在過去的20年間為啟發式方法來求解連續和不連續問題之時代來臨。有許多隨手可得的範例，像是粒子群優演算法(PSO)在數學上最佳化領域中具有重要程度之影響。藉由調整其慣性權重、位置以及速度上的更新方程式來改善PSO演算法的性能。當這些方程式仍然需要用於離散問題時，二進制粒子群優演算法(BPSO)已被提出，其中之速度轉換程序比上述三個方程式還來得重要，尤其在處理離散最佳化過程時。
因此，本論文提出一種改良型二進制粒子群優演算法，藉由考慮兩組速度轉換函式名為S型和V型群組來求解日前機組排程問題。一個新型樞紐啟發式修補演算法能有效處理系統限制和時間相依的限制條件相互衝突之問題，用於獲得一組可行的機組排程解。而經濟調度問題則是利用增強型λ疊代法(ELI)求解每個時段之調度解。
本文以MATLAB模擬驗證所提方法之可行性，並且以兩個標準系統來做驗證，分別為IEEE 10機組和IEEE 26機組測試系統。所求出的結果將以總成本和運算時間等方面展現改良型粒子群優演算法具備比其它近期文獻提出的幾種方法更優異的性能。此外，三個外加的案例將包含其它的限制條件與目標函式，並對所得結果做一個詳細探討。

The last two decades have seen the advent of metaheuristic-based methods to solve both continuous and discrete optimization problems. While there are many paradigms available, the Particle Swarm Optimization (PSO) algorithm has had a profound impact in the mathematical optimization field. Extensive efforts, often with good results, have been made in the literature to improve the performance of the PSO algorithm by modifying the inertia weight, the position, and the velocity update equations. While these equations are still fundamental in its discrete counterpart, the Binary Particle Swarm Optimization (BPSO) algorithm, they are secondary to the velocity mapping procedure, which is essential in the discrete optimization process.

Therefore, this thesis proposes a Modified Binary Particle Swarm Optimization algorithm (VS-BPSO) to solve the first stage of the forward day-ahead Thermal Unit Commitment Problem by considering two families of velocity mapping functions, namely the S-Shaped and V-shaped families. A novel pivot heuristic repair algorithm which effectively handles the conflict between system-wide and time-dependent constraints, is used to obtain a feasible Unit Commitment (UC) schedule. The Economic Dispatch (ED) subproblem is then solved for each time slot of the study period with an Enhanced Lambda Iteration Method (ELI).

The viability of the proposed solution methodology is simulated in the MATLAB © environment and is verified with the use of two benchmark systems, namely the IEEE 10-unit and the IEEE 26-unit test case systems. The obtained numerical results demonstrate the enhanced performance of the VS-BPSO algorithm in terms of total cost and computational time when compared to other methods in the recent literature. Furthermore, three additional cases involving other constraints and objectives are included. Comprehensive discussion of the obtained results is provided.

