Bayesian parameter estimation for direct load control of populations of air conditioners

Recent approaches for direct load control (DLC) of populations of air conditioners (ACs) to provide demand-side services in the electricity grid rely on mathematical models of the aggregate demand dynamics of these populations. These models can be parametrised by the physical characteristics of the ACs in the population, for example their thermal power. The knowledge of how their physical parameters are distributed in the population of real devices is instrumental in the analysis and implementation of controllers based on such models. For large populations, it is typically assumed that these parameters are stochastically distributed according to some probability distribution, e.g., log-normal, which has been effective in simulations. However, the identification of such distribution for a specific population remains an open problem for real-world deployments of DLC. This paper formulates a Bayesian framework for the state and parameter estimation of a previously developed input/output model for the aggregate demand response of heterogeneous populations of ACs. This framework enables us to assign a prior distribution to the parameters of the model, which is then updated using measurements of power demand data for the population to reach a posterior distribution that is more informative about the true value of these parameters. The framework uses sequential Monte Carlo methods, which are well-suited to existing high-performance computer hardware, and aims to provide a way to fill a gap between simulation and real implementation by validating posterior parameter distributions using real measurements. Simulation results indicate that our approach can successfully capture the values defining the distributions of physical parameters in a population simulated by 10,000 ACs with a standard hybrid dynamic model for each device.