Optimal Investments to Improve Grid Resilience Considering Initial Transient Response and Long-term Restoration

This paper presents a multi-time period two-stage stochastic mixed-integer linear optimization model which determines the optimal hardening investments to improve power system resilience to natural disaster threat scenarios. The input to the optimization model is a set of scenarios for specific natural disaster events, that is based on historical data. The objective of the optimization model is to minimize the expected weighted load shed from the initial impact and the restoration process over all scenarios. The optimization model considers the initial impact of the severe event by using electromechanical transient dynamic simulations. The initial impact weighted load shed is determined by the transient simulation, which allows for secondary transients from protection devices and cascading failures. The rest of the event, after the initial shock, is modeled in the optimization with a multi-time period dc optimal power flow (DCOPF) which is initialized with the solution from the dynamic simulation. The first stage of the optimization model determines the optimal investments. The second stage, given the investments, determines the optimal unit commitment, generator dispatch, and transmission line switching during the multi-time period restoration process to minimize the weighted load shed over all scenarios. Note, an investment will change the transient simulation result, and therefore change the initialization to the DCOPF restoration model. The investment optimization model encompasses both the initial impact (dynamic transient simulation results) and the restoration period (DCOPF) of the event, as components come back online. The model is tested on the IEEE RTS-96 system.