Energy Conversion and Management 92 (2015) 82–91

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Energy Conversion and Management

journal homepage: www.elsevier .com/locate /enconman

Combined emission economic dispatch of power system including solarphoto voltaic generation

http://dx.doi.org/10.1016/j.enconman.2014.12.0290196-8904/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +92 03315079549.E-mail addresses: anzarmahmood@comsats.edu.pk, anzarmahmood@gmail.com

(A. Mahmood).URL: http://www.njavaid.com/anzar.aspx (A. Mahmood).

Naveed Ahmed Khan a, Ahmed Bilal Awan c, Anzar Mahmood a,⇑, Member IEEE, Sohail Razzaq b,Adnan Zafar a, Guftaar Ahmed Sardar Sidhu a

a EE, COMSATS Institute of Information Technology Islamabad, Pakistanb EE, COMSATS Institute of Information Technology Abbottabad, Pakistanc EE, College of Engineering, Majmaah University, Al-Majmaah, Saudi Arabia

a r t i c l e i n f o

Article history:Received 28 August 2014Accepted 10 December 2014

Keywords:Economic DispatchRenewable energyParticle Swarm OptimizationSolar PV generationCombined Emission Economic DispatchDynamic Emission Economic Dispatch

a b s t r a c t

Reliable and inexpensive electricity provision is one of the significant research objectives since decades.Various Economic Dispatch (ED) methods have been developed in order to address the challenge of con-tinuous and sustainable electricity provision at optimized cost. Rapid escalation of fuel prices, depletionof fossil fuel reserves and environmental concerns have compelled us to incorporate the RenewableEnergy (RE) resources in the energy mix. This paper presents Combined Emission Economic Dispatch(CEED) models developed for a system consisting of multiple Photo Voltaic (PV) plants and thermal units.Based on the nature of decision variables, our proposed model is essentially a Mixed Integer OptimizationProblem (MIOP). Particle Swarm Optimization (PSO) is used to solve the optimization problem for a sce-nario involving six conventional and thirteen PV plants. Two test cases, Combined Static Emission Eco-nomic Dispatch (SCEED) and Combined Dynamic Emission Economic Dispatch (DCEED), have beenconsidered. SCEED is performed for full solar radiation level as well as for reduced radiation level dueto clouds effect. Simulation results have proved the effectiveness of the proposed model.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction and related work

Significant research has been conducted throughout the worldfor development of sustainable, renewable and efficient energysystems in order to meet the requirements of increased populationand to reduce the extensive use of fossil fuels. Increasing energyprices, environmental concerns and rapid depletion of the knownfuel reserves have significantly increased the scope of renewableenergy resources.

The power sector of Pakistan is designed as an interconnectedsystem and heavily relies on conventional sources of generation.This system needs modifications and enhancements in order tomeet the twenty first century requirements. Pakistan’s energymix comprises of almost 67% thermal and 30% hydel resources.According to Pakistan’s energy year book 2012 [1], total generatedelectrical energy in Pakistan during 2010–2011 was 95,365 GW hand share of different sources is: thermal power 64.3%; hydel29.9% and nuclear and imported 5.8%. In thermal power, oil had

the largest share of 35.2% followed by natural gas 29.0% and coal0.1%. On the other hand, the country has a large potential of solarenergy which has been estimated to be around 2900 GW in [2]. In[3], the author discussed the energy scenario of Pakistan andreviewed conventional and Renewable Energy (RE) resources ofthe county in detail. The author has presented the supply, genera-tion and exploitation of available resources in quantitative manner.The paper is focused on RE development projects in the country,recent progress, planning and public sector goals in this area. Onaverage, solar global insolation of 5–7 kW h/m2/day in almost95% areas of Pakistan with persistence factor of over 85% has beenreported in [4,5].

Economic Dispatch (ED) is a vital and most frequent step inpower system operational planning [6]. ED is an optimizationproblem that allocates power to each committed generating unitso as to minimize the total operational cost, subject to constraints.Various constraints include power balance, power limits ofgenerators, prohibited operating zones, ramp rate limits etc.Several optimization techniques with equality and non-equality constraints have been used for ED and reported inliterature [7].

History of ED dates back to 1920 [8]. Up till 1930 optimizationmethods used were the base load method and best point loading.

N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91 83

In early 30s, equal incremental cost method was utilized to achievebetter results [8]. In those days analog computers were used forcomputational effort. First computer for transmission loss penaltyfactor was built up in 1954. By 1955 electronic differential analyzerwas developed. Digital computers were used for ED first time everin 1954 and are being used till date [9]. The authors in [10] havereviewed the techniques of ED used during 1977–1988; optimalpower flow, dynamic dispatch, ED in relation to Automatic Gener-ation Control (AGC) and ED with non-conventional sources havebeen analyzed. Power system consisting of thermal generatorshas been extensively used to evaluate ED problem. Input–outputcost curves of thermal generating units are required for ED. Theinput–output cost curve of a thermal generating unit is obtainedby multiplying cost per unit heat and its input–output heat ratecurve [11]. In modern days multi-valve steam turbines and multi-ple fuel turbines are often used in generating units.

The ED with piecewise quadratic cost function (EDPQ) and EDwith prohibited operating zones (EDPO) are the two non-convexED problems [12]. Valve point effects produce a ripple like nonconvex input–output heat rate curve. Complex constrained ED isaddressed by intelligent methods including Genetic Algorithm(GA), PSO [13,14], Neural Network (NN), Evolutionary Program-ming (EP), Tabu search etc. [15–17]. Kennedy and Eberhart intro-duced PSO in 1995 [18]. In this method, movement of particles isdependent on local and social components of velocity. Moreover,maximum value of velocity, Vmax, is also a significant parameter.Its low value results in local exploitation while a higher valueresults in global exploration. To obtain a better control over localexploitation and global exploration, an inertia factor x is intro-duced in [19].

