Hybrid method for achieving Pareto front on economic emission dispatch

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 4, August 2020, pp. 3358~3366
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i4.pp3358-3366  3358
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Hybrid method for achieving Pareto front on economic
emission dispatch
K. Rajesh, N. Visali
Department of Electrical and Electronics Engineering, JNTUA College of Engineering, India
Article Info ABSTRACT
Article history:
Received Mar 18, 2019
Revised Feb 4, 2020
Accepted Feb 12, 2020
In this paper hybrid method, Modified Nondominated Sorted Genetic
Algorithm (MNSGA-II) and Modified Population Variant Differential
Evolution(MPVDE) have been placed in effect in achieving the best optimal
solution of Multiobjective economic emission load dispatch optimization
problem. In this technique latter, one is used to enforce the assigned percent
of the population and the remaining with the former one. To overcome
the premature convergence in an optimization problem diversity preserving
operator is employed, from the tradeoff curve the best optimal solution is
predicted using fuzzy set theory. This methodology validated on IEEE 30 bus
test system with six generators, IEEE 118 bus test system with fourteen
generators and with a forty generators test system. The solutions are
dissimilitude with the existing metaheuristic methods like Strength Pareto
Evolutionary Algorithm-II, Multiobjective differential evolution, Multi-
objective Particle Swarm optimization, Fuzzy clustering particle swarm
optimization, Nondominated sorting genetic algorithm-II.
Keywords:
Cost function
Economic load dispatch
Multiobjective function
Tradeoff curve
Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
K. Rajesh,
EEE Department,
JNTUA College of Engineering,
Ananthapuramu, Andhra Pradesh, India.
Email: 2016rajesh75@gmail.com
1. INTRODUCTION
In a common parlance of power systems multiobjective economic emission load dispatch is an
optimization problem which concerns with incompatible objectives like cost and emission. Best power
generation with minimum emission is the desired task which leads to the optimization problem with many
constraints. Power generation with optimum incremental fuel cost can be compatible with the allocation of
generators in the thermal plant. The vast use of combustible fossil fuels in thermal plants produces harmful
gases like CO,NO2,SO2 leading to contamination of atmosphere which is a major issue from a global
warming perspective. With the awareness of gaseous pollutant, the United States has passed a Clean Air Act
Amendments of 1990 [1] has made enforcement to all the power plants to follow the strategies to minimize
the emissions from the thermal power plant. The incorporation of emission objective with Economic
Dispatch(ED) problem has become a multiobjective with its complexity. Many techniques were developed
for the solution of multiobjective nonlinear problems one of the possible things to convert multiobjective to
mono objective. Linear Programming technique [2] considered as a single objective with a lot of assumptions
and doesn’t provide the easy solution. Another approach [3] conversion of multiobjective to mono objective
is implemented by using suitable weights and drawbacks associated with this one it requires multiple runs to
achieve the trade-off curve, to compensate this ε constraint method was developed [4] considering another
objective as a constraint with its limitation of ε levels, but this is a time consuming with the process of weak
non dominated solutions. Later a novel fuzzy optimization technique [5] was applied but due to lack of
composition in directing the search towards the trade-off curve which is not preferred one. A fuzzy

Int J Elec & Comp Eng ISSN: 2088-8708 
Hybrid method for achieving Pareto front on economic emission dispatch (K. Rajesh)
3359
satisfaction maximizing decision making [6] approach implemented satisfactorily but the extension of
objectives has became a tedious process. A novel approach introduced in [7] which is a formidable and
exhibiting untimely convergence characteristic.
Recent development tends towards Evolutionary Algorithms (EA) for solving EELD problems
compensating the downside of the classical methods to obtain Pareto set. These algorithms are based on
the population which generates optimal solution on a single run having its own merits. Nondominated sorting
Genetic Algorithm [8] is applied which exhibited the suboptimal solution of result and consuming more time
for the evaluation. NSGA-II [9] exhibits elitism, ranking but fails in its uniformity of the trade-off, and this
can be compensated using dynamic crowding distance and more MOEAs are Strength Pareto Evolutionary
Algorithm [10], Niched pareto genetic algorithm [11], Multiobjective Particle swarm optimization [12],
Multiobjective θ-Particle swarm optimization [13], Multiobjective Differential Evolution [14], semidefinite
Programming [15], self adaptive learning bat algorithm [16], Multiobjective Global Best Artificial Bee
Colony [17], Grey Wolf Optimization [18]. In an MOEA a set of solutions are obtained, which utilizes
the fuzzy set theory to achieve the best compromise solution [19]. In this paper, two objectives are
considered simultaneously without converting to a single objective and layouted with modification of
NSGA-II and PVDE.
