Áp dụng các phương pháp thông minh nhân tạo giải bài toán phối hợp hệ thống thủy nhiệt điện.

TÓM TẮT Luận án trình bày ứng dụng các phương pháp thông minh nhân tạo giải các bài toán phối hợp tối ưu hệ thống thủy nhiệt điện. Mục tiêu của các bài toán là cực tiểu chi phí phát điện tại các nhà máy nhiệt điện trong khi đó không xét đến chi phí phát điện tại các nhà máy thủy điện sao cho các ràng buộc cân bằng và bất cân bằng của hệ thống như ràng buộc cân bằng công suất có xét đến tổn hao truyền tải đường dây, các giới hạn công suất phát của nhà máy thủy điện và nhiệt điện và các ràng buộc từ hồ thủy điện như thể tích hồ chưa, lưu lượng xả, thể tích nước cho phép sử dụng phải được thỏa mãn. Ngoài ra, ràng buộc trên lưới truyền tải như khả năng truyền tải đường dây, điện áp tại các nút, cài đặt đầu phân áp, chọn công suất tụ bù cũng được xét đến. Mức độ phức tạp của các ràng buộc được tăng dần từ bài toán thứ nhất đến bài toán cuối cùng. Ba phương pháp cuckoo Search như cuckoo Search cổ điển (CCSA), Cuckoo Search cải biên (MCSA) và Cuckoo Search chọn lọc thi nghi (ASCSA), và phương pháp mạng Hopfield Lagrange tăng cường (ALHN) đã được áp dụng để giải các bài toán trên. CCSA là phương pháp Cuckoo Search đầu tiên được xây dựng năm 2009 trong khi đó MCSA được phát triển dựa trên CCSA vào năm 2011. ALHN cũng là một phương pháp được phát triển từ phương pháp Hopfield Neural Network và đã được áp dụng trong lĩnh vực kỹ thuật điện. Khác với ba phương pháp này, ASCSA chưa được áp dụng cho bất cứ bài toán nào trước đây vì ASCSA là phương pháp được phát triển đầu tiên trong luận này dựa trên các cải biên từ CCSA. Tính hiệu quả của các phương pháp được kiểm tra trên các hệ thống khác nhau với năm bài toán khác nhau. Kết quả được so sanh giữa bốn phương pháp với nhau và giữa bốn phương pháp với các phương pháp đã được nghiên cứu trước đây để đưa ra nhận xét về tính hiệu quả của bốn phương pháp này so với các phương pháp khác và tìm ra phương pháp hiệu quả nhất trong bốn phương pháp cũng như đề xuất khả năng áp dụng của từng phương pháp cho từng bài toán cụ thể. Kết quả đánh giá cho thấy ALHN chỉ hiệu quả cho hai bài toán đầu tiên với chiều cao cột nước cố định bỏ qua thể tích hồ chứa và bỏ qua hiệu ứng xả van tại các nhà máy nhiệt điện. Trong khi đó, phương pháp được đề xuất ASCSA tỏ ra hiệu quả hơn CCSA và MCSA cho tất cả các hệ thống ở năm bài toán này và hiệu quả hơn ALHN cho ba bài toán còn lại. MCSA hiệu quả hơn CCSA ở hai bài toán đầu tiên và bài toán cuối nhưng kém hiệu quả hơn ở bài toán thứ ba và thứ tư. So với các phương pháp trước đây, bốn phương pháp áp dụng được đánh giá khá hiệu quả khi hầu hết nổi trội hơn các phương pháp khác về chất lượng lời giải tối ưu với tốc độ hội tụ nhanh.

MINISTRY OF EDUCATION AND TRAINING

HCMC UNIVERSITY OF TECHNOLOGY AND EDUCATION

BIOGRAPHY

1 Personal details

street, District 7, HCMC

No 65, Huynh Thuc Khang street, District 1, HCMC

HCM city, 06 / 10 /2017 PhD Candidate

Thang Trung Nguyen

CERTIFICATE

I hereby certify that the work which is being presented in the study entitled, “The applications of artificial intelligence based methods for solving hydrothermal scheduling problems” in partial fulfillment of the requirements for the award of

degree of Doctor of engineering in electrical engineering, is an authentic record of my own work carried out under the supervision of Assoc Prof Dieu Ngoc Vo and Assoc

Prof Anh Viet Truong

The matter presented in the study has not been submitted elsewhere for the award of any other degree

ACKNOWLEDGEMENTS

After a long hard working period of time to finish the dissertation, I could not forget the people who have helped and supported me over the years I could not have completed my dissertation without these people

First of all, I would like to express my deeply attitude to my Program Examination Committee Chairperson, Assoc Prof Dieu Ngoc Vo who has given me very valuable guidance, suggestions and comments toward the completion of the study He is very patient in giving me appropriate advices so that I can complete my dissertation I really appreciate his supervision and supports during my research Besides, Assoc Prof Anh Viet Truong is also a very enthusiastic Program Examination Committee Member, who always give me useful suggestions that can make my study more perfect and more realistic I really appreciate his contribution to my study I could not forget good knowledge that Prof Anh Huy Quyen taught me when I was a university student and his comments on the study as well as his friendly behavior and his encouragement in

my friend, Mr Ly Huu Pham, who supported me many things in teaching and administrative works and went to coffee shop with me for writing my study Besides, I also thank Mr Au Ngoc Nguyen and Mr Tho Quang Tran, who are my classmates and

encouraged me when I coped with disappointment

TÓM TẮT

Luận án trình bày ứng dụng các phương pháp thông minh nhân tạo giải các bài toán phối hợp tối ưu hệ thống thủy nhiệt điện Mục tiêu của các bài toán là cực tiểu chi phí phát điện tại các nhà máy nhiệt điện trong khi đó không xét đến chi phí phát điện tại các nhà máy thủy điện sao cho các ràng buộc cân bằng và bất cân bằng của hệ thống như ràng buộc cân bằng công suất có xét đến tổn hao truyền tải đường dây, các giới hạn công suất phát của nhà máy thủy điện và nhiệt điện và các ràng buộc từ hồ thủy điện như thể tích hồ chưa, lưu lượng xả, thể tích nước cho phép sử dụng phải được thỏa mãn Ngoài ra, ràng buộc trên lưới truyền tải như khả năng truyền tải đường dây, điện áp tại các nút, cài đặt đầu phân áp, chọn công suất tụ bù cũng được xét đến Mức độ phức tạp của các ràng buộc được tăng dần từ bài toán thứ nhất đến bài toán cuối cùng

Ba phương pháp cuckoo Search như cuckoo Search cổ điển (CCSA), Cuckoo Search cải biên (MCSA) và Cuckoo Search chọn lọc thi nghi (ASCSA), và phương pháp mạng Hopfield Lagrange tăng cường (ALHN) đã được áp dụng để giải các bài toán trên CCSA là phương pháp Cuckoo Search đầu tiên được xây dựng năm 2009 trong khi đó MCSA được phát triển dựa trên CCSA vào năm 2011 ALHN cũng là một phương pháp được phát triển từ phương pháp Hopfield Neural Network và đã được áp dụng trong lĩnh vực kỹ thuật điện Khác với ba phương pháp này, ASCSA chưa được

áp dụng cho bất cứ bài toán nào trước đây vì ASCSA là phương pháp được phát triển đầu tiên trong luận này dựa trên các cải biên từ CCSA

Tính hiệu quả của các phương pháp được kiểm tra trên các hệ thống khác nhau với năm bài toán khác nhau Kết quả được so sanh giữa bốn phương pháp với nhau và giữa bốn phương pháp với các phương pháp đã được nghiên cứu trước đây để đưa ra nhận xét về tính hiệu quả của bốn phương pháp này so với các phương pháp khác và tìm ra phương pháp hiệu quả nhất trong bốn phương pháp cũng như đề xuất khả năng

áp dụng của từng phương pháp cho từng bài toán cụ thể Kết quả đánh giá cho thấy ALHN chỉ hiệu quả cho hai bài toán đầu tiên với chiều cao cột nước cố định bỏ qua thể tích hồ chứa và bỏ qua hiệu ứng xả van tại các nhà máy nhiệt điện Trong khi đó, phương pháp được đề xuất ASCSA tỏ ra hiệu quả hơn CCSA và MCSA cho tất cả các

hệ thống ở năm bài toán này và hiệu quả hơn ALHN cho ba bài toán còn lại MCSA hiệu quả hơn CCSA ở hai bài toán đầu tiên và bài toán cuối nhưng kém hiệu quả hơn ở bài toán thứ ba và thứ tư So với các phương pháp trước đây, bốn phương pháp áp dụng được đánh giá khá hiệu quả khi hầu hết nổi trội hơn các phương pháp khác về chất lượng lời giải tối ưu với tốc độ hội tụ nhanh

