Economic Load Dispatch Optimization of Six Interconnected Generating Units Using Particle Swarm Optimization

IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE)
e-ISSN: 2278-1676,p-ISSN: 2320-3331, Volume 6, Issue 2 (May. - Jun. 2013), PP 21-27
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Economic Load Dispatch Optimization of Six Interconnected
Generating Units Using Particle Swarm Optimization
Ravinder Singh Maan1
, Om Prakash Mahela2
, Mukesh Gupta3
1
(Assistant Professor, Dept. of Electrical Engineering, Jaipur National University, Jaipur, India)
2
(Graduate Student Member IEEE & Junior Engineer-I, RRVPNL, Jaipur, India)
3
(Assistant Professor, Department of Electrical Engineering, JNIT Jaipur, India)
Abstract : This paper describe about the optimization of economic loading dispatch (ELD) problem. Economic
loading dispatch is one of the important optimization tasks which provide economic condition for a power
system. The ELD problems have non-smooth objective function with equality and inequality constraints. This
paper presents particle swarm optimization (PSO) method for solving the economic dispatch(ED) problem in
power system. The particle swarm optimization is an efficient and reliable evolutionary computational
technique, which is used to solve economic load dispatch with line power flows. This paper describes, a new
PSO framework used to deal with the equality and inequality constraints in ELD problem. The proposed PSO
can always provide satisfying results within a realistic computation time. The PSO is applied with non-smooth
cost function. The six thermal units, 26 buses and 46 transmission lines system is used in this paper. The
proposed PSO method results are compared with the genetic algorithm (GA) and conventional method to show
the effectiveness of PSO method to solve the ELD problems in power system.
Keywords- Economic load dispatch, generating unit, genetic algorithm, power system, loss minimization,
particle swarm optimization.
I. INTRODUCTION
The electric utility systems are interconnected in such a way to achieve the benefits of minimum
production cost, maximum reliability and better operating conditions. The economic load dispatch is to
minimize the total operating cost of generating units while satisfying system equality and inequality constraints.
The economic load dispatch (ELD) is most of power system optimization problem which have complex and
non-linear characteristics with heavy equality and inequality. An Economic loading dispatch means
minimization of fuel cost of generating unit under some constraints and also reduced transmission losses [1].
The main objective of the optimization problem is to reduce the total generation cost of units while satisfying
constraints [3]-[5]. To solve these problems, various salient mathematical approaches have been suggested in
the past decades and the multi-objective optimization of power plant such as reduction of fuel cost, heat loss
rate, minimize the transmission losses and minimization of pollutant emissions [5]-[7].
The mathematical approaches also include non-linear programming, linear programming [8], Newton
based technique [1], Base point and participation method, lambda iteration method [7], gradient method [4]. In
this technique the required essential assumption is that the incremental cost curves of the units are
monotonically increasing piece wise-linear function but these methods are infeasible because of its non-linear
characteristics in practical system [4]-[7].
There are some powerful solution schemes to obtain global optimum solution or to solve ELD problem
in power system optimization problems which are Evolutionary technique such as Genetic algorithms (GA),
Artificial Neural Network (ANN), Tabu search, Simulated annealing and Particle swarm optimization (PSO). In
the past decade, Genetic Algorithm (GA) has been successfully used to solve power optimization problem such
as feeder reconfiguration and capacitor placement in a distribution system [4] & [7].
For solving continuous non-linear optimization problems, the PSO technique is robust; generate high
quality solutions within shorter computational time [4] & [8]. The Genetic algorithm (GA), Evolutionary
programming (EP), Artificial Neural Network (ANN) require high computational time and enhanced
computational efficiency [9]. The PSO is also easy to implement, flexible mechanism to obtain global optimum
solution, sensitive to turning of its parameters, improve the solution quality rapidly and simple in concept [8] &
[10]-[11]. The PSO is employed for complex optimization problem [12]. The PSO method gives the result for
lower generation cost compared with other hierarchical methods and provides better solution than others [5].
The PSO is also fast convergence technique. This method considers the maximum and minimum value of each
generator limits and line flow. This paper presents the application of PSO method for optimization of Economic
Load Dispatch problem of six interconnected generating units and the results are compared with the GA method
and conventional method. The results show the superiority of PSO as compared to the Genetic Algorithm and

