An approximate dynamic programming algorithm for short-term electric vehicle fleet operation under uncertainty

This paper considers the dynamic problem of optimally operating a fleet of plug-in hybrid electric vehicles in a market environment. With uncertainty in future electricity prices and driving demands, we formulate a Markov decision process and determine a cost-minimizing policy for using the engine and charging and discharging the battery. As such, the policy is based on the trade-off between the costs of gasoline and electricity and between current and future power prices. To accommodate an inhomogeneous fleet composition and overcome the computational challenges of stochastic and dynamic optimization, including large-scale state and action spaces, we adopt the methodology of approximate dynamic programming. More specifically, using simulation and value function approximation by linear regression, we apply a least squares Monte Carlo method. This methodology allows for scaling with respect to fleet size and we are able to establish convergence of our algorithm for 100 vehicles by using 5000 samples in the simulation. Our results show that the vehicles should generally discharge the battery rather than using the engine unless battery capacity is insufficient to fully cover driving demand, but the timing of battery charging should be according to power prices. When comparing our policy to the simple policy of immediate charging, we demonstrate superiority for small and medium-sized fleets, with 2%-4% cost differences.

Automated summary

This paper discusses the optimal operation of a fleet of plug-in hybrid electric vehicles in a market setting. By formulating a Markov decision process, the study seeks to minimize costs by determining the best policy for engine utilization and battery charging/discharging, considering uncertainties in electricity prices and driving demands. The methodology of approximate dynamic programming, using simulation and value function approximation, is employed to address computational challenges. The results show that discharging the battery, rather than using the engine, is generally preferred, unless the battery capacity is insufficient. Charging the battery should be timed according to power prices. The proposed policy demonstrates superiority over the simple policy of immediate charging, with a cost difference of 2%-4% for small and medium-sized fleets.