Maximizing the Control Range of Matrix Converters by the Complex Synthesis PWM

The complex synthesis pulse–width modulation is proposed as a versatile modulation method for matrix converters. It draws on the idea of complex representation of converter voltages. That representation, proposed earlier without mathematical justification, is reintroduced here with a rigorous proof of its validity and properties. The method permits the use of barycentric coordinates in the calculation of duty cycles, just like in the case of dc/ac inverters, thus avoiding any dependence on symmetry or harmonic purity of input voltages. Based on that idea, this article discusses two important modulation variants and demonstrates how they can be combined in a hybrid modulation which enjoys maximum control range of input displacement angle, while not sacrificing the voltage transfer ratio and exposing the opportunities to reduce the switching frequency.