Combining two or more algorithms are referred to as hybridization which is a successful one in
solving environmental economic load dispatch problem. The main task of the hybrid method is to provide
diversified Pareto front. In this paper a hybrid method where used with the combination of MPVDE and
MNSGA-II is employed which is at the initial stage half of the population is applied with MNSGA-II where
non-dominated sorting is implemented and the remaining half of the population is carried with refreshed
population concept of semi-interquartile range and midquartile range to eliminate immovable local optima
using MPVDE and finally, Euclidean distance is evaluated for the next generation of the population. This
hybrid method is tested on IEEE 30 bus system with six generators and IEEE 118 bus system with fourteen
generators and 40 generators system. The remainder of the paper is organized as follows: in section 2,
the mathematical formulation of EELD, in section 3 on multiobjective optimization and in section 4 on
the brief description on MNSGA-II and MPVDE and hybrid method is presented in section5 results of three
test cases showing better performance in comparison with existing methods is presented.
2. PROBLEM FORMULATION
The combined economic emission dispatch is incorporated with two contradictory objectives, cost
and emission with constraints. The quadratic equation related to the cost function of every individual power
generation unit is given as
𝐶 = ∑ 𝐹𝑘(𝑃𝐺𝑘)𝑛
𝑘=1 (1)
𝐹𝑘(𝑃𝐺𝑘) = (𝑎 𝑘 + 𝑏 𝑘 𝑃𝐺𝑘 + 𝑐 𝑘 𝑃𝐺𝑘
2
) (2)
where Fk(PGk) is kth
generator cost function. The ak, bk, and ck are referred to kth
unit fuel cost coefficients.
n is the no.of generators. 𝐶 is the total fuel cost in dollars per hour. The below (3) is a combination of
quadratic and exponential functions represents the emission levels of which all harmful toxic gases.
𝐸(𝑃𝐺𝑘) = ∑ ((𝛼 𝑘 + 𝛽𝑘 𝑃𝐺𝑘 + 𝛾 𝑘 𝑃𝐺𝑘
2
) + 𝜉 𝑘exp(𝜆 𝑘 𝑃𝐺𝑘)𝑛
𝑘=1 ) (3)
where αk, βk, γk ,𝜉 𝑘, 𝜆 𝑘 are the emission coefficient of kth
unit. The constraints are explained in the following.
2.1. Power balance equations
The Power balance equation is represented in (4)
∑ 𝑃𝐺𝑘 = 𝑃𝐷 + 𝑃𝐿𝑂𝑆𝑆
𝑛
𝑘=1 (4)
here, PGk, PD, and PLOSS are represented the real power output at kth
generator, total laod demand and power
losses in transmission line respectively. The power loss is approximately calculated using (5).
𝑃𝐿𝑂𝑆𝑆 = ∑ ∑ 𝑃𝐺𝑙 𝐵𝑙𝑘 𝑃𝐺𝑘 + ∑ 𝑃𝐺𝑘 𝐵 𝑘𝑜 + 𝐵𝑜𝑜
𝑛
𝑘=1
𝑛
𝑘=1
𝑛
𝑙=1 (5)
where, Blk, Bko, B00 are powerloss coefficients or B coefficients.

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 4, August 2020 : 3358 - 3366
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2.2. Power capacity limits constraints
𝑃𝐺𝑘𝑚𝑖𝑛 ≤ 𝑃𝐺𝑘 ≤ 𝑃𝐺𝑘𝑚𝑎𝑥 (6)
where PGkmax and PGkmin are the maximum and minimum values of output power at the kth
generator.
2.3. Valve point effect of cost function
With the incorporation of these effects in the linear problem of optimization is transﬁgured to a non
convex problem with cost function including the ripple curve. The modiﬁed quadratic equation with these
effects is represented in (7).
𝐹𝑘(𝑃𝐺𝑘) = 𝑎 𝑘 + 𝑏 𝑘 𝑃𝐺𝑘 + 𝑐 𝑘 𝑃𝐺𝑘
2
+ |𝑒 𝑘(sin(𝑓𝑘(𝑃𝐺𝑘𝑚𝑖𝑛 − 𝑃𝐺𝑘)))| (7)
3. EVOLUTIONARY ALGORITHMS
Evolutionary algorithms overcome the drawbacks associated with classical methods. In this paper,
a hybrid method implemented to achieve efficient, good diversity and faster convergence rate.
