58] 32 7067358 48 50 200 40GHz- 10 GBPSO [61] 32858 5945 100 200 Pentium III-256MBGA [61] 33113 818 100 200 Pentium III-256MBCCSA 32 7089 445 20 400 240Ghz- 40 GBICSA 32 705998 46 20 400 240Ghz- 40 GB

test systems with SFS and PPZ and RPR constraints areconsidered The test system size is up to 60 and 90 units forSubcases 41 and 42 respectively Comparison for the casesis only performed with two Genetic algorithms consisting ofGA and IGA-MU in [9] and two other versions of Cuckoosearch algorithms including CCSA [23] and OSE-CSA [59]and presented in Table 9 Other studies have tended toignore such complicated constraints of PPZ and RPR Thecosts reported in Table 9 indicate that ICSA approach canobtain more effective solution than CCSA and OSE-CSAbecause it has reached lower minimum cost than the twoones Furthermore the proposed method also takes shortercomputation time for the two cases from about two timesto about three times although the processor of the proposedmethod is slightly strongerThemean costs of ICSA approachare much less than those from IGA-MU and GA and slightlyhigher than those from OSE-CSA but there is a trade-off between the proposed method and CCSA for the twosubcases In fact the proposed method obtains higher meancost for Subcase 41 but lower cost for Subcase 42 AlthoughGAmethods have been runon aweak computerwith 07 GHzof the processor compared to that with 24GHz in the studytheir execution times are significantly higher namely 56381seconds (GA) and 16258 seconds (IGA-MU) compared to09153 seconds of ICSA approach for Subcase 41 and 94093seconds (GA) and 25545 seconds (IGA-MU) compared to15892 seconds (the proposedmethod)The analysis can pointout that ICSA approach ismore efficient than these comparedmethods in terms of optimal solutions and execution time

Optimal solutions obtained by ICSA for Subcase 42 areshown in Table 24

55 Obtained Results on Case 5 with a 15-Unit System consid-ering SFS and RRL PPZ and PL Constraints In this section

a 15-unit system considering RRL PPZ and PL constraintsis considered to be solved for finding optimal solution Forefficiency investigation of the proposed ICSA we have alsoimplemented CCSA for comparison As listed in Table 10the proposed ICSA is the most effective method with thesmallest fuel cost The comparisons of control parameters aswell asCPU time are also good evidence to confirm the strongsearch of the proposed ICSA approach since it has been runby smaller values of control parameter and faster executiontime as compared to all methods excluding CCSA


56 Obtained Results on Case 6 withThree Systems consideringMFS and EoVLP In this section three test systems with thechallenge on objective function including multi-fossil fuelsources and effects of valve loading process are consideredThe scale is up to 80 units 160 units and 320 units forSubcases 61 62 and 63 respectively

Comparison for Subcase 61 reported in Table 11 revealsthat the proposed method is the best method in terms of thelowest best cost the lowestmean cost and the lowest standarddeviation and the fastest execution time The processor fromthis proposedmethod is about four times stronger thanCGA-MU and IGA-MU but the speed is from ten times to 35 timesfaster than these methods Compared to CCSA and OSE-CSA the proposed method is about two times faster but theprocessor is slightly stronger

Comparison for Subcase 62 is reported in Table 12Clearly the proposed ICSA approach obtains better values ofthe best mean and worst costs than most methods exceptMSOS [34] where the best cost difference is about $ 024However the proposed method is the second fastest onewith 1119 seconds where the first fastest one CBA [44] has


Table 11 Comparisons of found results for Subcase 61

Approach Best cost Mean cost Worst cost Std dev CPU time Computer($h) ($h) ($h) ($h) (s) (Processor-Ram)

CGA-MU [15] - 50081426 - - 30941 07GHzIGA-MU [15] - 50038832 - - 8567 07GHzCCSA [23] 49926853 49937307 50034294 10931 1825 210GHz-20 GBOSE-CSA [59] 49924215 49944987 49956717 04939 1524 20 GHz- 20GBICSA 4990867 4991384 5007106 22483 84828 240GHz- 40 GB


Approach Best cost Average cost Worst cost Std dev CPU time Computer($h) ($h) ($h) ($h) (s) (Processor-Ram)

CGA-MU [15] - 101437263 - - 62130 07GHzIGA-MU [15] - 100424742 - - 17462 07GHzCCSA [23] 99906548 99966390 100140183 49268 7542 21 GHz-2 GBSOS [34] 1012120529 1017903436 1024107846 24960 - 22GHz-4GBMSOS [34] 99813114 99819798 99836394 0477 2572 22GHz-4GBTLBO [35] 100060117 100062821 10005994 0069 48216 2GHz-1 GBCRBA [36] 99899444 9992050362 99968317 - 6750 -CBA [44] 100028596 100063251 100452265 95811 571 33GHz -4GBOSE-CSA [59] 99899444 99920503 99968317 14138 6750 2GHz- 2GBProposed method 9981556 998276 1001816 50904 1119 24GHz-4GB



SOS [34] 200810151 203465908 204702934 10553 - 22GHz-40 GBMSOS [34] 199626238 199637147 199652493 064 9641 22GHz-40 GBCCSA [54] 1996417 1997639 1998276 1664 5982 306GHz-10 GBICSA 199628485 199653410 199965234 45673 171384 24GHz-40 GB

spent 571 seconds Clearly MSOS is better than the proposedICSA approach with respect to slightly less best cost butis worse than the proposed method in terms of executiontime namely 2572 seconds compared to 1119 seconds whileCBA [44] is faster than the proposed method but obtainssignificantly worse costs The analysis can conclude that theproposed ICSA approach is very powerful for the subcasewith 160 units

Table 13 presents the comparison of three other methodsincludingCCSA [54] SOS [34] andMSOS [34] accompaniedwith the proposed method for Subcase 63 The obtainedresult comparisons imply that ICSA approach can obtainbetter values of the best and standard deviation costs thanCCSA and SOS but obtains slightly higher cost than MSOSby approximately $ 022 Besides the execution time fromICSA approach is much shorter than others especially it ishigher than five times faster than MSOS The four methodshave been run on approximately strong computers Brieflythe proposed ICSA approach can find and converge to morefavorable solution than other methods with shorter CPUtime except the comparison with MSOS which had bettersolution but spent higher than five times execution times

Consequently the proposed method is a very promisingoptimization algorithm for Subcase 63 a system up to 320units and with multi-fossil fuel sources and effects of valveloading process

Optimal solution obtained by ICSA for Subcase 63 isshown in Table 26

57 The Improvement of ICSA Approach Performance

571 The Outstanding Improvement over CCSA In this sec-tion the performance improvement of ICSA over CCSAhas been investigated by analyzing obtained results and setcontrol parameters Table 14 has been formed by addingreduction cost improvement level of the best cost executiontime and control parameters consisting of 119873119901119904 and 119866119898119886119909Among the compared factors reduction cost is the deviationof the cost of CCSA and that of ICSA whereas the improve-ment level is the ratio of the reduction cost to the cost ofCCSA The reduction costs indicate the proposed methodcould find either equal quality of solutions or higher qualityof solutions than CCSA for all study casesThe reduction costis from $0 to $42839 corresponding to the improvement level


