實數型Jacobi-Davidson演算法應用於大型電力系統小訊號穩定度之分析

Application of the Real Variant of the Jacobi-Davidson Method to the Small-Signal Stability Analysis of Large Power Systems

蔡少宏(Shao-Hong Tsai)

指導教授 ： 李清吟 ； 陳昭榮

國立臺北科技大學/機電學院/機電科技研究所/博士(2010年)

摘要

本論文針對大型電力系統之小訊號穩定度問題作研究與分析。文中應用實數型Jacobi-Davidson數值演算法並結合一個具有彈性選擇關鍵特徵值之策略，以求解大型電力系統狀態矩陣之關鍵特徵值。
實數型Jacobi-Davidson是一種嶄新且有效率之演算法，用於求解非對稱實數矩陣部分特徵值之子空間疊代法，並且適用於電力系統小訊號穩定度問題之特徵值求解。實數型Jacobi-Davidson演算法採用實數運算法則以建構實數搜尋子空間和部分實數Schur型，藉以改善原有Jacobi-Davidson演算法所採行之複數運算法則，再者實數型Jacobi-Davidson演算法可實際運用於具有高度稀疏特性的電力系統動態模型，這些技術可有效加速演算法收斂速度以及避免重複計算已收斂之特徵值，同時保證數值運算的強鍵性。此外本論文亦提出一種具有彈性選擇特徵值之策略可提供三種選擇關鍵特徵值方案：(a)求解低阻尼特徵值，(b)求解靠近某一指定頻率之特徵值，(c)求解具有較大實部之特徵值，致使有效求解電力系統之低頻振盪模式以及不穩定振盪現象。
數值模擬分析以台電89及120機組測試系統，做為實數型Jacobi-Davidson演算法以及原有Jacobi-Davidson演算法之比較分析與數值驗證。

關鍵字

小訊號穩定度 ； 關鍵特徵值 ； 低頻振盪 ； Jacobi-Davidson演算法

並列摘要

This dissertation is aimed at exploring issues relating to the analysis of the small-signal stability of large power systems. An improved numerical method incorporated with a comprehensive selection strategy for the calculation of critical eigenvalues of the system state matrix has been proposed.
The real variant of the Jacobi-Davidson QR (RJDQR) method is a novel and efficient subspace iteration method to find a selected subset of eigenvalues of a real unsymmetric matrix and is favorable to eigenanalysis for the power system small-signal stability. Compared with the original JDQR method, the RJDQR method utilizes real arithmetic to keep the search subspace real and construct a partial real Schur form iteratively. Moreover, the RJDQR method can be practically implemented on highly sparse power system dynamical models. These techniques significantly accelerate iteration convergence and completely avoid repeated computations of the detected eigenvalues, as well as numerical robustness can be guaranteed. In addition, the RJDQR method in conjunction with a flexible selection strategy of critical eigenvalue detection criteria is presented in this dissertation. The selection strategy provides three options for critical eigenvalue detection criteria: (a) detection of the low damped eigenvalues, (b) detection of values in the immediate neighborhood of the specified target value, and (c) detection of the rightmost eigenvalues. By using this selection strategy, the low damped oscillatory modes and/or unstable oscillations in power systems can be found effectively.
Numerical experiments demonstrate the efficiency of the RJDQR method adopting the proposed selection strategy for pursuing eigenanalysis tasks based on 89- and 120-machine systems. The results show that the proposed method is capable of effectively finding critical eigenvalues in large power systems.

並列關鍵字

Small-signal stability ； Critical eigenvalue ； Low frequency oscillation ； Jacobi-Davidson method

參考文獻

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