Relevance of Particle Swarm Optimization Technique for the Solution of Economic Load Dispatch Problem

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 11 | Nov -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 633
Relevance of Particle Swarm Optimization Technique for the Solution of
Economic Load Dispatch Problem
Mr. Jatinder Kumar1, Mr. Harkamal Deep Singh2
1M.tech. Research Scholar, Department of EEE, IKGPTU University, Punjab
2Assistant professor, Department of EEE, IKGPTU University, Punjab
-------------------------------------------------------------------***----------------------------------------------------------------
Abstract- Economic Load Dispatch is very vital research in
generation of electrical power system. It is method by which
we can make a plan of the preeminent achievable output of
a number of generators power units so that to meet the
domestic, industrial agriculture load demand at minimum
possible cost, while satisfy all transmissions loss and
operational constraints. This research paper tries to present
the relevance of particle swarm optimization technique for
the mathematical formulation of Economic load dispatch
problem using soft computing technique in power
generation system considering various parameters like load
demand, physical and generation system constraints.
Index Terms- Economic Load Dispatch problem (ELDP),
relevance Particle Swarm Optimization, Basic
mathematical formulation,.
I. INTRODUCTION
In electrical power system, seven types of generation
system mostly are used in world like thermal, hydro,
nuclear, bio-mass, tidal wave, solar and wind energy etc.
Consumer load demand it may be (industrial, agriculture,
domestic etc.) change according to load parameters and
reaches the different maximum values. so, it is very
essential to scheduling of power generating units by
which units can turn off and on to meet the desire power
load demand and also keeping in mind cost parameter
order in which the units must be shut down. The entire
effort of draw round and manufacture these evaluations
are known as economic load dispatch. It means that
generation unit output (Min. MW to Max. MW) are
permissible to diverge within certain confines so that to
meet a particular load demand obtained by minimum fuel
cost.
II. ECONOMIC LOAD DISPATCH
Economic Load Dispatch problem is very important in
electric power generation plant units. The main objective
of the Economic Load Dispatch problems is to create the
best probable schedule of power generators outputs of all
units so as to bring together the required load demand at
minimum operating cost while satisfying the equality and
inequality constraints.[1] The cost function for each
generators unit in Load Dispatch problems has been
around defined by a quadratic function in which fuel cost,
power load demand, equality and inequality constrained
are involved.
III. PROBLEM FORMULATION
The economic dispatch problem is a constrained
optimization problem and it can be expressed as
Follows.[1-4]
Minimize
2
1
( ) ( ) /
NG
i i i i i i
i
F P a P b P c Rs h

   (1)
Where, ai (Rs/MW2h), bi (Rs/MWh) and ci (Rs/h) are fuel
cost coefficients of ith unit.
Subject to (i) the energy balance equation
1
NG
i D L
i
P P P

  (2)
(ii) The inequality constraints
 min max
i 1,2,3,.............,NGi i iP P P   (3)
Where, ,i ia b and ic are cost coefficients
LP is power transmission Loss.
NG is the number of generation units
DP is Load Demand.
iP is real power generation and will act as decision
variable.
The very simple and fairly accurate method of expressing
power transmission loss, LP as a function of generator

powers is through George's Formula using B-coefficients
and mathematically can be expressed as:
1 1
i j
NG NG
L g ij g
i j
P P B P
 