Table 14 Summary of results obtained by CCSA and ICSA for all study cases

Study case Reduction cost ($) Improvement level () Execution time (s) Nps Gmax

CCSA ICSA CCSA ICSA CCSA ICSASubcase 11 0 00000 - 008 - 10 - 15Subcase 12 105642 00213 - 011 - 10 - 25Subcase 13 0476 00297 - 009 20 10 5000 15Subcase 14 42839 08968 - 012 20 10 5000 25Case 2 18485 00093 72 76 10 10 1000 1000Subcase 31 02 00024 01 01 5 5 20 20Subcase 32 0 00000 37 095 10 10 20000 5000Subcase 33 0 00000 38 095 10 10 20000 5000Subcase 34 0 00000 303 303 10 10 10000 6000Subcase 35 41 00017 32 33 20 20 6000 6000Subcase 41 04329 00003 21 092 10 10 1500 1200Subcase 42 30227 00015 306 159 10 10 1900 1500Case 5 2902 00089 445 46 20 20 400 400Subcase 61 182 00364 1825 848 20 10 4000 4000Subcase 62 90988 00911 7542 1119 20 10 6000 6000Subcase 63 13215 00066 5982 1714 320 10 1200 9000

0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105

Figure 4 The best run obtained by CCSA and ICSA for Case 2

that is from 0 to 08968The saving cost is not too much forone hour but the operation in one day onemonth or one yearis very high However it should be noted that CCSA has beenrun by setting much higher population size and iterations formany cases excluding study cases implemented in the studysuch as Case 2 Subcase 31 Subcase 35 and Case 5 Forinstance ICSA has used 119873119901119904 = 10 and 119866119898119886119909 = 15 for Subcase13 and119873119901119904 = 10 and119866119898119886119909 = 25 for Subcase 14 whereas CCSAhas been run by setting119873119901119904 = 20 and 119866119898119886119909 = 5000 for the twosubcases Similarly CCSA has been run for Subcases 32 33and 34 with much higher number of iterations For the lastsubcase CCSA has been run by setting 119873119901119904 = 320 and 119866119898119886119909

= 1200 but those of ICSA have been 10 and 9000 Due tothe higher value of control parameters CCSA has tended tospend more time in finding such high quality solutions foralmost all study cases Execution time of ICSA is less than18 seconds while that of CCSA is up to higher 75 secondsIt is clear that the proposed ICSA could find better optimalsolutions thanCCSA for such considered systems For furtherinvestigation of performance comparison the best runs over50 runs and fuel cost values of 50 runs obtained by CCSA andthe proposed ICSA for Case 2 Subcase 31 Subcase 35 andCase 5 have been plotted in from Figures 4ndash11 The best runcurves show the faster search of the proposed ICSA method


0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105

Figure 5The best fuel cost of 50 runs obtained by CCSA and ICSA for Case 2

0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA

Figure 6 The best run obtained by CCSA and ICSA for Subcase 31

whereas 50 values of fuel cost indicate that the proposedICSA can find many solutions with better quality Clearlythe proposed ICSA is outstanding in terms of stabilizationof solution search and faster convergence As a result it canconclude that the proposed ICSA approach is more effectivethanCCSA in solvingOLDproblemwith considered systems

572The Improvement of Results over Other Methods In thisarticle we have tested ICSA approach on 6 cases with 16

systems with different fuel cost forms different constraintsand different scale systems from 3 units to 320 units We havecompared the yielded results from ICSA approach and otherexisting ones for evaluating the efficiency of ICSA approachIn subsections above we have shown yielded results fromICSA approach and compared these results to those of otheronesHowever the demonstrationhad not been very good forobserving and comparing to lead to a conclusionThus in thesubsectionwehave summarized the result comparisons of the


0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA

Figure 7 The best fuel cost of 50 runs obtained by CCSA and ICSA for Subcase 31

0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105


proposed and other ones Table 15 has reported the reductioncost (in $) of ICSA approach compared to other ones Inaddition we have converted the reduction cost into improve-ment level (in ) for better comparison The improvementhas been shown from the lowest level to the highest levelin terms of reduction cost and improvement percentageIn addition we have also given the slowest and the fastestexecution time of other compared methods together withthat of the proposed method The table implies that ICSA

approach can find better optimal solutions with less fuel costup to $052 for Subcase 13 $75229 for Subcase 14 $1775149for Case 2 $1181256 for Subcase 31 $8438 for Subcase 32$9113 for Subcase 33 $121181 for Subcase 34 $3412 forSubcase 35 $04329 for Subcase 41 $30227 for Subcase42 $407002 for Case 5 $18183 for Subcase 61 $13965 forSubcase 62 and $11817 for Subcase 63 These reductioncosts are equivalent to improvement level (IL) of 0032908968 82282 14143 047 038 099 001405


0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104


00003 0002 12291 004 138 and 059 Thesequantitative comparisons reveal that larger scale systems canlead to better reduction cost but the improvement level isnot high because total cost of compared methods tends tobe large for large scale systems Furthermore very large scalesystems with nondifferentiable objective have been normallysolved by strong methods In fact systems in Case 3 havethe same characteristic with single fuel and effects of valveloading process but Subcase 34 is a larger scale system with

40 units while Subcases 31 32 and 33 are constructed by 3units 13 units and 13 units So the improvement percentageof Subcase 34 can be up to 099 whilst that of Subcases32 and 33 is 047 and 038 respectively Subcase 35 iswith the largest system 80 units but the reduction cost is notmuch only $3412 because compared methods with ICSA areeither state-of-the-art ones or improved ones Also Subcase41 and Subcase 42 have considered single fuel and PPZ andspinning reserve constraints but Subcase 42 is larger scale


Table 15 Performance improvement summary of the proposed method

Study cases Reduction cost ($) Improvement level () Execution time (s)From To From To Slowest method Fastest method Proposed method

Subcase 13 0486 0526 00304 00329 - - 009Subcase 14 59049 75229 07053 08968 - - 012Case 2 017 1775149 00001 82282 - - 76Subcase 31 02 1181256 00024 14143 - - 01Subcase 32 0 8438 0 047 29496 085 095Subcase 33 0 9113 0 038 3425 065 095Subcase 34 0 121181 0 099 116735 155 146Subcase 35 41 3412 0001688 001405 12797 - 33Subcase 41 0 04329 0 00003 56381 2028 092Subcase 42 01457 30227 0 0002 94093 3036 159Case 5 07378 407002 00023 12291 818 48 46Subcase 61 15545 18183 0031 004 30941 1524 848Subcase 62 0 13965 0 138 7542 571 1119Subcase 63 0 11817 0 059 9641 5982 1714

0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104

Figure 11 The best fuel cost of 50 runs obtained by CCSA and ICSA for Case 5

system with 90 units and Subcase 41 is only with 60 unitsThus the improvement of Subcase 41 is lower with 00003but that of Subcase 42 is 0002 Similarly systems in Cases 6have the same featurewithmulti-fossil fuel sources and effectsof valve loading process but they are respectively constructedby 80 160 and 320 units As a result the improvements ofSubcase 62 138 and Subcase 63 059 are much higherthan Subcase 61 004 However Subcase 62 with smallernumber of units but getting higher improvement is easilyunderstood because there were nine compared methods butonly three compared methods are considered for Subcase 63In general the improvement is not high it is about under onedollar several dollars tens of dollars and over one thousand

dollars per hour however the saving cost will be significantif the operation is considered to be onemonth with 720 hoursor one year with 8760 hours

Execution time comparison can be evaluated by observ-ing the fastest and the slowest compared methods in Table 15These execution times of the proposed method are approxi-mately equal to that of the fastest methods for Subcases 3233 and 34 and much shorter than other fastest comparedmethods for other cases especially for Subcases 61 and 63The fastest method for Subcase 62 is CBA [44] showing 57seconds while that of the proposed method is 1119 secondsHowever it cannot conclude that CBA is more effective thanthe proposed method because the proposed method could


Table 16 Optimal solutions for Subcase 11

119875D (MW) P1 (MW) P2 (MW) P3 (MW) Cost ($h)350 703452 1562332 1291983 18564484400 820693 1749981 1505007 208122936450 939197 1938184 1718748 231123635500 1058786 2127296 1933062 254654692550 1179104 2317314 214835 278724051600 1300261 2508404 2364375 303339858650 142231 2700616 2581069 328510461700 1545059 2893434 279919 35424442