TABLE OF CONTENTS

Acceptance Decision

CHAPTER 1: INTRODUCTION

1.1 Background 1

1.2 Statement of the problem 1

1.3 Objectives of the research 4

1.4 Contributions 4

1.5 Scope and limitation 4

1.6 Organization of the dissertation 5

CHAPTER 2: LITERATURE REVIEW 2.1 Introduction 6

2.2 Fixed-head short-term hydrothermal scheduling problem neglecting reservoir volume constraints 6

2.3 Fixed-head short-term hydrothermal scheduling problem considering reservoir volume 10

2.4 Variable-head short-term hydrothermal scheduling problem 13

2.5 Multi-objective fixed head short-term hydrothermal scheduling problem 18

2.6 Hydrothermal optimal power problem 20

2.7 Summary 21

CHAPTER 3: CUCKOO SEARCH ALGORITHMS AND AUGMENTED LAGRANGE HOPFIELD NETWORK 3.1 Introduction 22

3.2 Conventional Cuckoo Search algorithm (CCSA) 23

3.3 Modified Cuckoo Search Algorithm (MCSA) 29

3.4 Adaptive Selective Cuckoo Search Algorithm (ASCSA) 32

3.5 Augmented Lagrange Hopfield Network (ALHN) 43

3.6 Summary 45

CHAPTER 4: ARTIFICIAL INTELLIGENCE BASED METHODS FOR FIXED-HEAD SHORT-TERM HYDROTHERMAL SCHEDULING PROBLEM NEGLECTING RESERVOIR VOLUME CONSTRAINTS 4.1 Introduction 46

4.2 Problem formulation 47

4.3 Calculation of power output for slack thermal and hydro units 51

4.4 Conventional Cuckoo Search Algorithm for the problem 53

4.5 Modified Cuckoo Search Algorithm for the problem 57

4.6 Adaptive Selective Cuckoo Search Algorithm for the problem 61

4.7 Augmented Lagrange Hopfield Network for the problem 63

4.8 Determining the best compromise solution by for multiobjective problem 69

4.9 Numerical results 70

4.10 Summary 103

CHAPTER 5: CUCKOO SEARCH ALGORITHMS FOR FIXED-HEAD SHORT-TERM HYDROTHERMAL SCHEDULING PROBLEM CONSIDERING RESERVOIR VOLUME CONSTRAINTS 5.1 Introduction 106

5.2 Problem formulation 106

5.3 Calculation of power output for slack thermal and hydro units 107

5.4 Cuckoo Search Algorithm for the problem 108

5.5 Modified Cuckoo Search Algorithm for the problem 112

5.6 Adaptive Selective Cuckoo Search Algorithm for the problem 114

5.7 Numerical results 116

5.8 Summary 122

CHAPTER 6: CUCKOO SEARCH ALGORITHMS FOR VARIABLE-HEAD SHORT-TERM HYDROTHERMAL SCHEDULING PROBLEM 6.1 Introduction 124

6.2 Problem formulation 124

6.3 Calculate slack water discharge and slack power output of thermal unit 1 126

6.4 Implementation of conventional Cuckoo Search for the problem 126

6.5 Modified Cuckoo Search Algorithm for the problem 130

6.6 Adaptive Selective Cuckoo Search Algorithm for the problem 132

6.7 Numerical results 134

6.8 Summary 145

CHAPTER 7: THE APPLICATION OF CSA METHODS FOR SOLVING HYDROTHERMAL OPTIMAL POWER FLOW PROBLEM 7.1 Introduction 147

7.2 Hydrothermal optimal power flow problem formulation 149

7.3 Application of Cuckoo Search Algorithms for solving HTOPF problem 152

7.4 Numerical results 161

7.5 Summary 174

CHAPTER 8: CONCLUSIONS 8.1 Summary and contributions 176

8.2 Future work 179

APPENDIX A 180

APPENDIX B 193

REFERENCES 210

PUBLICATIONS RELATED TO THE STUDY 218

LIST OF ABBREVIATIONS

-PSO Particle swarm optimization and gamma based method

ABCA Adaptive artificial bee colony algorithm

ACABCA Adaptive chaotic artificial bee colony algorithm

ACRCGA Adaptive Chaotic Real Coded Genetic Algorithm

AIS Artificial immune system

ASCSA adaptive selective Cuckoo Search algorithm

BBO Biogeography-Based Optimization

BCGA Binary coded genetic algorithm

CA Cultural algorithm

CABC Chaotic artificial bee colony algorithm

CHDE Chaotic hybrid differential evolution

CSA Clonal selection algorithm

CSA Cuckoo Search algorithm

DE Differential evolutionary

DRQEA Differential real-coded quantum-inspired evolutionary algorithm

EGA Enhanced GA

EP Evolutionary programming

EPSO Enhanced PSO

FEP Fast Evolutionary programming

FGA Fast Genetic Algorithm

FH-ST-HTS Fixed-head short-term hydrothermal scheduling

FIPSO Fully-informed particle swarm optimization

GA Genetic algorithm

GWPSO Global vision of PSO with inertia weight factor

GCPSO Global vision of PSO with constriction factor

GS Gradient search

GSA Gravitational Search Algorithm

HBMOA Honey-bee Mating Optimization Algorithm

HDE Hybrid DE

HDE–SQP Hybrid differential evolution and sequential quadratic programming HEP Hybrid Evolutionary programming

HNN Hopfield neural networks

HTOPF Hydrothermal optimal power flow

IBFA Improved Bacterial Foraging Algorithm

IDE Improved differential evolution

IFEP Improved fast evolutionary programming

IGA-MU Improved genetic algorithm, multiplier updating and the ε-constraint

technique IPSO Improved particle swarm optimization

IRM-MEDA Improved regularity model-based multiobjective estimation of

distribution algorithm ISPSO Improved self-adaptive PSO

LCEL Linearization of coordination equation based Lagrange method

LCPSO Global vision of PSO with constriction factor

LRA Lagrangian relaxation approach

LWPSO Local vision of PSO with inertia weight

MB-EPSO Mixed-binary evolutionary particle swarm optimizer

MBFA Modified Bacterial Foraging Algorithm

MCDEA Modified chaotic differential evolution algorithm

MCSA Modified Cuckoo Search algorithm

MDE Modified DE

MDNLPSO Modified dynamic neighborhood learning based particle swarm

optimization MHDE Modified hybrid DE

MODE Multiobjective differential evolution

NSGA-II Non-dominated sorting genetic algorithm-II

OGB-GA Optimal gamma based Genetic algorithm

PPO Predator prey optimization

PPO Predator-prey optimization

PPO-PM PPO with penalty method

PPO-PS PPO and Powell Search Method

PPO-PS-PM PPO and PS method with penalty method

PSO Particle swarm optimization

PSO-PM PSO with penalty method

QMBBO Quadratic Migration of Biogeography based Optimization

QOTLBO Quasi-oppositional teaching learning based optimization

RCCRO Real coded chemical reaction based optimization

RCGA Real coded genetic algorithm

RCGA Real-coded genetic algorithm

RCGA–AFSAReal coded genetic algorithm and artificial fish swarm algorithm

RIFEP Running Improved fast EP

SA Simulated annealing

SA-BGA A simulated annealing-based goal-attainment

SOH-PSO Self-Organizing Hierarchical particle swarm optimization

TLBO Teaching learning based optimization

TPNN Two-phase neural network

VH-ST-HTS Variable-Head Short-Term Hydrothermal Scheduling

λ-γ Lamda-gamma method

LIST OF FIGURES

Figure 3.1 Conventional Cuckoo search algorithm

Figure 3.2 The flowchart of using CCSA for solving optimization problems

Figure 3.3 Modified Cuckoo search algorithm

Figure 3.4 The flowchart of using MCSA for solving optimization problems

Figure 3.5 Egg chart for CCSA and ASCSA

Figure 3.6 Solutions at the first iterations of the search process

Figure 3.7 Solutions at the last iterations of the search process

Figure 3.8 The proposed way to obtain new solution

Figure 3.9 The proposed Adaptive selective cuckoo search algorithm

Figure 3.10 The flowchart of using the proposed ASCSA for solving optimization problems

Figure 3.11 The flowchart of using ALHN for solving optimization problem

Figure 4.1 The fuel cost curve with and without valve-point loading effect

Figure 4.2 The flowchart of using CCSA for solving the considered problem

Figure 4.3 The flowchart of using MCSA for solving the considered problem

Figure 4.4 The flowchart of using ASCSA for solving the considered problem

Figure 4.5 The flowchart of using ALHN for solving the problem

Figure 4.6 Fitness convergence characteristic for system 1 without valve-point loading effect

Figure 4.7 Maximum error convergence characteristic of ALHN for system 1

Figure 4.8 Fitness convergence characteristic obtained by CSA methods for system 2 Figure 4.9 Convergence characteristic of ALHN for system 2

Figure 4.10 Fitness convergence characteristics for system 6

Figure 4.11 Fitness convergence characteristics for system 7

Figure 4.12 Convergence characteristics for fuel cost of the system 8

Figure 4.13 Convergence characteristics for emission of the system 8

Figure 5.1 The flowchart of using CCSA for solving the considered problem

Figure 5.2 The flowchart of using MCSA for solving the considered problem

Figure 5.3 The flowchart of using ASCSA for solving the considered problem

Figure 5.4 Fitness convergence characteristic for system 1 without valve-point loading effects

Figure 5.5 Fitness convergence characteristics for system 2 with valve-point loading effects

Figure 6.1 The cascaded reservoirs

Figure 6.2 The flowchart of using CCSA for solving the considered problem

Figure 6.3 The flowchart of using MCSA for solving the considered problem

Figure 6.4 The flowchart of using ASCSA for solving the considered problem

Figure 6.5 Fitness convergence characteristics for system 1 without valve-point

Figure 7.1 The flowchart of using CCSA for solving the considered problem

Figure 7.2 The flowchart of using MCSA for solving the considered problem

Figure 7.3 The flowchart of using ASCSA for solving the considered problem

Figure 7.4 The IEEE 30-bus system

Figure 7.5 Fitness function convergence characteristics for the IEEE 30-bus system Figure 7.6 Fitness function convergence characteristics for the IEEE 118-bus system Figure 8.1 The whole work of the dissertation

