# 7.1 Problems - chapter 7  (Page 3/6)

a. Sketch the general form of the curve of armature current versus speed over the entire range. Ignore machine losses and armature-reaction effects.

b. Suppose that, instead of operating with constant torque, the load torque at any given speed is adjusted to maintain the armature current at its rated value. Sketch the general form of the allowable torque as a function of speed assuming the motor is controlled as described above.

7.11 Two adjustable-speed dc shunt motors have maximum speeds of 1800 r/min and minimum speeds of 500 r/min. Speed adjustment is obtained by field-rheostat control. Motor A drives a load requiring constant power over the speed range; motor B drives one requiring constant torque. All losses and armature reaction may be neglected.

a. If the power outputs of the two motors are equal at 1800 r/min and the armature currents are each 125 A, what will the armature currents be at 500 r/min?

b. If the power outputs of the two motors are equal at 500 r/min and the armature currents are each 125 A, what will the armature current be at 1800 r/min?

c. Answer parts (a) and (b) with speed adjustment by armature-voltage control with conditions otherwise the same.

7.12 Consider a dc shunt motor connected to a constant-voltage source and driving a load requiring constant electromagnetic torque. Show that if ${E}_{a}>0\text{.}{5V}_{t}$ (the normal situation), increasing the resultant air-gap flux decreases the speed, whereas if ${E}_{a}<0\text{.}{5V}_{t}$ (as might be brought about by inserting a relatively high resistance in series with the armature), increasing the resultant air-gap flux increases the speed.

7.13 A separately-excited dc motor is mechanically coupled to a three-phase, four-pole, 30-kVA, 460-V, cylindrical-pole synchronous generator. The dc motor is connected to a constant 230-V dc supply, and the ac generator is connected to a 460-V, fixed-voltage, fixed-frequency, three-phase supply. The synchronous reactance of the synchronous generator is 5.13 $\Omega$ /phase. The armature resistance of the dc motor is 30 mA. The four-pole dc machine is rated 30 kW at 230 V. All unspecified losses are to be neglected.

a. If the two machines act as a motor-generator set receiving power from the dc source and delivering power to the ac supply, what is the excitation voltage of the ac machine in volts per phase (line-to-neutral) when it delivers 30 kW at unity power factor? What is the internal voltage of the dc motor?

b. Leaving the field current of the ac machine at the value corresponding to the condition of part (a), what adjustment can be made to reduce the power transfer between the two machines to zero? Under this condition of zero power transfer, what is the armature current of the dc machine? What is the armature current of the ac machine?

c. Leaving the field current of the ac machine as in parts (a) and (b), what adjustment can be made to cause the transfer of 30 kW from the ac source to the dc source? Under these conditions what are the armature current and internal voltage of the dc machine? What will be the magnitude and phase of the current of the ac machine?

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