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1

Thomas, James Jamal, and Santiago Grijalva. "Flexible Security-Constrained Optimal Power Flow." IEEE Transactions on Power Systems 30, no. 3 (May 2015): 1195–202. http://dx.doi.org/10.1109/tpwrs.2014.2345753.

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2

Harsan, H., N. Hadjsaid, and P. Pruvot. "Cyclic security analysis for security constrained optimal power flow." IEEE Transactions on Power Systems 12, no. 2 (May 1997): 948–53. http://dx.doi.org/10.1109/59.589787.

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3

Fu, Cong, Yashan Zhong, Pingping Zhang, Xiangzhen He, Yun Yang, and Jian Zuo. "VSC-HVDC Incorporated Corrective Security-Constrained Optimal Power Flow." Journal of Physics: Conference Series 2320, no. 1 (August 1, 2022): 012006. http://dx.doi.org/10.1088/1742-6596/2320/1/012006.

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Abstract With the rapid development and diverse engineering applications of VSC-HVDC technology, development in power industry has put forward higher economic and security requirements for the security-constrained optimal power flow. Under these circumstances, this paper proposes a security-constrained optimal power flow model for hybrid AC/DC power grids that incorporates the VSC-HVDC corrective control. The linear relationship between the pre-contingency state power flow and post-contingency state power flow is established based on the shift factor and the reliability constraints are described as the linear inequality constraints of the post-contingency state active power flow which is expressed by the pre-contingency state branch power flow. With the inherent ability of the VSC-HVDC converter station (short as VSC station) to rapidly regulate active power taken into account, this paper utilizes the linear relationship between the active power adjustment of the VSC station and the power flows of transmission lines and electrical equipment and corrects the reliability constraints with the sensitivity coefficient. Hence the correction of the post-contingency state power flow is reflected in the constraints. By solving the proposed model with the primal-dual interior-point method, the pre-contingency state optimal security operating point that considers the corrective capability of the VSC stations is obtained. Finally, the correctness and validity of the proposed model is verified based on a VSC-HVDC modified IEEE 14-bus system.
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4

Mohammadi, Javad, Gabriela Hug, and Soummya Kar. "Agent-Based Distributed Security Constrained Optimal Power Flow." IEEE Transactions on Smart Grid 9, no. 2 (March 2018): 1118–30. http://dx.doi.org/10.1109/tsg.2016.2577684.

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5

Gutierrez-Martinez, Victor J., Claudio A. Canizares, Claudio R. Fuerte-Esquivel, Alejandro Pizano-Martinez, and Xueping Gu. "Neural-Network Security-Boundary Constrained Optimal Power Flow." IEEE Transactions on Power Systems 26, no. 1 (February 2011): 63–72. http://dx.doi.org/10.1109/tpwrs.2010.2050344.

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6

Correa-Posada, Carlos M., and Pedro Sanchez-Martin. "Security-Constrained Optimal Power and Natural-Gas Flow." IEEE Transactions on Power Systems 29, no. 4 (July 2014): 1780–87. http://dx.doi.org/10.1109/tpwrs.2014.2299714.

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7

Somasundaram, P., K. Kuppusamy, and R. P. Kumudini Devi. "Evolutionary programming based security constrained optimal power flow." Electric Power Systems Research 72, no. 2 (December 2004): 137–45. http://dx.doi.org/10.1016/j.epsr.2004.02.006.

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8

Vaahedi, E., Y. Mansour, C. Fuchs, S. Granville, M. D. L. Latore, and H. Hamadanizadeh. "Dynamic security constrained optimal power flow/VAr planning." IEEE Transactions on Power Systems 16, no. 1 (2001): 38–43. http://dx.doi.org/10.1109/59.910779.

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9

Binkou, Alhabib, and Yixin Yu. "Security constrained distributed optimal power flow of interconnected power systems." Transactions of Tianjin University 14, no. 3 (June 2008): 208–16. http://dx.doi.org/10.1007/s12209-008-0038-2.

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10

Li, Hang, Zhe Zhang, Xianggen Yin, and Buhan Zhang. "Preventive Security-Constrained Optimal Power Flow with Probabilistic Guarantees." Energies 13, no. 9 (May 8, 2020): 2344. http://dx.doi.org/10.3390/en13092344.

