A Novel Fourier Series Simulation Tool for Pulsewidth Modulation (PWM) in Pulsed Power Systems

PWM is an efficient power transfer mechanism in switch mode power supply units (PSUs) and in speed and torque control of electric motors. Power dispatch is effected by PWM regulators in PSUs while variable voltage and frequency control of motors is achieved with sinusoidal reference PWM inverter amplifiers. Hence this pulse strategy can be used in power supply control of magnetic field currents for improved tokamak plasma confinement. Wide bandwidth current control is achieved in motor drives by natural sampled PWM because of its inherent simplicity and ease of implementation using analog comparator circuitry. For this reason a tractable mathematical model of the natural sampled PWM process is required for accurate simulation of such devices before hardware construction for performance related prediction and evaluation of plasma confinement control. In this paper a novel description of PWM is presented using a modulated Fourier series (MFS) for modelling, spectral analysis and rapid PWM inverter simulation in pulsed power applications. The MFS time function consists of a sum of sinusoidal carrier basis functions with time dependent amplitudes incorporating the modulated pulsewidth determined by the control current reference signals. Arbitrary non periodic signals are easily accommodated for rapid device simulation and performance evaluation. The MFS eliminates the need for accurate pulse edge transition searches during PWM inverter simulation because of the analytical expression for the time dependent modulated amplitudes, which contain the encoded signal information. Elimination of iterative searches for modulated pulse transitions, currently employed in simulation packages, results is substantial savings in simulation runtime during accurate PWM waveform synthesis. The accuracy of the MFS strategy can be easily controlled by adjusting the number of carrier harmonics during simulation. PWM simulation results are presented for MFS model validation, which are indistinguishable from those for an analog comparator modulator employing arbitrary non-periodic signals. A software algorithm with additional simulation traces are presented of MFS fidelity in replicating high frequency harmonic current ripple when compared with experimental test data. Substantial savings of up to fiftyfold in motor drive simulation time are presented without loss of simulation accuracy.