電力系統之分叉性分析與控制

Abstract

本篇論文主要針對一個四階電力系統為分析對象, 並以分叉理論為基礎探 討此非線性系統所可能存在之非線性現象, 並針對這些現象瞭解此類電力 系統可能發生電壓崩潰的條件。由系統的動態特性分析得知, 此系統中存 在有靜態的 (saddle-node) 分叉及動態振盪的 (Hopf) 分叉現象, 而經 由數值分析的結果可以知道, 在 (Hopf) 分叉之後的週期振盪中又可以發 現 (cyclic fold) 分叉及 (period doubling) 分叉現象 , 並且在兩 個 (period doubling) 分叉之間會出現混沌的情形。且電壓崩潰可能發 生在兩個 (period doubling)分叉之間及(saddle-node)分叉附近。為了 抑制混沌現象或電壓崩潰的情況發生, 在此論文中, 我們分別使用直接系 統狀態迴授及 (washout filter) 迴授兩種方法來控制系統中的不穩定點 及由 (Hopf) 分叉所造成的不穩定的週期使其成為穩定, 並進而消除混沌 現象的發生。 In this thesis, we study the phenomena in the power systems, specifically, at which the voltage collapse may occur. By employing bifurcation theory, we analyze the dynamical behavior of power systems and obtain the conditions for the occurrence of voltage collapse. Several different of bifurcation scenarios are observed from the numerical simulations. These include static bifurcations (i.e., saddle- node bifurcation) and three types of dynamic bifurcations. Among these dynamic bifurcations, we have found two Hopf bifurcations, and two period doubling bifurcations as well as one cyclic fold bifurcation, occurring in the periodic solutions emergying from those Hopf bifurcation points. Moreover, there exist chaotic phenomena occurring between the two period doubling bifurcations. Voltage collapse is found either to appear between the two period doubling bifurcations or to occur near the neighborhood of the saddle-node bifurcation. Both direct state feedback control laws and the washout filter feedback control laws are proposed to prevent the occurrence of the voltage collapse which lies between the two period doubling bifurcations by changing the characteristic or removing the residence of Hopf bifurcation point.