Efficient solution approaches for locating electric vehicle fast charging stations under driving range uncertainty

Abstract

We seek to determine the best locations for electric vehicle fast charging stations under driving range uncertainty. Two stochastic programming based models have been recently proposed to handle the resulting stochastic flow refueling location problem: a first one maximizing the expected flow coverage of the network, a second one based on joint chance constraints. However, significant computational difficulties were encountered while solving large-size instances. We thus propose two efficient solution approaches for this problem. The first one is based on a new location-allocation type model for this problem and results in a MILP formulation, while the second one is a tabu search heuristic. Our numerical experiments show that when using the proposed MILP formulation, the computation time needed to provide guaranteed optimal solutions is significantly reduced as compared to the one needed when using the previously published MILP formulation. Moreover, our results also show that the tabu search method consistently provides good quality solutions within short computation times.

Locating electric vehicle charging stations under uncertain battery energy status and power consumption

“…the joint probability that the power consumption on each portion of the trip comprised between two opened charging stations is smaller than the energy available in the battery after recharging, should be introduced in the model. To the best of our knowledge, only three recent works, [6], [13] and [17] have studied this problem. However, they all relied on rather strong assumptions on the random variables in order to be able to compute the coverage probability.…”

“…However, they all relied on rather strong assumptions on the random variables in order to be able to compute the coverage probability. Namely, de Vries and Duijzer [6] and Kchaou Boujelben and Gicquel [13] consider a single random variable representing the stochastic driving range over the entire road network. This accounts for the uncertainties related to the age and technology of the battery and to the general weather conditions.…”

“…An efficient formulation of the flow refueling location problem (FRLP) with symmetric power consumption has been recently proposed in [13]. This formulation relies on the idea that, in order to cover a trip q, we should assign to each node l ∈ N q a single station k ∈ N qo l located within the driving range of the vehicle to enable the EV driver to recharge his battery at station k and travel at least up to node l. In case trip q is not covered, there is no need to assign a charging station to each node l ∈ N q .…”

“…Namely, in any optimal solution, ∀l ∈ N qo , there is at most one node k ∈ N qo l such that w q kl = 1. Similarly, ∀l ∈ N qr , there is at most one node k ∈ N qr l such that w q kl = 1 (see [13]). This enables us to reformulate constraints (9) as:…”

“…The FRLP with a stochastic driving range was recently studied by de Vries and Duijzer [6], Kchaou Boujelben and Gicquel [13] and Lee and Han [17]. These works introduced the notion of coverage probability of a trip, which is defined as the probability that the drivers can carry out the trip without running out of fuel, i.e.…”