ED with both cost and emission minimization becomes multi-objective optimization problem and is named as Combined Emis-sion Economic Dispatch (CEED). Using PSO, CEED has been solvedby Selvakumar et al. [20]. Zhao et al. [21] solved bid based ED usingConstriction Factor PSO (CFPSO) and inertia weight. In [22], ahybrid PSO, a combination of PSO and Sequential Quadratic Pro-gramming (SQP), is introduced in order to solve a non-convex con-strained ED problem with valve point effects. In [23], CEED hasbeen solved using a novel PSO scheme taking into account the gen-erator limits and power balance constraints. An improved PSO hasbeen proposed to solve ED problem of hydro-thermal co-ordina-tion in [24]. Authors in [25] have proposed an Enhanced PSO(EPSO) for hydro-thermal scheduling problem which takes intoaccount various constraints such as power balance, hydro and ther-mal generation limit, reservoir storage volume, initial and terminalstorage limit, water balance equation and hydro discharge limit. In[26], PSO has been used to evaluate CEED problem with equalityconstraints handled by novel techniques and multi-objective opti-mization problem converted into a single objective one.

A lot of research on Economic Dispatch (ED) problem has beencarried out during last five years. A few instances are as follows. In[8], a non-convex ED problem has been addressed by various hybridoptimization techniques. The problem has been addressed first bydeveloping an extensible and flexible computational frameworkcalled ‘‘PED Frame’’, used as a platform for the computer implemen-tation of different algorithms under consideration. This frameworkhas been used to implement Genetic Algorithm (GA) based modelsand Hybrid models for ED. In [27], a PSO based technique with con-striction factor (CFPSO) has been proposed for ED with valve pointeffects; CFPSO technique proved to be fast converging. In [28], amulti-objective CEED solution has been proposed by using ArtificialBee Colony (ABC) algorithm. For the solution of the problem, multi-objective CEED has been converted into single-objective CEED byusing penalty factor. In [29], iteration PSO with time varying accel-eration coefficients (IPSO-TVAC) has been proposed for ED withvalve-point effects; Iteration term in velocity equation and time

varying acceleration coefficients improved the performance(searching ability) of PSO technique. In [30], a novel optimizationmethodology has been proposed to solve a large scale non-convexED problem. The proposed approach is based on a hybrid ShuffledDifferential Evolution (SDE) algorithm that combined the benefitsof shuffled frog leaping algorithm and differential evolution. Theproposed algorithm integrated a new differential mutation operatorin order to address the problem of ED.

In [31], Economic Environmental Dispatch (EED) has been car-ried out using one Photo Voltaic (PV) plant and one wind turbine.Authors used Strength Pareto Evolutionary Algorithm (SPEA) andtests have been conducted for an IEEE bus system with 30 nodes,8 machines and 41 lines. Dynamic Economic Emission Dispatch(DEED) model with security constraints has been used for ED in[32]. The authors have carried out their work on a system incorpo-rating three thermal units, two solar PV plants and two wind tur-bines. Authors in [33] have presented modified harmony searchalgorithm to solve Combined Economic and Emission Load Dis-patch (CEELD) problem. Practical constraints of real-world powersystems have been used and the experiments carried out on sevensystems in order to check the validity and behavior of the proposedalgorithm.

This paper presents a Combined Emission Economic Dispatch(CEED) using 13 PV plants and 6 thermal units. Two test cases ofStatic Combined Emission Economic Dispatch (SCEED) andDynamic Combined Emission Economic Dispatch (DCEED) havebeen considered. SCEED is performed for full solar radiation levelas well as for reduced radiation level due to clouds effect whereasDCEED for full radiation only. PSO is used for optimization of theproblem and simulation results have been computed in MATLAB.The proposed model contains multiple solar plants unlike the workdiscussed in [31,32]. Power demand data has been obtained fromIslamabad Electric Supply Company (IESCO) [34].

2. Problem formulation

This section is dedicated for problem formulation of CEED for apower system having thermal and solar PV generations. As men-tioned earlier, an ED problem can be formulated either staticallyor dynamically. The mathematical formulation for both cases isworked out in the following subsections.

2.1. Mathematical formulation of SCEED with solar power

CEED is a multi-objective optimization problem consisting ofboth economic and environmental dispatch. The CEED problemcan be formulated as:

min G ¼Xn

i¼1

Fi Pið Þ þ Ei Pið Þð Þ ð1Þ

where G is objective function to be minimized, Fi(Pi) represents fuelcost and Ei(Pi) denotes the emissions of ith generating unit. Thisfunction is to be minimized subject to following constraints.

Equality constraint:

Xn

i¼1

Pi

!� PL � Pd ¼ 0 ð2Þ

where Pi is power generated by ith unit, PL represents power loss, Pd

is power demand and n is the total number of generating units.Inequality constraint:

Pimin 6 Pi 6 Pimax ð3Þ

where Pimin and Pimax are the minimum and maximum power limitsof ith generating unit, respectively.

84 N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91

Fi(Pi), Ei(Pi) in Eq. (1) and PL in Eq. (2) can be formulated as fol-lows [35].

Fi Pið Þ ¼ aiP2i þ biPi þ ci þ ei � sin f i � Pimin � Pið Þð Þj j$=h ð4Þ

where ai, bi, ci, ei and fi are fuel cost coefficients of ith generatingunit.

Ei Pið Þ ¼ /iP2i þ biPi þ ci þ ei � exp di � Pið Þ kg=h ð5Þ

where /i, bi, ci, ei and di are emission coefficients of ith generatingunit.

Power losses can be calculated using the equation:

PL ¼Xn

i¼1

Xn

j¼1

PiBijPj ð6Þ

where B is loss coefficient matrix.By introducing a price penalty factor ‘h’, the multi-objective

optimization function presented by Eq. (1) can be converted intosingle objective optimization function. Therefore, by substitutingFi and Ei from Eqs. (4) and (5) respectively and introducing ‘h’ inEq. (1), the CEED objective function can be defined as [28]:

Min FC ¼Xn

i¼1

aiP2i þ biPi þ ci þ ei � sin f i � Pimin � Pið Þð Þj j

�

þhi aiP2i þ biPi þ ci þ ei � exp di � Pið Þ

� �� $

hð7Þ

where hi is given as:

hi ¼aiP

2imax þ biPimax þ ci þ ei � sin f i � Pimin � Pimaxð Þð Þj j/iP

2imax þ biPimax þ ci þ ei � exp di � Pimaxð Þ

ð8Þ

The power generated by a solar plant can be represented as[31]:

Pgs ¼ Prated 1þ Tref � Tamb

� �� /

� �� Si

1000ð9Þ

where Prated is its rated power, Tref is the reference temperature, Tamb

is the ambient temperature, / is temperature coefficient and Si isthe incident solar radiation.

