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Applied Soft Computing 11 (2011) 1295–1302

Contents lists available at ScienceDirect

Applied Soft Computing

journa l homepage: www.e lsev ier .com/ locate /asoc

hort-term combined economic emission scheduling of hydrothermal systemsith cascaded reservoirs using particle swarm optimization technique

.K. Mandal ∗, N. Chakrabortyadavpur University, Department of Power Engineering, Kolkata 700098, India

r t i c l e i n f o

rticle history:eceived 25 January 2008eceived in revised form 5 March 2010ccepted 14 March 2010vailable online 19 March 2010

eywords:

a b s t r a c t

This paper develops an efficient and reliable particle swarm optimization (PSO) based algorithm forsolving combined economic emission scheduling of hydrothermal systems with cascaded reservoirs. Amulti-chain cascaded hydrothermal system with non-linear relationship between water discharge rate,power generation and net head is considered in this paper. The water transport delay between connectedreservoirs is also considered. The problem is formulated considering both cost and emission as competingobjectives. Combined economic emission scheduling (CEES) is a bi-objective problem. A price penalty

ombined economic emission schedulingCEES)article swarm optimization (PSO)ydrothermal Systemsascaded reservoirs

factor approach is utilized here to convert this bi-objective CEES problem into a single objective one.The effect of valve-point loading is also taken into account in the present problem formulation. Thefeasibility of the proposed method is demonstrated on a sample test system consisting of four cascadedhydro units and three thermal units. The results of the proposed technique based on PSO are comparedwith other evolutionary programming method. It is found that the results obtained by the proposedtechnique are superior in terms of fuel cost, emission output etc. It is also observed that the computation

ced b

time is considerably redu

. Introduction

Optimum scheduling of hydrothermal systems is of great impor-ance to electric utility systems. The generation scheduling problemonsists of determining optimum operation strategy for allocationf generations to different units so as to minimize the total oper-tional cost subjected to a variety of constraints. The operationalost of hydroelectric plants is insignificant. Thus, the problem ofinimizing the operational cost of a hydrothermal system reduces

o minimizing the fuel cost of thermal plants subjected to varietyf constraints of hydraulic and power system network. The lim-ted energy storage capability of water reservoirs and the stochasticature of availability of water make the solution more difficult forydrothermal systems compared to pure thermal systems. Due to

ncreasing concern over the environmental considerations, societyemands adequate and secure electricity not only at the cheap-st possible price, but also at minimum level of emission andt has become almost compulsory for electric utilities to reduce

he emission level below certain limit. The thermal units pro-uce harmful emission that must be minimized simultaneouslylong with economic generation for the environmental consider-tion. Beside other methods, the harmful effects of the emission

∗ Corresponding author. Tel.: +91 33 23355813; fax: +91 33 23357254.E-mail address: kkm567@yahoo.co.in (K.K. Mandal).

568-4946/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.asoc.2010.03.006

y the proposed technique based on PSO.© 2010 Elsevier B.V. All rights reserved.

of gaseous pollutants from thermal units can also be reduced byproper load allocation among the various generating units. Thismay lead to an increase in generation cost. So a revised power dis-patch program is required that considers both the generation costand emission as the objectives. One of the major complicationsin the above considerations is that the cost and emission func-tions are of conflicting nature. In other words, minimizing pollutionincreases cost and vice versa.

Emissions in power dispatch problems have been includedeither in objective function or treated as additional constraintsby many research groups. Many methods to reduce the emissionshave been proposed and discussed [1–3] by several researchers.Some of the important soft computing methods that are utilizedfor solving this problem are; improved back-propagation neuralnetwork methodology [4], evolutionary algorithm based multi-objective technique [5], evolutionary programming technique [6],fuzzy satisfaction maximizing decision approach [7], Hopfield neu-ral network methodology [8] and genetic algorithm procedures [9]etc.

The generation scheduling problem of hydrothermal systemshas been the subject of intensive research work for several decades.

Several researchers have used many methods to solve this difficultoptimization problem. Some of these solution methods are decom-position techniques [10], dynamic programming approach [11] andnon-linear network flow technique [12]. In recent times optimalhydrothermal scheduling problems have been solved by different

1296 K.K. Mandal, N. Chakraborty / Applied Sof

Nomenclature

asi, bsi, csi, esi, fsi cost curve coefficients of ith thermal unitC1j, C2j, C3j, C4j, C5j, C6j power generation coefficients of jth

hydro unitIhjt inflow rate of jth reservoir at time tNs number of thermal generating unitsNh number of hydro generating unitsPsit output power of ith thermal unit at time tPmin

si, Pmax

silower and upper generation limits for ith thermal

unitPDt load demand at time tPhjt output power of jth hydro unit at time tPmin

hj, Pmax

hjlower and upper generation limits for jth hydro

unitQhjt water discharge rate of jth reservoir at time tQ min

hj, Q max

hjminimum and maximum water discharge rate of

jth reservoirRuj number of upstream units directly above jth hydro

plantShjt spillage of jth reservoir at time tVhjt storage volume of jth reservoir at time tVmin

hj, Vmax

hjminimum and maximum storage volume of jth

reservoir

Greek letter

hasises

tsttscsefoaptptralpfoanpss

�mj water transport delay from reservoir m to j

euristic techniques such as genetic algorithm [13–15], simulatednnealing [16], evolutionary programming [17] and evolutionarytrategy [18]. Multi-objective short-term hydrothermal schedul-ng problems have also been solved by many heuristic techniquesuch as fuzzy decision-making methodology [19], fuzzy satisfyingvolutionary programming [20] and methods based on heuristicearch technique [21] etc.

