The mathematical model for selective harmonic elimination or selective harmonic control is a group of highly coupled nonlinear equations which are difficult to solve.However,in this letter,by using the theories of symmetric polynomials and Groebner bases,the nonlinear equations are equivalently converted to a group of univariate linear equations,which can be solved very easily and their solutions are used to construct a polynomial whose real roots are the final solutions.Then,an algebraicnumerical hybrid method is developed to solve the constructed polynomial,which uses the Sturms theorem to bracket each real root into an individual interval and then the secant method is used to find all the exact real roots.This method is implemented on several MCUs and shows very good real-time performance.Experiments verify the correctness of the solved switching angles.