Safety-Aware Allocation of Hybrid PV-WT Generation in Unbalanced Feeders Incorporating Load-Following Errors and Power Unbalance Ratio Limits

Existing DG allocation studies commonly rely on static or balanced feeder assumptions, leaving two practical issues insufficiently addressed: the hourly mismatch between renewable outputs and feeder demands and diesel-backup phase-imbalance safety in unbalanced networks. This paper presents a safety-aware allocation framework for hybrid photovoltaic (PV) and wind turbine (WT) systems in unbalanced three-phase feeders. The methodology explicitly accounts for 24 h generation–load coordination and diesel backup operating limits through two post-load-flow indicators: load-following error (LFE), which measures the hourly mismatch between aggregate distributed generation (DG) outputs and a load-proportional target, and power unbalance ratio (PUR), which limits diesel-unit phase-power imbalance to 10% during dispatch. The constrained siting and sizing problem is solved using a genetic algorithm (GA) on the IEEE 37-bus feeder under realistic diurnal load, solar, and wind profiles. While an unconstrained allocation achieves 64.57% active-power loss reduction, it exceeds the adopted diesel PUR screening threshold. Enforcing the PUR constraint yields a feasible operating state with 60.87% loss reduction, retaining 94.27% of the unconstrained benefit. Robustness checks across 30 independent runs and GA/PSO/ACO benchmarking confirm that the adopted GA provides the lowest dispersion and highly repeatable feasible outcomes. The results show that the framework improves energy efficiency, voltage regulation, and daily coordination while satisfying the adopted diesel phase-power screening criterion under severe feeder asymmetry.