Particle swarm optimization (PSO) is one of the modern heuris-ic algorithms and has gained lots of attention in various powerystem optimization problems. The PSO technique has been appliedo various fields of power system optimization such as reac-ive power control [22], economic dispatch [23,24], hydrothermalcheduling [25] etc. But the performance of PSO on short-termombined economic emission scheduling (CEES) of hydrothermalystems has not yet been reported by any group. In this paper, anfficient and reliable PSO based optimization technique is proposedor solving short-term combined economic emission schedulingf cascaded hydrothermal systems considering several equalitynd non-equality constraints on thermal as well as hydroelectriclants. The main constraints included are the cascaded nature ofhe hydraulic network, the time coupling effect of the hydro subroblem where the water inflow of an earlier time interval affectshe discharge capability at a later period of time, the varying hourlyeservoir inflows, the physical limitations on the reservoir storagend turbine flow rate, the varying system load demand and theoading limits of both thermal and hydro plants. The effect of valve-oint loading of the thermal units is also included in the problemormulation. The effectiveness of the proposed technique is testedn a sample test system comprising of four cascaded hydro units

nd three thermal units. It is observed that the proposed tech-ique based on PSO performs effectively in comparison to otheropulation-based heuristic techniques. A comparison with fuzzyatisfying evolutionary programming [20] is presented here whichhows PSO could provide quite encouraging results.

t Computing 11 (2011) 1295–1302

2. Problem formulation

Short-term combined economic emission scheduling ofhydrothermal systems involves the optimization of a problemwith non-linear objective functions subject to a mixture of linearand non-linear constraints. As the fuel cost of hydroelectric plantsis insignificant in comparison with that of thermal power plants,the objective is to minimize the fuel cost and as well as theemission of thermal units, while making use of the availability ofhydro-resources as much as possible.

2.1. Economic scheduling

The pure economic load-scheduling (ELS) problem is one of themajor problems in hydrothermal system’s operation and planning.The classical ELS problem may be described by minimizing the totalfuel cost of the thermal units under several operating constraints.For a given hydrothermal system, the problem may be describedas optimization (minimization) of total fuel cost as defined by (1)under a set of operating constraints:

2.1.1. Minimize

F(Psit) =T∑

t=1

Ns∑

i=1

[fit(Psit)] (1)

where F(Psit) is the total fuel cost, T is the total number of timeinterval for the scheduling horizon, Ns is the total number of ther-mal generating unit, Psit is the power generation of ith thermalgenerating unit at time t and fit(Psit) is the fuel cost function.

Conventionally, the fuel cost curve for any thermal generatingunit can be represented by segments of quadratic functions of theactive power output of the generator. So fit(Psit) can be defined by(2) as:

fit(Psit) = asi + bsiPsit + csiP2sit (2)

where asi, bsi, csi are fuel cost coefficients of the ith thermal gener-ating unit

However, for more practical and accurate modeling of fuelcost function, the above expression needs to be modified suitably.Modern thermal power plants consist of generating units havingmulti-valve steam turbines in order to incorporate flexible oper-ational facilities. The generating units with multi-valve turbineshave very different cost curve compared with that defined by (2).The effect of valve-point effect loading may be considered by addinga sinusoidal function to the quadratic cost function described above.Hence, the function described by (2) is revised as follows:

f vit(Psit) = asi + bsiPsit + csiP

2sit +

∣∣esi × sin{fsi × (Pminsi − PPsit

)}∣∣ (3)

where f vit

(Psit) is the fuel cost function of thermal units includingthe valve-point loading effect and esi, fsi are fuel cost coefficients ofthe ith thermal generating unit reflecting the valve-point effect.

2.2. Emission scheduling

The solution of pure economic load-scheduling problem willgive the amount of active power to be generated by different unitsat a minimum fuel cost for each time interval during the entirescheduling period. But the amount of emission or emission costis not considered in the above pure ELS problem. The amount of

emission from a fossil-based thermal generator unit depends onthe amount of power generated by the unit as well as the conditionof the unit. The emission generated can be expressed as a sum of aquadratic and an exponential function [5]. The economic emission-scheduling (EES) problem can be described as the optimization

ed Sof

(a

E

wt

2

dvclip

2T

wp

b

2T

wlsc

moi

(

(

(

((

(

peftl

s

2a

K.K. Mandal, N. Chakraborty / Appli

minimization) of total amount of emission release defined by (4)s:

(Psit) =T∑

t=1

Ns∑

i=1

[˛si + ˇsiPsit + �siP2sit + �si exp(ısiPsit)] (4)

here E(Psit) is total amount of emission and ˛si, ˇsi, �si, �si, ısi arehe emission coefficients of the ith unit.

.3. Combined economic and emission dispatch

The economic load scheduling and emission scheduling are twoifferent problems. Emission scheduling can be included in con-entional economic load scheduling by the addition of emissionost to the normal load scheduling cost. The bi-objective prob-em of combined economic emission scheduling can be convertednto a single objective optimization problem by introducing a priceenalty factor ht [4] as follows:

.3.1. MinimizeC = F(Psit) + ht × E(Psit) (5)

here TC is the total operational cost of the system and ht is therice penalty factor during time t.

Now, for a trade off between fuel cost and emission cost (5) cane revised as (6) follows:

.3.2. MinimizeC = w1 × F(Psit) + w2 × ht × E(Psit) (6)

here w1 and w2 are the weight factors. For pure economicoad scheduling w1 = 1 and w2 = 0; for pure economic emissioncheduling w1 = 0 and w2 = 1 while w1 = w2 = 1 yields results forombined economic emission scheduling.

