Frequency Dynamics-aware Real-time Marginal Pricing of Electricity Under Uncertainty

This paper presents a real-time electricity marginal pricing method that captures the impact of frequency dynamics in the presence of i) aggressive net-load variability and ii) substantial net-load forecast uncertainty, both made more likely by extensive renewable integration. The proposed method augments a traditional economic dispatch with constraints pertaining to system frequency dynamics and explicit models for the net-load forecast uncertainty, while minimizing the sum of expected operation cost and expected frequency deviations from the synchronous speed across the scheduling horizon of interest. Chance constraints in the modified problem dictate the tolerable probability of violating lower and upper limits of dynamic system frequency and generator outputs. To facilitate solution efficiency, the chance-constrained economic dispatch transforms into a deterministic optimization problem under the assumption that the uncertainty in the net-load forecast is Gaussian. The effectiveness of the proposed model is demonstrated through case studies based on the Western System Coordinating Council test system. The results show that the proposed pricing method can reflect the impact of transient frequency deviations, yield greater profits for generators, and hedge against net-load uncertainty.