Economic Load Dispatch Optimization of Six Interconnected Generating Units Using Particle Swarm
conventional method. The ELD problem is represented as a non-smooth optimize problem and to solve these
problem various salient method have been proposed.
II. PARTICLE SWARM OPTIMIZATION TECHNIQUE
Particle swarm optimization (PSO) algorithm was developed by Kennedy and Eberhart in 1995, which
is a kind of heuristic global optimization technique [1]-[2]. The PSO method is also applied to various fields of
the power system optimization such as reactive power and voltage control, stabilizer design and dynamic
security border identification. In practice, an ELD problem is more difficult to obtain optimize problem solution.
Particle swarm optimization (PSO) is population based stochastic optimization technique and based on the
behaviour of birds flocking or fish schooling (called particle or agent) of a swarm [10]. The study of PSO is
performed in two dimensional spaces with the simulation of birds flocking or fish schooling and each bird or
fish positions is called agent or particle which is represented in the X-Y coordinates by a point.
The current position of the agent or particle is called 𝑝𝑏𝑒𝑠𝑡 value and the 𝑝𝑏𝑒𝑠𝑡 value is not in the
group of birds. There is some another value which is known as 𝑔𝑏𝑒𝑠𝑡 value. The 𝑔𝑏𝑒𝑠𝑡 value is defined as the
value of the agent or position of the agent in a whole group among 𝑝𝑏𝑒𝑠𝑡 of all agents.
Using the concept of velocity, each agent tries to modify its position which is given as:
𝑣𝑖
𝑘+1
= 𝜔𝑣𝑖
𝑘
+𝐸1 𝑟𝑎𝑛𝑑1 ×(𝑝𝑏𝑒𝑠𝑡𝑖 − 𝑐𝑖
𝑘
) +𝐸2 𝑟𝑎𝑛𝑑2 × 𝑔𝑏𝑒𝑠𝑡𝑖 − 𝑐𝑖
𝑘
………… (1)
Where,
𝒗𝒊
𝒌+𝟏
= velocity of agent i at iteration k
𝒗𝒊
𝒌
=velocity of agent 𝑖 at iteration 𝑘
𝝎 = weighting function
𝒄𝒊
𝒌
= current position of agent i at iteration k
𝐄 𝟏 𝐚𝐧𝐝 𝐄 𝟐 = weighting Factors
𝒓𝒂𝒏𝒅 𝟏, 𝒓𝒂𝒏𝒅 𝟐 = random number functions Between 0.0 to 1.0
𝒑𝒃𝒆𝒔𝒕𝒊 = personal best of agent 𝑖
𝒈𝒃𝒆𝒔𝒕𝒊 =best value of agent 𝑖 within whole group
The weighting function is defined as which is used in equation (1):
𝜔 = 𝜔 𝑚𝑎𝑥 −
𝜔 𝑚𝑎𝑥 −𝜔 𝑚𝑖𝑛
𝑖𝑡𝑒𝑟 𝑚𝑎𝑥
𝑖𝑡𝑒𝑟 … … . ….(2)
Where,
𝝎 𝒎𝒊𝒏 =final Weight
𝝎 𝒎𝒂𝒙 =initial Weight
𝒊𝒕𝒆𝒓 𝒎𝒂𝒙 =maximum Iteration Number
𝒊𝒕𝒆𝒓 =current iteration number
The current position (in the swarm) can be modified by the following equation:
𝑐𝑖
𝑘+1
= 𝑐𝑖
𝑘
+ 𝑣𝑖
𝑘+1
… … … … . (3)
By the equation (1), we can find the 𝑔𝑏𝑒𝑠𝑡 model. The inertia weight approach (IWA) is defined using
equation (2) in (1). Fig.1 shows the concept of modification of a search point by a PSO.
Fig.1 Concept of modification of a searching point by PSO
The value of parameters in equations (1) and (2) are selected as given in Table 1.
Y
X
ck
𝒗 𝒌
𝒄 𝒌+𝟏
𝒗 𝒈𝒃𝒆𝒔𝒕
𝒗 𝒑𝒃𝒆𝒔𝒕
𝒗 𝒌+𝟏

