| Abstract: |
This paper presents a rewritten research-paper version of the mathematical modelling chapter for a shunt active power filter (SAPF) controlled through a synchronous dq-frame instantaneous power strategy and nonlinear hysteresis current regulation. The proposed framework connects a voltage source inverter in shunt with a three-phase nonlinear load at the point of common coupling. Harmonic and reactive current components are extracted through Clarke and Park transformations, while the DC-link voltage loop supports the active current component required for inverter losses and voltage stabilization. A nonlinear hysteresis regulator then forces the filter current to track the generated reference current with adaptive switching boundaries. The model includes the three-phase source, diode-rectifier nonlinear load, coupling inductor, DC-link capacitor, voltage source inverter, dq-frame controller, reference-current generation, switching logic, and performance indices such as current THD, voltage THD, power factor, tracking error, DC-link voltage deviation, settling time, and filter efficiency. The resulting formulation provides a compact simulation-ready basis for evaluating harmonic mitigation and power-quality enhancement under nonlinear loading conditions. |
