2018/02/28 by Arman C. Kizilkale, Kizilkale, Arman C., Rabih Salhab +3
Engineering · Physics and Astronomy · #Advanced Control Systems Optimization #Advanced Thermodynamics and Statistical Mechanics #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Smart Grid Energy Management #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1803.00040
openalex publication_date 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Pressure on ancillary reserves, i.e.frequency preserving, in power systems\nhas significantly mounted due to the recent generalized increase of the\nfraction of (highly fluctuating) wind and solar energy sources in grid\ngeneration mixes. The energy storage associated with millions of individual\ncustomer electric thermal (heating-cooling) loads is considered as a tool for\nsmoothing power demand/generation imbalances. The piecewise constant level\ntracking problem of their collective energy content is formulated as a linear\nquadratic mean field game problem with integral control in the cost\ncoefficients. The introduction of integral control brings with it a robustness\npotential to mismodeling, but also the potential of cost coefficient\nunboundedness. A suitable Banach space is introduced to establish the existence\nof Nash equilibria for the corresponding infinite population game, and\nalgorithms are proposed for reliably computing a class of desirable near Nash\nequilibria. Numerical simulations illustrate the flexibility and robustness of\nthe approach.\n