ABSTRACT
The generation of electric power using different fuel resources to meet load demand and losses while satisfying various constraints on the system involves high running cost (cost of fuel). Therefore, it requires electric utilities to minimize the cost of production of electric power by planning and dispatching generating units in an economic and efficient manner to meet the system demand. The aim of the proposed research is to develop an efficient unit commitment based economic load dispatch (ELD) method using the monarch butterfly optimization algorithm in MATLAB R2017a software environment. The above aim was achieved by formulating the economic load dispatch method to minimize cost of generation considering the impact of cost function as system constraints using the application of monarch butterfly optimization algorithm as a tool to optimize the cost. MBO method was used to minimize the cost of supply of electric power to meet increasing demand of customers. The method was modelled and the performance was evaluated by applying the model on the three IEEE standards test system (3-unit IEEE test system, 6-unit test system and the 15-unit). Finally, analysis is done, validated and results. For the 3- unit system, the minimized cost obtained by the MBO model was $1,722.4130/hr for power demand of 150MW and $3,561.3973/hr for 300MW power demand. Similarly, for the 6-unit test system, $9,978.9427/hr was obtained for power demand of 700MW while $17,720.085/hr was obtained for power demand of 1400MW. The model also obtained $32,582.8863/hr for a demand of 2,630MW and $22,797.1231/hr for a demand of 5,260MW on the 15-unit test system. The developed model was finally validated by comparing the result of the 15-unit generator with Differential Evolution Particle Swarm Optimization (DEPSO) technique. For the same power demand of 2,630MW, the DEPSO obtained $32,588.81/h. This comparison showed that the application of MBO ELD model performed better than the DEPSO by 0.0157 (≈ 0.02%) percent in terms of generating cost per hour for load demand of 2,630MW with significant reduction in total power loss when compared with the DEPSO result.
TABLE OF CONTENTS
Declaration i
Certification ii
Dedication iii
Acknowledgement iv
Abstract vi
Table of Contents vii
List of Figures x
List of Tables xi
List of Abbreviation xii
CHAPTER ONE: INTRODUCTION
1.1 Background of the study
1.2 Significance of The Study 3
1.3 Statement of Problem 4
1.4 Aim and Objectives 4
1.5 Methodology 5
1.6 Dissertation Organization 6
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction 7
2.2 Review of Fundamental Concepts 7
2.2.1 Economic load dispatch 7
2.2.1.1 Economic load dispatch neglecting losses 8
2.2.1.2 Economic load dispatch (ELD) with loss 10
2.2.2 Load dispatch cost function formulation 12
2.2.3 System constraints 14
2.2.3.1 Equality constraints (Energy balance equation) 14
2.2.3.2 Inequality constraints (Generating capacity limit constraints) 15
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2.2.3.3 Generator constraints 16
2.2.3.4 Voltage constraints 17
2.2.3.5 Running spare capacity constraints 17
2.2.3.6 Transmission line constraints 18
2.2.3.7 Network security constraints 18
2.2.3.8 Ramp rate limit constraint 19
2.2.4 Conventional Methods for Solving Economic Load Dispatch Problem 19
2.2.4.1 Gradient-search method 19
2.2.4.2 Lambda –Iteration Method 21
2.2.4.3 Newton’s Method 22
2.2.4.4 Linear Programming 22
2.2.5 Computational Intelligent Methods for ELD Problem 23
2.2.5.1 Particle Swarm Optimization for ELD problem 24
2.2.5.2 Artificial bee colony for ELD problem 25
2.2.6 Monarch Butterfly Optimization 27
2.2.6.1 Monarch Butterfly Optimization 29
2.2.6.2 Adjusting operator 30
2.2.7 IEEE standard test system 33
2.2.7.1 The IEEE 3-unit Generators System 34
2.2.7.2 The IEEE 6-unit Generators System 34
2.2.7.3 The IEEE 15-unit Generators System 35
2.3 Review of Similar Works 37
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CHAPTER THREE: MATERIALS AND METHOD
3.1 Introduction 44
3.2 Materials 44
3.2.1 MATLAB Simulation Environment 44
3.2.2 IEEE Test System 45
3.3 Methods 46
3.3.1 Monarch Butterfly Optimization (MBO) for ELD problem 47
3.3.2 Economic Load Dispatch Problem Modeling 51
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Introduction 56
4.2 Simulation Result of the Proposed Model on IEEE 3-Units ELD Test System 56
4.3 Simulation Result of the Proposed Model on IEEE 6-Units ELD Test System 58
4.4 Simulation Result of the Proposed Model on IEEE 15-Units ELD Test System 59
4.5 Comparison 62
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION
5.1 Summary 63
5.2 Limitations 63
5.3 Conclusion 64
5.4 Significant Contribution 65
5.5 Recommendations for Future Research 65
REFERENCES 67
APPENDICES
Appendix A: MATLAB Code for MBO 71