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The traditional security-constrained optimal power flow (SCOPF) model under the classical N-1 criterion is implemented in the power industry to ensure the secure operation of a power system. However, with increasing uncertainties from renewable energy sources (RES) and loads, the existing SCOPF model has difficulty meeting the practical requirements of the industry. This paper proposed a novel chance-constrained preventive SCOPF model that considers the uncertainty of power injections, including RES and load, and contingency probability. The chance constraint is used to constrain the overall line flow within the limits with high probabilistic guarantees and to significantly reduce the constraint scales. The cumulant and Johnson systems were combined to accurately approximate the cumulative distribution functions, which is important in solving chance-constrained optimization problems. The simulation results show that the model proposed in this paper can achieve better performance than traditional SCOPF.
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11

Salem, Reham H., M. Ezzat Abdelrahman, and Almoataz Y. Abdelaziz. "Security constrained optimal power flow by modern optimization tools." International Journal of Engineering, Science and Technology 9, no. 3 (June 26, 2017): 22. http://dx.doi.org/10.4314/ijest.v9i3.3.

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12

de Magalhaes Carvalho, Leonel, Armando Martins Leite da Silva, and Vladimiro Miranda. "Security-Constrained Optimal Power Flow via Cross-Entropy Method." IEEE Transactions on Power Systems 33, no. 6 (November 2018): 6621–29. http://dx.doi.org/10.1109/tpwrs.2018.2847766.

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13

Wu, Xi, Zhengyu Zhou, Gang Liu, Wanchun Qi, and Zhenjian Xie. "Preventive Security-Constrained Optimal Power Flow Considering UPFC Control Modes." Energies 10, no. 8 (August 13, 2017): 1199. http://dx.doi.org/10.3390/en10081199.

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14

Monticelli, A., M. V. F. Pereira, and S. Granville. "Security-Constrained Optimal Power Flow with Post-Contingency Corrective Rescheduling." IEEE Power Engineering Review PER-7, no. 2 (February 1987): 43–44. http://dx.doi.org/10.1109/mper.1987.5527553.

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15

Dvorkin, Yury, Pierre Henneaux, Daniel S. Kirschen, and Hrvoje Pandzic. "Optimizing Primary Response in Preventive Security-Constrained Optimal Power Flow." IEEE Systems Journal 12, no. 1 (March 2018): 414–23. http://dx.doi.org/10.1109/jsyst.2016.2527726.

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16

Capitanescu, Florin, Mevludin Glavic, Damien Ernst, and Louis Wehenkel. "Contingency Filtering Techniques for Preventive Security-Constrained Optimal Power Flow." IEEE Transactions on Power Systems 22, no. 4 (November 2007): 1690–97. http://dx.doi.org/10.1109/tpwrs.2007.907528.

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17

Monticelli, A., M. V. F. Pereira, and S. Granville. "Security-Constrained Optimal Power Flow with Post-Contingency Corrective Rescheduling." IEEE Transactions on Power Systems 2, no. 1 (1987): 175–80. http://dx.doi.org/10.1109/tpwrs.1987.4335095.

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18

Zhang, Rui, Yan Xu, Mingyong Lai, Zhao Yang Dong, and Kit Po Wong. "Hybrid computation of corrective security-constrained optimal power flow problems." IET Generation, Transmission & Distribution 8, no. 6 (June 1, 2014): 995–1006. http://dx.doi.org/10.1049/iet-gtd.2013.0384.

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19

Devaraj, D., and J. Preetha Roselyn. "Improved genetic algorithm for voltage security constrained optimal power flow problem." International Journal of Energy Technology and Policy 5, no. 4 (2007): 475. http://dx.doi.org/10.1504/ijetp.2007.014888.

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20

Chunduri, Rambabu, Y. P. Obulesu, and Ch Saibabu. "Particle swarm optimisation for security constrained optimal power flow including TCSC." International Journal of Power and Energy Conversion 5, no. 3 (2014): 298. http://dx.doi.org/10.1504/ijpec.2014.063202.

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21

Won, Jong-Ryul, and Kil Choi. "Security-Constrained Optimal Power Flow Using First-Order Contingency Sensitivity Matrix." IFAC Proceedings Volumes 36, no. 20 (September 2003): 1019–23. http://dx.doi.org/10.1016/s1474-6670(17)34608-6.

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22

Wang, Qin, James D. McCalley, and Wanning Li. "Voltage instability performance of risk-based security constrained optimal power flow." Electric Power Systems Research 116 (November 2014): 45–53. http://dx.doi.org/10.1016/j.epsr.2014.04.006.

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23

Chavez-Lugo, Miguel, Claudio R. Fuerte-Esquivel, Claudio A. Canizares, and Victor J. Gutierrez-Martinez. "Practical Security Boundary-Constrained DC Optimal Power Flow for Electricity Markets." IEEE Transactions on Power Systems 31, no. 5 (September 2016): 3358–68. http://dx.doi.org/10.1109/tpwrs.2015.2504870.

