Dynamic Locational Marginal Emissions via Implicit Differentiation

Anthony Degleris, Stanford University

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Locational marginal emissions rates (LMEs) estimate the rate of change in emissions due to a small change in demand in a transmission network, and are an important metric for assessing the impact of various energy policies or interventions. In this work, we develop a new method for computing the LMEs of an electricity system via implicit differentiation. The method is model agnostic; it can compute LMEs for almost any convex optimization-based dispatch model, including some of the complex dispatch models employed by system operators in real electricity systems. In particular, this method lets us derive LMEs for dynamic dispatch models, i.e., models with temporal constraints such as ramping and storage. We validate the proposed method using real data from the U.S. electricity system and show that incorporating dynamic constraints improves marginal emissions prediction by 8.2%. Finally, simulations on a 240-bus model of WECC demonstrate the relevance of dynamic LMEs in transmission systems with high storage penetration: static LMEs and dynamic LMEs exhibit an average RMS deviation of 28.40%.

Abstract Author(s): Anthony Degleris, Lucas Fuentes Valenzuela, Marco Pavone, Ram Rajagopal, Abbas El Gamal