Given a stochastic net demand process evolving over a transmission-constrained power network, we consider the system operator's problem of minimizing the expected cost of generator dispatch, when it has access to spatially distributed energy storage resources. We show that the expected benefit of storage derived under the optimal dispatch policy is concave and non-decreasing in the vector of energy storage capacities. Thus, the greatest marginal value of storage is derived at small installed capacities. For such capacities, we provide an upper bound on the locational (nodal) marginal value of storage in terms of the variation of the shadow prices of electricity at each node. In addition, we prove that this upper bound is tight, when the cost of generation is spatially uniform and the network topology is acyclic. These formulae not only shed light on the correct measure of statistical variation in quantifying the value of storage, but also provide computationally tractable tools to empirically calculate the locational marginal value of storage from net demand time series data.

%B 2014 IEEE 53rd Annual Conference on Decision and Control (CDC) %I IEEE %C Los Angeles, CA, USA %P 3259 - 3265 %8 12/2014 %@ 978-1-4799-7746-8 %R 10.1109/CDC.2014.7039893 %0 Journal Article %J International Journal of Electrical Power & Energy Systems %D 2013 %T Risk-limiting dispatch for integrating renewable power %A Ram Rajagopal %A Eilyan Bitar %A Pravin Varaiya %A Felix Wu %K CERTS %K reliability and markets %K renewables integration %K reserve markets %K RM11-006 %X Risk-limiting dispatch or RLD is formulated as the optimal solution to a multi-stage, stochastic decision problem. At each stage, the system operator (SO) purchases forward energy and reserve capacity over a block or interval of time. The blocks get shorter as operations approach real time. Each decision is based on the most recent available information, including demand, renewable power, weather forecasts. The accumulated energy blocks must at each time t match the net demand D(t) = L(t) − W(t). The load L and renewable power W are both random processes. The expected cost of a dispatch is the sum of the costs of the energy and reserve capacity and the penalty or risk from mismatch between net demand and energy supply. The paper derives computable ‘closed-form’ formulas for RLD. Numerical examples demonstrate that the minimum expected cost can be substantially reduced by recognizing that risk from current decisions can be mitigated by future decisions; by additional intra-day energy and reserve capacity markets; and by better forecasts. These reductions are quantified and can be used to explore changes in the SO’s decision structure, forecasting technology, and renewable penetration. %B International Journal of Electrical Power & Energy Systems %V 44 %P 615 - 628 %8 01/2013 %N 1 %! International Journal of Electrical Power & Energy Systems %R 10.1016/j.ijepes.2012.07.048 %0 Conference Paper %B 2012 IEEE 51st Annual Conference on Decision and Control (CDC) %D 2012 %T Optimal power and reserve capacity procurement policies with deferrable loads %A Anand Subramanian %A Taylor, J. A. %A Eilyan Bitar %A Duncan S. Callaway %A Kameshwar Poolla %A Pravin Varaiya %K load management %K load modeling %K power system economics %K reliability and markets %K renewables %K RM11-006 %XDeferrable loads can be used to mitigate the variability associated with renewable generation. In this paper, we study the impact of deferrable loads on forward market operations. Specifically, we compute cost-minimizing ex-ante bulk power and reserve capacity procurement policies in the cases of fully deferrable and non-deferrable loads. For non-deferrable loads, we analytically express this policy on a partition of procurement prices. We also formulate a threshold policy for deferrable load scheduling in the face of uncertain supply, that minimizes grid operating costs.

%B 2012 IEEE 51st Annual Conference on Decision and Control (CDC) %I IEEE %C Maui, HI, USA %P 450 - 456 %8 12/2012 %@ 978-1-4673-2065-8 %R 10.1109/CDC.2012.6426102 %0 Conference Paper %B 2012 American Control Conference (ACC) %D 2012 %T Risk limiting dispatch of wind power %A Ram Rajagopal %A Eilyan Bitar %A Felix Wu %A Pravin Varaiya %K CERTS %K reliability and markets %K reserve generation %K risk-limiting dispatch %K RM11-006 %K wind power %XIntegrating wind and solar power into the grid requires dispatching various types of reserve generation to compensate for the randomness of renewable power. The dispatch is usually determined by a system operator (SO) or an aggregator who `firms' variable energy by bundling it with conventional power. The optimal dispatch is formulated as the solution to a stochastic control problem and shown to have a closed form that can be quickly computed. Different objectives and risk constraints can be included in the formulation and trade-offs can be evaluated. In particular one can quantify the influence of sequential forecasts on the total integration cost and the choice of dispatched generation. When the forecast error is Gaussian, the optimal dispatch policy can be precomputed.

%B 2012 American Control Conference (ACC) %I IEEE %C Montreal, QC %P 4417 - 4422 %8 06/2012 %@ 978-1-4577-1095-7 %R 10.1109/ACC.2012.6315239 %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