Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications (IJERA) - Particle Swarm Optimization Approach For Economic Load Dispatch: A Review

Jaya Sharma, Amita Mahor / International Journal of Engineering Research and Applications
(IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 3, Issue 1, January-February 2013, pp.013-022
Particle Swarm Optimization Approach For Economic Load
Dispatch: A Review
Jaya Sharma1 Amita Mahor2
1
Asst. prof., Electrical Department, SVITS, Indore
2Prof. & Head, Electrical Department NRI,Bhopal

ABSTRACT
Particle swarm optimization (PSO ) is an conventional & nonconventional optimization
effective & reliable evolutionary based approach techniques available in literature are applied to solve
.Due to its higher quality solution including such problems. Quadratic linear programming [45],
mathematical simplicity, fast convergence & Mathematical linear programming [44], Non linear
robustness it has become popular for many programming[46], dynamic programming [31,26] are
optimization problems. There are various field of the conventional methods. Conventional methods
power system in which PSO is successfully have simple mathematical model and high search
applied. Economic Load Dispatch(ELD) is one of speed but they are failed to solve such problem
important tasks which provide an economic because they have the drawbacks of Multiple local
condition for a power system. it is a method of minimum points in the cost function, Algorithms
determine the most efficient, low cost & reliable require that characteristics be approximated,
operation of a power system by dispatching the however, such approximations are not desirable as
available electricity generation resources to supply they may lead to suboptimal operation and hence
the load on the system. This paper presents a huge revenue loss over time, Restrictions on the
review of PSO application in Economic Load shape of the fuel-cost curves.
Dispatch problems. Other methods based on artificial
intelligence have been proposed to solve the
I INTRODUCTION economic dispatch problem, these are genetic
The efficient optimum economic operation algorithm [32,33], Tabu search[27], particle swarm
and planning of electric power generation system optimization [14]. The PSO first introduced by
have always been occupied an important position in kennedy and eberhart is a flexible, robust,
the electric power industry. With large population based algorithm. This method solve
interconnection of electric networks, energy crisis in variety of power systems problems due to its
the world and continuous rise in prices, it is very simplicity, superior convergence characteristics and
essential to reduce the running charges of electric high solution quality. Classical PSO approach
energy. The main aim of electric supply utility has suffers from premature convergence, particularly
been identified as to provide the smooth electrical for complex functions having multiple minima.
energy to the consumers. While doing so, it should be
ensured that the electrical power is generated with II PROBLEM FORMULATION
minimum cost. Hence in order to achieve an The Economic Dispatch problem may be
economic operation of the system, the total demand formulated as single objective & multi objective
must be appropriately shared among the units. This problem, however in this case following objective
will minimize the total generation cost for the system functions can be formulated, ECD with valve point
with the voltage level maintained at the safe loading effect[36,37,38], ECD with valve point
operating limits. Major considerations to fulfilling the loading effect & multiple fuel option(ECD-VPL-
objectives are Loss minimization. Fuel cost ME)[39,40,41] and EMD & ECED[42,43,25].
minimization, Profit maximization (fuel costs/load
tariffs).The main factor controlling the most desirable 1.1 OBJECTIVE FUNCTION
load allocation between various generating units is The primary objective of any ED problem
the total running cost. is to reduce the operational cost of system fulfilling
In electrical power system, there are many the load demand within limit of constraints.
optimization problems such as optimal power flow, However due to growing concer of
economic dispatch, generation and transmission environment,there are various kinds of objective
planning, unit commitment, and forecasting & function formulation can be done as given in
control. Economic dispatch is one of the major subsequent sections.
optimization issue in power system. Its objective is to
allocate the demand among committed generator in
the most economical manner, while all physical &
operational constraints are satisfied. Many

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1.1.1 SIMPLIFIED ECONOMIC COST 1.1.3 ECONOMIC COST FUNCTION
FUNCTION WITH MULTIPLE FUELS.
