A Framework for Inertia Pricing in Renewable-Rich Power Systems Using Convex Hull Pricing

With the rapid development of power systems rich in renewable energy, inertia shortages pose significant challenges to frequency security. There is an urgent need for appropriate market pricing mechanisms to quantify the economic value of inertia and incentivize inertia resources to participate in system frequency regulation. Existing market pricing mechanisms struggle to address non-convex generation scheduling problems involving inertia constraints, often resulting in substantial uplift payments that undermine market efficiency and reduce market transparency. To address this issue, this paper proposes a novel convex hull pricing framework specifically designed for the integrated energy–inertia market. The core innovation lies in combining Dantzig–Wolfe decomposition with column generation algorithms to efficiently solve non-convex optimization problems by dynamically constructing the convex hull of feasible dispatch schemes. Based on transient frequency security metrics, the method derives the minimum inertia requirement constraint for the system and calculates the economic value of inertia in non-convex markets using convex hull pricing. Simulation studies on a modified IEEE 39-node system demonstrate two major breakthroughs: the method accurately assesses the economic value of synchronous inertia, with prices reflecting scarcity as wind penetration increases and significantly reduces total system uplift payments compared to integer relaxation pricing schemes. Consequently, this research provides a transparent, incentive-compatible, and cost-effective tool for designing and operating future inertia ancillary service markets.