Recently it has been shown that an aggregation of Thermostatically Controlled Loads (TCLs) can be utilized to provide fast regulating reserve service for power grids and the behavior of the aggregation can be captured by a stochastic battery with dissipation. In this paper, we address two practical issues associated with the proposed battery model. First, we address clustering of a heterogeneous collection and show that by finding the optimal dissipation parameter for a given collection, one can divide these units into few clusters and improve the overall battery model. Second, we analytically characterize the impact of imposing a no-short-cycling requirement on TCLs as constraints on the ramping rate of the regulation signal. We support our theorems by providing simulation results.
This paper develops new methods to model and control the aggregated power demand from a population of thermostatically controlled loads, with the goal of delivering services such as regulation and load following. Previous work on direct load control focuses primarily on peak load shaving by directly interrupting power to loads. In contrast, the emphasis of this paper is on controlling loads to produce relatively short time scale responses (hourly to sub-hourly), and the control signal is applied by manipulation of temperature set points, possibly via programmable communicating thermostats or advanced metering infrastructure. To this end, the methods developed here leverage the existence of system diversity and use physically-based load models to inform the development of a new theoretical model that accurately predicts – even when the system is not in equilibrium – changes in load resulting from changes in thermostat temperature set points. Insight into the transient dynamics that result from set point changes is developed by deriving a new exact solution to a well-known hybrid state aggregated load model. The eigenvalues of the solution, which depend only on the thermal time constant of the loads under control, are shown to have a strong effect on the accuracy of the model. The paper also shows that load heterogeneity – generally something that must be assumed away in direct load control models – actually has a positive effect on model accuracy. System identification techniques are brought to bear on the problem, and it is shown that identified models perform only marginally better than the theoretical model. The paper concludes by deriving a minimum variance control law, and demonstrates its effectiveness in simulations wherein a population of loads is made to follow the output of a wind plant with very small changes in the nominal thermostat temperature set points. As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time-scale fluctuations in generated power. Recent numerical modeling of thermostatically controlled loads (TCLs) has demonstrated that such load following is feasible, but analytical models that satisfactorily quantify the aggregate power consumption of a group of TCLs are desired to enable controller design. We develop such a model for the aggregate power response of a homogeneous population of TCLs to uniform variation of all TCL setpoints. A linearized model of the response is derived, and a linear quadratic regulator (LQR) has been designed. Using the TCL setpoint as the control input, the LQR enables aggregate power to track reference signals that exhibit step, ramp and sinusoidal variations. Although much of the work assumes a homogeneous population of TCLs with deterministic dynamics, we also propose a method for probing the dynamics of systems where load characteristics are not well known. Demand-side Demand-side control is playing an increasingly important role in smart grid control strategies. Modeling the dynamical behavior of a large population of appliances is especially important to evaluate the effectiveness of various load control strategies. In this paper, a high accuracy aggregated model is first developed for a population of HVAC units. The model efficiently includes statistical information of the population, systematically deals with heterogeneity, and accounts for a second-order effect necessary to accurately capture the transient dynamics in the collective response. Furthermore, the model takes into account the lockout effect of the compressor in order to represent the dynamics of the system under control more accurately. Then, a novel closed loop load control strategy is designed to track a desired demand curve and to ensure a stable and smooth response. Abstract In this paper, a coordination approach for thermostat-controlled household appliances is developed. Under consideration are heating and cooling devices such as refrigerators, freezers, water boilers and heat pumps, which are usually characterized by an intermittent (duty cycle) operation. Without influence from the outside, an internal hysteresis switching controller toggles the “on off” state of a device when its temperature boundary is reached. In order to realize the approach proposed here, the devices are connected to a central control entity by two-way communication. The coordination consists of a step-wise heuristic solution of a binary optimization problem, which serves to select a number of devices in each time step that are subject to compulsory switching, i.e. toggling the “on off” state. It allows a large group of devices to track a setpoint trajectory with its aggregated power consumption, acting like a distributed virtual energy storage, while the individual temperature bounds of the appliances are not violated. This behavior can be used for grid-control purposes, such as the provision of active power reserves. It will be shown that