MATHEMATICAL MODELING AND A TECHNIQUE FOR GENERATING A SPECIFIED OUTPUT VOLTAGE WAVEFORM IN A SINGLE-PHASE THYRISTOR FREQUENCY CONVERTER

This paper presents a comprehensive mathematical model and a hysteresis-based control technique for a single-phase thyristor frequency converter designed to synthesize an arbitrary output voltage waveform. The converter comprises a full-wave controlled rectifier with a center-tapped transformer, an LC DC link filter, and a parallel bridge inverter with a commutating capacitor. The model employs a state-space representation with nonlinear differential equations, incorporating logical variables to capture the variable topology induced by thyristor switching states, including magnetic flux linkages, winding currents, and capacitor voltages. Phase-angle control regulates the rectifier's DC output, while hysteresis control governs the inverter by switching thyristor pairs to maintain the output voltage within a predefined tolerance band around a reference signal. Numerical simulations evaluate performance across a range of operating frequencies, demonstrating smooth transients and high-fidelity sinusoidal waveforms at low frequencies, with damped oscillations settling rapidly; furthermore, at higher frequencies, the system continues to exhibit robust performance and high-fidelity tracking, demonstrating the control technique's wide operational bandwidth and fast dynamic response. The work bridges a gap in applying non-linear control to thyristor topologies for precise waveform generation, enhancing power quality in grid-connected renewable systems and industrial applications, with prospects for adaptive damping and high-frequency refinements.