adaptive robust method for dynamic economic emission dispatch … · 2019. 7. 30. · complexity...

Research ArticleAdaptive Robust Method for Dynamic Economic EmissionDispatch Incorporating Renewable Energy and Energy Storage

Tingli Cheng 1 Minyou Chen 1 Yingxiang Wang 1 Bo Li 1

Muhammad Arshad Shehzad Hassan 1 Tao Chen2 and Ruilin Xu2

1State Key Laboratory of Power Transmission Equipment amp System Security and New Technology School of Electrical EngineeringChongqing University Chongqing 400044 China2State Grid Chongqing Electric Power Research Institute Chongqing 400021 China

Correspondence should be addressed to Tingli Cheng tingli cheng126com

Received 16 March 2018 Accepted 10 April 2018 Published 26 June 2018

Academic Editor Liang Hu

Copyright copy 2018 Tingli Cheng et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In association with the development of intermittent renewable energy generation (REG) dynamic multiobjective dispatch facesmore challenges for power system operation due to significant REG uncertainty To tackle the problems a day-ahead optimaldispatch problem incorporating energy storage (ES) is formulated and solved based on a robust multiobjective optimizationmethod In the proposed model dynamic multistage ES and generator dispatch patterns are optimized to reduce the cost andemissions Specifically strong constraints of the chargingdischarging behaviors of the ES in the space-time domain are consideredto prolong its lifetime Additionally an adaptive robust model based on minimax multiobjective optimization is formulated tofind optimal dispatch solutions adapted to uncertain REG changes Moreover an effective optimization algorithm namely thehybrid multiobjective Particle Swarm Optimization and Teaching Learning Based Optimization (PSO-TLBO) is employed toseek an optimal Pareto front of the proposed dispatch model This approach has been tested on power system integrated withwind power and ES Numerical results reveal that the robust multiobjective dispatch model successfully meets the demands ofobtaining solutions when wind power uncertainty is considered Meanwhile the comparison results demonstrate the competitiveperformance of the PSO-TLBO method in solving the proposed dispatch problems

1 Introduction

The traditional economic dispatchmethod aims to determinea generation schedule that minimizes total generation costwhile being subjected to generator and system operatinglimits [1ndash3] With increasing concerns of environmentalpollution harmful emissions such as SO2 NO119909 CO andCO2 have attracted widespread attention Therefore simul-taneously minimizing total generation cost and emissionshas become a crucial research topic In some studies theseparate economic and environmental dispatch problemsare converted to an economic and emission dispatch (EED)problem formulating a multiobjective optimization issue [3ndash5] The EED can provide a set of dispatch solutions fordecision marker to choose from with different preferencesin economic and emission Many methods and approacheshave been proposed to solve the multiobjective EED problem

[6ndash13] In the initial studies [6ndash8] researchers attempted totransform the EED problem into a single-objective modelbased on a linear combination of different objectives as aweighted sum However this method cannot obtain Paretofront solutions in a single run and does not address how toselect weighting factors for the system operators Moreoverthese approaches fail to achieve optimal solutions when theobjective functions are not convex or when the objectivefunctions have a discontinuous variable space To addressthese problems several artificial intelligent techniques haveshown good performance An improved Hopfield neuralnetwork (NN) in [9] and an improved back-propagation NNin [10] were reported to optimize EED problems Howeverthese approaches are readily trapped within the local opti-mum since the achieved results are not sufficiently accurateOn the other hand multiobjective evolutionary algorithmshave been successfully applied to solve the EED problem

HindawiComplexityVolume 2018 Article ID 2517987 13 pageshttpsdoiorg10115520182517987

2 Complexity

[3 11 12] In [3] a novel modified adaptive 120579-particle swarmoptimization is presented to investigate the multiobjectiveEEDThe fuzzy IFTHEN rule is used to self-adaptively adjustthe cognitive and social parameters in the PSO to avoid theevolution stagnation for continuous generation Reference[11] presents a multiobjective differential evolution algorithmfor EED problems In [12] a robust EED model based on aneffective function is built to handle wind power uncertaintiesCarbon capture and storage are considered in the modelformulation to reduce carbon emission and a multiobjectivebacterial colony chemotaxis method is adopted to solve theproposed robust EED model However none of these papersconsider energy storage (ES) integration

Due to the long-term fossil fuel energy crisis and therecent Paris agreement tasks to reduce fossil fuel dependencyin traditional power generation significant renewable energygeneration (REG) for example wind power photovoltaicenergy and tidal energy is integrated into multiple levelsof the power grid The uncertainty and variability of thepower production provided by REG raise the risk of systeminstability particularly in distribution networks To solve thisproblem the integration of ES is an effective solution toalleviate the negative effects caused by the intermittent natureof REG According to reviews [14ndash16] ES plays a vital rolein smoothing the production of REG improving the REGpenetration level and peak shaving ensuring system reliabil-ity and increasing the economic and environmental benefitsof the power system [17] Improper dispatch scheduling ofgeneration may lead to undesired cost increases or systemreliability deterioration Typical ES has dynamic power andenergy formulations in which the constraints are coupledalong the time and space domainThe operation of ES in onetime step affects the evolving operation in the other time slotsTherefore a multistage EED integrated with ES is a strongcoupling and dynamic problem in the space-time domain[18 19]

In past studies some economic or EED dispatch ap-proaches are presented First some literature has focusedon economic ES dispatch or EED focused on single-interval(1 hour) dispatch [12 20 21] In this setup the economicor emission objectives in one time interval are optimizedand then shifted to the next time interval Second in day-ahead scheduling problems current research is focused oninvestigating the composite economic cost with ES withinmultiperiods [22ndash25] Multiobjective multistage dispatchoptimization problems with ES are rarely considered Inaddition the prediction error in day-ahead REG prediction isinevitable in real cases which should be carefully taken intoconsideration in the EED process At the most time chanceconstraint is used to ensure that the loss of load probabilityis lower than predefined risk level to deal with uncertainREG problems [26 27] However it is difficult to obtain thedistribution function of REG

To the best of the authorsrsquo knowledge very few research-ers emphasized the study on ES scheduling in dynamicmultiperiod EED while simultaneously dealing with theuncertainty of intermittent REG [17] Motivated by the aboveconcerns this paper proposes a dynamic EED approachto schedule the output of ES together with controllable

generations over the next 24-hour time span The main con-tributions of this paper are organized as follows (i) To addressthe uncertainties of REG robust multiobjective optimizationis proposed based on minimax optimization approach (ii)The EED dispatch problem with REG prediction error isconverted to a robust multiobjective dispatch model (iii)Aiming at effectively solving the proposed model a novelmultiobjective PSO-TLBO is proposed and employed to seekthe Pareto solutions

The organization of this paper is decomposed into sevensections Section 2 introduces the energy storage modelfollowed by the day-ahead generators and ES dispatch prob-lem formulation presented in Section 3 Further the robustmultiobjective day-ahead dispatch model is explained inSection 4 Section 5 proposes the multiobjective algorithmto solve the given complex problem The numerical casestudy and conclusions are then presented in Sections 6 and7 respectively

2 Energy Storage Model

ES is connected to the gird by converters capable of flexiblyoperating in charge and discharge modes [25 28] It istherefore promising for ES to handle the intermittent REGintegration problem and to improve the flexibility of energydispatch However ES has significant dynamic and evolvingpower and energy characteristics leading to a batch of techni-cal limits with time-evolving decision variables particularlyin multistage scheduling operation [22] Details of the ESgeneral model and its dynamic constraints are expressed asfollows [29]

ES chargedischarge power limits are as follows

minus119875ES119894 le 119875ch119894 (119905) le 00 le 119875dis119894 (119905) le 119875ES119894 (1)

where 119875ch119894(119905) and 119875dis119894(119905) denote the charge and dischargepower of the 119894th ES at the hour 119905 with the power output ofES being positive when discharging and vice versa 119875ES119894 isthe power capacity of 119894th ES

The state of charge (SOC) is a crucial state variable in theprocess of ES schedule and operation