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24

Velay, M., M. Vinyals, Y. Besanger, and N. Retiere. "Fully distributed security constrained optimal power flow with primary frequency control." International Journal of Electrical Power & Energy Systems 110 (September 2019): 536–47. http://dx.doi.org/10.1016/j.ijepes.2019.03.028.

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25

Marcelino, Carolina G., Paulo E. M. Almeida, Elizabeth F. Wanner, Manuel Baumann, Marcel Weil, Leonel M. Carvalho, and Vladimiro Miranda. "Solving security constrained optimal power flow problems: a hybrid evolutionary approach." Applied Intelligence 48, no. 10 (April 17, 2018): 3672–90. http://dx.doi.org/10.1007/s10489-018-1167-5.

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26

Sharifzadeh, Hossein, and Nima Amjady. "Stochastic security-constrained optimal power flow incorporating preventive and corrective actions." International Transactions on Electrical Energy Systems 26, no. 11 (March 22, 2016): 2337–52. http://dx.doi.org/10.1002/etep.2207.

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27

Pandya, Sundaram B., James Visumathi, Miroslav Mahdal, Tapan K. Mahanta, and Pradeep Jangir. "A Novel MOGNDO Algorithm for Security-Constrained Optimal Power Flow Problems." Electronics 11, no. 22 (November 21, 2022): 3825. http://dx.doi.org/10.3390/electronics11223825.

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The current research investigates a new and unique Multi-Objective Generalized Normal Distribution Optimization (MOGNDO) algorithm for solving large-scale Optimal Power Flow (OPF) problems of complex power systems, including renewable energy sources and Flexible AC Transmission Systems (FACTS). A recently reported single-objective generalized normal distribution optimization algorithm is transformed into the MOGNDO algorithm using the nondominated sorting and crowding distancing mechanisms. The OPF problem gets even more challenging when sources of renewable energy are integrated into the grid system, which are unreliable and fluctuating. FACTS devices are also being used more frequently in contemporary power networks to assist in reducing network demand and congestion. In this study, a stochastic wind power source was used with different FACTS devices, including a static VAR compensator, a thyristor- driven series compensator, and a thyristor—driven phase shifter, together with an IEEE-30 bus system. Positions and ratings of the FACTS devices can be intended to reduce the system’s overall fuel cost. Weibull probability density curves were used to highlight the stochastic character of the wind energy source. The best compromise solutions were obtained using a fuzzy decision-making approach. The results obtained on a modified IEEE-30 bus system were compared with other well-known optimization algorithms, and the obtained results proved that MOGNDO has improved convergence, diversity, and spread behavior across PFs.
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28

Gan, D., R. J. Thomas, and R. D. Zimmerman. "Stability-constrained optimal power flow." IEEE Transactions on Power Systems 15, no. 2 (May 2000): 535–40. http://dx.doi.org/10.1109/59.867137.

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29

Azevedo, Anibal T. de, Carlos A. Castro, Aurelio R. L. Oliveira, and Secundino Soares. "Security constrained optimal active power flow via network model and interior point method." Sba: Controle & Automação Sociedade Brasileira de Automatica 20, no. 2 (June 2009): 206–16. http://dx.doi.org/10.1590/s0103-17592009000200008.

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This paper presents a new formulation for the security constrained optimal active power flow problem which enables the representation of three basic constraints: branch outage, generator outage and multiple equipment congestion. It consists of a network model with additional linear equality and inequality constraints and quadratic separable objective function, which is efficiently solved by a predictor-corrector interior point method. Sparsity techniques are used to exploit the matricial structure of the problem.Case studies with a 3,535-bus and a 4,238-branch Brazilian power system are presented and discussed, to demonstrate that the proposed model can be efficiently solved by an interior point method, providing security constrained solutions in a reasonable time.
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30

Minh Le, Phuong, Thanh Long Duong, Dieu Ngoc Vo, Tung Thanh Le, and Sy Quoc Nguyen. "An Efficient Hybrid Method for Solving Security-Constrained Optimal Power Flow Problem." International Journal on Electrical Engineering and Informatics 12, no. 4 (December 31, 2020): 933–55. http://dx.doi.org/10.15676/ijeei.2020.12.4.14.