3.1. Modified NSGA-II
In MNSGA-II the Euclidean distance is implemented in the selection process of each front in 2N
Population of the combined parent and offspring population. Euclidean distance implements midpoints to
enhance the diversity in each front. Population members which are out of the range of Euclidean distance will
be discarded and rest include in Population N, during the selection process, selected members Ni exceeds
the N then best fitness members are selected, and if the selected population is less than N, a new population is
generated which is within Euclidean distance.
Euclidean distance 𝐷 𝑎,𝑏
𝑖
= (√∑ (𝑑 𝑚
𝑎 − 𝑑 𝑚
𝑏 )2𝑛
𝑚=1 )/(𝑛 − 1) ; i=1, 2, 3...... (8)
If Ni > N then best fitness population members selected.
If Ni < N then new random population is generated which should lie in the range of Euclidean distance.
The range of Euclidean distance is developed as ((𝐷 𝑎,𝑏 + 𝐷𝑜, 𝐷 𝑎,𝑏 − 𝐷𝑜), where 𝐷𝑜 is selected such
that the maximum population members should exist within the range of Euclidean distance, the application of
Euclidean distance is to enhance the diversity among the population members.
3.2. Modified population variant differential evolutionary algorithm
In PVDE [20] the initial population is refreshed using the interquartile range concept at the initial
stage to make an efficient algorithm. Scaling factor and crossover probability variation, place a vital role in
the production of offspring. In MPVDE the concept coefficient of Quartile deviation is used.
Step 1: The initial half random population is generated.
Step 2: A two row vector is initialized for scaling factor and crossover probability parameters in the range
[0,1] and it minimum size is [1x3] vectors. Evaluation of maximum, minimum and median values
for each parameter is determined.
Step 3:
 Initially vector difference Varmin is evaluated with generation limits its difference is multiplied with 0.01.
 Var is calculated using the concept of coefficient of Quartile deviation with each column of parent
population.
Var =
𝑄1−𝑄2
𝑄1+𝑄2
; (9)
where Q1 is the semi interquartile range and Q2 is the mid quartile range
Q1 = (High quartile – Low quartile)/2; (10)
Q2 = (High quartile + Low quartile)/2; (11)
 With new limits 𝑜𝑓 𝐿𝑜𝑤𝑒𝑟 𝑎𝑛𝑑 𝐻𝑖𝑔ℎ𝑒𝑟 new refreshment population is evaluated with step 1.

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Step 4:
 Evaluate the fitness of the refresh parent population and find the best one which gives the minimum
fitness value and up gradation of scaling factor (sf) and crossover probability (cp) is done.
 Find the mutation and crossover, the selection is made from the merge population of offspring and parent.
 Upgradation of the parameter is done.
3.3. Hybrid method
In this paper the combination of MNSGA-II and MPVDE is used as a hybrid method for the solving
environmental economic load dispatch with two objectives cost and emission. In PVDE [20] two objectives
are converted into mono objective using the weighted sum method but in this paper cost function and
emission function is considered as two objectives. In this paper the entire population is splited into two
half’s, the first half of the population is applied with MNSGA-II and second half of the population is
encountered by MPVDE to achieve the best optimal solution the steps in the application of MNSGA-II and
MPVDE for solving environmental economic load dispatch is as follows
 Initialize the number of objectives, decision variables, and load demand, maximum number of iterations
and also cost and emission coefficients. Let k= [k1, k2, k3, k4, k5 ...] where k is the decision vector and
each element corresponds to the output power of each generator.
 Generate the random population such that it has to satisfy equality constraint in (4).
 MNSGA-II is applied for the first part of the initial population and using (2) and (3) evaluate
the objective function of both cost and emission.
 From the existing population initially identify the nondominated individuals. Predict the nondominated
sorting such that the ranking selection method is implemented to highlight the ranking fronts.
 For the evaluation of crowding distance, a sorted population of each objective function value in
the increasing order is required.
 The generation of half of the initial population of the offspring is evaluated by performing the mutation
and crossover.
 Evaluate the objective functions from (2) and (3) for the next half of the population using MPVDE, for
this population refreshment is done by using the concept of semi interquartile and mid quartile.
 Predicting the best population which gives minimum cost value and performs the crossover and mutation
for the generation of offspring.
 Merge both the offsprings that will equalise to the population in number. Combine parent population and
offspring that leads to twice the population.