Figure 8.2 Summary of the dissertation

LIST OF TABLES

Table 3.1 New solutions obtained by CSA and ASCSA using Lévy flights at the second iteration

Table 3.2 Three benchmark functions

Table 3.3 Comparison of results obtained by ASCSA-V1 and ASCSA-V2 for

Rosenbrock function by setting NP=20; Gmax=1,500 and 100 run trials

Table 3.4 Comparison of results obtained by ASCSA-V1 and ASCSA-V2 for Sphere function by setting NP=20; Gmax=200 and 100 run trials

Table 3.5 Comparison of results obtained by ASCSA-V1 and ASCSA-V2 for

Griewangk function by setting NP=20; Gmax=500 and 100 run trials

Table 3.6 Comparison of results obtained by ASCSA-V1 and ASCSA-V2 for HTS system 1 by setting NP=30; Gmax=50 and 100 run trials

Table 3.7 Comparison of results obtained by ASCSA-V1 and ASCSA-V2 for HTS system 6 by setting NP=30; Gmax=50 and 100 run trials

Table 4.1 CSA methods control parameters for systems with quadratic fuel cost

Table 4.5 Obtained result from ASCSA for system 1 with different values of

threshold, 30 nests and 70 iterations

Table 4.6 The sensitivity analysis with respect to the stopping criterion for the system

1 obtained CCSA with 30 nests

Table 4.7 The sensitivity analysis with respect to the stopping criterion for the system

1 obtained MCSA with 30 nests

Table 4.8 The sensitivity analysis with respect to the stopping criterion for the system

1 obtained ASCSA with 30 nests

Table 4.9 The sensitivity analysis with different number of nests for the system 1 obtained CCSA with 100 iterations

Table 4.10 The sensitivity analysis with different number of nests for the system 1 obtained MCSA with 100 iterations

Table 4.11 The sensitivity analysis with different number of nests for the system 1 obtained ASCSA with 100 iterations

Table 4.12 The sensitivity analysis with different ratio values (top group:abandoned group) for the system 1 obtained MCSA with 30 nests and 100 iterations for 500 independent run trials

Table 4.13 The result comparisons obtained by three CSA and ALHN methods for system 1 with quadratic fuel cost function of thermal units

Table 4.14 The result comparison obtained by three CSA method for system 2 with quadratic fuel cost function of thermal units

Table 4.15 Results obtained by CSA methods and ALHN for the systems 3, 4 and 5 Table 4.16 Result comparison for the five convex systems

Table 4.17 The result comparison obtained by three CSA methods for system 6 with nonconvex fuel cost function of thermal units

Table 4.18 The result comparison obtained by three CSA methods for system 7 with nonconvex fuel cost function of thermal units

Table 4.19 Result comparison for system 6

Table 4.20 Result comparison for system 7

Table 4.21 Adjusted computational time comparison for nonconvex systems

Table 4.22 Selection of control parameters for CSA methods for the first system Table 4.23 The result comparison obtained by three CSA and ALHN methods for emission dispatch of system 1 with quadratic fuel cost function of thermal units

Table 4.24 A set of non-dominated solutions obtained by ALHN and CCSA for

Table 4.27 Result comparisons for system 1

Table 4.28 Selection of CSA control parameters for systems 3, 4 and 5

Table 4.29 Result comparison for the economic dispatch for systems 3, 4 and 5

Table 4.30 Result comparison for the emission dispatch for systems 3, 4 and 5

Table 4.31 Result comparison for the emission-emission dispatch for systems 3, 4 and

5

Table 4.32 Comparison of total computational time (in seconds)

Table 4.33 Selection of CSA control parameters for system 8

Table 4.34 Result comparison for system 8 with valve point loading effects of thermal units

Table 5.1 Obtained results by CCSA for system 1 by considering thermal generations and water discharges as control variables

Table 5.2 Obtained results by CCSA for system 1 by considering thermal generations and reservoir volumes as control variables

Table 5.3 Obtained results by CCSA for system 1 by considering thermal generations and reservoir volumes as control variables and using initialization method

Table 5.4 Comparison of the best result from three CSA methods for system 1

without valve point loading effects

Table 5.5 Comparison of the results for system 1 with quadratic fuel cost function Table 5.6 Obtained results from ASCSA for system 2

Table 5.7 Result comparison obtained by ASCSA, CCSA and MCSA for system 2 Table 6.1 Selection of control parameters for the first two systems

Table 6.2 Statistical test results for test systems 1 and 2 with quadratic objective Table 6.3 Comparison of obtained results by CSA and other methods for system 1 Table 6.4 Comparison of obtained results by CSA and other methods for system 2 Table 6.5 Adjusted computational time comparison for 2 convex systems

Table 6.6 Statistical test results for systems 3 and 4

Table 6.7 Comparison of obtained results by CSA and other methods for system 3 Table 6.8 Comparison of obtained results by CSA and other methods for system 4 Table 6.9 Adjusted computational time comparison for systems 3 and 4

Table 7.1 Active power and reactive power limitations of generators

Table 7.2 Coefficients of cost function of 4 thermal units

Table 7.3 Hydraulic data of hydro units

Table 7.4 Capacitor limits for the IEEE 30-bus system

Table 7.6 Maximum power flow limits of transmission lines of the IEEE 30-bus system

Table 7.6 Ảnh hưởng của Pa lên kết quả của CCSA cho hệ thống IEEE 30 nút Table 7.7 Ảnh hưởng của Pa lên kết quả của MCSA cho hệ thống IEEE 30 nút Table 7.8 Ảnh hưởng của Pa lên kết quả của ASCSA cho hệ thống IEEE 30 nút Table 7.9 The impact of Gmax on CCSA for IEEE-30 bus system

Table 7.10 The impact of Gmax on MCSA for IEEE-30 bus system

Table 7.11 The impact of Gmax on ASCSA for IEEE-30 bus system

Table 7.12 The impact of Np on CCSA for IEEE-30 bus system

Table 7.13 The impact of Np on MCSA for IEEE-30 bus system

Table 7.14 The impact of Np on ASCSA for IEEE-30 bus system

Table 7.15 Comparison of obtained results for the IEEE 30-bus system

Table 7.16 Comparison of obtained results for the IEEE 118-bus system

Table 7.17 The impact of Gmax on CCSA for IEEE-118 bus system

Table 7.18 The impact of Gmax on MCSA for IEEE-118 bus system

Table 7.19 The impact of Gmax on ASCSA for IEEE-118 bus system

NOMENCLATURE

 Entry-wise multiplications;

(.) Gamma distribution function

X d new Increased value for nest d

A 0 Maximum value of update step size, set to 1

a hj , b hj , c hj Water discharge coefficients of hydropower plant j

a si , b si , c si Fuel cost coefficients of thermal plant i

B ij , B 0i , B 00 Transmission loss coefficients

C 1hj , C 2hj , C 3hj Coefficients of the jth hydropower plant

C 4hj , C 5hj , C 6hj Coefficients of the jth hydropower plant

e si , f si Fuel cost coefficients of thermal plant i considering the

valve-point loading effect

F 1 , F 2 Fuel cost objective and emission objective

F i Fuel cost function of thermal unit i

FT d Fitness function value of nest d

FT r Fitness function value of a random nest

I j,m Water inflow of the jth hydropower plant within the mth interval

K Updated coefficient

K s , K h , K V , K Q Penalty factors

N 1 Number of thermal units

N 2 Number of hydro units

N g Sum of number of hydro units and number of thermal units

Notop Number of nests in top group

N P Number of nests or population size

Nu Set of up-stream units directly above hydro-plant j

P a Probability of alien egg to be abandoned

P D,m Load demand at subinterval m

P hj,m Power output of hydro plant j at subinterval m

P hj,min , P hj,max Lower and upper limits of hydropower plant j

P L,m Transmission loss at subinterval m

P s1md Thermal slack unit 1

P si,m Power output of thermal unit i at subinterval m

P si,min , P si,max Minimum and maximum power output of thermal plant i

P si,md Power output of thermal unit i at subinterval m for solution d

Q j,m Total water discharge of hydro plant j in subinterval m (in m3/t m

hour)

q j,m,d Water discharge of hydro unit j at subinterval m for solution d (in

m3/hour)

Q j,min , Q j,max Lower and upper limits of total water discharge of hydro plant j

over one subinterval (in m3/t m hour)

q j,min , q j,max Lower and upper limits of water discharge of hydro plant j over

one hour (in m3/hour)

q j,m Water discharge of hydro plant j for each hour at subinterval m (in

m3/hour)

q j,M,d Water discharge of hydropower plant j at the Mth subinterval

corresponding nest d (in m3/hour) rand Random number within the range of [0, 1]

randp 1 (Xbest d) The first random perturbation for positions 1 of the nests

randp 2 (Xbest d) The second random perturbation for position 2 of the nests

Randper Random perturbation

rand x , rand y Normally distributed stochastic variables with standard deviation