The price penalty factor ht can be found out by a practicalethod as discussed in [4]. The following steps can be used to find

ut the price penalty factor for a particular load during each timenterval over the entire scheduling period.

1) Find out the average cost of each generator at maximum poweroutput.

2) Find out the average emission of each generator at its maximumoutput.

3) Divide the average cost of each generator by its average emis-sion and thus hit is given as:

F(Pmaxsi

)/(Pmaxsi

)

E(Pmaxsi

)/(Pmaxsi

)= hit $/lb (7)

1) Arrange the values of price penalty factor in ascending order.2) Add the maximum capacity of each unit (Pmax

si) one at a time

starting from the smallest hit unit until∑

Pmaxsi

≥ PDt is realized.3) At this stage, hit associated with last unit in the process is the

price penalty factor ht for the given load during the time t.

From the above description, it is clear that the value of the priceenalty factor ht is dependent on the total power demand duringach time interval and hence it will have different values for dif-erent power demand. It is also important to note that the value ofhe price penalty factor ht will be the same for ELS, EES and CEES asong as the power demand is the same.

The above objective function described by (6) is to be minimizedubject to a variety of constraints as follows:

.3.2.1. Active power balance. The total power generated must bal-nce the power demand plus losses, at each time interval over the

t Computing 11 (2011) 1295–1302 1297

entire scheduling period

Ns∑

i=1

Psit +Nh∑

j=1

Phjt − PDt − PLt = 0 (8)

where Phjt is the power generation of jth hydro generating unit attime t, PDt is power demand at time t and PLt is total transmissionloss at the corresponding time. In this work the power loss is notconsidered for simplicity. However, it may be calculated by usingB-loss matrix directly.

The hydropower generation is a function of water discharge rateand reservoir storage volume, which can be described by (9) asfollows:

Phjt = C1jV2hjt + C2jQ

2hjt + C3jVhjtQhjt + C4jVhjt + C5jQhjt + C6j (9)

where C1j, C2j, C3j, C4j, C5j, C6j are power generation coefficients ofjth hydro generating unit, Vhjt is the storage volume of jth reservoirat time t and Qhjt is water discharge rate of jth reservoir at time t.

2.3.2.2. Power generation limit.

Pminsi ≤ Psit ≤ Pmax

si (10)

Pminhj ≤ Phjt ≤ Pmax

hj (11)

where Pminsi

and Pmaxsi

are the minimum and maximum powergeneration by ith thermal generating unit, Pmin

hjand Pmax

hjare the

minimum and maximum power generation by the jth hydro gen-erating unit respectively.

2.3.2.3. Water dynamic balance.

Vhjt = Vhj,t−1 + Ihjt − Qhjt − Shjt +Ruj∑

m=1

(Qhm,t−�mj+ Shm,t−�mj

) (12)

where Ihjt is natural inflow of jth hydro reservoir at time t, Shjt isspillage discharge rate of jth hydro generating unit at time t, �mjis the water transport delay from reservoir m to j and Ruj is thenumber of upstream hydro generating plants immediately abovethe jth reservoir.

2.3.2.4. Reservoir storage volume limit.

Vminhj ≤ Vhjt ≤ Vmax

hj (13)

where Vminhj

, Vmaxhj

are the minimum and maximum storage volumeof jth reservoir.

2.3.2.5. Water discharge rate limit.

Q minhj ≤ Qhjt ≤ Q max

hj (14)

where Q minhj

and Q maxhj

are the minimum and maximum water dis-charge rate of the jth reservoir respectively.

Now incorporating these constraints, combined economicemission-scheduling problem of the hydrothermal system can besolved using the proposed algorithm based on particle swarm opti-mization technique.

3. Particle swarm optimization

The particle swarm optimization is one of the recent devel-

opments in the category of heuristic optimization technique. Themethod is based on the backgrounds of artificial life and is inspiredby the natural phenomenon of fish schooling or bird flocking.Kennedy and Eberhart [26] originally developed the PSO con-cept based on the behavior of individuals (i.e. particles or agents)

1298 K.K. Mandal, N. Chakraborty / Applied Soft Computing 11 (2011) 1295–1302

oparoaptptv

Table 1Hourly load demand.

Hour PD (MW) Hour PD (MW) Hour PD (MW)

1 750 9 1090 17 10502 780 10 1080 18 11203 700 11 1100 19 10704 650 12 1150 20 10505 670 13 1110 21 9106 800 14 1030 22 8607 950 15 1010 23 850

TH

Fig. 1. Hydraulic system network.

f a swarm or group. PSO, as an optimization tool, provides aopulation-based search procedure in which individuals calledgents or particles change their position with time. In a PSO algo-ithm, the particles fly around the multidimensional search space inrder to find the optimum solution. Each particle adjusts its positionccording to its own experience and the experience of neighboring

article. PSO is basically based on the fact that in quest of reachinghe optimum solution in a multidimensional space, a population ofarticles is created whose present coordinate (position) determineshe objective function to be minimized. After each iteration the newelocity and hence the new position of each particle is updated on

able 2ydrothermal generation (MW) for pure economic load scheduling (ELS) (w1 = 1 and w2

Hour Ph1 Ph2 Ph3

1 74.3646 51.7113 0.00002 81.7202 87.2371 0.00003 94.2077 51.9381 48.90584 88.4222 73.3031 49.61295 79.3886 65.1279 29.68306 59.8509 51.3167 49.24077 91.2318 82.7106 57.04048 65.1266 81.9009 34.58249 65.6486 71.9949 12.5990

10 96.8762 57.9604 28.617711 97.3842 65.9984 40.640212 92.0700 57.9864 30.562413 93.5797 60.5004 42.056914 74.7631 23.6494 24.032415 58.8737 48.5593 56.624416 83.8202 33.6748 39.780317 62.8905 42.0218 0.000018 96.3006 35.0104 58.727519 92.6579 38.0312 36.194520 58.0271 19.2307 31.734921 80.5654 40.4909 48.162622 77.4824 45.6399 40.206823 84.1830 20.3328 59.987324 56.5055 44.0510 60.6322

8 1010 16 1060 24 800

the basis of a summated influence of each particle’s present veloc-ity, distance of the particle from its own best performance achievedso far during the search process and the distance of the particle fromthe leading particle, i.e. the particle which at present is globally thebest particle producing till now the best performance i.e. minimumof the objective function achieved so far.

