This paper discusses the possible applications of particle swarm optimization (PSO) in the Power system. One of the problems in Power System is Economic Load dispatch (ED). The discussion is carried out in view of the saving money, computational speed – up and expandability that can be achieved by using PSO method. The general approach of the method of this paper is that of Dynamic Programming Method coupled with PSO method. The feasibility of the proposed method is demonstrated, and it is compared with the lambda iterative method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
Includes Introduction, Derivation of power flow through transmission line, Single line diagram of three phase transmission, methods of finding the performance of transmission line. 1.Analytical Method 2.Graphical method (circle diagram)., circle diagram of receiving end side and sending end side.
Includes Introduction, Derivation of power flow through transmission line, Single line diagram of three phase transmission, methods of finding the performance of transmission line. 1.Analytical Method 2.Graphical method (circle diagram)., circle diagram of receiving end side and sending end side.
Phasor measurement unit and it's application pptKhurshid Parwez
The effective operation of power systems in the present and the future depends to a large extent on how well the emerging challenges are met today. Power systems continue to be stressed as they are operated in many instances at or near their full capacities. In order to keep power systems operating in secure and economic conditions, it is necessary to further improve power system protection and control system. Phasor measurement unit (PMUs), introduced into power system as a useful tool for monitoring the performance of power system, has been proved its value in the extensive applications of electric power system. In response, a research program that is specifically aimed at using PMU to improve the power system protection and control. To ensure that the proposed research program is responsive to particular industry needs in this area, and participants of the workshop identified two major research areas in which technological and institutional solutions are needed: 1) PMU implementation, 2) PMU applications. It’s recommends research, design, and development (RD&D) projects in this report. The objective of these projects is to improve the reliability of local and wide transmission grid by enabling and enhancing the system protection and control schemes by using PMU measurement data, reduce the economic burden of utilizes to implement PMUs.
ECONOMIC LOAD DISPATCH USING GENETIC ALGORITHMIJARIIT
This paper present the application of Genetic Algorithm (GA) to Economic Load Dispatch problem of the power system. Economic Load Dispatch is one of the major optimization problems dealing with the modern power systems.ELD determines the electrical power to be generated by the committed generating units in a power system so that the total generation cost of the system is minimized, while satisfactory the load demand. The objective is to minimize the total generation fuel cost and maintain the power flow within safety limits. The introduced algorithm has been demonstrated for the given test systems considering the transmission line losses.
A comparative study has been carried by Gensol on Solar-Wind Hybrid Policies issued by Central Government, Gujarat State & Andhra Pradesh (A.P.) in terms of following:
1) Incentives & Pertinent Charges
2) Evacuation & Metering Scheme
3) Energy Accounting & Banking
4) AC-DC Integration & other important clauses.
Wide area monitoring systems (WAMS) are essentially based on the new data acquisition technology of phasor measurement and allow monitoring transmission system conditions over large areas in view of detecting and further counteracting grid instabilities.
Phasor measurement unit and it's application pptKhurshid Parwez
The effective operation of power systems in the present and the future depends to a large extent on how well the emerging challenges are met today. Power systems continue to be stressed as they are operated in many instances at or near their full capacities. In order to keep power systems operating in secure and economic conditions, it is necessary to further improve power system protection and control system. Phasor measurement unit (PMUs), introduced into power system as a useful tool for monitoring the performance of power system, has been proved its value in the extensive applications of electric power system. In response, a research program that is specifically aimed at using PMU to improve the power system protection and control. To ensure that the proposed research program is responsive to particular industry needs in this area, and participants of the workshop identified two major research areas in which technological and institutional solutions are needed: 1) PMU implementation, 2) PMU applications. It’s recommends research, design, and development (RD&D) projects in this report. The objective of these projects is to improve the reliability of local and wide transmission grid by enabling and enhancing the system protection and control schemes by using PMU measurement data, reduce the economic burden of utilizes to implement PMUs.
