Chance-Constrained Real-Time Pricing of Reserves Incorporating System Frequency Dynamics

This paper presents a method to internalize the impact of system frequency dynamics into real-time pricing of reserves. The proposed frequency dynamics-aware price of reserves helps to incentivize and compensate generators for setting aside reserves that contribute to de-risking real-time dynamic performance subject to uncertainty in the net-load forecast. Central to the proposed method is to augment a static chance-constrained economic dispatch (CCED) with constraints modelling system frequency dynamics driven by generator inertia response along with primary and secondary frequency controls. Chance constraints in the resulting dynamics-aware CCED enforce tolerable probability of dynamic system frequency and generator power trajectories violating their respective limits. We show that the dynamics-aware price of reserves internalizes uncertainty in dynamic state variables along with the risk of violating limits in frequency excursions and generator outputs during frequency transients as well as in steady state. We also assess the sensitivity of the dynamics-aware price of reserves with respect to generator parameters that directly affect system dynamic performance. Numerical case studies involving the Western System Coordinating Council and New England test systems confirm dynamics in the proposed price of reserves, reveal additional revenue for generators, and demonstrate computational scalability.