S j,m Spillage discharge rate of jth hydropower plant in the mth

subinterval

t m Duration of subinterval m

t M number of hours of the Mth subinterval

V j,end Volume of the reservoir j at the end of the scheduled horizon

V j,initial Volume of the reservoir j at the beginning of the optimal horizon

V j,m Volume of reservoir j at subinterval m

V j,min , V j,max Lower and upper limits of volume of reservoir j

Xbest_discard d The dth nest in the abandoned group

Xbest_nodiscard d The dth nest the top group

Xbest_nodiscard r Randomly picked nest among the nests in top group

Xbest d Local best nest d

X d dis New solution generated via the discovery action of alien eggs

X d new New solution for nest d

XGbest Global best nest

X r1 , X r2 Random perturbation for positions of the nests in X d

β Value of distribution factor

τ i,j Water delay time between reservoir j and its up-stream i at

subinterval m

φ The golden ratio

CHAPTER 1: INTRODUCTION

1.1 BACKGROUND

An electrical power system is mainly composed of thermal plants and hydro power plants connected via transmission lines in order to supply electricity to loads such as industrial zones or manufacturers, etc For electrical generation, thermal plants use fossil fuel including gas, coal and oil, which are very expensive, become exhausted

in the near future whereas water, the primary fuel utilized only at hydropower plants,

is from nature rivers, and considered negligible for generation cost In addition, as comparing the response speed to the electrical load change, the hydropower plants have advantages over the thermal units because they can produce from very small power to full capacity in several minutes due to rapid water control On the contrary, the startup and the response speed of thermal plants to load change are very slow Therefore, thermal plants need to run continuously for some hours once they started Based on the advantage as well as disadvantages analyzed on thermal and hydropower plants, it is clear that the coordination of thermal and hydropower plants in electrical generation operation becomes more effective and economical The operation coordination of hydrothermal plants is more complicated than pure thermal system and pure hydropower plants once the main objective of the coordination system is to minimize electrical generation fuel cost for only thermal plants; however, the constraints for both thermal plants and hydropower plants must be satisfied

Thermal plants are constrained electrically only whereas hydropower plants are constrained both electrically and hydraulically The electrical constraints considered here are upper and lower generations for thermal and hydropower plants while the hydraulic constraints considered only at the hydropower plants are available water resources, continuity water, water discharge limits and reservoir volume limits Which hydraulic constraints included in scheduled time is dependent on the mathematical model of hydropower plant There have been a huge number of methods applied for finding the optimal solution of the hydrothermal scheduling problem including deterministic algorithms, meta-heuristic algorithm, Neural Networks (NN) and Fuzzy logic Solution methods are constantly improved in aim to deal with complex problems where complicated constraints, non-differential objective and large-scale systems are taken into consideration However, studied problems are always developed so that the theory is closer and closer to the practical problems Therefore, the hydrothermal scheduling problems have attracted a vast number of optimization algorithms so far

1.2 STATEMENT OF THE PROBLEM

Because of the considerable importance of the hydrothermal scheduling, a huge number of studies has focused on the scheduling problems to find the best solution method for the problem so that the fuel cost of electricity generation is minimized

Short-term hydrothermal scheduling considers optimization horizon from one day to one week involving hour-by-hour generation planning of all generating units in the hydrothermal system so that the total generation fuel cost of thermal units is minimized while satisfying all constraints from hydropower plants including hydraulic constraint such as water discharge limits, volume reservoir limits, continuity water, generation limits, thermal plant constraints including prohibited operating zone and generation limits There is a fact that the load demand on the power system changes cyclically over one day or one week and changes corresponding to the short-term scheduling horizon which is in range from one day to one week A set of beginning conditions consisting of initial and final reservoir volumes for the scheduling horizon, inflow into reservoir, and the water amount to be used for the scheduling horizon is assumed known During the scheduling generation process it is necessary to take the capacity of the reservoir and inflow into account once they have a significant impact

on the water head variation leading to be represented by different hydro models

In the dissertation, five hydrothermal scheduling problems solved by using different optimization algorithms are as follows

of used water must be equal to the expected amount, which was predetermined by operation expert In addition, power losses in transmission lines are also included in power balance constraint

2) Fixed-head short-term hydrothermal scheduling with reservoir volume constraints

The reservoir water head is supposed to be fixed during the scheduling horizon

So, the water discharge is still a second order function of hydro generation and coefficients The total amount of water is not required to be calculated and constrained; however, initial value and end value of the reservoir volume must be exactly met when optimally operating the hydrothermal system The capacity of reservoir to contain water during the operation must be observed and followed by the

constrained values such as minimum volume corresponding to the dead head and maximum volume corresponding to the highest head Besides, the continuity of water

is always constrained at each subinterval over the scheduling horizon Other issues related to transmission lines such as power balance and power losses are also taken into account for most test systems

3) Variable-head short-term hydrothermal scheduling with cascaded hydropower plants

The water head of reservoir is supposed to be a variable because the reservoir of the hydropower plant has small capacity or a large enough difference between inflow and discharge via turbine leading to the big change of the volume in the considered scheduling period The variable-head short-term scheduling is more complex than fixed-head short-term scheduling because the hydro generation is represented by a complicated function of water discharge, reservoir volume and coefficients All constraints related to reservoir volumes such as initial volume, end volume, minimum volume, maximum volume as well as the water continuity are always taken into account over the scheduling horizon The most complicated constraint of the variable-head short-term here is the water continuity since there are cascaded reservoirs taken into consideration The water discharge of upper plants will flow into the lower reservoirs and become the inflow into the lower plant The delay transport time of water from the upper reservoir to the lower is also considered and included in the water continuity equation The power balance constraints are also considered in the problem

4) Multi-objective fixed-head short-term hydrothermal scheduling problem

Mutliobjetive fixed-head short-term hydrothermal scheduling problem considers minimization of both fuel cost and emission in objective function All assumptions and constraints in the problem such as fixed head of reservoir, water discharge function, available water constraint, power balance constraint, transmission power losses are the same as those in the fixed-head short-term hydrothermal scheduling problem

5) Hydrothermal optimal power flow

The main task of the problem is to minimize fuel cost of thermal units located at generator buses in two IEEE test systems with 30 buses and 118 buses while satisfying all constraints from the transmission grid such as transmission capacity of lines, voltage at buses, tap setting, the limitation of generators etc In the problem, each hydropower plant is represented as fixed-head short-term model where the water discharge via turbine is a second order function with respect to the hydro generation and coefficients Thus, the constraints from reservoir except ones related to volume are

like to those from the fixed-head short-term hydrothermal scheduling problem such as water discharge limitations and available water constraint

1.3 OBJECTIVES OF THE RESEARCH

The main objectives of this dissertation are as follows

 To apply conventional Cuckoo Search Algorithm (CCSA), Modified Cuckoo Search algorithm (MCSA) and Augmented Lagrange Hopfield Network (ALHN) for solving the optimal hydrothermal scheduling problems

 To build a new adaptive selective Cuckoo Search Algorithm for solving the optimal hydrothermal scheduling problems

 To test the performance of the proposed methods including CCSA, MCSA, ASCSA and ALHN on several test systems corresponding to each considered problem and compare the obtained results in terms of quality of solution and execution time with other methods reported in the literature

 To suggest the applicability of the proposed methods to large-scale practical systems

1.4 CONTRIBUTIONS

The main contributions of this dissertation are as follows

 Construct an effectively new algorithm, called Adaptive Selective Cuckoo Search algorithm for solving hydrothermal scheduling problems

 Indicate the best ways to apply several existing algorithms, CCSA, MCSA and ALHN, and the proposed ASCSA for the HTS problems

 Successfully construct formulation of HTOPF problem in detail

 Successfully apply three CSA methods for solving the hydrothermal scheduling problem

 Investigate efficiency of CCSA, MCSA, ASCSA and ALHN when applied to the HTS problems and find the best one for the problems

 Introduce an effectively new algorithm to researchers and show the best way to apply the algorithm

1.5 SCOPE AND LIMITATION

The scope and limitation of the dissertation are as below

 In the considered problems, the objective function is represented as a quadratic function or a nonconvex function and the scheduling period is over one day to one

week

 The system constraints taken into account are transmission losses and load power balance, which is the balance between total generation and transmission losses plus load demand

 Two IEEE systems with 30 buses and 118 buses are employed where the transmission grid constraints such as transmission capacity of lines, voltage at buses, tap setting, etc are taken into consideration

 The hydraulic constraints considered are water discharge, reservoir volume, and hydro and thermal generation limits

1.6 ORGANIZATION OF THE DISSERTATION

The dissertation is organized in 8 chapters

Chapter 1: Introduction

Chapter 2: Literature review

Chapter 3: Cuckoo search algorithms and Augmented Lagrange Hopfield network Chapter 4: Artificial intelligence based methods for fixed-head short-term hydrothermal scheduling problem neglecting reservoir volume constraints

Chapter 5:Cuckoo search algorithms for fixed-head short-term hydrothermal

scheduling problem considering reservoir volume constraints

Chapter 6:Cuckoo Search Algorithms for variable-head short-term hydrothermal scheduling problem

Chapter 7: The application of CSA methods for solving hydrothermal optimal power

flow problem

Chapter 8: Conclusions

CHAPTER 2: LITERATURE REVIEW

2.1 INTRODUCTION

Owing to highly economical effectiveness of the generation coordination of the hydrothermal system, many methods based on conventional algorithms and modern algorithms have been proposed for determining the best solution to the optimal generation scheduling so far To show clear advantages and disadvantages of the methods a review of them is presented and analyzed The methods are generally classified into two main groups consisting of classical methods and artificial intelligence and will be discussed in the chapter according to each particular problem

