PROBLEMS

10.1

Calculate the torque constant, similar to that in Equation 10.6, for a 4-pole

machine, where N, equals the total number of turns per-phase.

10.2 Prove that Equation 10.11 is correct.

10.3 Repeat Example 10.1 for Om = -45°

192

Electric Machines and Drives: A First Course

10.4 Repeat Example 10.1 for a 4-pole machine with the same value of ks as in

Example 10.1.

10.5 The PMAC machine of Example 10.2 is supplying a load torque Tu = 5 Nm at a

speed of 5,000 rpm. Draw a phasor diagram showing 7and 1, along with their

calculated values.

10.6 Repeat Problem 10.5 if the machine has p=4, but has the same values of kp, kt.

and L, as before.

10.7 Repeat Problem 10.5, assuming that at time t = 0, the rotor angle (0) = 0°.

10.8 The PMAC motor in Example 10.2 is driving a purely inertial load. A constant

torque of 5 Nm is developed to bring the system from rest to a speed of 5,000 rpm

in 5 s. Neglect the stator resistance and the leakage inductance. Determine

and plot the voltage valt) and the current it) as functions of time during this

5-second interval.

10.9 In Problem 10.8, the drive is expected to go into a regenerative mode at t = 5+ s,

with a torque Tem = -5 Nm. Assume that the rotor position at this instant is zero:

Am = 0. Calculate the three stator currents at this instant.

10.10 Redraw Figure 10.3 if the PMAC drive is operating as a generator.

10.11 Recalculate Example 10.2 if the PMAC drive is operating as a generator, and

instead of it supplying a torque of 37 Nm, it is being supplied this torque from the

mechanical system connected to the machine-shaft.

10.12 The 2-pole motor in a PMAC drive has the following parameters: R = 0.4162,

Ls = 1.365mH, and kr = 0.0957 Nm/A. Draw the space vector and phasor

diagrams for this machine if it is supplying its continuous rated torque of

Tem = 3.2 Nm at its rated speed of 6,000 rpm.

10.13 Draw the phasor diagrams associated with under-excited and over-excited syn-

chronous motors and show the power factor of operation associated with each.

10.14 Calculate the expression for the reactive power in a 3-phase synchronous machine

in terms of Es, V, Xs, and 8. Discuss the influence of Ep.

Tem=kt 1,

where

N.

k=rl B, (p=2)

(10.6)

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