Electric drive system technologies - Propulsion Systems for Hybrid Vehicles - page 264

Example 3: A 3-phase sine wave BDCM has the properties listed in Table 5.3 and
is operated in a power inverter configured as shown in Figure 5.13 with waveforms
according to Figure 5.14. Referring to the phasor diagram for this BDCM shown
here (Figure 5.15) and the parameters listed, calculate:

The d - and q -axis components of the input stator voltage, U s ●

The d - and q -axis components of the input stator current, I s , when g ¼ 15 ●

The input electrical power at n b (calculate the magnet voltage first) ●

Table 5.3 Sine wave PM machine, 3-phase, inset magnet design

U r 110 V rms phase L d 0.1 mH

I r 255 A rms L q 0.1 mH

I pk 600 A Torque ( m r ) 65 Nm

R ph 3m W Peak torque ( m pk ) 155 Nm

P 8 poles Base speed ( n b ) 4,400 rpm

Flux linkage ( l m ) 0.03 Wb-t

g

jX q I q

jX d I d

U s

R s I s

U g

E g

I s = I d + jI g

U s = U d + jU g
U d = U s sin d
U g = U s cos d

I q

I d = I s sin g
I g = I s cos g

d

g

f

d

I d

U d

Figure 5.15 Phasor diagram for the sine wave BDCM

In the following solutions, the machine voltage expression for stator phase
voltage U s and electromagnetic torque, m em , will be used:

U s ¼ E q þ R ph I s þ jX d I d þ jX q I q

sin2 d

U s E q
X d

u s 2
2

3
2

P
2

1
X q

1
X d

P e ¼ sin d