Sustainable Multi-Period AC Optimal Power Flow in Active Networks with Photovoltaic Generation, Battery Energy Storage Systems, and a Data-Driven Pathway Toward Warm-Start Strategies

This paper presents a multi-period formulation of alternating current optimal power flow for active networks with conventional generation, photovoltaic generation, battery energy storage systems, renewable curtailment, and hourly electricity prices. The model is implemented on the IEEE 14-bus system over a 24 h horizon and solved as a nonlinear optimization problem to minimize total operating cost while preserving electrical feasibility. The formulation includes nodal active and reactive power balances, generator operating limits, photovoltaic inverter constraints, BESS charging and discharging dynamics, state of charge, voltage limits, and branch flow constraints. The results show a total demand of 5796.42 MWh, conventional generation of 5412.56 MWh, photovoltaic generation of 562.40 MWh, and active losses of 167.07 MWh, equivalent to 2.88% of the supplied energy. No photovoltaic curtailment was required, and the BESS exhibited a clear energy arbitrage pattern, charging during low-price hours and discharging during periods of higher economic value. In addition, a supplementary IEEE 39-bus assessment confirmed the computational applicability of the proposed formulation on a larger benchmark system. Furthermore, the optimal solutions enabled the construction of a supervised dataset to support the future development of machine learning-based warm-start strategies.