the group of appliances can be characterized by an approximate aggregated dynamical model consisting of a first-order differential equation together with an approximate aggregated nonlinear cost function penalizing the control actions. The developed methodology is evaluated in a numerical simulation with a small appliance cluster corresponding to a residential housing area. This paper presents a novel modeling and con- trol approach for the aggregation of large numbers of hetero- geneous thermostatically controlled loads, such as refrigera- tors, electric water heaters, and air conditioners, and their usage for Demand Response. Unlike traditional Demand Re- sponse methods that act on time scales of hours, this ap- proach is able to provide short-term (e.g., second-to-second) ancillary services, such as balancing and frequency control. A statistical modeling approach based on Markov Chains is used to describe the evolution of probability mass in a tem- perature state space. The Markov state transition matrix is identified using state information from the population of thermostatically controlled loads. A predictive controller is used to control the aggregate population of loads such that it tracks a signal. A simulation example shows the applicabil- ity of the approach to realistic systems, and includes a com- parison of control performance depending on available state information and controller parameterization.  Due to the potentially large number of Distributed Energy Resources (DERs) - demand response, distributed generation, distributed storage - that are expected to be deployed, it is impractical to use detailed models of these resources when integrated with the transmission system. Being able to accurately estimate the transients caused by demand response is especially important to analyze the stability of the system under different demand response strategies, where dynamics on time scales of seconds to minutes are important. On the other hand, a less complex model is more amenable to study stability of a large power system, and to design feedback control strategies for the population of devices to provide ancillary services. The main contribution of this paper is to develop an aggregated model for a heterogeneous population of Thermostatic Controlled Loads (TCLs) to accurately capture their collective behavior under demand response. The aggregated model efficiently includes statistical information of the population, systematically deals with heterogeneity, and accounts for a second-order effect necessary to accurately capture the transient dynamics in the collective response. The developed aggregated model is validated against simulations of thousands of detailed building models using GridLAB-D (an open source distribution simulation software) under both steady state and severe dynamic conditions. The thermal storage potential of Thermostatically Controlled Loads (TCLs) is a tremendous flexible resource for providing various ancillary services to the grid. In this work, we study aggregate modeling, characterization, and control of TCLs for frequency regulation service provision. We propose a generalized battery model for aggregating flexibility of a collection of TCLs. A theoretical characterization of the aggregate power limits and energy capacity of TCLs is provided. Moreover, we propose a priority-stack-based control strategy to manipulate the power consumption of TCLs for frequency regulation, while preventing short cycling on the units. Numerical experiments are provided to show the accuracy of the proposed model and the efficacy of the developed control method. We investigate the potential for aggregations of residential thermostatically controlled loads (TCLs), such as air conditioners, to arbitrage intraday wholesale electricity market prices via non-disruptive direct load control. Since wholesale electricity prices reflect power system conditions, arbitrage provides a service to the grid, helping to balance real-time supply and demand. While previous work on the energy arbitrage problem has used simple energy storage models, we use high fidelity TCL-specific models which allow us to understand and quantify the full capabilities and constraints of these time-varying systems. We explore two optimization control frameworks for solving the arbitrage problem, both based on receding horizon linear programming. Since we find that the first approach requires significant computation, we develop a second approach involving decomposition of the optimal control problem into separate optimization and control problems. Simulation results show that TCLs could save on the order of 10 of wholesale energy costs via arbitrage, with savings decreasing with price forecast error. Thermostatically controlled loads (TCLs), such as refrigerators, air conditioners, and electric water heaters, can be aggregated and used to deliver power systems services. The effectiveness of control strategies depends on the level of infrastructure and communications. This paper explores the use of TCLs for load following when measured state information is not available in real time. We use Markov Chain models to describe the temperature state evolution of populations of TCLs, and Kalman filtering techniques for both state estimation and joint parameter state estimation. We find power tracking RMS errors in the range of 2-16 of the aggregate steady state power consumption of the TCL population. Results depend upon the information available for system identification, state estimation, and control. If high precision tracking is not required, TCLs may not need to be metered to provide state information to the central controller in real time or at all.