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The integration of distributed energy generation systems has begun to impact the operation of distribution feeders within the balancing areas of numerous electrical utilities. Battery energy storage systems may be used to facilitate greater integration of renewable energy generation. This paper describes a method for determining the power and energy capacities a battery energy storage system would need in order to accommodate a particular photovoltaic penetration level within a distribution feeder, or conversely, the amount of photovoltaic that could be installed on a feeder with a minimal investment in power and energy battery energy storage system (BESS) capacities. This method determines the BESS capacities required to compensate both intra-hour and inter-hour load and photovoltaic fluctuations to achieve a flat feeder power profile. By managing the feeder power, the voltage drop along the length of feeder may be managed, thereby mitigating the voltage fluctuation induced by the stochastic nature of both renewables generation and load. Doing so facilitates system benefits, such as conservation voltage reduction, fewer operations of load tap changers, and voltage regulators, and allows for deferment of capital expenditures. INDEX TERMS Battery energy storage systems, firming, photovoltaic (PV) integration, shaping.

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Abstract:This paper provides an analysis of RC and RL electrical circuits described by a fractional difierential equation Illustrative examples are presented.

Lanthanum-containing Y (LaY) zeolites were prepared by ionic exchange from NaY parent zeolite. The LaY zeolites were de-aluminated by steaming. De-aluminated zeolites presented different Si/Al ratio. The physicochemical properties of these catalysts were characterized by X-ray diffraction, pyridine and xenon adsorption, infrared spectroscopy and 29 Si, 27 Al, 129 Xe, 139 La solid-state nuclear magnetic resonance spectroscopy. Furthermore, a fractal geometry approach was adopted to describe the evolution in the texture as a consequence of de-alumination. The catalytic properties of materials were evaluated in the n-hexane cracking reaction. The catalyst with the highest catalytic activity was the zeolite highest de-aluminated (Si/Al ratio of 3.7). Such performance was attributed on the one hand, to active extra-framework aluminum species hosted in the large cavities of zeolites and, on the other hand to redistribution of lanthanum species into the zeolite as a consequence of de-alumination.

By using the notion of endpoints for set-valued functions and some classical fixed point techniques, we investigate the existence of solutions for two fractional [Formula: see text]-differential inclusions under some integral boundary value conditions. By providing an example, we illustrate our main result about endpoint. Also, we give some related algorithms and numerical results.