Pulse width modulation strategy for power converters

In power electronics, pulse width modulation is often used with voltage inverters [D 3 176] . This control technique, which involves applying control commands to power switches, makes it possible to control the exchange of electrical energy between a source and a receiver. The successive sequences of control commands are generated via modulation schemes. Indeed, for a given conversion structure, there are often several solutions for obtaining the control order sequences. While it is generally accepted that there is a range of indicators for quantifying the performance of one modulation scheme over another, it is not clear from the state of the art that there is a method for modelling static modulation converters that facilitates the expression of solutions for modulation schemes.

This paper proposes a method for obtaining the generic linear model of a pulse-width modulation converter, and how linear algebra techniques lead to the expression of admissible solutions.

In this way, all conversion architectures and their modulation schemes can be represented by a single modeling approach. Expressed in this way, the problem to be solved is to find all the modulations, or solutions, of the model. The linear nature of the model makes it easy to determine the solution using tools for processing linear systems.

These tools not only demonstrate that there is an infinite number of pulse-width modulations, solutions to the model expressed as a generic linear system, but also enable it to be solved. In this way, all solutions, whatever the number m of equations and the number n of unknowns, are obtained. A degree of freedom is exhibited, enabling the set of solutions to be explored. The expression of physical limit values for the quantities associated with the defined conversion architectures determines the admissible limits for the solutions. The methodical approach explicitly links the expression of the degree of freedom to indicators of the quality of the modulation function, but also to the boundary values. Practical examples of how to use the method are given. In particular, the application of the method to a multi-level structure, where the switching cell has three switches, is described. This not only verifies the genericity of the method, but also its particularly advantageous use when the conversion structure has several degrees of freedom to be fixed.

At the end of the article, readers will find a glossary and table of symbols and acronyms....