A Graph Automorphic Approach for Placement and Sizing of Charging Stations in EV Network Considering Traffic

Abstract

This paper proposes a novel graph-based approach with automorphic grouping for the modelling, synthesis, and analysis of electric vehicle (EV) networks with charging stations (CSs) that considers the impacts of traffic. The EV charge demands are modeled by a graph where nodes are positioned at potential locations for CSs, and edges represent traffic flow between the nodes. A synchronization protocol is assumed for the network where the system states correspond to the waiting time at each node. These models are then utilized for the placement and sizing of CSs in order to limit vehicle waiting times at all stations below a desirable threshold level. The main idea is to reformulate the CS placement and sizing problems in a control framework. Moreover, a strategy for the deployment of portable charging stations (PCSs) in selected areas is introduced to further improve the quality of solutions by reducing the overshooting of waiting times during peak traffic hours. Further, the inherent symmetry of the graph, described by graph automorphisms, are leveraged to investigate the number and positions of CSs. Detailed simulations are performed for the EV network of Perth Metropolitan in Western Australia to verify the effectiveness of the proposed approach.

Robust Placement and Sizing of Charging Stations From a Novel Graph Theoretic Perspective

“…One of the main focus of studies related to EV networks during the last few years has been the Optimal placement and sizing of CSs in order to maintain the waiting time below a threshold level ( [5]- [6], and [12]- [14]) where a sort of optimization technique is used in almost all of the proposed approach. The optimization techniques implemented for EV problems usually suffer from computational issues such as complexity and intractable solution [13].…”

“…A novel approach to CS placement and sizing is proposed in [14] which, unlike the majority of current approaches based on optimization techniques, relies on graph theoretic properties of the graph of EV networks. It transforms the CS placement to the problem of finding the set of required driver nodes for CN controllability using the exact controllability method (ECM).…”

“…To address the above challenges, we have developed the control framework first introduced in [14] in order to address the CS placement and sizing for a network with existing CSs and variable flow of EVs. Firstly, the mathematical model of the underlying graph of EV network is improved by separating the traffic flow at individual node from the trafic flow between nodes.…”

“…A model of underlying EV network is constructed using a graph where nodes are the potential locations of CSs and edges link two nearby nodes where the weights of edges represent the number of EVs in the area. The ECM implemented in [14] is not applicable for CS placements in networks with existing CSs. Thus we use another graph theoretic property, known as maximum matching principle, by modifying it to a case where there are some pre-set unmatched nodes, and then the locations of new CSs are determined by finding the remaining unmatched nodes on the graph of CS network.…”

“…Moreover, the proposed approach in [14] determines the locations and sizes of CSs according to a static EV flow corresponding to few traffic instances during the day, while in this paper, the control framework and the graph theoretic approach of [14] are adapted to a more general and practical case that considers variable traffic flow. Throughout the paper, the term "traffic flow" refers to the flow of EVs at the charging stations.…”