Competitive Equilibrium for Electricity Markets with Spatially Flexible Loads

Electric vehicle charging and geo-distributed datacenters introduce spatially flexible loads (FLs) that couple power, transportation, and datacenter networks. These couplings create a closed-loop feedback between locational marginal prices (LMPs) and decisions of the FL systems, challenging the foundations of conventional competitive equilibrium (CE) in electricity markets. This paper studies a notion of generalized competitive equilibrium (GCE) that aims to capture such price-demand interactions across the interconnected infrastructures. We establish structural conditions under which the GCE preserves key properties of the conventional CE, including existence, uniqueness, and efficiency, without requiring detailed knowledge of decision processes for individual FL systems. The framework generalizes to settings where the grid is coupled with multiple FL systems. Stylized examples and case studies on the New York ISO grid, coupled with the Sioux Falls transportation and distributed datacenter networks, demonstrate the use of our theoretical framework and illustrate the mutual influence among the grid and the studied FL systems.

💡 Research Summary

This paper investigates the emerging class of spatially flexible loads (FLs) – exemplified by electric‑vehicle (EV) charging and geo‑distributed data centers – and their two‑way interaction with wholesale electricity markets. Traditional competitive equilibrium (CE) theory assumes exogenous, location‑fixed demand, so locational marginal prices (LMPs) serve as price signals that align generation decisions with social welfare. FLs, however, can relocate their electricity consumption in response to LMPs, and the resulting spatial load profile feeds back into the LMP calculation, breaking the one‑way assumption of classical CE.

To address this, the authors introduce a Generalized Competitive Equilibrium (GCE) framework. The power system is modeled with N buses, M transmission lines, generators with convex cost functions, and fixed inelastic loads. An FL system is abstracted by a decision vector x∈X (convex, compact) and a linear mapping s = A_FL x that translates internal decisions into nodal power consumption. A strictly convex “preference” function Φ(x) captures the internal cost or disutility of the FL system independent of electricity price. The FL’s best response to a price vector λ is defined as the solution of a convex optimization problem that trades off Φ(x) against electricity expenditure λᵀA_FL x.

From this, a value function J(s) = min_{x∈X, A_FL x=s} Φ(x) is derived; J(s) is also strictly convex. The aggregate FL response can then be expressed as σ(λ) = arg min_{s∈S}