Generalized Wardrop Equilibrium for Charging Station Selection and Route Choice of Electric Vehicles in Joint Power Distribution and Transportation Networks

TL;DR

This paper models the complex interactions between electric vehicles, charging stations, and power and transportation networks as a generalized game, proposing a decentralized algorithm to find equilibrium and analyzing its properties and impacts.

Contribution

It introduces a generalized Wardrop equilibrium model for joint EV charging and route choice considering power and transportation network constraints, with a decentralized learning algorithm and convergence proof.

Findings

Existence and convergence of the equilibrium are proven.

Numerical studies demonstrate the impact of network characteristics on demand and prices.

The model captures interdependencies between EV decisions, congestion, and pricing.

Abstract

This paper presents the equilibrium analysis of a game composed of heterogeneous electric vehicles (EVs) and a power distribution system operator (DSO) as the players, and charging station operators (CSOs) and a transportation network operator (TNO) as coordinators. Each EV tries to pick a charging station as its destination and a route to get there at the same time. However, the traffic and electrical load congestion on the roads and charging stations lead to the interdependencies between the optimal decisions of EVs. CSOs and the TNO need to apply some tolling to control such congestion. On the other hand, the pricing at charging stations depends on real-time distributional locational marginal pricing, which is determined by the DSO after solving the optimal power flow over the power distribution network. This paper also takes into account the local and the coupling/infrastructure constraints of EVs, transportation and distribution networks. This problem is modeled as a generalized aggregative game, and then a decentralized learning method is proposed to obtain an equilibrium point of the game, which is known as variational generalized Wardrop equilibrium. The existence of such an equilibrium point and the convergence of the proposed algorithm to it are proven. We undertake numerical studies on the Savannah city model and the IEEE 33-bus distribution network and investigate the impact of various characteristics on demand and prices.