Electrical Power and Energy Systems 63 (2014) 285–292

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Robust economic/emission dispatch considering wind poweruncertainties and flexible operation of carbon capture and storage

http://dx.doi.org/10.1016/j.ijepes.2014.05.0640142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +86 0335 8387565.E-mail addresses: zhglu@ysu.edu.cn (Z. Lu), ysuheshoulong@126.com (S. He).

Zhigang Lu a,⇑, Shoulong He a,b, Tao Feng a, Xueping Li a, Xiaoqiang Guo a, Xiaofeng Sun a

a Key Lab of Power Electronics for Energy Conservation and Motor Drive of Hebei Province, Yanshan University, Qinhuangdao, Hebei 066004, Chinab State Grid Jibei Sanhe Power Supply Co. Ltd., Sanhe Hebei 065200, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 6 September 2013Received in revised form 20 May 2014Accepted 27 May 2014

Keywords:Robust economic/emission dispatchCarbon capture and storageFlexible operationWind power uncertaintiesLatin hypercube sampling

With increasing wind farm development, solutions of Economic/Emission Power Dispatch (EED) arebecoming more difficult to meet the demand of both optimality and robustness because of wind poweruncertainties. In this paper, a Robust Economic/Emission Dispatch (REED) model based on effectivefunction is built to deal with wind power uncertainties and Latin hypercube sampling (LHS) method isemployed to improve the calculation precision of effective function. As carbon capture and storage(CCS) plays an important role in reducing carbon emission, the impact of CCS, which operates in flexiblemode, on EED problem is also investigated. Multi-objective bacterial colony chemotaxis (MOBCC) isadopted to solve the REED problem. Finally, tests of the proposed method are carried out in the IEEE30-bus test system. Results demonstrate that the REED model can meet the demand of obtaining robustsolutions in the presence of wind power uncertainties and flexible operation of CCS has the advantage ofdealing with different carbon reduction index.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

According to preliminary estimates from the InternationalEnergy Agency (IEA), global carbon dioxide (CO2) emissions fromfossil-fuel combustion reached a record high of 31.6 Giga tons(Gt) in 2011. Coal accounted for 45% of total energy related CO2

emissions. China made the largest contribution to the globalincrease, with its emissions rising by 720 million tons (Mt), or9.3%, primarily due to higher coal consumption [1]. Greenhouseeffect has received considerable attention in the 21st Centuryand carbon emission reduction is inevitable. China is in the phaseof industrialization which determines the huge demand for elec-tricity. The emission content of CO2 from electric power systemaccounted for 38.76% of the total CO2 emission in China [2]. Sothe pollution of the earth’s atmosphere caused by the emissionsfrom thermal power plants is of great concern to power utilitiesand communities in recent years. The increasing public awarenessof the environmental protection and the Clean Air Act Amend-ments of 1990 have forced the power utilities to modify their oper-ational strategies to reduce emissions [3,4]. The transformationfrom traditional Economic Dispatch (ED) to Economic/EmissionDispatch is becoming more and more important.

CCS is one family of technologies that could be used to reduceglobal carbon dioxide emissions significantly. Huaneng BeijingPower Plant, the first CO2 capture industrial scale plant in China,shows the technology is a good option for capturing CO2 from com-mercial thermal power plants [5]. In [6], performances in powerpeak-load shaving scheme and generation output limits of carboncapture power plant were revealed by studying the fundamentalprinciple of CCS technology. Literature [7,8] studied how toscheduling CCS equipment to reduce energy consumption andnetwork loss to meet the request of the emission reduction targets.Based on flexible operation, Chen et al. [9] presented CO2 captureschedule, and bidding strategies in response of volatile powerand carbon prices in a day-ahead energy market and a cap-and-trade carbon emission market. The importance of flexible-operation mechanism in enhancing economic returns and ensuringthe secure operation of power system is also addressed by Chenet al. in [10]. Further studies show that flexible operation of CCScan also be of economic value in being able to provide ancillaryservices [11]. In practice, future large scale deployment ofvariable-output renewables such as wind power and/or inflexiblenuclear power plants may make flexible operation of CCS obliga-tory [11,12]. So far, the characteristic of flexible operation of CCSis rarely studied in EED problem.

