(637c) A Stochastic Optimization Approach for Improving Power Systems Resilience through Operations and Planning

Electricity is one of the three components of the energy sector, one of sixteen critical infrastructure sectors defined by U.S. Presidential Policy Directive 21. Resilience of the electricity grid is vital for both the economy and public safety and health. Economic operation of power systems alone is difficult. Improving the resilience of the system to a wide range of scenarios (i.e., potential future events) is even more challenging due to the inherent uncertainty in the problem. Additionally, extreme events that disable many system components must be considered as opposed to the traditional N-1 contingency analysis where the system loses one transmission line per scenario [1]. Nominal operations of the system, where the primary manipulated variables are generator setpoints, is generally not enough to make systems resilient to such events. Other operational and planning decisions, such as transmission switching or physical protection of critical components, must be considered, adding even more complexity to the problem through the introduction of binary variables [2].

In this work, we present two-stage stochastic programming formulations for minimizing the consequence of extreme weather events to the electricity grid. While the second stage decisions are made in response to a particular event, the number and flexibility of options for recourse are limited. Therefore, the first stage decisions must be made carefully to make the system resilient to all scenarios. We utilize generator dispatch, transmission switching, and physical protection of transmission lines in the first stage, and we compare the effectiveness of each, along with combinations of the three. A linearized AC transmission model is used in the optimization, resulting in a large-scale stochastic mixed-integer linear program. The effectiveness of the approach is validated with the full nonlinear AC transmission model. The optimization problem is formulated with Pyomo, a flexible, python-based optimization modeling language. The analysis is performed on a real system with thousands of buses and transmission lines, and the scenarios used for the stochastic programming problem are generated with historical outage data.

[1] Jia Kang, John Siirola, Jean-Paul Watson, and Carl Laird, "Parallel Solution of Nonlinear Contingency-constrained Network Problems", Proceedings of, Foundations of Computer-Aided Process Design 2014 (FOCAPD), July, 2014.

[2] Emily B. Fisher, Richard P. Oâ??Neill, and Michael C. Ferris. "Optimal transmission switching." Power Systems, IEEE Transactions on 23.3 (2008): 1346-1355.