With m solar plants taking part in the dispatch, the solar share(the scheduled solar power) is given as:

Solar share ¼Xm

j¼1

Pgsj � Usj ð10Þ

where Pgsj is power available from jth solar plant and Usj denotesstatus of jth solar plant which is either 1 (ON) or 0 (OFF).

The cost of solar power is represented as follows.

Solar cost ¼Xm

j¼1

PUCostj � Pgsj � Usj ð11Þ

where PUCostj is per unit cost of jth solar plant.Along with cost minimization, another objective is to minimize

the difference between the total available solar power and thesolar share in order to achieve the maximum benefit of solaravailability. Therefore, with solar generation included in thedispatch, the objective function in Eq. (7) becomes:

Min FT ¼Xn

i¼1

aiP2i þ biPi þ ci þ ei � sin f i � Pimin � Pið Þð Þj j

�

þ hi aiP2i þ biPi þ ci þ ei � exp di � Pið Þ

� ��

þXm

j¼1

P:UCostj � Pgsj � Usj þ KsXm

j¼1

Pgsj �Xm

j¼1

Pgsj � Usj

!

ð12Þ

Subject to

Pdþ PL �Xn

i¼1

Pi �Xm

j¼1

Pgsj � Usj ¼ 0 ð13Þ

Pimin 6 Pi 6 Pimax ð14Þ

Xm

j¼1

Pgsj � Usj 6 0:3� Pd ð15Þ

8Usj 2 0;1f g

where Ks is a constant used to make the last term of Eq. (12) com-patible with the other terms. Moreover this allows us to control therelative importance of the difference term compared to other terms.

2.2. Mathematical formulation of dynamic CEED with solar power

DCEED is a more practical case in which it is aimed to allocatepowers to generating units for minimum cost of operation in ascheduling horizon over twenty-four hours a day. The ramp ratelimits are considered in this problem. In case of DCEED problem,the mathematical formulation in Eq. (12) becomes:

Min FT ¼XN

t¼1

Xn

i¼1

ai Pti

� �2 þ biPti þ ci þ ei � sin f i � Pimin � Pt

i

� �� ��� ���

þhi ai Pti

� �2 þ biPti þ ci þ ei � exp di � Pt

i

� �� ��

þXm

j¼1

P:UCostj � Pgsj � Ustj þ Ks

Xm

j¼1

Pgstj �Xm

j¼1

Pgstj � Ust

j

!

ð16Þ

The ramp rate limits determine the range within which the gen-eration of a thermal unit may increase or decrease. The power gen-eration of thermal units is constrained by the ramp rate limits asfollows:

Pti � Pt�1

i 6 URi ð17Þ

Pt�1i � Pt

i 6 DRi ð18Þ

where URi and DRi are the up rate and down rate of ith generatingunit respectively.

Due to ramp rate limits, the minimum and maximum generat-ing limits of thermal units are modified as follows:

max Pimin;URi � Pti

� �6 Pt

i 6 min Pimax; Pt�1i � DRi

� �ð19Þ

The power balance constraint for DCEED can be formulated as:

Pdt þ PtL �

Xn

i¼1

Pti �Xm

j¼1

Pgstj � Ust

j ¼ 0 ð20Þ

The share of solar power at any time, based on 30% upper limit[31], is constrained as:

Xm

j¼1

Pgstj � Ust

j 6 0:3� Pdt ð21Þ

8 Ustj 2 0;1f g

3. Optimization method

It is obvious from the above mentioned problem formulationthat CEED with solar generation is a Mixed Integer OptimizationProblem (MIOP). The decision variables for thermal machines are

Start

Ini�alize all par�cles with random posi�on and velocity vectors

N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91 85

continuous whereas the variables for solar plants are binary. Inorder to solve this problem, PSO for MIOP is used in this work.The PSO for MIOP is essentially a combination of classical PSOand Binary PSO (BPSO).

3.1. Classical PSO

PSO is an optimization technique inspired by bird flocking. Toexplain PSO we can imagine a swarm of birds searching for food.This swarm flocks to search the food randomly in a specific region.All the birds are supposed to be searching for a single piece of food.At any time during search, each bird has a position and velocity.Birds move with knowledge of distance to food but not its exactlocation. Best Strategy planned by birds is to follow a bird nearestto food. PSO makes use of above mentioned scenario to solveoptimization problems. In PSO each bird is known as particlewhich is a possible solution in search space. Number of all particlesin a search space represents size of swarm (or population). Eachparticle has a position in search space, velocity and fitness value.Fitness value for a particle is obtained by objective (fitness)function evaluation.

Following are the steps of PSO procedure.

� Starts with decision of swarm/population size which is problemspecific i.e. it depends on complexicity of problem.� Particles are then initiallized randomly for their positions and

valocities. In an N dimensional optimization problem, the posi-tion of an ith particle is an array of 1 � N. i.e.,

Xi ¼ Xi1;Xi2; . . . . . . . . . ;XiN½ � ð22Þ

Similarly valocity is presented by,

Vi ¼ Vi1;Vi2; . . . . . . . . . ;ViN½ � ð23Þ

� Fitness for each particle is obtained by evaluating the objectivefunction given as:

F ¼ f X ;X ; . . . . . . . . . ;Xð Þ ð24Þ

For each par�cle posi�on “X”, evaluate fitness “f(X)”

First itera�on ?For each par�cle, set pbest equal

to its posi�on “X” i.e.pbest=X

For each par�cle, if f(X) is be�er than f(Pbest) then

Pbest=X

Set best of pbest as gbest

Update velocity and posi�on of each par�cle

Convergence criteria sa�sfied

?