PD (MW) P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Cost ($h)600 251066 10 955958 1009756 2032808 1791733 251066650 286187 10 1045932 1053786 2182103 1998954 286187700 29007 104656 1168803 1216634 2245097 2167929 29007750 299964 12141 1315535 1303179 2415602 2265418 299964800 337513 145234 1422418 1357029 2553572 2435787 337513850 349093 180112 1526422 1419012 2714989 2594877 349093900 393589 198696 1628286 1552237 2828438 2716499 393589950 411506 252743 1751899 1622651 2949102 2865136 411506

Table 18 Optimal solutions for Subcases 13 and 14

Variables Subcase 13 Subcase 14P1 (MW) 334743 3035073P2 (MW) 640977 1137678P3 (MW) 55094 1434992P4 (MW) - 50P5 (MW) - 50P6 (MW) - 50Cost ($h) 1599984 8313221

find better optimal solution with less fuel cost by $2130As considering execution time of the slowest comparedmethods it can point out that ICSA is a very fast optimizationtool since the execution time of these methods is 29496 and3425 seconds for Subcases 32 and 33 116735 seconds forSubcase 34 56381 seconds for Subcase 41 94093 secondsfor Subcase 42 12797 seconds for Case 5 30941 seconds forSubcase 61 7542 seconds for Subcase 62 and 9641 secondsfor Subcase 63 while the execution time of the proposedmethod for these cases is respectively 095 146 091 1589246 84828 1119 and 171384 seconds It is clearly shown thatICSA is very fast as compared to these methods

In summary the proposed method has found approx-imately high quality solutions with several standard state-of-the-art meta-heuristic algorithms and improved versionsof them together with other old methods In addition theproposed method could improve result better than approx-imately all methods with faster execution time Comparedto other methods with the fastest convergence speed andhigh quality solutions the proposed method has been as

fast as for some cases and much faster for other cases Thecomparison with the slowest methods could show that theproposed method was extremely powerful since it was up tonearly one thousand times faster Consequently the proposedICSA approach can be one of the strongest optimization toolsfor OLD problem

6 Conclusions

This paper has proposed a good ICSA method for solvingOLD problem in which many test systems with differentobjective functions and complicated constraints from simpleto complex have been used as studied cases The proposedICSA method has been developed by performing severalmodifications on the second solution update of CCSA whichcontained several drawbacks to global convergence and fastmanner The OLD problem has covered from single fuelto multi-fossil fuels from quadratic objective function tononconvex objective function in addition to PPZ RPR andRRL constraints Many existing optimization algorithms have


Table 19 Optimal solutions for Case 2

119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006

Table 20 Optimal solution for Subcase 31

119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083


Subcase 32 Subcase 33119894 119875119894 (MW) 119894 119875119894 (MW)1 6283185 1 62831852 1495997 2 29919933 2227491 3 29919934 1098666 4 15973315 1098666 5 15973316 1098666 6 15973317 1098666 7 15973318 600000 8 15973319 1098666 9 159733110 400000 10 77399911 400000 11 77399912 550000 12 92399913 550000 13 876845

been concerned in aim to compare the performance and givethe final conclusion on the proposed method There have

been six main cases with sixteen subcases The evaluationshave been made at the end of each study case Clearly theproposed ICSA approach has yielded more effective optimalsolutions with faster execution time than almost all methodsConsequently it can be concluded that the proposed methodis much more superior to CCSA and is a very promisingmethod for solving OLD problem

Appendix

See Tables 16ndash26

Nomenclature

120575119894 120582119894 120572119894 120573119894 120574119894 Fuel cost functioncoefficients of the 119894119905ℎthermal generationunit11986100 1198610119895 119861119895119894 Power loss matrixcoefficients119865119865119909 119865119865119887119890119904119905 The values of fitness ofsolution 119909 and theso-far most effectivesolution among thecurrent set ofsolutions119898119894 Number of fuels burntin the 119894119905ℎ thermalgeneration unit



119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 11079981 11 9400001 21 52327939 31 19000002 11079978 12 9400001 22 52327938 32 19000003 9739992 13 21475979 23 52327942 33 19000004 17973308 14 39427940 24 52327941 34 16479985 8779992 15 39427940 25 52327937 35 19439786 14000001 16 39427940 26 52327942 36 20000007 25959969 17 48927940 27 100000 37 11000008 28459969 18 48927940 28 100000 38 11000009 28459969 19 51127941 29 100000 39 110000010 1300000 20 51127938 30 877999 40 51127939


119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 1121507 21 5232804 41 1108005 61 52327952 1107998 22 5232796 42 1107998 62 52328113 9739771 23 52328 43 9739996 63 52329034 1797288 24 5232891 44 1797331 64 52327945 8780075 25 5232793 45 8779894 65 52327946 140 26 52327 46 140 66 52327947 2595996 27 10 47 2596004 67 108 2845997 28 10 48 2845997 68 109 2845981 29 10 49 284598 69 1010 130 30 8779985 50 130 70 877998511 9400001 31 190 51 9400001 71 19012 9400001 32 190 52 9400001 72 19013 2147584 33 190 53 2147593 73 19014 3942826 34 1647999 54 3942643 74 164828115 3942789 35 1874316 55 3942841 75 20016 3942791 36 200 56 3942793 76 20017 4892798 37 110 57 489292 77 11018 4892794 38 110 58 4892805 78 11019 5112794 39 110 59 5112752 79 11020 5112794 40 5112696 60 5112784 80 5112681


119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 4549445 16 4549003 31 4549473 46 455 61 4550000 76 45496522 4549987 17 454945 32 4550000 47 4549701 62 4550000 77 45499843 1300000 18 1299896 33 1299783 48 130 63 1299938 78 12999394 1300000 19 130 34 1300000 49 1299796 64 1300000 79 12997745 335495 20 312884 35 3228285 50 3216314 65 2870957 80 32194096 4594493 21 4599967 36 4599993 51 4598946 66 4599971 81 46000007 4649997 22 464977 37 4649712 52 465 67 4648247 82 46485648 600058 23 600018 38 600394 53 600000 68 600173 83 6000669 250027 24 250001 39 250000 54 250188 69 250000 84 25004210 200000 25 200027 40 200193 55 200036 70 200378 85 20221911 200001 26 200038 41 200122 56 200357 71 200002 86 20000012 584585 27 551457 42 593489 57 589256 72 594547 87 57733113 25001 28 25 43 250082 58 250006 73 250094 88 25003214 150000 29 150333 44 150016 59 150000 74 150000 89 15007815 150007 30 15 45 150000 60 150033 75 150038 90 150031