The Let Fi mean the cost, expressed for The different type of fuels can be used in
example in dollars per hour, of producing energy in thermal generating unit, hence fuel cost objective
the generator unit i. The total controllable system function can be represented with piecewise
production cost such an approach will not be quadratic function reflecting the effect of fuel type
workable for nonlinear functions in practical changes.
systems. Therefore will be Fi ( Pi )  ai  bi Pi  ci Pi 2 if Pimin ≤ Pi ≤ Pi1
ai  bi Pi  ci Pi 2 if Pi1 ≤ Pi ≤ Pi2 (4)
N
F   F (P )
i 1
i i (1) -
-
ai  bi Pi  ci Pi 2
if Pin-1 ≤ Pi ≤ Pimax
The fuel input-power output cost function of the ith the nth power level (Fig. 2).
unit is given as
2.1.3 EMISSION FUNCTION
Fi ( P )  ai  bi P  ci P
i i i
2
(2)
Different mathematical formulations are
used to represent the emission of green house gases
in EMD problem. It can be represented in quadratic
where F Total generating cost, Fi Cost function of form [42,43],addition of quadratic polynomial with
ith generating unit, Pi power of generator, N no. of exponential terms [48,49], or addition of linear
generators, ai, bi, ci cost coefficients of generator i. equation with exponential terms [50] of generated
power
1.1.2 ECONOMIC COST FUNCTION
WITH VALVE POINT LOADING
Ei ( Pi )   i   i Pi   i Pi 2 (5)
EFFECT
The generating units with multi- valve
steam turbine exhibit a greater variation in the fuel- Ei ( Pi )   i   i Pi   i Pi 2   i exp(   Pi ) (6)
cost function. Since the valve point results in the
ripple. To take account for the valve point effect E i ( Pi )   i   i Pi   i Pi 2   1 i exp( 1  Pi )
sinusoidal functions are added to the quadratic cost
function. Therefore eq.(2 )should be replaced by   2 exp( 2 i  Pi ) (7)
eq.(3 ) where  i ,  i ,  i , 1i , 2i , 1 , 2 are the emission
function coefficients.
Fi ( Pi )  ai  bi Pi  ci Pi 2  abs (ei sin( f i ( Pi min  Pi )))
(3) 2.2 SYSTEM CONSTRAINTS
where ei & fi are the coefficient of unit i Broadly speaking there are two types of
considering valve point loading effect. constraints-Equality constraint and Inequality
constraints.The inequality constraints are of two
types (i) Hard type and, (ii) Soft type. The hard
type are those which are definite and specific like
the tapping range of an on-load tap changing
transformer whereas soft type are those which have
some flexibility associated with them like the nodal
voltages and phase angles between the nodal
voltages, etc. Soft inequality constraints have been
very efficiently handled by penalty function
Fig. 1. Incremental fuel
methods.
cost curve for 5 valve steam turbine unit.
2.2.1 EQUALITY AND INEQUALITY
CONSTRAINT
From observation we can conclude that
cost function is not affected by the reactive power
demand. So the full attention is given to the real
power balance in the system.Different types of
constrints are as under
Fig. 2. Piecewise 2.2.1.1 Active power balance equation:
quadratic and incremental fuel cost function. For power balance equation, equality
constraints should be satisfied. The total generated

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power should be the same as total load demand Zi are the no. of prohibited zones in the ith generator
plus the total line loss, curve k is the index of prohibited zones of the ith
N L
generator Pik is the lower limit of the kth
P  P i D  Ploss (8)
U
i 1 prohibited zone and Pik is the upper limit of the
Where PD is the total system demand and kth prohibited zone of the ith generator.