End

Yes

No

Yes

No

Fig. 1. Flow chart of PSO algorithm.

i i1 i2 iN

� Two best positions, known as pbest and gbest, are selected fornext iteration. pbest is personal best position obtained by a par-ticle so far and gbest is global best position among all pbest. Incase of first iteration, pbest is same as randomly initiallizedposition of a particle while in case of next iterations, it is theposition of a particle having best fitness value up to that specificiteration.� Velocity of each particle is updated using following equation.

Vkþ1i ¼ xkVk

i þ C1r1 pbestki � Xk

i

� �þ C2r2 gbestk � Xk

i

� �ð25Þ

where Vki is valocity of ith particle at iteration k. xk is a parameter

known as inertia weight at iteration k. C1 and C2 are accelerationcoefficients. r1 and r2 are random numbers between (0,1). pbestk

i

is best position of ith particle at iteration k. Xki is position of ith

particle at iteration k. gbestk is global best position at iteration kand Vkþ1

i is updated velocity at iteration k + 1.Vk

i which is the velocity of ith particle at kth iteration should bewithin range of its minimum and maximum values, i.e.,

Vmin 6 Vki 6 Vmax ð26Þ

Inertia weight, xk, at each iteration is modified using followingequation.

xk ¼ xmax �xmax �xmin

itermax� k ð27Þ

where xmax is maximum value of inertia weight. xmin isminimum value of inertia weight. itermax is maximum number ofiterations.

� After having value of updated velocity, position of each particleis updated using following equation.

Xkþ1i ¼ Xk

i þ Vkþ1i ð28Þ

� Fitness is evaluated for updated position of each particle; pbestand gbest are obtained for next iteration.� The process is repeated until a convergence criterion is satisfied.

All the above mentioned steps for PSO procedure are depicted inthe flow chart given in Fig. 1.

3.2. Binary PSO (BPSO)

Binary version of PSO is used to optimize the problems havingbinary decision variables i.e. having values either 0 or 1. The stepsof BPSO procedure are same as that of real valued PSO except fol-lowing differences:

� As the variables in BPSO are binary, therefore particles are ini-tialized randomly for their binary positions.

Xi ¼ Xi1;Xi2; . . . . . . . . . ;XiN½ � ð29Þ

8Xi1;Xi2; . . . . . . . . . ;XiN 2 0;1f g

Each dimension of a particle is assigned a binary value with aprobability of 0.5 as following:

Xid ¼ f xð Þ ¼1; if rand > 0:50; otherwise

ð30Þ

where d = 1, 2, . . .. . ., N

Table 2Emission coefficients of thermal generating units [36].

Machine no. F (kg/MW2 h) b (kg/MW h) c (kg/h)

1 0.00419 0.32767 13.859322 0.00419 0.32767 13.859323 0.00683 �0.54551 40.26694 0.00683 �0.54551 40.26695 0.00461 �0.51116 42.895536 0.00461 �0.51116 42.89553

86 N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91

� Position is updated as following:

Xkþ1id ¼ 1; if rand < sigmoid Vkþ1

id

� �0; otherwise

(ð31Þ

The sigmoid function in above equation, used to scale velocitiesbetween 0 and1, is calculated as:

sigmoid Vkþ1id

� �¼ 1

1þ e�Vkþ1id

ð32Þ

Table 3Power ratings and per unit rates of solar plants.

Plant # Prated (MW) Unit rate ($/KW h) [37]

1 20 0.222 25 0.233 25 0.234 30 0.245 30 0.246 35 0.257 35 0.268 40 0.279 40 0.27

10 40 0.27511 40 0.2812 40 0.2813 40 0.28

Table 4Solar radiation, power demand and temperature for 17th day of July 2012.

Time Global solarradiation (W/m2)

Power demand(MW) [34]

Temperature (�C)[38]

1:00 0 965 302:00 0 1142 293:00 0 1177 284:00 0 1198 285:00 5.4 1153 286:00 101 1136 –7:00 253.7 1138 298:00 541.2 1060 319:00 530.4 1155 3310:00 793.9 1244 3411:00 1078 1088 3512:00 1125.6 1240 3613:00 1013.5 1135 3714:00 848.2 1318 3715:00 726.7 1074 3716:00 654 1190 3817:00 392.9 1276 3818:00 215.1 1154 3719:00 38.5 1333 3520:00 0 1322 3421:00 0 1269 3422:00 0 1139 3323:00 0 1202 320:00 0 1291 –

3.3. PSO for MIOP applied to CEED with solar power

Following are the steps to optimize the SCEED problem (Eqs.(12)–(15)) by means of PSO.

� Control parameters are selected.� Initialization of position and velocity for each particle. Each par-

ticle contains continuous as well as binary variables.

Xi ¼ Pi1; Pi2; . . . . . . . . . ; Pin;Usi1;Usi2; . . . . . . ;Usim �

ð33Þ

where Pid and UsiD are the power of dth thermal unit and Dth solarplant in ith particle.

Each Pid is initialized randomly using following equation:

Pid ¼ LBþ rand� UB� LBð Þ ð34Þ

LB and UB represent lower bound and upper bound of thermalunits respectively.

Each UsiD is initialized randomly using Eq. (30).Where D = 1, 2, . . ., m

� Velocity for each particle is initialized between 0 and 1. Fitnessfor each particle in Eq. (12) is evaluated and pbest and gbest areselected.� Velocity is updated using Eq. (25) while positions are updated

using Eqs. (28) and (31) for thermal and solar generatorsrespectively.� Fitness in Eq. (12) is evaluated for each updated position, pbest

and gbest are obtained for next iteration. The process is repeateduntil the convergence criterion is satisfied.

4. Test system

In this section the proposed model has been implemented ontwo test systems in order to investigate both SCEED and DCEED.

4.1. Test system-I

The test system-I includes 6 thermal units and 13 solar plantsand is supposed to be operated in Islamabad region of Pakistan.The data for thermal units has been taken from [36] and ispresented in Tables 1 and 2.

Table 1 presents fuel cost coefficients as well as minimum andmaximum power limits whereas Table 2 contains emission

Table 1Fuel cost coefficients and generating capacities of thermal generating units [36].