Table 25 Optimal solution for Case 5

119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882


119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 2191364 56 23993 111 2191364 166 2399298 221 2191364 276 23992952 2124025 57 2877776 112 2124025 167 2877776 222 2124025 277 28777763 2806577 58 2388802 113 2806577 168 2388802 223 2806577 278 23888024 2392836 59 4260203 114 2392836 169 4260203 224 2392836 279 42602035 2799217 60 2758712 115 2799217 170 2758712 225 2799217 280 27587126 23993 61 2191364 116 23993 171 2191364 226 23993 281 21913647 2877776 62 2124025 117 2877776 172 2124025 227 2877776 282 21240258 2388802 63 2806577 118 2388802 173 2806579 228 2388802 283 28065779 4260203 64 2392836 119 4260203 174 2392836 229 4260203 284 239283610 2758712 65 2799217 120 2758712 175 2799217 230 2758712 285 279921711 2175651 66 23993 121 2191364 76 23993 231 2191364 286 2399312 2124022 67 2877776 122 2124025 77 2877776 232 2124025 287 287777613 2826687 68 2388802 123 2806577 78 2388802 233 2806577 288 238880214 2400905 69 4260203 124 2392836 79 4260203 234 2392836 289 426020315 280165 70 2758712 125 2799217 80 2758712 235 2799217 290 275871216 2404661 71 2191364 126 23993 181 2191364 236 23993 291 219136417 2875061 72 2124025 127 2877776 182 2124025 237 2877776 292 212402518 2396852 73 2806577 128 2388802 183 2806577 238 2388802 293 280657719 4261049 74 2392836 129 4260203 184 2392836 239 4260203 294 239283620 2770318 75 2799217 130 2758712 185 2799217 240 2758712 295 279921721 2191364 76 2399301 131 2191364 186 2399298 241 2191364 296 239930522 2124025 77 2877776 132 2124025 187 2877776 242 2124025 297 287777623 2806577 78 2388802 133 2806577 188 2388802 243 2806577 298 238880224 2392836 79 4260203 134 2392836 189 4260203 244 2392836 299 426020325 2799217 80 2758712 135 2799217 190 2758712 245 2799217 300 275871226 23993 81 2191363 136 2399309 191 2191364 246 23993 301 219136427 2877776 82 2124025 137 2877776 192 2124025 247 2877776 302 212402528 2388802 83 2806577 138 2388802 193 2806577 248 2388802 303 280657729 4260203 84 2392836 139 4260203 194 2392836 249 4260203 304 239283630 2758712 85 2799217 140 2758712 195 2799217 250 2758712 305 279921731 2191365 86 23993 141 2191364 196 23993 251 2191364 306 2399332 2124025 87 2877776 142 2124025 197 2877776 252 2124025 307 287777633 2806577 88 2388802 143 2806577 198 2388802 253 2806577 308 238880234 2392836 89 4260203 144 2392836 199 4260203 254 2392836 309 426020335 2799217 90 2758712 145 2799217 200 2758712 255 2799217 310 275871436 23993 91 2191344 146 23993 201 2191364 256 23993 311 219136937 2877776 92 2124025 147 2877776 202 2124025 257 2877776 312 212402538 2388802 93 2806577 148 2388802 203 2806577 258 2388802 313 280657739 4260203 94 2392836 149 4260193 204 2392836 259 4260203 314 239283640 2758712 95 2799217 150 2758712 205 2799217 260 2758712 315 279921741 2191364 96 23993 151 2191364 206 23993 261 2191364 316 2399342 2124025 97 2877776 152 2124025 207 2877776 262 2124025 317 287777643 2806577 98 2388802 153 2806577 208 2388802 263 2806577 318 2388802


Table 26 Continued

119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)44 2392836 99 4260203 154 2392832 209 4260203 264 2392836 319 426020345 2799217 100 2758712 155 2799217 210 2758712 265 2799217 320 275871046 23993 101 2191384 156 23993 211 2191359 266 2399347 2877776 102 2124025 157 2877776 212 2124025 267 287777648 2388798 103 2806577 158 2388806 213 2806577 268 238880249 4260203 104 2392840 159 4260213 214 2392836 269 426020350 2758712 105 2799217 160 2758712 215 2799217 270 275871251 2191364 106 23993 161 2191364 216 23993 271 219136452 2124025 107 2877776 162 2124025 217 2877776 272 212402553 2806577 108 2388802 163 2806577 218 2388802 273 280657754 2392836 109 4260203 164 2392836 219 4260203 274 239283655 2799217 110 2758712 165 2799217 220 2758712 275 2799217

119873 Number of allavailable thermalgeneration units119899119894 Number of prohibitedpower zones of the 119894119905ℎthermal generationunit119875119906119894119896 119875119897119894119896 Upper and lowerlimits of the 119894119905ℎthermal generationunit corresponding tothe kth PPZ119875119886 Probability ofreplacing controlvariables in each oldsolution119875119863 Real power demand ofall loads in system119875119894119898119886119909 119875119894119898119894119899 The highest andlowest real poweroutputs of the iththermal generationunit119875119894119895119898119886119909 119875119894119895119898119894119899 The highest andlowest real poweroutputs of the 119894119905ℎthermal generationunit corresponding tothe 119895119905ℎ fuel type119878119894119898119886119909 Maximum real powerreserve contributionof the thermalgeneration unit 1198941198781199001198971199031198861198991198891 1198781199001198971199031198861198991198892 1198781199001198971199031198861198991198893 1198781199001198971199031198861198991198894 Randomly mixedsolutions from the setof current solutions119878119900119897119909 119878119900119897119866119887119890119904119905 The old solution x andthe most effectivesolution119878119877 Real power reserverequirement of system

120575119894119895 120582119894119895 120572119894119895 120573119894119895 120574119894119895 Fuel cost functioncoefficients of the 119894119905ℎthermal generationunit corresponding tothe 119895119905ℎ fuel type1205761 1205762 1205763 1205764 1205765 1205766 Random numbersbetween 0 and 1Ω Number of generationunits considering PPZconstraint

Data Availability

No data were used to support this study

Conflicts of Interest

The authors declare no conflicts of interest

References

[1] N Sinha R Chakrabarti and P K Chattopadhyay ldquoEvolution-ary programming techniques for economic load dispatchrdquo IEEETransactions on Evolutionary Computation vol 7 no 1 pp 83ndash94 2003

[2] P Hansen ldquoA separable approximation dynamic programmingalgorithm for economic dispatch with transmission lossesrdquoYugoslav Journal of Operations Research vol 12 no 2 2002

[3] N T Thang ldquoSolving economic dispatch problem with piece-wise quadratic cost functions using lagrange multiplier theoryrdquoin Proceedings of the 3rd International Conference on ComputerTechnology and Development (ICCTD rsquo11) pp 359ndash364 ASMEPress 2011

[4] S K Mishra and S K Mishra ldquoA comparative study of solutionof economic load dispatch problem in power systems in theenvironmental perspectiverdquoProcedia Computer Science vol 48pp 96ndash100 2015

[5] A A Al-Subhi and H K Alfares ldquoEconomic load dispatchusing linear programming a comparative studyrdquo InternationalJournal of Applied Industrial Engineering vol 3 no 1 pp 16ndash362016


[6] C Zhou G Huang and J Chen ldquoPlanning of electric powersystems considering virtual power plants with dispatchableloads included an inexact two-stage stochastic linear program-ming modelrdquoMathematical Problems in Engineering vol 2018Article ID 7049329 12 pages 2018

[7] T T Nguyen N V Quynh and L Van Dai ldquoImproved fireflyalgorithm a novel method for optimal operation of thermalgenerating unitsrdquo Complexity vol 2018 Article ID 7267593 23pages 2018

[8] S S Haroon S Hassan S Amin et al ldquoMultiple fuel machinespower economic dispatch using stud differential evolutionrdquoEnergies vol 11 no 6 pp 1ndash20 2018

[9] C-T Su and C-L Chiang ldquoNonconvex power economic dis-patch by improved genetic algorithm with multiplier updatingmethodrdquo Electric Power Components and Systems vol 32 no 3pp 257ndash273 2004

[10] NNoman andH Iba ldquoDifferential evolution for economic loaddispatch problemsrdquo Electric Power Systems Research vol 78 no8 pp 1322ndash1331 2008

[11] P Somasundaram and K Kuppusamy ldquoApplication of evolu-tionary programming to security constrained economic dis-patchrdquo International Journal of Electrical Power amp EnergySystems vol 27 no 5-6 pp 343ndash351 2005