Ploss is the total line loss.To calculate system losses
, Method based on constant loss formula coefficient III PARTICLE SWARM OPTIMIATION
or B coefficient are used. The transmission loss Kennedy and Eberhart [1] developed a
equation expressed as: particle swarm optimization (PSO) algorithm based
on the behavior of individuals (i.e., particles or
N N N agents) of a swarm. Its roots are in zoologist's
PL   PBij Pj   Boi Pi  Boo (9)
i
modeling of the movement of individuals (i.e.,
i 1 j 1 i 1 fishes, birds and insects) within a group. It has been
2.2.1.2 Minimum and maximum power limits: noticed that members of the group seem to share
Generator output of each generator should be laid information among them, a fact that leads to
between maximum and minimum limits. The increased efficiency of the group. PSO as an
corresponding inequality constraints for each optimization tool, provide a population-based
generator are search procedure in which individuals called
particles change their position (states) with time. In
P min  P  P max
i i i (10) a PSO system particles fly around in a
Where Pimin and Pimax
are the minimum and multidimensional search space.
maximum output of generator i. During flight each particle adjusts its position
2.2.1.3 Generator ramp rate limits: according to its own experience & the experience
Operating range of all online units is restricted by of neighboring particles, making use of the best
their ramp rate limits as follows: position encountered by it & neighbors. The swarm
direction of a particle is defined by the set of
max( P min , P 0  DRi )  P  min( P max , P 0  URi )
i i i i i
particles neighboring the particle & its history
experience.
(11)
According to the PSO algorithm, a swarm of
The previous operating point of the ith generator is
particles that have predefined restrictions starts to
Pi0 and URi and DRi are the up and down ramp rate
fly on the search space. The performance of each
limits respectively.
particle is evaluated by the value of the objective
2.2.1.4 Prohibited operating zones:
function and considering the minimization
A unit with prohibited operating zones has
problem, in this case, the particle with lower value
discontinuous input-output characteristic as shown
has more performance. The best experiences for
in fig.(3)
each particle in iterations is stored in its memory
and called personal best (pbest). The best value of
pbest (less value) in iterations determines the
global best (gbest).By using the concept of pbest
and gbest the velocity of each particle is updated in
equation (13)

Vik+1 = ωVik + C1 r1 Xipbest − Xik + C2 r2 (Xigbest − Xik )
(13)
Where
Vik+1 Particle velocity at iteration
(k+1)
Vik Particle velocity at iteration k
r1 , r2 Random number between [0, 1]
C1 , C2 Acceleration constant
the constraints is described by eq.(12) ω Inertia weight factor
 Pi min  Pi  Pi L  After this, particles fly to a new position:
Xik+1 = Xik + Vik+1
 U 
(14)
Pi   Pik 1  Pi  PikL 
Where
(12) Xik+1 Particle position at iteration k+1
 U  Xik
 PiZi  Pi  Pi max  𝑉𝑖 𝑘 +1
Particle position at iteration k
Particle velocity at iteration (k+1)

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Inertia weight in attempting to increase the rate of illustrated that the fuzzy adaptive particle swarm
convergence of the standard PSO algorithm to optimization was a promising optimization method,
global optimum, the inertia weight is proposed in which was especially useful for optimization
the velocity equation 4.1 is set according to the problems with a dynamic environment.
following equation (4.3) Ratnaweera Asanga, Halgamuge Saman K. [5]
introduced a novel parameter automation strategy
(𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 −𝑖𝑡𝑒𝑟 ) for the particle swarm algorithm and two further
𝜔= 𝜔 𝑚𝑎𝑥 − 𝜔 𝑚𝑖𝑛 × + 𝜔 𝑚𝑖𝑛 (15)
𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 extensions to improve its performance after a
Where predefined number of generations. Initially, to
𝜔 Inertia weight factor efficiently control the local search and convergence
𝜔 𝑚𝑎𝑥 Maximum value of weighting to the global optimum solution, Time-varying
factor acceleration coefficients (TVAC) were introduced
𝜔 𝑚𝑖𝑛 Minimum value of weighting in addition to the time-varying inertia weight factor
factor in particle swarm optimization. From the basis of
𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 Maximum number of iterations TVAC, two new strategies were discussed to
iter Current number of iteration improve the performance of the PSO. First, the
concept of Mutation was introduced to the Particle
IV REVIEWS FOR PSO IN ECONOMIC Swarm Optimization along with TVAC (MPSO-
DISPATCH PROBLEM TVAC), by adding a small perturbation to a
In electrical power system, there are many randomly selected modulus of the velocity vector
optimization problems such as optimal power flow, of a random particle by predefined probability.
