Search

Aggregate load modeling is of fundamental importance for systematic analysis and design of various demand response strategies. Instead of keeping track of the trajectories of individual loads, the aggregate modeling problem focuses on characterizing the density evolution of the load population. Most existing models are only applicable to thermostatically controlled loads (TCLs) with first-order linear dynamics. This paper develops a unified aggregate modeling approach that can be used for general TCLs as well as deferrable loads. We propose a deterministic hybrid system model to describe individual load dynamics under demand response rules, and develop a general stochastic hybrid system (SHS) model to capture the population dynamics. We also derive a set of partial differential equations (PDEs) that govern the probability density evolution of the SHS. Our results cannot be obtained using the existing SHS tools in the literature as the proposed SHS model involves both random and deterministic switchings with general switching surfaces in multidimensional domains. The derived PDE model includes many existing aggregate load modeling results as special cases and can be used in many other realistic modeling scenarios that have not been studied in the literature. [ABSTRACT FROM AUTHOR]

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it is shown that local control can be designed so that the aggregate of loads behaves as a controllable resource, with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements, and to provide the grid operator with accurate estimates of the mean and variance of quality of service (QoS) for an individual load. [ABSTRACT FROM AUTHOR]