Optimal controlled-islanding with AC power flow constraints: A benders-decomposition approach

The controlled-islanding process aims to prevent large devastating blackouts through an optimal splitting of a power network into smaller islands followed by corrective control actions. Generally, the controlled-islanding problem is cast as a mixed-integer non-linear programming (MINLP) model, which can be prohibitively cumbersome, particularly when it accommodates AC power flow constraints. This paper exploits the Benders decomposition to enhance the mathematical tractability of the problem. The AC power flow constraints are converted to equality constraints using proper auxiliary variables. These new constraints are applied to form a modified Jacobian matrix. The modified equations are embedded in the Benders subproblem involving slack variables in a linear iterative-based optimization structure. Hence, the obtained solution is totally free of any approximation or linearization error. The objective function of the controlled-islanding problem is a combination of total load shedding and generation curtailment of the network. This objective function implicitly mitigates the stability concerns in the islands, which can threaten their steady operation. As opposed to a unique value, adaptive lower bound are considered for the steady-state frequency deviation of islands. This adaptive setting prevents an incomplete frequency recovery after the islanding, considering the reserve capacity of each island. The proposed method yields more practically sound results than a standard mixed-integer linear programming (MILP) model with DC or linearized AC power flow constraints as voltage and apparent power quantities are retained in the permissible ranges. The effectiveness of the proposed algorithm is examined via the IEEE 30-bus test system and a 76-bus case as a part of an actual power system. The time-domain simulation results are also provided to support the accuracy of the frequency stability model captured in the optimization problem.