[12] T Jayabarathi K Jayaprakash andD Jeyakumar ldquoEvolutionaryprogramming technique for different kinds of economic dis-patch problemsrdquo Electric Power Systems Research vol 73 no 2pp 169ndash176 2005

[13] P Subbaraj R Rengaraj and S Salivahanan ldquoEnhancementof combined heat and power economic dispatch using selfadaptive real-coded genetic algorithmrdquo Applied Energy vol 86no 6 pp 915ndash921 2009

[14] C-L Chiang and C-T Su ldquoAdaptive-improved genetic algo-rithm for the economic dispatch of units with multiple fueloptionsrdquo Cybernetics and Systems vol 36 no 7 pp 687ndash7042005

[15] C Chiang ldquoImproved genetic algorithm for power economicdispatch of units with valve-point effects and multiple fuelsrdquoIEEE Transactions on Power Systems vol 20 no 4 pp 1690ndash1699 2005

[16] K Meng H G Wang Z Y Dong and K P Wong ldquoQuantum-inspired particle swarm optimization for valve-point economicload dispatchrdquo IEEE Transactions on Power Systems vol 25 no1 pp 215ndash222 2010

[17] P Erdogmus A Ozturk and S Duman ldquoEnvironmen-taleconomic dispatch using genetic algorithm and simulatedannealingrdquo in Proceedings of the International Conference onElectric Power and Energy Conversion Systems EPECS rsquo09 pp1ndash4 IEEE 2009

[18] L D S Coelho and V C Mariani ldquoImproved differentialevolution algorithms for handling economic dispatch opti-mization with generator constraintsrdquo Energy Conversion andManagement vol 48 no 5 pp 1631ndash1639 2007

[19] H Dakuo W Fuli and M Zhizhong ldquoA hybrid genetic algo-rithm approach based on differential evolution for economicdispatch with valve-point effectsrdquo Electrical Power and EnergySystems vol 30 pp 31ndash38 2008

[20] C-F Chang J-J Wong J-P Chiou and C-T Su ldquoRobustsearching hybrid differential evolution method for optimalreactive power planning in large-scale distribution systemsrdquoElectric Power Systems Research vol 77 no 5-6 pp 430ndash4372007

[21] M R Farooqi P Jain and K R Niazi ldquoUsing Hopfield neuralnetwork for economic dispatch of power systemsrdquo in Proceed-ings of the National Power Engineering Conference PECon rsquo03pp 5ndash10 Bangi Malaysia 2003

[22] T Yalcinoz H Altun and U Hasan ldquoConstrained economicdispatch with prohibited operating zones a Hopfield neuralnetwork approachrdquo in Proceedings of the 10th MediterraneanElectrotechnical Conference Information Technology and Elec-trotechnology for the Mediterranean Countries ProceedingsMeleCon rsquo00 (Cat No 00CH37099) pp 570ndash573 LemesosCyprus 2000

[23] D N Vo P Schegner and W Ongsakul ldquoCuckoo searchalgorithm for non-convex economic dispatchrdquo IET GenerationTransmission amp Distribution vol 7 no 6 pp 645ndash654 2013

[24] J-B Park K-S Lee J-R Shin and K Y Lee ldquoA particleswarm optimization for economic dispatch with non-smoothcost functionsrdquo IEEETransactions on Power Systems vol 20 no1 pp 34ndash42 2005

[25] T Niknam H D Mojarrad and M Nayeripour ldquoA newfuzzy adaptive particle swarm optimization for non-smootheconomic dispatchrdquo Energy vol 35 no 4 pp 1764ndash1778 2010

[26] L D S Coelho and V C Mariani ldquoAn improved harmonysearch algorithm for power economic load dispatchrdquo EnergyConversion and Management vol 50 no 10 pp 2522ndash25262009

[27] M Mahdavi M Fesanghary and E Damangir ldquoAn improvedharmony search algorithm for solving optimization problemsrdquoAppliedMathematics and Computation vol 188 no 2 pp 1567ndash1579 2007

[28] A Bhattacharya and P K Chattopadhyay ldquoSolving complexeconomic load dispatch problem using biogeography-basedoptimizationrdquo Expert Systems with Applications vol 37 no 5pp 3605ndash3615 2010

[29] D Simon ldquoBiogeography-based optimizationrdquo IEEE Transac-tions on Evolutionary Computation vol 12 no 6 pp 702ndash7132008

[30] J S Alsumait J K Sykulski and A K Al-Othman ldquoAhybrid GA-PS-SQP method to solve power system valve-pointeconomic dispatch problemsrdquo Applied Energy vol 87 no 5 pp1773ndash1781 2010

[31] M S Turgut andGKDemir ldquoQuadratic approximationndashbasedhybrid Artificial Cooperative Search algorithm for economicemission load dispatchproblemsrdquo International Transactions onElectrical Energy Systems vol 27 no 4 pp 1ndash14 2017

[32] T A A Victoire and A E Jeyakumar ldquoHybrid PSO-SQPfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 71 no 1 pp 51ndash59 2004

[33] D-KHe F-LWang andZ-ZMao ldquoHybrid genetic algorithmfor economic dispatch with valve-point effectrdquo Electric PowerSystems Research vol 78 no 4 pp 626ndash633 2008

[34] D C Secui ldquoA modified symbiotic organisms search algorithmfor large scale economic dispatch problem with valve-pointloading effectsrdquo Energy vol 113 pp 366ndash384 2016

[35] K BhattacharjeeA Bhattacharya and S H N Dey ldquoTeaching-learning-based optimization for different economic dispatchproblemsrdquo Scientia Iranica vol 21 no 3 pp 870ndash884 2014

[36] K Bhattacharjee A Bhattacharya and S H N Dey ldquoOppo-sitional Real Coded Chemical Reaction Optimization for dif-ferent economic dispatch problemsrdquo International Journal ofElectrical Power amp Energy Systems vol 55 pp 378ndash391 2014


[37] V Hosseinnezhad M Rafiee M Ahmadian and M T AmelildquoSpecies-basedQuantum Particle SwarmOptimization for eco-nomic load dispatchrdquo International Journal of Electrical Poweramp Energy Systems vol 63 pp 311ndash322 2014

[38] M S P Subathra S E Selvan T A A Victoire A HChristinal andU Amato ldquoA hybrid with cross-entropymethodand sequential quadratic programming to solve economic loaddispatch problemrdquo IEEE Systems Journal vol 9 no 3 pp 1031ndash1044 2015

[39] J Zhan Q H Wu C Guo and X Zhou ldquoEconomic dispatchwith non-smooth objectives part I local minimum analysisrdquoIEEE Transactions on Power Systems vol 30 no 2 pp 710ndash7212015

[40] A K Barisal andR C Prusty ldquoLarge scale economic dispatch ofpower systems using oppositional invasive weed optimizationrdquoApplied Soft Computing vol 29 pp 122ndash137 2015

[41] M Basu ldquoImproved differential evolution for economic dis-patchrdquo International Journal of Electrical Power amp EnergySystems vol 63 pp 855ndash861 2014

[42] V S Aragon S C Esquivel and C C Coello ldquoAn immunealgorithm with power redistribution for solving economicdispatch problemsrdquo Information Sciences vol 295 pp 609ndash6322015

[43] M Ghasemi M Taghizadeh S Ghavidel and A AbbasianldquoColonial competitive differential evolution an experimentalstudy for optimal economic load dispatchrdquo Applied Soft Com-puting vol 40 pp 342ndash363 2016

[44] B R Adarsh T Raghunathan T Jayabarathi and X-S YangldquoEconomic dispatch using chaotic bat algorithmrdquo Energy vol96 pp 666ndash675 2016

[45] N Ghorbani and E Babaei ldquoExchange market algorithm foreconomic load dispatchrdquo International Journal of ElectricalPower amp Energy Systems vol 75 pp 19ndash27 2016

