SHIBAURA INSTITUTE OF TECHNOLOGY Economic planning and operation in electric power system using meta-heuristics based on Cuckoo Search Algorithm by Nguyen Phuc Khai A thesis submitted in partial fulfillment for the degree of Doctor of Philosophy in the Regional environment systems September 2017 Abstract The main purpose of this thesis is to propose an improved Cuckoo Search Algorithm and evaluate it on various economic problems of the electric power system in order to investigate its effectiveness. Cuckoo Search Algorithm is a meta-heuristic developed by Yang and Deb since 2009. This method is based on the Lévy distribution to generate new solutions and illustrate the process of Cuckoo’s reproduction strategy to carry better solutions over the next generation. In this study, the proposed method gives a chance for Cuckoo eggs to modify itself following better solutions to enhance the performance.
A learning factor pl is employed to control the modification stage of Cuckoo eggs and prevent the search engine fall into local optimum points. Thus, the proposed is named Self-Learning Cuckoo Search Algorithm. In order to investigate the efficiency, Self-Learning Cuckoo Search Algorithm is evaluated on four common economic problems on the power system. The first application is the Multi-Area Economic Dispatch.
The objective of this problem is to minimize the total fuel cost when combining power systems of many areas together while satisfying the power balance in each area. This problem consists of many non-convex fuel cost functions, such as multi-fuel cost function, the functions considering valve-point effects or prohibited operating zone. Numerical results of three case studies show that the proposed method is better than the conventional Cuckoo search algorithm. The second obtained problem is the Optimal Power Flow, which is the major tool to operate and analyze the power system.
This problem determines power and voltage of generators to minimize the total fuel cost while handling a huge of equal and unequal operational constraints. Self-Learning Cuckoo Search Algorithm is evaluated up to the IEEE 300-bus system to investigate its efficiency on large-scale problems. Numerical results show that the proposed method is successful in solving the large-scale problem while the conventional is unsuccessful. Thirdly, Self-Learning Cuckoo Search Algorithm is evaluated on the Optimal Reactive Power Dispatch.
This problem is a special type of the Optimal Power Flow when its objective function is to minimize the total power loss. According to numerical results of 30-, 57- and 118-bus systems, the proposed method keeps giving better solutions than the conventional. The final problem is the optimal sizing and placement of shunt-VAR compensators. This problem has multiple objectives and combines integer and real numbers together.
In this study, Self-Learning Cuckoo Search Algorithm is compared with the Teaching-Learning based Optimization, Particle Swarm Optimization, Improved Harmony Search and the conventional Cuckoo Search Algorithm. According to numerical results of obtained problems, the proposed Self-Learning Cuckoo Search Algorithm is better than the conventional in giving the optimal solutions, especially on large-scale systems. Thus, the proposed method is favorable to apply for practical operation. Acknowledgements I would like to use this opportunity to thank my advisor, my fellow and diploma students, my many friends and my family for their time, ideas and encouragement.
First of all, I would like to thank my advisor, Prof Goro Fujita. You gave me professional assistance, careful reading, valuable feedbacks and, especially, the opportunity of writing this thesis. You helped me not only on professional research but also on my life. I am deeply grateful and proud to become a student of yours.
I also would like to thank to Assoc. Vo Ngoc Dieu at Ho Chi Minh University of Technology in Viet Nam and Prof. Fukuyama at Meiji University, for your useful comments and pointing me in right directions. Special thank to Shibaura Institute of Technology for your financial support through the Hybrid Twin Program.
Your support gives my whole mind to study. Warmly thank to other fellow doctoral students in my lab for your significant contribution and your supports when I write this thesis. I am also thankful to other master and diplomat students in my laboratory for your always being helpful. Last I would like thank to my family and numerous friends who always encouraged me to finish my research.
