Optimizing a System of Electric Vehicle Charging Station

There has been a significant increase in the number of electric vehicles (EVs) mainly because of the need to have a greener living. Thus, ease of access to charging facilities is a prerequisite for large scale deployment for EV.;The first component of this dissertation research seeks to formulate a deterministic mixed-integer linear programming (MILP) model to optimize the system of EV charging stations, the locations of the stations and the number of slots to be opened to maximize the profit based on the user-specified cost of opening a station. Despite giving the optimal solution, the drawback of MILP formulation is its extremely high computational time (as much as 5 days). The other limit of this deterministic model is that it does not take uncertainty in to consideration.;The second component of this dissertation is to overcome the first drawback of the MILP model by implementing a two-stage framework developed by (Chawal et al. 2018), which integrates the first-stage system design problem and second-stage control problem of an EV charging stations using a design and analysis of computer experiments (DACE) based system design optimization approach. The first stage specifies the design of the system that maximizes expected profit. Profit incorporates costs for building stations and revenue evaluated by solving a system control problem in the second stage. The results obtained from the DACE based system design optimization approach, when compared to the MILP, provide near optimal solutions. Moreover, the computation time with the DACE approach is significantly lower, making it a more suitable option for practical use.;The third component of this dissertation is to overcome the second drawback of the MILP model by introducing stochasticity in our model. A two-stage framework is developed to address the design of a system of electric vehicle (EV) charging stations. The first stage specifies the design of the system that maximizes expected profit. Profit incorporates costs for building stations and revenue evaluated by solving a system control problem in the second stage. The control problem is formulated as an infinite horizon, continuous-state stochastic dynamic programming problem. To reduce computational demands, a numerical solution is obtained using approximate dynamic programming (ADP) to approximate the optimal value function. To obtain a system design solution using our two-stage framework, we propose an approach based on DACE. DACE is employed in two ways. First, for the control problem, a DACE-based ADP method for continuous-state spaces is used. Second, we introduce a new DACE approach specifically for our two-stage EV charging stations system design problem. This second version of DACE is the focus of this paper. The "design" part of the DACE approach uses experimental design to organize a set of feasible first-stage system designs. For each of these system designs, the second-stage control problem is executed, and the corresponding expected revenue is obtained. The "analysis" part of the DACE approach uses the expected revenue data to build a metamodel that approximates the expected revenue as a function of the first-stage system design. Finally, this expected revenue approximation is employed in the profit objective of the first stage to enable a more computationally-efficient method to optimize the system design. To our knowledge, this is the only two-stage stochastic problem which uses infinite horizon dynamic programming approach to optimize the second stage dynamic control problem and the first stage system design problem. Moreover, when the designs obtained from our DACE approach and MILP design are solved using DACE-based ADP method (simulation), an improvement of approximately 8% is observed in the simulated profit obtained from ADP design compared to that of MILP design indicating that when uncertainty is considered, DACE ADP design provides the better solution.