ECONOMIC LOAD DISPATCH USING GENETIC ALGORITHMIJARIIT
This paper present the application of Genetic Algorithm (GA) to Economic Load Dispatch problem of the power system. Economic Load Dispatch is one of the major optimization problems dealing with the modern power systems.ELD determines the electrical power to be generated by the committed generating units in a power system so that the total generation cost of the system is minimized, while satisfactory the load demand. The objective is to minimize the total generation fuel cost and maintain the power flow within safety limits. The introduced algorithm has been demonstrated for the given test systems considering the transmission line losses.
A comparative study has been carried by Gensol on Solar-Wind Hybrid Policies issued by Central Government, Gujarat State & Andhra Pradesh (A.P.) in terms of following:
1) Incentives & Pertinent Charges
2) Evacuation & Metering Scheme
3) Energy Accounting & Banking
4) AC-DC Integration & other important clauses.
Wide area monitoring systems (WAMS) are essentially based on the new data acquisition technology of phasor measurement and allow monitoring transmission system conditions over large areas in view of detecting and further counteracting grid instabilities.
Economic Load Dispatch (ELD) is a process of scheduling the required load demand among available generation units such that the fuel cost of operation is minimized. The ELD problem is formulated as a non-linear constrained optimization problem with both equality and inequality constraints. In this paper, two test systems of the ELD problems are solved by adopting the Cuckoo Search (CS) Algorithm. A comparison of obtained simulation results by using the CS is carried out against six other swarm intelligence algorithms: Particle Swarm Optimization, Shuffled Frog Leaping Algorithm, Bacterial Foraging Optimization, Artificial Bee Colony, Harmony Search and Firefly Algorithm. The effectiveness of each swarm intelligence algorithm is demonstrated on a test system comprising three-generators and other containing six-generators. Results denote superiority of the Cuckoo Search Algorithm and confirm its potential to solve the ELD problem.
ECONOMIC LOAD DISPATCH USING PARTICLE SWARM OPTIMIZATIONMln Phaneendra
In this ppt particle swarm optimization (PSO) is applied to allot the active power among the generating stations satisfying the system constraints and minimizing the cost of power generated.The viability of the method is analyzed for its accuracy and rate of convergence. The economic load dispatch problem is solved for three and six unit system using PSO and conventional method for both cases of neglecting and including transmission losses. The results of PSO method were compared with conventional method and were found to be superior.
HYBRID PARTICLE SWARM OPTIMIZATION FOR SOLVING MULTI-AREA ECONOMIC DISPATCH P...ijsc
We consider the Multi-Area Economic Dispatch problem (MAEDP) in deregulated power system
environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation
to the power generators in such a manner that the total fuel cost is minimized while all operating
constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm
Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of
proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration
Coefficients (PSO-TVAC) and RCGA.
Hybrid Particle Swarm Optimization for Solving Multi-Area Economic Dispatch P...ijsc
We consider the Multi-Area Economic Dispatch problem (MAEDP) in deregulated power system environment for practical multi-area cases with tie line constraints. Our objective is to generate allocation to the power generators in such a manner that the total fuel cost is minimized while all operating constraints are satisfied. This problem is NP-hard. In this paper, we propose Hybrid Particle Swarm Optimization (HGAPSO) to solve MAEDP. The experimental results are reported to show the efficiency of proposed algorithms compared to Particle Swarm Optimization with Time-Varying Acceleration Coefficients (PSO-TVAC) and RCGA.
Evolutionary algorithm solution for economic dispatch problemsIJECEIAES
A modified firefly algorithm (FA) was presented in this paper for finding a solution to the economic dispatch (ED) problem. ED is considered a difficult topic in the field of power systems due to the complexity of calculating the optimal generation schedule that will satisfy the demand for electric power at the lowest fuel costs while satisfying all the other constraints. Furthermore, the ED problems are associated with objective functions that have both quality and inequality constraints, these include the practical operation constraints of the generators (such as the forbidden working areas, nonlinear limits, and generation limits) that makes the calculation of the global optimal solutions of ED a difficult task. The proposed approach in this study was evaluated in the IEEE 30-Bus test-bed, the evaluation showed that the proposed FA-based approach performed optimally in comparison with the performance of the other existing optimizers, such as the traditional FA and particle swarm optimization. The results show the high performance of the modified firefly algorithm compared to the other methods.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
Security constrained optimal load dispatch using hpso technique for thermal s...eSAT Journals
Abstract This paper presents Hybrid Particle Swarm Optimization (HPSO) technique to solve the Optimal Load Dispatch (OLD) problems with line flow constrain, bus voltage limits and generator operating constraints. In the proposed HPSO method both features of EP and PSO are incorporated, so the combined HPSO algorithm may become more effective to find the optimal solutions. In this paper, the proposed Hybrid PSO, PSO and EP techniques have been tested on IEEE14, 30 bus systems. Numerical simulation results show that the Hybrid PSO algorithm outperformed standard PSO algorithm and Evolution Programming method on the same problem and can save considerable cost of Optimal Load Dispatch.