Economic Load Dispatch (ELD), generation and Second, it had introduced a novel particle swarm
transmission planning, unit commitment, and concept “Self-organizing Hierarchical Particle
forecasting & control. Amongst all optimization Swarm Optimizer with TVAC (HPSO-TVAC).”
problems, ELD is important fundamental issue in Under this method, only the “social” part and the
power system operation and planning. Its main “cognitive” part of the particle swarm strategy were
objective is to allocate the optimal power considered to estimate the new velocity of each
generation from different units at the lowest cost particle and particles were reinitialized whenever
possible while meeting all system constraints. It is they were stagnated in the search space.
a problem of high dimension, non-linear, multiple Chen Guimin et al. [7] gave new idea of
constraints and real time specialty. There are Exponential Decreasing Inertia Weight (EDIW), in
various conventional and non-conventional which two strategies of natural exponential
optimization techniques that have been adopted by functions were proposed. Four different benchmark
the researchers to approach the ELD problem. functions i.e. Shere, Rosenbrock, Griewank and
Exhaustive literature review in the subject area is Rastrigin were used to evaluate the effects of these
given below: strategies on the PSO performance. The results of
Kennedy James and Eberhart R. [1] said that the experiments showed that these two new
particle swarm optimization is an extremely simple strategies converge faster than linear one during the
algorithm that seems to be effective for optimizing early stage of the search process. For most
a wide range of functions. PSO method is continuous optimization problems, these two
composed of a set of particles called individuals, strategies perform better than the linear one.
which are able to follow a certain algorithm to Park Jong-Bae et al. [8] presented a novel and
obtain the best solution for an optimization efficient method for solving the economic dispatch
problem. These particles explore the search space problems with valve-point effect by integrating the
with different velocities and positions. particle swarm optimization with the chaotic
Shi Yuhui and Eberhart Russell [2] had sequences. In the ED problems, the inclusion of
introduced a parameter inertia weight into the valve point loading effects made the modeling of
original particle swarm optimizer. It was concluded the fuel cost functions of generating units more
that the PSO with the inertia weight in the range practical. However, this increases the nonlinearity
[0.9, 1.2] on average had a better performance with as well as number of local optima in the solution
respect to find the global optimum point within a space; also the solution procedure can easily trap in
reasonable number of iterations. the local optima in the vicinity of optimal value.
Gaing Z.-L. et al. [4] presented an approach in The proposed Improved Particle Swarm
which, a fuzzy system was implemented to Optimization (IPSO) combined the PSO algorithm
dynamically adapt the inertia weight of the particle with chaotic sequences technique. The application
swarm optimization algorithm. Three benchmark of chaotic sequences in PSO was an efficient
functions with asymmetric initial range settings strategy to improve the global searching capability
were selected as the test functions. The same fuzzy and escape from local minima. To demonstrate the
system had been applied to all the three test effectiveness of the proposed method, the
functions with different dimensions. The results numerical studies had been performed for two

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different sample systems. The results clearly on the PSO performance and select the best one.
showed that the proposed IPSO outperformed other The experimental results showed that for most
state-of-the-art algorithms in solving ED problems continuous optimization problems, the best one
with the valve-point effect. gains an advantage over the linear strategy and
Adhinarayanan T. et al. [9] presented an efficient others.
