Real-time selective harmonic elimination algorithm for two level inverters

Abstract

Solving the switching angles in real time is the key point to apply selective harmonic elimination (SHE) to engineering project. In this paper, a real time algorithm is presented to solve the SHE equations for two level inverters, which can be easily implemented on the micro-controllers and includes two computing stages, the offline computing stage and the online computing stage. In the offline stage, the SHE equations are transformed into an equivalent polynomial system which includes a set of univariate linear equations and a univariate high order equation by using symmetric polynomials and Groebner bases theory. Then, the univariate linear equations are stored into the micro-controllers and solved online according to the input modulation indices, and their solutions are used to construct a univariate high order polynomial equation whose real roots are actually the solutions for the original SHE equations. In order to find all the real roots of this constructed high order polynomial equation, the Sturm theorem is used to isolate every real root into non overlapping intervals and then the secant method is applied to every interval to find the exact real root, i.e., the final solutions for the SHE equations. Compared to the traditional numerical method, the executing efficiency is increased 20 times on STM32F407. Finally, a two-level inverter test platform is built based on the proposed algorithm, and the experimental results show that the algorithm is effective.

Keywords

• selective harmonic elimination
• groebner bases
• sturm theorem
• real-time solution