新型差分進化演算法設計及其在電力系統之應用

Design of a Novel Differential Evolution Algorithm and its Applications to Power Systems

王勝寬(Sheng-Kuan Wang)

指導教授 ： 劉志文

國立臺灣大學/電機資訊學院/電機工程學研究所/博士(2007年)

https://doi.org/10.6342/NTU.2007.02016

摘要

在本論文中提出一個混合整數與實數的或然性啟發式最佳化演算法，並將它應用於電力系統的兩個重要的最佳化問題上。第一個問題是包含各種系統與發電機限制的經濟調度(ED)問題，另一個問題為多機電力系統內的電力系統穩定器(PSSs)參數調整問題。論文內所提出的最佳化演算法稱為混合整數蟻行混合差分進化法(MIADHDE)，在文中利用此演算法分別找出電力系統經濟調度及電力系統穩定器參數調整問題整體性的最佳解。MIADHDE演算法是在原始的混合差分進化(HDE)演算法內的五種突變策略中，利用螞蟻群聚覓食的習性，去搜尋出較適合本次疊代使用的突變運算策略，以此加速找出一組包含整數與實數決定變數整體性的最佳解。
當MIADHDE演算法應用於電力系統的經濟調度問題時，在實際上許多發電機在正常運轉時，就會有一些機械上的一些極限及安全上的一些考量，諸如：斜坡率極限、禁止操作區、閥點效應及備轉容量，在做經濟調度問題時，以上所提及的這些限制條件也都必需被考慮進來。由於這些限制條件的影響，使得電力系統的經濟調度問題變成一個非平滑/非凸集求最小值的最佳化問題。在此將使用，六機組、十五機組和四十機組的三個測試系統，配合本論文所提的MIADHDE演算法。另外還有以往在許多文獻上所提及的遺傳基因演算法(GA)、模擬退火(SA)法、差分進化(DE)法與混合差分進化(HDE)法共五種最佳化演算法在經濟調度問題上互相比較。然而由以上這五種演算法所計算出來的結果顯示，本論文所提議的MIADHDE演算法的性能，在實際大型電力系統的經濟調度問題上，無論是在燃料成本或所使用的計算時間上，MIADHDE演算法都優於其它四種演算法。
在另一方面，由於MIADHDE演算法在經濟調度問題上有較優越的表現，故接下來本論文僅以MIADHDE演算法應用於求解電力系統內PSSs的參數調整問題上。在許多文獻上PSSs的參數調整其目標函數通常是由阻尼比和阻尼係數所共同或單獨建構的方程式組成，在本論文中也利用阻尼係數和阻尼比的結合提出了三種不同的目標函數，並比較其對系統阻尼的影響。第一種是與以前文獻上相仿的目標函數，第二種是僅有本地端輸入訊號的目標函數，而第三種目標函數，特別將本地端機組和遠端回授訊號機組角速度變化量的差值，作為本地端電力系統穩定器的輸入訊號，以改善系統的阻尼。10機組39匯流排的新英格蘭標準系統，在不同的系統結構和負載條件下，被用來測試這三個目標函數，應用MIADHDE演算法在PSSs參數調整上。我們在Matlab平台上所執行的頻域小訊號穩定度分析程式，及在Siemens PTI公司開發的PSS/E平台上，所模擬的非線性時域的動態響應結果，驗證了利用MIADHDE所搜尋出來的三組PSSs參數中，第三個目標函數所搜尋出來的一組包含遠端輸入訊號的PSSs參數，在整個系統阻尼上優於其它兩者。
然而，當在PSS/E平台上做時域模擬時，含有遠端角速度變化量輸入訊號的電力系統穩定器，必需使用PSS/E軟體內的使用者自建模型(UWM)來新建。在本論文內也針對了PSS/E所提供的電廠相關設備的使用者自建模型，其撰寫方法和結構詳加描述，在PSS/E內每一個使用者自建模型都是由八個MODE所組成，每一個MODE的特性在論文內都有詳細的說明。在此我們也將以台電系統內的新天輪發電廠勵磁機模型當成一個實例，說明利用PSS/E內使用者自建模型建立的方法及執行結果，而此模型在台電系統上被命名為MITLOT，至今仍為台電公司各單位做系統規劃及模擬時所使用。