Let in a physical d-dimensional search space, the position andvelocity of the ith particle (i.e. ith individual in the populationof particles) be represented as the vectors Xi = (xi1, xi2, . . . , xid)and Vi = (vi1, vi2, . . . , vid) respectively. The previous best posi-tion of the ith particle is recorded and represented as pbesti =(pbesti1, pbesti2, ...., pbestid). The index of the best particle amongall the particles in the group is represented by the gbestd. The mod-ified velocity and position of each particle can be calculated usingthe current velocity and the distance from pbestid to gbestd as shownin the following formulas:

Vk+1id

= w × Vkid

+ c1 × rand( )

×(pbestid − Xkid

) + c2 × rand( ) × (gbestd − Xkid

)

i = 1, 2, . . . , Np, d = 1, 2, . . . , Ng

(15)

where: Np: number of particles in a swarm or group; Ng: num-ber of members or elements in a particle; Vk

id: velocity of individual

i at iteration k; w: weight parameter or swarm inertia; c1, c2: accel-eration constant; rand( ): uniform random value in the range [0 1];Xk

id: position of individual i at iteration k;

= 0).

Ph4 Ps1 Ps2 Ps3

156.5540 102.0764 133.4035 231.8901246.8776 95.1026 40.0000 229.0625207.0780 27.8012 40.0000 230.0691148.0105 20.0000 40.0000 230.6513194.6124 31.4522 40.0000 229.7358154.6876 125.0840 40.0000 319.8201355.9539 20.0000 293.0633 50.0000195.2661 101.2785 211.948 319.8975218.1911 102.5335 300.0000 319.0329255.3471 21.2761 300.0000 319.9224172.1069 104.4371 300.0000 319.4331227.2464 126.9265 297.0804 318.1279272.8220 21.8486 300.0000 319.1925270.0450 107.2591 300.0000 230.2509211.7773 105.3227 300.0000 228.8425329.0842 21.8726 233.5281 318.2398298.8613 112.0618 125.1748 408.9897330.1295 171.9745 288.6604 139.1971204.2311 175.0000 294.3089 229.5764325.6474 175.0000 300.0000 140.3599285.1566 20.0000 295.2462 140.3783331.9240 20.0000 294.7469 50.0000300.4328 39.1397 295.9244 50.0000349.2662 20.0000 40.0000 229.5451

K.K. Mandal, N. Chakraborty / Applied Sof

Table 3Hourly plant discharge (×104 m3) for pure economic load scheduling (ELS) (w1 = 1and w2 = 0).

Hour Qh1 Qh2 Qh3 Qh4

1 7.8807 6.3882 29.5050 7.90852 9.0109 13.7918 27.3533 18.63293 11.9404 6.8056 12.5315 15.55674 10.7304 10.4429 10.7213 10.57465 9.0713 8.9529 22.0098 13.18626 6.1778 6.7305 17.1235 7.92507 5.0736 10.6412 18.3736 14.36778 6.7355 14.9705 21.4043 11.46899 6.7158 13.2874 24.5265 12.7018

10 13.2824 10.3772 21.5775 16.534811 14.5020 13.1768 19.0935 8.046412 12.1284 11.6765 21.8842 11.786213 13.3036 13.9924 19.8600 15.302314 8.4307 6.3358 23.8385 14.422315 5.9100 10.8154 16.2612 8.982516 9.5377 7.9125 21.8157 19.852617 6.2381 9.4028 27.2793 16.020418 12.5090 8.5823 14.1225 19.080019 11.8769 9.7786 21.9772 7.682620 5.8412 6.6391 22.8366 17.4814

p

X

btt

w

wc

ag

TH

21 12.6785 10.7728 15.0469 12.952022 11.7702 13.2122 18.8466 17.385323 11.3081 7.6212 12.4204 14.029324 6.1591 14.8134 15.5002 18.4465

The updated velocity can be used to change the position of eacharticle in the swarm as depicted in (16) as:

k+1id

= Xkid + Vk+1

id(16)

Suitable selection of inertia weight w provides a balanceetween global and local explorations, thus requiring less itera-ion on average to find a sufficiently optimal solution. In general,he inertia weight w is set according to the following equation:

= wmax − wmax − wmin

itermax× iter (17)

here itermax is the maximum number of iterations and iter is theurrent number of iterations.

