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.

[1]. Peter. W. Sauer, and M. A. Pal, “Power System Dynamics and Stability,” Upper, Saddle, River, N, J: Prentice Hall, 1998.
[2]. A.R. Bergen, “Power Systems Analysis, 2nd ed,” Prentice Hall, Englewood Cliffs, NJ 1986.
[3]. Tao Wang, and Hsiao-Dong Chiang, On the Number of Unstable Equilibrium Points on Spatially-Periodic Stability Boundary, IEEE Trans. on Automatic Control, vol. 61, no. 9, Sep 2016.
[4]. K. S. Chandrashekhar, and D. J. Hill, “Cutset stability criterion for power systems using a structurepreserving model,” Electrical Power and Energy Systems, 1986 Butterworth & Co (Publishers) Ltd.
[5]. K. R. Padiyar, “Power System Dynamics – Stability and Control, 2nd ed,” Hyderabad, India: B.S Publications, 2002.
[6]. Jan Machowski, Janusz W. Bialek, and James R. Bumby, “Power System Dynamics Stablilty and Control,” Second Edition, John Wiley & Sons, Ltd, 2008.
[7]. Hsiao-Dong Chiang, Chia-Chi Chu, and Gerry Cauley, “Direct Stability Analysis of Electric Power System Using Energy Functions: Theory, Applications, and Perspective,” Proceeding of the IEEE, vol. 83, No.11, Nov 1995.
[8]. Yu Yi-xin, Fan Ji-chao, and Feng Fei, “Relationship between the Number of Critical Cut-sets and the Type of Unstable Equilibrium Point with Respect to Transient Angle Stability,” Proceedings of the CSEE. vol. 26, No.8, Apr. 2006.
[9]. K. R. Padiyar, and S. Krishna, “Online Detection of Loss of Synchronism Using Energy Function Criterion,” IEEE Trans. on Power Delivery, vol. 21, no. 1, pp. 0885-8977, Jan 2006.
[10]. M. A. Pai, “Energy Function Analysis for Power System Stability,” Boston: Kluwer academic publishers, 1989.
[11]. A. H. El-Abiad, and K. Nagappan, “Transient Stability Region of Multi-Machine Power Systems,” IEEE Trans. Power Appar. Syst., PAS-85, 2, Feb. 1966, 169–178.
[12]. N. Kakimoto, Y. Ohsawa, and M. Hayashi, “Transient Stability Analysis of Electric Power Systems Via Lure Type Lyapunov Functions, Parts I and II,” Trans. IEE of Japan, 98, 5/6, May/June 1978.
[13]. T. Athay, R. Podmore, and S. Virmani, “A Practical Method for Direct Analysis of Transient Stability,” IEEE Trans. Power Appar. Syst., PAS-98, 2, Mar./Apr. 1979, 573–584.
[14]. C. A. Desoer, and E. S. Kuh, “Basic Circuit Theory,” New York: Mc-Graw-Hill, 1969.
[15]. G.W. Cai, K.W. Chan, W.P. Yuan and G. Mu, “Identification of the vulnerable transmission segment and cluster of critical machines using line transient potential energy,” Electrical Power and Energy Systems, 29 (2007) 199–207.
[16]. Wang Ke, You Dahai, Yin Xianggen, Ye Lei, Huang Ruoyin, and Wu Junchun, “Power System Transient Stability Analysis and Critical Cutset Detection Based on Branch Ridge,” Trans. of China Electrotechinical Society, vol. 28, No. 11, Nov. 2013.
[17]. Guowei Cai, Z.L. Sun, Deyou Yang, and Y.W. Wang, “Analogous elastic network for the analysis of power system energy structure,” IET Generation, Transmission & Distribution, 2017, vol. 11, Iss. 4, pp. 924-934.
[18]. Henrik Ronellenfitsch, Debsankha Manik, Jonas H¨orsch, Tom Brown, and Dirk Witthaut, “Dual Theory of Transmission Line Outages,” IEEE Trans. on Power Systems, vol. 32, no. 5, Sep 2017.
[19]. Yue Song, R. David J. Hill, Life Fellow and Tao Liu, “Characterization of Cutsets in Networks with Application to Transient Stability Analysis of Power Systems,” IEEE Trans. on Control of Network Systems, 2016 IEEE.
[20]. W. P. Yuan, and K. W. Chan, “Identification of Critical Cluster in Transient Stability Study Using Line Potential Energy Method,” 2006 IEEE Trans. 1-4244-0493-2/06.
[21]. Yiping Yu, Santiago Grijalva, James Jamal Thomas, Leilei Xiong, and Ping Ju,and Yong Min, “Oscillation Energy Analysis of Inter-Area Low-Frequency Oscillations in Power Systems,” IEEE Trans. on Power Systems, vol. 31, no. 2, Mar. 2016.
[22]. Tao Wang, and Hsiao-Dong Chiang, “On the Number of System Separations in Electric Power Systems,” IEEE Trans. on Circuits and Systems, vol. 63, no. 5, May 2016.
[23]. A. A. Fouad, and S. E. Stanton, “Transient Stability of a Multi-Machine Power System, Part I: Investigation of System Trajectories,” IEEE Trans. on Power Appaeatus and Systems, vol. PAS-100, No. 7, July 1981.
[24]. Shikha Sharma, Sai Pushpak, Venkatesh Chinde, and Ian Dobson, “Sensitivity of Transient Stability Critical Clearing Time,” IEEE Trans. on power system 33 (6), 6476-6486.
[25]. Miyagi, Hayao, and T. Taniguchi. "Construction of Lyapunov function for power systems." Proceedings of the Institution of Electrical Engineers. Vol. 124. No. 12. IET, 1977.
[26]. Moon, Y. H., Ryu, H. S., Lee, J. G., and Kook, H. J. "Equivalent mechanical model of power systems for energy-based system analysis." Decision and Control, 2001. Proceedings of the 40th IEEE Conference on. Vol. 1. IEEE, 2001.
[27]. N. Amutha, and B. Kalyan, “Effect of modeling of induction generator based wind generating systems on determining CCT,” IEEE Transactions on Power Systems, Vol. 28, No. 4 : 4456-4464, Nov 2013