Machine no. a ($/MW2 h) B ($/MW h) c ($/h) Pmin (MW) Pmax (MW)

1 0.15247 38.53973 756.79886 10 1252 0.10587 46.15916 451.32513 10 1503 0.02803 40.39655 1049.32513 40 2504 0.03546 38.30553 1243.5311 35 2105 0.02111 36.32782 1658.5696 130 3256 0.01799 38.27041 1356.27041 125 315

Table 5Data of thermal units.

Unit no. a ($/MW2 h) b ($/MW h) c ($/h) a (kg/MW2 h) b (kg/MW h) c (kg/h) Pmax (MW) Pmin (MW) UR (MW/h) DR (MW/h)

1 0.007 7 240 0.00419 0.32767 13.8593 500 100 80 1202 0.0095 10 200 0.00419 0.32767 13.8593 200 50 50 903 0.009 8 220 0.00683 �0.54551 40.2669 300 80 65 1004 0.009 11 200 0.00683 �0.54551 40.2669 150 50 50 905 0.008 10.5 220 0.00461 �0.51116 42.8955 200 50 50 906 0.0075 12 190 0.00461 �0.51116 42.8955 120 50 50 90

Table 6Load demand for 24 h.

Hour 1 2 3 4 5 6 7 8 9 10 11 12Demand (MW) 955 942 953 930 935 963 989 1023 1126 1150 1201 1235

Hour 13 14 15 16 17 18 19 20 21 22 23 24Demand (MW) 1190 1251 1263 1250 1221 1202 1159 1092 1023 984 975 960

Table 7Fitness value obtained in 10 runs for dispatch at t = 10:00 h.

xmin xmax

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

0.5 277,640 274,330 278,700 271,740 – – – –0.4 254,820 262,640 277,550 281,290 254,560 – – –0.3 254,890 272,750 284,720 272,050 258,930 271,670 – –0.2 281,310 286,340 271,130 257,140 262,870 258,120 26,0470 –0.1 309,970 257,520 259,710 266,070 256,210 252,210 257,800 26,1030

Bold shows the minimum value of objective function for the selected parameters.

N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91 87

coefficients for the selected machines. The data for solar plants hasbeen presented in Tables 3 and 4.

Table 3 presents power ratings and per unit costs of differentsolar plants, approximated to be within the range provided in[37]. Table 4 encompasses global solar radiation as well as temper-ature and load profiles of Islamabad for the 17th day of July 2012.In this paper, global solar radiation data has been generated usingGeospatial Toolkit, data related to power demand of Islamabadregion has been taken from IESCO [34] and temperature profilehas been taken from [38]. The 17th day of July has been selectedarbitrarily from the only available demand data of July, 2012.

4.2. Test system-II

The test system-II is also comprised of 6 thermal units and 13solar plants. The data used for solar plants is the same as givenin test system-I whereas the data for thermal units and loaddemand has been taken from [39] and are presented in Tables 5and 6 respectively.

0 500 1000 1500

105.4

105.5

105.6

105.7

105.8

105.9

ITERATION

FITN

ESS

VALU

E

10:00 hrs11:00 hrs12:00 hrs13:00 hrs14:00 hrs15:00 hrs

Fig. 2. Simulation results for full solar radiation.

5. Results

This section shows the results for proposed PSO based MIOPmodel. The above mentioned method was implemented inMATLAB R2013a. The proposed model has been implemented ontwo cases as follows.

Case I: In case I, the proposed model has been implemented ontest system-I to investigate the problem of SCEED.

Case II: In case II, the proposed model has been implemented ontest system-II to investigate the problem of DCEED.

Control settings used for PSO were: C1, C2 = 2; r1, r2 = randomnumbers between 0 and 1; Maximum number of iterations = 1500;swarm size = 10. Maximum and minimum values of velocity are0.5 ⁄ Pmax and �0.5 ⁄ Pmin respectively. Best results were obtained

by setting maximum and minimum values of x to 0.4 and 0.1respectively, as evident from Table 7.

The table presents the best values of objective function (Eq.(12)) obtained with various settings of x.

Solar plants are considered to be operating for 6 h a day, from10:00 to 16:00 h, as In Pakistan, these hours provide maximumradiation and are free of shadow effects in almost all the seasons.Following are the results and discussions for both cases.

5.1. Case I

In this case, the simulations have been carried out for both fulland reduced solar radiation; later is the case of cloudy weather.Simulation results of static CEED are depicted in Figs. 2–4 as wellas in Tables 8–13. Graphs in Figs. 2–4 show simulation results interms of the fitness value (FT) versus iterations. As evident fromFigs. 2–4, the algorithm converges within 1000 iterations which

0 500 1000 1500105.3

105.4

105.5

105.6

105.7

105.8

105.9

ITERATION

FIT

NE

SS

VA

LUE

10:00 hrs11:00 hrs12:00 hrs13:00 hrs14:00 hrs15:00 hrs

Fig. 3. Simulation results for 15% reduced solar radiation.

0 500 1000 1500

105.3

105.4

105.5

105.6

105.7

ITERATION

FIT

NE

SS

VA

LUE

10:00 hrs11:00 hrs12:00 hrs13:00 hrs14:00 hrs15:00 hrs

Fig. 4. Simulation results for 30% reduced solar radiation.

Table 9Results of CEED with solar power for 1088 MW demand at 11:00 h.

Thermalgeneration

P1 (MW) 10.1062P2 (MW) 10P3 (MW) 99.1P4 (MW) 168.682P5 (MW) 235.8781P6 (MW) 246.7809

Solar generation Us1, Us2, . . ., Us13 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0,0

Solar power share (MW) 317.471

Cost Fuel cost ($/h) 1.0e + 04 ⁄ 3.9426Emission cost ($/h) 1.0e + 04 ⁄ 2.7712Solar cost ($/h) 1.0e + 04 ⁄ 8.2286Total cost ($/h) 1.0e + 05 ⁄ 1.4942

Others Emissions (kg/h) 1.0e + 03 ⁄ 0.6073Demand-generation gap(MW)

0.0181

Table 10Results of CEED with solar power for 1240 MW demand at 12:00 h.