and reliable particle swarm optimization algorithm Gao Yue-lin & Duan Yu-hong [12] modified
for solving the economic dispatch problems with Random Inertia Weight Particle Swarm
smooth cost functions as well as cubic fuel cost Optimization (REPSO) in which a new particle
functions. The practical ED problems have non- swarm optimization algorithm with random inertia
smooth cost functions with equality and inequality weight and evolution strategy proposed. The
constraints that made the problem of finding the proposed random inertia weight was using
global optimum difficult using any mathematical simulated annealing idea and the given evolution
approaches. For such cases, the PSO was applied to strategy was using the fitness variance of particles
the ED problems with real power of generator in a to improve the global search ability of PSO. The
system as state variables. However when the experimented with six benchmark functions
incremental cost of each unit was assumed to be showed that the convergent speed and accuracy of
equal, the complexity involved in this may be REPSO was significantly superior to the one of the
reduced by using the incremental cost as state PSO with Linearly Decreasing inertia Weight
variables. The proposed PSO algorithm had been Particle Swarm ( LDW-PSO).
tested on 3 generator systems with smooth cost Chaturvedi K.T. et al. [13] proposed to apply a
functions and 3 generator systems, 5 generator novel Self-Organizing Hierarchical Particle Swarm
systems and 26 generator systems with cubic fuel Optimization (SOH_PSO) for the Non-Convex
cost function. The results were compared with Economic Dispatch (NCED) to handle the problem
genetic algorithm (GA) and showed better results of premature convergence. The performance further
and computation efficiency than genetic algorithm. improves when time-varying acceleration
Al Rashidi M. R. et al. [20] presented a PSO coefficients were included.
algorithm to solve an Economic-Emission Dispatch Kuo Cheng-Chien et al. [14] proposed a new
problem (EED). This problem had been getting approach and coding scheme for solving economic
more attention recently due to the deregulation of dispatch problems in power systems through
the power industry and strict environmental Simulated Annealing Particle Swarm Optimization
regulations. It was formulated as a highly nonlinear (SA-PSO). This novel coding scheme could
constrained multi-objective optimization problem effectively prevent obtaining infeasible solutions
with conflicting objective functions. PSO algorithm through the application of stochastic search
was used to solve the formulated problem on two methods, thereby dramatically improving search
standard test systems, namely the 30-bus and 14- efficiency and solution quality. Many nonlinear
bus systems. Results obtained show that PSO characteristics of power generators and their
algorithm outperformed most previously proposed operational constraints such as generation
algorithms used to solve the same EED problem. limitations, ramp rate limits, prohibited operating
These algorithms included evolutionary algorithm, zones, transmission loss and nonlinear cost
stochastic search technique, linear programming, functions were all considered for practical
and adaptive hopfield neural network. PSO was operation. The effectiveness and feasibility of the
able to find the pareto optimal solution set for the proposed method were demonstrated by four
multi-objective problem. system case studies and compared with previous
Sai H. Ling et al. [10] introduced new hybrid literature in terms of solution quality and
particle swarm optimization that incorporates a computational efficiency. The experiment showed
wavelet theory based mutation operation for encouraging results, suggesting that the proposed
solving economic load dispatch. It applied a approach was capable of efficiently determining
wavelet theory to enhance PSO in exploring higher quality solutions addressing economic
solution spaces more effectively for better dispatch problems.
solutions. The results showed that the proposed Wilasinee Sugsakarn et al. [15] presented an
method had performed significantly better, in terms effective method for solving economic dispatch
of the s olution quality and solution stability, than problem (EDP) with non-smooth cost function
some other hybrid PSOs and standard PSO. using a hybrid method that integrates Particle
Chongpeng Huang et al. [11] modified the Swarm Optimization with Sequential Quadratic
concept of Decreasing Inertia Weight (DIW) by Programming (PSO-SQP). PSO was the main
introducing some non-linear strategies on the optimizer to find the optimal global region while
existing Linear DIW (LDIW). Then a power SQP was used as a fine tuning to determine the
function was designed to unify them. Four optimal solution at the final stage. The proposed
benchmark functions sphere, rastrigrin, rosenbrock hybrid PSO-SQP method was applied to solve EDP
and Shaffer’s were used to evaluate these strategies of a test system with ten generator units.

