ABSTRACT
he restructuring of the electrical power industry has given rise to a high degree of vibrancy and competitive market, which changed many features of the power industry. Energy resources become scarce, the cost of power generation increases, environmental concerns are raised, and an ever-increasing demand for electrical energy characterizes this now-altered scenario. In this perspective, Economic Load Dispatch (ELD) is necessitated. Strong heuristic techniques can go a long way in determining the optimum solution to such technical problems having large number of possible solutions. In the proposed research work, two heuristic algorithms namely: Genetic Algorithm (GA) and Artificial Fish Swarm Algorithm (AFSA) are hybridized to yield a more robust technique called “Hybrid Genetic-Artificial Fish Swarm Algorithm”, (HGAFSA) that is suitable for solving complex ELD problems. The technique is then applied to solve a multi-objective ELD problem involving higher order cost functions that includes the effects of valve-point loading and multiple fuel cost function. The proposed approach was validated using five standard IEEE test systems for 13, 40, 110, 140, and 160 generating unit systems. Testing of the developed HGAFSA based ELD algorithm (HGAFSAELDA) yielded reduction in fuel cost by 1.53%, 0.03%, 0.07%, 0.00012% and 1.37% for the 13, 40, 110, 140 and 160 generating units respectively. An annual savings in fuel cost of $3.254e+06, $3.8235e+05, $2135.7, $9.5563e+06, and $1.1588e+06 for the 13, 40, 110, 140, and 160-generating-units respectively were achieved over the existing best costs presented in (Pradhan et al., 2017). HGAFSA based optimization curves and the Cumulative Power Generation curves are also presented to demonstrate how the inequality constraints are satisfied by each of the generating units.
TABLE OF CONTENTS
DECLARATION …………………………………………………………………………………………………………….. i
CERTIFICATION ………………………………………………………………………………………………………….. ii
DEDICATION ………………………………………………………………………………………………………………. iii
ACKNOWLEDGEMENT ………………………………………………………………………………………………. iv
ABSTRACT …………………………………………………………………………………………………………………… v
TABLE OF CONTENTS ………………………………………………………………………………………………… vi
LIST OF FIGURES ………………………………………………………………………………………………………… x
LIST OF ABBREVIATIONS …………………………………………………………………………………………. xii
NOMENCLATURE …………………………………………………………………………………………………….. xiv
CHAPTER ONE: GENERAL INTRODUCTION ………………………………………………………………. 1
1.1 Background of Research …………………………………………………………………………………………. 1
1.2 Problem Statement …………………………………………………………………………………………………. 5
1.3 Aim and Objectives ………………………………………………………………………………………………… 6
1.4 Scope of Work and Limitation …………………………………………………………………………………. 6
1.5 Dissertation Organization Outline …………………………………………………………………………….. 7
CHAPTER TWO: LITERATURE REVIEW ……………………………………………………………………… 8
2.1 Introduction …………………………………………………………………………………………………………… 8
2.2 Review of Fundamental Concepts…………………………………………………………………………….. 8
2.2.1 Thermal power plant …………………………………………………………………………………………. 8
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2.2.2 Generator operating cost ……………………………………………………………………………………. 9
2.2.3 Fuel efficiency ……………………………………………………………………………………………….. 10
2.2.4 Incremental cost (IC) ………………………………………………………………………………………. 10
2.2.5 Economic Load Dispatch (ELD) formulation …………………………………………………….. 11
2.2.6 The cost function ……………………………………………………………………………………………. 11
2.2.7 Solution by Lagrange method …………………………………………………………………………… 14
2.2.8 Dynamic programming ……………………………………………………………………………………. 16
2.2.9 Quadratic programming method ……………………………………………………………………….. 16
2.2.10 Non-linear programming ……………………………………………………………………………….. 17
2.2.11 Newton’s method ………………………………………………………………………………………….. 18
2.2.12 Heuristic approaches ……………………………………………………………………………………… 18
2.2.12.1 Particle swarm optimization …………………………………………………………………….. 19
2.2.12.2 Artificial fish swarm algorithm …………………………………………………………………. 19
2.2.12.3 Genetic algorithm……………………………………………………………………………………. 25
2.2.12.4 Hybrid algorithms …………………………………………………………………………………… 32