Thermalgeneration

P1 (MW) 10P2 (MW) 10.2191P3 (MW) 194.9316P4 (MW) 177.4014P5 (MW) 224.8683P6 (MW) 303.5647

Solar generation Us1, Us2, . . ., Us13 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0,1

Solar power share (MW) 319.1076

Cost Fuel cost ($/h) 1.0e + 04 ⁄ 4.6762Emission cost ($/h) 1.0e + 04 ⁄ 3.8326Solar cost ($/h) 1.0e + 04 ⁄ 8.2436Total cost ($/h) 1.0e + 05 ⁄ 1.6752

Others Emissions (kg/h) 1.0e + 03 ⁄ 0.8607Demand-generation gap(MW)

0.0927

Table 11Results of CEED with solar power for 1135 MW demand at 13:00 h.

Thermalgeneration

P1 (MW) 10.8593P2 (MW) 118.1312P3 (MW) 147.9272

88 N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91

corresponds to a maximum of 3.56 s using 1.8 GHz core i5 proces-sor. Generation of thermal units in MW is given in Tables 8–13 forthe timings 10:00, 11:00, . . .. . ., 15:00 respectively. Us1,. . .., Us13correspond to status of solar plants which is either ON (repre-sented by 1) or OFF (represented by 0). Power balance constraintviolation is represented by demand-generation gap. Positive valueof demand-generation gap means that generation is greater thandemand while the negative value corresponds to generation notcoping up with the demand.

It can be seen from all tables that the proposed algorithm is wellbehaved. For instance, in Table 8 the thermal generation values for

Table 8Results of CEED with solar power for 1244 MW demand at 10:00 h.

Thermalgeneration

P1 (MW) 120.4479P2 (MW) 92.2947P3 (MW) 155.8062P4 (MW) 76.4153P5 (MW) 257.9089P6 (MW) 302.2846

Solar generation Us1, Us2, . . ., Us13 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,1

Solar power share (MW) 238.825

Cost Fuel cost ($/h) 1.0e + 04 ⁄ 5.2626Emission cost ($/h) 1.0e + 04 ⁄ 4.2322Solar cost ($/h) 1.0e + 04 ⁄ 6.2322Total cost ($/h) 1.0e + 05 ⁄ 1.5727

Others Emissions (kg/h) 1.0e + 03 ⁄ 0.8808Demand-generation gap(MW)

�0.0173

P4 (MW) 186.3632P5 (MW) 150.7713P6 (MW) 221.0182

Solar generation Us1, Us2, . . ., Us13 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1,1

Solar power share (MW) 300.0974

Cost Fuel cost ($/h) 1.0e + 04 ⁄ 4.4136Emission cost ($/h) 1.0e + 04 ⁄ 3.0728Solar cost ($/h) 1.0e + 04 ⁄ 7.8311Total cost ($/h) 1.0e + 05 ⁄ 1.5318

Others Emissions (kg/h) 1.0e + 03 ⁄ 0.6395Demand-generation gap(MW)

0.1678

units P1–P6 are well within constraint limits. It can be noted fromTables 8–13 that the solar power share is well within the upperbound. The optimized cost values are consistent with the respec-tive shares of thermal and solar power generation. The algorithmincreases or decreases the solar share based on available solar radi-ation and temperature at any time as evident from Fig. 5.

Table 12Results of CEED with solar power for 1318 MW demand at 14:00 h.

Thermalgeneration

P1 (MW) 65.2834P2 (MW) 97.2893P3 (MW) 250P4 (MW) 107.6407P5 (MW) 252.7949P6 (MW) 297.7576

Solar generation Us1, Us2, . . ., Us13 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0,1

Solar power share (MW) 247.1655

Cost Fuel cost ($/h) 1.0e + 04 ⁄ 5.5082Emission cost ($/h) 1.0e + 04 ⁄ 4.7011Solar cost ($/h) 1.0e + 04 ⁄ 6.4662Total cost ($/h) 1.0e + 05 ⁄ 1.6675

Others Emissions (kg/h) 1.0e + 03 ⁄ 1.0376Demand-generation gap(MW)

�0.0686

Table 13Results of CEED with solar power for 1074 MW demand at 15:00 h.

Thermalgeneration

P1 (MW) 82.7064P2 (MW) 60.696P3 (MW) 249.2579P4 (MW) 96.2554P5 (MW) 182.7257P6 (MW) 190.6486

Solar generation Us1, Us2, . . ., Us13 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0,1

Solar power share (MW) 211.7604

Cost Fuel cost ($/h) 1.0e + 04 ⁄ 4.5057Emission cost ($/h) 1.0e + 04 ⁄ 3.2438Solar cost ($/h) 1.0e + 04 ⁄ 5.5399Total cost ($/h) 1.0e + 05 ⁄ 1.3289

Others Emissions (kg/h) 1.0e + 03 ⁄ 0.7149Demand-generation gap(MW)

0.0504

0

50

100

150

200

250

300

350

10:00 hours

11:00 hours

12:00 hours

13:00 hours

14:00 hours

15:00 hours

Sola

r sha

re (M

W)

Full Radia�on 15% Reduced 30% Reduced

Fig. 5. Solar shares at different solar radiation levels.

N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91 89

The solar share is increased or decreased by turning ON or OFFthe appropriate solar units. For instance, the number of solar unitsthat are OFF in both Tables 8 and 10 is 4. Turning OFF the solar unitnumber 1, 3, 8 and 11 at time 10:00 h, as clear from Table 8, resultsin the solar share of 238.825 MW. On the other hand, Table 10describes that Turning OFF the solar unit number 3, 7, 8 and 12 attime 12:00 h accounts for the solar share of 319.1076 MW. As thesolar share is increased, thermal share gets reduced for a given loaddemand. Therefore by increasing the solar share, the solar cost isincreased whereas fuel cost, emission cost and emissions getreduced; which is evident from Tables 8 and 10 where the loaddemands are approximately equal, i.e. 1244 MW and 1240 MWrespectively. In Table 8, the solar cost is 1.0e + 04 ⁄ 6.2322 $/h andthe fuel cost, emission cost and emissions are 1.0e + 04 ⁄5.2626 $/h, 1.0e + 04 ⁄ 4.2322 $/h and 1.0e + 03 ⁄ 0.8808 kg/hrespectively, with solar share of 238.825 MW whereas in Table 10,the solar cost is increased to 1.0e + 04 ⁄ 8.2436 $/h while thefuel cost, emission cost and emissions are reduced to1.0e + 04 ⁄ 4.6762 $/h, 1.0e + 04 ⁄ 3.8326 $/h and 1.0e + 03 ⁄0.8607 kg/h respectively, for increased solar share of319.1076 MW. The influence of solar share on total cost is muchgreater as compared to thermal share because of higher per unitcosts of solar generating units. Therefore, the total cost is higherin Table 10 as compared to that in Table 8. This effect can also beseen in Fig. 2, where the fitness value increases from time 10 to12 as the solar share is increased. Similar relations can be found

