Distribution-Level PV Representative Bands: Blockwise BGMM and NSGA-II for Coverage and Tail-Risk

Power system planning requires reliable information about feeder-level photovoltaic (PV) variability, but point forecasts are often uncertain. This study proposes a procedure for constructing explainable, frequency-aware representative bands for daily PV output at the feeder section level. The method segments the annual PV series into homogeneous periods, derives reference shapes from probabilistically clustered daily profiles, and selects an upper band that balances coverage, shape fidelity, and upper tail risk through multi-objective optimization. Validation on real feeder data shows that the bands enclose frequent and recent shapes (average weighted coverage ≈ 0.85), limit upward exceedances (≈0.06), and remain compact. The approach supports practical threshold and reserve planning and provides a transparent complement to point forecasts by emphasizing typical operating regimes while remaining cautious about extremes.