CHAPTER 1 - Shodhganga

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CHAPTER 1
INTRODUCTION
1.1
OVERVIEW
Efficient and optimum planning and operation of electric power
generation systems have always occupied an important position in the electric
power industry. The challenge to optimize power system operation, while
maintaining system security and quality of supply to customers is growing
(Wood and Wollenberg 2003). Rising demand without matching expansion of
generation and transmission facilities and more tightly interconnected power
systems contribute to the increased complexity of system operation. Even
under disturbed conditions the power system operator has to ensure the quality
and reliability of supply to the customers by maintaining the load bus voltages
in their permissible limits. Normally power losses in the transmission of
electrical energy cause a loss of revenue. Even a small percentage of savings
in loss will be very much appreciated as the total generated power is in the
order of thousands of megawatts. While real power dispatch with the objective
of minimizing losses is very well established, more attention has been paid to
Reactive Power Optimization (RPO) problems in the last few decades.
RPO is an important task in planning for both the future and day-today operations of power systems. RPO is a sub-problem of the Optimal Power
Flow (OPF) calculation, which determines all kinds of reactive power control
variables such as reactive power outputs of generators, tap-ratios of
transformers, outputs of shunt capacitors/reactors etc., to minimize
transmission losses or voltage deviation and/or Volt-Ampere reactive (VAr)
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investment cost or to maximize voltage stability margin etc, which are
considered as objectives, while satisfying a given set of physical and operating
constraints.
The two major problems of RPO are Reactive Power Dispatch
(RPD) and Reactive Power Planning (RPP). The main purpose of RPD is to
minimize real power transmission losses of the network while maintaining the
system voltage profile in an acceptable range, with control variables such as
the generator voltages, tap-ratios of transformer and reactive power generation
of VAr sources. The main goal of RPP is to determine the location and amount
of shunt reactive power compensation to be installed in order to keep adequate
voltage profile during normal and anticipated contingency conditions at
minimum cost. Normally, the cost based objective function is employed in
RPP, which includes the variable and fixed VAr installation cost, real power
loss cost and fuel cost. Another possible objective is the minimization of
voltage deviation or the maximization of voltage margin (Zhang et al 2007).
Many classical optimization techniques have been reported in
literature to solve the RPO problems. Linear Programming (LP), Nonlinear
Programming (NLP), Quadratic Programming (QP), Interior Point (IP)
methods, Integer Programming (IP) Newton and Decomposition Methods
have been applied for solving RPO problems. However, classical optimization
techniques have severe limitations in handling nonlinear, discontinuous
functions and constraints, and functions having multiple local minima. Also,
the classical techniques depend upon the initial search points and easily
converge to local minimum or even diverge. The other main difficulty in
handling RPO problems are the integer nature of some of control variables like
transformer tap-ratios and VAr sources. RPO problems are usually modeled as
a large-scale Mixed Integer Nonlinear Programming (MINLP) problem
(Wei et al 2006). The Combinatorial-Search approaches, Branch-and-Bound
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and Cutting-Plane algorithms are normally used to handle the MINLP
problems. But these classical methods suffer from dimensionality problem for
large scale applications.
To overcome these difficulties, many researchers employed the
robust and flexible Evolutionary Algorithms (EAs) to solve RPO problem.
EAs such as Simple Genetic Algorithms (SGA), Evolutionary Strategies (ES),
Evolutionary Programming (EP), Particle Swarm Optimization (PSO),
Differential Evolution (DE) and Real coded Genetic Algorithm (RGA) have
been applied for RPO problems. These EAs have shown success in solving the
RPO problems since they do not need the objective and constraints as
differentiable and continuous functions.
Recently, Estimation of Distribution Algorithm (EDA) has been
introduced for optimizing deceptive and non-separable functions. EDAs use
probability distributions derived from the function to be optimized to generate
search points instead of crossover and mutation as done by GAs. In this thesis,
EDA based RPO problems are presented. A popular EDA method namely,
Covariance Matrix Adapted Evolution Strategy (CMAES) developed by
Hansen (2006) is considered for this purpose.
Also, the performance of
CMAES is compared with RGA with Simulated Binary Crossover (RGASBX) and non-uniform polynomial mutation proposed by Deb (2001),
Modified PSO (MPSO) developed by Shi and Eberhart (1998), and Selfadaptive Differential Evolution (SaDE) introduced by Qin et al (2009).