Dynamic Economic Dispatch Assessment Using Particle Swarm Optimization TechniquejournalBEEI
This paper presents the application of particle swarm optimization (PSO) technique for solving the dynamic economic dispatch (DED) problem. The DED is one of the main functions in power system planning in order to obtain optimum power system operation and control. It determines the optimal operation of generating units at every predicted load demands over a certain period of time. The optimum operation of generating units is obtained by referring to the minimum total generation cost while the system is operating within its limits. The DED based PSO technique is tested on a 9-bus system containing of three generator bus, six load bus and twelve transmission lines.
Genetic Algorithm for Solving the Economic Load DispatchSatyendra Singh
In this paper, comparative study of two approaches, Genetic Algorithm
(GA) and Lambda Iteration method (LIM) have been used to provide
the solution of the economic load dispatch (ELD) problem. The ELD
problem is defined as to minimize the total operating cost of a power
system while meeting the total load plus transmission losses within
generation limits. GA and LIM have been used individually for solving
two cases, first is three generator test system and second is ten
generator test system. The results are compared which reveals that GA
can provide more accurate results with fast convergence characteristics
and is superior to LIM.
IMPROVED SWARM INTELLIGENCE APPROACH TO MULTI OBJECTIVE ED PROBLEMSSuganthi Thangaraj
Electrical power industry restructuring has created highly vibrant and competitive market that altered many aspects of the power industry. In this changed scenario, scarcity of energy resources, increasing power generation cost, environment concern, ever growing demand for electrical energy necessitate optimal economic dispatch. Practical economic dispatch (ED) problems have nonlinear, non-convex type objective function with intense equality and inequality constraints. The conventional optimization methods are not able to solve such problems as due to local optimum solution convergence. Metaheuristic optimization techniques especially Improved Particle Swarm Optimization (IPSO) has gained an incredible recognition as the solution algorithm for such type of ED problems in last decade. The application of IPSO in ED problem, which is considered as one of the most complex optimization problem has been summarized in present paper. This paper illustrates successful implementation of the Improved Particle Swarm Optimization (IPSO) to Economic Load Dispatch Problem (ELD). Power output of each generating unit and optimum fuel cost obtained using IPSO algorithm has been compared with conventional techniques. The results obtained shows that IPSO algorithm converges to optimal fuel cost with reduced computational time when compared to PSO and GA for the three, six and IEEE 30 bus system.
Optimal power flow with distributed energy sources using whale optimization a...IJECEIAES
Renewable energy generation is increasingly attractive since it is non-polluting and viable. Recently, the technical and economic performance of power system networks has been enhanced by integrating renewable energy sources (RES). This work focuses on the size of solar and wind production by replacing the thermal generation to decrease cost and losses on a big electrical power system. The Weibull and Lognormal probability density functions are used to calculate the deliverable power of wind and solar energy, to be integrated into the power system. Due to the uncertain and intermittent conditions of these sources, their integration complicates the optimal power flow problem. This paper proposes an optimal power flow (OPF) using the whale optimization algorithm (WOA), to solve for the stochastic wind and solar power integrated power system. In this paper, the ideal capacity of RES along with thermal generators has been determined by considering total generation cost as an objective function. The proposed methodology is tested on the IEEE-30 system to ensure its usefulness. Obtained results show the effectiveness of WOA when compared with other algorithms like non-dominated sorting genetic algorithm (NSGA-II), grey wolf optimization (GWO) and particle swarm optimization-GWO (PSOGWO).
