The Location Of Charging Stations For Electric Cars Under Demand Uncertainty

Nowadays,electric cars have rapidly developed due to their huge advantages in energy saving and environmental protection,but the problem of difficulty in charging is very common.Therefore,this paper studies the issues related to the location of charging stations for electric cars and the configuration of charging piles.The location problem is a classic problem in operations research.Compared with the previous prob-lems,the difficulty of the model in this paper is that the demand is uncertain,so the idea of robust optimization is adopted and probability constraints are introduced when modeling.In terms of theoretical research,this article considers a set of demand points and a set of candidate points,the charging stations are chosen from the set of candidate points,and the users at the demand points will go to nearby charging stations to seek charging,this process will cause charging costs.The objective function of the model in this paper is to maximize the total profit,so it is necessary to estimate the length of time that the servers are occupied to obtain the parking revenue,and some queuing models are used to simulate the process of customers’arrival and charging.Based on the conclusion of the homogeneous queue,the article gives two methods for solving the steady state of the///queue and proves the monotonicity of the number of queues in the steady state with respect to the arrival rate and the number of servers.Considering that the arrival of customers in reality changes with time,this article focus-es on non-homogeneous queue models such as//and///,and proves the expectations of people served by the system and the upper and lower bounds of expectations.In terms of applied research,a series of simulation experiments are done to sim-ulate the homogeneous Poisson process and the non-homogeneous Poisson process,in order to study the system occupancy and the process of users’leaving.The experi-ments focuses on three KS test of the users’leaving distribution:CU KS,Log KS,and Lewis KS.Then,the numerical results of the simulation are combined with the theory of robust optimization to solve the model.Finally,a case study is carried out to prove the rationality of the model in this paper.