Home energy management based on optimal production control scheduling with unknown regime switching

We propose a novel home energy management framework to intelligently schedule the distributed energy storage (DES) for the cost reduction of customers in this paper. The proposed optimal production control technique determines the action policy (e.g., charging or discharging) and the power allocation policy of the DES to provide DES power at proper time with lower price than that of the utility grid, resulting in the reduction of the long term financial cost. Specifically, we first formulate the optimal decision problem for home energy systems with solar and energy storage devices, when the demand, renewable energy, electricity purchase from grid are all subject to Brownian motions. Both drift and variance parameters are modulated by a continuous-time Markov chain that represents the regime of electricity price. In particular, we set up a mean-variance problem where the cost function is both the running cost of diesel generator and deviation from the target State of Charge (SOC) of batteries. We assume the regime information follows a Hidden Markov Model (HMM), and then estimate the state by change of measure based on the Girsanov's theorem. Finally, the problem boils down to solving a stochastic differential equation (SDE), which we provide both the explicit and numerical solutions to this specific SDE. An example is provided to illustrate the effectiveness of our proposed approach. Moreover, we compare it with the traditional Model Predictive Control (MPC) technique, and show it outperforms MPC.