NGUYEN PHUC KHAI vi Contents Abstract iv Acknowledgements vi List of Figures xiii List of Tables xv Abbreviations xvii 1 Introduction 1 1.2 Process of economic operation in the control of a generating unit .3 Input-Output characteristic of thermal unit .1 Quadratic fuel cost function: .2 Fuel cost function with valve-point loading effect: .3 Fuel cost function with multiple fuels: .4 Power flow analysis .5 Conventional optimization techniques .2 Motivation of this thesis .4 Structure of this thesis: .1 Heuristics and meta-heuristics: .2 Particle Swarm Optimization .4 Harmony Search Algorithm .5 Teaching-learning-based optimization .6 Moth-Flame Optimization. 23 vii Contents viii 2.1 Apply a meta-heuristic for solving a problem .2 Effectiveness of meta-heuristics. 24 3 Self-Learning Cuckoo search algorithm 27 3.1 Cuckoo search Algorithm .1 Cuckoos breeding behavior .2 Lévy flight .3 Conventional Cuckoo search algorithm .2 Proposed Self-learning Cuckoo Search Algorithm .3 Evaluation on tested benchmarks .4 Applications on engineering problems. 35 4 Multi-Area Economic dispatch problem 39 4.2 Multi-area economic dispatch: .1 Real balanced-power constraint: .2 Limitation of output power: .3 Limitation of transmission lines: .4 Prohibited operating zone constraint: .3 Previous works on Multi-area economic dispatch problem .4 Implementation for Multi-area economic dispatch problem .1 Determining output power of slack generator in each area .4 Overall procedure of the proposed method for MAED:.
55 5 Optimal power flow problem 57 5.1 Power balance constraint .2 Limited constraints of generators .3 Shunt-VAR compensators capacity .4 Limitation of tap changers of transformers .5 Limitation of load bus voltages .6 Capacity of transmission lines .3 Previous works on optimal power flow studies .4 Implementation of Self-learning Cuckoo Search for OPF .1 Controllable and dependent variables: .4 Example of Optimal power flow problem .1 Case study 1: IEEE 30-bus system .2 Case study 2: IEEE 57-bus system .1 Continuous variables of capacitors .3 Case study 3: IEEE 118-bus system .4 Case study 4: IEEE 300-bus system. 81 6 Optimal Reactive Power Dispatch 83 6.1 Previous works on optimal reactive power dispatch .1 Power balance constraint: .2 Limitation constrains of generators .3 Limitation of shunt-VAR compensators .4 Limitation of transformer load changers .5 Limitation of load bus voltages .6 Limitation of transmission lines .3 Implementation of Self-Learning Cuckoo Search for ORPD .1 Case study 1: IEEE 30-bus system .2 Case study 2: IEEE 57-bus system .3 Case study 3: IEEE 118-bus system. 93 7 Optimal sizing and placement of shunt VAR compensators 95 7.1 Previous works on optimal reactive power dispatch .2 Objectives and operational constraints .1 The active power losses .2 The voltage deviation .3 The investment cost .1 Power balance constraint .2 Limitation of SVC devices .3 Limitation of bus voltages .3 Implementation and the fitness function .3 Limitation of solution vector and initialization .1 Case study 1: IEEE 30-bus system .2 Case study 2: IEEE 57-bus system .3 Case study 3: IEEE 118-bus system .1 Alignment with research issues:. 110 A Data of Multi-Area Economic Dispatch 113 A.1 Data of 6 generators considering Prohibited Operation Zones .2 Data of 10 generators considering Multiple fuel cost functions .3 Data of 40 generators considering valve-point-effect fuel cost functions .4 Data of 140 generators considering valve-point-effect fuel cost functions.
116 B Data of the IEEE 30-bus system 123 B. 126 C Data of the IEEE 57-bus system 129 C. 134 D Data of the IEEE 118-bus system 137 D. 149 E Data of the IEEE 300-bus system 153 E.
