A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads

Zhao, Lin; Zhang, Wei; Hao, He; Kalsi, Karanjit

doi:10.1109/tpwrs.2017.2674699

A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads

Journal Article · Thu Feb 23 23:00:00 EST 2017 · IEEE Transactions on Power Systems

DOI:https://doi.org/10.1109/tpwrs.2017.2674699· OSTI ID:2458240

Zhao, Lin ^[1]; ^[1]; ^[2]; Kalsi, Karanjit ^[2]

The Ohio State Univ., Columbus, OH (United States)
Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Coordinated aggregation of a large population of thermostatically controlled loads (TCLs) presents a great potential to provide various ancillary services to the grid. One of the key challenges in coordination and control of TCLs is developing a simple and portable model to accurately extract their aggregate flexibility. In this paper, we propose a novel geometric approach to model the aggregate flexibility of TCLs. We show that the set of admissible power profiles of an individual TCL is a polytope, and their aggregate flexibility is the Minkowski sum of the individual polytopes. In order to represent their aggregate flexibility in an intuitive way and achieve a tractable approximation, we develop optimization-based algorithms to approximate the polytopes by the homothets of a given convex set. As a special application, this set is chosen as a virtual battery model and the corresponding optimal approximation problems are solved efficiently by equivalent linear programs. Numerical results show that our algorithms yield significant improvement in characterizing the aggregate flexibility over existing modeling methods. Finally, we also conduct case studies to demonstrate the efficacy of our approaches by coordinating TCLs to track a frequency regulation signal from the Pennsylvania-New Jersey-Maryland (PJM) Interconnection.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE; National Science Foundation (NSF)

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 2458240

Report Number(s):: PNNL-SA--120065

Journal Information:: IEEE Transactions on Power Systems, Journal Name: IEEE Transactions on Power Systems Journal Issue: 6 Vol. 32; ISSN 0885-8950

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

References (27)

