Frequency vulnerability will be prominent in future low-inertia power systems with high renewable penetration, which calls for primary frequency response (PFR) services from a wide range of entities. The challenge, however, is to design effective and fair market mechanisms to incentivize diverse PFR resources. To this end, this paper proposes a PFR ancillary service market mechanism to ensure the security of frequency nadir and quasi-steady-state (QSS) frequency while providing equitable settlements to multiple PFR providers. First, bidding rules are designed for accurate depictions of dynamic performances from diverse PFR resources. Then, a PFR market-clearing model, incorporating frequency security constraints that explicitly express PFR providers' contributions, is developed to deploy sufficient PFR resources while maximizing social welfare. Finally, two unified marginal PFR prices are derived to reflect the scarcity of frequency support capabilities for maintaining frequency nadir and QSS frequency security, enabling fair settlements to successful bidders based on their contributions. Moreover, the pricing and settlement mechanism is theoretically proven incentive-compatible, ensuring the PFR market stability. Case studies verify the proposed PFR market's effectiveness in ensuring frequency security, providing fair incentives to diverse PFR providers, maintaining market stability, and supporting scalable implementations.
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