隨著經濟發展，電網的需求持續增加，導致電網供電日益趨緊與難以維護。近年的事故紀錄指出大規模停電事件通常是起因於隱故障所衍生之連鎖故障，亦即建立一個精確的隱故障模型是必要的。過去關於隱故障模型的研究皆著重在各種參數對系統的衝擊分析與評估可能的緩解方法，因此直流隱故障模型被建立來驗證線路流量、備轉容量與隱故障機率等參數於各系統中的影響。另一方面，為了控制模型參數，使用了隨機規劃以找出最佳的發電策略來改善連鎖故障模型，也採用班德氏分解法來提升此類複雜問題的運算速度。可以分成兩種類型的模擬算法：一個是控制器再跑隱故障模型前計算並導入；另一類則是在連鎖故障之間求解控制器策略並改善。兩種類型皆有用來改善IEEE系統的直流隱故障模型以驗證其個別特性。
考量到直流模型的不足之處，隱故障模型被擴展到交流系統。利用Python語法來編寫程式以使用電力系統分析軟體PSS/E中的套裝函數，最終保證軟體能有最佳效能。另外因為交流隱故障模型包含了電壓穩定度的議題，故利用負載裕度程式來計算系統到電壓崩潰臨界點的系統裕度，以作為電壓穩定度的參考指標。預防性安全限制最佳潮流被導入來改善交流系統，控制器使用時機一樣能分成兩種類別，兩種也皆會被用來模擬與驗證IEEE測試系統與台電系統在交流隱故障模型中導入預防性控制的情況。

As the electrical demand continuously rises up due to economic growth, the power system becomes more stressed and hard to maintain. The recent records indicate that the large-scale blackouts are usually referred from the effect of cascading failures and the precise construction of hidden failure model is necessary. The researches of hidden failure model have been focused on the impacts of several parameters and assessing possible mitigation methods. Therefore, DC hidden failure model is built to verify the system parameters such as loading level, spinning reserve and the probability of hidden failures. To improve the system with hidden failures, stochastic programming is introduced to solve generation expansions that can efficiently deal with cascading events. Benders decomposition is applied to speed up computing time of complex problem. Two types of simulation algorithm are addressed: one is that the control actions are solved before the whole hidden failure simulation and the other type is that the controls are calculated and applied between the cascading stages. Both types of procedure will be tested with several IEEE systems.
Considering the shortage of DC model, the hidden failure model is extended to AC form. To guarantee the high performance of cascading model, the programs are written in python script to utilize the package function from PSS/E, a powerfully commercial program. AC hidden failure model contains the issue of voltage stability. Hence, load margin evaluation is used to measure the system margin to voltage collapse. Preventive security constraint optimal power (PSCOPF) is applied to improve the system. There are also two types of algorithms. Both of them will be simulated and compared. IEEE test systems and Taipower system will be used to verify AC hidden failure model and PSCOPF.

[1] Hines, Paul, Jay Apt, and Sarosh Talukdar. “Large blackouts in North America: Historical trends and policy implications.” Energy Policy, Vol. 37, No.12, pp. 5249-5259, 2009.
[2] J.-J. Wong, C.-T. Su, and C. S. L. C.-L. Chang, “Study on the 729 blackout in the Taiwan power system,” International Journal of Electrical Power & Energy Systems, Vol. 29, No. 8, pp. 589-599, 2007.
[3] J. S. Thorp, A.G. Phadke, S.H. Horowitz, S. Tamronglak, ‘‘Anatomy of power system disturbances: importance sampling,’’ International Journal of Electrical Power & Energy Systems, Vol.20, No. 2, pp. 147-152, 1998.
[4] J. Chen, J. S. Thorp, and I. Dobson, “Cascading dynamics and mitigation assessment in power system disturbance via a hidden failure model,” International Journal of Electrical Power & Energy Systems, Vol. 27, 2005.
[5] Qiu, J, and A. A. Girgis. “Optimization of power system reliability level by stochastic programming.” Electric Power Systems Research, Vol. 26, No. 2, pp. 87-95, 1993.
[6] I. Dobson, B. A. Carreras, and D. Newman, “An intiial model for complex dynamics in electric power system blackouts.” Hawaii International Conference on System Sciences, Vol. 2, 2001.
[7] 梅生偉, 薛安成, and 張雪敏. 電力系統自組織臨界特性與大電網安全. 清華大學出版社, 2009.
[8] K. Sun and Z.-X. Han, “Analysis and comparison on several kinds of models of cascading failure in power system,” IEEE/PES on Transmission and Distribution Conference and Exhibition: Asia and Pacific, 2005.
[9] I. Dobson, K. R. Wiezbicki, B. A. Carreras, V. E. Lynch, and D. E. Newman, “An estimator of propagation of cascading failure.” Proceedings of the 39th Hawaii International Conference on System Sciences, Vol. 10, 2006.
[10] N. A. Salim, M. M. Othman, M. S. Serwan, M. Fotuhi-Firuzabad, A. Safdarian, and I. Musirin, “Determination of available transfer capability with implication of cascading collapse uncertainty,” IET Generation, Transmission & Distribution, pp. 1-12, 2013
[11] A. O. Ekwue, “Economics and reliability of supply of developing power systems,” IEE Proceedings C on Generation, Transmission and Distribution, Vol. 133. No. 7, 1986.
[12] R. Billinton and J. Oteng.Adjei, “Cost/benefit approach to establish optimum adequacy level for generating system planning,” IEE Proceedings C. Vol. 135. No. 2, 1988.