The constants c1 and c2 represent the weighting of the stochasticcceleration terms that pull each particle towards the pbest andbest positions. Low values allow particle to roam far from the target

able 4ydrothermal generation (MW) for economic emission scheduling (EES) (w1 = 0 and w2

Hour Ph1 Ph2 Ph3

1 70.1324 85.5638 53.86172 97.3026 70.8531 33.68503 90.3135 63.3081 43.44674 62.1599 68.7620 54.06665 65.7978 53.7083 51.42546 58.6863 46.4092 34.25437 91.0549 74.5669 47.52838 93.9804 62.4091 47.53409 90.8687 39.5672 42.5547

10 59.6872 71.6967 49.597211 71.0574 55.9368 27.134412 87.2328 71.4641 54.844813 54.0551 51.4653 54.819914 80.1544 61.0424 9.346215 70.1884 41.2020 26.008316 99.2123 71.0763 57.732017 102.6029 39.6392 21.394918 97.6959 33.6861 51.047519 81.1155 43.1478 41.340220 66.3300 16.1001 49.253821 96.2711 84.7123 56.364222 96.0962 37.7633 33.260323 68.7537 39.5841 20.445224 85.8266 32.5979 58.3157

t Computing 11 (2011) 1295–1302 1299

regions before being tugged back. On the other hand, high valuesresult in abrupt movement crossing target regions.

4. Development of the proposed algorithm

In this section, an algorithm based on PSO is described toobtain quality solutions for CEES problems for the practical ornear practical hydrothermal systems with cascaded reservoirs. Forany population-based evolutionary algorithm like PSO, the rep-resentation of individuals and their elements is very important.For the present problem, the position of each particle (i.e. eachindividual in the population of particles) is composed of a setof elements and for the present problem it is the discharge rateof each hydro plant and the power generated by each thermalunit. The algorithm starts with the initialization process. Let P(0) =[X(0)

1 , X(0)2 , . . . X(0)

k, . . . , X(0)

NP] be the initial population of Np number

of particles. For a system with Nh number of hydro units and Ns

number of thermal units, position of kth individual of a populationis initialized randomly satisfying the constraints defined by (14)and (10) and can be represented by

X(0)k

= [Q (0)h1

, Q (0)h2

, . . . . . . Q (0)hj

, . . . . . . , Q (0)hNh

, P(0)s1 , P(0)

s2 , . . . . . . P(0)si

, . . . . . . , P(0)sNs

]T

(18)

with Q (0)hj

= [Q (0)hj1, Q (0)

hj2, . . . Q (0)hjt

, . . . Q (0)hjT

]T

and P(0)si

=[P(0)

si1 , P(0)si2 , . . . , P(0)

sit, . . . , P(0)

siT]T.

The elements Q (0)hjt

and P(0)sit

are the discharge rate of the jthhydro plant and the power output of the ith thermal unit at timet. The range of the elements Q (0)

hjtand P(0)

sitmust satisfy the water

discharge rate and the thermal generating capacity constraints asdepicted in Eqs. (14) and (10) respectively. Assuming the spillagein Eq. (12) to be zero for simplicity, the water discharge rate ofthe jth hydro plant in the dependent interval is then calculatedusing (12) to meet exactly the restrictions on the initial and finalreservoir storage. The dependent water discharge rate must satisfythe constraints in Eq. (14). At the same time, to meet exactly the

power balance constraints, the thermal generation of the depen-dent thermal generating unit is calculated using (8). Thus, theinitial generation is checked against all the constraints. If the con-straints are satisfied then movement towards the next step isundertaken. The above scheme always generates individuals sat-

= 1).

Ph4 Ps1 Ps2 Ps3

215.4614 121.5777 85.2696 118.1334141.4150 163.4680 162.0538 111.2225193.9141 142.8517 93.3077 72.8582189.4164 108.4244 95.8904 71.2803151.9245 133.5206 130.3693 83.2541139.5791 175.0000 202.1007 143.9703356.207 137.8663 145.7917 96.9849278.4357 175.0000 207.5694 145.0714209.6102 175.0000 295.7753 236.6222304.6687 175.0000 242.6920 176.6581248.8923 175.0000 291.3881 230.5911199.0966 175.0000 300.0000 262.3615320.5115 175.0000 260.3969 193.7513280.3527 175.0000 245.1870 178.9173263.7398 175.0000 250.0666 183.7949283.8386 140.8170 197.1398 210.1836247.3728 175.0000 264.9036 199.0866340.5855 175.0000 244.1696 177.8155276.5961 175.0000 259.3419 193.4584334.0192 175.0000 237.4441 171.8528266.6471 113.2933 108.6944 184.0176255.5385 175.0000 156.7707 105.5710269.4606 163.1549 175.1314 113.4701315.9834 120.5074 129.1255 57.6435

1300 K.K. Mandal, N. Chakraborty / Applied Soft Computing 11 (2011) 1295–1302

Table 5Hourly plant discharge (×104 m3) for economic emission scheduling (EES) (w1 = 0and w2 = 1).

Hour Qh1 Qh2 Qh3 Qh4

1 7.2440 13.5732 23.9567 7.50892 13.0346 10.4462 21.3168 7.05273 11.3466 9.2067 23.8373 9.29204 6.3227 10.3993 12.8382 12.68515 6.7897 7.6664 17.0591 7.97996 5.8777 6.4747 21.6148 6.08817 7.5403 12.0106 22.7931 9.33588 12.7250 10.0645 17.9000 17.52959 12.1654 6.3519 19.1568 10.2531

10 6.1736 13.0000 17.6814 19.828511 10.2573 14.7601 14.4394 8.260812 5.1794 9.9519 15.9265 19.464913 8.5534 13.4344 26.0117 14.746614 12.2679 11.3194 11.9666 10.623315 14.0986 9.2533 24.6621 10.815816 7.5703 9.5786 23.0939 12.743717 6.9509 8.9463 23.4684 12.573818 12.6529 8.4560 18.7031 19.040419 8.9508 11.3039 21.6287 12.333720 6.7367 6.4616 19.8919 17.903721 6.7560 12.8830 29.9051 9.9669

if

Table 7Hourly plant discharge (×104 m3) for combined economic emission scheduling(CEES) (w1 = 1 and w2 = 1).