When the ES is charging (119875(119905) lt 0)119878oc119894 (119905 + 1) = 119878oc119894 (119905) minus 120578119888119875 (119905) Δ119905119864max (2)

When the ES is discharging (119875(119905) gt 0)119878oc119894 (119905 + 1) = 119878oc119894 (119905) minus 119875 (119905) Δ119905120578119863119864max (3)

When the ES is idling (119875(119905) = 0)119878oc119894 (119905 + 1) = 119878oc119894 (119905) (4)

where 119878oc119894(119905) is the SOC of the 119894th ES at the hour 119905 119875(119905) is thecharge or discharge power at the hour 119905 120578119888 is the chargingefficiency 120578119863 is the discharging efficiency Δ119905 is the scheduleinterval and 119864max is the ES energy capacity

Complexity 3

Economic emission dispatch model

Load 1 Load 2 Load n

Generator 1 Energy storageGenerator Ngmiddot middot middot

middot middot middot

Figure 1 Scheme of economic emission dispatch problem

The ES SOC limits are as follows

119878ocmin le 119878oc119894 (119905) le 119878ocmax (5)

where 119878oc119894(119905) is the SOC of the 119894th ES at the hour 119905 and 119878ocminand 119878ocmax are the minimum and maximum limits of theSOC respectively

The initial SOC of each ES is the same at the beginning ofeach day where 119879 stands for all the time slots [30]

119878oc119894 (119879) = 119878oc119894 (0) (6)

To prolong the lifetime of the ES it is assumed that itis only eligible for one charge-discharge cycle per day foroptimal operation [31 32] Meanwhile in this paper ES isused for peak shaving It stores energy during off-peak andreturn the power during peak-load hours

3 Problem Formulation

The day-ahead dispatch performs the generation dispatchevery 24 hours scheduling all generators and ES units thenext day in hourly time slots [33 34] The scheme of EEDmodel is illustrated in Figure 1 This is a typical dynamicmultiperiod decision problemThe decision variables at eachhour influence the decisions at the remaining hours Thedynamic multiobjective dispatch problem is described asfollows

31 Variables The input variables of the dispatch problem arethe REG power load demand and ES parameters over theplanning period The decision (control) variables set 119875 is thepower outputs of all the controllable units

119875 = [1198751 (1) sdot sdot sdot 1198751 (119879) sdot sdot sdot 119875119894 (119905) sdot sdot sdot 119875119873 (119905) sdot sdot sdot 119875119873 (119879)] (7)

where 119875119894(119905) stands for the power generation of the 119894th unit atthe time slot 119905 119873 is the number of control variables and 119879presents the total number of time slots

32 Objective Function The overall objective function of theday-ahead dispatch problem includes the total generationcost of the whole system 1198911 and the pollutant emissions 1198912

min119891 = (1198911 1198912) (8)

The controllable generations are the fuel-based gener-ators The operational costs of renewable generation and

ES within the short-term dispatch optimization horizonunder strong constraints mentioned above are ignored [22]Therefore the first objective 1198911 is the accumulated economiccost of all the conventional generatorsThese generation costsare normally modeled using a quadratic function of theirpower outputs [27] The economic objective is minimizedover the scheduling period for example 24 hours of the nextday which can be described as follows

1198911 = 119879sum119905=1

(119873119866sum119894=1

(1198861198941198752119894 (119905) + 119887119894119875119894 (119905) + 119888119894)) (9)

The environmental objective is to minimize the totalemission pollutants of all generators as much as possibleThese emission costs are also formulated as a quadraticfunction of their power outputs [27] and the emissions of theES are taken to be zeroThe objective function1198912 is expressedas follows

1198912 = 119879sum119905=1

(119873119866sum119894=1

(1205721198941198752119894 (119905) + 120573119894119875119894 (119905) + 120574119894)) (10)

In (9) and (10) 119879 is the total number of time slots fornext day which is 24 hours in this paper 119873119866 is the numberof conventional generators 119886119894 119887119894 119888119894 are the cost coefficientsof the generators and 120572119894 120573119894 120574119894 are the emission coefficients ofthe generators

33 Technical Constraints To maintain the power grid oper-ation a set of equation and in-equation constraints should beconsideredThe system constraints include the overall systemconstraints and the ES constraints The ES constraints areshown in Section 2 and the overall system constraints areexpressed as follows(1) Power flow balance constraint is

119873119866sum119894=1

119875119894 (119905) = 119897sum119894=1

119871 119894 (119905) + 119875loss (119905) minus 119875REG (119905) minus 119873ESsum119894=1

119875119894ES (119905) (11)

119875loss (119905) = 119873119866sum119894=1

119873119866sum119895=1

119875119894 (119905) 119861119894119895119875119895 (119905) (12)

where 119875REG(119905) 119875119894(119905) and 119875119894ES(119905) are the active power injectedby the REG 119894th controllable generator and 119894th ES at time119905 respectively 119873119866 119873ES and 119897 are the total number ofcontrollable generator energy storage and load respectively119861 is the power loss coefficient(2) Generation output limits are

119875119894min le 119875119894 (119905) le 119875119894max (119894 = 1 2 119873119866) (13)

(3) Generators ramp up and down limits are

119875119894 (119905) minus 119875119894 (119905 minus 1) le UR119894119875119894 (119905 minus 1) minus 119875119894 (119905) le DR119894

(119894 = 1 2 119873119866) (14)

4 Complexity

where119875119894min and119875119894max represent theminimumandmaximumpower output of 119894th generator respectively UR119894 and DR119894are the ramp up and ramp down limits for 119894th generatorrespectively

4 Robust Multiobjective Day-Ahead Dispatch

It is well known that renewable energy is intermittent anduncertain The error in REG prediction is inevitable for anyprediction technique Hence dealing with the uncertainty ofrenewable energy is a key issue

41Worst-Case BasedOptimization Therobust optimizationwith the worst-case scenario is one of the most commonapproaches The worst-case optimization in a minimizationproblem can be formulated as follows

min119909isin119883

max119901isin119875

119891 (119909 119901) (15)

where 119909 is the decision variable over a feasible region 119883 and119901 is an uncertain parameter in the uncertainty set 119875For environmental uncertainties the function values of119891(119909) become 119865(119909) [35 36]

119865 (119909) = 119891 (119909 119910 119901) 119901 = 119888 + 120575 (16)

where 119909 = [1199091 119909119899] are the decision variables and 119910 =[1199101 119910119898] are the configuration variables defined by 119910 =120593(119909) 119888 is the nominal value of the environmental parameterand 120575 is the change condition Once a decision variable 119909 isimplemented the configuration variable 119910 can be termed asthe solutionrsquos adaptability The value of 119910 will be determinedaccording to uncertain environmental parameter The aboverobust optimizationwith theworst-casemethod is focused onthe best decision to worst-case performance and to minimizethe risk of severe consequences

42 Robust Multiobjective Optimization Most robust opti-mal dispatch problems considering REG uncertainty aresingle-objective models or are converted from the multiob-jective EED problems to a single objective They ignore theimportance of Pareto optimality which could provide multi-ple optimal solutions for operators in the dispatch decision-making process Robust optimization means to search forthe solution that is the least sensitive to perturbations ofthe decision variables in its neighborhood [12] The REGforecast error is unavoidable resulting in the possibility thatthe optimal deterministic solutions may not be practicallysuitable in reality On the other hand stochastic methodsbased on the probability model have difficulty obtainingaccurate probability functions In this paper we utilize theminimax multiobjective optimization method based on theworse case in day-ahead generator and ES dispatch problems

We assume a robust multiobjective optimization prob-lem

min119865 (119883) = (1198911 (119883 119884 1198751015840) 119891119896 (119883 119884 1198751015840)) 1198751015840119894 = 119875 + 120575119894 119883 isin Ω 119884 isin Ω119910 (17)

where 119883 119884 and 1198751015840 are the decision configuration anduncertain input variables respectively 119891119896 is the 119896th objectivefunction 120575 = (1205751 1205752 120575119899) denotes the perturbation pointsand Ω and Ω119910 are the feasible space of 119883 and 119884