  MW (4)
where, igP and jgP are the real power generations at the
ith and jth buses, respectively. ijB are the loss coefficients
which are constant under certain assumed conditions.
IV. THERMAL CONSTRAINTS
In this system thermal generation unit needs to undergo
gradual temperature vary and thus it takes some period of
time to carry a thermal generation unit online. Also,
thermal unit can be manually controlled. So a crew
member is required to perform this task in operation.. This
leads to a lot of limitations in the power system operation
of thermal unit and thus it provide rise to many
constraints.
V. GENERATION CONSTRAINTS
In order to convince the forecasted in power system load
demand, the sum of all generating units on-line must equal
the power system load over the time horizon.
(5)
Where, hD is load demand at hth hour.
ihP is the power output of ith unit at hth hour
ihU is the On/Off status of the ith unit at the hth hour.
NG is the number of thermal generating units
VI. UNIT GENERATION RESTRICTIONS
The power output induced by the individual units must be
within max. and min. generation limits i.e.
(6)
Where, (min)iP and (max)iP is the minimum and maximum
power output of the ith unit.
VII. PARTICLE SWARM OPTIMIZATION
Particle Swarm Optimization (PSO) is a soft computing
technique. It is swarm-based intelligence algorithm
predisposed by the group behaviour of animals such as a
flock of birds finding a food source which likely fly in sky
or a school of fish protecting them from a difficulty or
predator. This soft computing technique particle swarm
optimization first described by james Kennedy and Russell
C. Eberhart in 1995 draw from two separate conce pts ,the
idea of swarm intelligence based off the surveillance of
swarming habits by certain kinds of animal s(such as fish
& birds) and field of evolutionary computation.
VIII. MATHEMATICS INVOLVED IN PSO
This algorithm works by discretely maintaining a no. of
runner solutions in the search space. for the ( Pih )
is
period of all iteration of the algorithm, every candidate
solution is calculated by objective function being
optimized, determining fitness of that solution. Every
runner solution can be thought of as particle ‘flying’ all
the way through fitness landscape finding the max. or min.
of the objective function. In beginning, particle swarm
optimization algorithm select candidate solutions
randomly within the search space.
Vi
new w *Vij C1 R1 Pbbest
ij P ij C2 R2 G best
J P
ij i 1, 2...NP;j 1, 2...NG
P
new P
i
j V new (8)
C1 , C2 are the acceleration constants
P is current position of jth member of ith particle at uth
iteration
NG is the no of members in a particle R1, R2 is random
number between 0 and 1 and W is the weighing function
or inertia weight factor NP is the number of particles in a
group.
In figure 1. Flow chart shows the initial parameter of state
of PSO constant, C1, C2 particle ( P )and dimension (D)
seeking the global maximum in a one-dimensional search
space. The investigate space is composed of all the
possible solutions along with the objective function. We
know that the particle swarm optimization algorithm has
no in sequence of the necessary objective function, and
thus has no idea of knowing if someone of the candidate
solutions are distance or far from a local or global max.
1
NG
i
ih ih hP U D


(min) (max)i ih iP P P 

IMPLEMENTATION OF CLASSICAL PSO FOR ELD SOLUTION
The main objective of ELD is to obtain the amount of real
power to be generated output by each committed generator,
while achieving a minimum generation cost within the
constraints. The details of the implementation of PSO
components are summarized in the following subsections.
The search procedure for calculating the optimal generation
output of each unit is summarized as follows:
1. Initialization of the swarm: For a population size P, the
particles are randomly generated in the range 0-1 and
Searched between the maximum and the minimum operating
limits of the generators. If there are N generating units, the ith
particle is represented as
Pi = (Pi1, Pi2, Pi3……………... PiN) (9)
The jth dimension of the ith particle is allocated a value of Pij as
given below to satisfy the constraints.
Pij = Pjmin + r (Pjmax - Pjmin ) (10)
Here r [0,1]
2. Defining the evaluation function: The merit of each
individual particle in the swarm is found using a fitness
function called evaluation function. The popular penalty
function method employs functions to reduce the fitness of the
particle in proportion to the magnitude of the equality
constraint violation. The evaluation function is defined to
minimize the non-smooth cost function given by equation The
evaluation function is given as Min f(x)=f(x)+ lambda (equality
constraints).
3. Initialization of P-best and G-best: The fitness values
obtained above for the initial particles of the swarm are set as
the initial Pbest values of the particle. The best value among all
the Pbest values is identified as G-Best .
4. Evaluation of velocity: The update in velocity as per flow
chart.
5. Check the velocity constraints of the members of each
individual from the following conditions
If, Vid (k+1) > Vd max, then Vid (k+1) = vd max, (11)
Vid (k+1) < Vd min
then, Vid (k+1)=vd min
Where, Vdmin = -0.5 Pgmin, Vdmax = +0.5 Pg max
6. Modify the member position of each individual Pg
according to the equation
Pgid (k+1) = Pgid (i) + Vid (k+1) (12)
Pgid (k+1) must satisfy the constraints, namely the
generating limits. If Pgid (k+1) violates the constraints,
then Pgid (k+1) must be modified towards the nearest
margin of the feasible solution.
7. If the evaluation value of each individual is better than
previous P-best, the current value is set to be P-best. If the
best P-best is better than G-best, the best P-best is set to
be G-best. The corresponding value of fitness function is
saved.