Hour Qh1 Qh2 Qh3 Qh4

1 6.0174 6.6129 16.1042 7.32982 9.0022 9.1189 26.7497 9.89743 10.8451 14.7058 18.7069 8.96384 13.7807 7.6243 22.0420 6.57945 11.7183 6.0873 28.7106 8.26276 5.0386 12.8625 14.4901 11.97257 11.7993 11.3992 12.5741 17.57188 10.8397 13.0498 19.3106 19.25959 11.0504 10.8592 22.5186 16.8223

10 13.1299 9.9287 24.6964 12.436911 11.4773 13.1585 16.4108 16.849512 10.1627 9.2012 24.4325 17.335113 5.8698 10.2341 20.8617 13.146114 12.0969 12.4960 16.6161 17.067615 5.2052 14.9613 27.5472 7.820616 7.4335 11.2749 22.0846 16.146817 9.2958 13.5992 29.3859 8.800218 9.9733 11.5779 11.0546 18.382619 10.5630 11.6506 14.9856 18.487520 5.7991 12.4534 13.3271 12.883421 13.4763 7.8281 13.6812 16.272922 14.9788 6.1527 11.1017 17.942023 13.9947 7.1222 15.4017 16.413524 8.4025 7.4002 21.8917 8.9128

Table 8Comparison of cost and CPU time for ELS, EES and CEES.

ELS EES CEES

Fuel cost ($) 42474.00 48263.00 43280.00

TH

22 13.3247 11.7873 22.6131 10.208123 7.3349 13.9783 24.2852 10.949124 10.3899 13.8799 14.4954 14.3817

sfying the constraints. Now, the algorithm can be described asollows:

Step 1. Initialize randomly each particle according to the limit ofeach unit including individual dimensions, searching points andvelocities according to (18). These initial particles must be fea-sible candidates for solutions that satisfy the practical operatingconstraints.Step 2. For each particle, calculate fitness value according to (6).Step 3. If the fitness value is better than the best fitness value inhistory, set current value as the pbest.

Step 4. Modify the member velocity of each particle according to(15).Step 5. Modify the member position of each particle according to(16) satisfying the constraints.

able 6ydrothermal generation (MW) for combined economic emission scheduling (CEES) (w1

Hour Ph1 Ph2 Ph3

1 61.0184 53.2392 56.35752 82.2398 69.1013 0.00003 91.0549 88.2669 41.44424 97.9199 76.2824 46.54435 80.2069 47.1498 0.00006 49.8974 82.0877 52.81767 98.6534 92.9564 96.02768 83.7492 74.0936 43.83959 83.5294 62.0017 30.8691

10 77.8915 45.7866 37.288911 83.1171 66.0771 54.797212 78.9637 48.1634 22.241113 54.2794 51.7140 42.106014 87.7341 57.4547 57.580915 50.8241 58.9417 0.000016 69.2295 44.6425 37.726917 80.9550 47.3587 0.000018 84.0709 35.3989 58.147819 85.7273 29.4884 60.738820 56.4086 76.2467 62.684021 91.7987 4.1083 63.757422 88.8950 0.0000 61.646623 84.0414 4.8674 64.868524 65.2474 87.338 49.5152

Emission (lb) 28132.00 16928.00 17899.00Comp. time (s) 123.52 124.66 132.45

Step 6. Choose the particle with the best fitness value of all theparticles as the gbest.Step 7. If the number of iterations reaches the maximum, then go

to Step 8 else go to Step 4.Step 8. The individual that generates the latest gbest is the solutionof the problem.

= 1 and w2 = 1).

Ph4 Ps1 Ps2 Ps3

149.3103 166.8905 124.4838 138.7003175.5664 98.5805 210.5114 144.0006157.2228 146.9586 125.0526 50.0000129.0750 125.7467 120.0978 54.3339161.2882 121.5151 209.8400 50.0000210.3414 122.4844 139.8798 142.4917394.4530 93.1106 124.7990 50.0000280.0504 175.0000 210.7053 142.5620273.6953 175.0000 235.6571 229.2476175.0000 232.3319 282.4697 229.2314271.6936 175.0000 219.3322 229.9828277.7804 175.0000 295.3086 252.5428246.3753 175.0000 294.8762 245.6490291.7615 107.7542 287.6334 140.0812192.6352 175.0000 300.0000 232.5980297.4667 175.0000 209.8583 226.0761217.9712 175.0000 298.7883 229.9268325.9284 175.0000 212.0854 229.3687333.5599 175.0000 245.9956 139.4900303.2717 90.6424 230.7614 229.9851326.1951 167.5238 124.7047 131.9120338.8450 110.2223 209.8669 50.5242322.9824 113.4758 209.7644 50.0000292.8678 49.6096 159.9502 95.4718

K.K. Mandal, N. Chakraborty / Applied Soft Computing 11 (2011) 1295–1302 1301

Table 9Comparison of results for CEES obtained by proposed method based on PSO, modified differential evolution (MDE) [27] and fuzzy satisfying evolutionary programming (EP)[20].

ELS EES CEES

uel cost ($) Emission (lb) Fuel cost ($) Emission (lb)

8263.00 16928.00 43280.00 17899.008714.00 15730.00 43198.00 20385.009228.00 16554.00 47096.00 26234.00

5

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sfsahttwT5iP

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poiEho

Fuel cost ($) Emission (lb) F

Proposed method 42474.00 28132.00 4MDE 42611.00 33323.00 4Fuzzy EP 45063.00 48797.00 5

. Simulation results

To evaluate the performance of the proposed algorithm, it waspplied to a test system that consists of a multi-chain cascade ofour hydro units and three thermal units [20]. The scheduling periodas been kept to 24 h with 1 h time interval. The water transportelay between connected reservoirs is also considered. The hydroub-system configuration and network matrix including water timeelays are shown in Fig. 1. Here, four hydro plants are cascadednd the power generation of plants at lower stream is effected byhe delay as well as the discharge of the plants at higher stream ashown. Hydro unit power generation coefficients, reservoir inflows,eservoir limits, generation limits, emission coefficients and costoefficients of thermal units are the same as that of [20,27] andence not reproduced here. However, the hourly load demand ishown in Table 1.

