Real-Time Switching Angle Computation for Selective Harmonic Control

A two-stage algorithm is proposed to compute switching angles for selective harmonic elimination or selective harmonic control. In the first offline computing stage, the multivariate nonlinear equations are equivalently converted to a group of univariate linear equations by using the theories of symmetric polynomials and Gröbner bases, which are then stored into the target microcontrollers (MCUs) and solved online. In the second online computing stage, the linear equations are solved, and their solutions are used to construct a polynomial whose real roots are actually the final solutions; then, an algebraic-numerical hybrid method is developed to solve the constructed polynomial, which uses the Sturm's theorem to bracket each real root into an individual interval, and then, the bisection method is used to find all the exact real roots. Compared to the traditional numerical methods, the executing efficiency is increased significantly. This method is implemented on several commonly used MCUs and shows very good real-time performance. Experiments verify the correctness of the solved switching angles and demonstrate the feasibility of applying this method in the real control system.