Operation cost reduction in unit commitment problem using improved quantum bi...IJECEIAES
Unit Commitment (UC) is a nonlinear mixed integer-programming problem. UC used to minimize the operational cost of the generation units in a power system by scheduling some of generators in ON state and the other generators in OFF state according to the total power outputs of generation units, load demand and the constraints of power system. This paper proposes an Improved Quantum Binary Particle Swarm Optimization (IQBPSO) algorithm. The tests have been made on a 10-units simulation system and the results show the improvement in an operation cost reduction after using the proposed algorithm compared with the ordinary Quantum Binary Particle Swarm Optimization (QBPSO) algorithm
Optimal Power Flow with Reactive Power Compensation for Cost And Loss Minimiz...ijeei-iaes
One of the concerns of power system planners is the problem of optimum cost of generation as well as loss minimization on the grid system. This issue can be addressed in a number of ways; one of such ways is the use of reactive power support (shunt capacitor compensation). This paper used the method of shunt capacitor placement for cost and transmission loss minimization on Nigerian power grid system which is a 24-bus, 330kV network interconnecting four thermal generating stations (Sapele, Delta, Afam and Egbin) and three hydro stations to various load points. Simulation in MATLAB was performed on the Nigerian 330kV transmission grid system. The technique employed was based on the optimal power flow formulations using Newton-Raphson iterative method for the load flow analysis of the grid system. The results show that when shunt capacitor was employed as the inequality constraints on the power system, there is a reduction in the total cost of generation accompanied with reduction in the total system losses with a significant improvement in the system voltage profile
Using particle swarm optimization to solve test functions problemsriyaniaes
In this paper the benchmarking functions are used to evaluate and check the particle swarm optimization (PSO) algorithm. However, the functions utilized have two dimension but they selected with different difficulty and with different models. In order to prove capability of PSO, it is compared with genetic algorithm (GA). Hence, the two algorithms are compared in terms of objective functions and the standard deviation. Different runs have been taken to get convincing results and the parameters are chosen properly where the Matlab software is used. Where the suggested algorithm can solve different engineering problems with different dimension and outperform the others in term of accuracy and speed of convergence.
International Journal of Engineering Research and DevelopmentIJERD Editor
• Electrical, Electronics and Computer Engineering,
• Information Engineering and Technology,
• Mechanical, Industrial and Manufacturing Engineering,
• Automation and Mechatronics Engineering,
• Material and Chemical Engineering,
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• Environmental Engineering,
• Petroleum and Mining Engineering,
• Marine and Agriculture engineering,
• Aerospace Engineering
Implementation of an Effective Biogeography Based Algorithm
(EBBO) for Economic Load Dispatch (ELD) problems in power system in order to obtain optimal
economic dispatch with minimum generation cost. Approach: A viable methodology has been
implemented for a 20 unit generator system to minimize the fuel cost function considering the
transmission loss and system operating limit constraints and is compared with other approaches such as
BBO, Lambda Iteration and Hopfield Model. Results: Proposed algorithm has been applied to ELD
problems for verifying its feasibility and the comparison of results are tabulated and pictorial
visualization for convergence of EBBO is represented. Conclusion: Comparing with the other existing
techniques, the EBBO gives better result by considering the quality of the solution obtained. This
method could be an alternative approach for solving the ELD problems in practical power system.
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A Case Study of Economic Load Dispatch for a Thermal Power Plant using Particle Swarm Optimization
1. International Journal of Science and Research (IJSR), India Online ISSN: 2319-7064
Volume 2 Issue 8, August 2013
www.ijsr.net
A Case Study of Economic Load Dispatch for a
Thermal Power Plant using Particle Swarm
Optimization
1
P. Ashok Kumar 2
M. Rajesh, 3
B. Venkata Prasanth
1
M. Tech Scholar, Department of Electrical & Electronics Engineering,
Narayana Engineering College, Nellore, (AP), India
2
Assistant Professor, Department of Electrical & Electronics Engineering,
Narayana Engineering College, Nellore, (AP), India
3
Professor & Head, Department of Electrical & Electronics Engineering,
QIS College of Engineering Technology, Ongole, (AP), India
Abstract: This paper discusses the possible applications of particle swarm optimization (PSO) in the Power system. One of the
problems in Power System is Economic Load dispatch (ED). The discussion is carried out in view of the saving money, computational
speed – up and expandability that can be achieved by using PSO method. The general approach of the method of this paper is that
of Dynamic Programming Method coupled with PSO method. The feasibility of the proposed method is demonstrated, and it is
compared with the lambda iterative method in terms of the solution quality and computation efficiency. The experimental results show
that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.