Besides CCS, Wind power also plays an important role in reduc-ing CO2 emission. In 2007, the Chinese government announced its

286 Z. Lu et al. / Electrical Power and Energy Systems 63 (2014) 285–292

medium- and long-term plan for renewable energy development,proposing that installed wind power capacity rise to 30 GW by2020. That target was achieved by 2010, ten years ahead of sche-dule. Over the last decade, researchers have made significant effortto evaluate the impact of large scale wind generation on the oper-ations, such as regulation and load following [13]. At the sametime, lots of studies have also been carried out on EED problemincorporating wind energy [14–17]. Ref. [14] derives a closed-formin terms of the incomplete gamma function (IGF) to characterizethe impact of wind power and the effects of wind power onemission control are investigated. In [15], Wind turbine powergeneration is considered to shave the power system load curves.In order to model the random nature of load demand andwind forecast errors, a scenario-based stochastic programmingframework is presented in [16–18].

Traditional EED models [19–22] pursued minimum total emis-sion and minimum total fuel cost by improving the performanceof intelligent optimization algorithms. They ignored the robust-ness of the solution that caused by wind power uncertainty.What’s more, conventional stochastic programming approachneed probability density functions of the uncertain data whichare hard-to-obtain. Considering the above factors, robust optimi-zation (RO) obtains much attention. RO which only requires adeterministic uncertainty set, is another choice to take theuncertainties into account. Ben-Tal and Nemirovski [23–26] madegreat contributions to RO problem in the field of convexoptimization and linear programs. Robust optimization of UnitCommitment (UC) [27] and Economic Dispatch (ED) [28] whichare non-convex and non-linear problem have also obtained muchattention. A two-stage adaptive robust unit commitment model isbuilt in the presence of nodal net injection uncertainty [27]. Therobust model of [28] considered both wind energy and plug-inelectric vehicles (PEV). Two-stage strategy is used to solved theRobust optimization model presented in [27,28], where thesecond-stage problem is to model decision making after thefirst-stage decisions are made and the uncertainty is revealed.Market-clearing procedures for energy markets are also challengedby the growth of stochastic production capacity. Refs. [29–31] takeadaptive robust optimization as an alternative approach to dealwith the impact of wind energy on Electricity Markets.

So far, few researchers emphasized the importance of robustmulti-objective optimization in EED problem. Deb and Guptapresented two different robust multi-objective optimizationprocedures in [32] and extended the concepts for finding robustsolutions in the presence of active constraints in [33]. So this papermainly focuses on the application of robust multi-objective optimi-zation based on intelligent optimization algorithms (IOA) in EEDproblem.

The paper is organized as follows: Section ‘Economic/emissiondispatch model’ describes the deterministic EED model; Sec-tion ‘Robust economic/emission dispatch model’ shows the processof converting the deterministic EED problem into REED problem;Section ‘Simulation results’ gives a case study and Section ‘Conclu-sions’ states the conclusion.

Fig. 1. Characteristic of penalty coefficient curve.

Economic/emission dispatch model

Economic objective function

The economic objective function is given in this section. Theproposed function, based on original EED model, consists of twoparts, namely fuel cost considering the effect of flexible operationof CCS and penalty cost of the wind generation uncertainties whichis represented by the wind forecast errors.

Fuel cost functionA liner function is used to describe the power consumption of

CCS that operating in flexible mode; it can be expressed as (1):

pccsi ¼ pmi þ p�ccsi ð1Þ

where pccsi denotes the ith CCS total consumption of real power, pmi

is the maintain power which is a constant value, p�ccsi is the variablepower when operating in flexible mode.

When the net output power of ith generator is pi, the totaloutput power pgi can be expressed as (2):

pgi ¼ pi þ pccsi ð2Þ

where pccsi is zero when the ith generator is not equipped with CCS.A quadratic function of the generator’s real output power is

used to describe the fuel cost function, considering a power systemwith N generators. The total fuel cost C(pgi) ($/h) can be expressedas (3):

CðpgiÞ ¼XN

i¼1

ðaip2gi þ bipgi þ ciÞ ð3Þ

where pgi denotes the ith generator’s total real power output, ai, bi

and ci are the coefficients of the ith generator’s fuel cost.According to formulas (2) and (3), the fuel cost function can be

expressed as (4)

Cðpi;pccsiÞ ¼XN

i¼1

ðaiðpi þ pccsiÞ2 þ biðpi þ pccsiÞ þ ciÞ ð4Þ

Penalty cost for wind forecast errorsIn order to encourage the development of renewable energy,

The State Grid is asked to accept wind energy as much as possible.Coal-fired power plants should decrease the output when the windenergy is underestimated, which leads to the reduction of coalconsumption and CO2 emission, so the penalty cost should belower. But when the wind energy is overestimated, Coal-firedpower plants should compensate the lack of power, resulting inmore coal consumption and more emission, so the penalty costshould be higher. It can be expressed as (5):