 Select the best individuals of population based on euclidean distance such that the best non-dominant one
placed in the repository. In the next iteration it is taken as a new parent population and the process repeats
until it reaches maximum generation. Generally in the multiobjective combined environmental economic
load dispatch solutions leads to multiple optimal points in which the best optimal is to be obtained,
for this purpose a fuzzy set theory [21] is implemented.
3.4. Best optimal value
Fuzzy set theory is helpful in achieving the best solution from the pareto optimal set for the decision
maker [22], decision maker decision is inaccurate in nature. kth
objective function of the solution in pareto set
Fk is indicated by a membership function µk is defined as
𝜇 𝑘 =
{
1, 𝐹𝑘 ≤ 𝐹𝑘
𝑚𝑖𝑛
𝐹𝑘
𝑚𝑎𝑥
−𝐹 𝑘
𝐹𝑘
𝑚𝑎𝑥−𝐹𝑘
𝑚𝑖𝑛 , 𝐹𝑘
𝑚𝑖𝑛
< 𝐹𝑘 < 𝐹𝑘
𝑚𝑎𝑥
0, 𝐹𝑘 ≥ 𝐹𝑘
𝑚𝑎𝑥
(12)
where Fk
min
and Fk
max
are the minimum and maximum values of kth
objective function, the normalized
membership function µi
𝜇𝑖
=
∑ 𝜇 𝑘
𝑖𝑁 𝑜𝑏𝑗
𝑘=1
∑ ∑ 𝜇 𝑘
𝑗𝑁 𝑜𝑏𝑗
𝑘=1
𝑀
𝑗=1
(13)
Nondominated solutions in number is represented as M, the best solution having maximum value of µi
.

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4. RESULTS AND DISCUSSION
This hybrid method is tested with three test cases. Case 1 it related to IEEE 30 bus test system with
six generators with and without losses and Case 2 applied to IEEE 118 bus test system with 14 generators
with and without valve point loading effect and Case 3 is implemented on a 40generators system without
losses. In all the cases cost and emission objective function are not converted into a single objective and not
considered as a constraint in the optimization problem. MATLAB program was developed on Intel i3
processor with 2GB RAM, an operating system is WINDOWs 10.
4.1. Case 1
IEEE 30 bus test system having a load demand of 2.834pu with a base of 100MVA and having
Population number 40 and the maximum no of iterations is 100. The tradeoff curve for the EELD without
losses is shown in Figure 1 and with losses is shown in Figure 2. The minimum fuel cost of 607.1265 ($/hr)
is achieved for the emission of 0.2031 (ton/hr) and the maximum fuel cost of 637.8721($/hr) with
the minimum emission of 0.1942(ton/hr) as shown in Table 1 the execution time taken without losses is
9.2020 sec and with the losses the lowest cost value is 614.2687 ($/hr) for the emission value of 0.2009
(ton/hr) is shown in Table 2 and the time taken for the computation is 9.840sec. The cost and emission
coefficients as well as maximum and minimum values of power generation is taken as in [23].
Figure 1. IEEE 30 bus test system without losses Figure 2. IEEE 30 bus test system with losses
Table 1. Comparison of cost and emission results of case 1 without losses
Method
MNMNSGA-II+MPVDE SPEA2[24] MODE MOPSO FCPSO[24]
Cost Emission Cost Emission Cost Emission Cost Emission Cost Emission
PG1 0.2227 0.4076 0.1097 0.4060 0.1162 0.4151 0.1194 0.3979 0.1070 0.4097
PG2 0.3719 0.4609 0.2993 0.4589 0.2865 0.4604 0.3072 0.4258 0.2897 0.4550
PG3 0.5589 0.5380 0.5243 0.5378 0.5605 0.5409 0.4907 0.5268 0.5250 0.5363
PG4 0.7362 0.3892 1.0162 0.3834 1.0098 0.3808 1.0041 0.3984 1.0150 0.3842
PG5 0.5247 0.5307 0.5245 0.5378 0.5060 0.5298 0.5212 0.5336 0.5300 0.5348
PG6 0.4196 0.5076 0.3598 0.5101 0.3550 0.5070 0.3914 0.5515 0.3673 0.5140
Cost 607.1265 637.8721 600.109 638.264 600.2071 638.9388 600.2823 636.9045 600.132 638.358
Emission 0.2031 0.1942 0.2221 0.1942 0.2219 0.1942 0.2205 0.1944 0.2222 0.1942
Table 2. Comparison of cost and emission results of case 1 with losses
Method
MNSGAII+MPVDE SPEA2[24] MODE MOPSO FCPSO[24]