PROBLEM NEGLECTING RESERVOIR VOLUME CONSTRAINTS

Algorithms have been used for solving the fixed-head short-term hydro thermal scheduling problem neglecting volume constraints so far such as Newton-Raphson [1], [2], Powell’s hybrid method [1], Lagrange multiplier factorization based Newton-Raphson method [3], Linearization of coordination equation based Lagrange method (LCEL) [4], Lamda-gamma method (λ-γ method) [2], Lagrangian relaxation approach [5], Hopfield neural networks (HNN) [6], Evolutionary programming (EP) [7], [8], Artificial immune system (AIS) [8], Particle swarm optimization (PSO) [8], Differential evolutionary (DE) [8], Modified Bacterial Foraging Algorithm (MBFA) [9], Optimal gamma based Genetic algorithm (OGB-GA) [10], Fast Genetic Algorithm (FGA) [11], Predator prey optimization technique (PPO) [12]. Among the methods, methods in [1], [2], [3], [4], [5] are classical ones and others in [6], [7], [8], [9], [10], [11], [12] belong to artificial intelligence The first method group is mainly based on the conventional Newton-Raphson or conventional Lagrange optimization theory or improvement of the two conventional ones meanwhile the second method group search optimal solution based on the number of population On the other hand, the methods in the first one can be called deterministic methods, which are defined as derivative based optimization methods to find optimal solution by a single path search line The single solution initially obtained has the worst quality because its objective function value is the highest and its constraints violation is maximum Due to the predetermined optimization algorithm, the single solution is improved on a single path going to the best final solution, which has the lowest objective function and negligible constraints violation The optimal solution is influenced by the initial point of the beginning of the iterative procedure Therefore, the starting condition for initializing a solution is very important for getting convergence The termination criterion of the methods is the predetermined threshold and the overall computing procedure is called

convergence There was a fact that the lower the predetermined threshold is set the more optimal the obtained solution is and the same optimal solution was obtained as the computing process was restarted in several times On the other hand, the deterministic methods must suffer the drawback that they cannot deal with the problems where there was nonconvex objective function and/or nonconvex constraints, and their applications on the large scale systems are also limited

On the contrary, the artificial intelligence algorithms excluding Hopfield neural networks [6] initialize a set of solutions at the beginning of the optimal solution search process The solutions are newly generated in each iteration and their quality are evaluated via a fitness function consisting of the objective function that needs to be minimized and penalty amount for constraint violation Unlike the deterministic ones, the meta-heuristic ones stop searching process dependent on the predetermined maximum iterations, and the solutions are capable of satisfying all constraints as the current iteration is much lower the maximum number and the solution might be out of feasible operating zones even if the termination criteria was already reached The meta-heuristic algorithms are considered stronger and more effective than deterministic ones once they can deal with problem where complex objective function and many complicated constraints as well as large-scale systems were taken into consideration

Newton-Raphson method was computationally stable, effective, and fast for solving a set of nonlinear equations Therefore, it has a high potential for implementation on optimization problems such economic load dispatch in hydrothermal power systems Besides, the Newton’s method mainly depended on the formulation and inversion of Jacobian matrix, leading to restriction of applicability on large-scale problems However, the Newton-Raphson method was considered the weakest method since it failed to converge although the test hydrothermal system employed was small with only one thermal and one hydropower plant [3] The Newton-Raphson was then improved by using Lagrange multiplier factorization, and interpolating between the Newton-Raphson and the steepest descent method These improved Newton-Raphson methods tested on several systems and compared to the conventional one have reported that the improvement was successful because they have obtained better solution and faster convergence In the LCEL method [4], the coordination equations were linearized and solved for the water availability constraint separately from generating units Thus the Lagrangian multiplier associated with water availability constraint was separately from the outputs of generating units Based on the obtained Lagrangian multiplier of water constraint, the Lagrangian multiplier associated with power balance constraint was determined and the outputs of thermal and hydro units were finally calculated In the - method [2], the  values of the different hydro plants were initially chosen and thereafter the  iterations were invoked for the given power demand at each interval of the scheduling period The HNN method [6] was an efficient neural network for dealing with optimization problems In order to solve the

hydrothermal scheduling problem, HNN first constructed an energy function containing fuel cost objective function, the square of available water constraint, power balance constraint and power losses in transmission lines accompany with four different coefficients corresponding to the four terms in the energy function The key word for dealing with all constraints and fast convergence to optimal solution is completely dependent on the four coefficients; however, the selection of the coefficients is not an easy task when applying HNN to the problem Therefore, HNN method also suffered slow convergence to optimal solution and the constraints of the problem must be linearized when applying in HNN [13], [14] Compared to Newton-Raphson method when tested on a four-plant system, HNN could also improve the quality of solution but it still coped with local optimal solution, which was so far from the best solution However, the persuasive demonstration that HNN was a real effective method is always a question In fact, the study in [6] have implemented HNN for one system only and the comparison has also been carried out between two methods, HNN and Newton’s method

Both the GA and EP algorithms were evolutionary based methods for solving optimization problems However, the essential encoding and decoding schemes in the both methods were different In the GA method, the crossover and mutation operations required to diversify the offspring might be detrimental to actually reaching an optimal solution In this regard, the EP was more likely better when overcoming these disadvantages In the EP method, the mutation was a key search operator generating new solutions from the current ones [13] Furthermore, the new solution generation and selection operation in EP are respectively mutation and competition but in GA the procedures are more complicated with three operations such as reproduction, mutation, and crossover Hence, the advantage of EP over GA is faster computation time.However, one disadvantage of the EP method in solving some of the multimodal optimization problems was its slow convergence to a near optimum DE is also a family of evolutionary algorithm with three popular operations such as mutation, crossover and selection The mutation is employed to produce new solution and crossover is a technique to keep a dominant population for next generation while selection is applied to determine the so-far best solution The performance of the mutation and crossover is mainly dependent on the selection of two control parameters including mutation factor and crossover factor, and the three randomly chosen solutions for mutation operation The crossover value range is from zero to one but the range is much larger for mutation value from zero to two The DE method has the ability to search in very large spaces of candidate solutions with few or no assumptions about the considered problem However, a set of selection of both mutation factor and crossover factor leads to a huge number of trials when using DE for solving optimization problem especially for a large-scale system with long simulation time In addition, the usual use of three random different solutions for mutation operation from the beginning to the end of the search process also limits the ability to jump out the

local zone when the search process comes to final generations Thus, the DE method is difficult to deal with large-scale problems with slow or no convergence to the near optimum solution Artificial immune system (AIS) was developed in 1998 by inspiring from the biological principles of clone generation, proliferation and maturation in humanity body The AIS main constructions are clonal proliferation, mutation of clone, application of aging operator and tournament selection Among the operations, clonal proliferation and clone mutation are the two main steps for generating new solutions in which the comer is used to clone antibodies directly proportional to their affinities and the latter uses the obtained result from the comer to produce new solutions The application of aging operator is a technique to avoid keeping aging antibodies and avoid premature convergence to a local optimum In order to mathematically formulate AIS in optimization problem, the antibodies and affinities are respectively considered as the feasibly optimal solutions and the objective function Real number is used to represent the attributes of the antibodies The performance of the AIS is mainly dependent on the mutation and the aging operator Thus, the selection of mutation factor and the elimination of aging antibodies are crucially important The advantages of the AIS method are few parameters and small maximum number of iterations However, the AIS method was also difficult to deal with large-scale problems like other meta-heuristic search methods because the process of elimination of aging antibodies must be carried out for one by one solution The AIS has been successfully applied for solving the nonconvex short-term hydrothermal scheduling compared to other methods such as EP, DE and PSO [8] In article [8], four methods such as EP, DE, PSO and AIS have been tested on two hydrothermal systems with nonconvex fuel cost function of thermal units For implementation, the population size of AIS was always half that of others such as PSO, DE, and EP meanwhile the maximum number of iterations remained unchanged among the methods The optimal fuel cost has shown that AIS was better than PSO,

EP and DE Besides, the convergence characteristics of fitness values vs iterations have indicated that PSO and DE have tended to be premature convergence with a local optimum and they have not jumped out the local to the global On the contrary, AIS could tackle this trap and yield better optimal solution Despite the advantage, the simulation time from AIS has still been approximately equal to those from others Optimal gamma based genetic algorithm (OGB-GA) [10] is an improvement of GA for efficiently solving the HTS problem by combining both Lagrange multiplier based method and classical GA In order to apply the OGB-GA, a Lagrange function comprised of objective function i.e fuel cost function and the constraints i.e power balance constraint and available water constraint was first constructed Then, all the operators from classical GA have been applied to solve the Lagrange function instead

of using the popular iterative algorithm in Lagrange based method The  values of the hydro plants were considered as the GA variables and the  iterations over the scheduling period can be called to find the thermal and hydro generations for each

chromosome in the population to calculate the value of the fitness function Therefore, the number of the GA variables was drastically reduced and did not even depend on the number of intervals in the scheduling period Four systems have been employed to test three methods such as Lagrange method, GA and OGB-GA and the comparison of results have revealed that the OGB-GA was very efficient for the test systems In fact, the optimal fuel cost and the average cost as well as the standard deviation from OGB-

