Drive system efficiency - Propulsion Systems for Hybrid Vehicles - page 407

In addition to the voltage polarization, the diode also has bulk resistance and
transport phenomena that can be modelled according to (8.8) for a more accurate
assessment of diode conduction losses [11]:

ln j i jþ c 1 i

T þ 273
300

g þ c 2 i 2

P D ¼ 0 : 026 f ð 8 : 8 Þ

where representative values for the constants c 1 and c 2 are 37 and 0.003. For the
power MOSFET transistor the conduction loss can be modelled as

P MOS ¼ i 2 R ds ð T Þ

P MOS ¼ i 2 f R ds ð T ¼ 20 Þ½ 1 þ g ð T 20 Þg

ð 8 : 9 Þ

1

R ds ð T Þ¼

m e ð T Þ C g ð U gs U gs ð TH Þ ð T ÞÞ ð Z = L Þ

where the temperature coefficient of resistance (i.e. second term in the Fourier
expansion) for a majority carrier device, g = 0.0073. R ds ( T ) is shown to be a
function of the device active source perimeter, Z , and channel length, L , with
multipliers of carrier mobility (m 2 /V-s), gate oxide capacitance per unit area (F/m 2 )
and effective voltage at the gate [12].
The ON-state losses for an IGBT device can be developed from (8.8) since its
behaviour is similar to that of a diode consisting of minority carrier injection, bulk
resistivity and contact resistance. Power loss of the IGBT device is given in (8.10)
where the dynamic resistance accounts for the MOS channel and contacts:

P IGBT ¼ U ce ð SAT Þ i þ i 2 R d

ð 8 : 10 Þ

In reality, the IGBT is more closely approximated using (8.11) in which
the exponent on device current is approximately 1.7 or less. The first term is the
collector-emitter saturation voltage and the last term the dynamic resistance. At a
junction temperature of 100 C the loss equation for an IGBT can be written as

P IGBT ¼ U ce ð SAT Þ i þ R d i h

U ce ð SAT Þ ¼ 0 : 6

ð 8 : 11 Þ

R d ¼ 0 : 135

h ¼ 1 : 645

The parameters in (8.11) are for a 130 A IGBT or the parallel combination of
IGBTs necessary to sustain that current when hot.