In the present approach, velocity updates are dealt with dynamicwarm inertia, rather than static one. The swarm inertia is variedrom a significantly high value of 0.9 to a low value of 0.3 in succes-ive iterations as the overall convergence became more acceleratednd the results were observed to be better. The values of c1 and c2ave been found to be the best for a value of 2.0 which implies thathe it gives the best performance in terms of the number of hits tohe global solution. At the same time it can be concluded that sameeights are given between pbest and gbest in the evolution process.

he optimization is done with a randomly initialized population of0 swarms. The maximum iteration was set at 500. The problem

s solved by an in-house MATLAB program on 1 GB RAM, 2.66 MHzC.

The problem is initially solved as a case of pure economic loadcheduling with w1 = 1 and w2 = 0. The results are then obtainedor a pure economic emission-scheduling (EES) problem with w1 =and w2 = 1. Finally it is solved again as a case of combined eco-omic emission scheduling incorporating w1 = 1 and w2 = 1.

Optimal hydrothermal generation schedule and optimal hourlyater discharge rate obtained by the proposed algorithm are shown

n Tables 2 and 3 respectively for ELS. Computation time for opti-al solution for this case is found to be 123.520 s and optimal fuel

ost is found to be $42474.00, while amount of emission is found toe 28132.00 lb. Tables 4 and 5 show the optimal hydro-generationchedule and optimal hourly water discharge rate respectively forES. The computation time and optimal amount of emission for EESs found to be 124.66 s and 16928.00 lb respectively, while fuel costs found to be $48263.00. Optimal hydro-generation schedule andptimal hourly water discharge rate are shown in Tables 6 and 7espectively for combined economic emission scheduling. The com-utation time is found to be 132.45 s, while suboptimal fuel costnd amount of emission is found to be $43280.00 and 17899.00 lbespectively for this case. Convergence characteristic of fuel costor ELS is shown in Fig. 2.

Table 8 compares the fuel cost, amount of emission and com-utation time for ELS, EES and CEES cases. The conflicting nature

f the two objectives (minimum fuel cost and minimum emission)s evident from the results. It is clear from the Table 7 that pureLS produces minimum fuel cost but the amount of emission isigher than pure EES and CEES. In the case of pure EES, the amountf emission is minimum, but with higher fuel cost. The CEES pro-

Fig. 2. Convergence characteristics for fuel cost.

duces a better solution with a little increase in fuel cost and a largereduction of emission in comparison to pure ELS. This shows thatwith some compromise in fuel cost, huge reduction in emission ispossible.

The results of the proposed method are compared with theresults obtained by fuzzy satisfying evolutionary programming [20]and modified differential evolution [27] and are shown in Table 9.It is clearly seen that the proposed method yields better results interms of fuel cost the amount of emission for ELS. For CEES, fuelcost is slightly more ($48263.00) obtained by proposed method incomparison with MDE ($43198.00), but emission is reduced to alarge extent (17899.00 lb) by the proposed method against MDE(20385.00 lb). While comparison is made with fuzzy satisfying evo-lutionary programming, it is found that proposed method producesbetter results for all the three cases ELS, EES and CEES.

6. Conclusion

Environmental concern is one of the important issues in theoperation of present day power systems. In this paper, an algorithmbased on particle swarm optimization technique has been proposedand successfully applied to solve short-term combined economicemission scheduling for a hydrothermal system. To evaluate theperformance of the proposed algorithm, it has been applied on asample test systems comprising of a multi-chain cascade of hydrounits and three thermal units and results are presented. The resultsobtained by the proposed algorithm have been compared withother population-based technique like fuzzy satisfying evolution-ary programming and modified differential evolution technique. Itis found that the proposed method can produce comparable resultsin terms of fuel cost and amount of emission.

Acknowledgment

We would like to acknowledge and thank Jadavpur University,Kolkata, India for providing all the necessary help to carry out thiswork.

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elor of electrical engineering in 1986 and masters of electrical engineering in 1989from Jadavpur University, Kolkata. He was awarded with the DIC from Imperial Col-lege, London, UK and PhD degree from University of London in 1999. At present he is

302 K.K. Mandal, N. Chakraborty / Appli

eferences

[1] M.R. Gent, J.W. Lamont, Minimum emission dispatch, IEEE Transaction onPower Systems PAS-90 (November/December) (1972) 2650–2660.

[2] A.A. El-Keib, H. Ma, J.L. Hart, Economic dispatch in view of the clean air act of1990, IEEE Transaction on Power Systems 9 (May) (1994) 972–978.

[3] J.H. Talaq, F. El-Hawary, M.E. El-Hawary, A summary of environmen-tal/economic dispatch algorithms, IEEE Transaction on Power Systems 9(August) (1994) 1508–1516.

[4] P.S. Kulkarni, A.G. Kothari, D.P. Kothari, Combined economic and emissiondispatch using improved back-propagation neural network, Electric PowerComponents and System 28 (2000) 31–44.

[5] M.A. Abido, Environmental/economic power dispatch using multi-objectiveevolutionary algorithms, IEEE Transactions on Power Systems 18 (November(4)) (2003) 1529–1537.

