由電力系統暫態穩定性分析下，系統是否穩定取決於發電機的同步電角。當電力網路系統發生故障並失去穩定後，伴隨著某些臨界切集中傳輸線的電角差劇烈增長，其中不穩定平衡點和系統能量函數與臨界切集必定有某種關聯性，並加以分析能量函數中傳輸線位能和故障後不同類型的系統。接著詳細介紹切集的概念，其中包含圖形理論和電力網路上的問題。圖形中”點”與”邊”之間的關係在電力網路系統就如同”傳輸線”與”匯流排”之間的關係，並用來解釋系統暫態穩定度與發電機的同步與否。結合系統切集與能量函數傳輸線位能的概念，可得知系統故障所產生的故障能量在傳輸線中轉換成位能，當此能量超過傳輸線位能的臨界值時，系統將不同步發生分群現象，稱為”臨界切集”。最後用臨界傳輸線指標計算出臨界傳輸線，進而預測臨界切集並觀察系統分群狀況。
此方案透過即時電力系統模擬器OP5600及Matlab/Simulink模擬環境下操作，建立電網系統並對此系統加入擾動，觀察其電壓、電角及角頻率的擾動且加以分析計算，來驗證不穩定平衡點和能量函數與切集之間的關聯性。

Under the transient stability analysis of power systems, whether the system is stable depends on the synchronous electrical angle of the generator. Angles difference of branches in critical cutsets change rapidly when the power system losses transient angle stability. We have realized that there are some relations between energy functions of the system and critical cutsets. The concept of the cutsets is importance in graph theory and the electrical component problems of network. In the graph theory, the relation between points and edges can be regarded as the relation between transmission lines and bus of power systems. It can explain a phenomenon in transient stability that the loss of synchronism from the angle separation. Moreover, the cutset combines with the concept of line transient potential energy, that leads to the system becomes more than two groups when the energy exceeds the critical value of line transient potential energy. We call this phenomenon as “critical cutset”. Using the critical cutset line index (CCSLI) that proposes in my thesis that to identified of critical cutsets and generators coherence.
This proposal operates under the real-time power system simulator OP5600 and Matlab/Simulink. It can build the power networks and adds some disturbance. Then, we analysis the voltages, angles, and frequency to verified the relations between energy functions and critical cutsets.

摘要 I
ABSTRACT II
致謝 III
目錄 IV
圖目錄 VII
表目錄 IX
符號表 X
第一章、 緒論 1
1.1 研究動機與文獻回顧 1
1.2 本篇貢獻 3
1.3 論文架構 3
第二章、 動態系統分析與數學模型 4
2.1 前言 4
2.2 里亞普諾夫理論(Lyapunov theorem) 5
2.2.1 基本理論 5
2.2.2 搖擺方程式(Swing Equation) 6
2.2.3 系統穩定域 7
2.3 能量函數(Energy Function) 9
2.4 位能邊界面法(PEBS) 11
2.4.1 概述 11
2.4.2 單機無限大匯流排系統與能量函數 11
2.4.3 等面積法 14
2.4.4 多機動態系統架構 17
2.5 傳輸線位能函數分析 25
2.6 小結 27
第三章、 切集原理與應用 28
3.1 前言 28
3.2 切集迴圈圖形化 29
3.2.1 圖形理論 29
3.2.2 最小樹狀圖(Minimum Tree)與切集 33
3.3 不穩定平衡點與切集分析 36
3.3.1 切集指標CI 36
3.3.2 改良切集指標ICI 38
3.4 切集之能量函數 40
3.4.1 數值分析 40
3.4.2 數值結果 44
3.5 臨界切集(Critical cutset) 47
3.6 小結 50
第四章、 模擬結果分析 51
4.1 前言 51
4.2 實驗平台簡介 52
4.2.1 即時電力系統模擬器OP5600 52
4.2.2 ePHASORsim 53
4.3 案例WSCC_9匯流排_3發電機 54
4.3.1 案例WSCC_9 臨界故障清除時間分析 54
4.3.2 案例WSCC_9臨界切集 57
4.4 案例IEEE_39 66
4.5 小結 71
第五章、 結論和未來研究方向 72
5.1 結論 72
5.2 未來展望 72
參考文獻 73

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