Keywords: Economic load dispatch, Particle Swarm Optimization, Dynamic Programming Method, Power Systems.
1. Introduction
Economic dispatch (ED) problem is one of the fundamental
issues in power system operation. In essence, it is an
optimization problem and its objective is to reduce the total
generation cost of units, while satisfying constraints.
Previous efforts on solving ED problems have employed
various mathematical programming methods and
optimization techniques. These conventional methods
include the lambda-iteration method, the base point and
participation factors method, and the gradient method [1, 2,
16, 17]. In these numerical methods for solution of ED
problems, an essential assumption is that the incremental
cost curves of the units are monotonically increasing
piecewise-linear functions. Unfortunately, this assumption
may render these methods infeasible because of its nonlinear
characteristics in practical systems. These nonlinear
characteristics of a generator include discontinuous
prohibited zones, ramp rate limits, and cost functions which
are not smooth or convex. Furthermore, for a large-scale
mixed-generating system, the conventional method has
oscillatory problem resulting in a longer solution time. A
dynamic programming (DP) method for solving the ED
problem with valve-point modelling had been presented by
[1, 2]. However, the DP method may cause the dimensions
of the ED problem to become extremely large, thus requiring
enormous computational efforts.
In order to make numerical methods more convenient for
solving ED problems, computational techniques, such as the
neural networks, genetic algorithm, particle swarm
optimization and etc., have been successfully employed to
solve ED problems for units [3, 4]. However, neural network
solution may suffer from excessive numerical iterations,
resulting in huge calculations. In the past decade, a global
optimization technique known as genetic algorithms (GA),
has been successfully used to solve power optimization
problems [1, 5–7]. The GA method is usually faster because
the GA has parallel search techniques, which emulate natural
genetic operations. Due to its high potential for global
optimization, GA has received great attention in solving ED
problems.
Though the GA methods have been employed successfully to
solve complex optimization problems, recent research has
identified some deficiencies in GA performance. This
degradation in efficiency is apparent in applications with
highly epistatic objective functions (i.e., where the
parameters being optimized are highly correlated) [the
crossover and mutation operations cannot ensure better
fitness of offspring because chromosomes in the population
have similar structures and their average fitness is high
toward the end of the evolutionary process] [10,14].
Moreover, the premature convergence of GA degrades its
performance and reduces its search capability that leads to a
higher probability toward obtaining a local optimum [10].
Particle swarm optimization (PSO), first introduced by
Kennedy and Eberhart, is one of the modern heuristic
algorithms. It was developed through simulation of a
simplified social system, and has been found to be robust in
solving continuous nonlinear optimization problems [11-15].
The PSO technique can generate high-quality solutions
within shorter calculation time and stable convergence
characteristic than other stochastic methods [12-15].
Although the PSO seems to be sensitive to the tuning of
some weights or parameters, many researches are still in
progress for proving its potential in solving complex power
system problems [14]. In this paper, a PSO method for
solving the ED problem in power system is proposed. The
feasibility of the proposed method was demonstrated [7,19],
respectively, and compared with the Lambda iteration
method.
458
2. International Journal of Science and Research (IJSR), India Online ISSN: 2319-7064
Volume 2 Issue 8, August 2013
www.ijsr.net
2. Economic Load Dispatch
The Economic Dispatch (ED) is a nonlinear programming
problem which is considered as a sub-problem of the Unit
Commitment (UC) problem [17]. In a specific power system
with a determined load schedule, ED planning performs the
optimal power generation dispatch among the existing
generation units. The solution of ED problem must satisfy
the constraints of the generation units, while it optimizes the
generation based on the cost factor of the generation units.
