Continuous-time model predictive control for coordinated electric vehicle charging and grid flexibility

Abstract

The integration of electric vehicles (EVs) and renewable energy sources into the power grid creates significant challenges. However, electric vehicles offer temporal flexibility that can be utilized to balance the grid load and absorb the renewable generation. The continuous-time model predictive control strategy has been used to manage the charging of EVs at a charging station equipped with the renewable energy source with aim to reduce the costs and peak demand for the grid. Unlike the conventional Discrete-Time MPC (DT-MPC) schemes based on the zero-order hold mechanism that results in unrealistic power profiles with high harmonics, the proposed Continuous-Time MPC (CT-MPC) algorithm utilizes fluid-queue (a model that represents discrete EV arrivals and charging as continuous flows to overcome computational complexity) and Bernstein polynomials to obtain a smooth charging power profile, represented as continuously differentiable function. By enforcing C¹ continuity at interval boundaries, impulse derivatives are eliminated and the ramping constraints can be accurately represented. Furthermore, an optimization problem in this framework can be formulated as a linear program in receding horizon that balances minimizing electricity costs according to a Time-of-Use tariff with meeting strict delay-based service quality constraints. The simulation was conducted for 2 days with 300 EV charging sessions to fully capture the deferred charging of the evening commuters. The results are presented over the complete charge cycle (when the backlog of the charging queue is cleared for day 1). The results show a 47.8% reduction in electricity costs and an 18.4% reduction in peak grid demand compared to the uncontrolled baseline charging scenario. Additionally, the continuous-time approach also presents itself as a more physically realistic and grid-friendly alternative (by ensuring smooth C¹ continuous power trajectories, eliminating high-frequency harmonics, and respecting ramping constraints) to the discrete-time approach.