2.3 Review of Similar Works ………………………………………………………………………………………. 33
CHAPTER THREE: METHODOLOGY …………………………………………………………………………. 42
3.1 Introduction …………………………………………………………………………………………………………. 42
3.2 Formulation of the Proposed HGAFSA …………………………………………………………………… 42
3.3 Decoder Function …………………………………………………………………………………………………. 43
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3.4 Encoder Function …………………………………………………………………………………………………. 44
3.5 Population Update ………………………………………………………………………………………………… 46
3.6 Model of the ELD Problem ……………………………………………………………………………………. 50
3.7 The Proposed HGAFSA based Higher Order ELD Algorithm ……………………………………. 54
CHAPTER FOUR: RESULTS AND DISCUSSION …………………………………………………………. 56
4.1 Introduction …………………………………………………………………………………………………………. 56
4.2 Simulation Setup ………………………………………………………………………………………………….. 56
4.3Test system 1 ………………………………………………………………………………………………………… 57
4.4Test system 2 ………………………………………………………………………………………………………… 60
4.5 Test system 3 ……………………………………………………………………………………………………….. 62
4.6 Test system 4 ……………………………………………………………………………………………………….. 65
4.7 Test system 5 ……………………………………………………………………………………………………….. 68
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION ……………………………………… 73
Introduction ………………………………………………………………………………………………………………. 73
5.1 Conclusion …………………………………………………………………………………………………………… 73
5.2 Significant Contributions ………………………………………………………………………………………. 74
5.3 Recommendations ………………………………………………………………………………………………… 74
5.4 Limitation ……………………………………………………………………………………………………………. 75
REFERENCES …………………………………………………………………………………………………………….. 76
APPENDICES ……………………………………………………………………………………………………………… 85
CHAPTER ONE
GENERAL INTRODUCTION
1.1 BACKGROUND OF RESEARCH
The efficient and optimum economic operation and planning of electric power generation systems have always occupied a vital position in the electric power industry (Gargeya & Pabba, 2013). Economic load dispatch (ELD) is a process of allocating generation levels to dispersed generating power plants so that the system is fully supplied in the most economical way (Harpreet Kaur et al., 2015). It can also be defined as the operation of generation facilities to produce energy at the lowest cost to reliably serve consumers recognizing any operational limits of generation and transmission facilities. ELD is simply a technique used to schedule the outputs of available generating units for a particular time that minimizes the total production cost while satisfying equality and inequality constraints (Pothiya et al., 2008), Prior to 1973 and the oil embargo that caused the rapid increase in fuel prices, electric utilities in the United States spent about 20% of their total income on fuel for the production of electrical energy (Alsumait et al., 2010). An idea of magnitude of the amounts of money was under consideration, and could be obtained by considering the annual operating expenses of a large utility for buying fuel. Based on assumption proposed by Gargeya & Pabba, 2013, the following parameters for a moderately large power system:
i. Annual peak load= 10,000MW;
ii. Annual load factor= 60%;
iii. Average annual heat rate for converting fuel to electric energy= 10,550.56KJ/kWh;
iv. Average fuel cost= $3.00/1.055GJ, corresponding to oil price at $18/Bbl.
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With these assumptions, the total annual fuel cost for the system is as follows:
I. Annual energy produced =107 MW * 8760h/year * 0.60 = 5.256 * 1010kWh;
II. Annual fuel consumption= 10,550.56KJ/kWh * 5.256 * 1010 kWh = 55.45 * 1013KJ;
III. Annual fuel cost = 55.45* 1013 * 3/1.055* 10-9 $/J = $1.5767million.
This cost represents a direct requirement for revenues for the average customer of the system of 3.15cents/kWh aimed at recovering the expense for fuel. A savings in the operation of the system of small percent represents a significant reduction in operating cost, as well as in the quantities of fuel consumed. It is not surprising that this area has warranted a great deal of attention from the engineers through the years.