GA were lower than those from GA and Lagrange method However, the further investigation of convergence speed for OGB-GA has not been fulfilled due to no the selection of control parameters and execution time reported in [10] Although the successful improvement of OGB-GA has been reflected, OGB-GA has suffered the disadvantage of Lagrange method of not dealing with systems considering nonconvex fuel cost function of thermal units Clearly, the improvement can tackle the disadvantage of GA but it must receive the weak point from Lagrange method In general, most of the artificial intelligence techniques usually suffer slow convergence

to the near optimum solution for the HTS problems

2.3 FIXED-HEAD SHORT-TERM HYDROTHERMAL SCHEDULING

PROBLEM CONSIDERING RESERVOIR VOLUME

In the problem, the volume capacity of reservoir as well as the initial volume and end volume of reservoirs are considered The problem has been studied so far and obtained many intentions from researchers Several algorithms have been applied such

as Gradient search (GS) [2], Newton-Raphson method [3], Simulated annealing approach (SA) [15], Evolutionary programming (EP) [16], [17] , [18], Genetic algorithm (GA) [19], Fast EP (FEP) [20], Improved fast EP (IFEP) [20], Hybrid EP (HEP) [21], Particle Swarm Optimization [22], Improved Bacterial Foraging Algorithm (IBFA) [23], Self-Organizing Hierarchical PSO [24], Running Improved fast EP (RIFEP) [25], Improved PSO [26], [27], Clonal selection algorithm [28], and Fully-informed particle swarm optimization (FIPSO) [29] These methods described above are mainly classified into two groups including deterministic algorithm group and meta-heuristic algorithm group The former was simply composed of Gradient search [2], and Newton-Raphson method [3] whereas the latter was a large set of meta-heuristic algorithms consisting of Simulated annealing (SA) [15], Genetic algorithm (GA) [19], evolutionary programming (EP) [16], [17], [18], [20], [21], [25], PSO [22], [24], [26], [27], [29], improved Bacterial Foraging algorithm [23], Clonal selection algorithm [28] Among the methods, GS was considered the weakest one GS method has been only applied to a problem where conventional hydro generation were represented as piecewise linear or polynomial approximation, which might be too rough and seems impractical [16] In order to solve the hydrothermal scheduling problem, at the beginning GS constructed a Lagrange function consisting of an objective function and other equality constraints accompany with corresponding

Lagrange multipliers Then taking partially derivative of the Lagrange function with respect to each variable was done and a set of equalities could be solved for optimal solution The fact that the solution speed of the GS is dependent on the number of equalities and the number of variables due to different scales of an increased step size corresponding to different number of equalities and variables Therefore, GS cannot deal with not only systems with complex constraints but also systems with large number of constraints and variables Furthermore, initial value of Lagrange multiplier associated with power balance constraint has a significant impact on the convergence capability and optimal solution quality So, the selection of the initial value for the multiplier must be considered thoroughly Derived from the drawbacks, GS has not been applied to complex large-scale systems so far The Newton-Raphson seemed to

be more effective than the GS when applied to systems where approximation of the hydro generation could not be performed; however, the method fully depended on the scale of Jacobi matrix and the capability of taking partial derivative of Jacobi matrix with respect to each variable It is clear that the complex level of constraints and the scale of Jacobi matrix have a high influence on the convergence speed and the quality

of solution similarly to GS

Contrary to the deterministic ones, methods in the latter group have been successfully and widely applied for solving the short-term hydrothermal scheduling problem taking the reservoir volume constraint into account Although the SA and GA could tackle the drawbacks that the two deterministic ones must suffer from, the SA has not been widely applied because it spent long simulation time as well as obtaining lower quality solution The applicability of SA to the hydrothermal scheduling problem is highly dependent on the selection of the initial temperature and the cooling rate value The optimal temperature is very hard to determine since it has a very large range from zero to infinite while the cooling rate is used to decrease the temperature and calculated based on the temperature If the temperature is set to a too high value, the hydrothermal system will be at a high objective function value and the minima will

not be easily yielded On the contrary, if the temperature is assigned to a too small

value, the hydrothermal system will able to be trapped in a local optimal solution because there is not enough energy to be out of the current local minimum zone to approach to the global zone where the global minimum is in So, an effectively proper initial temperature should be determined Besides, a crucially important task is how to tune the cooling process helping the system cools down gradually from a high temperature to a lower appropriate value A high initial temperature will lead to a large cooling rate and a large decreased temperature Consequently, a convergence capability to a global optimal solution by using SA is not easy especially with a large-scale system with multi-constraints

Compared to SA and GA, PSO and EP were more effective and robust and they have been constantly applied to obtain better quality solution and speed up the convergence In EP [16], [17], [18], at creation of offspring step, only Gauss random

variable was used to generate offspring and the scaling factor was regarded as a constant whereas in the improved versions of EP [20], [25] the number of offspring were generated from randomly generated initial parents using Gauss or Cauchy mutations in addition to using the scaling factor as a variable during the search process The EP could improve the solution and speed up convergence and they were superior to conventional EP via only one test system The improvement of the modified versions of EP such as FEP and IFEP in [20], and HEP in [21] has not been validated although the authors have stated that their improved methods were better than original one In fact, only one system with one thermal unit and one hydro unit scheduled in six twelve-hour subintervals and quadratic fuel cost function of thermal unit has been employed to run the proposed methods Moreover, the optimal solutions for the simple system reported in [20] and [21] have indicated that the water discharge was lower than minimum value predetermined in data of problem Other information such as population size and execution time not reported in the articles for improved versions of EP has led to a difficulty when readers would like to comparison the convergence speed

Compared to the group of three algorithms such as GA, SA and EP, the implementation of PSO for solving the hydrothermal scheduling problem is simpler because the PSO construction is only based on the three simple operations such as updating velocity, updating position and selection In PSO, each solution is represented as a position of a particle and the way to update the new solution is based

on the current position and updated velocity The updated velocity is obtained by using three different particles including the current particle, the so-far best particle and the global best particle among the population In order to improve the effectiveness and robustness of the conventional PSO, a weight factor [26] and a constriction factor [27] were respectively suggested to update new velocity and new position The weight factor was adaptive meanwhile the constriction factor was fixed at a value depending

on the selection of two acceleration constants The improvement also led to an optimal solution with shorter execution time but the two studies have reported invalid optimal solution since the water discharge have violated the lower limit In the FIPSO [29], the new version of updated velocity was proposed to obtain better position for each particle and the method has been tested on a system and compared to other methods’ result Despite the statement that the method was superior to other methods, the method was still not recommended to be a strong tool to search optimal solution for the problem since the optimal solution reported in the study was an invalid one violating the lower limit Farhat et al in study [23] have proposed IBFA for solving the problem; however, the study has shown an invalid optimal solution when they have used more water than availability Clonal selection algorithm was also a member of meta-heuristic algorithms where the search process was done by performing five steps including initialization, affinity evaluation, Clonal proliferation, mutation and selection The search process was more complicated than that from evolutionary

algorithms like GA, EP and DE The method has obtained solution as good as other methods such as IFEP and FEP

It is clear that many meta-heuristic algorithms including conventional versions and improved versions have been developed for solving the hydrothermal scheduling problem considering reservoir volume constraints The obtained results have tended to

be compared to point out the effectiveness and robustness but acceptable level for the demonstration is still a challenge when only one simple system without complex objective function has been employed and invalid optimal solutions have been reported

2.4 VARIABLE-HEAD SHORT-TERM HYDROTHERMAL SCHEDULING PROBLEM

Methods have been applied for solving the variable-head short-term hydrothermal scheduling problem so far such as Clonal selection algorithm (CSA) [28], Genetic algorithm (GA) [30], Improved fast evolutionary programming (IFEP) [18], Evolutionary programming (EP) [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], Simulated annealing (SA) [31], Particle swarm optimization (PSO) [31], Modified DE (MDE) [32], [33], Hybrid DE (HDE) [33], Modified hybrid

DE (MHDE) [33], Global vision of PSO with constriction factor (GCPSO) [34], Global vision of PSO with inertia weight GWPSO [34], Global vision of PSO with constriction factor (LCPSO) [34], Local vision of PSO with inertia weight LWPSO [34], Enhanced GA (EGA) [35], Enhanced PSO (EPSO) [35] , Improved PSO (IPSO) [36], Adaptive artificial bee colony algorithm (ABCA) [37], Chaotic artificial bee colony algorithm CABCA [37], Adaptive chaotic artificial bee colony algorithm (ACABCA) [37], Real coded genetic algorithm and artificial fish swarm algorithm (RCGA–AFSA) [38], Two-phase neural network (TPNN) [39], Cultural algorithm (CA) [40], Real coded genetic algorithm (RCGA) [41], Binary coded genetic algorithm (BCGA) [41], Cuckoo search algorithm (CSA) [42], Chaotic hybrid differential evolution (CHDE) [43], Hybrid differential evolution and sequential quadratic programming (HDE–SQP) [44], Honey-bee Mating Optimization Algorithm (HBMOA) [45], Biogeography-Based Optimization (BBO) [46], Differential real-coded quantum-inspired evolutionary algorithm (DRQEA) [47], Gravitational Search Algorithm (GSA) [48], Improved self-adaptive PSO (ISPSO) [49], Mixed-binary evolutionary particle swarm optimizer (MB-EPSO) [50], Teaching learning based optimization (TLBO) [51], Quasi-oppositional teaching learning based optimization (QOTLBO) [51], Adaptive Chaotic Real Coded Genetic Algorithm (ACRCGA) [52], Improved differential evolution (IDE) [53], Quadratic Migration of Biogeography based Optimization (QMBBO) [54], Real coded chemical reaction based optimization (RCCRO) [55], Modified chaotic differential evolution algorithm (MCDEA) [56], and Modified dynamic neighborhood learning based particle swarm optimization

