Harmonics Orders Modeling of DC Winding Induced Voltage Pulsation in Wound Field Switched Flux Machines Under PWM Excitation

The wound field switched flux (WFSF) machine operates under pulsewidth modulation (PWM) excitation suffers from more dc winding induced voltage (DCWIV) harmonics around the PWM frequency and its integral multiples than that operates under ideal current sources. This article proposes an analytical model to predict the DCWIV harmonics orders for the WFSF machines having
$N_{s}$
-stator-slot and
$N_{r}$
-rotor-pole under PWM excitation, including both open-circuit and on-load ones. The analytical model reveals that the harmonics orders in DCWIV for WFSF machines under PWM excitation can be divided into low-frequency (LF) components, i.e.,
$jN_{\text {pe}(f)}$
and high-frequency (HF) components, i.e.,
$rf_{\text {PWM}f}/f_{e}$
and
$rf_{\text {PWM}f}/f_{e} \pm jN_{\text {pe}(f)}$
, where
$r= 1, 2, 3, \ldots \,\,j = 1, 2, 3, \ldots \,\,f_{\text {PWM}f}$
and
$f_{e}$
are the dc winding PWM frequency and the machine fundamental electric frequency, respectively,
$N_{\text {pef}}$
and
$N_{\text {pe}}$
are the DCWIV cycles per electric period under open-circuit and on-load conditions when the WFSF machine is fed by ideal current sources, respectively, and
$N_{\text {pe}(f)}$
=
$N_{\text {pef}}$
for open circuit and
$N_{\text {pe}(f)}$
=
$N_{\text {pe}}$
for on-load. Co-simulation between magnetic field and electric circuit of three WFSF machines
$N_{s}/N_{r}$
= 24/10, 24/11, and 12/4 is conducted to verify the proposed model. A 24-stator-slot/10-rotor-pole WFSF prototype is built and tested to validate the proposed model.