Electric vehicle scheduling and optimal charging problem: complexity, exact and heuristic approaches

Abstract

This paper deals with the Electric Vehicle (EV) Scheduling and Optimal Charging Problem. More precisely, given a fleet of EVs and Combustion Engine Vehicles (CVs), a set of tours to be processed by vehicles and a charging infrastructure, the problem aims to optimise the assignment of vehicles to tours and minimise the charging cost of EVs while considering several operational constraints mainly related to chargers, electricity grid and EVs driving range. We prove that the Electric Vehicle Scheduling and Charging Problem (EVSCP) is NP-hard in the ordinary sense. We provide a mixed-integer linear programming formulation to model the EVSCP and use CPLEX to solve small and medium instances. To solve large instances, we propose two heuristics: a Sequential Heuristic (SH) and a Global Heuristic (GH). The SH considers the EVs sequentially. To each EV, it assigns a set of tours and guarantees the feasibility of a charging schedule. Then, it generates an optimal charging schedule for this EV. However, the GH computes, in the first step, a feasible assignment of tours to all EVs. In the second step, it applies a global Min-Cost-Flow-based charging algorithm to minimise the charging cost of the EVs fleet. To evaluate the efficiency of our solving approaches, computational results on a large set of real and randomly generated test instances are reported and compared.

Classification of Electric Vehicle Fleets Considering the Complexity of Fleet Charging Schedules

“…Xi and Siohansi [8] propose a decentralized price/quantity based approach. Mixed Integer Programming solution (MIP) is applied as described by Álvaro and Fraile-Ardanuy [1], Detzler and Karnouskos [2] or Sassi and Oulamara [6]. The latter also use a Min-Cost-Flow-Problem based heuristic [6].…”

“…Mixed Integer Programming solution (MIP) is applied as described by Álvaro and Fraile-Ardanuy [1], Detzler and Karnouskos [2] or Sassi and Oulamara [6]. The latter also use a Min-Cost-Flow-Problem based heuristic [6]. Other approaches include for example a binary linear programming method [5] or stochastic approaches [4].…”

“…Other approaches include for example a binary linear programming method [5] or stochastic approaches [4]. Also a partition into time slots allows discrete solving approaches [3][4][5][6][7]. All authors present different methods to solve the CSP, but they often use different constraints of the CSP and it is unclear which method applies to which fleet type.…”

Voltage Analysis on MV/LV Distribution Networks with the Integration of DC Fast Chargers

“…According to [3], the EV stock is projected to reach 230 million vehicles by 2030. However, a limited capacity of the existing power networks, long charging durations and limited charging options for vehicles, and the high investment costs of EVs associated with battery prices are some of the main challenges to consider [4,5]. The massive deployment of EVs may also significantly affect the operation and planning of medium voltage (MV) and low voltage (LV) distribution networks.…”

Using Electric Vehicles and Demand Side Response to Unlock Distribution Network Flexibility

“…On the contrary, the main concerns with the EV technology include the limited capacity of existing power networks, lack of charging infrastructures, limited charging options, long charging durations, limited driving ranges of vehicles, and high investment costs due to high battery prices [6], [9]. Among the EV drivers, 'range anxiety' is one of the main issues due to long charging durations and lack of charging infrastructures.…”