Synchronous Machines
Practice QuestionsMarks 1
1
Instruments required to synchronize an alternator to the grid is/are
GATE EE 2025
2
The induced emf in a 3.3 kV , 4-pole, 3-phase, star-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of $2^{\circ}$ mechanical with respect to the terminal voltage phasor. If the synchronous reactance is $2 \Omega$, and stator resistance is negligible, then the motor armature current magnitude, in ampere, during loaded condition, is closest to __________ . (round off to two decimal places)
GATE EE 2025
3
In a salient pole synchronous motor, the developed reluctance torque attains the maximum
value when the load angle in electrical degrees is
GATE EE 2018
4
If a synchronous motor is running at a leading power factor, its excitation induced voltage (Er) is
GATE EE 2017 Set 2
5
A three-phase, 50Hz, star-connected cylindrical-rotor synchronous machine is running as a
motor. The machine is operated from a 6.6 kV grid and draws current at unity power factor
(UPF). The synchronous reactance of the motor is 30 Ω per phase. The load angle is $$30^\circ$$. The
power delivered to the motor in kW is _______.
GATE EE 2017 Set 1
6
In a synchronous machine, hunting is predominantly damped by
GATE EE 2014 Set 3
7
A star connected 400 V, 50 Hz, 4 pole synchronous machine gave the following open circuit
and short circuit test results:
Open circuit test: VOC = 400 V (rms, line–to–line) at field current, If = 2.3 A
Short circuit test: ISC = 10 A(rms, phase) at field current, If =1.5 A
The value of per phase synchronous impedance in Ω at rated voltage is __________.
Open circuit test: VOC = 400 V (rms, line–to–line) at field current, If = 2.3 A
Short circuit test: ISC = 10 A(rms, phase) at field current, If =1.5 A
The value of per phase synchronous impedance in Ω at rated voltage is __________.
GATE EE 2014 Set 1
8
A three-phase, salient pole synchronous motor is connected to an infinite bus. It
is operated at no load a normal excitation. The field excitation of the motor is
first reduced to zero and then increased in reverse direction gradually. Then the
armature current
GATE EE 2011
9
Distributed winding and short chording employed in AC machines will result in
GATE EE 2008
10
In a stepper motor, the detent torque means
GATE EE 2008
11
A three phase synchronous motor connected to ac mains is running at full load and unity power factor. If its shaft load is reduced by half, with field current held constant, its new power factor will be
GATE EE 2007
12
A synchronous generator is feeding a zero power factor (lagging) load at rated current the armature reaction is
GATE EE 2006
13
In relation to the synchronous machines, which one of the following statements is
false?
GATE EE 2005
14
The following motor definitely has a permanent magnet rotor
GATE EE 2004
15
For a given stepper motor, the following torque has the highest numerical value.
GATE EE 2004
16
A stand-alone engine driven Synchronous generator is feeding a partly inductive
load. A capacitor is now connected across the load to completely nullify the
inductive current. For this operating condition.
GATE EE 2003
17
Curves X and Y in Figure denote open circuit and full-load zero power factor (zpf)
characteristics of asynchronous generator. Q is a point on the zpf characteristics
at 1.0 p.u. voltage. The vertical distance PQ in Figure gives the voltage drop
across
GATE EE 2003
18
It is desirable to eliminate 5th harmonic voltage from the phase voltage of an
alternator. The coils should be short-pitched by an electrical angle of
GATE EE 2001
19
Figure shows the magnetization curves of an alternator at rated armature
current, unity power factor and also at no load. The magnetization curve for rated
armature current, 0.8 power factor leading is given by
GATE EE 2001
20
Xd, Xd' and Xd" are steady stated-axis synchronous reactance, transient d-axis
reactance and sub-transient d-axis reactance of a synchronous machine
respectively. Which of the following statements is true?
GATE EE 2001
21
The phase sequence of a three-phase alternator will reverse if
GATE EE 2000
22
Higher synchronous reactance is preferred in the present day alternators,
because one can have
GATE EE 1999
23
A synchronous generator connected to an infinite bus is overexcited. Considering
only the reactive power, from the point of view of the system, the machine acts
as
GATE EE 1998
24
During hunting of synchronous motor
GATE EE 1996
25
In Figure. The characteristic that corresponds to the variation of synchronous reactance of synchronous motor with field current is
GATE EE 1996
26
A synchronous motor on load draws a current at a leading power factor angle $$\phi$$.
