Pulsewidth modulation based on real-time solution of algebraic harmonic elimination equations

Determination of pulse patterns for the elimination of some low-order harmonics of a PWM inverter necessitates solution of a system of nonlinear transcendental equations. When Newton´s algorithm is applied, it can be estimated that at each iteration, 2×N² trigonometric functions have to be evaluated, N being the number of unknown switching angles in the first quarter-period interval. This is very time-consuming when the equations are to be solved in real-time, even when a digital signal processor (DSP) is used. A new system of algebraic harmonic elimination equations, in which no trigonometric function appears explicitly, are derived in this paper. The time necessary for solving the equations using a DSP is thus reduced. For single-phase inverters, the local linear model, which is to be formulated at each iteration and then solved to provide a new iterative solution, is a special Vandermonde system. Since algorithms which are more efficient than Gauss elimination can be used to solve a linear Vandermonde system, total solution time can be further reduced