TABLE 1
PARAMETER VALUES
III. PROBLEM FORMULATION
3.1 Objective Function Formulation
The main objective of economic load dispatch is that of the minimization of total fuel cost for each
generating unit and also reduced the transmission losses with increased each generating unit output also with
load demand of power system while satisfying various constraints. The objective function of ELD problem is
defined as:
𝑀𝑖𝑛𝐶𝑡 = 𝐶𝑖
𝑛 𝑔
𝑖=1
(𝑃𝑖)
= 𝛼𝑖 + 𝛽𝑖 𝑃𝑖 + 𝛾𝑖 𝑃𝑖
2𝑛 𝑔
𝑖=1
… (4)
Where,
𝑪𝒊 𝑷𝒊 =: Generation cost function
𝜶𝒊, 𝜷𝒊, 𝜸𝒊 = Cost coefficient of the 𝑖 𝑡ℎ
generator
𝒏 𝒈 =The total number of dispatchable generating plants
𝑷𝒊 = The Generation of the 𝑖 𝑡ℎ
Plant
3.2 Constraints Formulation
The power balance and generator operation are the two important constraints while optimizing the
economic load dispatch of interconnected generator units. These constraints are as given below:
(i) Power balance
𝑃𝑖 = 𝑃𝐷
𝑛 𝑔
𝑖=1
+ 𝑃𝐿 (𝑖 = 1, . . 𝑛 𝑔)…… (5)
(ii) Generator operation constraints
𝑃𝑖
𝑚𝑖𝑛
≤ 𝑃𝑖 ≤ 𝑃𝑖
𝑚𝑎𝑥
(𝑖 = 1, . . 𝑛 𝑔)… (6)
Where
𝑷𝒊
𝒎𝒊𝒏
,𝑷𝒊
𝒎𝒂𝒙
= are the minimum and maximum output power generation of unit 𝑖.
The total transmission network losses is a function of unit power output that can be represented using
B-coefficient. The simplest quadratic form of transmission network power losses is
𝑃𝐿 = 𝑃𝑖 𝐵𝑖𝑗 𝑃𝑗
𝑛 𝑔
𝑗=1
𝑛 𝑔
𝑖=1
………….…. (7)
A more general formula containing a linear term and a constant term, referred to as Kron’s loss formula, is
𝑃𝐿 = 𝑃𝑖 𝐵𝑖𝑗 𝑃𝑗 + 𝐵0𝑖 𝑃𝑖 + 𝐵00
𝑛 𝑔
𝑖=1
𝑛 𝑔
𝑗=1
𝑛 𝑔
𝑖=1
………………………...……….. (8)
IV. PROPOSED ALGORITHM OF PSO FOR SOLVING ELD PROBLEM
In this paper a new approach to implement the PSO algorithm for solving the economic load dispatch
problem is used. The following steps are used while solving the ELD problem by using PSO techniques.
Step 1: Initialize the group (swarm size, initial velocity, particle position).
Step 2: Set the value for iteration count
Step 3: Check for fitness value of each particle
Step 4: If step 3 is satisfactory then update 𝑝𝑏𝑒𝑠𝑡 𝑎𝑛𝑑 𝑔𝑏𝑒𝑠𝑡
Step 5: Update position and velocity using equations (3) and (1)
Step 6: Go to step 3 until satisfying stopping criteria and go to step 7 when stopping criteria is satisfied.
Step 7: Print the final results.
The result of the PSO method is compared with GA method and conventional method. The MATLAB
7.10.0(R2010a) language is used for simulation and executed on an Intel CORE i3 laptop with 4 GB RAM. The
flow chart of proposed PSO algorithm for solving ELD problem is shown in Fig. 2.
𝑬 𝟏 = 𝑬 𝟐 𝒘 𝒎𝒂𝒙 𝒘 𝒎𝒊𝒏
2.0 0.9 0.4

Set for the initial conditions like swarm size, particle
velocity, initial velocity
Evaluate for particles by fitness value
If fitness value
satisfactory
Fitness Satisfactory
Fitness Satisfactory
Find 𝑝𝑏𝑒𝑠𝑡 𝑎𝑛𝑑 𝑔𝑏𝑒𝑠𝑡
Update Position and velocity using Eq. 7 and
5 respectively& check for modifying
velocity and position
If find solution
Stopping criteria met
Stop
NO
O
YES
YES
NO
Start
Update personal best and global best
Fig. 2. Flow Chart of Proposed Algorithm for ELD Optimization using PSO
V. SIMULATION RESULTS AND DISCUSSION
The six unit test system consisting of six thermal units, 26 buses, and 46 transmission lines is used for
simulation of proposed problem of economic load dispatch. This system is simulated for 50 iterations. The
characteristics of the six thermal units are given in Table 2.

