Abstract-The high variability of renewable energy is a major obstacle toward its increased penetration. Energy storage can help reduce the power imbalance due to the mismatch between the available renewable power and the load. How much can storage reduce this power imbalance? How much storage is needed to achieve this reduction? This paper presents a simple analytic model that leads to some answers to these questions. Considering the multitimescale grid operation, we formulate the power imbalance problem for each timescale as an infinite horizon stochastic control problem and show that a greedy policy minimizes the average magnitude of the residual power imbalance. Observing from the wind power data that in shorter timescales the power imbalance can be modeled as an iid zero-mean Laplace distributed process, we obtain closed form expressions for the minimum cost and the stationary distribution of the stored power. We show that most of the reduction in the power imbalance can be achieved with relatively small storage capacity. In longer timescales, the correlation in the power imbalance cannot be ignored. As such, we relax the iid assumption to a weakly dependent stationary process and quantify the limit on the minimum cost for arbitrarily large storage capacity.

Abstract-The large short time-scale variability of renewable energy resources presents significant challenges to the reliable operation of power systems. This variability can be mitigated by deploying fast-ramping generators. However, these generators are costly to operate and produce environmentally harmful emissions. Fast-response energy storage devices, such as batteries and flywheels, provide an environmentally friendly alternative, but are expensive and have limited capacity. To study the environmental benefits of storage, we introduce a slotted-time dynamic residual dc power flow model with the prediction error of the difference between the generation (including renewables) and the load as input and the fast-ramping generation and the storage (charging/discharging) operation as the control variables used to ensure that the demand is satisfied (as much as possible) in each time slot. We assume the input prediction error sequence to be i.i.d. zero-mean random variables. The optimal power flow problem is then formulated as an infinite horizon average-cost dynamic program with the cost function taken as a weighted sum of the average fast-ramping generation and the loss of load probability. We find the optimal policies at the two extremes of the cost function weights and propose a two-threshold policy for the general case. We also obtain refined analytical results under the assumption of Laplace distributed prediction error and corroborate this assumption using simulated wind power generation data from NREL.

Abstract-We investigate distributed source coding of two correlated sources X and Y where messages are passed to a decoder in a cascade fashion. The encoder of X sends a message at rate R 1 to the encoder of Y. The encoder of Y then sends a message to the decoder at rate R 2 based both on Y and on the message it received about X. The decoder's task is to estimate a function of X and Y. For example, we consider the minimum mean squared-error distortion when encoding the sum of jointly Gaussian random variables under these constraints. We also characterize the rates needed to reconstruct a function of X and Y losslessly.Our general contribution toward understanding the limits of the cascade multiterminal source coding network is in the form of inner and outer bounds on the achievable rate region for satisfying a distortion constraint for an arbitrary distortion function d (x, y, z). The inner bound makes use of a balance between two encoding tactics-relaying the information about X and recompressing the information about X jointly with Y. In the Gaussian case, a threshold is discovered for identifying which of the two extreme strategies optimizes the inner bound. Relaying outperforms recompressing the sum at the relay for some rate pairs if the variance of X is greater than the variance of Y.

Abstract-A 3-node lossy source coding problem for a 2-DMS (X1, X2) is considered. Source nodes 1 and 2 observe X1 and X2, respectively, and each wishes to reconstruct the other source with a prescribed distortion. To achieve these goals, nodes 1 and 2 send descriptions of their sources to relay node 3. The relay node then broadcasts a joint description to the source nodes. A cutset outer bound and a compress-linear code inner bound are established and shown to coincide in several special cases. A compute-compress inner bound is then presented and shown to outperform the compress-linear code in some cases. An outer bound based on Kaspi's converse for the two-way source coding problem is shown to be strictly tighter than the cutset outer bound.

Abstract-An information theoretic form ulation of distributed averaging is presented. We assume a network with m nodes each observing an i.i.d, source; the nodes communicate and perform local processing with the goal of com puting the average of the sources to within a prescribed mean squared error distortion. The network rate distortion function R* (D) for a 2-node network with correlated Gaussian sources is established. A general cutset lower bound on R* (D) with independent Gaussian sources is established and shown to be achievable to within a factor of 2 via a centralized protocol. A lower bound on the network rate distortion function for distributed weighted-sum protocols that is larger than the cutset bound by a factor of log m is established. An upper bound on the expected network rate distortion function for gossip-based weighted-sum protocols that is only a factor of log log m larger than this lower bound is established. The results suggest that using distributed protocols results in a factor of log m increase in communication relative to centralized protocols.