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Ahmed Y. Saber et al. [16] presented a novel decreasing exponential method. In this method
modified Bacterial Foraging Technique (BFT) to merely used an iteration to make an inertia weight
solve economic load dispatch problems. BFT was and it was fast and had highly accurate results
already used for optimization problems, and rather than other strategies.
performance of basic BFT for small problems with Peng Chen et al. [21] introduced the floating point
moderate dimension and searching space was representation to the Genetic Particle Swarm
satisfactory. Search space and complexity grow Optimization (GPSO). GPSO was derived from the
exponentially in scalable ELD problems, and the Standard Particle Swarm Optimization (SPSO) and
basic BFT is not suitable to solve the high incorporated with the genetic reproduction
dimensional ELD problems, as cells move mechanisms, namely crossover and mutation. A
randomly in basic BFT and swarming was not modified heuristic crossover was introduced, which
sufficiently achieved by cell-to-cell attraction and was derived from the differential evolution and
repelling effects for ELD. However, chemo taxis, genetic algorithm along with the mechanism of
swimming, reproduction and elimination-dispersal GPSO.
steps of BFT were very promising. On the other Bhattacharya A. et al. [47] presented a novel
hand, particles move toward promising locations particle swarm optimizer combined with roulette
depending on best values from memory and selection operator to solve the economic load
knowledge in particle swarm optimization. dispatch problem of thermal generators of a power
Therefore, best cell (or particle) biased velocity system. Several factors such as quadratic cost
(vector) was added to the random velocity of BFT functions with valve point loading, transmission
to reduce randomness in movement (evolution) and Loss, generator ramp rate limits and prohibited
to increase swarming in the proposed method to operating zone are considered in the computation
solve ELD. Finally, a data set from a benchmark models. This new approach provided a new
system was used to show the effectiveness of the mechanism to restrain the predominating of super
proposed method. (global best) particles in early stage and can
Ren Zihui et al. [17] modified the basic structure effectively avoid the premature convergence
of the original PSO algorithm. It proposed that the problem and speed up the convergence property.
particle’s position have relationship with the one Ming-Tang T. sai et al. [23] presented an
particle’s and the whole swarm’s perceive extent in Improved Particles Swarm Optimization (IPSO)
the processing of this time and last time, and where integration of random particles and fine-
presents the inertial weight based on simulated tuning mechanism have been added in traditional
annealing temperature. So New Particle Swarm PSO to solve the economic dispatch problems
Optimization algorithm (NPSO) was proposed. It with carbon tax consideration. This economic
cannot improve the one particle’s and the whole dispatch problem had a non-convex cost function
swarm’s perceivable extent and improve the and nonlinear emission cost function with linear
searching efficient but also increase variety of and nonlinear constraints that it was difficult to
particles and overcome the defect of sinking the find the compromised solution using mathematical
local optimal efficiently. At the same time the approaches, the proposed method used to solve this
convergence condition given for this new problem. By considering the emissions, the carbon
algorithm. The algorithm of PSO and NPSO and was embedded in the economic dispatch problem.
LPSO were tested with four well-known Many nonlinear characteristics of generating units
benchmark functions. The experiments showed that could be handled properly with a reasonable time.
the convergence speed of NPSO was significantly Wanga Yongqiang et al. [22] proposed a Hybrid
superior to PSO and LPSO. The convergence Particle Swarm Optimization combined Simulated
accuracy was increased. Annealing method (HPSAO) to solve economic
Yadmellat P. et al. [18] proposed a new Fuzzy load dispatch. The Simulated Annealing (SA)
tuned Inertia Weight Particle Swarm Optimization algorithm was used to help PSO to jump out the
(FIPSO), which remarkably outperformed the local optimum. Furthermore, a feasibility-based
standard PSO, previous fuzzy as well as adaptive rule was introduced to deal with the constraints.