[6] K.P. Wong, J. Yuryevich, Evolutionary programming based algorithm forenvironmentally constrained economic dispatch, IEEE Transaction on PowerSystems 13 (May (2)) (1998) 301.

[7] C.M. Huang, H.T. Yang, C.L. Huang, Bi-Objective power dispatch using fuzzysatisfaction-maximizing decision approach, IEEE Transaction on Power Sys-tems 12 (November) (1997) 1715–1721.

[8] T.D. King, M.E. El-Hawary, F. El-Hawary, Optimal environmental dispatching ofelectric power systems via an improved Hopfield neural network model, IEEETransactions on PWRS 10 (3) (1995) 1559–1565.

[9] Y.H. Song, G.S. Wang, P.Y. Wang, A.T. Johns, Environmental/economic dispatchusing fuzzy logic controlled genetic algorithm, IEE Proceedings Generation,Transmission and Distribution 144 (4) (1997) 377–382.

10] M.V.F. Pereira, L.M.V.G. Pinto, A decomposition approach to the economic dis-patch of the hydrothermal systems, IEEE Transactions on PAS 101 (10) (1982)3851–3860.

11] S. Chang, C. Chen, I. Fong, P.B. Luh, Hydroelectric generation scheduling withan effective differential dynamic programming, IEEE Transactions on PWRS 5(3) (1990) 737–743.

12] H. Brannud, J.A. Bubenko, D. Sjelvgren, Optimal short term operation planningof a large hydrothermal power system based on a non linear network flowconcept, IEEE Transaction on PWRS 1 (November (4)) (1986) 75–82.

13] S.O. Orero, M.R. Irving, A genetic algorithm modeling framework and solutiontechnique for short term optimal hydrothermal scheduling, IEEE Transactionon PWRS 13 (May (2)) (1998).

14] E. Gil, J. Bustos, H. Rudnick, Short-term hydrothermal generation schedul-ing model using a genetic algorithm, IEEE Transaction on Power Systems 18(November (4)) (2003) 1256–1264.

15] M. Ramirez, P.E. Ontae, The short-term hydrothermal coordination via geneticalgorithms, Electric Power Components and Systems 34 (2006) 1–19.

16] K.P. Wong, Y.W. Wong, Short-term hydrothermal scheduling part 1: simulatedannealing approach, IEE Proceedings Generation, Transmission and Distribu-tion 141 (5) (1994) 497–501.

17] P.C. Yang, H.T. Yang, C.L. Huang, Scheduling short-term hydrothermal genera-tion using evolutionary programming techniques, IEE Proceedings Generation,Transmission and Distribution 143 (July (4)) (1996) 371–376.

t Computing 11 (2011) 1295–1302

18] T.G. Werner, J.F. Verstege, An evolutionary strategy for short term operationplanning of hydro-thermal power systems, IEEE Transaction on Power Systems14 (4) (1999) 1362–1368.

19] J.S. Dhillon, S.C. Parti, D.P. Kothari, Fuzzy decision-making in stochastic multi-objective short-term hydrothermal scheduling, IEE Proceedings Generation,Transmission and Distribution 149 (March (2)) (2002) 191–200.

20] M. Basu, An interactive fuzzy satisfying method based on evolutionary pro-gramming technique for multi-objective short-term hydrothermal scheduling,Electric Power Systems Research 69 (2004) 277–285.

21] S. Jarnail, J.S. Dhillon, D.P. Dhillon, Kothari, Multi-objective short-termhydrothermal scheduling based on heuristic search technique, Asian Journalof Information Technology 6 (4) (2007) 447–454.

22] H. Yoshida, K. Kawata, Y. Fukuyama, S. Takayama, Y. Nakanishi, A particle swarmoptimization for reactive power and voltage control considering voltage secu-rity assessment, IEEE Transaction on Power Systems November (15) (2000)1232–1239.

23] Z.L. Gaing, Particle swarm optimization to solving the economic dispatch con-sidering the generator constraints, IEEE Transaction on Power Systems 18(August (3)) (2003) 1187–1195.

24] J.B. Park, K.S. Lee, J.R. Shin, K.Y. Lee, A particle swarm optimization for solvingthe economic dispatch with non-smooth cost functions, IEEE Transaction onPower Systems 20 (February (1)) (2005) 34–42.

25] B. Yu, X. Yuan, J. Wang, Short-term hydro-thermal scheduling using particleswarm optimization method, Energy Conversion & Management 48 (2007)1902–1908.

26] J. Kennedy, R. Eberhart, Particle swarm optimization, Proceedings of the IEEEInternational Conference on Neural Networks IV (1995) 1942–1948.

27] L. Lakshminarasimman, S. Subramanian, Short-term scheduling of hydrother-mal power system with cascaded reservoirs by using modified differentialevolution, IEE Proceedings Generation, Transmission and Distribution 153 (6)(2006) 693–700.

K.K. Mandal was born in Kolkata, India on 25 December 1964. He received the BEdegree in electrical engineering from Jadavpur University, Kolkata, India in 1986and ME degree from Allahabad University, Allahabad, India in 1998 and PhD fromJadavpur University. His employment experience includes Indian Telephone Indus-tries, National Institute of Technology, Durgapur, India. He is presently working as aReader in the Department of Power Engineering, Jadavpur University, Kolkata, India.His present research interest includes power economics, deregulated electricityindustry and power electronics.

N. Chakraborty was born in Kolkata, India on 27 August 1964. He received his bach-

a professor in the Department of Power Engineering, Jadavpur University, Kolkata.His fields of research interest include power economics, applied superconductivityand environmental measurements and analysis.