Thesis Validation Letter in Chinese…...……………………………………………….….i
Thesis Validation Letter in English.....………………………………………………..….ii
Acknowledgements…………………………………………………………………......iii
Chinese Abstract…………………………………………………….…………………..iv
Abstract…………………………………………………………………………....…......v
Table of contents………………………………………………………………………...vi
List of Figures ...………………………………………………………………………...xi
List of Tables ...…………………………………………………….……………….….xiii
List of Symbols ...…………………………………………………….…………….......xv
Chapter 1
Introduction
1.1 The scheduling problem in the power system……………………………………..….1
1.2 Thesis objectives………………………………………………………………….….3
1.3 Research methodology…………………………………………………………….…4
1.4 Thesis outline…………………………………………………………………….......5
Chapter 2
The role of the day-ahead unit commitment procedure
2.1 Basic structure of the Electrical power system …………………….…………………7
2.1.1 Motivation…………………………………………………………………….7
2.1.2 Characteristics of the conventional Electric Power System…………...…........7
2.2 The market based electric power system……………………………………….........11
2.3 The day-ahead unit commitment procedure ……………….……….……….….......13
Chapter 3
Formulation of the Thermal Unit Commitment Problem
3.1 Introduction………………………………………………………………………...14
3.2 Characteristics of Thermal Generating Units….…………………………………...14
3.3 TUCP problem formulation………………………………………………………...17
3.3.1 Objective function……………………………………………………………17
3.3.2 Startup and shutdown costs………………………………………………......19
3.3.3 Constraints……………………………………………………………………21
3.3.3.1 System constraints…………………………………………………...21
3.3.3.2 Unit constraints…………………………………………………........24
3.3.3.3 Time-dependent constraints………………………………………….26
3.4 Constraint handling and schedule repair by a proposed pivot heuristic……………27
3.4.1 The conflict between system and time dependent constraints………………27
3.4.2 TUCP constraint handling methods………………………………………...29
3.4.2.1 Penalty function-based methods………………………..……………29
3.4.2.2 Heuristic based methods…………………………………………......31
3.4.3 A proposed pivot heuristic algorithm……………………………………...33
3.4.3.1 Initialization algorithm………………………………………………33
3.4.3.2 Constraint handling algorithm……………………………………….35
3.5 The Economic Dispatch subproblem……………………………………………….44
3.5.1 ED Problem formulation and related theory……………………..………..44
3.5.2 ED Problem solution by an enhanced lambda iteration method…………..46
Chapter 4
A Modified Binary Particle Swarm Optimization Algorithm
4.1 Foundations of Particle Swarm Optimization……………………………….……..48
4.2 Continuous Particle Swarm Optimization……………………………………….....53
4.2.1 The building blocks of the PSO algorithm…………………………….…....53
4.2.2 PSO algorithm implementation I: The Why………………………………...56
4.2.3 PSO algorithm implementation II: The How……………………………….60
4.3 A Modified Binary Particle Swarm Optimization Algorithm...…………….………65
4.3.1 Introduction…………………………………………………….…………...65
4.3.2 Redefining particle position and velocity ………………………………......66
4.3.3 Families of mapping functions……………………………………………...70
4.4 VS-BPSO-TUCP Swarm generation module………………………………………73
4.4.1 Representation of a UC schedule as a particle………………….………......73
4.5 VS-BPSO-TUCP Optimization module…………………………………………....76
Chapter 5
Simulation Results
5.1 Introduction………………………………………………………………………...78
5.2 IEEE 10-unit test case I…..………………………………………………………...79
5.2.1 System and load demand data………………………..………………………79
5.2.2 VS-BPSO algorithm application results I……..………………………….......80
5.2.3 Optimal UC and ED schedule I………………………………………………83
5.2.4 Performance comparison with the literature………………………………….86
5.3 IEEE 10-unit test case II…..…………………………………...…………………...87
5.3.1 VS-BPSO algorithm application results II……..……………………...…......87
5.3.2 Optimal UC and ED schedule II..…………………………...………………..88
5.4 IEEE 10-unit test case III…..……………………………….……………………...90
5.4.1 Description and formulation of the emission problem…………….…………90
5.4.2 VS-BPSO algorithm application results III……..………………..………......91
5.4.3 Optimal UC and ED schedule III……….……………………………………93
5.5 IEEE 10-unit test case IV…..……………………………….……………………...95
5.5.1 Demand Response Unit Commitment……………… …………….…………96
5.5.2 VS-BPSO algorithm application results IV…….………………..…………...97
5.5.3 Optimal UC and ED schedule IV……….……………………………………98
5.6 IEEE 26-unit test case V…..……………………………….………………….......100
5.6.1 System and load demand data………………………..…………………......100
5.6.2 VS-BPSO algorithm application results V…….………………..…………..101
5.6.3 Optimal UC and ED schedule V……….………………………...………….102
Chapter 6
Thesis Conclusion
6.1 Conclusions…………………………………………………………………..…...105
6.2 Future Work……………..……………………………………………………...…106
References
References…………………………………………………………………………….107
Appendix
A.1 Source code example of SRREQ status check function…………………………...113
A.2 CPU runtime comparison of several ED solution methods………………………..114

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