Pricing Short-Circuit Current via a Primal-Dual Formulation for Preserving Integrality Constraints

Abstract: Synchronous Generators (SGs) currently provide important levels of Short-Circuit Current (SCC), a critical ancillary service that ensures line protections trip during short-circuit faults. Given the ongoing replacement of SGs by power-electronics-based generation, which have a hard limit for current injection, it has become relevant to optimize the procurement of SCC provided by remaining SGs. Pricing this service is however challenging due to the integrality constraints in Unit Commitment (UC). Existing methods, e.g., dispatchable pricing, restricted pricing and marginal unit pricing, attempt to address this issue but exhibit limitations in handling binary variables, resulting in SCC prices that either fail to cover the operating costs of units or lack interpretability. To overcome these pitfalls, we propose a primal-dual formulation of the SCC-constrained dispatch that preserves the binary nature of UC while effectively computing shadow prices of SCC services. Using a modified IEEE 30-bus system, a comparison is carried out between the proposed approach and the state-of-the-art pricing schemes, highlighting the advantages of the primal-dual method in preserving UC integrality for SCC pricing.