Energy Storage: Optimal Sizing and Operations in the presence of Dynamic Pricing and Renewable Energy

A limited supply of existing fossil fuels together with the increasing demand for energy and the impending problem of the global climate change has motivated the need to incorporate a vast amount of renewable energy in our energy portfolio. Renewable sources are non-dispatchable sources that are both intermittent and uncertain in nature. At large penetration levels this variability can pose significant challenges in the operation of the power grid. This is because renewables introduce large ramps leading to grid stability issues amidst other concerns as listed in [Ene10]. Moreover, load-following with inefficient fast ramping generators offsets the very benefit of using renewables. One method in the emerging smart grid paradigm to mitigate the uncertainties introduced by renewables and promote system efficiency is the use of grid-level distributed energy storage devices. These devices facilitate power balancing as they delink the time of generation and consumption. However, storage is very expensive and its cost has been the main barrier in its deployment. Owing to their benefits, governments and industries have been significantly investing in the research and development of storage technologies and storage will be an integral part of the future smart grid. Our work broadly focuses on the interplay between renewable energy and storage in the presence of dynamic pricing. In particular, we want to quantify the value of storage, study tradeoff between storage value and capital cost and finally understand how other factors influence the storage value. In order to do so, we consider a setting involving conventional generation, renewable generation, elastic demand and energy storage. Here, any energy that is drawn from the conventional generation has a real-time price associated with it and any energy drawn from the renewable generation is assumed to have a zero marginal cost and hence free. We address two problems: optimal storage management problem and the optimal storage sizing problem. The goal in the management problem is to find an optimal policy to manage the energy storage device so as to minimize the cost of conventional generation used over a finite time horizon while satisfying the elastic demand at all times. The goal in the sizing problem is to both optimally manage and size the storage device to minimize the average cost of conventional generation used and the investment cost in storage, if any, over an infinite horizon while satisfying the elastic demand at all times. Through these problems we capture the main characteristics of the operations and decisions of a distributed renewable generator with energy storage devices. Consider for example renewable generators such as a solar or wind farm in industries, game parks, smart cities like Masdar, microgrids or even solar panels on roof tops of homes that aim to satisfy a local potentially elastic