The following robust multiobjective optimizationapproach is defined in (18) where a robust multiobjectivesolution 119883lowast is defined as the Pareto-optimal solution withrespect to a 120575-neighborhood

min119865 (119883) = (1198911Ro (119883) 1198912Ro (119883) 119891119896Ro (119883)) (18)

Subject to 119883 isin Ω where Ω is the feasible region of thedecision variables the function 119891119896Ro(119883) is defined as follows

119891119896Ro (119883) = max (119891119896 (119883 119884 119875 + 1205751) sdot sdot sdot 119891119896 (119883 119884 119875 + 120575119894)sdot sdot sdot 119891119896 (119883 119884 119875 + 120575119899)) (19)

where 119899 denotes the sampling point number in the perturba-tion domain and 120575119894 is the 119894th perturbation sampling point

43 Robust EED Dispatch In the day-ahead predispatchstage the intermittent renewable power such as wind usuallydeviates from its forecasted value The forecast error of anREG exists in any prediction models In view of this a robustEED dispatch model is developed to adapt to the uncertaintyof wind power (WP) and handle its prediction error whenspinning reserve is not considered In order to balance thegenerated power with the power demand and power lossone of generators is chosen as the slack generator withoutput limits According to (11) and (12) the power outputof the slack generator 1198751(119905) can be calculated by solving thefollowing quadratic equation [37]

0= 1198611111987512 (119905) + (2119873119892sum

119894=2

1198611119894119875119894 (119905) minus 1) 1198751 (119905)

+ (119875119863 (119905) + 119873119892sum119894=2

119873119892sum119894=2

119875119894 (119905) 119861119894119895119875119895 (119905) minus 119873119892sum119894=2

119875119894 (119905))

119875119863 (119905) = 119897sum119894=1

119871 119894 (119905) minus 119875REG (119905) minus 119873ESsum119894=1

119875119894ES (119905)

(20)

According to (20) once the other controlled units isdetermined the output of the slack generator 1198751(119905) is tem-porarily fixed 1198751(119905) is regarded as a configuration variableThen the adaptive adjustment of the slack generator out-put associated with other fixed control variables allowsthe robust dispatch solutions to follow other operationalconditions In other words only the output of the slackgenerator 1198751(119905) will be adjusted with robust optimal dis-patch solutions according to the realization of different REGoutput

Complexity 5

Sampling 119867 schemes (119875WP(119905)) for each time slot (119905 = 1 2 24) for WP generation with certain error by LHS119875WPmin(119905) = max(min(119875WP(119905)) 0 119875WP(119905) minus 196120575(119905))119875WPmax(119905) = min(max(119875WP(119905)) 119875WP(119905) + 196120575(119905) 119875WPcap)119875WP(119905) = max(min(119875WP(119905) 119875WPmax(119905)) 119875WPmin(119905))The first extreme scenario

WP(1) = ⋃119905isin119879

119875WPmin(119905) (119879 = 1 2 24)The second extreme scenario

WP(2) = ⋃119905isin119879

119875WPmax(119905) (119879 = 1 2 24)Other 119899 minus 2 stochastic scenariosFor 119894 = 3 119899

Randomly select 119875WPstochastic(119905) from samples of 119875WP(119905)WP(119894) = ⋃

119905isin119879

119875WPstochastic(119905) (119879 = 1 2 24)End for

Algorithm 1 24-hour WP scenarios selection

The original EED dispatch objective functions that min-imize cost and emissions in (9) and (10) are transformed inthe robust model which can be expressed as follows

1198911RO (119875) = max (1198911 (119875 119875WP + 1205751) 1198911 (119875 119875WP + 1205752)sdot sdot sdot 1198911 (119875 119875WP + 120575119899)) = max (1198911 (119875 119875WP (120575)))

120575 isin 1205751 1205752 sdot sdot sdot 120575119899 1198912RO (119875) = max (1198912 (119875 119875WP + 1205751) 1198912 (119875 119875WP + 1205752)

sdot sdot sdot 1198912 (119875 119875WP + 120575119899)) = max (1198912 (119875 119875WP (120575))) 120575 isin 1205751 1205752 sdot sdot sdot 120575119899

(21)

where 119875 is the power output of controllable power units and119875WP(120575) is the uncertain set of WPThe robust day-ahead EED dispatch model is expressed

as follows

min (1198911RO 1198912RO) (22)

The constraints are formulated as (1)ndash(6) and (11)ndash(14)

44 Uncertainty Wind Power To further analyze the uncer-tainty of WP the actual WP output at time 119905 (119875WP(119905)) limitscan be described as follows

0 le 119875WP (119905) le 119875WPcap (23)

Commonly the minimum output of WP is 0 and themaximum is defined as the installed capacity

In the robust optimization the uncertainty has a directimpact on its performance WP generations follow the Gaus-sian distribution with the predicted value as themean119875WP(119905)and prediction error 120575(119905) as the standard variance A 95percentage of 119875WP(119905) samples fall in the range [119875WP(119905) minus196120575(119905) 119875WP(119905) + 196120575(119905)] To generate typical scenariosLatin hypercube sampling (LHS) has been utilized to generateWP uncertain dates each time slot [38] To efficiently capture

1198911RO and 1198912RO with uncertainty in 24-hour time slots in (21)two extreme scenarios as well as several stochastic scenariosare selected using LHS To ensure robust optimal solutionsthe method to obtain 24-hour WP scenarios is shown asAlgorithm 1

5 Multiobjective PSO-TLBO toSolve the Problem

The robust dispatch problem is formulated as a mathematicmodel and the task in this section is to rapidly and effectivelyseek a balance between the total economic and emissionbenefits over all intervals during the next day We adopt anovel multiobjective metaheuristic based method called thePSO-TLBO to solve the problem

51 Multiobjective PSO-TLBO To find the optimal solutionsin the aforementioned multistage day-ahead dispatch prob-lem an effective and efficient multiobjective optimizationmethod is required It is noted that PSO is a popular tech-nique but lacks sufficient exchange within different parti-cles Its premature convergence limits the performance ofthe MOPSO [39] The multiobjective Teaching LearningBased Optimization (TLBO) can achieve the satisfactoryperformance on some benchmark functions with respectto convergence rate and calculation time but sometimesweak in diversity and distribution especially in nonconvexPareto functions and multimodal function [40] MeanwhileEED dispatch problem has lots of equation and in-equationconstraints When energy storages with strong couplingconstraints incorporated into EED EED problem becomesmore complex The current multiobjective PSO or TLBOcannot simultaneously capture satisfactory optimal solutionswith respect to good convergence and well-spread goals forsuch a complex EED problem To capture better dynamic androbust EED schemes the effective PSO update is employedfor the global search and gives a good direction to the optimalregion In addition the TLBO algorithm is activated peri-odically to improve the exploration and exploitation ability

6 Complexity

of the PSO Meanwhile a circular crowded sorting (CCS)strategy is proposed to truncate the nondominated solutionsarchive The multiobjective PSO-TLBO is implemented in[41]

52 Constraints Handling To satisfy the power balance in(11) one generator is assumed to be in slack generator opera-tion and the limit constraints will be handled using the staticpenalty method [37] The constraints of other generators andES outputs will be handed using their boundaries If thedimension of the particle moves outside of its boundaries itwill be assigned the value of the corresponding boundaryTheconstraint of the ES chargedischarge power will be handledby the following equations

119875ch119894 (119905) = max(119875ch119894 (119905) minus119875ES119894 (119878ocmin minus 119878oc119894 (119905))times 119864max

120578119888 ) 119875dis119894 (119905) = min (119875dis119894 (119905) 119875ES119894 (119878ocmax minus 119878oc119894 (119905))

times 119864max times 120578119863)

(24)

The slack generator limits generator ramp limits and SOClevel in the end constraint will be handled using the staticpenalty method with the penalty function belowThe penaltyfunction will be expressed as (25) when the constraints areviolated

