tiolynomi:lI time algorilhni is tlc~clopctl for the spnrsc polynomi;tl inlcrpohtion problem. The numhcr of cv;~lu:~lions nccdcd by this algorithm is very small. The algorithm also has a simple NC implcmcntation.

It is an exciting time for power systems as there are many ground-breaking changes happening simultaneously. There is a global concensus in increasing the share of renewable energy-based generation in the overall mix, transitioning to a more environmental-friendly transportation with electric vehicles as well as liberalizing the electricity markets, much to the distaste of traditional utility companies. All of these changes are against the status quo and introduce new paradigms in the way the power systems operate. The generation penetrates distribution networks, renewables introduce intermittency, and liberalized markets need more competitive operation with the existing assets. All of these challenges require using some sort of storage device to develop viable power system operation solutions. There are different types of storage systems with different costs, operation characteristics, and potential applications. Understanding these is vital for the future design of power systems whether it be for short-term transient operation or long-term generation planning. In this paper, the state-of-the-art storage systems and their characteristics are thoroughly reviewed along with the cutting edge research prototypes. Based on their architectures, capacities, and operation characteristics, the potential application fields are identified. Finally, the research fields that are related to energy storage systems are studied with their impacts on the future of power systems.INDEX TERMS Storage systems, electric vehicles, power system optimization, market liberalization, renewable energy, new operation schemes, power system planning.

Abstract. View an n-vertex, m-edge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the commute time between two vertices s and t (the expected length of a random walk from s to t and back) is precisely characterized by the eective resistance R st between s and t: commute time = 2mR st . As a corollary, the cover time (the expected length of a random walk visiting all vertices) is characterized by the maximum resistance R in the graph to within a factor of log n: mR cover time O(mR log n). For many graphs, the bounds on cover time obtained in this manner are better than those obtained from previous techniques such as the eigenvalues of the adjacency matrix. In particular, we improve known bounds on cover times for high-degree graphs and expanders, and give new proofs of known results for multidimensional meshes. Moreover, resistance seems to provide an intuitively appealing and tractable approach to these problems.

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