期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 66, 期 12, 页码 6164-6170出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2021.3061625
关键词
Load management; Heuristic algorithms; Power system dynamics; Optimization; Convex functions; Load modeling; Time factors; Binary decision; demand response; dynamic regret; online convex optimization; thermostatically controlled loads
资金
- Natural Sciences and Engineering Research Council of Canada
- Institute for Data Valorization
- National Science Foundation [1351900]
- Advanced Research Projects Agency-Energy [DE-AR0001061]
- Div Of Electrical, Commun & Cyber Sys
- Directorate For Engineering [1351900] Funding Source: National Science Foundation
This study focuses on online optimization with binary decision variables and convex loss functions. A new algorithm, binary online gradient descent (bOGD), is designed and its expected dynamic regret is bounded. The research provides a regret bound applicable for any time horizon and a specialized bound for finite time horizons. The application of bOGD in demand response systems shows significant effectiveness.
We consider online optimization with binary decision variables and convex loss functions. We design a new algorithm, binary online gradient descent (bOGD) and bound its expected dynamic regret. We provide a regret bound that holds for any time horizon and a specialized bound for finite time horizons. First, we present the regret as the sum of the relaxed, continuous round optimum tracking error, and the rounding error of our update in which the former asymptomatically decreases with time under certain conditions. Then, we derive a finite-time bound that is sublinear in time and linear in the cumulative variation of the relaxed, continuous round optima. We apply bOGD to demand response with thermostatically controlled loads, in which binary constraints model discrete on/off settings. We also model uncertainty and varying load availability, which depend on temperature deadbands, lockout of cooling units and manual overrides. We test the performance of bOGD in several simulations based on demand response. The simulations corroborate that the use of randomization in bOGD does not significantly degrade performance while making the problem more tractable.
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