119891V = 119862 119873sum119894=1

120575119894 (25)

where 119873 is the total number of constraints handled usingthe static penalty method and 119862 is the penalty coefficient(119862 = 11198645 in subsequent simulation of this paper) 120575 = 0 ifthere are no constraint violations in the given variable and120575 = 1 if a constraint is violated for a given variable Thepenalty function will be added to the objective function andthe infeasible particles have a lower chance to be selected

53 Solution Framework of the Dispatch Problem Theoutlineof the multiobjective PSO-TLBO to solve the robust day-ahead EED problem is presented as follows

Step 1 Choose the appropriate parameters of the multiobjec-tive PSO-TLBO such as the population size the maximumiteration numbers inertia weight and social coefficient

Step 2 Initialize all particles in the swarm randomly andensure that the positions of the particles are in the problemspace

Step 3 Obtain the REG prediction data during the 24 hoursof the next day Obtain the robust day-ahead EED modelfrom Section 4 Update the particle positions according tothemultiobjective PSO-TLBO from Section 51 Compute thefitness (1198911Ro 1198912Ro) (objective functions) of all particles in theswarm

Table 1 Algorithm parameters

Size Population 100 archive 50Iterations Maximum 200

OtherParameters

TV-MOPSO [42] PSO-TLBO [41](1198631 = 1 1198632 = 1 INV = 7)1199081 = 07 1199082 = 04 1198881119894 = 25 1198881119891 = 05 1198882119894 = 05 1198882119891 =25

4 8 12 16 20 240Time (hour)

40

45

50

55

60

65

70

75

Win

d po

wer

(MW

)

Figure 2 Predicted wind power for the 24 hours next day

Step 4 Judge the constraints of the control and state variablesIf constraints are violated handle the constraints with thereferences from Section 52

Step 5 Iterative process continues if the maximum iterationis not reached Otherwise output the optimal Pareto solu-tions

6 Case Study

The six generators bus system is used for the case studyThe algorithm parameters are listed in Table 1 The detailedgenerator limit and the economic and emission coefficients[27] are shown in Table 2 Generator G1 is assumed to be aslack generator A wind farm is connected and its predictionpower production for the 24 hours next day is shown inFigure 2Theprediction load information in the next 24 hoursis illustrated in Figure 3 It is assumed that load predictionis accurate The storage is incorporated with a capacity of200MWh and maximum chargedischarge power is 80MWThe charge and discharge efficiencies of ESS are 92 It isassumed that the initial SOC is 05 before day-ahead dispatchand the limit of the SOC is [02 1]

To verify the efficiency of the robust EED optimization inthe dispatch problem with ES three cases are tested

Case 1 The deterministic EED with ES test without WPprediction error is considered

Case 2 The robust EED with ES test with different WPprediction errors is considered

Case 3 Repeat Cases 1 and 2 without ES respectively

Complexity 7

Table 2 Generator parameters

Generators G1 G2 G3 G4 G5 G6119875min (MW) 10 15 15 15 15 15119875max (MW) 200 170 150 180 130 120UR (MWh) 60 40 40 40 40 40DR (MWh) 60 40 40 40 40 40Cost119886 ($(MW)2 h) 000375 00175 00625 000834 0025 0025119887 ($MWh) 2 175 1 325 3 3119888 ($h) 0 0 0 0 0 0Emission120572 (lb(MW)2 h) 00649 005638 004586 003380 004586 005151120573 (lbMWh) minus005554 minus006047 minus005094 minus003550 minus005094 minus005555120574 (lbh) 004091 002543 004258 005326 004258 006131

4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)

Figure 3 Predicted load demand for the 24 hours next day

61 Simulation Results of Cases 1 and 2 For comparison thePareto fronts obtained from the deterministic EED withoutWP prediction error in Case 1 and withWP prediction errorsof 10 15 and 20 in Case 2 both of which use the PSO-TLBO are shown in Figure 4 We can see from Figure 4 thatthere is a shift in the Pareto front in Case 2 from the Paretofront in Case 1 without the WP prediction error This meansthat the acquisition of the robustness is at the expense of agreater generation cost and more emissions It is clear that astheWPprediction error increases the gap between the robustPareto fronts in Case 2 and original front in Case 1 enlargesThis reveals that more accurate WP prediction techniquesresult in lower costs and emissions

The aforementioned results can be understood as followsIn Case 1 the output of the generator and ES is controlledto satisfy the power consumption and to maintain thesystem reliability while ensuring that all equations and in-equation constraints are satisfied In the robust EED withWP prediction in Case 2 the methods attempt to find thebest Pareto fronts under the worst-case problem for exampleto minimize the maximum objective values in (21) In thissituation the generators and ES dispatch have to remarkablychange their output when the WP shows dramatic changesCompared with the deterministic EED in Case 1 the robust

times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)

without WP errorwith 10 WP errorwith 15 WP error

with 20 WP error

Figure 4 Pareto fronts obtained from the PSO-TLBO inCases 1 and2

EED has to schedule with more costs and emissions whendealing with the uncertainty of the WP

62 Robustness Analysis To obtain the extreme and stochas-tic scenarios in uncertainty sets we use the LHS method togenerate 1000 variables in each time slot Figures 5(a) 5(b)and 5(c) represent the boxplots of theWP values at each hourwith errors of 10 15 and 20 respectively Fifty deter-ministic solutions (DS) in Case 1 and fifty robust solutions(RS) in Case 2 (WP error of 10) shown in Figure 4 areused for the robustness analysis As generator G1 is assumedto be a slack generator its output is determined by otherdecision variables and WP output The adaptive adjustmentof the slack generator allows the dispatch solutions to adaptto otherWP scenarios Twenty new stochastic scenarios fromthe boxplots with a 10 WP error in Figure 5(a) are selectedfor the case study Figure 6 shows the Boxplot for functionvalues of DS and RS under worse case on twenty 24-hourWPstochastic scenarios It is clearly that most 1198911 and 1198912 values of

8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)

Figure 5 Boxplot for the wind power at each hour WP error of (a) 10 (b) 15 and (c) 20

DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)

Figure 6 Boxplot for results of deterministic solutions (DS) and robust solutions (RS) (a) 1198911 (cost) (b) 1198912 (emission)

DS are larger than the penalty coefficient 119862 (11198645) Howeverthe 1198911 and 1198912 values of the Pareto front in Figure 4 with a10WP error are smaller than the penalty coefficient119862 (11198645)This means that most DS are not all feasible simultaneouslyfor twenty 24-hourWP stochastic scenarios and punished bythe penalty when dealing with the dispatch problem with a10 WP error Most of RS in Figure 6 are feasible and lesssensitive to WP changes It is proved that RS have a betterrobustness to uncertain WP

63 Generators and ESDispatch Analysis Thegenerators andES dispatch of the compromise solutions [11] in Case 1 andin the scenario of Case 2 (10 WP error) are given as theexamples in Tables 3 and 4 respectively All generator outputsand ES at each time period properly satisfy the output limitsThe functional values are smaller than the penalty coefficient119862 (11198645) which reveals that no constraints are violated Thismeans that the constraints have been properly handled

The results of the ES dispatch analyses are reported inthis part The compromise solutions from the PSO-TLBO inTables 3 and 4 are listed for the ES SOC analysis Figure 7reports the daily SOC profiles during the entire dispatchprocess Under the SOC profiles with relevant ES dispatchpatterns in Figure 7 ES helps to successfully ensure that allsystem operation constraints are satisfied during all intervalsand to improve the economic and environmental benefits Asforeseeable in Figure 7 the SOC varies within the admissible

range between 02 and 1 The ES works in charging modefollowed by discharging mode and is then charged to thesame SOC level as the initial SOC The ES nearly followsthis same pattern each day The ES has an average of onecomplete charge-discharge cycle every day Therefore theES constraints in each period and over the entire dispatchperiod are properly satisfied