TABLE 2
GENERATING UNIT CAPACITY AND COEFFICIENTS
Unit
𝑷𝒊
𝒎𝒊𝒏
𝑷𝒊
𝒎𝒂𝒙
𝜶𝒊($) 𝜷𝒊($/𝑴𝑾) 𝜸𝒊($/𝑴𝑾 𝟐
)
1 100 500 240 7.0 0.0070
2 50 200 200 10.0 0.0095
3 80 300 220 8.5 0.0090
4 50 150 200 11.0 0.0090
5 50 200 220 10.5 0.0080
6 50 120 190 12.0 0.0075
The equations used in simulation for fuel cost (Rs /hr) of six generating units are given below:
𝑭 𝟏𝟏 = 0.0070𝑷 𝟏
𝟐
+ 7.0𝑷 𝟏 + 240
𝑭 𝟏𝟐= 0.0095𝑷 𝟐
𝟐
+ 10.0𝑷 𝟐 + 200
𝑭 𝟏𝟑 = 0.0090 𝑷 𝟑
𝟐
+ 8.5𝑷 𝟑 + 220
𝑭 𝟏𝟒 = 0.0090 𝑷 𝟒
𝟐
+ 11.0𝑷 𝟒 + 200
𝑭 𝟏𝟓=0.0080𝑷 𝟓
𝟐
+10.5𝑷 𝟓 + 220
𝑭 𝟏𝟔 = 0.0075𝑷 𝟔
𝟐
+12.0𝑷 𝟔+ 190
The best solution of economic load dispatch optimization of 6 interconnected unit systems is given in
Table 3. The results of GA method and conventional method presented in [4] are also given in Table 3. The
results of genetic algorithm and conventional methods are used to compare the performance of proposed
method. The simulation results of relation between nos. of iterations and fuel cost (Rs /hr) using MATLAB is
shown in Fig. 3.
TABLE 3
BEST SOLUTION OF PROPOSED PSO METHOD AND GA*, CONVENTIONAL* METHODS
*Source [4].
Fig. 3 Relation between Nos. of Iteration and Cost in Rs/ hr
0 5 10 15 20 25 30 35 40 45 50
5000
6000
7000
8000
9000
10000
11000
12000
13000
# of iterations
CostinRs./hr
Unit Power
Output
PSO Method GA Method Conventional Method
P1(MW) 499.9170 444.64 474.1196
P2(MW) 199.5562 160.13 173.7886
P3(MW) 299.950 278.31 190.9515
P4(MW) 162.5222 140.55 150.0000
P5(MW) 199.8994 199.58 196.7196
P6(MW) 119.9644 107.74 103.5772
Total power
output(MW)
1561.8092 1331.35 1325.61
Total Generation
Cost (Rs. /hr.)
1.5269e+004 1.6198e+004 16760.73