Appendix B: MATLAB Code for MBO Parameter Initialization 75
Appendix C: MATLAB Code for Sorting Population 76
Appendix D: MATLAB Code for ELD Cost Function 77
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CHAPTER ONE
INTRODUCTION
1.1 Background to the Study
Planning, operation and the control of interconnected power system bring about numerous challenging problems caused by unwanted requirements which are imposed on electric utility companies. This likelihood has brought about the need to attain system planning as well as system operation of higher level and greater sophistication (Alam, et al. 2015). The system Operators are highly interested and obligated to maintain and determine the optimal system state, by satisfying many kinds of operational constraints. To solve this class of problems, elaborate studies of power have really been taken on economic dispatch.
The Economic Load Dispatch (ELD) problem pertains to the optimum generation scheduling of available generating units in a power system to minimize the cost of generation subject to system constraints Kaur, et al., (2015). Due to the rapid growth in demand and supply of electricity, electric power system is becoming increasingly bigger and larger every day. Regular electric supply is the greatest requirements for growing industry and other fields of life. With the increasing reliance of industry, agriculture and day-to-day household comfort upon the continuity of electric supply, reliability of power system has become very important.
Furthermore, Babu & Samala, (2013), said Economic Dispatch (ED) of electric power generation involves the schedule of committed generating unit outputs so as to meet the load demand at minimum operating cost while satisfying all units and system equality and inequality constraints. This involves allocation of active power between the units, as the operating cost is insensitive to the reactive loading of a generator (Kamboj, et al. 2016; Kumar, et al. 2014).
The economic dispatch problem involves the solution of two different problems. The first of these is the unit commitment or pre-dispatch problem wherein it is required to select optimally
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out of the available generating sources to operate, to meet the expected load and provide a specified margin of operating reserve over a specified period of time. The second aspect of the economic dispatch is the online economic dispatch wherein it is needed to distribute the load among the generating units actually paralleled with the system in such a manner to minimize the total cost of supplying the minute – to – minute requirements of the system (Mahdi, et al. 2017).
In fact, every electric utility is normally under intense pressure and obligation to provide to its customer’s certain level and degree of continuity and quality of service (power flow on transmission lines in a specified range). Therefore, economy and other objectives of power system must be properly coordinated in reaching optimal power dispatch. It is required to look for better and realistic planning system to achieve different objectives along with desired quality of power supply and satisfying at the same time various system constraints (Saber and Rahman 2011; Tiwari and Pandit 2016; Wang and Li 2013).
In a practical power system, the power plants are not located at the same distance from the center of loads and their fuel costs are different. Also, under normal operating conditions, the generating capacity is more than the total load demand and losses. Thus, there are many options for scheduling the generation. With large interconnection of electrical networks, energy crisis, and high prices of energy, it is very important to reduce the running charges of electrical energy that is reduce the fuel consumption for meeting a particular demand (Zhang, et al. 2012).
In an interconnected power system, the objective is to find the real and reactive power scheduling of each power plant in such a way as to minimize the operating cost. This means that the generators real and reactive powers are allowed to vary within certain limits so as to meet a particular load demand with minimum fuel cost. This is called the optimal power flow (OPF) problem which is used to optimize the power solution of large scale power system. This
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is done by minimizing selected objective functions, while maintaining an acceptable system performance in terms of generator capability limits and output of the compensating devices. The objective functions, also known as cost functions may present economic costs, system security or other objectives (Suman, et al. 2016). The cost function associated with economic load dispatch in power system which inspired this research work is presented.