64 ES Benefits Analysis ES in this paper is used for simul-taneously improving flexibility of energy dispatch and peakshaving To test the benefits of ES the deterministic dispatchwithout WP error and the robust dispatch with a 15 WPerror but without ES in Case 3 are shown in this part ThePareto solutions of EED problem with ES and without ESare compared in Figures 8(a) and 8(b) respectively It isobserved that the Pareto solutions without ES are dominatedby the Pareto solutions with ES The results reveal the testwithout ES performance worse in minimizing 1198911 and 1198912compared with that with ES in both cases This is becausethe dispatch problem becomes more flexible and generatorswith lower cost and emission can be better utilized whenES is incorporated Also peak shaving characteristics ofcompromise dispatch solutions in Cases 1 and 2 are shownin Table 5 with respect to the distance ratio between peak tovalley in (26) It is clear in Table 5 that the demands at thepeak hours decrease and shift to the valley periods when ESis incorporated

Complexity 9

Table 3 Dispatch of the compromise solution in Case 1 (1198911 = 508 times 104 $ 1198912 = 581 times 104 lb)Time (hour) G1 G2 G3 G4 G5 G6 ES1 5327 3085 4148 2848 269 2444 minus12612 4588 4627 2649 2302 3886 4225 minus9723 3899 4565 3256 396 4532 4252 minus8334 4078 4511 6494 39 6048 3859 minus9575 8832 6612 7225 5366 6338 6915 minus54336 972 5628 5975 719 7263 6473 minus4867 10661 8618 8387 10592 6447 7374 minus9288 12706 11634 9311 10054 7332 8463 13419 12486 10906 8942 10596 8669 9463 297710 12041 10249 7025 14136 947 8739 85211 13658 10387 8966 12937 9885 7982 241512 1359 8226 6889 11308 9282 9407 300213 12822 1048 9364 10504 8443 8842 311714 13236 8437 803 11545 7772 8726 02815 11521 953 8349 10653 7627 8303 01916 9146 10348 786 10701 99 8127 00517 1187 1031 7109 1279 9272 8086 018 15422 10919 8557 10239 9299 9943 019 13911 11171 8838 12777 9815 10093 020 14049 9868 7861 12396 9334 9099 96421 13755 10158 7177 1129 10339 8306 minus34522 12281 6801 896 9344 9603 5754 minus183323 10069 6417 7242 9062 7574 7617 minus284224 9336 7935 5195 8301 5145 6156 minus1501

4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(a) Without WP error

4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error

Figure 7 ES SOC at different scenarios in Cases 1 and 2 with 10WP error

peak to valley = 100 times (119889max (119905) minus 119889min (119905)119889max (119905) ) (26)

65 Comparison of PSO-TLBO with TV-MOPSO To investi-gate the performance of the PSO-TLBOalgorithm in themul-tiobjective day-ahead dispatch problem comparison simula-tions for Cases 1 and 2 are studied One of the most popularand effectivemultiobjective PSOalgorithms the TV-MOPSO

[42] is used for the comparison The typical Pareto frontsusing two algorithms on the aforementioned cases are shownin Figure 9 We observe from the subfigures in Figure 9that most of the solutions obtained with the TV-MOPSOare dominated by those achieved with the PSO-TLBO It isobserved that the TV-MOPSO performs worse when findingthe whole Pareto front The multiobjective PSO-TLBO hasbeen found to have better convergence and better spreadsolutions compared with the TV-MOPSO in both cases This

10 Complexity

Table 4 Dispatch of compromise solution in Case 2 with 10WP error (1198911 = 540 times 104 $ 1198912 = 589 times 104 lb)Time (hour) G1 G2 G3 G4 G5 G6 ES1 6744 3108 2813 3932 3669 2667 minus26512 4661 6489 4054 2651 304 441 minus3093 3848 5598 3654 5233 5171 4129 minus30644 7774 4707 3383 4097 4474 5078 minus6845 7270 7097 5029 7159 6251 5034 minus11636 7861 7509 4084 9395 6051 8107 minus2177 8101 7253 7583 12263 9247 7824 08 11236 8584 10078 12358 9426 8311 20169 11964 11573 9014 13142 9007 8942 164410 12553 10733 9192 12256 8418 8498 200111 13745 1175 10357 13107 8456 8713 1412 11297 11129 10312 11969 7522 8797 197313 12149 11147 9676 12098 8595 8591 277214 10981 9387 931 9469 9494 852 197615 11329 784 8593 12217 8809 8479 24116 11815 10218 7563 10819 7971 9043 01117 10740 11908 1075 9757 922 8485 00418 13797 11981 11421 12128 7975 851 00219 15010 11449 8182 13486 9127 10744 02720 12353 10315 8878 14077 9599 899 65421 10454 11251 9579 11886 9805 9886 minus98722 9375 8926 9622 9031 7908 7669 minus51523 6187 7443 9408 1038 9016 7167 minus328724 6548 6708 7202 9089 6711 7149 minus1733

with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error

Figure 8 Pareto fronts obtained in scenarios with ES and without ES from the PSO-TLBO

is because that hybrid PSO-TLBO search strategy and CCSstrategy in multiobjective PSO-TLBO algorithm promote thepopulation diversityThey are helpful in improving the searchability The performance of multiobjective PSO-TLBO hasbeen improved by comparing with single PSO evolutionHence the PSO-TLBO performs well in solving day-aheadEED dispatch problems

7 Conclusion

The increasing development and penetration of REG area major challenge for transmission and distribution net-works ES presents the potential to supportively optimizesystem operations with REG and reduce other excessiveparticipations to grid operation such as voltage and VAR

Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)

PSO-TLBO without WP errorTV-MOPSO without WP errorPSO-TLBO with 10 WP errorTV-MOPSO with 10 WP error

(a) Without WP error in Case 1 and 10WP error in Case 2

times104

times10465753 54 55 56 58 5952515

f1 Cost ($)

PSO-TLBO with 15 WP errorTV-MOPSO with 15 WP errorPSO-TLBO with 20 WP errorTV-MOPSO with 20 WP error

58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)

(b) With 15WP error and with 20WP error in Case 2

Figure 9 Pareto fronts obtained using the PSO-TLBO and TV-MOPSO in Cases 1 and 2

Table 5 Peak to valley in different scenarios

Scenarios Peak to valleyWithout ES 6667Case 1 without WP error 6492Case 2 with 10WP error 6297Case 2 with 15WP error 6381Case 2 with 20WP error 6296

regulation In this paper based on conventional EED expe-riences we combine a robust multiobjective optimizationmethod and an EED problem formulation to solve the day-ahead ES dispatch problemwith REG uncertaintyThe robustoptimal dispatch solutions are adaptive to uncertain REGand only one generator (slack generator) production needsto be adjusted The numerical study explores the differentWP prediction errors on the impact of the robust objectivefunction valuesThe results show that a higherWPpredictionerror will lead to more economic cost and greater emissionsMoreover the ES dispatch patterns provide ancillary servicessuch as peak shaving to provide economic emission andtechnical benefits The simulation case results also revealthat the multiobjective PSO-TLBO performs well in solvingrobust EED dispatch problems compared with TV-MOPSO

In future research the complex dispatch tasks requiremore objective functions that could be added such asthe REG penetration rate and carbon emission especiallytechnical objective functionsTheproposed robust generatorsand ES dispatch method can be verified in real powersystemwith a high penetration of REG and REG curtailmentcan be considered Moreover the increasing number ofES deployments to active distribution networks will be anincreasingly complex problemThese will be dealt with in thefuture improvements

Conflicts of Interest

The authors declare that there are no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Grant no 51177177 Nationalldquo111rdquo Project of China under Grant no B08036 and theScience and Technology Project of State Grid Corporationof China under Grant no 5220001600V6 (Key Technologyof the Optimal Allocation and Control of Distributed EnergyStorage Systems in Energy Internet)

References

[1] H Zhang D Yue and X Xie ldquoRobust Optimization forDynamic Economic Dispatch under Wind Power Uncertaintywith Different Levels of Uncertainty Budgetrdquo IEEE Access vol4 pp 7633ndash7644 2016

