A generator has an open circuit emf of 1.15 per unit at the excitation that gives rated terminal voltage on load. Its regulation is
Answer: A
Regulation is the rise in terminal voltage when the load is removed at fixed excitation, expressed as a fraction of the rated value, so \( 1.15 - 1.00 = 0.15 \). A lagging load gives a figure of that order in a typical machine.
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A machine whose per unit synchronous reactance is 1.25 has a short circuit ratio of
Answer: B
Correct answer: 0.8
\[ \mathrm{SCR} = \frac{1}{X_s\ (\mathrm{per\ unit})} = \frac{1}{1.25} = 0.8. \] A short circuit ratio below one indicates a machine with a relatively high synchronous reactance, which gives poorer regulation but usefully limits its contribution to a system fault.
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A generator with a synchronous reactance of 1.0 per unit, an excitation emf of 1.4 per unit and rated terminal voltage has a pull-out power of
Answer: C
Correct answer: 1.4 per unit
\[ P_{max} = \frac{EV}{X_s} = \frac{1.4 \times 1.0}{1.0} = 1.4\ \mathrm{per\ unit}, \] reached at a load angle of ninety degrees. The machine cannot be loaded to that point in practice: the synchronising coefficient falls to zero there, so any disturbance pulls it out of step.
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That machine delivering 0.7 per unit power has a load angle of
Answer: D
Correct answer: 30 degrees
\[ 0.7 = 1.4\sin\delta \quad\Rightarrow\quad \sin\delta = 0.5 \quad\Rightarrow\quad \delta = 30^\circ. \] Half the pull-out power is delivered at only thirty degrees, not forty-five, because the relation is sinusoidal - and the machine still retains \( \cos 30^\circ \), or 87 per cent, of its maximum synchronising stiffness.
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Consider the following statements about armature reaction.
1. It is demagnetising at lagging power factor.
2. It is magnetising at leading power factor.
3. It is absent at unity power factor.
Which are correct?
Answer: A
The first two are the standard results and explain why regulation is worst at lagging power factor. At unity power factor the effect is cross-magnetising rather than absent, distorting the field without much changing its magnitude.
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Match the method with the result it gives for voltage regulation.
1. Emf method 2. Mmf method 3. Potier method
P. The most accurate of the three Q. Optimistic, understating the regulation R. Pessimistic, overstating the regulation
Answer: B
The two simple methods err in opposite directions, which is convenient because the truth is bracketed between them. The Potier construction separates leakage reactance from armature reaction and does better than either.
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Match the reactance with the period it governs after a sudden short circuit.
1. Subtransient 2. Transient 3. Synchronous
P. The sustained condition Q. The first few cycles R. The following second or so
Answer: C
Flux trapped first in the damper winding and then in the field winding gives the two shorter periods, and once all the trapped currents have decayed the synchronous value applies. Switchgear making capacity is set by the first.
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Assertion (A): A generator's excitation controls its reactive rather than its active power.
Reason (R): Active power is set by the prime mover torque.
Select the correct option.
Answer: D
On a network the speed is fixed, so the torque the prime mover applies fixes the power, and the excitation is left to determine the reactive exchange. The two controls are very nearly independent, which is what makes the machine so manageable.
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Assertion (A): A machine with a large short circuit ratio has good regulation.
Reason (R): The ratio is the reciprocal of the per unit synchronous reactance.
Select the correct option.
Answer: A
Correct answer: Both A and R are true, and R is the correct explanation of A
Both are true and the reason gives the mechanism. Since the short circuit ratio is \( 1/X_s \) in per unit, a large ratio means a small synchronous reactance, and a small reactance means a small voltage drop between the excitation emf and the terminals as load is applied. Good regulation follows directly - as does, unavoidably, a large fault current.
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True or false: a synchronous generator's speed determines the frequency it produces.
Answer: B
Correct answer: True, through the speed and the number of poles together
\[ f = \frac{PN}{120}. \] The speed alone is not enough, since the pole number must be known, but the two together fix the frequency exactly. This is why frequency control on a power system is speed control, and why the generators of an interconnected system all turn in step.
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