1.2 Significance of the Study
The modern power system around the world has grown in interruption, complexity and demand. The focus has shifted from mere satisfying demand towards enhanced performance, increased customer focus, low cost, reliable and clean power. In this change perspective, scarcity of energy resources, increasing power generation cost, environmental concern necessitates optimal economic dispatch. 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 various power stations in a way which results in lowest cost for generation. Practical economic dispatch (ED) problems have highly non-linear objective function with rigid equality and inequality constraints. Thus, the need to develop a new optimal approach which will solve ELD problems considering unit commitment while satisfying constraints has becomes important in a deregulated electricity markets. Hence, the needs for this research work.
The transition of many states utility around the globe including Nigeria from a vertically integrated monopoly structure to a deregulated system of electric utility has brought high demand on the operators of these systems as well as the customers. The cost of maintenance, operation and particularly fuel (running) cost is variable and often high. To minimize this cost, utilities have to find an optimal way of reducing the fuel cost of generating units for better
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economic dispatch of all the units in the power station required to satisfy the total load in the system. The application of economic load dispatch of generating units of a power plant using the incremental cost methodology in this study would aid the right use of generators in the system to meet all load demand and losses taking into account the equality and inequality constraints of the system.
1.3 Statement of Problem
The problem of economic load dispatch is to find the optimal output of a number of electricity generating facilities, to meet the minimum operating cost, subject to a number of constraints (usually equality and inequality constraints). This problem is nonlinear in nature which is associated with the unit commitment, valve point effect, multi fuels operation and ramp rate. This is usually a difficult optimization problem to solve by using the conventional method due to lots of local minima associated with the ELD problem. Recently, application of computational intelligence paradigm has presented a number of efficient tools for addressing this problem. However, the review of earlier research work in this area failed to consider critical real-life constraints that has impact on minimizing cost. Therefore, this research work is aim at solving ELD problem using practical constraints that has direct impact on the cost by using application of monarch butterfly optimization (MBO) algorithm which is capable of obtaining a more efficient result.
1.4 Aim and Objectives
The aim of the research is to develop an efficient unit commitment based economic load dispatch method using the application of monarch butterfly optimization in MATLAB software environment. In order to achieve the stated aim, the following objectives were employed
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I. To formulate the mathematical model of the economic load dispatch (ELD) problem considering the various constraints. This is to establish all the mathematical information needed to perform the optimization.
II. To use the MBO algorithm developed in the ELD mathematical problem model formulated in I.
III. To evaluate and compare the performance of the proposed technique with the work of Sayah & Hamouda, (2013).
1.5 Methodology
The following methodology will be adopted
I. Formulation of the economic load dispatch cost minimization problem
a. Formulate the constraints and initializing the boundary condition of each constraint
b. Formulate the objective function based on the economic load dispatch and the initialized constraints in (a)
II. Developing the monarch butterfly optimization algorithm
III. Initialization of algorithm parameters (such as: counter, population, maximum generation, Land1 position, Land2 position, BAR, Peri, Migration ratio and maximum step)
a. Generate initial position randomly
b. Perform butterfly migration operator
c. Perform butterfly adjustment operator
d. Fitness Evaluation
e. Divide the butterfly population into two subpopulations (Land1 and Land2)
f. Generate new positions according to migration and adjustment operator
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g. Merge the population in (g) and evaluate the fitness
h. Update until the best solution is obtained.
IV. Obtain and model the IEEE standard ELD test system in MATLAB R2017a.
V. Perform evaluation by applying the developed models in items I and II on item III.
VI. Presentation of result, analysis and validation.
1.6 Dissertation Outline
The general introduction has been presented in chapter one. The rest of chapters in this dissertation is organized as follows: Details of the Review of literatures comprises of the review of fundamental concepts and similar works is presented in chapter two. Chapter three contains the research materials and methods, while chapter four gives details of the results obtained and followed by discussion of such results. Finally, chapter five presents the conclusion and recommendations which gives the summary and provide guidelines for future work. Quoted references and Appendices are also provided at the end of the dissertation.
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