# 7.1 Problems - chapter 7

PROBLEMS

This lecture note is based on the textbook # 1. Electric Machinery - A.E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans- 6th edition- Mc Graw Hill series in Electrical Engineering. Power and Energy

7.1 Consider a separately-excited dc motor. Describe the speed variation of the motor operating unloaded under the following conditions:

a. The armature terminal voltage is varied while the field current is held constant.

b. The field current is varied while the armature terminal voltage is held constant.

c. The field winding is connected in shunt directly to the armature terminals, and the armature terminal voltage is then varied.

7.2 A dc shunt motor operating at an armature terminal voltage of 125 V is observed to be operating at a speed of 1180 r/min. When the motor is operated unloaded at the same armature terminal voltage but with an additional resistance of 5 $\Omega$ in series with the shunt field, the motor speed is observed to be 1250 r/min.

a. Calculate the resistance of the series field.

b. Calculate the motor speed which will result if the series resistance is increased from 5 $\Omega$ to 15 $\Omega$ .

7.3 For each of the following changes in operating condition for a dc shunt motor, describe how the armature current and speed will vary:

a. Halving the armature terminal voltage while the field flux and load torque remain constant.

b. Halving the armature terminal voltage while the field current and load power remain constant.

c. Doubling the field flux while the armature terminal voltage and load torque remain constant.

d. Halving both the field flux and armature terminal voltage while the load power remains constant.

e. Halving the armature terminal voltage while the field flux remains constant and the load torque varies as the square of the speed. Only brief quantitative statements describing the general nature of the effect are required, for example, "speed approximately doubled."

7.4 The constant-speed magnetization curve for a 25-kW, 250-V dc machine at a speed of 1200 r/min is shown in Fig.7.1. This machine is separately excited and has an armature resistance of 0.14 $\Omega$ . This machine is to be operated as a dc generator while driven from a synchronous motor at constant speed.

a. What is the rated armature current of this machine?

b. With the generator speed held at 1200 r/min and if the armature current is limited to its rated value, calculate the maximum power output of the generator and the corresponding armature voltage for constant field currents of (i) 1.0 A, (ii) 2.0 A and (iii) 2.5 A.

Figure 7.1 1200 r/min magnetization curve for the dc generator.

c. Repeat part (b) if the speed of the synchronous generator is reduced to 900 r/min.

7.5 The dc generator of Problem 7.4 is to be operated at a constant speed of 1200 r/min into a load resistance of 2.5 $\Omega$ .

a. Using the "spline0" function of MATLAB and the points of the magnetization curve of Fig. 7.1 at 0, 0.5, 1.0, 1.5, 2.0, and 2.5 A, create

a MATLAB plot of the magnetization curve of Fig. 7.1.

b. Using the "spline0" function as in part (a), use MATLAB to plot (i) the terminal voltage and (ii) the power delivered to the load as the generator field current is varied from 0 to 2.5A.

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