Cost Emission Cost Emission Cost Emission Cost Emission Cost Emission
PG1 0.2606 0.4048 0.1189 0.4107 0.1318 0.4169 0.1145 0.3872 0.1130 0.4063
PG2 0.4012 0.4625 0.3085 0.4635 0.2925 0.4478 0.3240 0.4209 0.3145 0.4586
PG3 0.5391 0.5436 0.5200 0.5447 0.5287 0.5488 0.5086 0.5271 0.5826 0.5510
PG4 0.7042 0.4110 1.0081 0.3903 0.9934 0.3847 1.0525 0.4545 0.9860 0.4084
PG5 0.5310 0.5380 0.5286 0.5444 0.5362 0.5635 0.5488 0.5950 0.5264 0.5432
PG6 0.4180 0.4942 0.3742 0.5155 0.3786 0.4995 0.3191 0.4828 0.350 0.4974
Cost 614.2687 640.2599 605.548 646.190 606.276 644.1750 607.8919 637.6409 607.786 642.896
Emission 0.2009 0.1942 0.2208 0.1942 0.2197 0.1942 0.2247 0.1947 0.2201 0.1942
Losses 0.0201 0.0351 0.0272 0.0335 0.0309

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4.2. Case 2
It is implemented on IEEE 118 bus system with 14 generators with and without Valve point loading
effect is exhibited. Total Demand was 2000MW [25] with a population of 40 and crossover probability and
mutation values are 0.85 and 0.166. Comparison is shown in Table 3 without valve point loading effect and
in Table 4 with valve point loading the corresponding Pareto optimal solutions are shown in Figure 3 and
Figure 4. For a minimum emission of 2776.1633(ton/hr) the cost value is 8968.1794($/hr) is obtained having
the execution time of 9.906sec in case of without valve point and with valve point minimum emission
2754.2895(ton/hr) and related cost value is 9004.3651($/hr) with execution time of 10.572sec.
Figure 3. IEEE 118 bus test system without
valve point
Figure 4. IEEE 118 bus test system with valve point
Table 3. Comparison of cost and emission results of case 2 without valve point
Table 4. Comparison of Cost and emission results of case 2 with valve point
Methods
Unit
MNSGA-II+MPVDE SPEA2 NSGA-2 MOPSO
Cost Emission Cost Emission Cost Emission Cost Emission
PG1 284.052875019457 197.626370894082 329.7295 236.8771 240.0744 219.0736 325.8810125 241.12950
PG2 192.18732935442 151.576676960222 150.0293 150.0267 302.1989 150.6923 150 150
PG3 130 130 95.3337 129.1020 95.4558 124.9328 130 130
PG4 128.3185708334 130 121.6660 127.7472 69.4093 128.1623 130 130
PG5 185.626065115719 163.104211030723 250.0010 150.6224 247.4409 153.9634 202.8506499 178.9299
PG6 179.495514517557 251.690474265875 182.3107 283.9287 236.9518 284.5399 194.7000195 222.3214
PG7 138.68198357291 180.541835667428 184.7832 184.8378 185.3728 187.2257 135 179.9619
PG8 139.637661586537 175.029843754326 158.0345 153.9764 160.0652 160.9197 109.6862982 145.6571
PG9 162 160.430587427345 123.2748 126.1220 76.8090 156.0239 162 162
PG10 160 160 155.5005 159.6728 137.0618 155.8425 160 160
PG11 80 80 60.4520 79.7902 60.5746 68.8119 79.9998255 80
PG12 80 80 71.0185 79.6400 63.6763 77.8466 80 80
PG13 85 85 62.9139 82.6572 71.5190 79.1796 84.8821944 85
PG14 55 55 54.9524 54.9995 53.3902 52.7858 55 55
Cost 8786.21988149318 9004.36512511877 9342.9384 9839.5134 9415.7144 10133.174 9701.492335 8908.9372
Emission 3212.8071442757 2754.28951669385 3605.6451 2850.8966 4799.8326 2850.4578 3255.166772 2827.1320

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4.3. Case 3
The proposed method is applied to the 40 generators system and the results are shown in the Table 5
and the corresponding Pareto graph is shown in Figure 5 showing the best compromise solution. The total
demand was 10500MW [26] with the population of 40 exhibited with 100 iterations and the trade off curve is
obtained for the trails of 30 times and for the minimum emission value 112444.1310 (ton/hr) the achieved
cost value 124483.5238 ($/hr) and the time taken for the execution of the Matlab program is 17.233 sec.