(MDNLPSO) [57] The conventional EP (CEP) [31] and several improved versions of

EP [18] consisting of fast EP (FEP) and improved fast EP (IFEP) have been developed

to solve the ST-CHTS problem The difference among the three EP methods is the different types of distribution for generating offspring from their parents In fact, CEP has employed Gaussian distribution, FEP has utilized Cauchy distribution meanwhile the better of both Gaussian and Cauchy distributions have been used in IFEP The effectiveness of the EP methods is mainly dependent on the distribution One system with one thermal unit and four hydro units and nonconvex objective was considered in [18] For the implementation of the three EP methods, the maximum number of iterations has been set to different values for the three methods in which CEP has owned the highest value with 1,200 iterations, FEP has used the second highest value with 800 iterations but the lowest value with 300 iterations has been set for IFEP In spite of the lower iterations, IFEP has obtained the best results with the lowest fuel cost and the fastest execution time while CEP has had the worst fuel cost and the longest execution time However, the further comparison among IFEP and others excluding CEP and FEP has not been investigated in [18] Therefore, the statement of the performance of the IFEP has been done around different versions of EP method

On the other hand, when testing CEP and SA on a lager system with three thermal units, four hydro units and nonconvex objective function in [31], EP has yielded much higher fuel cost and longer execution time compared to SA In addition, the conventional PSO has also been tested in [31] and has been considered the best one among CEP, SA and PSO in terms of the lowest fuel cost and the fastest execution time

The first classical GA (CGA) and its improved version, real-coded genetic algorithm (RCGA) applied for the ST-CHTS problem were respectively presented in [30], [41] and [52] In [30], CGA was applied to a system with one thermal unit and four cascaded hydro units scheduled in 24 hours considering water travel time delays from the upper reservoirs to lower reservoirs In addition, many practical constraints were also included in the formulation, however, the scale of the system was small and there was not any evidence to point out the CGA could solve the larger test systems The applicability of the algorithm was considered good although violation of constraints such as end-volume constraint and water discharge was not completely satisfied Moreover, no comparison between CGA and other ones was carried out in order to evaluate if CGA was competitive In Ref [41], binary coded genetic algorithm (BCGA) and real coded genetic algorithm (RCGA) have been successfully applied for solving the two identical scale systems with one thermal unit and four cascaded hydro units However, the second system was more complicated when valve point loading effects has been taken into consideration Comparison of yielded results has shown the superiority of RCGA over BCGA in terms of quality of solution for both systems; however, the two algorithms have not been compared to other applied methods and there have not been any conclusions of the performance of the better one, RCGA with

other ones An adaptive chaotic real coded genetic algorithm (ACRCGA) has been proposed to solve short-term hydrothermal scheduling (SHS) problem In [52], crossover and mutation have been adaptive to improve the global search ability while the chaotic search and the RCGA have been combined to exploit the local search ability In addition, a new effective technique has also been proposed for handling the power balance constraint and the continuity water constraint Only one system with one thermal unit, four hydro units and without valve point loading effects has been employed to run the ACRCGA The reported results including fuel cost and execution time have indicated that ACRCGA has been superior to RCGA and BCGA, and other ones; however, the verify of optimal solutions have pointed out that ACRCGA has violated the end volume constraint at reservoirs 3 and 4 and its optimal solution has been invalid to compare performance with others In Ref [39], a two-phase neural network based method taking the scheduled water discharge of hydro reservoirs as the states of the analogue neurons was developed for dealing with the problem and compared to the standard augmented Lagrange method (ALM) A system with one thermal unit and four hydro units without valve point loading effects has been employed to run both ALM and TPNN These authors in [39] have slightly modified the input data such as water transportation delay time and fuel cost function of thermal unit Therefore, TPNN has been only compared to ALM for the system only Comparison of fuel cost has led to a conclusion that TPNN could obtain higher quality solution than ALM; however, there has not been evidence to conclude if TPNN could

be faster for convergence than ALM once the information of tolerance and the number

of iterations have not been reported In addition, there has not been any conclusion of the performance of TPNN compared to other applied methods in the study In Ref [32], a modified DE has been proposed to satisfy all constraints from hydropower plant reservoirs In the study, modifications have not been carried out for DE method but for the way to handle the end-volume constraint at all reservoirs In the main steps

of DE, initialization and mutation, two modifications have been proposed in which the first modification at initialization could satisfy water discharge constraint while the second modification at mutation operation could meet the end-volume The MDE has been implemented for solving two test systems considering valve point loading effects and considering different objective functions The first system with one thermal unit and four hydro units has focused on minimizing fuel cost aspect while the second system with three thermal units and four hydro units has focused on minimization of both fuel cost and emission For the first system, the comparison has been extended since there have been many studies but that has been limited for the second system since only Fuzzy EP method has been applied Based on the improvements, MDE has obtained better results than others such as GA, DE and IFEP in addition to the valid optimal solution for system one; however, for system 2 MDE has been demonstrated better than only Fuzzy EP method Clearly, the elaboration of the superiority for MDE

is not completely persuasive A new modified hybrid DE (MHDE) [33] has been

developed by the authors in [32] by combining both the modifications and a Hybrid

DE in which the modifications were to deal with equality constraints like MDE in [32] and the hybrid DE has focused to reduce computational time The hybrid DE was built

by developing two extra operations including acceleration one and migration one where the comer allows the fitness quality to be improved, leading to fast convergence and the later enables the search space exploration to be updated, leading to the global optimal solution The MHDE has been tested on two test systems with valve point loading effects and different scales The obtained results have revealed that the MHDE could obtain better solution and much faster simulation time than conventional DE, MDE, HDE and other methods It has been stated in [43] that CDE has coped with the difficulty of setting control parameter because mutation factor and crossover factor have been set to large range Therefore, Chaotic hybrid differential evolution (CHDE) has been proposed by using chaos theory to set self-adaptive parameters automatically The chaos theory has been used to calculate mutation factor and crossover factor automatically for each generation in stead of being fixed at a value similar to CDE Due to the improvement, the CHDE could reduce a huge number of trials for selecting the values for the two control parameter Despite the advantage, the CHDE has not shown its potential persuasively when only one small system has been run to implement the proposed method A hybrid method based on the combination of one heuristic algorithm, differential evolution and one deterministic algorithm, sequential quadratic programming (HDE–SQP) has been applied to hydrothermal system scheduling problem and presented in [44] In the method, the DE has played a main role to search solution meanwhile the SQP has enabled the search process closed to the global optimal solution or near global optimum Several study cases were performed to test the efficiency of the method considering nonconvex objective and prohibited zone

of hydro units Ref [53] has proposed an improved differential evolution (IDE) to determine the optimal power generation for hydrothermal scheduling problem In stead

of using the mutation factor for mutation operation during searching new solutions, the IDE has used Gaussian distribution in aim to reduce a large number of trials for mutation factor and to improve the local search for CDE The Gaussian distribution has generated a vector for each variable in each solution The improvement of the IDE has been verified via testing on two systems with valve point loading effects The result comparison among the IDE, MDE [32], IPSO [36], GA [30] and IFEP [18] have illustrated the effectiveness and robustness of the IDE over these methods; however, the optimal solutions reported have indicated that water discharges at reservoir 4 has violated the lower bound for system 1 The optimal value was six while the input data has pointed out that it was thirteen For the second system, optimal solution has been correct Due to the violation, the performance of IDE has been still a variable and there have no any studies developing the IDE for the further investigation Conventional cuckoo search algorithm has been applied for solving the variable head short-term hydrothermal scheduling problem [42] The CSA has been tested on one system with

one thermal unit and four hydro units considering two cases, quadratic fuel cost function case and nonconvex fuel cost functions case The result comparisons have indicated the CSA has outperformed GA, PSO, DE and TLBO; however, the study have also reported invalid solutions Thus, there is no evidence to conclude the performance of CSA for the study Modified chaotic differential evolution algorithm (MCDEA) [56] has been developed by integrating an adaptive dynamic control mechanism for crossover factor, was used to control the recombination and chaotic local search operation to avoid premature convergence effectively Compared to other versions of DE, the MHDE was the best version obtaining the high solution quality and fast computational time The conventional PSO has been applied for solving a large scale hydrothermal system with four hydro plants and three thermal plants considering nonconvex fuel cost function [31] The system has also been employed to test the conventional simulated annealing and conventional EP to evaluate the performance of the PSO via comparison of obtained results Certainly, the PSO outperformed the two methods Several improved versions of PSO have been developed in [34] by combining different factors such as inertia weight and constriction factor, and the best particle among several particles and among the whole particles As a result, the version with inertia weight and the best particle among a small group was the best one Despite the advantage, the version of PSO could not get better solution than improved versions of DE Clonal selection algorithm [28], a member of evolutionary computation based methods with fast convergence and high quality solution, has been employed for solving hydrothermal systems with fixed head and variable head The study has demonstrated that the method could successfully deal with a large system with short simulation time An adaptive chaotic artificial bee colony (ACABC) [37] has been implemented for searching the solution of the short-term hydrothermal scheduling problem considering nonlinear constraints and nonlinear objective The method could avoid the premature convergence and avoid falling into the local optimal thank to the chaotic search and adaptive coordinating mechanism A novel teaching learning based optimization (TLBO) [51] has been applied to the problem with nonconvex fuel cost function and prohibited zone The TLBO was mainly based on teaching phase and learning phase, and did not need any algorithm determining the control parameters A combination of Modified dynamic neighborhood learning and particle swarm optimization (MDNLPSO) has been proposed in [57] for solving the short-term cascaded hydrothermal scheduling problem In the MDNLPSO, all particles were integrated into one group of neighborhoods and each individual one learnt experience from any another one available in the group The memberships were changed to exchange the information in aim to update new solution The method has been tested on three systems and the obtained results compared to other methods such as TLBO, QOTLBO, ALM and TPNN have revealed that the method was capable of searching high quality solution