Cw ¼XNw

i¼1

CeDPwi

DPwi�a Dpwij j ð5Þ

where CeDPwi

DPwi�a denotes the variable penalty coefficient and C is aconstant value, Fig. 1 shows the characteristic of Penalty Coefficient

Z. Lu et al. / Electrical Power and Energy Systems 63 (2014) 285–292 287

Curve; DPwi represents the forecast errors, DPwi > 0 means windenergy is underestimated, On the contrary, wind power is overesti-mated, when DPwi = 0, there is no forecast error. a is a parameter toadjust inclination of the penalty coefficient curve. Nw is the numberof wind farms.

Economic objective functionAccording to formulas (3) and (4), the economic objective

function can be expressed as (6):

min fcðpi; pccsiÞ ¼XN

i¼1

Cðpi;pccsiÞ þ Cw ð6Þ

Emission objective function

The objective is to minimize total emission content. In thispaper, the emission of CO2 is considered only. Then the total emis-sion of CO2 (ton/h) caused by N thermal generators can be repre-sented as (7):

min fe pi; pccsið Þ ¼XN

i¼1

E pi;pccsið Þ

¼XN

i¼1

1� pccsi

pccs max;i� ei

!

� ui þ miðpi þ pccsiÞ þwi pi þ pccsið Þ2� �

ð7Þ

where E(pi, pccsi) denotes the ith generator’s emission of CO2, ui, vi

and wi are the ith generator’s emission coefficients. ei [34] repre-sents carbon capture efficient rate of the ith CCS. When a generatoris not equipped with CCS, ei = 0. when a CCS operates in flexiblemode, its efficiency declines, so ei is multiplied by pccsi

pccs max;i, pccsmax,i

is the full output power of ith CCS.

Deterministic economic/emission dispatch model

The bi-objective EED model with constraints can be formulatedas follows:

minðfcðpi; pccsiÞc; feðpi;pccsiÞÞ ð8Þ

Subject to constraints:

(1) Power balance constraint

XN

i¼1

Pi þXNw

j¼1

Pwj ¼ Pload þ Ploss ð9Þ

For a given total real load demand Pload, the system loss Ploss in(9) is a function of active power generation at each generating unit.To calculate system losses, methods based on Kron’s loss formula[35] are used. The transmission losses are expressed as

Ploss ¼XN

i¼1

XN

j¼1

PiBijPj þXN

i¼1

Bi0Pi þ B00 ð10Þ

where Bij, Bi0 and B00 denote the transmission network power loss Bcoefficients.

(2) Unit operating limits constraint

Pi;min � Pgi � Pi;max ð11Þ

where Pi,min and Pi,max are the minimum and maximum power gen-eration limits of the ith unit respectively.

(3) Spinning reserve constraints

XN

i¼1

ðPi;max � PgiÞ �XNw

i¼i

DPwi � g1ðPload þ PlossÞ ð12Þ

XN

i¼1

ðPgi � Pi;minÞ þXNw

i¼1

DPwi � g2ðPload þ PlossÞ ð13Þ

where DPwj is wind forecast error. g1 and g2 denote the coefficientsfor spinning reserve.

Robust economic/emission dispatch model

A robust solution is defined as the one which is less sensitive tothe perturbation of the decision variables in its neighborhood. Thepresent researches on IOA in EED problem mainly focused on find-ing the global optimal frontier or improving the calculation speedof IOA instead of searching the frontier which is the trade-offbetween optimality and robustness. The solution which is optimalmay not practical in reality, robustness determines the practicalapplication. So this paper tries to find the robust Pareto solutionsin EED problem in the presence of wind uncertainties.

Robustness in optimization

We consider a robust multi-objective optimization of the fol-lowing type

min FðX0Þ ¼ ðf1ðX0Þ; � � � ; frðX0ÞÞ ð14Þ

X0 ¼ Xþ d; X0 ;X 2 X

where d = (d1, d2, � � �, dn) denotes the perturbation vector, n is thedimension of the variables, X is the feasible search space.

