Chain Rule for Extracting Resilience Procurement Costs from Locational Marginal Prices

Power system resilience procurement costs in $N$ - $k$ contingencies have gained more prominence as number of extreme events continues to increase. A chain rule is presented in this paper for extracting resilience procurement costs from a fully decomposed locational marginal price (LMP) model. First, power transfer distribution factor (PTDF) matrices with AC power flow (i.e., AC-PTDF) are determined. AC-PTDF and AC-LODF (line outage distribution factor) equations are derived for $N$ - $k$ contingencies and a fully decomposed LMP model is developed where generation and transmission security components are established for specific contingencies. Furthermore, resilience procurement costs can be measured at different buses for the proposed security components. Impact of $N$ - $k$ contingencies on resilience procurement costs at specific buses can be determined as proposed security components will gain more insight for resilience procurement in power systems. The modified IEEE 6-bus and 118-bus systems are adopted to verify effectiveness of the proposed resilience procurement method.