Publication
This paper proposes a novel integer-mixed probabilistic optimal power flow (IM-POPF) strategy for frequency regulation in islanded microgrids under uncertain operating conditions. Existing load-shedding approaches face critical limitations: continuous frameworks fail to reflect the discrete nature of actual load disconnections, while deterministic models inadequately capture the stochastic behavior of renewable generation and load variations. The proposed approach formulates load shedding as an integer optimization problem where variables are categorized as integer (load disconnection decisions at specific nodes) and continuous (voltages, power generation, and steady-state frequency), better reflecting practical power system operations. The key innovation combines integer load-shedding optimization with efficient uncertainty propagation through Unscented Transformation, eliminating the computational burden of Monte Carlo simulations while maintaining accuracy. Load and renewable uncertainties are modeled as normally distributed variables, and probabilistic constraints ensure operational limits compliance with predefined confidence levels. The methodology integrates Differential Evolution metaheuristics with Unscented Transformation for uncertainty propagation, requiring only 137 deterministic evaluations compared to 5000 for Monte Carlo methods. Validation on an IEEE 33-bus radial distribution system configured as an islanded microgrid demonstrates significant advantages over conventional approaches. Results show 36.5-fold computational efficiency improvement while achieving 95.28% confidence level compliance for frequency limits, compared to only 50% for deterministic methods. The integer formulation requires minimal additional load shedding (21.265%) compared to continuous approaches (20.682%), while better aligning with the discrete nature of real-world operational decisions. The proposed IM-POPF framework successfully minimizes total load shedding while maintaining frequency stability under uncertain conditions, providing a computationally efficient solution for real-time microgrid operation.