Electric drive system technologies - Propulsion Systems for Hybrid Vehicles - page 279

The caption of Figure 5.22 describes the magnet length dimension along its
direction of polarization, the width as lying in the rotor tangential direction and
depth as its axial length along the rotor axis.
Recall that an IPM can have almost an infinite variety of magnet to reluctance
torque ratios as the magnet strength ranges from weak to strong. It is common in
fact to describe the buried magnet machine from the perspective of its characteristic
current, I c , defined according to (5.22) as the ratio of magnet flux to stator direct
axis inductance:

y m
L ds

I c ¼ ð A pk ) ð 5 : 22 Þ

where the magnet flux linkage times speed corresponds to the machine back-emf
voltage as follows:

U oc ¼ wy m ð V pk ) ð 5 : 23 Þ

In (5.23), the inverter must supply d -axis, or demagnetizing current, of this
magnitude to suppress the magnet voltage given by (5.23) in field weakening. For a
given rated inverter current, there are now three variations in the IPM design,
according to (5.22), that must be considered. In these cases, the value of the IPM
characteristic current is compared to the inverter rated current, I r .

When y m / L ds < I r , the inverter has sufficient current overhead to source q -axis
current and hence produce torque at high speeds while the d -axis component of
inverter current sustains the field weakening. In this regime, IPM power at high
speeds drops below its peak value but does not decrease to zero.

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When y m / L ds ¼ I r , the output power of the IPM is sustained at high speeds and
monotonically approaches its maximum value. This is the important class of
theoretical infinite CPSR that the IPM is noteworthy of.

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When y m / L ds > I r , there is a finite speed above which the IPM output power
has peaked and decreases monotonically to zero. This is understandable
because according to (5.22) the inverter has insufficient current rating to
completely suppress the magnet emf. The inverter simply cannot deliver q -axis
current to the machine, so its output decreases monotonically.

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This analysis simply illustrates the fact that for buried magnet designs the
inverter must be overrated, or the machine must be overrated, in order to develop
the targeted CPSR desired. A valuable metric to assess buried magnet machines is
its saliency ratio, x , defined as the ratio of q -axis stator inductance to its d -axis
inductance as follows:

L qs
L ds

x ¼ ð 5 : 24 Þ

The influence of saliency ratio, x , on IPM machine performance in the case of
an inverter fault was studied by Tom Jahns [9] and was found to have an unsettling
effect on UCG mode operation when x > 2. In this regime, all IPM machines for