Probabilistic BESS Scheduling for Duck-Curve Mitigation Under Correlated DER Penetration in Distribution Systems

High penetration levels of photovoltaic (PV) generation and electric vehicles (EVs) exacerbate the duck-curve effect in distribution systems. This paper proposes a probabilistic scheduling framework for battery energy storage systems (BESSs) to mitigate substation power variability under uncertain and correlated distributed energy resource (DER) penetration. Correlated PV, EV, and BESS penetration scenarios are generated by Gaussian-copula-based Monte Carlo sampling, weighted by a fuzzy duck-curve relevance index, and reduced to ten representative scenarios by K-means clustering; their substation power profiles are obtained with OpenDSS. BESSs are allocated to the six buses with the highest power variability and scheduled in 2-h intervals using a three-state (charge, idle, discharge) binary encoding. For each scenario, a day-ahead schedule is optimized with an improved binary Equilibrium Optimizer (IBiEO). On the IEEE 34-bus feeder, IBiEO achieves the lowest probability-weighted objective, 48.0% below the no-action case, and significantly outperforms four of five binary benchmark algorithms under equal evaluation budgets, while performing comparably to a hybrid DBA-PSO algorithm. The OpenDSS-validated schedules reduce the probability-weighted maximum ramp, peak-to-valley range, and evening ramp by 38.2%, 47.4%, and 53.8%, respectively. Under Monte Carlo propagation of the measurement uncertainty of the state-of-charge estimate, BESS capacity, and PV peak power, the probability-weighted mean improvement of the duck-curve indices remains 25.2% (95% coverage interval: 20.4–29.7%). These findings demonstrate the effectiveness of the proposed framework in mitigating the duck-curve effect under correlated DER penetration and device-parameter uncertainty, supporting the reliable integration of high PV and EV shares in distribution systems.