Particle
Swarm
Optimization
For
Security
Constrained
Economic
Dispatch
Rohit Kumar Pancholi, K.S.Swarup
Department
of
Electrical Engineering
Indian Institute of Technology Madras, Chennai
600036
Abstract:
This paper presents an efficient and reliable
evolutionary based approach to solve the economic load
dispatch (ELD) with security constraints .The proposed
approach -employ particle swarm optimization (PSO)
algorithm for ELD. Incorporation
of
Type
1
PSO as a
derivative-free optimization technique in solving ELD with
voltages and lineflow constraints significantly relieves the
assumptions imposed on the optimized objective function.
The proposed approach has been tested on three
representative systems
,
i.e. IEEE 14 bus, IEEE
30
bus and
IEEE 57 bus systems respectively. The feasibility of the
proposed method is demonstrated and the results are
compared with Linear Programming, Quadratic Programming
and Genetic Algorithm respectively. The developed
algorithms are computationally faster(no. of load flows) than
the other methods.
Index Term
’
Economic Load dispatch; Particle swarm optimization;
security constraints; lineflow constraints: voltage constraints
I.
INTRODUCTION
Economic load dispatch (ELD) pertains
to
optimum
generation scheduling
of
an available generation in an
interconnected power system to minimize the cost
of
generation subject to relevant system constraints. In this paper
the line flow and bus voltage constraints, which are
so
important for any practical implementation of ELD, are taking
into consideration. The present work solves the ELD problem
with lineflow constraints through effective application
of
Particle Swarm Optimization (PSO), considering the sys-tem
transmission losses, power balance equation as an equality
constraint, limits on the active power generations
of
the units
and limits on the currents in different lines as the inequality
constraints. Four test systems, i.e. IEEE
14
bus, IEEE
30
bus,
IEEE 57 bus systems [l] have been considered for the
investigation. A wide variety
of
optimization techniques have
been applied in solving the ELD problems such as Linear
Programming, Quadratic Programming and Genetic
Algorithm. Heuristic algorithm such as genetic algorithm has
been recently proposed for solving the
ELD
problem with
lineflows constraints. The premature convergence
of
GA
degrades its performance and reduces its search capability.
Classical optimization methods are highly sensitive to starting points
and
frequently converge
to
local optimum solution
or
diverge
altogether.
Linear programming methods are fast and reliable
but the main disadvantage associated with the Piecewise
linear cost approximation. Nonlinear Programming methods
have a problem of convergence and algorithmic complexity.
Newton based algorithm have a problem in handling large
number
of
inequality constraint.
So
recently, a new
evolutionary computation technique, called particle“ swarm
optimization has been proposed and introduced [2],
[3].
This
technique combines social psychology principles in socio-
cognition human agents and evolutionary computations.
PSO
has been motivated by the behavior of the organisms such as
fish schooling and bird flocking. The particle swarm is an
algorithm for finding optimal regions of complex search spaces
through the interaction
of
individuals in a population of
particles. Particle swarm adaptation has been shown to
successfully optimize a wide range of continuous function
[2],
[4]-[7]. The algorithm, which is based on a metaphor
of
social
interaction. Searches a space by adjusting the trajectories
of
individual vectors, called “particles” as they are conceptualized
as moving points in points in multidimensional space. The
individual particles
are
drawn stochastically towards the
positions of their own previous best performances and the best
previous performance of their neighbors.
Since the algorithm inception,
two
notable improvements on
the initial
PSO
have been introduced which attempt to strike a
balance between two conditions. The first introduced by
Eberhart and Shi uses an extra “inertia weight” term which is
used to scale down the velocity
of
each particle and this term is
typically decreased linearly throughout a run
[5].
The second
version introduced by Clerc involves a “constriction factor” in
which the entire right side of the formula is weighted by a
coefficient. Clerc’s generalized particle swarm model allows
an infinite number of ways in which the balance between
exploration and convergence can be controlled. The simplest of
these is called Type
1
PSO.In this paper the economic load
dispatch problem having lineflow constraints has been solved
by the Type
1
PSO.
2.
ECONOMIC
LOAD
DISPATCH
PROBLEM
WITH
CONSTRAINTS
The primary objective of the ELD problem with lineflow and
voltage constraints is to determine the most economic loading
of
the generators such that the load demand in the power
system can be meet with all the line loading is in their limit.
Consider a system having
N
buses and
NL
lines. Let
NG
buses have sources €or power generation. The objective
is
to
determine the optimal set of generation
pGi
(
i
=1,2,. .
...
to
minimize the total cost
of
generation
F,
given by:
subject to equality constraint,
0-7803-8243-9104/$17.00
0
2004
IEEE
7
IClSlP
2004
