Theoretical Formulation and Simulation-Based Verification of a Grid-Connected Photovoltaic-Battery Microgrid with Smart-Inverter Support for High-Irradiance Residential Applications in Saudi Arabia

Grid-connected photovoltaic (PV) systems paired with battery storage are becoming a core element of low-carbon distribution networks. This paper develops a complete closed-form formulation together with an independent, simulation-based verification of a single-phase grid-connected PV-battery microgrid sized for high-irradiance residential conditions in Saudi Arabia, using measured solar-resource and tariff data for Riyadh. A 6.25 kW monocrystalline array feeds a 400 V DC link through a perturb-and-observe boost stage; a bidirectional converter couples a 13.5 kWh LiFePO4 battery; and an IEEE 1547 smart inverter interfaces a 230 V grid through an LCL filter. Governing equations for every subsystem are derived and evaluated numerically, and a Python re-implementation of the phasor power-flow model verifies the analysis over a 24 h cycle run to periodic steady state, reproducing the reference design values with a mean absolute error of 0.5%. Using measured monthly solar-resource and temperature data for Riyadh, a full twelve-month analysis gives an annual self-sufficiency of 51.8% and a PV self-consumption of 72.9% for the optimised energy-management scheme. A dedicated time-domain switching simulation with FFT analysis shows that the LCL filter limits grid-current total harmonic distortion to 0.8%, far below the L-filter value of 6.2% and below the 5% current-distortion reference of IEEE 519 (full compliance additionally requires the PCC short-circuit ratio). Twelve-month, battery-size and load-sensitivity studies confirm robustness, and a techno-economic assessment based on the Saudi Electricity Company residential tariff quantifies levelized cost, payback and battery degradation, showing that economic viability hinges on tariff reform.