Chapter 7 Additional Problems

Chapter 7 Additional Problems

X7.1 A three-phase, 1200 HP, 2300 V, 60 Hz, RR synchronous machine has and . When operated with the mechanical load disconnected with rated voltage and frequency, the field current is adjusted until line current has a minimum value. At this point, , the measured input power is , and the measured field circuit values are and . (a) Determine the rotational losses (core losses plus friction and windage) for this machine. (b) If the field current, frequency, and impressed terminal voltage are unchanged, but a mechanical load requiring 600 HP is attached, predict the power factor, line current, and efficiency.

(a) Using the no-load data,

(b) Since the no-load current was a minimum value, the machine was operating at unity power factor. The excitation voltage corresponding to can be determined.

Since , little error is introduced if is neglected in calculation of the torque for the loaded condition. From energy balance,

or

Based on [7.36],

Hence,

The losses are

X7.2 If the synchronous motor of Problem X7.1 still operates the 600 HP load with terminal voltage and frequency unchanged, but the field current is increased to 80 A, predict (a)the input power factor and (b) the leading VARs supplied to the three-phase grid. Assume that core losses (lumped with friction and windage losses) of Problem X7.1 are valid.

(a) For the new field current, the excitation voltage is

Assuming negligible,

(b)

X7.3 If the synchronous motor of Problem X7.1 now supplies rated power to a coupled mechanical load with rated voltage and frequency applied to the stator and , calculate (a) line current and (b) efficiency. Assume that can be neglected in torque angle determination. Also, assume that core losses have changed negligibly from Problem X7.1.

(a) The excitation voltage for is determined in Problem X7.2 to be .

or

(b) From the values of and given in Problem X7.1,

X7.4 The synchronous machine of Problem X7.1 is now operated as a 2300 V, 60 Hz alternator supplying 800 kW to a 0.8 PF lagging load. Field current . Determine the required input mechanical power to drive the rotor and coupled exciter if the exciter has an efficiency of 91% when supplying the field voltage and current given in Problem X7.1. Assume the lumped friction and windage losses and core losses of Problem X7.1 are valid.

Since is unchanged from Problem X7.1, is still valid. Assume on the reference.

X7.5 Fig. X7.1 shows the phase a circuit of a three-phase synchronous generator that has a per phase load consisting of a pure inductive load. The machine is operating at zero power factor lagging. Determine the ratio .

By voltage division,

or

X7.6 Fig. X7.2 shows the phase a circuit of a three-phase synchronous generator that has a per phase load consisting of a pure capacitive load. The machine is operating at zero power factor leading. Determine the ratio .

By voltage division,

or

X7.7 A 3600 rpm, 60 Hz, 13.8 kV synchronous generator has a synchronous reactance of . The generator is operating at rated voltage and speed with the excitation voltage and the torque angle . Calculate (a) stator current, (b) power factor, and (c) total output power.

(a)

(b)

(c)

X7.8 For the synchronous generator of Problem X7.7, determine (a) the maximum power that can be converted from mechanical to electrical form without loss of synchronism if the field current is unchanged and (b) the value of current for this condition.

(a) Since ,

(b)

X7.9 A three-phase synchronous generator, rated at 240 V, 50 A, 60 Hz, has the stator winding schematic of Fig. X7.3. All 12 phase group leads () are available at the generator terminals. In addition to the given rating, list the balanced, three-phase voltage-current ratings available from the generator by coil reconnection without mix of phase coils that is, use only phase a coils in phase a connections.

Three additional ratings are possible under the stated constraint.

1. Series connect phase coils and use wye configuration: 480 V, 25 A

2. Series connect phase coils and use delta configuration: 277 V, 43.3 A

3. Leave phase coils parallel-connected and use delta configuration: 139 V, 86.6 A

X7.10 The three-phase synchronous generator of Problem X7.9 is to be reconnected as a single-phase alternator. What is the largest possible voltage that can be obtained?

Connect the phase coils in series with additive polarity to give

Or the largest voltage possible is .

X7.11 A 500 MVA, 24 kV, 60 Hz three-phase alternator is operating at rated voltage and frequency with a terminal power factor of 0.8 lagging. The leakage reactance and the synchronous reactance . Stator coil resistance is negligible. The excitation voltage . Determine (a) the torque angle , (b)the total output power, (c) the line current , and (d) the resultant voltage .

(a) The power converted must equal the output power.

or

(b)

EMBED Equation.DSMT4 (c)

(d)

X7.12 A 250 MVA, 24 kV, 60 Hz, three-phase alternator is operating at rated voltage, rated frequency, and rated apparent power with a terminal power factor of 0.8 lagging. Stator coil resistance is negligible. The excitation voltage . Determine (a) the torque angle and (b) the value of synchronous reactance .

(a) Assume on the reference.

Power converted must equal power output.

or

(b)

or

X7.13 A 100 MVA, 13.8 kV, 60 Hz, salient-pole, synchronous generator with 8 poles has and . The stator coil resistance is negligible. The generator is supplying rated apparent power at a power factor of 0.866 lagging. Determine the value of excitation voltage and torque angle .

By [3] of Example 7.10,

Thus,

X7.14 For the salient-pole synchronous generator of Problem X7.13, calculate the developed torque by two methods.

By [7.53] with values from solution of Problem X7.13,

Alternatively for this machine with ,

X7.15 Determine the maximum power that the salient-pole synchronous generator of Problem X7.13 can convert if the field circuit were open circuit.

In [7.53], set , , and multiply by to give

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