Frequency dynamics-aware real-time marginal pricing of electricity

This paper presents a frequency dynamics-aware marginal pricing method for real-time electricity markets. The proposed method captures the impact of system frequency dynamics on the marginal price of electricity in the presence of aggressive net-load variations made more likely by greater renewable integration. We formulate a dynamics-aware economic dispatch (ED) by augmenting the traditional single-snapshot ED with constraints pertaining to system frequency dynamics, and frequency deviations from the synchronous speed are penalized in the modified objective function. The resulting ED embeds two distinct time steps to optimize over fast system dynamics and slower decisions on generator set-points. We prove that the dynamics-aware marginal price is the (suitably scaled) Lagrange multiplier of the power balance constraint and that it converges in steady state to the marginal price obtained from traditional ED solved with comparable system load. Numerical case studies involving the Western System Coordinating Council test system validate our findings and confirm added revenue opportunities for generators contributing to frequency regulation.