Synchronous Generators Questions and Answers

Answer: D

Running alternators in parallel instead of one large unit gives reduced operating cost, because units can be switched on and off to follow the load, better reliability, because the loss of one unit does not stop the supply, and easier maintenance, because one machine can be taken out for service while the others carry the load. A set of machines can also be run near full load, where each is most efficient.

So poor efficiency is not an effect of parallel operation, and it is the incorrect statement. The answer is option D.

Answer: D

The distribution factor of a winding is \(k_d = \dfrac{\sin(m\beta/2)}{m \sin(\beta/2)}\), where \(m\) is the number of slots per pole per phase and \(\beta\) is the slot angle in electrical degrees.

\[ \begin{aligned} m = \frac{36}{6 \times 3} = 2,\qquad \beta \\ &= \frac{180^\circ \times P}{S} \\ &= \frac{180^\circ \times 6}{36} = 30^\circ \end{aligned} \]

\[ \begin{aligned} k_d \\ &= \frac{\sin(2 \times 30^\circ / 2)}{2 \sin(30^\circ / 2)} \\ &= \frac{\sin 30^\circ}{2 \times \sin 15^\circ} \approx 0.966 \end{aligned} \]

That is the fourth option. The other fractions have the wrong denominators for \(m = 2\): the third option would be right for \(m = 3\) with a 30 degree angle, and the first two use angles of 20 degrees that do not occur here. The answer is option D.

Answer: C

The turbine torque equals the input power divided by the angular speed, because losses are neglected. A two pole machine on 60 Hz runs at 3600 rpm.

\[ \begin{aligned} \omega = \frac{2\pi \times 3600}{60} \\ &= 377\ \text{rad/s} \end{aligned} \]

\[ \begin{aligned} T = \frac{112 \times 10^3}{377} = 297\ \text{N m} \\ &= 297 \times 0.7376 = 219\ \text{lb-ft} \end{aligned} \]

The synchronous reactance and the power angle fix the terminal conditions but are not needed once the power is known. The answer is 219 lb-ft, option C.

Answer: A

The frequency is 40 Hz. The frequency of the voltage generated by an alternator depends on the number of poles and the speed.

\[ f = \frac{P N}{120} \]

\[ = \frac{4 \times 1200}{120} = 40\ \text{Hz} \]

A frequency of 50 Hz would need 1500 rpm for 4 poles, 60 Hz would need 1800 rpm, and 100 Hz would need 3000 rpm. At 1200 rpm none of these frequencies results, so the first option is the answer.

Answer: A

For connecting an alternator to the grid, the phase angle between the generated voltage and the grid voltage must be 0°, that is the two voltages must be in phase. Along with equal voltage, equal frequency and the same phase sequence, this lets the breaker be closed without a surge of current.

A phase angle of 45°, 60° or 90° would mean a voltage difference across the breaker at the moment of closing, which would cause a large circulating current and a mechanical shock to the machine. So the first option is correct.

Answer: C

A synchroscope is used for synchronizing an alternator with the bus bars or the grid. It shows whether the incoming machine is faster or slower than the system and when the two are in phase, so the operator knows the right instant to close the breaker.

It does not start, brake or reverse a machine. With the lamp method the lamps go dark together when the machine is in step, and the synchroscope shows the same thing on a dial: the pointer turns one way if the incoming machine is fast and the other way if it is slow, and stands still at the top when the two are in phase. So the third option is the answer.

Answer: B

At zero power factor leading, the armature reaction in an alternator is purely magnetising. When the armature current leads the voltage by 90°, its flux acts in the same direction as the main field, and so it assists the field and raises the terminal voltage.

At zero power factor lagging the reaction is purely demagnetising, at unity power factor it is cross-magnetising, and for intermediate power factors it is part cross and part demagnetising or magnetising. So the second option is correct.

Answer: B

Both statements are false. Salient pole rotors have projecting poles and are used in low speed machines, such as those driven by hydraulic turbines and diesel engines. Turbo alternators run at high speed and use cylindrical (non-salient) rotors, so the first statement is false.

Cylindrical rotor alternators are driven by steam or gas turbines, and not by a solar cell, which is a source of electrical power and not a prime mover. So the second statement is also false. The key gives 'False, False', the second option.

Answer: D

The statement that is not true is that a salient type rotor is used in high speed turbine driven generators.

High-speed turbo-alternators driven by steam or gas turbines run at 3000 or 1500 rpm and use smooth cylindrical (non-salient) rotors of small diameter and great length, which can withstand the centrifugal forces. Salient pole rotors, with large diameter and many poles, are used in slow-speed machines such as hydro generators.

The other statements are true: synchronous generators normally have a stationary armature and rotating field, the cores are built of laminated steel to reduce eddy current loss, and the armature winding is distributed to improve the waveform.

Answer: B

Short pitch coils and distributed windings are used to make the generator emf more sinusoidal.

Distributing the winding in several slots and short-chording the coils both reduce the harmonics in the generated emf: the coil emfs are slightly out of phase, which suppresses harmonics strongly, and a suitable short pitch can eliminate a chosen harmonic altogether. The result is a waveform much closer to a sine wave.

The price is a slight reduction in the fundamental emf, since the distribution and pitch factors are each a little less than one. So these measures do not increase the magnitude of the emf, which rules out the first and third options, and they reduce rather than increase the distribution factor.