2.5 MULTI-OBJECTIVE FIXED HEAD SHORT-TERM HYDROTHERMAL SCHEDULING PROBLEM

In recent years, several artificial intelligence based methods have been implemented for solving the multiobjective short-term HTS problem such as simulated annealing-based goal-attainment (SA-BGA) [58], Particle swarm optimization and gamma based (-PSO) method [59], Real-coded genetic algorithm (RCGA) [60], Multiobjective differential evolution (MODE) [60], Non-dominated sorting genetic algorithm-II (NSGA-II) [60], Improved genetic algorithm, multiplier updating and the ε-constraint technique (IGA-MU) [61], Particle Swarm Optimization (PSO) [62], PSO with penalty method (PSO-PM) [62], Predator-prey optimization (PPO) [62], PPO with penalty method (PPO-PM) [62], PPO and Powell Search Method (PPO-PS) [62], PPO and PS method with penalty method (PPO-PS-PM) [62], and Improved regularity model-based multiobjective estimation of distribution algorithm (IRM-MEDA) [63] Simulated annealing-based goal-attainment (SA-BGA) method [58] has been applied

to the multi-objective short-term HTS problem with nonsmooth fuel cost function In this paper, the problem has dealt with economic and emission as competing objectives Two objectives including fuel cost and emission have been converted into one objective by using weight factors associated with fuel cost and emission and then the goal-attainment method has been applied to determine the best compromise solution This study has only obtained a few solutions corresponding to a few different values of weight factors and then the best compromise solution has been found based on the goal-attainment method Therefore, the best emission could be reasonable but the best fuel cost was so far the reasonable value Furthermore, there has been no any comparison between SA-BGA and other applied methods So, the conclusion of the performance of the SA-BGA has not been done in the paper The execution time for searching optimal solution for each dispatch case could be up to half hour This illustration has given an advice that SA-BGA should not be applied for solving the multi-objective hydrothermal scheduling problem especially for large-scale systems

In fact, only this paper has applied the SA-BGA for solving the multi-objective problem so far Contrary to ref [58], three larger systems considering both fuel cost and emission have been employed to test a proposed method based on PSO and Lagrange multipliers in [59] Similar to LGM in [2], a particle swarm optimization and gamma based (-PSO) method [59] has utilized the coordination equations in the iterative algorithm to obtain the optimal solution In order to apply the coordination, a Lagrange function has first been constructed consisting of multiobjective and constraints of power balance constraint and available water constraint Secondly, PSO has been carried out to search optimal gamma, which was Lagrange multiplier associated with available water constraint Finally, the optimal gamma would be substituted into the coordination equations to calculate hydro and thermal generations Unlike the original PSO method, each particle in this method was represented with

respect to gamma in stead of water discharge and thermal generations The modifications were regarded as the advantages of the -PSO method, leading to easy convergence and short computational time The method to determine the best compromise between ref [58] and ref [59] were completely different The goal-attainment method has been used in [58] but it was very simple in [59] when both fuel cost weight factor and emission weight factor have been set to 0.5 Three dispatch cases have been implemented and resulted in optimal solutions with optimal fuel cost and emission The improvement has been clearly seen since the -PSO has not only yielded lower objective than PSO for all study cases but also has used much lower population size and iterations compared to PSO In spite of the good performance, the method had to cope with the disadvantage of the gamma based method that it was not capable of solving the problem considering the valve point loading effects Non-dominated sorting genetic algorithm-II (NSGA-II) [60] has been implemented to deal with the economic environmental dispatch problem with non-smooth fuel cost and emission functions of thermal power generators in coordination with fixed head hydro units This method was considered superior to other methods since it could determine the compromise solution without using fuzzy mechanism To investigate the performance, other methods such as Real-coded genetic algorithm (RCGA) and multiobjective differential evolution (MODE) have also been implemented to run on two different systems in which the smaller system has ignored valve point loading effects and the larger system has considered valve effects The comparisons have mainly focused on fuel cost and emission whereas the execution time comparison has not led to any conclusion because all the methods have used identical population and identical iterations As a result, NSGA-II has been considered very good for the problem when its fuel cost and emission have been lower than those from others However, this method still suffered long execution time for obtaining optimal solution due to the characteristic of conventional GA Chiang has proposed an approach based

on the improved genetic algorithm, multiplier updating and the ε-constraint technique (IGA-MU) to solve the optimal economic emission dispatch of hydrothermal power systems [61] The improved GA had a high performance by using multiplier updating for handling all constraints and the ε-constraint technique for managing the multiobjective problem Therefore, this method was more efficient than the conventional GA although the result comparison between the two methods has not been given Moreover, the method has obtained better solution quality and faster execution than GA-MU and SA-BGA [58] Although the authors have emphasized the effectiveness of IGA-MU over SA-BGA [58] and GA-MU, the further investigation of the performance has not been good enough because they have implemented the methods for solving only one system with three dispatch cases and even the execution time has still been long Another method based on the integration of predator-prey optimization and Powell search method (PPO-PS) [62] has been implemented for solving the economic emission dispatch for fixed-head hydrothermal systems

Predator-prey optimization (PPO) has been used as a global search tool meanwhile Powell’s method has played focused on local search ability Predator-prey has been constructed based on particle swarm optimization configuration In addition to several advantages of PSO such few control parameters, easy implementation, it had to suffer some main drawbacks such as local optimal trapping and lack of effective capability to deal with the constraints PPO model includes both predator and prey particles in initial population The prey target is to escape from the predators whilst the purpose of predator is to capture the prey in order to improve exploration and exploitation capability of PSO Furthermore, Powell’s method has played a crucially important role searching around the solutions obtained from PPO In addition, a penalty handling method for dealing with the equality constraints and inequality constraints has also been integrated into the PPO-PS to form a more potential method, called PPO-PS-PM The PPO-PS-PM has combined the capability of global search from PPO, the capability of local search from Powell search method and the capability of exactly satisfying constraints from Penalty method The performance of PPO-PS-PM has been investigated via testing on three different systems with different scales and different objective functions A set of methods related to PPO-PS-PM has been carried out such

as PSO, PSO-PM, PPO, PPO-PM and PPO-PS The obtained result comparison from these methods have revealed that PPO-PS-PM was the best method among the applied ones An improved regularity model-based multiobjective estimation of distribution algorithm (IRM-MEDA) [63] has been successfully applied for solving the HTS problem with nonconvex fuel cost function of thermal units IRM-MEDA is an improved version of the original regularity model-based multiobjective estimation of distribution algorithm by adding a local learning operation in aim to enhance the local search ability and speed up the convergence speed In addition, another technique, called repair mechanism, has also been used together with IRM-MEDA to fix infeasible solutions during new solution generations IRM-MEDA has been tested on one system with three dispatch cases The result comparison has revealed that the IRM-MEDA was not more effective and robust than MODE , NSGA-II and IGA-MU since it could not get better solutions than the two methods for all cases Furthermore, the improved version has not been demonstrated efficient compared to original methods because RM-MEDA has not been implemented for comparison

It is clear that all studies tend to apply original algorithms and/or propose improved version of original ones so as to get better solutions The analysis has shown that the latter methods can be better than the previous ones in terms of optimal solution quality However, there are still drawbacks when apply the methods to a real system with larger scale and more complex

2.6 HYDROTHERMAL OPTIMAL POWER PROBLEM

This problem was to determine optimal generations for thermal units and hydro units so that the fuel cost from thermal units was minimized and all constraints from the units as well as from hydro reservoirs must be exactly met Besides, the units were located at generator buses especially several generators driven by thermal units were replaced with hydro units The optimal interval was also divided into multi subintervals where each one consist of a number of hours within a day There have been several papers related to the field; however, they have been limited when only a few optimization algorithms were applied and problem data or a comparison to validate their algorithms were also limited The problem will be mentioned, discussed and solved in chapter 7

2.7 SUMMARY

This chapter describes five hydrothermal scheduling problems including four ones with single objective and one with multi objectives and many methods which have been applied to the three ones are also analyzed so as to point out advantages as well

as disadvantages that these methods own Obviously, conventional methods searching optimal solutions based on one path forward to the final best solution is limited for applying on system where non-differential functions are considered whereas other ones, a family of meta-heuristic algorithms, are more efficient when they are capable

of solving systems consisting of complex constraint as well as non-differential functions