Optimal scaling of balls and polyhedra Eaves, B. C.; Freund, R. M. Mathematical Programming, Vol. 23, Issue 1 https://doi.org/10.1007/BF01583784	journal	December 1982
On the Hardness of Computing Intersection, Union and Minkowski Sum of Polytopes Tiwary, Hans Raj Discrete & Computational Geometry, Vol. 40, Issue 3 https://doi.org/10.1007/s00454-008-9097-3	journal	July 2008
Tapping the energy storage potential in electric loads to deliver load following and regulation, with application to wind energy Callaway, Duncan S. Energy Conversion and Management, Vol. 50, Issue 5, p. 1389-1400 https://doi.org/10.1016/j.enconman.2008.12.012	journal	May 2009
A concise, approximate representation of a collection of loads described by polytopes Barot, Suhail; Taylor, Josh A. International Journal of Electrical Power & Energy Systems, Vol. 84 https://doi.org/10.1016/j.ijepes.2016.05.001	journal	January 2017
Improved battery models of an aggregation of Thermostatically Controlled Loads for frequency regulation Sanandaji, Borhan M.; Hao, He; Poolla, Kameshwar 2014 American Control Conference https://doi.org/10.1109/ACC.2014.6858956	conference	June 2014
A geometric approach to virtual battery modeling of thermostatically controlled loads Zhao, Lin; Zhang, Wei 2016 American Control Conference (ACC) https://doi.org/10.1109/ACC.2016.7525121	conference	July 2016
YALMIP : a toolbox for modeling and optimization in MATLAB Lofberg, J. 2004 IEEE International Symposium on Computer Aided Control Systems Design, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508) https://doi.org/10.1109/CACSD.2004.1393890	conference	January 2004
Exact constraint aggregation with applications to smart grids and resource distribution Trangbaek, Klaus; Bendtsen, Jan 2012 IEEE 51st Annual Conference on Decision and Control (CDC), 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2012.6426475	conference	December 2012
Aggregation of energetic flexibility using zonotopes Muller, Fabian L.; Sundstrom, Olle; Szabo, Jacint 2015 54th IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2015.7403253	conference	December 2015
A unified Stochastic Hybrid System approach to aggregated load modeling for demand response Zhao, Lin; Zhang, Wei 2015 54th IEEE Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2015.7403269	conference	December 2015
Extracting flexibility of heterogeneous deferrable loads via polytopic projection approximation Zhao, Lin; Hao, He; Zhang, Wei 2016 IEEE 55th Conference on Decision and Control (CDC) https://doi.org/10.1109/CDC.2016.7799293	conference	December 2016
Fast Regulation Service Provision via Aggregation of Thermostatically Controlled Loads Sanandaji, Borhan M.; Poolla, Kameshwar 2014 47th Hawaii International Conference on System Sciences https://doi.org/10.1109/HICSS.2014.300	conference	January 2014
Achieving Controllability of Electric Loads Callaway, D. S.; Hiskens, I. A. Proceedings of the IEEE, Vol. 99, Issue 1 https://doi.org/10.1109/JPROC.2010.2081652	journal	January 2011
Value of thermostatic loads in future low-carbon Great Britain system Trovato, Vincenzo; Teng, Fei; Strbac, Goran 2016 Power Systems Computation Conference (PSCC) https://doi.org/10.1109/PSCC.2016.7540879	conference	June 2016
Combined Load Frequency Control and active distribution network management with Thermostatically Controlled Loads Vrettos, Evangelos; Andersson, Goran 2013 IEEE International Conference on Smart Grid Communications (SmartGridComm) https://doi.org/10.1109/SmartGridComm.2013.6687965	conference	October 2013
Generalized aggregation and coordination of residential loads in a smart community Hao, He; Somani, Abhishek; Lian, Jianming 2015 IEEE International Conference on Smart Grid Communications (SmartGridComm) https://doi.org/10.1109/SmartGridComm.2015.7436278	conference	November 2015
Modeling and Control of Aggregate Air Conditioning Loads for Robust Renewable Power Management Bashash, Saeid; Fathy, Hosam K. IEEE Transactions on Control Systems Technology, Vol. 21, Issue 4 https://doi.org/10.1109/TCST.2012.2204261	journal	July 2013
A State-Queueing Model of Thermostatically Controlled Appliances Lu, N.; Chassin, D. P. IEEE Transactions on Power Systems, Vol. 19, Issue 3, p. 1666-1673 https://doi.org/10.1109/TPWRS.2004.831700	journal	August 2004
Operational Impacts of Wind Generation on California Power Systems Makarov, Y. V.; Loutan, C.; Ma, Jian IEEE Transactions on Power Systems, Vol. 24, Issue 2, p. 1039-1050 https://doi.org/10.1109/TPWRS.2009.2016364	journal	May 2009
State Estimation and Control of Electric Loads to Manage Real-Time Energy Imbalance Mathieu, Johanna L.; Koch, Stephan; Callaway, Duncan S. IEEE Transactions on Power Systems, Vol. 28, Issue 1 https://doi.org/10.1109/TPWRS.2012.2204074	journal	February 2013
Aggregated Modeling and Control of Air Conditioning Loads for Demand Response Zhang, Wei; Lian, Jianming; Chang, Chin-Yao IEEE Transactions on Power Systems, Vol. 28, Issue 4, p. 4655-4664 https://doi.org/10.1109/TPWRS.2013.2266121	journal	November 2013
Aggregate Flexibility of Thermostatically Controlled Loads Hao, He; Sanandaji, Borhan M.; Poolla, Kameshwar IEEE Transactions on Power Systems, Vol. 30, Issue 1 https://doi.org/10.1109/TPWRS.2014.2328865	journal	January 2015
Arbitraging Intraday Wholesale Energy Market Prices With Aggregations of Thermostatic Loads Mathieu, Johanna L.; Kamgarpour, Maryam; Lygeros, John IEEE Transactions on Power Systems, Vol. 30, Issue 2 https://doi.org/10.1109/TPWRS.2014.2335158	journal	March 2015
Market-Based Coordination of Thermostatically Controlled Loads—Part I: A Mechanism Design Formulation Li, Sen; Zhang, Wei; Lian, Jianming IEEE Transactions on Power Systems, Vol. 31, Issue 2 https://doi.org/10.1109/TPWRS.2015.2432057	journal	March 2016
Identification of Virtual Battery Models for Flexible Loads Hughes, Justin T.; Dominguez-Garcia, Alejandro D.; Poolla, Kameshwar IEEE Transactions on Power Systems, Vol. 31, Issue 6 https://doi.org/10.1109/TPWRS.2015.2505645	journal	November 2016
Distributionally Robust Chance-Constrained Optimal Power Flow with Uncertain Renewables and Uncertain Reserves Provided by Loads Zhang, Yiling; Shen, Siqian; Mathieu, Johanna IEEE Transactions on Power Systems https://doi.org/10.1109/TPWRS.2016.2572104	journal	January 2016
Ramping Rate Flexibility of Residential HVAC Loads Sanandaji, Borhan M.; Vincent, Tyrone L.; Poolla, Kameshwar IEEE Transactions on Sustainable Energy, Vol. 7, Issue 2 https://doi.org/10.1109/TSTE.2015.2497236	journal	April 2016

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24 POWER TRANSMISSION AND DISTRIBUTION
Minkowski sum
aggregate flexibility
frequency regulation
thermostatically controlled loads
virtual battery model

A Geometric Approach to Aggregate Flexibility Modeling of Thermostatically Controlled Loads

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