Energy Storage Modeling: from Mixed-Integer Linear Programming to Network Flow Optimization

Energy storage (ES) is typically modeled as either a mixed-integer linear programming (MILP) problem involving binary variables or a quadratic constraint programming (QCP) problem with complementarity constraints due to the mutually exclusive characteristics of charging and discharging. The MILP model is an NP-hard problem that suffers from the curse of dimensionality. The solution time for QCP problems increases rapidly as the problem scale expands. To address these challenges, this paper proposes the energy storage network flow (ES-NF) model. Initially, the conditional MILP (C-MILP) model is derived from the MILP through variable substitution. Next, the conditional extreme point is introduced and proven equivalent to the extreme point of MILP. The ES-NF model is then established as a directed acyclic state transition diagram. Finally, the network flow algorithms can solve the ES-NF model efficiently. Numerical results indicate that when ES participates in independent scheduling, the proposed model significantly enhances computational efficiency without compromising accuracy. Compared with the MILP and QCP models, the proposed ES-NF model can effectively reduce the average solution time.