8. If the number of iterations reaches the maximum, then go to
step 10. Otherwise, go to step-2
IX. TEST SYSTEM , RESULT AND DISCUSSION
In order to show the effectiveness of the Proposed PSO
Algorithm for Short-term Unit Commitment Problem, three
different types of test systems have been taken into
consideration:
o The first test system consists of 5-Generating
units has been taken from IEEE 14-Bus System
with a time varying load demand for one day.
o The second test system consists of 6-Generating
units has been taken from IEEE 30-Bus System
with a time varying load demand for one day.
o Proposed PSO result Compare the result of firefly
algorithm
Test System-I
Table-I: Generator characteristics of 5-Unit Test System
Table-II: Time varying load demand and result of 5 units
Table III. Optimal output of 5 units system which show the load demand fulfill with min. cost
UNITS Pmax Pmin A B C
Unit1 250 10 0.00315 2 0
Unit2 140 20 0.0175 1.75 0
Unit3 100 15 0.0625 1 0
Unit4 120 10 0.00834 3.25 0
Unit5 45 10 0.025 3 0
Load Demand
(MW)
No. of
Iteration
U1 U2 U3 U4 U5 Min Cost Rs./h.
148 30000 86.9737 26.0257 15.0000 10.0000 10.0000 21276.6
173 30000 107.8218 30.1765 15.0000 10.0000 10.0000 25878.8
220 30000 145.0667 38.2486 16.7040 10.0000 10.0000 33696.5

Test System-II
Table-IV: Generator characteristics of 6-Unit Test System
UNITS Pmax Pmin A B C
Unit1 200 50 0.00375 2 0
Unit2 80 20 0.0175 1.7 0
Unit3 50 15 0.0625 1 0
Unit4 35 10 0.00834 3.25 0
Unit5 30 10 0.025 3 0
Unit6 40 12 0.025 3 0
Table-V: Time varying load demand and result of 6 units
Table VI. Optimal output of 6 units system which show the load demand fulfill with min. cost
244 30000 163.9007 42.2674 17.8340 10.0000 10.0000 38238.6
259 30000 175.7110 43.7893 18.5164 10.0000 10.0000 41198.0
248 30000 167.1512 42.9141 17.9329 10.0000 10.0000 39036.4
227 30000 130.5524 35.4128 15.0340 10.0000 10.0000 34985.6
202 30000 131.0699 35.2017 15.8565 10.0000 10.0000 30442.2
Load
Demand
(MW)
No. of
Iterations
U1 U2 U3 U4 U5 U6 Min Cost
Rs/h
166 30000 91.3180 27.6778 15.0000 10.0000 10.0000 12.0000 24561.6
196 30000 115.7033 33.2949 15.0000 10.0000 10.0000 12.0000 29516.6
229 30000 141.5913 38.9124 16.4955 10.0000 10.0000 12.0000 35383.1
267 30000 171.4119 45.3026 18.2847 10.0000 10.0000 12.0000 42651.5
283.4 30000 183.9935 48.1629 19.2428 10.0000 10.0000 12.0000 45965.8
272 30000 175.3349 46.1432 18.5211 10.0000 10.0000 12.0000 43632.6
246 30000 155.0839 41.6795 17.2346 10.0000 10.0000 12.0000 38571.8
213 30000 129.0093 36.2425 15.7474 10.0000 10.0000 12.0000 32587.6

