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 to solve a system of nonlinear transcendental equations. When Newton’s algorithm is applied, it can be estimated that at each iteration, 2xN2 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 [14]. A new system of algebraic h m o n i c 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 singlephase 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.