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Description
The optimal power flow problem lies at the intersection of power system engineering and operations research. Its application areas compromise expansion planning, operation, market clearing, network resiliency and unit commitment. Optimal power flow calculates optimal generator power and voltage setpoints to minimize the cost of system losses and costs of power generation. Security-constrained optimal power flow (SC-OPF) [1] calculates an optimal power flow which will not break any current or voltage limits in case of one of the n-1 anticipated scenarios of system state due to a line fault or generator shutdown.
The security-constrained optimal power flow is modeled as a nonlinear program (NLP), which minimizes the economic dispatch under the constraints of maintaining power balance for active and reactive power as well as voltage and current bounds across the network. Any deviation from the bounds enter the objective function as penalties.
For the solution of SC-OPF problem we compare a holistic formulation with a scenario-based formulation. The scenario-based formulation allows for Benders decomposition [2,3] to decouple the base problem (also called master problem) from the scenarios (also called subproblems). Benders decomposition solves the SC-OPF problem in an iterative procedure, alternating between base problem and scenarios.
The performance of holistic approach and Benders decomposition approach are evaluated on multiple IEEE example networks [4] in terms of solution quality, speed and robustness.
[1] J. K. Skolfield and A. R. Escobedo, “Operations research in optimal power flow: A guide to recent and emerging methodologies and applications,” European Journal of Operational Research, vol. 300, no. 2, pp. 387–404, 2022.
[2] S. Cvijic and J. Xiong, “Security constrained unit commitment and economic dispatch through benders decomposition: A comparative study,” in 2011 IEEE Power and Energy Society General Meeting, pp. 1–8, 201
[3] M. G. R. Rahmaniani, T.G. Crainic and W. Rei, “The benders decomposition algorithm: A literature review,” Cirrelt, 2016
[4] F. Li and R. Bo, “Small test systems for power system economic studies,” in IEEE PES General Meeting, pp. 1–4, 2010
