In this work, we investigate scheduling problems for electrical energy storage systems and formulate an algorithm that finds an optimal solution with minimal charging cycles in the case of a single device. For the considered problems, the storage system is used to reduce the peaks of the production and consumption within (part of) the electricity distribution grid, while minimizing device wear. The presented mathematical model of the storage systems captures the general characteristic of electrical energy storage devices while omitting the details of the specific technology used to store the energy. In this way, the model can be applied to a wide range of settings. Within the model, the wear of the storage devices is modeled by either: (1) the total energy throughput; or (2) the number of switches between charging and discharging, the so-called charging cycles. For the first case, where the energy throughput determines the device wear, a linear programming formulation is given. For the case where charging cycles are considered, an NP-hardness proof is given for instances with multiple storage devices. Furthermore, several observations about the structure of the problem are given when considering a single device. Using these observations, we develop a polynomial time algorithm of low complexity that determines an optimal solution. Furthermore, the solutions produced by this algorithm also minimize the throughput, next to the charging cycles, of the device. Due to the low complexity, the algorithm can be applied in various decentralized smart grid applications within future electricity distribution grids.
- device aging
- mixed integer linear program (MILP)
- Peak Shaving
- polynomial time optimal algorithm
- electrical energy storage