by comparing the results in Tables 9 and 13 where the loaddemands are 1088 MW and 1074 MW respectively.

The value of Ks has been experimentally set to 1.0e + 03 whichresults in maximum solar share of 319.1076 MW which is 25.73%of load demand, a value near to the solar share upper bound. Byreducing the value of Ks, the importance of difference in availablesolar power and the solar share in Eq. (12) gets reduced and viceversa; the resulting solar share varies accordingly.

Fig. 5 shows the solar share for various levels of solar radiation.The solar radiation often gets reduced due to clouds, depending onvarious parameters like thickness, height, amount, etc. of clouds.As we have taken into account the global solar radiation which isless affected by clouds as compared to beam radiation, thereforetests have been carried out for assumed reductions of 15% and30% in solar radiation. It is evident from Fig. 5 that the solar sharegets reduced for reduced solar radiation, in an expected manner.

5.2. Case II

Table 14 presents the results of DCEED problem which is similarto SCEED except an additional constraint of ramp rate limits andthe problem has been expanded over the time horizon of 1 day.The results in Table 14 satisfy all the constraints discussed in Sec-tion 2.2. The system operates from hour 1 to hour 10 and fromhour 15 to hour 24 with only thermal generation and therefore isdealt with as an ordinary DCEED problem. The solar power contrib-utes from hour 10 to hour 15 as in case of SCEED. The solar sharevaries in a manner similar to that of SCEED. The results at hour12 can be compared with that of hour 14 due to comparable loaddemands of 1235 MW and 1251 MW respectively. The larger solarshare of 335.063 MW results in less fuel cost, emission cost andemissions while higher solar cost and total cost at hour 12 as com-pared to the respective quantities at hour 14, where solar share is239.192 MW, for the same reasons discussed earlier in the case ofSCEED.

When solar generation is included to or removed from the sys-tem, the load ramp seen by the other plants gets increased. Thegreater the amount of solar share included or removed, the largerthe load ramp seen by thermal which may cause failure of opera-tion due to ramp rate limits of thermal units. Fig. 6 shows the loadramps seen by thermal units with and without solar powerincluded in the system.

Table 14Results for DCEED.

Hour P1 (MW) P2 (MW) P3 (MW) P4 (MW) P5 (MW) P6 (MW) Us1, Us2, . . .., Us13 Solar share(MW)

Fuel cost ($/h) Emission cost ($/h)

Solar cost ($/h) Total cost ($/h) Emissions ($/h)

1 298.7907 139.766 170.8483 50 200 95.5949 1.0e + 04 ⁄ 1.1237 1.0e + 04 ⁄ 0.802 1.0e + 04⁄1.9257 1.0e + 03 ⁄ 0.96512 321.0318 113.6014 162.5339 94.8329 200 50 1.0e + 04 ⁄ 1.1028 1.0e + 04 ⁄ 0.7931 1.0e + 04 ⁄ 1.8959 1.0e + 03 ⁄ 0.9923 201.0318 124.6422 223.4963 105.3914 200 98.4383 1.0e + 04 ⁄ 1.1355 1.0e + 04 ⁄ 0.8084 1.0e + 04 ⁄ 1.9439 1.0e + 03 ⁄ 0.84934 255.8099 130.6614 164.1621 87.6478 200 91.7187 1.0e + 04 ⁄ 1.099 1.0e + 04 ⁄ 0.7511 1.0e + 04 ⁄ 1.8502 1.0e + 03 ⁄ 0.83965 335.8099 103.7868 172.4276 50 200 72.9757 1.0e + 04 ⁄ 1.0935 1.0e + 04 ⁄ 0.781 1.0e + 04 ⁄ 1.8746 1.0e + 03 ⁄ 1.02396 338.0287 151.024 80 97.2356 202.2665 94.4452 1.0e + 04 ⁄ 1.1497 1.0e + 04 ⁄ 0.8407 1.0e + 04 ⁄ 1.9903 1.0e + 03 ⁄ 1.01837 316.362 174.9805 144.0999 50 201.2571 102.3006 1.0e + 04 ⁄ 1.1711 1.0e + 04 ⁄ 0.8672 1.0e + 04 ⁄ 2.0383 1.0e + 03 ⁄ 1.03558 344.7516 84.9805 198.2418 100 200 95.0262 1.0e + 04 ⁄ 1.2021 1.0e + 04 ⁄ 0.8725 1.0e + 04 ⁄ 2.0746 1.0e + 03 ⁄ 1.11249 395.6592 78.4906 228.5335 83.7331 246.861 92.7227 1.0e + 04 ⁄ 1.3348 1.0e + 04 ⁄ 1.0559 1.0e + 04 ⁄ 2.3907 1.0e + 03 ⁄ 1.4124

10 297.8072 50.2762 141.5124 78.3317 296.861 50 0, 1, 1, 0, 1, 1, 1, 0, 1,0, 1, 1, 1

235.034 1.0e + 04 ⁄ 1.1002 1.0e + 03 ⁄ 8.58 1.0e + 04 ⁄ 6.1374 1.0e + 05 ⁄ 0.8096 1.0e + 03 ⁄ 0.9895

11 236.8295 50.7576 203.368 95.6474 237.9027 69.1967 1, 1, 0, 1, 1, 0, 1, 0, 1,0, 1, 1, 1

