On Using Storage and Genset for Mitigating Power Grid Failures

Although modern society is critically reliant on power grids, even modern power grids are subject to unavoidable outages due to storms, lightning strikes, and equipment failures. The situation in developing countries is even worse, with frequent load shedding lasting several hours a day due to unreliable generation. We study the use of battery storage to allow a set of homes in a single residential neighbourhood to avoid power outages. Due to the high cost of storage, our goal is to choose the smallest battery size such that, with high target probability, there is no loss of power despite a grid outage. Recognizing that the most common approach today for mitigating outages is to use a diesel generator (genset), we study the related problem of minimizing the carbon footprint of genset operation. Drawing on recent results, we model both problems as buffer sizing problems that can be addressed using stochastic network calculus. We show that this approach greatly improves battery sizing in contrast to prior approaches. Specifically, a numerical study shows that, for a neighbourhood of 100 homes, our approach computes a battery size, which is less than 10% more than the minimum possible size necessary to satisfy a one day in ten years loss probability (2.7∗10). Moreover, we are able to estimate the carbon footprint reduction, compared to an exact numerical analysis, within a factor of 1.7. We also study the genset scheduling problem when the rate of genset fuel consumption is given by an affine function instead of a linear function of the current power. We give alternate scheduling, an online scheduling strategy that has a competitive ratio of k1 G C +k2 k1+k2 , where G is the genset capacity, C is the battery charging rate, and k1, k2 are the affine function constants. Numerically, we show that for a real industrial load alternate scheduling is very close to the offline optimal strategy.