[46] J X V Neto G Reynoso-Meza T H Ruppel V C Marianiand L D S Coelho ldquoSolving non-smooth economic dispatchby a new combination of continuous GRASP algorithm anddifferential evolutionrdquo International Journal of Electrical Poweramp Energy Systems vol 84 pp 13ndash24 2017

[47] A Kavousi-Fard and A Khosravi ldquoAn intelligent 120579-ModifiedBat Algorithm to solve the non-convex economic dispatchproblem considering practical constraintsrdquoElectrical Power andEnergy Systems vol 82 pp 189ndash196 2016

[48] M A Al-Betar M A Awadallah A T Khader and A L BolajildquoTournament-based harmony search algorithm for non-convexeconomic load dispatch problemrdquo Applied Soft Computing vol47 pp 449ndash459 2016

[49] M A Al-Betar M A Awadallah I A Doush E Alsukhni andH ALkhraisat ldquoA non-convex economic dispatchproblemwithvalve loading effect using a new modified 120573-hill climbing localsearch algorithmrdquo Arabian Journal for Science and Engineeringpp 1ndash8 2018

[50] M A Awadallah M A Al-Betar A L Bolaji E M Alsukhniand H Al-Zoubi ldquoNatural selection methods for artificial beecolony with new versions of onlooker beerdquo Soft Computing pp1ndash40 2018

[51] S H Kaboli and A K Alqallaf ldquoSolving non-convex economicload dispatch problem via artificial cooperative search algo-rithmrdquo Expert Systems with Applications vol 128 pp 14ndash272019

[52] D Singh and J Dhillon ldquoAmeliorated greywolf optimization foreconomic load dispatch problemrdquo Energy vol 169 pp 398ndash4192019

[53] X S Yang and S Deb ldquoCuckoo search via Levy flightsrdquo inProceedings of the World Congress on Nature and BiologicallyInspired Computing (NaBIC rsquo09) pp 210ndash214 India 2009

[54] S Sahoo K M Dash R C Prusty and A K Barisal ldquoCom-parative analysis of optimal load dispatch through evolutionaryalgorithmsrdquo Ain Shams Engineering Journal vol 6 pp 107ndash1202015

[55] M Basu and A Chowdhury ldquoCuckoo search algorithm foreconomic dispatchrdquo Energy vol 60 pp 99ndash108 2013

[56] A B Serapiao ldquoCuckoo search for solving economic dispatchload problemrdquo Intelligent Control and Automation vol 04 no04 pp 385ndash390 2013

[57] A H Bindu and M D Reddy ldquoEconomic load dispatch usingcuckoo search algorithmrdquo International Journal of EngineeringResearch and Applications vol 3 pp 498ndash502 2013

[58] E Afzalan and M Joorabian ldquoAn improved cuckoo searchalgorithm for power economic load dispatchrdquo InternationalTransactions on Electrical Energy Systems vol 25 no 6 pp 958ndash975 2015

[59] T T Nguyen and D N Vo ldquoThe application of one rank cuckoosearch algorithm for solving economic load dispatch problemsrdquoApplied Soft Computing vol 37 pp 763ndash773 2015

[60] S M Islam S Das S Ghosh S Roy and P N Suganthan ldquoAnadaptive differential evolution algorithm with novel mutationand crossover strategies for global numerical optimizationrdquoIEEE Transactions on Systems Man and Cybernetics Part BCybernetics vol 42 no 2 pp 482ndash499 2012

[61] Z L Gaing ldquoParticle swarm optimization to solving theeconomic dispatch considering the generator constraintsrdquo IEEETransactions on Power Systems vol 18 no 3 pp 1187ndash1195 2003

[62] X-S Yang and S Deb ldquoEngineering optimisation by Cuckoosearchrdquo International Journal of Mathematical Modelling andNumerical Optimisation vol 330 pp 43ndash51 2010

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the OLD problem successfully by separating three-curveobjective function into three different single curve objectivefunctions In [7] amore realistic representation of the electricgeneration fuel function corresponding to multi fossil fuelsources was introduced in which the authors considered adiscontinuous cost function and the effects of valve loadingprocess (EoVLP) of thermal units More complicated modelswere also introduced For example some thermal generationunits were driven by burning multi fossil fuel sources (MFS)to generate electricity [8] or some operating conditions ofgenerators including upper generation boundary lower gen-eration boundary and prohibited power zones were added[9] However these methods have been only applied to thesystems where the generation power-fuel cost characteristicof thermal generation units was mathematically modelled asthe second order function and the effects of valve loadingprocess were ignored [10]

Other artificial intelligence-based advanced methodshave been recently applied for solving OLD problem Evolu-tionary programming-based approaches (EP) [1 11 12] andgenetic algorithm (GA) [13ndash15] were considered as fast algo-rithms because of their parallel search ability In addition GAand EP possessed good properties such as finding solutionsnearby global optimum capability of effectively handlingnonlinear constraints reliable search ability and not manyadjustment parameters [10] Thus it could become a suitablechoice for successfully solving OLD problem However GAwas prematurely convergent to local optimum solutions[16] In this regard simulated annealing approach (SA)[17] was a better probabilistic approach in finding solutionswith appropriate fitness but there was a high possibility ofeasily converging to local optimal zones when coping withcomplicatedly constrained problem It converges slower thanGA and EP though Differential evolution algorithm (DE)[10 18] also belongs to the same class as GA and EP Howeverit is more popular thanks to simple structure with severaladjustment parameters and high rate of success DE has beenmore widely and successfully applied than SA and GA [19]But its faster convergence manner led to the same drawbackas GA like high rate of falling into local optimum andhardly ever toward promising zones quickly In fact theseshortcomings could be tackled by setting population size tohigher value But high population size could suffer from longsimulation time to calculate fitness function and evaluatequality of solutions [20] Hopfield neural network (HNN)[21 22] focused on optimizing energy function and wasonly successfully applied for optimization problems whereobjective functions were differentiable HNN could be anappropriatemethod for large-scale systemswith highnumberof generation units but it needed long simulation time andmay also converge to local optimum solution zones [23]Particle swam optimization (PSO) [16 24] is a random searchapproach developed by behavior of a swarm or flock duringfood search process In comparison with GA PSO ownedmore advantages such as simpler implementation and fewparameters with easy selection However the success rateof PSO was highly influenced by adjustment parametersand it copes with high rate to be trapped in many zoneswith local optimum solutions [25] Harmony search (HS)

[26] is a metaheuristic-based method inspired from musicInstead of using gradient search HS has employed stochasticrandom search to exploit its potential ability Thus it tendedto converge to local optimal zones rather than global optimalzones [27] Biogeography-based optimization (BBO) [28]could compete with PSO and DE since its solutions weredirectly updated by migration from other existing solutionsand its solutions directly shared their attributes with othersolutions [29]

