Incorporating System Frequency Dynamics into Real-time Locational Marginal Pricing of Electricity

This paper presents a method to generalize locational marginal prices (LMPs) to embed the impact of system frequency dynamics into real-time electricity markets. The proposed frequency dynamics-aware LMPs can help to mitigate costs associated with setting aside ever more reserve capacity to offset larger, faster, and more frequent transient excursions arising from greater renewable integration. We formulate a dynamics-aware economic dispatch (ED) by augmenting a traditional static ED with constraints pertinent to system frequency dynamics, including those from inertial response, primary frequency control, and the automatic generation control. We show that, similar to their traditional static counterparts, dynamics-aware LMPs are composed of Lagrange multipliers associated with the power balance and transmission line power flow constraints. Furthermore, through analysis, we detail dynamic and steady-state behaviours of dynamics-aware LMPs. Finally, numerical simulations involving standard test systems validate our findings, confirm added revenue opportunities for generators contributing to frequency support, and demonstrate computational scalability.