Robust optimization approaches

One of the main approaches to search robust solutions is to usea mean effective objective function (feff(X)) [36] for optimizationinstead of the original objective function (f(X)) itself. The followingexpression is the definition of robust multi-objective solution [28]:a solution X⁄ is called a robust multi-objective solution if it is thePareto-optimal solution to the following multi-objective minimi-zation problem defined with respect to a d – neighborhood (Bd)

min Feff ðXÞ ¼ ðf eff1 ðXÞ; f

eff2 ðXÞ; � � � ; f eff

r ðXÞÞ ð15Þ

Subject to X 2 X

where feff(X) is defined as follows:

f eff ðXÞ ¼Z þ1

�1f ðX þ dÞpðdÞdd ð16Þ

where p(d) is the continuous density function of d.As p(d) is hard to obtain. Usually Eq. (16) is calculated by Monte

Carlo, it can be expressed as follows:

f eff ðXÞ ¼ 1H

XH

i¼1

f ðX þ diÞ ð17Þ

where H denotes the sampling points in the perturbation domain. di

is the ith sampling point.

Effective objective function calculation

It can be seen from Eq. (18) that the precision of feff(X) will affectthe optimization result, so Latin hypercube sampling [37] isadopted to calculate feff(X), the procedures are as follows:

Step 1: Set the sample size as H;

Table 1Generator cost coefficients and emission coefficients of the IEEE 30-bus system.

NO a b c u v w Pmax Pmin

P1 10 200 100 39.12 �57.65 31.56 1.50 0.05P2 10 150 120 171.73 �184.06 60.83 1.50 0.05P3 20 180 40 57.71 �45.19 21.13 1.50 0.05P4 10 100 60 76.65 �92.07 40.00 1.50 0.05P5 20 180 40 27.46 �19.22 16.06 1.50 0.05P6 10 150 100 20.26 �14.41 15.98 1.50 0.05

Note: All the units related to the active power, i.e., Pi, Pmin and Pmax, are p.u., and thebase value is 100 MW. All the units of u, v and w are (10�3 ton/h).

Fig. 2. Comparison of the Pareto fronts obtained by REED and EED for test case 1and case 2.

288 Z. Lu et al. / Electrical Power and Energy Systems 63 (2014) 285–292

Step 2: Divide the perturbation domain of each variable intoexactly H equal intervals;Step 3: Generate the Latin hypercube matrix A which is H � n (nis the numbers of variables), each column is a random permuta-tion of the sequence of integers 1, 2, . . ., H;Step 4: Each column of the table corresponds to a variable, eachrow to a sample. By this way H samples are generated;Step 5: Calculate the corresponding objective values using the Hsamples;Step 6: Calculate feff(X) based on Eq. (17);

Robust Economic/Emission Dispatch (REED) model

As we know that all the wind energy should be accepted inChina in order to encourage the development of clean energy, forthe sake of meeting the requirement of power balance constraintwhen considering the forecast errors of wind energy, coal-firedpower plants should decrease the output in case of wind energyis underestimated, but when the forecast wind energy is overesti-mated, coal-fired power plants are requested to increase theiroutput power. So the prediction errors on wind energy have animpact on other Coal-fired power plants [38], then the robustmodel can be expressed as follows:

min fcðpi;pccsiÞ ¼XN

i¼1

Cðpi þ di; pccsiÞ þ Cw ð18Þ

min feðpi;pccsiÞ ¼XN

i¼1

Eðpi þ di;pccsiÞ ð19Þ

Transform the original objective function into mean effectiveobjective function

f effc ðPi; pccsiÞ ¼

1N

XN

i¼1

fcðPi þ di; pccsiÞ ð20Þ

f effe ðPi; pccsiÞ ¼

1N

XN

i¼1

feðPi þ di;pccsiÞ ð21Þ

So the REED problem can be formulated as follows:

minðf effc ðPi; pccsiÞ; f eff

e ðPi; pccsiÞÞ ð22Þ

The constraints of the robust model are formulas (9)–(13).The bacterial colony chemotaxis (BCC) algorithm is a new

colony intelligence optimization algorithm which was introducedby [39]. This novel algorithm considers not only the chemotacticalstrategy but also the communication between the colony mem-bers, and the performance has improved greatly. Multi-objectivebacterial colony chemotaxis (MOBCC) algorithm [40] is used tosolve the EED problem. So this paper adopts MOBCC to solve REEDproblem, the details of MOBCC referring to [40]. As the solutionsobtained by MOBCC are a Pareto frontier, The technique for orderpreference similar to an ideal solution (TOPSIS) which was initiallypresented by Hwang and Yoon [41] is employed to provide thedecision maker with a final solution.