Figure 6 shows the graph between best values from refreshed population verses number of iterations. From
the graph, it is predicted that the best value of the cost function value over iteration 100 reaches
the minimum cost value which is used for mutation and crossover evaluation in MPVDE. The flow chart
shown in Figure7 gives the major steps in the implementation of a hybrid method for solving economic
emission dispatch problem. Initially modified non-dominant sorting genetic algorithm –II is applied followed
by modified Population Variant Differential Evolution and in both the methods non-dominant sorting is
applied for the generation of offspring’s and in this stream elitism concept is attributed to make the best one
in the repository which enhances the convergence rate. The selection process is ordered by the crowding
distance operator for improving the uniform spread over trade off curve. In MNSGA-II simulated binary
crossover and the polynomial mutation is carried over for the generation of corresponding offspring’s and
the latter method MPVDE best value which produce minimum fitness is predicted among the refreshed
population which is used in the calculations of mutation and crossover and generating a trust worthy results.
Figure 5. 40 generators system with no losses Figure 6. Best value verses no of iterations
Table 5. Cost and emission results of case 3
Method
Unit
MNSGA-II + MPVDE
Cost Emission Cost Emission
PG1 112.591217758152 103.149113447733 PG21 550 465.709353396319
PG2 113 106.916479663274 PG22 550 450.89835272927
PG3 119 115.205494222967 PG23 525.971565676971 475.842309302858
PG4 185.933992542511 163.636394629782 PG24 550 487.304987512046
PG5 97 96 PG25 533.525235230105 452.236324840282
PG6 132.722909130973 133.937743775726 PG26 550 441.114781162747
PG7 300 289.463756018975 PG27 10 39.6554649635563
PG8 300 297.274612619789 PG28 14.1412493106588 16.7022149967359
PG9 300 267.870157819963 PG29 10.4334632792134 26.4557096753855
PG10 185.670710236017 272.358792216004 PG30 97 92.836464973358
PG11 101.399856467714 243.910619018213 PG31 190 161.546942834624
PG12 128.999684988988 283.505029083938 PG32 157.744911648874 169.834574740498
PG13 125 370.647321748841 PG33 190 178.659794824307
PG14 244.159417496869 427.208944115737 PG34 200 194.972526053006
PG15 276.55263718383 379.776496078575 PG35 200 193.486955182649
PG16 426.349359613756 394.236973739718 PG36 200 188.995222780554
PG17 480.658436526678 409.90548362534 PG37 110 99.7272370525773
PG18 500 421.969560032622 PG38 110 100.394493141124
PG19 474.512320286505 472.586514658067 PG39 110 102.819750031863
PG20 550 473.661327061807 PG40 487.633032622187 437.585726229166
Cost
Emission
119633.313579596
380189.359156827
124483.523855686
112444.131071802

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Figure 7. Flow chart of hybrid method
5. CONCLUSION
The multiobjective economic emission load dispatch optimization problem has been solved with
many heuristic and novel methods. In this paper, two conflicting objectives are considered simultaneously
and the combination of MNSGA-II and MPVDE is highlighted as one of the hybrid methods in achieving
the best optimal solution. It is tested on IEEE 30 bus test system with 6 generators and IEEE 118 bus test
system with 14 generators and with standard 40 generators system. The results obtained are compared with
the existing methods. In all the three test cases population parameter and the maximum number of iterations
100 remain same in achieving the Pareto optimal set. Many numbers of trails of about 30 were implemented
for all methods like SPEA-II, MOPSO, and MODE, for achieving the optimal solution among this Hybrid
method achieved the best optimal solution with good convergence.
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 ISSN: 2088-8708
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BIOGRAPHIES OF AUTHORS
K. Rajesh currently pursuing Ph.D degree at JNTUA, Ananthapuramu, Andhra Pradesh, India.
His area of interest includes optimization techniques on Economic load dispatch, Renewable
energy sources and Demand side management.
Dr. N. Visali is received Ph.D from JNTUA, Anathapuramu. She is presently working as Professor
and PRINCIPAL, JNTUACE, Kalikiri, Chittoor district, Andhra Pradesh, India. Her area of
interest includes Economic load scheduling using optimization techniques, Controllers for FACTS
Devices, optimization techniques in placement of capacitor, Demand side management, DG.

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