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

TL;DR

The paper tackles the challenge of pricing Short-Circuit Current (SCC) support in power systems undergoing high inverter-based resource penetration, where Unit Commitment (UC) non-convexity complicates pricing. It introduces a Primal-Dual (P-D) formulation that preserves UC integrality while deriving explicit SCC shadow prices through a four-step process that linearizes bilinear terms, relaxes binaries, derives the dual, and minimizes the duality gap to recover integer solutions. The approach yields accurate SCC prices (e.g., at critical buses like 26) and avoids spurious signals and uplift payments observed in existing methods such as Dispatchable and Restricted pricing. Case studies on a modified IEEE 30-bus system demonstrate that the P-D method delivers interpretable, economically meaningful SCC remuneration for SCC-contributing units, including synchronous condensers, and offers a more reliable framework for integrating SCC pricing with other ancillary services. Overall, the Primal-Dual formulation provides a practical, integrality-preserving approach to SCC pricing with tangible economic and reliability benefits in modern grids.

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.

Figures (7)

• Figure 1: Lowest SCC of buses without constraints in one-day operation.
• Figure 2: SCC prices for critical buses with P-D and dispatchable methods. The SCC price with the P-D method for bus 26 at 03:00 is 83.22 k€/p.u. The price for all other buses is zero in both methods.
• Figure 3: Variation in system operation cost as reflected by '$\psi_{g,t}^{\textrm{max}}$', due to the commitment of units in buses 27 and 30.
• Figure 4: Daily SCC revenue of each SG with the two pricing methods.
• Figure 5: Commitment price for SGs under the restricted method. The price for units in buses 27 and 30 is always positive.