179 F Matlab code of Self-Learning Cuckoo search algorithm for Example 4.1185 Contents xi Bibliography 191 List of Publications 201 List of Figures 1.1 Simplified block diagram of a thermal generating unit .2 Approximate time scale controlling a generator according to the standard of the Central Europe system .3 Example of the primary and secondary controls .4 Example of a quadratic fuel cost function with a = 0.5 Example of a fuel cost function considering valve-point effects .6 Diagram of a common-header plant using multiple fuel cost function .7 Example of a multi-fuel cost function .8 One-line diagram of the example system with bus numbers .9 Disadvantages of conventional methods .1 Illustration of crossover stage of Differential Evolution algorithm .2 Illustration of potential idea of the Teaching-learning based optimization .3 Spiral-flying path around a close light [1] .4 Logarithmic spiral, space around a flame, and the position with respect to t [1] .1 Cuckoo bird in nature .2 Neighbors nest with a Cuckoo egg .3 Cumulative of the Lévy distribution .4 Flow chart of Self-Learning Cuckoo search Algorithm .5 Convergence characteristics of the Shifted Sphere function .6 Mean fitness values of the Schwefel’s problem with 10 dimensions .7 Mean fitness values of the Schwefel’s problem with 30 dimensions .8 Convergence characteristics of SLCSA and CSA for the Schwefel’s problem with 30 dimensions .1 Illustration of N thermal-generating units serving a load .2 Example of a Multi-area economic dispatch problem .3 Flow chart of the implementation for MAED .4 Illustration of the problem of case study 1 .5 Illustration of the problem of case study 2 .6 Comparison of convergence characteristics of three methods in case study 2 53 4.7 Comparison of convergence characteristics of three methods in case study 3 54 4.8 Illustration of the problem of case study 2 [2]. 65 xiii List of Tables 1.1 Line data of Example 1.2 Bus data of Example 1.3 Power-flow solution of Example 1.4 Line flow of Example 1.1 Number of controlled vectors for each case study .2 Numerical results of three methods in 2-area system .3 Numerical results in the 3-area system .4 Optimal solution proposed by SLCSA .5 Numerical results of three methods in 4-area system .6 Numerical results of three methods in 5-area system .1 Bus data of Example 5.2 Number of controlled variables .3 Setting parameters of the SLCSA for evaluated benchmarks .4 Comparison of numerical results proposed by the proposed SLCSA and other methods for IEEE 30-bus system .5 Optimal solutions for the IEEE 30-bus system .6 Comparison of numerical results proposed by the proposed SLCSA and other methods for IEEE 57-bus system with continuous values of capacitors 71 5.7 Comparison of numerical results proposed by the proposed SLCSA and other methods for IEEE 57-bus system with binary values of capacitors .8 Comparison of numerical results proposed by the proposed SLCSA and other methods for IEEE 118-bus system .9 Optimal solution for the IEEE 118-bus system .10 Numerical results of the SCLCSA and the conventional CSA for IEEE 300- bus system .11 Optimal solution for the IEEE 300-bus system .1 Numerical results of compared methods for IEEE 30-bus tested system .2 Optimal solutions of compared methods for IEEE 30-bus system .3 Numerical results of SLCSA and CSA for IEEE 57-bus system .4 Optimal solutions of SLCSA and CSA for IEEE 57-bus system .5 Reactive power generation limits in IEEE 118-bus system .1 Example of duplicated solutions .2 Size of search space and number of iterations .3 Numerical results of CSA and TLBO for IEEE 30-bus system. 104 xv List of Tables xvi 7.4 Optimal solution of CSA in IEEE 30-bus case study .5 Numerical results of compared methods for IEEE 57-bus system .6 Optimal solution of CSA in IEEE 57-bus case study .7 Best results of compared methods for IEEE 118-bus system .1 Fuel cost coefficients of 6 generators .2 Transmission loss coefficients of two areas .3 Fuel cost coefficients of 10 generators .4 Data of 40 generators .5 Data of 140 generators .1 Data of buses of the IEEE 30-bus system .2 Data of transformers and transmission lines of IEEE 30-bus system .4 Valve-point-effect functions .1 Data of buses of the IEEE 57-bus system .2 Data of transformers and transmission lines of IEEE 57-bus system .3 Data of generators of the IEEE 57-bus system .