Solving a nonlinear and incomplete equation system for a programmed PWM: application to electric traction

Series or parallel connected rectifiers are frequently used in electric traction. It is known that programmed PWM can give very good results in the control of one rectifier. The authors study the characteristics of a programmed PWM suitable for parallel connected rectifiers. The authors show the special way in which the unknown switching instants appear in the equations and the subsequent computing difficulties. It is then deduced that a minimization resolution method is the best way to cope with this kind of equations while giving the wanted harmonic spectrum of the catenary current. The second important problem is the one of the initial estimates of the solution. A new, simple, effective and computing time saving method is proposed. Finally, the resulting harmonic reduction is compared, in the electric traction context, with the one which is obtained with the combinations of carrier modulated sine PWM