Learning the state-of-charge of heterogeneous fleets of distributed energy resources with temporal residual networks

With increased use of renewable energy such as wind and solar, electric power generation is experiencing increased variability and uncertainty, which drives larger imbalances between the electric demand and supply. To mitigate this challenge, one can use distributed energy resources to beget flexible demand from coordinating fleets of smart electric water heaters (EWH) and residential (kW-scale) batteries. To effectively coordinate and characterize such a large and heterogeneous fleet of distributed energy resources (DERs), a common abstraction is denoted a virtual battery (VB). While the state of charge (SoC) of individual DERs (e.g., EWHs's water temperature) can be easily measured, determining the SoC of a controlled virtual battery aggregation is a technically challenging task due to the fleet's heterogeneous nature, characterized by nonlinear, stochastic, partial differential equations with time-varying parameters. In this paper, a data-driven approach is presented that utilizes a deep-learning-based Temporal Residual Causal Network to determine the SoC for a heterogeneous fleet of DERs, updated using only available end-use measurements. Unlike existing literature that generally relies on complex physics-based models, our deep learning (DL) model is trained using practical input-output data. The simulation results demonstrate that accurate estimation can be achieved with a low computational burden, considering a range of parametric variations at the device and fleet levels, such as fleet population size, background demand, DER device parameters, and coordinator communication losses. The results suggest that the proposed approach has appropriate generalization and robustness properties for practical, real-time control settings.