It is clear that each method has advantages as well asdisadvantages for different applications for finding OLDproblem solutions Hence another natural approach is tocombine different methods to exploit the advantages of eachmethod and enhance the overall searching capability Severalhybrid methods have been developed in such way includ-ing hybrid Genetic algorithm Pattern Search and Sequen-tial Quadratic Programming (GAndashPSndashSQP) method [30]hybrid Artificial Cooperative Search algorithm (HACSA)[31] hybrid PSO-SQP [32] and hybrid GA (HGA) [33]Basically these hybrid methods could deal with OLD prob-lem more effectively than each member method On theother hand they could suffer from the difficulty of selectingmany controllable parameters In addition to such popularoriginal algorithms and hybrid methods there are manyother original and improved methods that have been appliedfor solving the considered OLD problem These methods areSymbiotic organisms search algorithm (SOS) [34] and itsmodified version (MSOS) [34] teaching activity and learningactivity-based optimization (TLBO) [35] chemical reaction-based approach (CRBA) [36] enhanced particle swarmoptimization (EPSO) [37] sequential quadratic technique-based cross entropy approach (CEA-SQT) [38] traversesearch-based optimization approach (TSBO) [39] invasiveweed approach (IWA) [40] Improved Differential evolu-tion (IDE) [41] immune algorithm using power redistribu-tion IAPR [42] Colonial competitive differential evolution(CCDE) [43] Chaotic Bat algorithm (CBA) [44] Exchangemarket algorithm (EMA) [45] adaptive search techniquealgorithm and differential evolution (GRASP-DE) [46] 120579-Modified Bat Algorithm (120579-MBA) [47] Tournament-basedharmony search algorithm (TBHSA) [48] New Modified 120573-Hill Climbing Local Search Algorithm (M120573-HCLSA) [49]improved version of artificial bee colony algorithm (IABCA)[50] artificial cooperative search algorithm (ACSA) [51]and ameliorated greywolf optimization algorithm (AGWOA)[52] Among these methods ACSA and AGWOA werethe two latest methods which were applied for OLD andpublished in early 2019 However the demonstration of realperformance of the two methods is still questionable In factACSA has been tested only on systemswith small scale singlefuel and simple constraints such as generation limits andpower balance The largest scale system was considered in[51] to be 40-unit system Unlike [51] different types of fuelcost function complicated constraints and large scale systemwith 140 units have been taken into account in [52] Viacomparisons withmany existing methods AGWOAhas beenstated to be the best one with many surprising results Thusthe validation of reported solutions from the methodmust beverified and its strong search ability must be reevaluated In
























Reduce 119865 = 119873sum119894=1

119865119894 (119875119894) (1)


119865119894 (119875119894) = 1205721198941198752119894 + 120582119894119875119894 + 120575119894 (2)




119873sum119894=1

119875119894 = 119875119863 + 119875119871 (4)


119875119871 = 11986100 + 119873sum119895=1

1198610119895119875119895 + 119873sum119895=1

119873sum119894=1

119875119895119861119895119894119875119894 (5)


119875119894min le 119875119894 le 119875119894max (6)



119865119894 (119875119894) =


(7)

119865119894 (119875119894) =


(8)




119875119894 isin


(9)



119873sum119894=1

119878119894 ge 119878119877 (10)




119878119894 = 0 forall119894 isin Ω (12)





1198751198940 minus 119863119878119878119894 le 119875119894 le 1198751198940 + 119868119878119878119894 (13)





119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572 (119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy (120573) (14)



119878119900119897119899119890119908119909=

119878119900119897119909 + 1205761 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) if 1205762 lt 119875119886119878119900119897119909 119900119905ℎ119890119903119908119894119904119890

(15)







Δ1198781199001198971198991198901199081199091 = 1205763 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) (16)


Δ1198781199001198971198991198901199081199092= 1205764 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894) (17)


1198781199001198971198991198901199081199091 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199091 (18)

1198781199001198971198991198901199081199092 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199092 (19)



ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2





1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)


ΔSol2

ΔSol1

Solx

Solnew1

Solnew2


Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)



Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)




else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018































Reduce 119865 = 119873sum119894=1

119865119894 (119875119894) (1)


119865119894 (119875119894) = 1205721198941198752119894 + 120582119894119875119894 + 120575119894 (2)




119873sum119894=1

119875119894 = 119875119863 + 119875119871 (4)


119875119871 = 11986100 + 119873sum119895=1

1198610119895119875119895 + 119873sum119895=1

119873sum119894=1

119875119895119861119895119894119875119894 (5)


119875119894min le 119875119894 le 119875119894max (6)



119865119894 (119875119894) =


(7)

119865119894 (119875119894) =


(8)




119875119894 isin


(9)



119873sum119894=1

119878119894 ge 119878119877 (10)




119878119894 = 0 forall119894 isin Ω (12)





1198751198940 minus 119863119878119878119894 le 119875119894 le 1198751198940 + 119868119878119878119894 (13)





119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572 (119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy (120573) (14)



119878119900119897119899119890119908119909=

119878119900119897119909 + 1205761 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) if 1205762 lt 119875119886119878119900119897119909 119900119905ℎ119890119903119908119894119904119890

(15)







Δ1198781199001198971198991198901199081199091 = 1205763 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) (16)


Δ1198781199001198971198991198901199081199092= 1205764 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894) (17)


1198781199001198971198991198901199081199091 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199091 (18)

1198781199001198971198991198901199081199092 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199092 (19)



ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2





1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)


ΔSol2

ΔSol1

Solx

Solnew1

Solnew2


Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)



Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)




else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018





















Reduce 119865 = 119873sum119894=1

119865119894 (119875119894) (1)


119865119894 (119875119894) = 1205721198941198752119894 + 120582119894119875119894 + 120575119894 (2)




119873sum119894=1

119875119894 = 119875119863 + 119875119871 (4)


119875119871 = 11986100 + 119873sum119895=1

1198610119895119875119895 + 119873sum119895=1

119873sum119894=1

119875119895119861119895119894119875119894 (5)


119875119894min le 119875119894 le 119875119894max (6)



119865119894 (119875119894) =


(7)

119865119894 (119875119894) =


(8)




119875119894 isin


(9)



119873sum119894=1

119878119894 ge 119878119877 (10)




119878119894 = 0 forall119894 isin Ω (12)





1198751198940 minus 119863119878119878119894 le 119875119894 le 1198751198940 + 119868119878119878119894 (13)





119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572 (119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy (120573) (14)



119878119900119897119899119890119908119909=

119878119900119897119909 + 1205761 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) if 1205762 lt 119875119886119878119900119897119909 119900119905ℎ119890119903119908119894119904119890

(15)







Δ1198781199001198971198991198901199081199091 = 1205763 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) (16)


Δ1198781199001198971198991198901199081199092= 1205764 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894) (17)


1198781199001198971198991198901199081199091 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199091 (18)

1198781199001198971198991198901199081199092 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199092 (19)



ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2





1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)


ΔSol2

ΔSol1

Solx

Solnew1

Solnew2


Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)



Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)




else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

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Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









119865119894 (119875119894) =


(7)

119865119894 (119875119894) =


(8)




119875119894 isin


(9)



119873sum119894=1

119878119894 ge 119878119877 (10)




119878119894 = 0 forall119894 isin Ω (12)





1198751198940 minus 119863119878119878119894 le 119875119894 le 1198751198940 + 119868119878119878119894 (13)





119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572 (119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy (120573) (14)



119878119900119897119899119890119908119909=

119878119900119897119909 + 1205761 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) if 1205762 lt 119875119886119878119900119897119909 119900119905ℎ119890119903119908119894119904119890

(15)







Δ1198781199001198971198991198901199081199091 = 1205763 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) (16)


Δ1198781199001198971198991198901199081199092= 1205764 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894) (17)


1198781199001198971198991198901199081199091 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199091 (18)

1198781199001198971198991198901199081199092 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199092 (19)



ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2





1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)


ΔSol2

ΔSol1

Solx

Solnew1

Solnew2


Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)



Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)




else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018










1198751198940 minus 119863119878119878119894 le 119875119894 le 1198751198940 + 119868119878119878119894 (13)





119878119900119897119899119890119908119909 = 119878119900119897119909 + 120572 (119878119900119897119909 minus 119878119900119897119866119887119890119904119905) oplus Levy (120573) (14)



119878119900119897119899119890119908119909=

119878119900119897119909 + 1205761 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) if 1205762 lt 119875119886119878119900119897119909 119900119905ℎ119890119903119908119894119904119890

(15)







Δ1198781199001198971198991198901199081199091 = 1205763 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892) (16)


