There has recently been interest in diversifying the technologies that provide primary frequency control of the power grid beyond generation. One method of interest to obtain frequency control by turning on or off flexible loads in response to local measurements of line frequency. Because of the large number of loads involved, it is desirable to implement this control without communication among the loads or to a centralized controller. One proposal that does not require communication is to have each load choose the frequency at which it switches on or off randomly. In this paper we use tail bounds and absolute stability to obtain stability guarantees that are satisfied with high probability. This stability result considers not only grid inertia and damping but local measurement delays.

%B 2016 American Control Conference (ACC) %I IEEE %C Boston, MA, USA %P 2328 - 2333 %8 08/2016 %R 10.1109/ACC.2016.7525265 %0 Conference Paper %B 2016 IEEE 55th Conference on Decision and Control (CDC) %D 2016 %T Stochastic AC optimal power flow with affine recourse %A Raphael Louca %A Eilyan Bitar %K RM14-002 %XWith the increasing penetration of intermittent renewable energy sources into the electric power grid, there is an emerging need to develop stochastic optimization methods to enable the reliable and efficient operation of power systems having a large fraction of their power supplied form uncertain resources. In this paper, we formulate the stochastic AC optimal power flow (OPF) problem as a two-stage stochastic program with robust constraints. This problem amounts to an infinite-dimensional nonconvex optimization problem. We develop a finite-dimensional inner approximation as a semidefinite program. Its solution yields an affine recourse policy that is guaranteed to be feasible for the stochastic AC OPF problem.

%B 2016 IEEE 55th Conference on Decision and Control (CDC) %I IEEE %C Las Vegas, NV, USA %P 2431 - 2436 %8 12/2016 %R 10.1109/CDC.2016.7798626 %0 Conference Paper %B 2012 45th Hawaii International Conference on System Sciences (HICSS) %D 2012 %T Selling Random Wind %A Eilyan Bitar %A Kameshwar Poolla %A Pramod P. Khargonekar %A Ram Rajagopal %A Pravin Varaiya %A Felix Wu %K CERTS %K electricity markets %K reliability %K reliability and markets %K renewables integration %K RM11-006 %XWind power is inherently random, but we are used to 100 percent reliable or 'firm' electricity, so reserves are used to convert random wind power into firm electricity. The cost of these reserves is frequently a hidden subsidy to wind power producers. We propose an alternative: package random wind power into electricity with different levels of reliability and sell them at different prices. This variable-reliability market is more efficient than the current firm-electricity market, and may require lower subsidy. However, we have to think of electricity differently. We also explore interesting differences between the variable-reliability and related real-time markets.

%B 2012 45th Hawaii International Conference on System Sciences (HICSS) %I IEEE %C Maui, HI, USA %P 1931 - 1937 %8 01/2012 %@ 978-1-4577-1925-7 %R 10.1109/HICSS.2012.523