AC-OPF Feasibility Analysis and Sensitivity-Guided Capacitor Placement in a High-PV Islanded Microgrid

Abstract

This paper presents a comparative AC Optimal Power Flow study on a real world city scale islanded microgrid with high solar PV penetration, implemented within a Digital Twin framework. Four objective function cases economic dispatch, voltage stress exposure via PV power factor variation, then optimal load delivery, and capacitor enhanced economic dispatch as recovery options are evaluated over a 47 hour time series horizon on the same network under a shared loading scenario. Optimization sensitivities OSQ and OSV extracted from all cases are combined into a composite placement score used to rank candidate buses for shunt capacitor upgrades. A post processing planning optimization balances capacitor upgrade cost against avoided value-of-lost-load, enabling direct economic comparison of infrastructure investment versus reliability penalties. Results demonstrate that sensitivity guided capacitor placement restores full load service across the horizon and provides targeted reactive support at a quantifiable cost trade off against corrective load shedding.