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Nearly Optimal Real-Time Deferrable Load Control

Nearly Optimal Real-Time Deferrable Load Control. Lingwen Gan 1 , Adam Wierman 1 , Ufuk Topcu 2 , Niangjun Chen 1 , Steven Low 1 1 California Institute of Technology 2 University of Pennsylvania. Balance demand and generation. Current practice. demand. generation. Tracking error. 0.

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Nearly Optimal Real-Time Deferrable Load Control

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  1. Nearly Optimal Real-Time Deferrable Load Control Lingwen Gan1, Adam Wierman1, Ufuk Topcu2, Niangjun Chen1, Steven Low1 1California Institute of Technology 2University of Pennsylvania

  2. Balance demand and generation Current practice demand generation Tracking error 0 Load control

  3. Two approaches Direct load control [Hsu et. al. 1991] [Wei et. al. 1995] [Ng et. al. 1998] [Huang et. al. 2004] [Ruiz et. al. 2009] reliable response consumer must give up control used today for household loads Pricing [Borenstein et. al. 2002] [Albadi et. al. 2008] [Roos et. al. 1998] [Zhang et. al. 2008] unreliable response consumer retain control used today for industrial loads

  4. Challenges generation demand Generation is stochastic ? real-time adaptive control [Li et. al. 2011], [Chen et. al. 2012], [Subramanian et. al. 2012]… Large number of diverse loads distributed control [Ma et. al. 2010], [Gan et. al. 2011], [Li et. al. 2011]…

  5. Our contribution A real-time distributed algorithm for direct load control. Analyze performance in the “average” sense.

  6. Outline • Model • Algorithm • Analysis

  7. Model overview generation demand ? arrival prediction individual load Goal: minimize tracking error. 1 2 3 4 Challenge: Uncertainty distributed solution.

  8. Renewable prediction • Finite, discrete time horizon. ? prediction generation • Generation is random • At time , prediction

  9. An example mean deviation noise filter models time correlation in prediction error. 0 0 Model any unbiased prediction process with stationary prediction error. Used in analysis, not in algorithm. 0

  10. Controllable loads Load arrive by time . Know at time . Each load arrives with a deadline. arrival time : power consumption load arrive deadline 1 2 3 4 Maximum power consumption. Meets energy request.

  11. The optimal scheduling problem load constraints • Challenge 1: • and are random

  12. By-pass uncertainties in and At time , Represent future load Future load Total energy request of future load

  13. Time- subproblem At time , load constraints pseudo load constraints • Challenge 2: • Distributed algorithm to solve the time- subproblem.

  14. Solve the time- subproblem through distributed gradient decent At time , Utility load Compute that minimizes Compute Update by minimizing cost penalty

  15. Analysis overview 1) Does the algorithm converge? 2) How big is the tracking error at convergence? 3) How much benefit over open-loop control?

  16. Does the algorithm converge? Thm: The algorithm converges to solutions of the time- subproblem at every time . t-valley-filling Tracking error t-valley-filling schedules tend to exist when there is a large number of controllable loads. t Prop: t-valley-filling schedules solve time-t subproblem. Assume -valley-filling schedules exist for all .

  17. How big is the tracking error? Corollary: The expected tracking error vanishes as prediction gets precise, i.e., Corollary: The expected tracking error vanishes as time horizon expands, provided that time correlation in prediction error is not too strong, i.e., , then

  18. Formula for tracking error Theorem: The expected tracking error is load arrival renewable load arrival prediction error the impact of time correlation in prediction error renewable prediction error

  19. Tracking error as prediction error increases • Wind generation data from Alberta Electric System Operator. • Wind prediction model as analysis, with . • Load data from Southern California Edison. • Scale to 10% renewable, 10% controllable loads. 16% 12% 8% 4% 0% 0 10 15 5 20 wind prediction error (%)

  20. How much benefit over open-loop control? Assume arrival is known. Let denote the tracking error of optimal open-loop control. Thm: The algorithm is better than the optimal open-loop control, i.e., Thm: Order improvement, i.e., for the following two types of filter . 0 0

  21. Quantify benefit (known arrival) • Wind generation data from Alberta Electric System Operator. • Wind prediction model as analysis, with . • Load data from Southern California Edison. • Scale to 10% renewable, 10% controllable loads. 16% 12% Open-loop 8% 4% 0% 0 10 15 5 20 Algorithm wind prediction error (%)

  22. Summary generation demand ? • Propose a distributed online algorithm to track generation. • Analyze performance in the “average” sense. Does the algorithm converge? Yes, to solutions of time- subproblem. 1 2 3 4 How big is the tracking error? Vanishes as time horizon expands. How much benefit over open-loop control? .

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