skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Modeling and control of thermostatically controlled loads

Abstract

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.

Authors:
 [1];  [1];  [2];  [2]
  1. Los Alamos National Laboratory
  2. UNIV OF MICHIGAN
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1045412
Report Number(s):
LA-UR-11-00040; LA-UR-11-40
TRN: US201215%%24
DOE Contract Number:
AC52-06NA25396
Resource Type:
Conference
Resource Relation:
Conference: 17th Power Systems Computation Conference ; August 26, 2011 ; Stockholm, Sweden
Country of Publication:
United States
Language:
English
Subject:
24 POWER TRANSMISSION AND DISTRIBUTION; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; DESIGN; ENERGY SOURCES; FLUCTUATIONS; LOAD ANALYSIS; POWER SYSTEMS; SIMULATION

Citation Formats

Backhaus, Scott N, Sinitsyn, Nikolai, Kundu, S., and Hiskens, I. Modeling and control of thermostatically controlled loads. United States: N. p., 2011. Web.
Backhaus, Scott N, Sinitsyn, Nikolai, Kundu, S., & Hiskens, I. Modeling and control of thermostatically controlled loads. United States.
Backhaus, Scott N, Sinitsyn, Nikolai, Kundu, S., and Hiskens, I. 2011. "Modeling and control of thermostatically controlled loads". United States. doi:. https://www.osti.gov/servlets/purl/1045412.
@article{osti_1045412,
title = {Modeling and control of thermostatically controlled loads},
author = {Backhaus, Scott N and Sinitsyn, Nikolai and Kundu, S. and Hiskens, I.},
abstractNote = {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.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2011,
month = 1
}

Conference:
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that hold this conference proceeding.

Save / Share:
  • This paper studies a multi-stage pricing problem for a large population of thermostatically controlled loads. The problem is formulated as a reverse Stackelberg game that involves a mean field game in the hierarchy of decision making. In particular, in the higher level, a coordinator needs to design a pricing function to motivate individual agents to maximize the social welfare. In the lower level, the individual utility maximization problem of each agent forms a mean field game coupled through the pricing function that depends on the average of the population control/state. We derive the solution to the reverse Stackelberg game bymore » connecting it to a team problem and the competitive equilibrium, and we show that this solution corresponds to the optimal mean field control that maximizes the social welfare. Realistic simulations are presented to validate the proposed methods.« less
  • 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 fast transients caused by demand response is especially important to analyze the stability of the system under different demand response strategies. On the other hand, a less complex model is more amenable to design feedback control strategies for the population of devices to provide ancillary services. The main contribution of this paper ismore » to develop aggregated models for a heterogeneous population of Thermostatic Controlled Loads (TCLs) to accurately capture their collective behavior under demand response and other time varying effects of the system. The aggregated model efficiently includes statistical information of the population and accounts for a second order effect necessary to accurately capture the collective dynamic behavior. The developed aggregated models are 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 caused due to temperature set point changes.« less
  • This paper presents a market-based control framework to coordinate a group of autonomous Thermostatically Controlled Loads (TCL) to achieve the system-level objectives with pricing incentives. The problem is formulated as maximizing the social welfare subject to feeder power constraint. It allows the coordinator to affect the aggregated power of a group of dynamical systems, and creates an interactive market where the users and the coordinator cooperatively determine the optimal energy allocation and energy price. The optimal pricing strategy is derived, which maximizes social welfare while respecting the feeder power constraint. The bidding strategy is also designed to compute the optimalmore » price in real time (e.g., every 5 minutes) based on local device information. The coordination framework is validated with realistic simulations in GridLab-D. Extensive simulation results demonstrate that the proposed approach effectively maximizes the social welfare and decreases power congestion at key times.« less
  • Abstract — To study the impacts of price responsive demand on the electric power system, requires better load models. This paper discusses the modeling of uncertainties in aggregated thermostatically controlled loads using a state queueing (SQ) model. The cycling times of thermostatically controlled appliances (TCAs) vary with the TCA types and sizes, as well as the ambient temperatures. The random consumption of consumers, which besides phase shifting, shortens or prolongs a specific TCA cycling period, introduces another degree of uncertainty. By modifying the state transition matrix, these random factors can be taken into account in a discrete SQ model. Themore » impacts of considering load diversity in the SQ model on simulating TCA setpoint response are also studied.« less