Long Duration Battery Sizing, Siting, and Operation Under Wildfire Risk Using Progressive Hedging

Battery sizing and siting problems are computationally challenging due to the need to make long-term planning decisions that are cognizant of short-term operations. This paper considers battery siting, sizing, and operation to maximize their benefits, including price arbitrage and load shed mitigation, during both normal operations and periods with high wildfire ignition risk. We formulate a multi-scenario optimization problem for long duration battery storage while considering the possibility of load shedding during Public Safety Power Shutoff (PSPS) events that de-energize lines to mitigate severe wildfire ignition risk. To enable computationally scalable solution of this problem with many scenarios of wildfire risk and power injection variability, we develop a customized temporal decomposition based on a progressive hedging framework. Extending traditional progressive hedging techniques, we consider coupling in both placement variables across all scenarios and state-of-charge variables at temporal boundaries. This enforces consistency across scenarios while enabling parallel computations despite both spatial and temporal coupling. This facilitates efficient and scalable modeling of a full year of hourly operational decisions to inform sizing and siting batteries. The proposed algorithm models a year of hourly operational decisions to inform optimal battery placement for a 240-bus WECC model in under 19 minutes of computing time.