Simulation results

Test system description and cases setup

(1) Test system description

In this section, the proposed REED problem is solved by MOBCCalgorithm in the standard IEEE 30-bus six generators testsystem [42]. The unit of emission objective function have beenchanged from ton/h to $/h by multiplying the CO2 cost constants0.0077 � 103 $/ton [43]. The value of system parameters including

fuel cost coefficients [44] and emission coefficients [45] are givenin Table 1, and the B-coefficients used in [35] are shown as follows:

B¼

0:1382 �0:0299 0:0044 �0:0022 �0:0010 �0:0008�0:0299 0:0487 �0:0025 0:0004 0:0016 0:00410:0044 �0:0025 0:0182 �0:0070 �0:0066 �0:0066�0:0022 0:0004 �0:0070 0:0137 0:0050 0:0033�0:0010 0:0016 �0:0066 0:0050 0:0109 0:0005�0:0008 0:0041 �0:0066 0:0033 0:0005 0:0244

2666666664

3777777775

B0 ¼ �0:0107 0:0060 �0:0017 0:0009 0:0002 0:0030½ �

B00 ¼ 9:8571E� 4

In the tests, settings of the proposed MOBCC algorithm andLatin hypercube sampling are shown as follows:

In all the simulation runs, both of the bacterial colony andarchive size as well as the maximal iterations are fixed at 100.

The strategy parameters T0, b and sc are relevant to the calcula-tion precision e:

T0 ¼ e0:30 � 10�1:73; b ¼ T0 � T�1:540 � 100:60

� �; sc ¼

bT0

� �0:30

� 101:16

The sample size of Latin hypercube sampling is 20.

(1) Cases setup

To demonstrate the effectiveness of the proposed method, thefollowing 5 cases have been considered:

Table 2Comparison of final solutions obtained by REED and EED.

P1 P2 P3 P4 P5 P6 Fuel cost Emission

REED 0.8967 0.5560 0.8459 0.1935 0.0888 0.2575 697.7064 1.5975EED 0.9344 0.5443 0.4929 0.2613 0.2651 0.3503 693.7788 1.2294

Fig. 5. Convergence characteristic of emission objective function obtained by REEDand EED.

Fig. 3. Fronts showing the effect of wind forecast error range on results.

Fig. 4. Convergence characteristic of economic objective function obtained by REEDand EED.

Z. Lu et al. / Electrical Power and Energy Systems 63 (2014) 285–292 289

Case1: Test of solving REED problem considering wind forecasterrors in the IEEE 30-bus system;Case2: Test of solving EED problem without considering windforecast errors in the IEEE 30-bus system;Case3: Test of wind energy prediction error range effect onREED problem in the IEEE 30-bus system;Case4: Test of solving REED problem with CCSs that operatingin flexible mode in the IEEE 30-bus system;Case5: Test of solving REED problem with CCSs that operatingin steady mode in the IEEE 30-bus system;

In all the cases, we set the base value as 100MVA. The total sys-tem load is set to 3.8 p.u. In the test system, only one wind farm is

considered which the output energy is forecasted as 1 p.u. Amongthe six generators, P1 and P2 are equipped with CCSs. The maxi-mum output and the minimum output of CCS are set to 0.3 p.u.and 0.01 p.u which is the maintain power respectively.

Simulation results of case 1 and case 2

For the purpose of comparison, the Pareto fronts obtained byREED and EED are shown in Fig. 2. As we can see from Fig. 2 thatthere is a shift in REED front from the EED front which meansthe acquisition of robustness is at the expense of more fuel cost

Table 3The best solution’s robustness analysis obtained by EED.

Original function Best solution Function values with Wind forecast errors

P1 P2 P3 P4 P5 P6 Functionvalue

5% 10% 15% 5% 10%

Economicobjective

0.3202 0.7389 0.6396 0.5857 0.408 0.1332 632.6716 633.2617 634.4233 636.4959 639.7497 644.3276

Emission objective 1.3974 0.704 0.0503 0.1617 0.0625 0.6651 1.045 1.047259 1.050866 1.056865 1.06461 1.073396

Table 4The best solution’s robustness obtained analysis by REED.

Effective function Best solution Function values with Wind forecast errors

P1 P2 P3 P4 P5 P6 Function value 5% 10% 15% 20% 30%

Economic objective 0.3181 0.7015 0.6502 0.5379 0.4222 0.1967 639.0248 639.2853 640.0953 641.2523 642.8815 644.9249Emission objective 1.295 0.6937 0.1592 0.1743 0.0586 0.626 1.0737 1.0745 1.075531 1.077006 1.07966 1.082992

Fig. 6. Comparison of CCS Operation modes effect on results.