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The optimal operation for different states such as normal and contingency cases of a power system has a very important role in the operation. Therefore, it is necessary to analyze contingencies in the system so as the most severe cases should be considered for integrating into the optimal power flow (OPF) problem and the security-constrained optimal power flow (SCOPF) becomes an important problem for considering in the power system operation. This paper proposes a combined pseudo-gradient based particle swarm optimization with constriction factor (PGPSO) and the differential evolution (DE) method for solving the SCOPF problem. The PGPSO-DE method is a newly developed method for utilizing the advantages of the pseudogradient guided PSO method with a constriction factor and the DE method. The proposed PGPSO-DE has been tested on the IEEE 30 bus system for the normal case and the contingency case with two types of the objective function. The results yielded from the proposed method have been validated via comparing to those from the conventional PSO, DE, and other methods reported in the literature. The comparisons for the results obtained from the proposed PGPSODE method have shown that it is very effective to solve the large-scale and complex SCOPF problem.
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31

Velloso, Alexandre, Pascal Van Hentenryck, and Emma S. Johnson. "An exact and scalable problem decomposition for security-constrained optimal power flow." Electric Power Systems Research 195 (June 2021): 106677. http://dx.doi.org/10.1016/j.epsr.2020.106677.

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32

Sakthivel, S., K. Kavipriya, P. Poovarasi, and B. Prema. "Application of Fruit Fly Algorithm for Security Constrained Optimal Power Flow Problem." International Journal of Computer Applications 162, no. 12 (March 15, 2017): 16–21. http://dx.doi.org/10.5120/ijca2017913420.

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33

Degeneff, R. C., W. Neugebauer, C. H. Saylor, and S. L. Corey. "Security constrained optimization: an added dimension in utility systems optimal power flow." IEEE Computer Applications in Power 1, no. 4 (October 1988): 26–30. http://dx.doi.org/10.1109/67.20549.

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34

Weinhold, Richard, and Robert Mieth. "Fast Security-Constrained Optimal Power Flow Through Low-Impact and Redundancy Screening." IEEE Transactions on Power Systems 35, no. 6 (November 2020): 4574–84. http://dx.doi.org/10.1109/tpwrs.2020.2994764.

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35

Capitanescu, Florin, and Louis Wehenkel. "Improving the Statement of the Corrective Security-Constrained Optimal Power-Flow Problem." IEEE Transactions on Power Systems 22, no. 2 (May 2007): 887–89. http://dx.doi.org/10.1109/tpwrs.2007.894850.

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36

Ardakani, Ali Jahanbani, and Francois Bouffard. "Identification of Umbrella Constraints in DC-Based Security-Constrained Optimal Power Flow." IEEE Transactions on Power Systems 28, no. 4 (November 2013): 3924–34. http://dx.doi.org/10.1109/tpwrs.2013.2271980.

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37

Thitithamrongchai, C., and B. Eua-Arporn. "Security-constrained Optimal Power Flow: A Parallel Self-adaptive Differential Evolution Approach." Electric Power Components and Systems 36, no. 3 (February 21, 2008): 280–98. http://dx.doi.org/10.1080/15325000701603942.

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38

Galvani, Sadjad, Vahid Talavat, and Saeed Rezaeian Marjani. "Preventive/Corrective Security Constrained Optimal Power Flow Using a Multiobjective Genetic Algorithm." Electric Power Components and Systems 46, no. 13 (August 9, 2018): 1462–77. http://dx.doi.org/10.1080/15325008.2018.1489432.

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39

Sun, Guoqiang, Sheng Chen, Zhinong Wei, Kwok W. Cheung, and Haixiang Zang. "Corrective Security-Constrained Optimal Power and Gas Flow With Binding Contingency Identification." IEEE Transactions on Sustainable Energy 11, no. 2 (April 2020): 1033–42. http://dx.doi.org/10.1109/tste.2019.2917016.

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40

Alizadeh, Mohammad Iman, Muhammad Usman, and Florin Capitanescu. "Envisioning security control in renewable dominated power systems through stochastic multi-period AC security constrained optimal power flow." International Journal of Electrical Power & Energy Systems 139 (July 2022): 107992. http://dx.doi.org/10.1016/j.ijepes.2022.107992.

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41

Roselyn, J. Preetha, D. Devaraj, and Subhransu Sekhar Dash. "Multi-Objective Differential Evolution for Voltage Security Constrained Optimal Power Flow in Deregulated Power Systems." International Journal of Emerging Electric Power Systems 14, no. 6 (November 2, 2013): 591–607. http://dx.doi.org/10.1515/ijeeps-2013-0086.

