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Recent studies show that the fast growing expansion of wind power generation may lead to extremely high levels of price volatility in wholesale electricity markets. Storage technologies, regardless of their specific forms, e.g., pump-storage hydro, large-scale, or distributed batteries, are capable of alleviating the extreme price volatility levels due to their energy usage time shifting, fast-ramping, and price arbitrage capabilities. In this paper, we propose a stochastic bilevel optimization model to find the optimal nodal storage capacities required to achieve a certain price volatility level in a highly volatile energy-only electricity market. The decision on storage capacities is made in the upper level problem and the operation of strategic/regulated generation, storage, and transmission players is modeled in the lower level problem using an extended stochastic (Bayesian) Cournot-based game. The South Australia (SA) electricity market, which has recently experienced high levels of price volatility, and a 30-bus IEEE system are considered as the case studies. Our numerical results indicate that 50% price volatility reduction in the SA electricity market can be achieved by installing either 430-MWh regulated storage or 530-MWh strategic storage. In other words, regulated storage firms are more efficient in reducing the price volatility than strategic storage firms. [ABSTRACT FROM PUBLISHER]

This paper investigates the possibility of having convex or concave formulations of optimization problems for interference coupled wireless systems. An axiomatic framework for interference functions proposed by Yates in 1995 is used to model interference coupling in our paper. The paper shows that under certain natural assumptions, the exponential transformation is the unique transformation (up to a positive constant) for “convexification” of resource allocation problems for linear interference functions. Furthermore, it is shown that under certain intuitive assumptions, it is sufficient to check for the joint concavity (convexity) of sum of weighted functions of SINR (inverse SINR) with respect to s (p=e^s, where p is the power vector of the users), if we would like the resulting resource allocation problem to be concave (convex). This paper characterizes the largest class of utility functions and the largest class of interference functions (respectively), which allow a convex and concave formulation of a problem for interference coupled wireless systems. It extends previous literature on log-convex interference functions and provides boundaries on the class of problems in wireless systems, which can be algorithmically tackled by convex optimization techniques. [ABSTRACT FROM AUTHOR]