[2] X Li J Lai and R Tang ldquoA Hybrid Constraints HANdlingStrategy for MULticonstrained MULtiobjective OptimizationProblem of MICrogrid EconomicalENVironmental DispatchrdquoComplexity Art ID 6249432 12 pages 2017

[3] T Niknam and H Doagou-Mojarrad ldquoMultiobjective eco-nomicemission dispatch by multiobjective 120579-particle swarmoptimisationrdquo IETGeneration TransmissionampDistribution vol6 no 5 pp 363ndash377 2012

[4] N A Khan G A S Sidhu and F Gao ldquoOptimizing CombinedEmission Economic Dispatch for Solar Integrated Power Sys-temsrdquo IEEE Access vol 4 pp 3340ndash3348 2016

[5] M Zheng X Wang C J Meinrenken and Y Ding ldquoEconomicand environmental benefits of coordinating dispatch amongdistributed electricity storagerdquoApplied Energy vol 210 pp 842ndash855 2018

12 Complexity

[6] J S Dhillon S C Parti and D P Kothari ldquoStochastic economicemission load dispatchrdquoElectric Power SystemsResearch vol 26no 3 pp 179ndash186 1993

[7] J Y Fan and L Zhang ldquoReal-time economic dispatch with lineflow and emission constraints using quadratic programmingrdquoIEEE Transactions on Power Systems vol 13 no 2 pp 320ndash3251998

[8] J X Xu C S Chang andXWWang ldquoConstrainedmultiobjec-tive global optimisation of longitudinal interconnected powersystem by genetic algorithmrdquo IEE ProceedingsmdashGenerationTransmission amp Distribution vol 143 no 5 pp 435ndash446 1996

[9] T D King M E El-Hawary and F El-Hawary ldquoOptimalenvironmental dispatching of electric power systems via animproved hopfield neural network modelrdquo IEEE Transactionson Power Systems vol 10 no 3 pp 1559ndash1565 1995

[10] P S Kulkarni A G Kothari D P K ldquoCombined Economic andEmission Dispatch Using Improved Backpropagation NeuralNetworkrdquo Electric Machines amp Power Systems vol 28 no 1 pp31ndash44 2010

[11] L H Wu Y N Wang X F Yuan and S W Zhou ldquoEnvi-ronmentaleconomic power dispatch problem using multi-objective differential evolution algorithmrdquo Electric Power Sys-tems Research vol 80 no 9 pp 1171ndash1181 2010

[12] Z Lu S He T Feng X Li X Guo and X Sun ldquoRobusteconomicemission dispatch considering wind power uncer-tainties and flexible operation of carbon capture and storagerdquoInternational Journal of Electrical Power amp Energy Systems vol63 pp 285ndash292 2014

[13] M S Li Q H Wu T Y Ji and H Rao ldquoStochastic multi-objective optimization for economic-emission dispatch withuncertain wind power and distributed loadsrdquo Electric PowerSystems Research vol 116 pp 367ndash373 2014

[14] H Zhao Q Wu S Hu H Xu and C N Rasmussen ldquoReviewof energy storage system for wind power integration supportrdquoApplied Energy vol 137 pp 545ndash553 2015

[15] X Luo JWangM Dooner and J Clarke ldquoOverview of currentdevelopment in electrical energy storage technologies andthe application potential in power system operationrdquo AppliedEnergy vol 137 pp 511ndash536 2015

[16] K W Wee S S Choi and D M Vilathgamuwa ldquoDesignof a least-cost battery-supercapacitor energy storage systemfor realizing dispatchable wind powerrdquo IEEE Transactions onSustainable Energy vol 4 no 3 pp 786ndash796 2013

[17] A A Moghaddam A Seifi and T Niknam ldquoMulti-operationmanagement of a typical micro-grids using Particle SwarmOptimization A comparative studyrdquo Renewable amp SustainableEnergy Reviews vol 16 no 2 pp 1268ndash1281 2012

[18] K Liu K Li andC Zhang ldquoConstrained generalized predictivecontrol of battery charging process based on a coupled thermo-electric modelrdquo Journal of Power Sources vol 347 pp 145ndash1582017

[19] K Liu K Li Z Yang C Zhang and J Deng ldquoAn advancedLithium-ion battery optimal charging strategy based on acoupled thermoelectric modelrdquo Electrochimica Acta vol 225pp 330ndash344 2017

[20] Y Xu and Z Li ldquoDistributed Optimal Resource ManagementBased on the Consensus Algorithm in a Microgridrdquo IEEETransactions on Industrial Electronics vol 62 no 4 pp 2584ndash2592 2015

[21] H Ma Z Yang P You and M Fei ldquoMulti-objective biogeog-raphy-based optimization for dynamic economic emission load

dispatch considering plug-in electric vehicles chargingrdquo Energyvol 135 pp 101ndash111 2017

[22] M Mahmoodi P Shamsi and B Fahimi ldquoEconomic dispatchof a hybrid microgrid with distributed energy storagerdquo IEEETransactions on Smart Grid vol 6 no 6 pp 2607ndash2614 2015

[23] H Chen R Zhang G Li L Bai and F Li ldquoEconomic dispatchof wind integrated power systems with energy storage consid-ering composite operating costsrdquo IET Generation Transmissionamp Distribution vol 10 no 5 pp 1294ndash1303 2016

[24] R Rigo-Mariani B Sareni X Roboam and C Turpin ldquoOpti-mal power dispatching strategies in smart-microgrids withstoragerdquo Renewable amp Sustainable Energy Reviews vol 40 pp649ndash658 2014

[25] N Yan Z X Xing W Li and B Zhang ldquoEconomic DispatchApplication of Power System with Energy Storage SystemsrdquoIEEE Transactions on Applied Superconductivity vol 26 no 72016

[26] Q Wang J Wang and Y Guan ldquoStochastic unit commitmentwith uncertain demand responserdquo IEEE Transactions on PowerSystems vol 28 no 1 pp 562-563 2013

[27] M H Alham M Elshahed D K Ibrahim and E E D AboEl Zahab ldquoA dynamic economic emission dispatch consideringwind power uncertainty incorporating energy storage systemand demand side managementrdquo Journal of Renewable Energyvol 96 pp 800ndash811 2016

[28] J Hetzer D C Yu and K Bhattarai ldquoAn economic dispatchmodel incorporating wind powerrdquo IEEE Transactions on EnergyConversion vol 23 no 2 pp 603ndash611 2008

[29] C Chen S Duan T Cai B Liu and G Hu ldquoOptimal allocationand economic analysis of energy storage system in microgridsrdquoIEEE Transactions on Power Electronics vol 26 no 10 articleno 43 pp 2762ndash2773 2011

[30] G Carpinelli G Celli SMocci FMottola F Pilo andD ProtoldquoOptimal integration of distributed energy storage devices insmart gridsrdquo IEEE Transactions on Smart Grid vol 4 no 2 pp985ndash995 2013

[31] A Gabash and P Li ldquoFlexible optimal operation of batterystorage systems for energy supply networksrdquo IEEE Transactionson Power Systems vol 28 no 3 pp 2788ndash2797 2013

[32] A Gabash and P Li ldquoActive-reactive optimal power flow indistribution networks with embedded generation and batterystoragerdquo IEEE Transactions on Power Systems vol 27 no 4 pp2026ndash2035 2012

[33] Z Li W Wu B Zhang and B Wang ldquoAdjustable Robust Real-Time Power Dispatch with Large-Scale Wind Power Integra-tionrdquo IEEE Transactions on Sustainable Energy vol 6 no 2 pp357ndash368 2015

[34] R MA K LI X LI and Z QIN ldquoAn economic and low-carbon day-ahead Pareto-optimal scheduling for wind farmintegrated power systems with demand responserdquo Journal ofModern Power Systems and Clean Energy vol 3 no 3 pp 393ndash401 2015

[35] Y S Ong P B Nair and K Y Lum ldquoMax-min surrogate-assisted evolutionary algorithm for robust designrdquo IEEE Trans-actions on Evolutionary Computation vol 10 no 4 pp 392ndash4042006