307.23 1.0e + 04 ⁄ 1.0633 1.0e + 03 ⁄ 7.5297 1.0e + 04 ⁄ 7.9931 1.0e + 05 ⁄ 0.9809 1.0e + 03 ⁄ 0.8419

12 308.5653 81.1024 106.8937 91.1342 262.2717 50 1, 1, 0, 0, 0, 1, 1, 1, 1,1, 0, 1, 1

335.063 1.0e + 04 ⁄ 1.0758 1.0e + 03 ⁄ 8.0197 1.0e + 04 ⁄ 8.8286 1.0e + 05 ⁄ 1.0706 1.0e + 03 ⁄ 0.944

13 379.7585 50.1201 87.6007 74.3231 226.1978 71.9097 1, 0, 0, 1, 1, 1, 0, 0, 1,1, 1, 1, 1

300.097 1.0e + 04 ⁄ 1.0616 1.0e + 03 ⁄ 7.7716 1.0e + 04 ⁄ 7.9026 1.0e + 05 ⁄ 0.9741 1.0e + 03 ⁄ 1.0588

14 418.2248 91.3466 120.0901 105.821 216.0514 60.2609 1, 1, 0, 1, 1, 1, 0, 1, 0,1, 1, 1, 0

239.192 1.0e + 04 ⁄ 1.1992 1.0e + 03 ⁄ 9.1687 1.0e + 04 ⁄ 6.1791 1.0e + 05 ⁄ 0.8295 1.0e + 03 ⁄ 1.2713

15 444.9107 118.6177 149.631 51.6389 204.8054 98.7275 1, 1, 1, 1, 1, 1, 0, 1, 0,0, 1, 0, 1

194.683 1.0e + 04 ⁄ 1.2654 1.0e + 03 ⁄ 9.845 1.0e + 04 ⁄ 4.9354 1.0e + 05 ⁄ 0.7185 1.0e + 03 ⁄ 1.4115

16 500 119.6441 214.631 95.7249 200 120 1.0e + 04 ⁄ 1.4918 1.0e + 04 ⁄ 1.2477 1.0e + 04 ⁄ 2.7395 1.0e + 03 ⁄ 1.799717 433.6712 118.8918 228.3949 145.7249 200 94.3172 1.0e + 04 ⁄ 1.4485 1.0e + 04 ⁄ 1.2011 1.0e + 04 ⁄ 2.6496 1.0e + 03 ⁄ 1.594518 366.9561 168.8241 179.9709 137.3386 249.1787 99.7314 1.0e + 04 ⁄ 1.4367 1.0e + 04 ⁄ 1.1722 1.0e + 04 ⁄ 2.6089 1.0e + 03 ⁄ 1.383919 306.7417 200 244.9709 112.5704 200 94.7169 1.0e + 04 ⁄ 1.3762 1.0e + 04 ⁄ 1.1047 1.0e + 04 ⁄ 2.4808 1.0e + 03 ⁄ 1.298420 386.7417 110 214.7914 86.5183 201.3953 92.5533 1.0e + 04 ⁄ 1.2836 1.0e + 04 ⁄ 0.9736 1.0e + 04 ⁄ 2.2572 1.0e + 03 ⁄ 1.312321 352.6291 50 227.9327 50 251.3953 91.043 1.0e + 04 ⁄ 1.2126 1.0e + 04 ⁄ 0.9471 1.0e + 04 ⁄ 2.1597 1.0e + 03 ⁄ 1.232322 311.8292 100 185.0233 50 248.9536 88.1939 1.0e + 04 ⁄ 1.1646 1.0e + 04 ⁄ 0.8635 1.0e + 04 ⁄ 2.0281 1.0e + 03 ⁄ 1.050223 237.8993 108.2409 250.0233 58.8365 200 120 1.0e + 04 ⁄ 1.1564 1.0e + 04 ⁄ 0.8613 1.0e + 04 ⁄ 22.0178 1.0e + 03 ⁄ 0.96324 265.8164 134.7064 200.7121 108.765 200 50 1.0e + 04 ⁄ 1.1285 1.0e + 04 ⁄ 0.8274 1.0e + 04 ⁄ 21.9559 1.0e + 03 ⁄ 0.9526

90N

.A.K

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92(2015)

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-250

-200

-150

-100

-50

0

50

100

150

200

250

9_10 10_11 11_12 12_13 13_14 14_15 15_16

Load

ram

p

Hour

Without solar With solar

Fig. 6. Load ramps seen by thermal units at different hours.

N.A. Khan et al. / Energy Conversion and Management 92 (2015) 82–91 91

6. Conclusions

We have presented a new dispatch model to solve CEED prob-lem for a system containing conventional thermal and solar PVplants. Two case studies with six thermal units and thirteen solarplants, employing PSO as an optimization tool, have been investi-gated. SCEED problem has been investigated for full and reducedsolar radiation and DCEED problem is solved for full radiation onlywith constraints of thermal generator limits, power balance andrenewable energy limits. However, the ramp rate limits have beentreated as an additional constraint in the case of DCEED. The larg-est solar shares of 319.1076 MW (25.73% of 1240 MW) and335.063 MW (27.13% of 1235 MW) have been recorded at12:00 h in case of SCEED and DCEED, respectively. It confirms thathigher solar radiations contribute larger solar shares in both thecases. Larger solar share for a given load demand results in highersolar cost and total cost as well as lower fuel cost, emission costand emissions. The dispatch during 12:00 h resulted in highestoperation cost of 167,520 $/h because of highest share of solarpower. In case of DCEED, although the load ramp seen by thermalunits were increased at the points of addition and removal of solargeneration, the algorithm converged successfully and solvedDCEED without violating any constraint. The simulation resultsdemonstrate satisfactory operation of the proposed model. Forthe sake of simplicity, in this work, power losses have been ignoredas well as thermal units with simple convex characteristics havebeen selected. The future work is aimed at investigating the CEEDproblem involving thermal units with non-convex characteristics,taking losses into account and implementation of proposed modelon large power systems. New constraints identification and inte-gration in the dispatch problem is also under consideration.

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