RPO problem is also formulated as Multiobjective Optimization
(MOO) problem by considering the transmission loss and voltage deviation or
cost of fuel and VAr investment etc, as multiobjectives. However, the MOO
problem was converted into a single objective optimization problem by
weighted sum of objectives (El-Dib et al 2007). Inadequate choice of weight
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factors may cause the non-commensurable objectives to lose their significance
on combining into a single objective function. Hence, this approach cannot be
applied to find Pareto-optimal solutions of problems like RPD which have
non-convex Pareto-optimal front. Classical optimization methods can at best
find one solution in one simulation run, thereby making these methods
inconvenient to solve multiobjective optimization problems. On the contrary,
the Evolutionary Multiobjective Optimization Algorithms (EMOAs) are
becoming immensely popular, mainly because of their ability to find a
widespread of Pareto-optimal solutions in a single simulation run (Deb 2001).
Some of the recent EMOAs are Nondominated Sorting Genetic
Algorithm (NSGA-II), Strength Pareto Evolutionary Algorithm (SPEA),
Pareto Archived Evolution Strategy (PAES), Multiobjective Differential
Evolution (MODE), Multiobjective PSO (MOPSO) and others. Among these
NSGA-II, SPEA, MODE, Vector Evaluated PSO (VEPSO) have been applied
to multiobjective RPD problem and MOPSO has been applied to
multiobjective RPP problem. In particular, NSGA-II is widely used to solve
the power system problems like economic dispatch, generation expansion and
transmission expansion planning problems etc (Kannan et al 2009).
Eventhough, NSGA-II (Deb et al 2002) algorithm encompasses advanced
concepts like elitism, fast nondominated sorting approach and diversity
maintenance along the Pareto-optimal front, it still falls short in maintaining
lateral diversity and in obtaining Pareto-front with high uniformity. To
overcome this shortcoming, Deb (2001) proposed a technique called
controlled elitism which can maintain the diversity of nondominated front
laterally. Also to obtain Pareto-front with high uniformity, Dynamic Crowding
Distance (DCD) based diversity maintenance strategy has been proposed by
Luo et al (2008). In this thesis, NSGA-II with controlled elitism and DCD
based diversity maintenance strategy is named as Modified NSGA-II
(MNSGA-II) and applied to multiobjective RPO problems.
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1.2
OBJECTIVES OF THE THESIS
1. The effectiveness and applicability of the EAs viz., MPSO,
RGA-SBX, CMAES and SaDE are demonstrated on the RPD
and RPP problems using different objectives and constraints.
2. To investigate the effectiveness and performances of various
multiobjective EAs viz., NSGA-II and MNSGA-II on RPD and
RPP problems.
3. To verify the optimality of solutions obtained by single and
multiobjective
EAs
using
Karush-Kuhn-Tucker
(KKT)
conditions developed by Deb et al (2007).
1.3
THESIS ORGANISATION
This thesis has been organized into nine chapters and the details are
given below.
Chapter 2 presents the basic concepts, general mathematical
expressions and previous work carried out on the RPO problems.
Chapter 3 explains the various EAs such as RGA-SBX, MPSO,
SaDE, CMAES, NSGA-II and MNSGA-II algorithms. The penalty parameterless constraint handling method is also given.
In Chapter 4, the RPD problem with FACTS devices are presented.
The parameters setting of FACTS devices are considered as additional
constraints. The performance evaluation of various EAs such as RGA-SBX,
MPSO, CMAES and SaDE on RPD problems is carried out and the results
obtained by EAs are discussed.
In Chapter 5, the RPP problem with voltage stability constraint is
solved by EAs such as RGA-SBX, MPSO, CMAES and SaDE for different
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case studies and results obtained by EAs are compared with already reported
results.
In Chapter 6, the RPP problem in both pool and hybrid electricity
markets are explained. The sum of real and reactive power production cost of
generator and VAr investment cost is determined for both pool and hybrid
markets using various EAs and the performance evaluation is carried out on
results obtained.
In Chapter 7, MNSGA-II algorithm is applied to solve
multiobjective RPD problem and results obtained is compared with NSGA-II.
Real power loss and voltage stability improvement are considered as
competing objectives.
In Chapter 8, a RPP problem is formulated as a multiobjective
problem and solved by MNSGA-II. Two competing objectives such as the
sum of annual energy cost and the installation cost of additional reactive
power sources and the bus voltage deviation are considered. The static voltage
stability index is considered as additional constraint. The results of MNSGA-II
are compared by NSGA-II.
Chapter 9 sums up the entire thesis and also suggests the future
scope of the present research work.

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