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.

10aenergy storage10aLocational marginal value10areliability and markets10aRM11-0061 aBose, Subhonmesh1 aBitar, Eilyan uhttps://certs.lbl.gov/publications/variability-and-locational-marginal01902nas a2200241 4500008003900000022001300039245005900052210005800111260001200169300001400181490000700195520121500202653001001417653002801427653002701455653002001482653001301502100001901515700001801534700002001552700001401572856007401586 2013 d a0142061500aRisk-limiting dispatch for integrating renewable power0 aRisklimiting dispatch for integrating renewable power c01/2013 a615 - 6280 v443 aRisk-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.10aCERTS10areliability and markets10arenewables integration10areserve markets10aRM11-0061 aRajagopal, Ram1 aBitar, Eilyan1 aVaraiya, Pravin1 aWu, Felix uhttps://certs.lbl.gov/publications/risk-limiting-dispatch-integrating01437nas a2200265 4500008003900000020002200039245008200061210006900143260003300212300001400245520059000259653002000849653001800869653002700887653002800914653001500942653001300957100002300970700001900993700001801012700002501030700002201055700002001077856007401097 2012 d a978-1-4673-2065-800aOptimal power and reserve capacity procurement policies with deferrable loads0 aOptimal power and reserve capacity procurement policies with def aMaui, HI, USAbIEEEc12/2012 a450 - 4563 aDeferrable 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.

10aload management10aload modeling10apower system economics10areliability and markets10arenewables10aRM11-0061 aSubramanian, Anand1 aTaylor, J., A.1 aBitar, Eilyan1 aCallaway, Duncan, S.1 aPoolla, Kameshwar1 aVaraiya, Pravin uhttps://certs.lbl.gov/publications/optimal-power-and-reserve-capacity01487nas a2200241 4500008003900000020002200039245004100061210004100102260003200143300001600175520079400191653001000985653002800995653002301023653002701046653001301073653001501086100001901101700001801120700001401138700002001152856007301172 2012 d a978-1-4577-1095-700aRisk limiting dispatch of wind power0 aRisk limiting dispatch of wind power aMontreal, QCbIEEEc06/2012 a4417 - 44223 aIntegrating 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.

10aCERTS10areliability and markets10areserve generation10arisk-limiting dispatch10aRM11-00610awind power1 aRajagopal, Ram1 aBitar, Eilyan1 aWu, Felix1 aVaraiya, Pravin uhttps://certs.lbl.gov/publications/risk-limiting-dispatch-wind-power01409nas a2200265 4500008003900000020002200039245002400061210002400085260003300109300001600142520068700158653001000845653002400855653001600879653002800895653002700923653001300950100001800963700002200981700002801003700001901031700002001050700001401070856005901084 2012 d a978-1-4577-1925-700aSelling Random Wind0 aSelling Random Wind aMaui, HI, USAbIEEEc01/2012 a1931 - 19373 aWind 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.

10aCERTS10aelectricity markets10areliability10areliability and markets10arenewables integration10aRM11-0061 aBitar, Eilyan1 aPoolla, Kameshwar1 aKhargonekar, Pramod, P.1 aRajagopal, Ram1 aVaraiya, Pravin1 aWu, Felix uhttps://certs.lbl.gov/publications/selling-random-wind