However, periodic changes in basic fuel price levels serve to accentuate the problem and increase its economic significance. Inflation also causes problems in developing and presenting methods, techniques, and examples of economic operation of electric power generating systems (Al-Othman & El-Naggar, 2008).
Moreover, rapid growth in power system size and electrical power demand has resulted into a problem of reducing the operating cost while maintaining voltage security and thermal limits of transmission line branches (Alsumait et al., 2010). A large number of mathematical Optimization Technique such as: GA based ELD; PSO based ELD; Hybrid GA-PSO based ELD; Dynamic Programming based ELD; Evolutionary Programming based ELD; to mention but a few have been applied to solve ELD problems. In most general formulation, the ELD problem is modeled as a non-linear, non-convex, large scale, static optimization problem with both continuous and discrete control variables (Burns & Gibson, 1975).
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Furthermore, the non-linear convex nature of ELD problems has led most researchers such as: (Burns & Gibson, 1975), (Pothiya et al., 2008), (Al-Othman & El-Naggar, 2008), and others to model ELD problem using purely quadratic functions in which the quadratic coefficients are defined at the beginning of the solution search process. Whereas, more realistic models have also been developed in some other research works which includes those of: (Alsumait et al., 2010), (Sinha & Chakrabarti, 2003), (Sun et al., 2014), (Mohammadi-Ivatloo & Rabiee, 2013), (Jubril & Komolafe, 2013); etc. These models incorporated the effect of valve point loading and multiple fuel cost functions into ELD problem formulation.
However, the proposed research work will try to address an ELD problem through the development of a more realistic model that will account for the following effects of Valve-Point Loading (VPL), Multiple Fuel Cost Function (MFCF), Ramp Rate (RR) and Prohibited Operating Zone (POZ).
These result into a multi-objective optimization problem that tends to minimize the cost of fueling the generating units during the operation. This kind of complex optimization problem requires the use of robust techniques to achieve a reliable solution. Although, this optimization problem can be solved to some extent, using the heuristic techniques earlier mentioned, but the effectiveness of the solution cannot be guaranteed in the case of large power system.
In order to proffer solution that can be reliable and more efficient, a hybridization of two conventional heuristic techniques (Genetic Algorithm and Artificial Fish Swarm Algorithm) is proposed for solving the complex optimization problem, which give rise to a technique called “ Hybrid G-AFS Algorithm” or simply HGAFSA. The choice of GA and AFSA were based on the following reasons:
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a. GA is a widely known heuristic technique that has a well-defined set of search equations that have been proven to be effective in solving problems such as: Optimal Location and Sizing of Distributed Generators and Capacitor Banks, (Moradi & Abedinie, 2010), (Atwa et al., 2010); Optimal Power Flow, (López-Lezama et al., 2012); Optimal Location of Tie and Sectionalizing Switches in Distribution System, (Rao et al., 2013); Optimal Network Expansion (Bernardon et al., 2014), A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems (Alsumait et al., 2010); etc.
b. AFSA on the other hand is a relatively new heuristic technique that is made up of well refined and sophisticated solution-search equations and has gained large application in areas like: Controller Design, (Fang et al., 2014); Optimal PID Tuning, (Amir Ghoreishi et al., 2011); Objective Function Minimization/ Maximization, (Wei Guo et al., 2011) (Huang et al., 2006); etc.
1.2 Motivation/Justification
I derive my motivation from the fact that over the years researchers have tried to address the problem of economic load dispatch with the main focus of how to commit the online generating units economically in order to generate electricity at a minimum cost while addressing generator constraints. The modern power systems encounter numerous technical and economic difficulties under competitive deregulated environment. The generation companies’ (GENCOs) aim is to produce electric power at minimum cost therefore; proper allocation of power generation of the existing units may lead to significant savings in cost. This could be achieved by incorporating multiple fuel option into the economic dispatch problems.
