A Unified Optimization Framework for Cost-Effective and Voltage-Stable Operation of Renewable Energy-Based Microgrids Using Mixed-Integer Nonlinear Programming

This study explores economic dispatch (ED) and optimal power flow (OPF) optimization for microgrid systems, focusing on single-bus islanded and three-bus grid-tied configurations. The methodologies integrate renewable energy sources (solar PV and wind turbines), battery energy storage systems (BESS), and conventional generators (CHP, diesel, and natural gas) to ensure cost-efficient and reliable operation. A mixed-integer nonlinear programming (MINLP) framework is employed to simultaneously optimize ED and OPF under dynamic demand and weather conditions. The economic dispatch analysis evaluates both daily and weekly performance, revealing that optimized scheduling achieves a total operational cost reduction of 29% for single-bus islanded and 31% for three-bus grid-tied microgrid configurations compared to non-optimized scenarios, respectively. In the islanded microgrid, weekly operational costs are reduced from $5,950 to $4,200, while in the grid-tied configuration, costs drop from $4,550 to $3,150. Renewable energy sources contribute over 60% of the total energy supplied across configurations, significantly minimizing dependence on costly grid electricity and fuel-based generation. The strategic deployment of BESS enhances operational flexibility by storing excess renewable energy during low-demand or low-price periods and supplying it during peak hours. However, frequent and rapid charging of BESS highlights the need for improved modeling of real-world storage constraints to prevent performance degradation. The OPF analysis focuses on the spatial and temporal distribution of active and reactive power within the three-bus grid-tied microgrid while ensuring voltage stability within a ±10% boundary of the nominal 6kV. Results reveal that Bus 1 consistently provides the largest share of power, supplying approximately 45% of the total demand due to its cost-efficient combination of renewable energy and CHP units. Bus 2 contributes around 20%, constrained by limited solar PV availability during non-daylight hours and the higher operational costs of its natural gas generator, while Bus 3 meets the remaining 35% of demand. More so, the optimization prioritizes cheaper energy sources to achieve substantial cost savings, with the total weekly operational cost reduced by 29% compared to non-optimized scenarios. Despite maintaining voltage variations within acceptable limits, occasional dips and spikes during dynamic load changes suggest potential stability challenges over prolonged operations, emphasizing the need for secondary voltage control mechanisms to further enhance reliability.