In this paper, a new approach to solve economic load dispatch problem using PSO method is used. The
PSO algorithm provides an optimal solution with less computational time and reasonable number of iterations.
The results presented in Table 3 shows that PSO has provided modified results as compared to genetic algorithm
and other conventional numerical methods. The PSO technique improves the computational time and
convergence. This PSO algorithm is also used to find the optimum solution for the multi-objective problems.
The PSO algorithm gives specified load demand with minimum fuel cost and increased power output
for each unit. Therefore, in future the PSO algorithm will be most important and efficient technique to solve the
large optimization problems with lower transmission losses because the PSO algorithm is simpler in structure
than other methods.
VI. CONCLUSION
In this paper, the economic load dispatch optimization problem is solved using PSO algorithm
successfully. The PSO algorithm is simple in concept, higher solution quality and lower computational time.
From the results, we conclude that the PSO algorithm or method is capable to obtain higher quality solution with
better convergence property and higher computational efficiency. The PSO algorithm is also used to solve
multi-objective optimization problems. The PSO algorithm solves the optimization problems effectively as
compared to the genetic algorithm method and conventional methods. The PSO technique is based on
experimental trials for searching the particles in the solution space.
REFERENCES
[1] S.G. Soni, and Dr. M. Pandit, “Hybrid PSO based optimization of emission and economic load dispatch problem,” Proceedings
National Conference on Advances in Power Systems and Energy Management, May 6-7, 2009, pp 462-467.
[2] G.N. Ajah, and B.O. Anyaka, “Optimization methods and algorithms for solving of hydro-thermal scheduling problems,” IOSR
Journal of Electrical and Electronics Engineering, Volume 5, Issue 3, Mar. - Apr. 2013, pp. 68-75.
[3] Nagendra Singh, and Yogendra Kumar, “Economic load dispatch with valve point loading effect and generator ramp rate limits
constraint using MRPSO,” International Journal of Advanced Research in Computer Engineering & Technology(IJARCET),
Volume 2, Issue 4, April 2013, pp 1472-1477.
[4] S.G. Soni, M. Pandit and L.Shrivastava, “Particle swarm optimization technique for solving economic dispatch problem of large
power system,” National Conference on Advances in Power Systems and Energy Management, March 1- 2, 2008.
[5] Jong-Bae Park, Ki-Song Lee, Joong-Rin Shin, and Kwang Y. Lee, “Economic load dispatch for non-smooth cost functions using
particle swarm optimization,” IEEE 0-7803-7989-6/03/$17.00, 2003, pp 938-943.
[6] Jin S. Heo, Kwang Y. Lee, and Raul Garduno-Ramirez, “Multi-objective control of power plants using particle swarm optimization
techniques,” IEEE Transactions on Energy Conversion, Vol. 21, No. 2, June 2006, pp. 552-561.
[7] A.Zaraki, and M.F.Bin Othman, “Implementing particle swarm optimization to solve economic load dispatch problem,”
International Conference of soft computing and Pattern Recognition, 2009, DOI 10.1109/SoCPaR.2009, 24.
[8] M.A.Abido, “Optimal power flow using particle swarm optimization” ELSEVIER, 2001, pp.563-571.
[9] Jong-Yul-Kim, Kyeong-Jun Mun, Hyung-Su Kim, and June Ho Park, “Optimal power system operation using parallel processing
system and PSO algorithm,” International Journal of Electrical Power and Energy System, Vol. 33, 2011, pp. 1457-1461.
[10] Vivek Kumar Jain, and Himmant Singh, “Hybrid particle swarm optimization based reactive power optimization,” International
Journal of Computational Engineering Research, ISSN: 2250-3005
[11] W. M. Mansour, S. M. Abdelmaksoud, M. M. Salama, and H. A. Henry, “Dynamic economic load dispatch of thermal power
system using genetic algorithm,” IRACST – Engineering Science and Technology: An International Journal, Vol.3, No.2, April
2013, pp 345-352.
[12] Mousumi Basu, “Bi-objective generation scheduling of fixed head hydrothermal power systems through an interactive fuzzy
satisfying method and particle swarm optimization,” International Journal of Emerging Electric Power Systems, Vol. 6, Issue 1,
2006.
BIOGRAPHIES
Ravinder Singh Maan was born in Bhathinda in Punjab State of India on March 19, 1991.
He studied at Poornima Institute of Engineering & Technology Jaipur and received the
Electrical Engineering degree from Rajasthan Technical University Kota, Rajasthan, India
in 2011. He is currently Pursuing M.Tech (Power System) from Jagannath University
Jaipur, India.
He has been Assistant Professor with Jaipur National University, Jaipur, India
since 2011. His special fields of interest are Application of AI Techniques in Power
System and Power Electronics Devices.
Om Prakash Mahela was born in Sabalpura (Kuchaman City) in the Rajasthan state of
India, on April 11, 1977. He studied at Govt. College of Engineering and Technology
(CTAE), Udaipur, and received the electrical engineering degree from Maharana Pratap
University of Agriculture and Technology (MPUAT), Udaipur, India in 2002. He is
currently pursuing M.Tech. (Power System) from Jagannath University, Jaipur, India.
From 2002 to 2004, he was Assistant Professor with the RIET, Jaipur. Since 2004,

he has been Junior Engineer-I with the Rajasthan Rajya Vidhyut Prasaran Nigam Ltd., Jaipur, India. His special
fields of interest are Transmission and Distribution (T&D) grid operations, Power Electronics in Power System,
Power Quality, Load Forecasting and Integration of Renewable Energy with Electric Transmission and
Distribution Grid, Applications of AI Techniques in power system. He is an author of 23 International Journals
and Conference papers. He is a Graduate Student Member of IEEE. He is member of IEEE Communications
Society. He is Member of IEEE Power & Energy Society. He is Fellow Member of IAEME. He is Reviewer of
TJPRC International Journal of Electrical and Electronics Engineering Research. Mr. Mahela is recipient of
University Rank certificate from MPUAT, Udaipur, India, in 2002.
Mukesh Kumar Gupta completed his B.E. Degree in Electronic Instrumentation &
Control Engineering Branch in 1995 and M.E. Degree in Power System in 2009 from
Engineering College Kota (RTU Kota) Rajasthan, India and he is pursuing Ph.D on Solar
Energy from Jagannath University Jaipur, Rajasthan, India.

Economic Load Dispatch Optimization of Six Interconnected Generating Units Using Particle Swarm Optimization

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