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1.3 Problem Statement
The modern power system around the world has grown in complexity of interconnection and power demand. The focus has shifted towards the enhanced performance, increased customer focus, low cost, reliable and clean power. In this changed perspective, scarcity of energy resources, increasing power generation cost and environmental concern necessitates economic load dispatch (ELD). In reality power stations, neither are at equal distances from load nor have similar fuel cost functions. Hence for providing cheaper power, load has to be distributed among the various power stations in a way that will result in lowest cost of generation. Practical economic dispatch (ED) problems have highly nonlinear objective function with equality and inequality constraints. Conventional methods such as lambda iteration method, gradient method and non-conventional method such as the heuristic method earlier discussed have been applied to solve the Economic Load Dispatch (ELD) problem. However, these techniques may not give optimal solution because they require incremental fuel cost curves which are piecewise linear and monotonically increasing to find the global optimal solution. In the proposed research work, a hybridization of two heuristic techniques namely: Artificial Fish Swarm Algorithm (AFSA); and Binary Coded Genetic Algorithm (BCGA), will be carried out in order to form a more robust technique called “Hybrid Genetic-Artificial Fish Swarm Algorithm”, (HGAFSA). The technique will then be applied to solve a non-linear ELD problem considering the effects of valve-point loading, multiple fuel cost functions, ramp rate and prohibited operating zone. The effectiveness of the proposed approach will be demonstrated using five standard IEEE test systems (13, 40, 110, 140, and 160 generating unit systems); and finally comparing the results with those presented in (Pradhan et al., 2017)
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1.4 Aim and Objectives
The aim of the proposed research work is to develop a Hybrid Genetic-Artificial Fish Swarm Algorithm (HGAFSA) and use it in solving a non-linear ELD problem considering the effects of: valve-point loading and multiple fuel cost. In achieving this, the following objectives will be met:
1. To hybridize Genetic Algorithm (GA) with Artificial Fish Swarm Algorithm (AFSA) to form a more robust algorithm called HGAFSA.
2. To model a higher order ELD problem while considering the effects of valve-point loading, multiple fuel cost function, ramp rate and prohibited operating zone.
3. To solve the resulting ELD problem in (2) using the developed algorithm in (1) and demonstrate the effectiveness of the proposed approach using five standard test systems (13, 40, 110, 140, and 160 generating unit systems); and finally comparing the results with those presented in (Pradhan et al., 2017).
1.5 Scope of Work and Limitation
The following items are the step by step approach that will constitute the scope of the proposed research work:
1. For the ELD, valve point loading, multi fuel cost function, ramp rate and prohibited operating zone effects were considered while emissions were not considered; hence the impact of emissions to ELD objective function was not quantified.
2. GA and AFSA algorithms were formulated using matrix definition method to aid hybridization.
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3. A simulation test framework is developed in MATLAB to demonstrate the effectiveness of the formulated multi-objective ELD problem using five standard IEEE test systems. Actual transmission network was not considered.
4. The power demand considered for the networks were based on the reference in Pradhan et al., (2017).
5. The proposed ELD uses Encoder and Decoder to serve as an interface between GA and AFSA.
1.6 Dissertation Organization Outline
This chapter describes ELD problem and a brief overview of its solution strategies. However, it forms the introductory chapter. The aim and objectives together with problem statement, methodology and significant contributions are also presented in this chapter. The rest of the chapters are organized as follows. Chapter two presents the literature review of the fundamental concepts and similar works regarding ELD problem formulation and solution approaches. Chapter three presents the methods and materials used for this research work. Chapter four presents the simulation setup, results and analysis. Finally Chapter five presents the conclusion, recommendations and limitations. Quoted references and appendices are also provided at the end of the dissertation.
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