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

KN and KbarN Elastic Scattering in the Quark Potential Model

The KN and KbarN low-energy elastic scattering is consistently studied in the framework of the QCD-inspired quark potential model. The model is composed of the t-channel one-gluon exchange potential, the s-channel one-gluon exchange potential and the harmonic oscillator confinement potential. By means of the resonating group method, nonlocal effective interaction potentials for the KN and KbarN systems are derived and used to calculate the KN and KbarN elastic scattering phase shifts. By considering the effect of QCD renormalization, the contribution of the color octet of the clusters (qqbar) and (qqq) and the suppression of the spin-orbital coupling, the numerical results are in fairly good agreement with the experimental data.Comment: 20 pages, 8 figure

Crossover from the pair contact process with diffusion to directed percolation

Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation/branching dynamics. The crossover exponents $\phi$ are estimated numerically as $1/\phi \simeq 0.58\pm0.03$ for the PCPD and $1/\phi \simeq 0.49 \pm 0.02$ for the DPCPD. Nontriviality of the PCPD crossover exponent strongly supports non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PCPD point. In addition, we find that the DPCPD crossover is consistent with the mean field prediction of the tricritical DP class as expected