Locational Marginal Prices Obey DC Circuit Laws

Abstract

Electricity markets often utilize the DC approximation of the AC power flow equations to facilitate solving an otherwise complex nonconvex optimization problem. These DC power flow equations have analogies to DC circuit laws such as Kirchhoff's Laws, resulting in an intuitive understanding of power flows under this model. Variables derived from the Lagrangian dual of the DC optimal power flow problem, such as locational marginal prices (LMPs) and congestion cost, are less intuitive without an understanding of optimization theory. Even with this understanding, LMP behavior, such as the conditions in which negative prices occur or the impact of individual congested lines on network-wide LMPs, remain somewhat mysterious. In this paper, we show that prices also obey DC circuit laws, which can help facilitate an intuitive understanding of their behavior and relationships throughout a network without explicitly understanding duality. In particular, prices can be modeled as voltages, and their differences can be modeled as flows, allowing for a physical interpretation of prices. This analogy also lends itself to the use of well-understood DC circuit concepts such as superposition and Kirchhoff's Laws, which can further facilitate a clearer understanding of price behavior.