Benders‐Decomposition‐Based Voltage‐Stability‐Constrained Unit‐Commitment Taking Reactive Power Limit into Account

Abstract

To determine economic-efficient and secure generation schedules, unit commitment (UC) with network and stability constraints will play an important role in the electricity market. We define a voltage-stability-constrained unit commitment problem taking reactive power limit into account (VSCUC-QLIM) since the decreasing of synchronous generators may threat the voltage stability of electricity systems. This VSCUC-QLIM problem is modeled as a mixed-integer nonlinear programming with equilibrium constraints, which is too complex to be solved directly. Therefore, we apply Benders decomposition to solve this complex problem: the master problem consists of the UC problem to determine the commitment states for generators, and the subproblem consists of the voltage-stability-constrained optimal power flow with complementarity constraints problem. However, the subproblem calculation may not converge depending on the commitment states due to the following reasons: (i) any power-flow solution cannot be obtained or (ii) the voltage stability requirement cannot be satisfied on the commitment state given by the master problem. To deal with these difficulties, two partial problems of the subproblem are added as a pre-subproblem and postsubproblem in the proposed method. The combination of these subproblems generate different types of Benders cut depending on the condition. The proposed method was implemented on MATPOWER, and evaluated for daily scheduling on an IEEE six-bus test system and IEEJ standard WEST10 system. The evaluation results validated the effectiveness of the proposed method from the perspective of economic efficiency and voltage stability.