Equation (1) represents the total fuel cost for a power system
which is the equal summation of all generation units fuel
costs, in a power system.
)1(
1
NG
j
jj PFCost
Where NG is the number of generation units and Pj is the
output power of jth
generation unit. The cost function in eq.
(1) can be approximated to a quadratic function of the power
generation; therefore, the total cost function (FT) will be
changed to eq. (2).
)2(cPbPamin
PFminF
NG
1j
jjj
2
jj
NG
1j
jjT
Where:
jP Generated power by jth
generation unit
jjj c,b,a Fuel cost coefficients of unit j
Two set of constraints are considered in the present study,
including equality constraints and inequality constraints.
2.1. Equality Constraints
Normally, in a power system the amount of generated power
has to be enough to feed the load demand plus transmission
lines loss. Since the transmission lines are located between
the generating units and loads, Ploss can occur anywhere
before the power reaches load (Pd) shown in eq. (3). Any
shortage in the generated power will cause shortage in
feeding the load demand which may cause many problems
for the system and loads.
)3(PPP lossd
NG
1j
j
Where Pd is the load demand and Ploss is the transmission
lines loss, while NG and Pj have the same definition as in eq.
(2).
Here, the loss coefficient method which is developed by
Kron and Kirchmayer, is used to include the effect of
transmission losses [19-21]. B-matrix which is known as the
transmission loss coefficients matrix is a square matrix with
a dimension of NG×NG while NG is the number of
generation units in the system. Applying B-matrix gives a
solution with generated powers of different units as the
variables. Eq. (4) shows the function of calculating Ploss as
the transmission loss through B-matrix.
)4(PBPP
NG
1i
NG
1j
jijjloss
Where:
lossP Total transmission loss in the system
ji P,P Generated power by ith
and jth
generating units
respectively
ijB Element of the B-matrix between ith
and jth
generating
units
2.2. Inequality Constraints
All generation units have some limitations in output power
regardless of their type. In existing power systems, thermal
units play a very important role. Thermal units can pose both
maximum and minimum constraints on the generating
power, so there is always a range of operating work for the
generating units. Generating less power than minimum may
cause the rotor to over speed whereas at maximum power, it
may cause instability issues for synchronous generators [21].
So, eq. (5) has to be considered in all steps of solving the ED
problem.
)5(PPP max
jj
min
j
For j=1, 2… NG.
Where
max
j
min
j P&P and are the constraints of generation
for jth
generating unit.
3. Particle Swarm Optimization
Particle swarm optimization (PSO), which is a stochastic
population based, evolutionary computer algorithm for
problem solving, based on social behaviour of groups like
flocking of birds or schooling of fish. It is a sort of swarm
intelligence that predicts everyone solution as ‘‘particles’’
which change their positions with change in time. pbest of
each particle modifies its position in search space in
accordance with its own experience and also gbest of
neighbouring particle by remembering the best position
visited by itself and its neighbours, then calculating local and
global positions. The particle updates its velocity and
positions with following equation (6) and (7).
)6()xgbest(rc
)xpbest(rcvwv
t
ii22
t
ii11
t
i
1t
i
)7(vxx 1t
i
t
i
1t
i
Where, vi is the particle velocity vector, xi is the particle
position vector. pbesti is the best position achieved by
particle ‘i' based on its own experience and gbesti is the best
position of the particle based on overall swarm experience.
r1, r2 is a random numbers between [0, 1]. c1, c2 are learning
factors. Usually these are two positive constants, c1= c2 = 2.
Inertia weight is w.
The following weighting function is usually utilized:
)8(Iter
Iter
ww
ww
max
minmax
max
Where
weightsfinalandInitialw,w minmax
numberiterationMaximumItermax
numberiterationCurrentIter
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3. International Journal of Science and Research (IJSR), India Online ISSN: 2319-7064
Volume 2 Issue 8, August 2013
www.ijsr.net
Suitable selection of inertia weight in above equation
provides a balance between global and local explorations,
thus requiring less number of iterations on an average to find
a sufficient optimal solution. As originally developed, inertia
weight often decreases linearly from about 0.9 to 0.4 during
a run. The algorithmic steps involved in particle swarm
optimization technique are as follows:
1) Select the various parameters of PSO.