[36] S Salomon G Avigad P J Fleming and R C PurshouseldquoActive robust optimization Enhancing robustness to uncertainenvironmentsrdquo IEEE Transactions on Cybernetics vol 44 no 11pp 2221ndash2231 2014

Complexity 13

[37] K Mason J Duggan and E Howley ldquoMulti-objective dynamiceconomic emission dispatch using particle swarm optimisationvariantsrdquo Neurocomputing vol 270 pp 188ndash197 2017

[38] Z Yang K Li Q Niu and Y Xue ldquoA comprehensive studyof economic unit commitment of power systems integratingvarious renewable generations and plug-in electric vehiclesrdquoEnergy Conversion andManagement vol 132 pp 460ndash481 2017

[39] J J Liang A K Qin P N Suganthan and S Baskar ldquoCom-prehensive learning particle swarm optimizer for global opti-mization of multimodal functionsrdquo IEEE Transactions on Evo-lutionary Computation vol 10 no 3 pp 281ndash295 2006

[40] F Zou LWang X Hei D Chen and BWang ldquoMulti-objectiveoptimization using teaching-learning-based optimization algo-rithmrdquo Engineering Applications of Artificial Intelligence vol 26no 4 pp 1291ndash1300 2013

[41] T Cheng M Chen P J Fleming Z Yang and S Gan ldquoA novelhybrid teaching learning based multi-objective particle swarmoptimizationrdquo Neurocomputing vol 222 pp 11ndash25 2017

[42] P K Tripathi S Bandyopadhyay and S K Pal ldquoMulti-objectiveparticle swarm optimization with time variant inertia andacceleration coefficientsrdquo Information Sciences vol 177 no 22pp 5033ndash5049 2007

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Submit your manuscripts atwwwhindawicom

2 Complexity

[3 11 12] In [3] a novel modified adaptive 120579-particle swarmoptimization is presented to investigate the multiobjectiveEEDThe fuzzy IFTHEN rule is used to self-adaptively adjustthe cognitive and social parameters in the PSO to avoid theevolution stagnation for continuous generation Reference[11] presents a multiobjective differential evolution algorithmfor EED problems In [12] a robust EED model based on aneffective function is built to handle wind power uncertaintiesCarbon capture and storage are considered in the modelformulation to reduce carbon emission and a multiobjectivebacterial colony chemotaxis method is adopted to solve theproposed robust EED model However none of these papersconsider energy storage (ES) integration

Due to the long-term fossil fuel energy crisis and therecent Paris agreement tasks to reduce fossil fuel dependencyin traditional power generation significant renewable energygeneration (REG) for example wind power photovoltaicenergy and tidal energy is integrated into multiple levelsof the power grid The uncertainty and variability of thepower production provided by REG raise the risk of systeminstability particularly in distribution networks To solve thisproblem the integration of ES is an effective solution toalleviate the negative effects caused by the intermittent natureof REG According to reviews [14ndash16] ES plays a vital rolein smoothing the production of REG improving the REGpenetration level and peak shaving ensuring system reliabil-ity and increasing the economic and environmental benefitsof the power system [17] Improper dispatch scheduling ofgeneration may lead to undesired cost increases or systemreliability deterioration Typical ES has dynamic power andenergy formulations in which the constraints are coupledalong the time and space domainThe operation of ES in onetime step affects the evolving operation in the other time slotsTherefore a multistage EED integrated with ES is a strongcoupling and dynamic problem in the space-time domain[18 19]

In past studies some economic or EED dispatch ap-proaches are presented First some literature has focusedon economic ES dispatch or EED focused on single-interval(1 hour) dispatch [12 20 21] In this setup the economicor emission objectives in one time interval are optimizedand then shifted to the next time interval Second in day-ahead scheduling problems current research is focused oninvestigating the composite economic cost with ES withinmultiperiods [22ndash25] Multiobjective multistage dispatchoptimization problems with ES are rarely considered Inaddition the prediction error in day-ahead REG prediction isinevitable in real cases which should be carefully taken intoconsideration in the EED process At the most time chanceconstraint is used to ensure that the loss of load probabilityis lower than predefined risk level to deal with uncertainREG problems [26 27] However it is difficult to obtain thedistribution function of REG

To the best of the authorsrsquo knowledge very few research-ers emphasized the study on ES scheduling in dynamicmultiperiod EED while simultaneously dealing with theuncertainty of intermittent REG [17] Motivated by the aboveconcerns this paper proposes a dynamic EED approachto schedule the output of ES together with controllable

generations over the next 24-hour time span The main con-tributions of this paper are organized as follows (i) To addressthe uncertainties of REG robust multiobjective optimizationis proposed based on minimax optimization approach (ii)The EED dispatch problem with REG prediction error isconverted to a robust multiobjective dispatch model (iii)Aiming at effectively solving the proposed model a novelmultiobjective PSO-TLBO is proposed and employed to seekthe Pareto solutions

The organization of this paper is decomposed into sevensections Section 2 introduces the energy storage modelfollowed by the day-ahead generators and ES dispatch prob-lem formulation presented in Section 3 Further the robustmultiobjective day-ahead dispatch model is explained inSection 4 Section 5 proposes the multiobjective algorithmto solve the given complex problem The numerical casestudy and conclusions are then presented in Sections 6 and7 respectively

2 Energy Storage Model

ES is connected to the gird by converters capable of flexiblyoperating in charge and discharge modes [25 28] It istherefore promising for ES to handle the intermittent REGintegration problem and to improve the flexibility of energydispatch However ES has significant dynamic and evolvingpower and energy characteristics leading to a batch of techni-cal limits with time-evolving decision variables particularlyin multistage scheduling operation [22] Details of the ESgeneral model and its dynamic constraints are expressed asfollows [29]

ES chargedischarge power limits are as follows

minus119875ES119894 le 119875ch119894 (119905) le 00 le 119875dis119894 (119905) le 119875ES119894 (1)

where 119875ch119894(119905) and 119875dis119894(119905) denote the charge and dischargepower of the 119894th ES at the hour 119905 with the power output ofES being positive when discharging and vice versa 119875ES119894 isthe power capacity of 119894th ES

The state of charge (SOC) is a crucial state variable in theprocess of ES schedule and operation

When the ES is charging (119875(119905) lt 0)119878oc119894 (119905 + 1) = 119878oc119894 (119905) minus 120578119888119875 (119905) Δ119905119864max (2)

When the ES is discharging (119875(119905) gt 0)119878oc119894 (119905 + 1) = 119878oc119894 (119905) minus 119875 (119905) Δ119905120578119863119864max (3)

When the ES is idling (119875(119905) = 0)119878oc119894 (119905 + 1) = 119878oc119894 (119905) (4)

where 119878oc119894(119905) is the SOC of the 119894th ES at the hour 119905 119875(119905) is thecharge or discharge power at the hour 119905 120578119888 is the chargingefficiency 120578119863 is the discharging efficiency Δ119905 is the scheduleinterval and 119864max is the ES energy capacity

Complexity 3










119878oc119894 (119879) = 119878oc119894 (0) (6)








min119891 = (1198911 1198912) (8)



1198911 = 119879sum119905=1

(119873119866sum119894=1

(1198861198941198752119894 (119905) + 119887119894119875119894 (119905) + 119888119894)) (9)


1198912 = 119879sum119905=1

(119873119866sum119894=1

(1205721198941198752119894 (119905) + 120573119894119875119894 (119905) + 120574119894)) (10)



119873119866sum119894=1

119875119894 (119905) = 119897sum119894=1


119875119894ES (119905) (11)

119875loss (119905) = 119873119866sum119894=1

119873119866sum119895=1

119875119894 (119905) 119861119894119895119875119895 (119905) (12)


119875119894min le 119875119894 (119905) le 119875119894max (119894 = 1 2 119873119866) (13)



(119894 = 1 2 119873119866) (14)

4 Complexity





min119909isin119883

max119901isin119875

119891 (119909 119901) (15)


