Mode-Aware Constrained Inverse Optimization for Behind-the-Meter Energy Storage Power Estimation Under Time-of-Use Tariffs

With the increasing penetration of behind-the-meter photovoltaic generation and distributed energy storage, distribution system operators usually observe only the net load at the point of common coupling, while the actual user load and energy storage charging/discharging power are difficult to measure directly. To address this problem, this paper proposes a mode-aware constrained inverse optimization method for behind-the-meter distributed energy storage power estimation under fixed time-of-use tariffs. The proposed method uses net load, photovoltaic power, and tariff information as inputs and estimates the hidden user load, storage power, SOC trajectory, and dominant storage arbitrage mode. A mode-aware joint representation model is developed by introducing single-cycle and dual-cycle charge–discharge templates, daily action intensity factors, mode weights, and local correction terms. In addition, power limits, SOC dynamics, SOC bounds, daily energy balance constraints, tariff-response consistency, and mode selection penalty are incorporated into the inverse optimization framework to improve the physical feasibility and interpretability of the estimation results. Case studies are conducted using a 40-day hybrid dataset with a 1 h sampling interval and a 70%/30% training/testing split. The dataset is constructed from park-level user load and photovoltaic data, while the storage power profile is reconstructed according to typical time-of-use arbitrage operation. For the main dual-cycle testing case, the NRMSEs of storage power, user load, and net load are 14.75%, 3.90%, and 3.76%, respectively. The results show that the proposed method can recover the main variation trend of hidden storage power under the studied fixed time-of-use tariff scenario and provides a preliminary basis for park-level storage monitoring and flexible resource perception.