Tyrone L. Vincent

Tyrone L. Vincent, Michael B. Wakin

An impulse response/equilibrium model (IREM) structure combines a linear convolution model with a nonlinear function that sets the current operating point via an equilibrium variable with integrator dynamics. This model structure is well suited for mildly nonlinear systems and in particular has been applied to battery fast charging control. This paper provides observability conditions for the IREM model structure and bounds on the prediction error. These conditions can be evaluated directly on the system impulse response.

Borhan M. Sanandaji, Michael B. Wakin, Tyrone L. Vincent

Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work builds upon recent results from Compressive Sensing (CS). In particular, we make the connection to CS analysis for random block diagonal matrices. By deriving Concentration of Measure (CoM) inequalities, we show that the observability matrix satisfies the Restricted Isometry Property (RIP) (a sufficient condition for stable recovery of sparse vectors) under certain conditions on the state transition matrix. For example, we show that if the state transition matrix is unitary, and if independent, randomly-populated measurement matrices are employed, then it is possible to uniquely recover a sparse high-dimensional initial state when the total number of measurements scales linearly in the sparsity level (the number of non-zero entries) of the initial state and logarithmically in the state dimension. We further extend our RIP analysis for scaled unitary and symmetric state transition matrices. We support our analysis with a case study of a two-dimensional diffusion process.

He Hao, Borhan M. Sanandaji, Kameshwar Poolla et al.

Residential Thermostatically Controlled Loads (TCLs) such as Air Conditioners (ACs), heat pumps, water heaters, and refrigerators have an enormous thermal storage potential for providing regulation reserve to the grid. In this paper, we study the potential resource and economic analysis of TCLs providing frequency regulation service. In particular, we show that the potential resource of TCLs in California is more than enough for both current and predicted near-future regulation requirements for the California power system. Moreover, we estimate the cost and revenue of TCLs, discuss the qualification requirements, recommended policy changes, and participation incentive methods, and compare TCLs with other energy storage technologies. We show that TCLs are potentially more cost-effective than other energy storage technologies such as flywheels, Li-ion, advanced lead acid, and Zinc Bromide batteries.