2) Initialize a population of particles with random positions
and velocities in the problem space.
3) Evaluate the desired optimization fitness function for
each particle.
4) For each individual particle, compare the particles fitness
value with its pbest. If the current value is better than the
pbest value, then set this value as the pbest for agent i.
5) Identify the particle that has the best fitness value. The
value of its fitness function is identified as gbest.
6) Compute the new velocities and positions of the particles
according to equation (6) & (7).
7) Repeat steps 3-6 until the stopping criterion of maximum
generations is met.
The procedure of the particle swarm optimization technique
can be summarized in the flowchart of Fig. 1.
Figure 1: The flowchart of PSO technique
4. Simulation Results and Analysis of
Performance
To verify the feasibility and effectiveness of the proposed
PSO algorithm, two different power systems were tested one
is 6 generating units and other is 9 generating units. Results
of proposed particle swarm optimization (PSO) are
compared with Lambda iterative method. A reasonable B-
loss coefficients matrix of power system network has been
employed to calculate the transmission loss. The software
has been written in the MATLAB-7 language.
Case Study-1: 6-units system
In this case, a standard six-unit thermal power plant (IEEE
30 bus test system) is used to demonstrate how the work of
the proposed approach. Characteristics of thermal units are
given in Table 1, the following coefficient matrix Bij losses.
Table 1: Generating Unit capacity and coefficients
Unit
min
jP
(MW)
max
jP
(MW)
ja
2
MW/.Rs
jb
MW/.Rs
jc
(Rs.)
1 100 500 0.0070 7 240
2 50 200 0.0095 10 200
3 80 300 0.0090 8.5 300
4 50 150 0.0090 11 150
5 50 200 0.0080 10.5 200
6 50 120 0.0075 12 120
0.0001500.000002-0.000008-0.000006-0.000001-0.000002-
0.000002-0.0001290.000006-0.0000100.000006-0.000005-
0.000008-0.000006-0.0000240.0000000.0000010.000001-
0.000006-0.000010-0.0000000.0000310.0000090.000007
0.000001-0.000006-0.0000010.0000090.0000140.000012
0.000002-0.000005-0.000001-0.0000070.0000120.000017
ijB
The comparison with Lambda iterative and proposed PSO
technique simulation results are shown in Table 2. Table 2
shows the optimal power output, total cost of generation, as
well as active power loss for the power demands of 1000
MW, 1200 MW, 1350 MW and 1450 MW. Table 2 shows
that the PSO method is better than Lambda iterative method
for each loading.
Table 2: Best power output for 6-generation system
Load
demand
(MW)
Method
P1
(MW)
P2
(MW)
P3
(MW)
P4
(MW)
P5
(MW)
P6
(MW)
Power
Loss
(MW)
Fuel
cost
(Rs./Hr)
500
Lambda Iterative 216.880 50.000 85.702 50.000 50.000 50.000 1.991 6106.21
PSO 216.106 50.000 85.880 50.000 50.000 50.000 1.991 6105.02
700
Lambda Iterative 312.282 73.420 159.487 50.000 59.140 50.000 4.164 8288.81
PSO 312.957 77.806 160.516 50.000 52.928 50.000 4.199 8267.55
1000
Lambda Iterative 391.557 132.135 220.812 93.182 122.043 50.000 8.127 11957.2
PSO 393.634 138.455 222.537 90.271 113.217 50.000 8.123 11930.4
1200
Lambda Iterative 434.380 163.796 254.043 128.659 15.661 76.594 11.307 14559
PSO 438.852 172.501 257.243 125.645 146.350 70.708 11.293 14538.1
1350
Lambda Iterative 466.385 187.465 278.916 150.000 180.562 101.657 14.212 16586.1
PSO 470.988 196.721 281.878 150.000 169.617 94.887 14.986 16575.5
1450
Lambda Iterative 497.110 200.000 300.000 150.000 200.000 120.000 16.739 17980.1
PSO 500.000 200.000 300.000 150.000 196.687 120.000 16.688 17975.2
Case Study-2: 9-units system
In this case, a 9-unit thermal power plant is used to
demonstrate how the work of the proposed approach. The
simulation results with conventional method and proposed
PSO technique are shown in Table 3. From the simulation
results show that the generation output of each unit is
obtained correction reduces the total cost of generation and
transmission losses when compared with the conventional
method.
