Polynomial Line Outage Distribution Factors for Estimating Expected Congestion and Security

Extreme weather events and simultaneous k faults pose significant challenges to the security of the power system, leading to sudden line congestion. Conventionally, Line Outage Distribution Factors (LODFs) are used to compute post-fault line flows. However, as k increases, the complexity and number of required matrix inversions make these computations impractical for large systems. This paper introduces a polynomial approximation for LODFs, a method that efficiently combines and multiplies the matrices corresponding to single-line faults using Taylor series expansion. This method is faster than performing matrix inversions for each fault scenario. Moreover, we apply polynomial LODFs to compute expected line flows and enhance probabilistic security, reducing computational demands by decomposing N-k faults into repeating basis functions. Case studies on 118-, 300-, 1354- and 2328-bus systems demonstrate the accuracy and computational superiority of polynomial LODFs in assessing expected congestion and security. These findings are a first step towards managing the reliability and efficiency of power systems in the face of increasing extreme weather events.