COMPARISION OF RESULT
Table VII. Cost coefficients and power limits of 3-Unit system
Unit A B C Pmin. Pmax.
1 756.79886 38.53 0.15240 10 125
2 451.32513 46.15916 0.10587 10 150
3 1049.9977 40.39655 0.02803 35 225
Table VIII Comparison of test results of firefly and particle swarm optimization method.
S.No. Power Demand(MW)
Fuel Cost (Rs/hr) Fuel Cost (Rs/hr) Fuel Cost (Rs/hr)
Lambda iteration
method
Firefly Algorithm Particle Swarm
Optimization
1 350 18570.7 18564.5 18320.80
2 400 20817.4 20812.3 20469.83
3 450 23146.8 23112.4 22670.54
4 500 25495.2 25465.5 24909.77
5 550 27899.3 27872.4 27189.47
6 600 30359.3 30334.0 29506.31
7 650 32875.0 32851.0 31859.80
8 700 35446.3 35424.4 34252.73
Table IX. Cost coefficients and power limits of 6-Unit system
Unit A B C Pmin. Pmax.
1 756.79886 38.53 0.15240 10 125
2 451.32513 46.15916 0.10587 10 150
3 1049.9977 40.39655 0.02803 35 225
4 1243.5311 38.30553 0.03546 35 210
5 1658.5696 36.32782 0.02111 130 325
6 1356.6592 38.27041 0.01799 125 315
Table X Comparison of test results firefly and particle swarm optimization method.
S.No. Power
Demand(MW)
Fuel Cost (Rs/hr) Fuel Cost (Rs/hr) Fuel Cost (Rs/hr)
Lambda iteration
method
Firefly Algorithm Particle Swarm
Optimization
1 600 32129.8 32094.7 31426.57
2 650 34531.7 34482.6 33680.10
3 700 36946.4 36912.2 35997.43
4 750 39422.1 39384.0 38291.39
5 800 41959.0 41896.9 40642.86
6 850 44508.1 44450.3 43019.66
7 900 47118.2 47045.3 45422.18
8 950 49747.4 49682.1 47835.37

The corresponding results has been obtained using
Particle Swarm optimization Technique using Population
Size=50 and Maximum Iteration=30000. The Flow chart
for economic load dispatch Problem using PSO is shown in
Figure-1. The MATLAB Simulation software 7.12.0
(R2010a) is used to obtain the corresponding results.
XI. CONCLUSION
In this research paper, researchers have done the
relevance Particle Swarm Optimization Algorithm for
solution of ELDP. The results for standard IEEE Bus system
consisting of five and six Generating system units has
been profitably evaluated using PSO. The following
important points are observed throughout whole research
works:
o By planned PSO algorithm, Fuel cost (FC) of 350
MW is 18564.5 and by firefly algorithm FC is
18320.80 for three unit system.
o Load demand 350 MW to700 MW is shown in
table (viii)
o By planned PSO algorithm, Fuel cost (FC) of 600
MW is 31426.57 and by firefly algorithm FC is
32094.7 for six unit system.
o Load demand 600 MW to 950 MW is shown in
table (x)
o Proposed algorithm has simple implementation,
require less computational time and very few
algorithm parameters.
XI. FUTURE SCOPE
(1) Particle Swarm Optimization Algorithm is based on the
intellect. It can be applied into both scientific engineering
work and research purpose.
(2 The search can be carried out by the speed of the
particle .Particle Swarm Optimization Algorithm has no
overlapping and mutation calculation.
REFERENCES
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[5] Divya Mathur ‘‘ New Methodology BBO for Solving
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