Storage Sizing and Placement through Operational and Uncertainty-Aware Simulations

As the penetration level of transmission-scale time-intermittent renewable generation resources increases, control of flexible resources will become important to mitigating the fluctuations due to these new renewable resources. Flexible resources may include new or existing synchronous generators as well as new energy storage devices. Optimal placement and sizing of energy storage to minimize costs of integrating renewable resources is a difficult optimization problem. Further,optimal planning procedures typically do not consider the effect of the time dependence of operations and may lead to unsatisfactory results. Here, we use an optimal energy storage control algorithm to develop a heuristic procedure for energy storage placement and sizing. We perform operational simulation under various time profiles of intermittent generation, loads and interchanges (artificially generated or from historical data) and accumulate statistics of the usage of storage at each node under the optimal dispatch. We develop a greedy heuristic based on the accumulated statistics to obtain a minimal set of nodes for storage placement. The quality of the heuristic is explored by comparing our results to the obvious heuristic of placing storage at the renewables for IEEE benchmarks and real-world network topologies.Comment: To Appear in proceedings of Hawaii International Conference on System Sciences (HICSS-2014

Local Control of Reactive Power by Distributed Photovoltaic Generators

High penetration levels of distributed photovoltaic (PV) generation on an electrical distribution circuit may severely degrade power quality due to voltage sags and swells caused by rapidly varying PV generation during cloud transients coupled with the slow response of existing utility compensation and regulation equipment. Although not permitted under current standards for interconnection of distributed generation, fast-reacting, VAR-capable PV inverters may provide the necessary reactive power injection or consumption to maintain voltage regulation under difficult transient conditions. As side benefit, the control of reactive power injection at each PV inverter provides an opportunity and a new tool for distribution utilities to optimize the performance of distribution circuits, e.g. by minimizing thermal losses. We suggest a local control scheme that dispatches reactive power from each PV inverter based on local instantaneous measurements of the real and reactive components of the consumed power and the real power generated by the PVs. Using one adjustable parameter per circuit, we balance the requirements on power quality and desire to minimize thermal losses. Numerical analysis of two exemplary systems, with comparable total PV generation albeit a different spatial distribution, show how to adjust the optimization parameter depending on the goal. Overall, this local scheme shows excellent performance; it's capable of guaranteeing acceptable power quality and achieving significant saving in thermal losses in various situations even when the renewable generation in excess of the circuit own load, i.e. feeding power back to the higher-level system.Comment: 6 pages, 5 figures, submitted to IEEE SmartGridComm 201

Pressure Fluctuations in Natural Gas Networks caused by Gas-Electric Coupling

The development of hydraulic fracturing technology has dramatically increased the supply and lowered the cost of natural gas in the United States, driving an expansion of natural gas-fired generation capacity in several electrical inter-connections. Gas-fired generators have the capability to ramp quickly and are often utilized by grid operators to balance intermittency caused by wind generation. The time-varying output of these generators results in time-varying natural gas consumption rates that impact the pressure and line-pack of the gas network. As gas system operators assume nearly constant gas consumption when estimating pipeline transfer capacity and for planning operations, such fluctuations are a source of risk to their system. Here, we develop a new method to assess this risk. We consider a model of gas networks with consumption modeled through two components: forecasted consumption and small spatio-temporarily varying consumption due to the gas-fired generators being used to balance wind. While the forecasted consumption is globally balanced over longer time scales, the fluctuating consumption causes pressure fluctuations in the gas system to grow diffusively in time with a diffusion rate sensitive to the steady but spatially-inhomogeneous forecasted distribution of mass flow. To motivate our approach, we analyze the effect of fluctuating gas consumption on a model of the Transco gas pipeline that extends from the Gulf of Mexico to the Northeast of the United States.Comment: 10 pages, 7 figure

Counting Independent Sets Using the Bethe Approximation

We consider the #P-complete problem of counting the number of independent sets in a given graph. Our interest is in understanding the effectiveness of the popular belief propagation (BP) heuristic. BP is a simple iterative algorithm that is known to have at least one fixed point, where each fixed point corresponds to a stationary point of the Bethe free energy (introduced by Yedidia, Freeman, and Weiss [IEEE Trans. Inform. Theory, 51 (2004), pp. 2282–2312] in recognition of Bethe’s earlier work in 1935). The evaluation of the Bethe free energy at such a stationary point (or BP fixed point) leads to the Bethe approximation for the number of independent sets of the given graph. BP is not known to converge in general, nor is an efficient, convergent procedure for finding stationary points of the Bethe free energy known. Furthermore, the effectiveness of the Bethe approximation is not well understood. As the first result of this paper we propose a BP-like algorithm that always converges to a stationary point of the Bethe free energy for any graph for the independent set problem. This procedure finds an ε-approximate stationary point in O(n2d42depsilon-4log3(nepsilon-1)) iterations for a graph of n nodes with max-degree d. We study the quality of the resulting Bethe approximation using the recently developed “loop series” framework of Chertkov and Chernyak [J. Stat. Mech. Theory Exp., 6 (2006), P06009]. As this characterization is applicable only for exact stationary points of the Bethe free energy, we provide a slightly modified characterization that holds for ε-approximate stationary points. We establish that for any graph on n nodes with max-degree d and girth larger than 8d log2 n, the multiplicative error between the number of independent sets and the Bethe approximation decays as 1+O(n-γ) for some γ>0. This provides a deterministic counting algorithm that leads to strictly different results compared to a recent result of Weitz [in Proceedings of the Thirty-Eighth Annual ACM Symposium on Theory of Computing, ACM Press, New York, 2006, pp. 140–149]. Finally, as a consequence of our analysis we prove that the Bethe approximation is exceedingly good for a random 3-regular graph conditioned on the shortest cycle cover conjecture of Alon and Tarsi [SIAM J. Algebr. Discrete Methods, 6 (1985), pp. 345–350] being true.National Science Foundation (U.S.) (NSF EMT/MISC collaborative project 0829893