119865 (119909) = 119891 (119909 119910 119901) 119901 = 119888 + 120575 (16)




min119865 (119883) = (1198911 (119883 119884 1198751015840) 119891119896 (119883 119884 1198751015840)) 1198751015840119894 = 119875 + 120575119894 119883 isin Ω 119884 isin Ω119910 (17)



min119865 (119883) = (1198911Ro (119883) 1198912Ro (119883) 119891119896Ro (119883)) (18)





0= 1198611111987512 (119905) + (2119873119892sum

119894=2

1198611119894119875119894 (119905) minus 1) 1198751 (119905)

+ (119875119863 (119905) + 119873119892sum119894=2

119873119892sum119894=2

119875119894 (119905) 119861119894119895119875119895 (119905) minus 119873119892sum119894=2

119875119894 (119905))

119875119863 (119905) = 119897sum119894=1


119875119894ES (119905)

(20)


Complexity 5


WP(1) = ⋃119905isin119879


WP(2) = ⋃119905isin119879



119905isin119879







(21)


as follows

min (1198911RO 1198912RO) (22)



0 le 119875WP (119905) le 119875WPcap (23)







6 Complexity





times 119864max times 120578119863)

(24)


119891V = 119862 119873sum119894=1

120575119894 (25)








OtherParameters


4 8 12 16 20 240Time (hour)

40

45

50

55

60

65

70

75

Win

d po

wer

(MW

)




6 Case Study






Complexity 7



4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)




times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)


with 20 WP error




8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3










119878oc119894 (119879) = 119878oc119894 (0) (6)








min119891 = (1198911 1198912) (8)



1198911 = 119879sum119905=1

(119873119866sum119894=1

(1198861198941198752119894 (119905) + 119887119894119875119894 (119905) + 119888119894)) (9)


1198912 = 119879sum119905=1

(119873119866sum119894=1

(1205721198941198752119894 (119905) + 120573119894119875119894 (119905) + 120574119894)) (10)



119873119866sum119894=1

119875119894 (119905) = 119897sum119894=1


119875119894ES (119905) (11)

119875loss (119905) = 119873119866sum119894=1

119873119866sum119895=1

119875119894 (119905) 119861119894119895119875119895 (119905) (12)


119875119894min le 119875119894 (119905) le 119875119894max (119894 = 1 2 119873119866) (13)



(119894 = 1 2 119873119866) (14)

4 Complexity





min119909isin119883

max119901isin119875

119891 (119909 119901) (15)


119865 (119909) = 119891 (119909 119910 119901) 119901 = 119888 + 120575 (16)




min119865 (119883) = (1198911 (119883 119884 1198751015840) 119891119896 (119883 119884 1198751015840)) 1198751015840119894 = 119875 + 120575119894 119883 isin Ω 119884 isin Ω119910 (17)



min119865 (119883) = (1198911Ro (119883) 1198912Ro (119883) 119891119896Ro (119883)) (18)





0= 1198611111987512 (119905) + (2119873119892sum

119894=2

1198611119894119875119894 (119905) minus 1) 1198751 (119905)

+ (119875119863 (119905) + 119873119892sum119894=2

119873119892sum119894=2

119875119894 (119905) 119861119894119895119875119895 (119905) minus 119873119892sum119894=2

119875119894 (119905))

119875119863 (119905) = 119897sum119894=1


119875119894ES (119905)

(20)


Complexity 5


WP(1) = ⋃119905isin119879


WP(2) = ⋃119905isin119879



119905isin119879







(21)


as follows

min (1198911RO 1198912RO) (22)



0 le 119875WP (119905) le 119875WPcap (23)







6 Complexity





times 119864max times 120578119863)

(24)


119891V = 119862 119873sum119894=1

120575119894 (25)








OtherParameters


4 8 12 16 20 240Time (hour)

40

45

50

55

60

65

70

75

Win

d po

wer

(MW

)




6 Case Study






Complexity 7



4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)




times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)


with 20 WP error




8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity





min119909isin119883

max119901isin119875

119891 (119909 119901) (15)


119865 (119909) = 119891 (119909 119910 119901) 119901 = 119888 + 120575 (16)




min119865 (119883) = (1198911 (119883 119884 1198751015840) 119891119896 (119883 119884 1198751015840)) 1198751015840119894 = 119875 + 120575119894 119883 isin Ω 119884 isin Ω119910 (17)



min119865 (119883) = (1198911Ro (119883) 1198912Ro (119883) 119891119896Ro (119883)) (18)





0= 1198611111987512 (119905) + (2119873119892sum

119894=2

1198611119894119875119894 (119905) minus 1) 1198751 (119905)

+ (119875119863 (119905) + 119873119892sum119894=2

119873119892sum119894=2

119875119894 (119905) 119861119894119895119875119895 (119905) minus 119873119892sum119894=2

119875119894 (119905))

119875119863 (119905) = 119897sum119894=1


119875119894ES (119905)

(20)


Complexity 5


WP(1) = ⋃119905isin119879


WP(2) = ⋃119905isin119879



119905isin119879







(21)


as follows

min (1198911RO 1198912RO) (22)



0 le 119875WP (119905) le 119875WPcap (23)







6 Complexity





times 119864max times 120578119863)

(24)


119891V = 119862 119873sum119894=1

120575119894 (25)








OtherParameters


4 8 12 16 20 240Time (hour)

40

45

50

55

60

65

70

75

Win

d po

wer

(MW

)




6 Case Study






Complexity 7



4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)




times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)


with 20 WP error




8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5


WP(1) = ⋃119905isin119879


WP(2) = ⋃119905isin119879



119905isin119879







(21)


as follows

min (1198911RO 1198912RO) (22)



0 le 119875WP (119905) le 119875WPcap (23)







6 Complexity





times 119864max times 120578119863)

(24)


119891V = 119862 119873sum119894=1

120575119894 (25)








OtherParameters


4 8 12 16 20 240Time (hour)

40

45

50

55

60

65

70

75

Win

d po

wer

(MW

)




6 Case Study






Complexity 7



4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)




times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)


with 20 WP error




8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity





times 119864max times 120578119863)

(24)


119891V = 119862 119873sum119894=1

120575119894 (25)








OtherParameters


4 8 12 16 20 240Time (hour)

40

45

50

55

60

65

70

75

Win

d po

wer

(MW

)




6 Case Study






Complexity 7



4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)




times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)


with 20 WP error




8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7



4 8 12 16 20 240Time (hour)

200

300

400

500

600

700

800

Load

(MW

)




times104

times104

48 5 52 54 56 5846 6f1 Cost ($)

5

55

6

65

7

75

f2

Emiss

ion

(lb)


with 20 WP error




8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity

40

50

60

70

80

90

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(a)

30405060708090

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(b)

30405060708090

100

Win

d po

wer

(MW

)

31 5 7 9 11 13 15 17 19 21 23

Time (hour)

(c)


DS RS

times105

05

1

15

2

25

3

35

f1

Cos

t ($)

(a)DS RS

times105

05

1

15

2

25

3

35

f2

Emiss

ion

(lb)

(b)







Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC


4 8 12 16 20 240Time (hour)

02

03

04

05

06

07

08

09

1

SOC

(b) With 10WP error





10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








10 Complexity


with ESwithout ES

times104

times10448 5 52 54 56 5846

f1 Cost ($)

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)


with ESwithout ES

times104

times104652 53 54 55 56 57 58 59515

f1 Cost ($)

58

6

62

64

66

68

7

72

74

f2

Emiss

ion

(lb)

(b) With 15WP error



7 Conclusion


Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








Complexity 11

times104

times104

52

54

56

58

6

62

64

66

68

7

f2

Emiss

ion

(lb)

48 5 52 54 56 58 646f1 Cost ($)



times104

times10465753 54 55 56 58 5952515

f1 Cost ($)


58

6

62

64

66

68

7

72

74

76

f2

Emiss

ion

(lb)









Acknowledgments


References






12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








12 Complexity

































Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018








Complexity 13














Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








adaptive robust method for dynamic economic emission dispatch … · 2019. 7. 30. · complexity...

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