Δ1198781199001198971198991198901199081199092= 1205764 (1198781199001198971199031198861198991198891 minus 1198781199001198971199031198861198991198892 + 1198781199001198971199031198861198991198893 minus 1198781199001198971199031198861198991198894) (17)


1198781199001198971198991198901199081199091 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199091 (18)

1198781199001198971198991198901199081199092 = 119878119900119897119909 + Δ1198781199001198971198991198901199081199092 (19)



ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2





1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)


ΔSol2

ΔSol1

Solx

Solnew1

Solnew2


Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)



Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)




else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









ΔSol2

Sol2

Sol3

Sol4

ΔSol1

Sol1

Solx

Solnew1

Solnew2





1198781199001198971198991198901199081 = 119878119900119897119909 + Δ1198781199001198971 (20)

1198781199001198971198991198901199082 = 119878119900119897119909 + Δ1198781199001198971 + Δ1198781199001198972 (21)


ΔSol2

ΔSol1

Solx

Solnew1

Solnew2


Δ1198781199001198971 = 1198781199001198971 minus 1198781199001198972 (22)

Δ1198781199001198972 = 1198781199001198973 minus 1198781199001198974 (23)



Δ119865119865119877119909 = 119865119865119909 minus 119865119865119887119890119904119905119865119865119887119890119904119905 (24)




else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018










else 119878119900119897119899119890119908119909 = 119878119900119897119909End

End
















119894 = 1 119873(25)


119894 = 1 119873(26)




119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018











119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



Else 119878119900119897119899119890119908119909 = 119878119900119897119909End


119878119900119897119909 = 119878119900119897119909 if 119865119865119909 lt 119865119865119899119890119908119909119878119900119897119899119890119908119909 119890119897119904119890 119909 = 1 119873119901119904

119865119865119909 = 119865119865119909 if 119865119865119909 le 119865119865119899119890119908119909119865119865119899119890119908119909 119900119905ℎ119890119903119908119894119904119890 119909 = 1 119873119901119904



119875119894max


119894 = 1 119873(27)

119875119894min


119894 = 1 119873(28)









119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018











119875119894 =


119894 = 2 119873 amp 119896 = 1 119899119894

(31)




where

Δ = (11986101 minus 1 + 2 119873sum119894=2

1198611119894119875119899)2 minus 411986111(119875119863 minus 119873sum

119894=2

119875119894+ 11986100 + 119873sum

119894=2

1198610119894119875119894 + 119873sum119894=2

119873sum119895=2

119875119894119861119894119895119875119895) amp Δ ge 0(33)



Δ1198751x =

0 if 1198751min le 1198751x le 1198751max


(34)



Δ1198751x

=


(35)



Δ119878119877119909 =

0 if119873sum119894=1

119878119894119909 ge 119878119877119878119877 minus 119873sum119894=1

119878119894119909 119890119897119904119890 (36)



119865119865119909 = 119873sum119894=1

119865119894 (119875119894119909) + 119870 (Δ119878119877119909)2 + 119870 (Δ1198751119909)2 (37)


119878119900119897119909 =


119909 = 1 119873119901 (38)
























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018





























Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









Select parameters









Stop

Start



P1xP1x

P1x

P1xP1x

P1x

P1xP1x

P1x

Sol＜ＭＮ

Sol＜ＭＮ

G = 1

G = Gmax G = G + 1









11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018











11 3 350 400 450 500 550 600 650 700 10 15 0912 6 600 650 700 750 800 850 900 950 10 25 0913 3 150 10 15 0914 6 700 10 25 09

2 SFS - 2 110 15000 10 1000 09

3 SFS EoVLP -

31 3 850 5 20 0532 13 1800 10 5000 0933 13 2520 10 5000 0634 40 2500 10 6000 0935 80 4100 20 6000 09

4 SFS PPZ RPR 41 60 10600 10 1200 0942 90 15900 10 1500 09

5 SFS and RRL PPZ PL 5 15 2630 20 400 05

6 MFS EoVLP -61 80 21600 10 4000 0162 160 43200 10 6000 0163 320 86400 10 9000 01










MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018











MCSA [58] 82188585 83521956 10 100CCSA 823427 823427 5 20ICSA 823407 823407 5 20



CEP [1] 1804821 29496 - -035Ghz-1128 GBFEP [1] 18018 16811 - -






















41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018























41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018











41



42

































0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018




























0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018












0 100 200 300 400 500 600 700 800 900 1000Iteration

197

198

199

2

201

202

203

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









0 5 10 15 20 25 30 35 40 45 50Run

19795

198

19805

1981

19815

1982

19825

1983

19835

Fuel

cost

($)

CCSAICSA

times105


0 2 4 6 8 10 12 14 16 18 20Iteration

8234

8236

8238

8240

8242

8244

8246

8248

8250

8252

Fitn

ess F

unct

ion

($)

CCSAICSA






0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









0 5 10 15 20 25 30 35 40 45 50Run

8234

82342

82344

82346

82348

8235

82352

82354

82356

82358

8236

Fuel

cost

($)

CCSAICSA


0 1000 2000 3000 4000 5000 6000Iteration

242

244

246

248

25

252

254

256

Fitn

ess F

unct

ion

($)

CCSAICSA

times105





0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









0 5 10 15 20 25 30 35 40 45 50Run

2428

243

2432

2434

2436

2438

244

2442

Fuel

cost

($)

CCSAICSA

times105


0 50 100 150 200 250 300 350 400Iteration

327

328

329

33

331

332

333

334

335

336

337

Fitn

ess F

unct

ion

($)

CCSAICSA

times104








0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018












0 5 10 15 20 25 30 35 40 45 50Run

32705

3271

32715

3272

32725

3273

Fuel

cost

($)

CCSA

times104















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018


















6 Conclusions




119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018










119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW) 119894 119875119894 (MW)1 24 23 689 45 6599972 67 70 89 8216672 24002 24 349991 46 6173078 68 70 90 8817483 24009 25 3999924 47 54001 69 70 91 5644084 24003 26 400 48 54015 70 3599917 92 1005 24003 27 4999948 49 84001 71 3999986 93 4406 40003 28 4999999 50 8401 72 400 94 49999997 40001 29 1999718 51 84024 73 1044979 95 6008 4 30 100 52 120011 74 191601 96 47348289 40001 31 100018 53 120001 75 90 97 3600410 640006 32 199875 54 120005 76 499996 98 3611 629079 33 80 55 12 77 1600246 99 4400712 368567 34 250 56 252 78 2966528 100 4400613 571595 35 3599919 57 252083 79 1756282 101 1000114 25001 36 3999946 58 350001 80 967143 102 10001315 250004 37 399782 59 350388 81 100008 103 20001316 25 38 699974 60 450023 82 12 104 20001817 1549936 39 99994 61 450005 83 202773 105 40003518 1549968 40 1199999 62 450002 84 1998833 106 4019 1549954 41 1576538 63 1849144 85 324744 107 50000820 1549989 42 2199983 64 1849969 86 4399977 108 30000521 689 43 4399987 65 18498 87 143477 109 40000822 689004 44 5599991 66 1849961 88 225542 110 200006


119894 119875119894 (MW)1 30024682 4003 1497532Cost ($h) 8234083





Appendix


Nomenclature











119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018

















119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018










119894 Pi (MW) 119894 Pi (MW) 119894 Pi (MW)1 45495546 6 460 11 802 380 7 430 12 803 130 8 8594226 13 2508314 130 9 4329983 14 1561975 170 10 160 15 157882




Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018









Table 26 Continued




Data Availability




References








































































Journal of












Journal of







Volume 2018






Volume 2018










































































Journal of












Journal of







Volume 2018






Volume 2018










































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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