Dynamic Programming versus Linear Programming Application for Charging Optimization of EV Fleet Represented by Aggregate Battery

Paper #:
  • 2018-01-0668

  • 2018-04-03
In order to facilitate optimizations of integrated transport-energy systems, which include electric vehicle fleet charging management strategies, individual EVs are usually modelled by means of a single aggregate battery. The aggregate battery model is parameterized based on several EV fleet-related input time distributions, such as average state-of-charge (SoC) time distributions of EVs connecting to and disconnecting from the electric grid. The aggregate battery models are mostly formulated in the energy domain considering EV batteries as an energy storage. From the standpoint of battery charging management, this modelling approach results in linear optimization problem due to a linear cost function which represents cumulative charging cost and linear charging constraints including linear EV fleet model. For this kind of optimization problem, widely used linear programming (LP) optimization approach results in globally optimal solution. However, in the case of more realistic and more accurate EV fleet models, e.g. those formulated in the charge domain (EV batteries are considered as a charge storage), which generally result in a nonlinear structure of model and constraints, the linear programming optimization approach would not be usable. In that case different nonlinear programming-based optimization techniques can be used. However, dynamic programming (DP) is considered and analyzed here since it results in globally optimal solution for the general problem of nonlinear system model with nonlinear constraints, and because it is still applicable here due to a low number of optimal problem state and control variables (for the aggregate battery modeling approach). Since DP is a discrete optimization algorithm, it assumes discrete state and control variables and its accuracy (i.e. deviation from the exact global optimal solution) depends to some extent on the resolutions of the corresponding variables. In order to investigate practical aspects (e.g. charging cost and algorithm execution time) of using considered optimization methods in real applications, charging optimizations of linear aggregate battery EV fleet model are performed both by using DP and LP. Since LP in the case of linear optimization problem results in the exact global optimal solution, its optimization results will serve as a benchmark for DP results which will be performed for different resolutions of state and control variables. Also, possibility of handling different constraints within optimization problem will be analyzed for the case of both optimization approaches.
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