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ABSTRACT
This paper presents particle swarm optimization (PSO) based approach for
solving optimal reactive power dispatch for minimizing power losses. The
control variables are bus voltage magnitudes (continuous type),
transformer tap settings (discrete type) and reactive power generation of
capacitor banks (discrete type). The algorithm solution of PSO is tested on
a standard IEEE 30 Bus system. The intention is to minimize power losses
by optimizing the reactive power dispatch with optimal setting of control
variables without violating inequality constraints and satisfying equality
constraint. The detailed results for different cases have been listed
INTRODUCTION
Power system is a very bulk, complex and
interconnected set-up having generation, transmission,
distribution and loads. The power system operates in a
constantly changing environment as generator outputs,
loads and key operating parameters keep changing
continually. The focus has been on implementation of
equipments that can keep the power system reliable. In
modern time, power networks operate under highly
stressful situations as power demand is continuously
increasing so the analysis of power system is don‟t while
considering thses factors. The major concerns for power
systems are: minimization of cost, minimization of losses,
cost and stability (both voltage stability & power sytem
stability) [1].
Optimization in power system governs with the
overall economics of the full system. The power system
optimization consists of best sizing and placement of
reactive power resources (reactors, capacitors, and SVCs).
The control settings like active power of generators,
electrical device faucets, and regular voltages of generators
are optimized not just for the base case system
configuration however conjointly for many completely
different system configurations.
Load flow or Power flow solution is essential for
continuous evaluation of power system, planning the
control and best operation of power system. The quest of
any power system is to run the system optimally. The
purpose of an Optimal Power Flow (OPF) algorithm is to
search out steady stateoperation point that minimize
generation cost, loss etc. or maximizes financial aid,
loadability etc. while maintaining satisfactory system
performance in terms of limits onreal and reactive powers
of generators, line flow bounds, output of numerous
compensatingdevices etc. The proper selection and
coordination of apparatus for governing reactive power
and voltage stability are amongst the main tasks of power
system engineers. Conventionally, classical optimization
methods were used to efficiently solve OPF. In recent
years, Artificial Intelligence (AI) methods have been
emerged that can solve extremely advanced OPF issues.
Reactive power optimization is having significant
importance for both in day-to-day operations of power
systems and for future planning. It utilizes all the reactive
power sources judiciously, while forecasting suitable
location and size of VAR compensation in a system. The
financial side of reactive power planning and scheduling
have a remarkable effect on the profitable and reliable
operation of a power system as the fuel costs and capital
investments are increasing day by day [2]. The electric
power systems all over the world are moving in the
direction of decontrolled or deregulated electricity
markets. Additional services like frequency control,
system control and system restart are required to control frequency, security, stability and voltage profile of the
system and to safeguard the generation and transmission.
Reactive power and voltage control is a mandatory service
to sustain voltage profile through injecting or absorbing
reactive power in electricity market.
The first comprehensive survey related to optimal
power dispatch was given by H.H. Happ which reviewed
the development of optimal dispatch (or economic
dispatch) and he summarized the different methodologies
to OPF along with their limitations and with both single
area and multiple area cases. Afterward an IEEE working
group presented bibliography survey of major economicsecurity
function which was mainly related to operating
economicsof the system. In the bibliography survey, the
economic dispatch was conferred under “Real Time
Operation” function with different categories [3].
Subsequently, Carpentier conferred a survey and classified
the optimal power flow algorithms established on their
solution methodology which included the power flow
equations, generator real and reactive power constraints,
bus voltage magnitude constraints, and bus voltage angle
difference constraints for buses connected by transmission
elements. If voltage and angle are taken as variables in
place of P and Q, the restriction of fixing the reference
voltage can be lifted.Later, Chowdhary prepared a survey
report on economic load methods which pointed out the
importance and related area to economic load dispatch,
optimal power flow, economic dispatch related to AGC
etc. [4]. E. Lobato et al. anticipated LP centered OPF for
optimization (minimization) of transmission losses and
generator reactive margins of the Spanish power system.
N. Grudinin suggested a reactive power optimization
model that was based on successive quadratic
programming (SQP) methods. A wide spread variety of
conventional optimization methods have been applied in
deciphering the RPO problems considering a single
objective function such as Newton-based techniques [5,6],
quadratic programming[7], linear programming[8-9], nonlinear
programming [9],Sequential unconstrained
minimization technique[10], interior point methods [11]
and parametric method [12].
For a power system, the difficulty of reactive power
planning may be categorized to be an optimization
problem for which numerous methods have been proposed
to solve. For solution of all optimization problems, no
known single optimization method is available. A lot of
optimization methodologies have been recognized in
recent years for deciphering different kinds of optimization
problems. The conventional optimization methodologies
are: Linear programming (LP), non-linear programming
and gradient based techniques for solving reactive power
optimization problems [13-16]. As linearized models use
approximations, consequently optimal results are not
signified by LP for objective function being utilized in reactive power optimization problem. Adding to that,
conventional or Traditional solution strategies have
tendency to converge to a local optimal solution instead of
the global one.
Expert System methodologies have also been
recommended for reactive power based calculations, which
are based mostly on „if-then‟ dependent rules. The
evolutionary computational methodologies i.e.
Evolutionary programming (EP), Genetic algorithm (GA)
and Evolutionary strategy have moreover been estimated
to solve the optimizations troubles involving to the
reactive power dispatch [17-19]. For deciphering complex
engineering difficulties, the modern (non-traditional)
optimization approaches are very influential and accepted
approaches. These approaches are genetic algorithm,
neural networks, fuzzy optimization, ant colony
optimization and particle swarm optimization algorithm.