based PSO methods. Different benchmark Finally, HPSAO was tested on three Gorges
functions with asymmetric initial range settings hydroelectric plants. The results were analyzed and
were used to validate the proposed algorithm and compared with other methods, which show the
compare its performance with those of the other feasibility and effectiveness of HPSAO method in
tuned parameter PSO algorithms. Numerical results terms of solution quality and computation time.
indicate that FIPSO was competitive due to its Park Jong-Bae et al. [28] presented an efficient
ability to increase search space diversity as well as approach for solving economic dispatch problems
finding the functions’ global optima and a better with non-convex cost functions using an Improved
convergence performance. Particle Swarm Optimization (IPSO). Although the
Ememipour Jafar et al. [19] proposed a new PSO approaches had several advantages suitable to
strategy to calculate inertia weight based on heavily constrained non-convex optimization

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problems, they still had the drawbacks such as local industry. In this changed scenario, the scarcity of
optimal trapping due to premature convergence energy resources, the ever increasing power
(i.e., exploration problem), insufficient capability generation cost, environmental concerns, ever
to find nearby extreme points (i.e., exploitation growing demand for electrical energy necessitate
problem) and lack of efficient mechanism to treat optimal economic dispatch. The conventional
the constraints (i.e., constraint handling problem). optimization methods are not able to solve such
This work proposed an improved PSO framework problems due to local optimum solution
employing chaotic sequences combined with the convergence. In the past decade, Met heuristic
conventional linearly decreasing inertia weights optimization techniques especially Imperialist
and adopting a crossover operation scheme to Competitive Algorithm (ICA) has gained an
increase both exploration and exploitation incredible recognition as the solution algorithm for
capability of the PSO. In addition, an effective such type of ED problems. The application of ICA
constraint handling framework was employed for in ED problem which is considered as the most
considering equality and inequality constraints. The complex optimization problem has been
proposed IPSO was applied to three different non- summarized in this paper.
convex ED problems with valve-point effects, Vo Ngoc. Dieu. et al. [54] proposed newly
prohibited operating zones, ramp rate limits as well improved particle swarm optimization(NIPSO) for
as transmission network losses, and multi-fuels solving economic load dispatch problem with valve
with valve-point effects. point loading effect. The proposed NIPSO is based
Meng K. et al. [29] proposed the Quantum- on the PSO with timevarying acceleration
inspired Particle Swarm Optimization (QPSO) coeficient (PSO-TVAC) with more improved
which has stronger search ability and quicker including the use of sigmoid function with random
convergence speed, not only because of the variation for inertia weight fctor, pseudo-gradiant
introduction of quantum computing theory, but also for guidance of particles,a and quadratic
due to two special implementations: self-adaptive programming for obtaing initial condition with new
probability selection and chaotic sequences improvement the search ability of the NIPSO
mutation. The proposed approach was tested with method has been considerably enhanced in
five standard benchmark functions and three power comparison with the PSO-TVAC method. The
system cases consisting of 3, 13, and 40 thermal proposed NIPSO has been tested on 13 unit &40
units. Comparisons with similar approaches units system & obtained better optimal solution
including the Evolutionary Programming (EP), than the many other methods.
genetic algorithm, Immune Algorithm (IA), and Sishaj P. Simon et al. [52] discussed dynamic
other versions of particle swarm optimization were economic load dispatch using Artificial Bee
given. The promising results was illustrated the Colony algorithm for generating units with valve-
efficiency of the proposed method and showed that point loading effect. The feasibility of the proposed
it could be used as a reliable tool for solving ELD method is validated with 10 & 5 units test systems
problems. for a period of 24 hours. In addition, the effects of
Vu PhanTu et al. [30] presented a novel Weight- control parameters on the performance of Artificial
Improved Particle Swarm Optimization (WIPSO) Bee Colony (ABC) algorithm for Dynamic
method for computing Optimal Power Flow (OPF) Economic Dispatch (DED) problem are studied.
