Comparative analysis of mathematical descriptions and pulse-width modulation methods

The article considers the mathematical description and comparison of the most common methods of pulse-width modulation (PWM) for a three-phase voltage inverter, namely vector PWM, PWM with third harmonic premodulation and classical PWM. In contrast to the classical mathematical description of PWM, a description is presented that is close to the implementation of modulation using modern microcontroller technology. The classic representation of PWM is based on comparing two signals. In this representation, the modulation pulse occurs at the moment when the modulating function is greater in value than the reference signal. When implementing PWM by a microcontroller, the pulse is placed within the period symmetrically with respect to the middle of the interval, while the pulse width is determined by the average value of the voltage modulating function. With a different mathematical description of PWM, the pulse is located differently within the modulation interval. There are presented the results of modeling and compares the mathematical descriptions of PWM methods according to the criterion of minimum dispersion of the current flowing in the load. As a result of the comparison, it was revealed that the same, differently described PWM algorithm gives different results. A comparison of vector PWM with a modified vector PWM was made. The modification consists in applying a dynamic pulse shift algorithm in such a way as to obtain a minimum of current dispersion in the load. Comparison of PWM methods was carried out at different frequencies of the reference signal; a static RL circuit was used as a load when simulating a three-phase voltage inverter. The results obtained allow us to recommend a pulse shift algorithm for implementing PWM in voltage inverters operating at relatively low PWM frequencies. Minimization of the current dispersion makes it possible to obtain improved energy and vibration-noise characteristics of the electric drive.