Limits on the Benefits of Energy Storage for Renewable Integration

The high variability of renewable energy resources presents significant challenges to the operation of the electric power grid. Conventional generators can be used to mitigate this variability but are costly to operate and produce carbon emissions. Energy storage provides a more environmentally friendly alternative, but is costly to deploy in large amounts. This paper studies the limits on the benefits of energy storage to renewable energy: How effective is storage at mitigating the adverse effects of renewable energy variability? How much storage is needed? What are the optimal control policies for operating storage? To provide answers to these questions, we first formulate the power flow in a single-bus power system with storage as an infinite horizon stochastic program. We find the optimal policies for arbitrary net renewable generation process when the cost function is the average conventional generation (environmental cost) and when it is the average loss of load probability (reliability cost). We obtain more refined results by considering the multi-timescale operation of the power system. We view the power flow in each timescale as the superposition of a predicted (deterministic) component and an prediction error (residual) component and formulate the residual power flow problem as an infinite horizon dynamic program. Assuming that the net generation prediction error is an IID process, we quantify the asymptotic benefits of storage. With the additional assumption of Laplace distributed prediction error, we obtain closed form expressions for the stationary distribution of storage and conventional generation. Finally, we propose a two-threshold policy that trades off conventional generation saving with loss of load probability. We illustrate our results and corroborate the IID and Laplace assumptions numerically using datasets from CAISO and NREL.Comment: 45 pages, 17 figure

An approximation theorem for nuclear operator systems

We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps \phi_\lambda : \cl S \to M_{n_\lambda} and \psi_\lambda : M_{n_\lambda} \to \cl S such that $\psi_\lambda \circ \phi_\lambda$ converges to {\rm id}_{\cl S} in the point-norm topology. Our proof is independent of the Choi-Effros-Kirchberg characterization of nuclear $C^*$-algebras and yields this characterization as a corollary. We give an example of a nuclear operator system that is not completely order isomorphic to a unital $C^*$-algebra.Comment: 10 pages; to appear in JF

A computational study of photoisomerization in Al3O3- ­clusters

Ab initio calculations are employed to understand the photoisomerization process in small Al3O3- clusters. This process is the first example of a photoinduced isomerization observed in an anion cluster gas-phase system. Potential energy surfaces for the ground state and the excited state (S1 and T1) are explored by means of B3LYP, MP2, CI-singles, and CASSCF methods. We demonstrate that the isomerization process occurs between the global minimum singlet state Book structure (C2v,1A1) and the triplet state Ring structure (C2v,3B2). The calculated vertical excitation energy is 3.62 eV at the CASSCF level of approximation, in good agreement with the experimental value (3.49 eV). A nonplanar conical intersection, which hosts the intersystem crossing between the S1 and T1 surfaces is identified at the region of around R(1,6)=2.4 Å. Beyond the experimental results, we predict, that this isomerization is reversible upon absorption of a phonon with energy of 1.92 eV. Our results describe a unique system, whose structure depends on its spin multiplicity; it exists as the Book structure on singlet states and as the Ring structure on triplet states

CHINA'S RURAL HOUSEHOLD DEMAND FOR FRUIT AND VEGETABLES

A two-stage budgeting LES-LA/AIDS system is sued to estimate rural household demand in China with special emphasis on changes in demand for fruit and vegetable commodities across different income groups. The own-price elasticity for food was found to be more elastic than that for clothing, housing, durable goods, and other items. Within the food group, price elasticities range from -1.042 to -0.019. Grain, with an expenditure elasticity of almost unity, is an important staple food for the average rural household. Vegetables are important nonstaple foods relative to fruits. Lower value vegetables are the most price elastic in the vegetable group. Fruits are more price elastic than vegetables, with grapes being the most price elastic. Different income groups share a common demand function.AIDS model, Chinese rural households, Elasticity, Household demand, Household demand, LES model, Two-stage budgeting, Demand and Price Analysis,