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Abstract Voltage stability is an important issue in the planning and operation of deregulated power systems. The voltage stability problems is a most challenging one for the system operators in deregulated power systems because of the intense use of transmission line capabilities and poor regulation in market environment. This article addresses the congestion management problem avoiding offline transmission capacity limits related to voltage stability by considering Voltage Security Constrained Optimal Power Flow (VSCOPF) problem in deregulated environment. This article presents the application of Multi Objective Differential Evolution (MODE) algorithm to solve the VSCOPF problem in new competitive power systems. The maximum of L-index of the load buses is taken as the indicator of voltage stability and is incorporated in the Optimal Power Flow (OPF) problem. The proposed method in hybrid power market which also gives solutions to voltage stability problems by considering the generation rescheduling cost and load shedding cost which relieves the congestion problem in deregulated environment. The buses for load shedding are selected based on the minimum eigen value of Jacobian with respect to the load shed. In the proposed approach, real power settings of generators in base case and contingency cases, generator bus voltage magnitudes, real and reactive power demands of selected load buses using sensitivity analysis are taken as the control variables and are represented as the combination of floating point numbers and integers. DE/randSF/1/bin strategy scheme of differential evolution with self-tuned parameter which employs binomial crossover and difference vector based mutation is used for the VSCOPF problem. A fuzzy based mechanism is employed to get the best compromise solution from the pareto front to aid the decision maker. The proposed VSCOPF planning model is implemented on IEEE 30-bus system, IEEE 57 bus practical system and IEEE 118 bus system. The pareto optimal front obtained from MODE is compared with reference pareto front and the best compromise solution for all the cases are obtained from fuzzy decision making strategy. The performance measures of proposed MODE in two test systems are calculated using suitable performance metrices. The simulation results show that the proposed approach provides considerable improvement in the congestion management by generation rescheduling and load shedding while enhancing the voltage stability in deregulated power system.
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42

Javanbakht, Pirooz, and Salman Mohagheghi. "A risk-averse security-constrained optimal power flow for a power grid subject to hurricanes." Electric Power Systems Research 116 (November 2014): 408–18. http://dx.doi.org/10.1016/j.epsr.2014.07.018.

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43

Velloso, Alexandre, and Pascal Van Hentenryck. "Combining Deep Learning and Optimization for Preventive Security-Constrained DC Optimal Power Flow." IEEE Transactions on Power Systems 36, no. 4 (July 2021): 3618–28. http://dx.doi.org/10.1109/tpwrs.2021.3054341.

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44

Liu, Daichen, Cuo Zhang, Guo Chen, Yan Xu, and Zhao Yang Dong. "Stochastic security-constrained optimal power flow for a microgrid considering tie-line switching." International Journal of Electrical Power & Energy Systems 134 (January 2022): 107357. http://dx.doi.org/10.1016/j.ijepes.2021.107357.

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45

Lyu, Jae-kun, Mun-Kyeom Kim, and Jong-Keun Park. "Security Cost Analysis with Linear Ramp Model using Contingency Constrained Optimal Power Flow." Journal of Electrical Engineering and Technology 4, no. 3 (September 1, 2009): 353–59. http://dx.doi.org/10.5370/jeet.2009.4.3.353.

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46

Capitanescu, F., and L. Wehenkel. "A New Iterative Approach to the Corrective Security-Constrained Optimal Power Flow Problem." IEEE Transactions on Power Systems 23, no. 4 (November 2008): 1533–41. http://dx.doi.org/10.1109/tpwrs.2008.2002175.

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47

Phan, Dzung, and Jayant Kalagnanam. "Some Efficient Optimization Methods for Solving the Security-Constrained Optimal Power Flow Problem." IEEE Transactions on Power Systems 29, no. 2 (March 2014): 863–72. http://dx.doi.org/10.1109/tpwrs.2013.2283175.

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48

Jiang, Quanyuan, and Kai Xu. "A Novel Iterative Contingency Filtering Approach to Corrective Security-Constrained Optimal Power Flow." IEEE Transactions on Power Systems 29, no. 3 (May 2014): 1099–109. http://dx.doi.org/10.1109/tpwrs.2013.2291775.

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49

Phan, Dzung T., and Xu Andy Sun. "Minimal Impact Corrective Actions in Security-Constrained Optimal Power Flow Via Sparsity Regularization." IEEE Transactions on Power Systems 30, no. 4 (July 2015): 1947–56. http://dx.doi.org/10.1109/tpwrs.2014.2357713.

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50

Xu, Yan, Hongming Yang, Rui Zhang, Zhao Yang Dong, Mingyong Lai, and Kit Po Wong. "A contingency partitioning approach for preventive-corrective security-constrained optimal power flow computation." Electric Power Systems Research 132 (March 2016): 132–40. http://dx.doi.org/10.1016/j.epsr.2015.11.012.

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