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4. International Journal of Science and Research (IJSR), India Online ISSN: 2319-7064
Volume 2 Issue 8, August 2013
www.ijsr.net
Table 3: Best power output for 6-generation system
Load
demand
(MW)
Method
P1
(MW)
P2
(MW)
P3
(MW)
P4
(MW)
P5
(MW)
P6
(MW)
P7
(MW)
P8
(MW)
P9
(MW)
Power
Loss
(MW)
Fuel
cost
(Rs./Hr)
700
Lambda
Iterative
250.1 50 111 50 50 50 45.38 71.24 25 3.6 8527.32
PSO 100 50.28 80 67.14 50 83.99 66.92 98.16 108.3 5.15 8526.02
1000
Lambda
Iterative
328.1 85.03 171.1 50 71.45 50 124.2 100 25 6.95 11885.1
PSO 100 104.4 80 139.7 104.9 120 138.7 100 120 7.63 11854.5
1200
Lambda
Iterative
364.1 111.7 199.3 72.88 107.8 50 150 100 54.69 9.61 14338.5
PSO 135.4 162.5 108.1 150 163.6 120 150 100 120 9.6 14137.1
1450
Lambda
Iterative
410.7 146.3 235.9 114.3 155.8 56.76 150 100 9.37 13.96 17545.3
PSO 235.5 200 187.8 150 200 120 150 100 120 13.2 17244.6
1600
Lambda
Iterative
435.5 164.7 254.8 136.7 182.3 77.5 150 100 118.7 17.05 19552.1
PSO 321 200 255.5 150 200 120 150 100 120 16.46 19251.4
1800
Lambda
Iterative
487.5 200 293.4 150 200 120 150 100 120 21.63 22257.5
PSO 481.7 200 300 150 200 120 150 100 120 21.66 22056.2
5. Conclusion
This paper presents an efficient and simple approach for
solving the economic load dispatch (ELD) problem. This
paper demonstrates with clarity, chronological development
and successful application of PSO technique to the solution
of ELD. Two test systems 6-generator and 9-generator
systems have been tested and the results are compared with
Lambda iteration method. The proposed approach is
relatively simple, reliable and efficient and suitable for
practical applications.
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Author Profile
Papareddy Ashok Kumar received the B. Tech.
degree in electrical & electronics engineering from Sri
Venkateswara University, Tirupati, India, in 2010. He
is a M. Tech. scholar of Jawaharlal Nehru
Technological University, Ananthapur, India. His interests are in
power system control design and electrical machines.
Mulumudi Rajesh received the M. Tech. degree in
electrical & electronics engineering from Jawaharlal
Nehru Technological University, Kakinada, India, in
2010. Currently, he is an Assistant Professor at
Narayana Engineering College, Nellore. His interests
are in power system operation & control, economic load dispatch
and dynamic load modelling.
Dr. B. Venkata Prasanth received the B.Tech. degree
in Electrical & Electronics Engineering from Sri
Krishnadevaraya University & M. Tech. degree in
Electrical Power Systems from Jawaharlal Nehru
Technological University, Ananthapur, India. He
received his Ph.D. degree in Electrical & Electronics Engineering
from Jawaharlal Nehru Technological University, Hyderabad,
India. He has got a teaching experience of more than 14 years.
Currently, he is working as Professor & Head in QIS College of
Engineering and Technology, Ongole, India in the Dept. of
Electrical & Electronics Engineering. He has published a number of
papers in various national & international journals & conferences.
He is also guiding a number of research scholars in various topics
of electrical engineering. His research interests include application
of intelligent controllers to power system control design, power
system restructuring, power system economics & optimization.
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