Structure of optimal schedules for charging non-ideal energy storage

Energy storage is becoming increasingly important to maintain the stability of the grid, to mitigate the intermittency of renewable generation and to reduce the peak demand in the grid. However, if energy storage is not managed optimally, the utility and the users might not be able to reap the benefits due to energy storage being an expensive technology. Therefore this thesis provides and finds the long term optimal operation schedule for non-ideal storage systems under real-time and arbitrary price increases and discusses the impact of the optimal policy when used for peak shaving in the power grid. Since the long term storage problem can be infinite when electricity prices increase arbitrarily, an alternate formulation of studying the long term storage schedule by finding the limit of the finite horizon solution is presented using convex optimisation and simulated using the dynamic programming algorithm. Based on this formulation, we show that under certain conditions, convergence and renewal points exists for ideal and non-ideal storage systems with charging inefficiency and self-discharge. Because of the existence of renewal points, the results in this thesis show that future demand and price do not affect the scheduling decisions before the renewal point for a given convergence time, allowing to investigate the behaviour of the long term schedule by investigating the properties of the finite horizon solution with convergence. The major findings on the structure of the optimal storage management schedule show that for ideal storage systems, the marginal generation cost is constant while storage does not fully saturate or empty. However for energy storage with charging inefficiency, fluctuations in generation are seen that depends on the efficiency of the storage. For peak shaving with inefficient storage systems, the simulations show that a trade-off exists in purchasing a smaller more efficient storage device or a larger less efficient storage device to achieve the same amount of peak shaving. Additionally, the same amount of peak shaving can also be achieved for a range of efficiency values for smaller energy storage systems allowing utilities and users to benefit if the utility provides a cheaper storage system for peak shaving and cost savings. Finally the structure of the generation schedule for storage devices with self-discharge shows that the generation would increase exponentially due to the self-discharge and that having rapid price increases greater than the rate of self-discharge caused the generation schedule to decrease exponentially, suggesting that moderate price increase could balance the generation and provide better peak shaving in the grid.