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

This paper proposes analytical approaches to extend the capacity of existing networks of electric vehicles (EVs) by placement of additional charging stations (CSs) as well as determining the sizes of existing and new CSs in order to handle future expansions of EVs. The EV flow at CSs is modeled by a graph where nodes are potential locations for CSs and edges are uncertain parameters representing the variable EV flow at CSs. The required extra CS locations are explored by transforming the CS placement problem into a controllability framework addressed by maximum matching principle (MMP). To find the sizes of each CS, the graph of CS network is partitioned featuring only one CS in each subgraph. The size of CS in each subgraph is then determined by transforming the problem into the problem of robust stability of a system with uncertain parameters where each parameter is associated with an edge of subgraph. The zero exclusion principle is then tested for the related Kharitonov rectangles and polygonal polynomials of closed loop system with selected feedback gain as CS capacity. The proposed analytical approach is tested on the existing Tesla CS Network of Sydney. The locations of extra required CSs as well as the sizes of existing and new CSs are determined to maintain the waiting times at all stations below the threshold level.