This paper studies capacity allocation of an energy storage (ES) device which is shared by multiple homes in smart grid. Given a time-of-use (TOU) tariff, homes use the ES to shift loads from peak periods to off-peak periods, reducing electricity bills. In the proposed ES sharing model, the ES capacity has to be allocated to homes before the homes’ load data is completely known. To this end, an online ES capacity allocation algorithm is developed based on the online convex optimization framework. Under the online algorithm, the complex allocation problem can be solved round by round: at each round, the algorithm observes current system states and predicts a decision for the next round. The proposed algorithm is able to minimize homes’ costs by learning from home load data in a serial fashion. It is proven that the online algorithm can ensure zero average regret and long-term budget balance of homes. Further, a distributed implementation of the online algorithm is proposed based on alternating direction method of multipliers framework. In the distributed implementation, the one-round system problem is decomposed into multiple subproblems that can be solved by homes locally, so that an individual home does not need to send its private load data to any other. In simulation, actual home load data and a TOU tariff of the United States are used. Results show that the proposed online approach leads to the lowest home costs, compared to other benchmark approaches.
Online Convex Optimization with Binary Constraints