290 Z. Lu et al. / Electrical Power and Energy Systems 63 (2014) 285–292

and more emissions. So how to get the equilibrium betweenrobustness and optimality seems very important if forecast errorsof wind energy are included in the REED model. The final solutionsof REED and EED obtained by TOPSIS are given in Table 2. It can beseen clearly from Table 2 that when robustness is considered in thepresence of wind prediction errors, all generators’ output changegreatly which result in an second-best solution with more fuel costand more emission but an robust solution.

Chart 1. Comparison of robustness between ori

Simulation results of case 3

(1) Error range effect on results

It is clear from Fig. 3 that as wind forecast errors increase, therobust front moves away from the original front. The result revealsthat getting a firm estimation of wind energy cannot only guaran-tee the robustness of the solution, but also economical and lowemissions.

The reason of lower wind uncertainty leads to the lower costcan be expressed as follows:

In traditional economic/emissions dispatch (EED) models, gen-erators of low energy consumption output power as much as pos-sible which are not able to increase the output power any more,and generators of high energy consumption has the lowest outputpower which are not able to decrease the output power. So thegenerators in EED model have to change output power greatlywhen wind energy changes dramatically. Compared with EED, Unitoutput is relatively uniform in the robust economic/emissionsdispatch (REED), though generators of low energy consumptionoutput power is still more than that of generators of high energyconsumption.

(2) Sensitivity analysis

However, we can only note that there is a shift in REED frontfrom the EED front and have no idea about the sensitivity of singleobjective function (economic and/or emission) value to thevariables variation because of the presence of wind forecast errors.In this part, we will verify the robustness of the best solutions

ginal function and mean effective function.

Chart 2. Comparison of robustness between original function and mean effective function.

Z. Lu et al. / Electrical Power and Energy Systems 63 (2014) 285–292 291

obtained by REED through sensitivity analysis to the variablesvariation. The evolutionary processes of REED and EED are showin Figs. 4 and 5. Their best solutions and comparison is summarizedin Tables 3 and 4.

In order to display the above data intuitively, data in Tables 3and 4 are transformed into Charts 1 and 2. It is clearly that the per-centage change of function value obtained by REED is smaller thanthat of function value obtained by EED, which means that the bestsolution obtained by REED is less sensitivity to variables variation.Charts 1 and 2 demonstrate that the performance in robustness ofREED solution is better than that of EED solution. In Chart 1 andChart 2, f represents the original function that used in EED model,and f_eff represents the effective function that used in REED model.

The simulation results of case 4 and case 5

It can be seen from Fig. 6 that the lower part of the red frontierand the whole blue frontier obviously overlapped, meaning thatsteady operation mode is a special case of flexible operation mode.Compared with flexible operation, steady operation costs more butis low emission. So when carbon emission index constraints exist,we can adjust CCS output to meet index, reduce cost and make aplant more profitable.

The upper part of the red frontier and the green frontier coin-cide corresponding CCS standing in no load condition. In this over-lap range, we noticed that the red frontier costs more comparedwith the green one when the emission content is the same. Thatis because the existences of CCS maintain energy.

In the middle part of the red frontier, we can adjust the flexibleoutput of CCS to meet the emission reduction targets. So the selec-tion of the final solution depends on the emission reduction tar-gets. CCS flexible operation mode provides us a more flexiblechoice between cost and emission.

Conclusions

In this paper, we combine robust optimization and multi-objective optimization to establish the Robust Economic/EmissionDispatch (REED) model. The REED model provides a practicalapproach to handle wind uncertainties. The study results showthat the larger uncertainties range we predict, the more cost wewill pay in order to meet the demand of robustness which is nec-essary in practical application. However the robust solutions weget are less sensitive to variables uncertainties, which is of greatimportance in practical power system operations. We also notethat not only cost but also emissions increase in the REED model.CCS provides a better choice for emission reduction. Results showthat steady state operation and system without CCS are two specialcases of flexible operation of CCS. Compared with steady state

operation, there are more advantages of flexible operation of CCS.CCS flexible operation mode provides us a wider range of Pareto-optimal solutions such that the decision makers can be presentedmore flexible and reasonable choices between cost and emission,which is valuable to meet different carbon reduction index.

Acknowledgements

The authors would like to thank the anonymous reviewers fortheir valuable comments. Project 61374098 supported by NationalNatural Science Foundation of China.

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