關鍵字

差分進化演算法 ； 經濟調度 ； 閥點效應 ； 動態穩定度 ； 電力系統穩定器 ； 使用者自建模型

並列摘要

This thesis presents a novel probabilistic heuristic optimization approach which is mixed integral and real decision variables applied to determining the feasible optimal solution of the economic dispatch (ED) problem while considering various generator constraints and the tuning of power system stabilizer (PSS) parameters for a multi-machine power system. The proposed optimization algorithm is called mixed-integer ant direction hybrid differential evolution, or MIADHDE. This algorithm is proposed to solve these two kinds of problems. MIADHDE utilizes the concept of an ant colony search to find a suitable mutation strategy of the five types of the strategies in the original hybrid differential evolution (HDE) to accelerate the search for a set of the global optimum solution, which is able to include integral and real decision variables.
In the economic dispatch problem of a power system, many practical constraints of the generators, such as ramp rate limits, prohibited operating zones, the valve point effect, and spinning reserve, must be considered. Those constraints make the ED problem of the power system as a non-smooth/non-convex minimization problem with constraints. Three test power systems, including six-, fifteen-, and forty-unit power systems, are applied to compare the performance of the proposed algorithm with those of genetic algorithms (GAs), the simulated annealing (SA) algorithm, the differential evolution (DE) algorithm, and the hybrid differential evolution (HDE) algorithm. Numerical results indicate that the performance of the proposed MIADHDE algorithm outperforms the other four algorithms in terms of computed minimum fuel cost and computational complexity.
As mentioned above, the performance of MIADHDE exceeds the four algorithms of GA, SA, DE and HDE in the ED problem. Therefore, we only employ the MIADHDE algorithm to solve the problem of tuning PSS parameters. This problem of PSS parameter tuning which is usually formulated as an objective function with constraints consisting of the damping factor and damping ratio. In this thesis, three different objective functions are proposed through combination of the damping factor and damping ratio. The first objective function proposed, which is similar to the literature, is used to compare the performance with the other two objective functions. The second objective function is to consider only local machine speed deviation as the input signal to the PSS. In he third objective function, both local and remote feedback signals of machine speed deviation measurements are selected as input signals to the PSS controllers. The 10-unit 39-bus New England standard power system, under various system configurations and loading conditions, is employed to test the performance of three objective functions for tuning of PSS parameters by the MIADHDE method. Eigenvalue analysis of frequency domain on the Matlab platform and nonlinear simulation results of time domain on the Siemens PTI PSS/E platformdemonstrate that the third objective function, searching for PSS parameters by MIADHDE algorithm, is superior to other the two objective functions.
In addition, the power system stabilizer model, including a remote feedback signal of speed deviation in the time domain simulation, must be created by the user written model method in the PSS/E software. In this thesis, the construction of the user-written model for the plant-related model in the PSS/E has been described. It consists of eight modes. The principles of each mode will also explained in detail this thesis. An exciter model at the New-Tien-Lun plant in the Taiwan Power System will be used as an example to show the coding method and results of execution of the user written model in PSS/E, the exciter model of which is called MITLOT. It was added to the Taiwan Power System is to perform system simulations and programming tasks by Taiwan Power Company and it in use up to the present.

並列關鍵字

differential evolution ； economic dispatch ； valve point effect ； dynamic stability ； power system stabilizer ； user-written model

參考文獻

[1]F. N. Lee and A. M. Breiohi, “Reserve constrained economic dispatch with prohibited operating zones,” IEEE Trans. Power Syst., vol. 8, no. 1, pp.246-254, February 1993.

[2]P. H. Chen, and H. C. Chang, “Large-scale economic dispatch by genetic algorithm,” IEEE Trans. Power Syst., vol. 10, no. 4, pp.1919-1926, 1995.

[3]J. O. Kim, D. J. Shina, J. N. Parka, and C. Singh, “Atavistic genetic algorithm for economic dispatch with valve point effect,” Electr. Power Syst. Res., vol. 62, no. 3, pp.201-207, 2002.

[4]D. C. Walters, and G. B. Sheble, “Genetic algorithm solution of economic dispatch with valve point loading,” IEEE Trans. Power Syst., vol. 8, no. 3, pp.1325-1332, 1993.

[5]F. P. de Mello, and C. Concordia, “Concepts of Synchronous Machine Stability as Affected By Excitation Control,” IEEE Trans. power syst., vol. PAS-88, pp.316-329, 1969.