and ELD problems. To evaluate the accuracy, Results obtained with the proposed approach are
convergence speed and applicability of the compared with other techniques.
proposed method, the OPF results of IEEE 30 bus Omaranpour H. et al. [51] presented a local
system by WIPSO are compared with traditional extremum escape approach to Particle Swarm
particle swarm optimization, genetic algorithm, Optimization (PSO) method. Here previous worst
Differential Evolution (DE) and Ant Colony position of the particles are also considered in he
Optimization (ACO) methods. Further solutions velocity update equation which makes the
of ELD problem of IEEE 13 & 40 units test system convergence of algorithm faster & capable to
have also being determined by the proposed escape from local minimum. For many
algorithm and results are compared with Classical optimization problems where other PSO variants
Evolutionary Programming (CEP), Improved Fast are stuck in local optimal solution, but the proposed
Evolutionary Programming (IFEP) and various method has been tested on standard bench mark
improved particle swarm optimization methods. functions and gave superior results.
The tested results indicated that the proposed M. Vanitha et al. [55] explians a new optimization
method is more efficient than existing one in terms technique efficient hybrid simulated annealing
of total fuel costs, total losses and computational algorithm(EHSA)for both convex & nonconvex
times. ELD problem. The mutation operator of differentail
Chahkandi H. Nejad et al. [53] introduced a evolution is used in particle swarm optimization to
highly vibrant and competitive market which improve its performance & it ishybridized with
altered revolutionized many aspects of the power simulated annealing to get EHSA technique.

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V CONCLUSION 5. Asanga Ratnaweera, Saman K.
Due to deregulation of the power industry Halgamuge “Self-Organizing Hierarchical
and strict environment regulations, highly non- Particle Swarm Optimizer With Time-
linear constraints, multi objective problem with Varying Acceleration Coefficients” IEEE
conflicting objective functions are involved in ELD Trans. on evolutionary computation,vol.
problem. 8,no.3, June 2004
In practical ELD problem it is necessary 6. Gao Yue-lin , Duan Yu-hong “A New
to consider valve point loading, prohibited zones Particle Swarm Optimization Algorithm
with ramp rate limit as well as transmission with Random Inertia Weight and
network losses and multi-fuels with valve point Evolution Strategy” International
effects. The complexity further increases when Conference on Computational
dimensionality of power system increases. The Intelligence and Security Workshops
basic PSO is insufficient to address the problem of 2007.
practical ELD. The global optimal solution and 7. Guimin Chen, Xinbo Huang, Jianyuan Jia
global search ability, premature convergence and and Zhengfeng Min “ Natural Exponential
convergence speed, and stuck in local optima are Inertia Weight Strategy in Particle Swarm
certain major issues for PSO. In this review, it is Optimization” 6th World Confress on
shown that many new algorithms are developed to Intelligent Control and Automation, June
solve this problem of PSO. 21 - 23, 2006, Dalian, China.
By adopting dynamic inertia weight, fuzzy 8. Jong-Bae Park, Yun-Won Jeong, Hyun-
tuned inertia weight, PSO with wavelet theory, SA- Houng Kim and Joong-Rin Shin “An
PSO, GPSO and QPSO with chaotic sequence, we Improved Particle Swarm Optimization
can get better global optimum solution and global for Economic Dispatch with Valve-Point
search ability. To improve the ability of PSO for Effect” International Journal of
premature convergence and convergence speed we Innovations in Energy Systems and Power,
can apply DIW PSO, SOH-PSO and PSO Vol. 1, no. 1 (November 2006)
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applying NPSO and HPSO. Economic Dispatch with Cubic Fuel Cost
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combined with DIW and crossover scheme Optimization Approach”sept.11 2007.
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