Optimal strategy to Charge a Car Using Stochastic Dynamic Programming

In this paper we want to compare different strategies to charge an electric vehicle and see whether price dependency between periods can be used to an advantage. An electric car needs to be charged regularly. Usually, a car is connected to the network for a longer period than is needed to charge. This gives flexibility to charge the car during periods when the prices are low. First, we approach the problem as a knapsack problem with no uncertainty. Then we consider the prices as independently distributed. Next, we want to include the dependency of the prices between periods. We test different forecasting methods to predict the price of the next period. However, this makes the problem computationally intractable. Instead, we use a Markov chain to include the price dependency between periods. Another approach is also attempted, where we forecast a whole timeseries and proceed by considering this as a knapsack model. A conceptual model to include weather dependence is presented. Simulations with real-world data shows that the strategy with price-dependency performed on average significantly better than to assume the prices are independent between periods.