Particle Swarm Optimizer is a population-based
stochastic method for global minimization of objective
functions [20]. Objective functions are a way of
quantifying everyday real world problems that describe
properties that need to be minimized to obtain some
particular outcome. Often objective functions can have
many parameters that will influence the property that is
being optimized. Objective functions will have a number
of characteristics that help determine the how well it will
be optimized. One of its main attractions is its ability to
find optimal solutions without the need to compute
derivatives. It is, in summary, multi-point derivative-free
optimizer.
II. REACTIVE POWER OPTIMIZATION
Reactive power is essential for reliable operation of
the bulk power system as it supports power flow. The
reactive power is an indispensable element of the AC
transmission grid. The demand of reactive power changes
at a greater rate than the active power for the same change
in voltage. Throughout the normal regular operation,
power systems can go through both over-voltage and
under-voltage violations which can be overcome by
voltage or reactive power control. By monitoring the
production, adsorption and flow of reactive power on all
the stages in the system, voltage or reactive power control
can retain the voltage profile inside permissible limit and
decrease the transmission losses. Generators connected for
transmission are usually essential for supporting reactive
power flow.
Reactive power optimization (RPO) is one of the
difficult optimization problems in operation and control of
power system. RPO problem is a special tool to obtain the
optimal state of the control variables by minimizing the
certain objectives while satisfying the equality and
inequality constraints. The most commonly used objective
is loss minimization. The control or independent variables of power system are real power generation excluding lack
bus, voltage magnitudes at generator buses, transformer
tap settings and reactive power injection due to
capacitor/inductor banks. The dependent or state variables
are load bus voltage magnitudes and angles, slack bus
power generation, reactive power generation at generator
buses and transmission line loadings.
A comparatively modern, new and powerful technique
Particle Swarm Optimization (PSO) has been practically
revealed to execute well on numerous optimization
problems [20-21]. The population based stochastic
optimization technique i.e. PSO algorithm is applied while
satisfying equality constraints and not violating inequality
constraints. The endeavour of minimising reactive power
losses is achieved by correct adjustment of reactive power
variables like reactive power generation of capacitor banks
(Qci), generator voltage magnitudes (Vgi) and transformer
tap settings (tk) [12].
The recommended PSO algorithm solution is tried on
the typical IEEE 30-Bus test system with both discrete and
continuous control variables while keeping the system
under safe voltage stability limit. The suggested algorithm
shows improved results.
III. PARTICLE SWARM OPTIMIZATION
Particle Swarm optimization (PSO) is a comparatively
new evolutionary algorithm that is used to find
optimum/best (or close to optimal) solutions to qualitative
and numerical issues. PSO applies the conception of social
interaction to problem solving.
Particle swarm optimization was originally established
by James Kennedy and Russell Eberhart [20]. The
Eberhart and Kennedy model makes an attempt to seek out
the most effective compromise between its two main parts,
individuality and sociality. Particle swarm optimisation
(PSO), that is a population based stochastic optimization
technique, shares several similarities with evolutionary
computation techniques like genetic algorithms (GA). The
system is initialized with a population of random realistic
solutions and searches for best by modernizing
generations. However, unlike GA, PSO has no evolution
operators like crossover and mutation. PSO algorithmic
program has additionally been demonstrated to perform
well on genetic algorithmic program test function. In PSO,
the potential solutions, referred as particles, fly through the
problem space by following the present optimum particles.
In a PSO algorithm, particles modify their positions
by flying around in multidimensional search area till a
comparatively unchanged position has been encountered,
or till machine limitations are exceeded. In scientific
discipline context, a PSO system combines a social-only
model and a cognition-only model. A particle changes its
position using these models. Every particle keeps track of
its coordinates within the problem space that are related to the most effective solution, fitness; it's achieved to this
point. The fitness value is additionally stored that is named
Pbest. Another best value that is traced by the optimizer is
the best value, achieved to this point by any particle within
the neighbors of the particle. This position is named lbest.
Once a particle receipts all the population as its topological
neighbors, the most effective value could be a global best
and is named Gbest. At each step PSO changes the velocity
(accelerates) of every particle toward its Pbest and lbest
locations (local form of PSO). Acceleration is weighted by
a random term, with discrete random numbers being
produced for acceleration toward Pbest and lbest locations. In
past proven years, PSO has been successfully applied in
research analysis and application areas.
It's incontestable that PSO gets better results in a
quicker, cheaper manner compared to alternative methods.
Another reason that PSO is eye-catching is that there are
not many parameters to regulate. One version, with slight
variations, works well in a big range of applications.
Particle swarm optimization has been utilized for
approaches which can be used across a large range of
applications, also as for specific applications centered on a
specific demand. In the past many years, PSO has been
successfully applied in several research and application
areas.
The fundamental terms employed in PSO technique are
[23, 24]:
Particle X (i): It is a candidate solution described by a kdimensional
real-valued vector, where k is the no. of
optimized parameters.
Population: It is basically a set of n particles at iteration i
and at time T.
Swarm: Swarm is defined as an apparently unsystematic
population of moving particles that tend to bunch together
while each particle appears to be moving in a random
direction.
Particle velocity V(i): Particle velocity is the velocity of
the moving particles signified by a d-dimensional real
valued vector.
Inertia weight w(i): It is a regulation parameter, which is
used to regulate the impact of the past (previous) velocity
on the present velocity. Hence, it effects the trade-off
between the global and local exploration capacities of the
particles. For the initial stages of the search method, large
inertia weight to reinforce the global exploration is usually
recommended while it must be reduced at the last stages
for higher local exploration. Therefore, the inertia factor
drops linearly from about 0.9 to 0.4 throughout a run.
Individual best X*(i): When particles move through the
search space , it matches its fitness value at the existing
position to the best fitness value it has ever grasped at any
iteration up to the current iteration. The best position that
is related with the best fitness faced so far is called the
individual best .