[13] K. Chu and R. Billinton, “A generalized probabilistic cost of service allocation approach for generation and transmission facilities,” IEEE Trans. on Power Systems, 1990.
[14] W. Li and R. Billinton, “A minimum cost assessment method for composite generation and transmission system expansion planning,” IEEE Trans. on Power Systems, Vol. 8 No. 2, pp. 628-635, 1993.
[15] A. M. Geoffrion, “Generalized Benders decomposition,” Journal of Optimization Theory and Applications, Vol. 10, No. 4, pp. 237-260, 1972.
[16] J. Chen, and J. S. Thorp. “A reliability study of transmission system protection via a hidden failure DC load flow model,” Power System Management and Control, Fifth International Conference on IET, pp. 384-389, 2002.
[17] Genz, Alan, and Frank Bretz. “Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts.” Journal of Statistical Computation and Simulation, Vol. 63, No. 4, pp. 103-117, 1999.
[18] Marnay, Chris, and Todd Strauss. “Effectiveness of antithetic sampling and stratified sampling in Monte Carlo chronological production cost modeling [power systems]." IEEE Trans. on Power Systems, Vol. 6, No. 2, pp. 669-675, 1991.
[19] Chen, Quan, and Lamine Mili. “Composite power system vulnerability evaluation to cascading failures using importance sampling and antithetic variates.” IEEE Trans. on Power Systems, Vol. 28, pp. 1-10, 2013.
[20] J. Bucklew, Introduction to Rare Event Simulation. Springer Series in Statistics, Ch. 4, pp. 57-61, 2004.
[21] Jian. Cheng, and Marek J. Druzdzel. “AIS-BN: An adaptive importance sampling algorithm for evidential reasoning in large Bayesian networks.” Journal of Artificial Intelligence Research, Vol. 13, No. 1, pp. 155-188, 2000.
[22] Ray D. Zimmerman, Carlos E. Murillo-Sánchez, and Deqiang Gan. “A MATLAB power system simulation package.” http://www. pserc.conrnell.edu/matpower, 1997.
[23] Sinha, Nidul, R. Chakrabarti, and P. K. Chattopadhyay. “Evolutionary programming techniques for economic load dispatch.” IEEE Transactions on Evolutionary Computation, Vol. 7, No. 1, pp. 83-94, 2003.
[24] 梅生偉, 薛安成, and 張雪敏. 電力系統自組織臨界特性與大電網安全. 清華大學出版社, 2009.
[25] Michael J. Cannon, et al. “Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series.” Physica A: Statistical Mechanics and its Applications, Vol. 241, No. 3, pp. 606-626, 1997.
[26] D. P. Nedic, I. Dobson, and D. S. Kirschen, “Criticality in a cascading failure blackout model,” Electrical Power and Energy Systems, 2006.
[27] Hui-min, G. U. O. “Distribution system reliability assessment minimal path method-BFS [J].” Relay, Vol. 35, No. 22, pp. 14-17, 2007.
[28] B. Carreras, V. E. Lynch, D. E. Newman, and I. Dobson, “Blackout mitigation assessment in power transmission systems,” IEEE Proceedings of the 36th Annual Hawaii International Conference on System Sciences, 2003.
[29] Nouy, Anthony. “A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations.” Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 45, pp. 4521-4537, 2007.
[30] García-Bertrand, Roberto Mínguez Raquel. Decomposition techniques in mathematical programming. Springer-Verlag Berlin Heidelberg, 2006.
[31] Shahidehpour, Mohammad, and Yong Fu. “Benders decomposition in restructured power systems.” IEEE Techtorial, Apr. 2005.
[32] R. Billinton and R. N. Allan, Reliability Assessment of Large Electric Power Systems, Kluwer, Boston, 1988.
[33] 祝瑞金 and 傅業盛. “電力系統高級仿真軟件PSS/E 的優化與應用.” 華東電力, Vol. 29, No. 2, pp. 8-11, 2001.
[34] Jadid, S., and Saeid Jalilzadeh. “Application of Neural Network for Contingency Ranking Based on Combination of Severity Indices.” WEC, pp. 225-228, 2005.
[35] Jadid, S., and S. Jalilzadeh. “Contingency ranking based on combination of severity indices in dynamic security analysis.” Proceeding of the 4th WSEAS conf. on Application of Electrical Engineering, Prague, CZ, 2005.
[36] Greene, Scott, I. Dobson, and Fernando L. Alvarado. “Sensitivity of the loading margin to voltage collapse with respect to arbitrary parameters.” IEEE Trans. on Power Systems, Vol. 12, No. 1, pp. 262-272, 1997.
[37] 熊寧, 程浩忠, 胡澤春, 俞國勤 and 祝達康. “基於PSS/E 的最大負荷極限的求解方法.” 電力系統保護與控制, Vol. 36, No. 20, pp. 1-4, 2008.
[38] Chiang, Hsiao-Dong, C-S. Wang, and Alexander J. Flueck. “Look-ahead voltage and load margin contingency selection functions for large-scale power systems.” IEEE Trans. on Power Systems, Vol. 12, No. 1, pp. 173-180, 1997.
[39] 張揚, and 杜振東. “電力系統仿真軟件PSS/E 簡介.” 華東電力, Vol. 25, No. 1, pp. 6-9, 1997.
[40] Monticelli, A., M. V. F. Pereira, and S. Granville. “Security-constrained optimal power flow with post-contingency corrective rescheduling.” IEEE Trans. on Power Systems, Vol. 2, No. 1, pp. 175-180, 1987.