Analytic Modeling and Integral Control of Heterogeneous Thermostatically Controlled Load Populations

Abstract

Thermostatically controlled loads (TCLs) account for approximately 50% of U.S. electricity consumption. Various techniques have been developed to model TCL populations. A High-fidelity analytical model of heterogeneous TCL populations facilitates the aggregate synthesis of power control in power networks. Such a model assists the utility manager to increase the stability margin of the network. The model, also, assists the customer to schedule his/her tasks in order to reduce his/her energy cost. We present a deterministic hybrid partial differential equation (PDE) model which accounts for heterogeneous populations of TCLs, and facilitates analysis of common scenarios like cold load pick up, cycling, and daily and/or seasonal temperature changes to estimate the aggregate performance of the system. The proposed technique is flexible in terms of parameter selection and ease of changing the set-point temperature and deadband width all over the TCL units. We provide guidelines to maintain the numerical stability of the discretized model during computer simulations. Moreover, the proposed model is a close fit to design output feedback algorithms for power control purposes. Our integral output feedback control, designed using the comparison principle, guarantees fast and efficient power tracking for various real-world scenarios. We present simulation results to verify the effectiveness of the proposed modeling and control technique.

A control system framework for privacy preserving demand response of thermal inertial loads

“…There has been a large body of literature [5]- [11] investigating different aspects of controlling TCLs to achieve demand response. Policies such as set-point displacement control [5]- [9], switching rate control [10], and set-point velocity control [11] have been considered.…”

Generation following with thermostatically controlled loads via alternating direction method of multipliers sharing algorithm

“…More recently, [9] developed a diffusion-advection partial differential equation (PDE) model and parameter identification scheme for an aggregated population of heterogeneous TCLs. In [10], the authors present a deterministic hybrid PDE-based model for heterogeneous TCL populations, and apply a uniform deadband shifting strategy for control.…”

Recursive parameter estimation of thermostatically controlled loads via unscented Kalman filter

“…More recently, [7] develops a diffusion-advection partial differential equation (PDE) model and parameter identification scheme for an aggregated population of heterogeneous TCLs. In [8], the authors present a deterministic hybrid PDE-based model for heterogeneous TCL populations, analyze its stability properties, and derive a power reference tracking control law.…”

“…In this section, we will present 4 closely related approaches for parameter estimation of a thermostatically controlled load (TCL) using the Kalman filter (KF) algorithm in (8) and unscented Kalman filter (UKF) algorithm in (25). In this paper, we will consider: (i) a single filter approach in which one UKF is used to estimate the parameters θ k ; (ii) a joint filter approach in which one UKF simultaneously estimates both θ k and T k ; (iii) a dual filter approach in which one UKF estimates the parameters θ k and one KF estimates the state T k ; and (iv) a triple filter approach in which we use one UKF to estimate θ k , one KF to estimate T k , and another KF to estimate the inputs, T k ∞ and m k .…”