Fair Blackout Rotation for Distribution Systems under Extreme Weather Events

This paper presents an optimization-based method for scheduling fair blackout rotation for distribution systems under extreme-weather induced power shortages. The method first partitions the system into a set of feeder sections according to the locations of switches, then simplifies the system as a connected network by modeling feeder sections as nodes and switches as links. The method simultaneously minimizes the total lost energy, total number of switch operations, maximal section isolation duration, and maximal section isolation frequencies of the system, while minimizing the maximal deviations of isolation durations and frequencies between any two feeder sections. The multiple-objective model is converted into a single objective one through defining each objective’s satisfaction degree using a generalized Rectified Linear Unit (ReLU) function. The resulted nonlinear model is further converted into a standard mixed integer linear programming by replacing each nonlinear item including satisfaction function, binary variable operation, and logic operation with an embedded optimization problem with a linear objective function constrained by its feasible region represented using linear equations. The method can be implemented either using a static horizon or rolling horizon strategy. The numerical examples on the modified IEEE 123-node test feeder are given to demonstrate the effectiveness of the proposed method.