Smart Charging of Electric Vehicles

Abstract

A crucial challenge in future smart energy grids is the large-scale coordination of distributed energy generation and demand. In the last years several Demand Side Management approaches have been developed. A major drawback of these approaches is that they mainly focus on realtime control and not on planning, and hence cannot fully exploit the flexibility of e.g. electric vehicles over longer periods of time.

In this chapter we investigate the optimization of charging an electric vehicle (EV). More precisely, the problem of charging an EV overnight is formulated as a Stochastic Dynamic Programming (SDP) problem. We derive an analytic solution for this SDP problem which in turn leads to a simple short-term bidding strategy. From an MDP point of view this solution has a number of special features:

• It leads to analytic optimal results based on order statistics.

• It allows for a more practical rule which can be shown to be nearly optimal.

• It is robust with respect to the modeling assumptions, showing little room for further improvement even when compared to a solution with perfect foresight.

Numerical results with real-world data from the Belgium network show a substantial performance improvement compared to standard demand side management strategies, without significant additional complexity. (This chapter is based on Kempker et al. (Proceedings of the 9th EAI international conference on performance evaluation methodologies and tools, Valuetools 2015, Berlin, 14–16 December 2015, pp 1–8, 2016).)

Appendix

1.1 Energy Terminology

Demand Side Management (DSM): Use of the flexibility of electric devices in households or offices to influence the electricity demand profile. Shiftable devices: Electricity consuming devices, for which the demand of electricity can be shifted in time. Examples are washing machines, dryers and dishwashers. Electric vehicles (EV): Vehicles like e.g., cars, busses, trucks or bicycles, which use electricity from batteries to drive or to support driving. PowerMatcher: A DSM technology using dynamic pricing and a hierarchical bidding process to support the matching of supply and demand of electricity.

1.2 Notation

S	State space (discrete/continuous)
T	Number of periods, time t = 0, 1, . . . , T − 1
s t  = (x t , p t )	State, with:
x t	Amount still to be charged after time t
p t	Price per unit of energy at time t
a t  = u t	Action/amount to be charged at time t
c a(s) = u t p t	Expected one step cost in state s t  = (x t , p t ), under charge action a = u t
A(s t ): u ≤ u max	Set of actions available in state s t
δ t	Decision rule at time t: u t (x t , p t )
P(j | (s; a))	$\mathbb{P}(x_{t} - u_{t}\vert (x_{t},p_{t}))$ One step transition probability under action u t (x t , p t ) = u t in state s t  = (x t , p t )
V t (s)	V t (x t , p t ) Optimal value function of expected cumulative costs over remaining T − t steps up to time T, starting in state s t  = (x t , p t ) at time t