If the internal power factor angle – which is the phase angle between the
excitation e.m.f. and the current in the time phasor diagram is $$\psi$$, then the air
gap excitation m.m.f lags the armature m.m.f by
GATE EE 1995
27
The developed electromagnetic force and or torque in electro $$-$mechanical energy conversion systems act in a direction that tends
GATE EE 1992
28
The torque angle of a synchronous machine operating from a constant voltage bus, is usually defined as the space angle between
GATE EE 1992
Marks 2
1
A 3-phase, 11 kV, 10 MVA synchronous generator is connected to an inductive load of power factor $(\sqrt{3}/2)$ via a lossless line with a per-phase inductive reactance of 5 $\Omega$. The per-phase synchronous reactance of the generator is 30 $\Omega$ with negligible armature resistance. If the generator is producing the rated current at the rated voltage, then the power factor at the terminal of the generator is
GATE EE 2024
2
Which of the following options is/are correct for the Automatic Generation Control (AGC) and Automatic Voltage Regulator (AVR) installed with synchronous generators?
GATE EE 2024
3
A three-phase synchronous motor with synchronous impedance of 0.1+j0.3 per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per unit is _________ (Round off to 2 decimal places).
GATE EE 2023
4
A star-connected 3-phase, 400 V, 50 kVA, 50 Hz synchronous motor has a synchronous reactance of 1 ohm per phase with negligible armature resistance. The shaft load on the motor is 10 kW while the power factor is 0.8 leading. The loss in the motor is 2 kW. The magnitude of the per phase excitation emf of the motor, in volts, is ________. (round off to nearest integer).
GATE EE 2022
5
Two generating units rated $$300$$ $$MW$$ and $$400$$ $$MW$$ have governor speed regulation of $$6\% $$ and $$4\% $$ respectively from no load to full load. Both the generating units are operating in parallel to share a load of $$600$$ $$MW.$$ Assuming free governor action, the load shared by the larger unit is _______ $$MW.$$
GATE EE 2017 Set 2
6
A $$25$$ $$kVA,$$ $$400$$ $$V,$$ $$\Delta $$ - connected, $$3$$-phase, cylindrical rotor synchronous generator requires a field current of $$5$$ $$A$$ to maintain the rated armature current under short-circuit condition. For the same field current, the open-circuit voltage is $$360$$ $$V.$$ Neglecting the armature resistance and magnetic saturation, its voltage regulation (in $$\% $$ with respect to terminal voltage), when the generator delivers the rated load at $$0.8$$ $$pf$$ leading, at rated terminal voltage is ____________.
GATE EE 2017 Set 2
7
A $$3$$-phase, $$2$$-pole, $$50$$ $$Hz,$$ synchronous generator has a rating of $$250$$ $$MVA,$$ $$0.8$$ $$pf$$ lagging. The kinetic energy of the machine at synchronous speed is $$100$$ $$MJ.$$ The machine is running steadily at synchronous speed and delivering $$60$$ $$MW$$ power at a power angle of $$10$$ electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for $$10$$ cycles, the value of the power angle after $$5$$ cycles is ________ electrical degrees.
GATE EE 2017 Set 2
8
Two parallel connected, three-phase, $$50Hz,$$ $$11kV,$$ star-connected synchronous machines $$A$$ and $$B,$$ are operating as synchronous condensers. They together supply $$50$$ $$MVAR$$ to a $$11$$ $$kV$$ grid. Current supplied by both the machines are equal. Synchronous reactances of machine $$A$$ and machine $$B$$ are $$1\,\,\Omega $$ and $$3\,\,\Omega ,$$ respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine $$A$$ to that of machine $$B$$ is ____________. (Give the answer up to two decimal places).
GATE EE 2017 Set 1
9
A three-phase, $$50$$ $$Hz$$ salient-pole synchronous motor has a per-phase direct-axis reactance $$\left( {{X_d}} \right)$$ of $$0.8$$ $$pu$$ and a per-phase quadrature-axis reactance $$\left( {{X_q}} \right)$$ of $$0.6$$ $$pu.$$ Resistance of the machine is negligible. It is drawing full-load current at $$0.8$$ $$pf$$ (leading). When the terminal voltage is $$1$$ $$pu,$$ per-phase induced voltage, in $$pu,$$ is ______________.
GATE EE 2016 Set 1
10
A three-phase, $$11$$ $$kV,$$ $$50$$ $$Hz,$$ $$2$$ pole, star connected, cylindrical rotor synchronous motor is connected to an $$11$$ $$kV,$$ $$50$$ $$Hz$$ source. Its synchronous reactance is $$50\Omega $$ per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is $$100$$ $$A$$ at unity power factor. If the load torque is increased so that the stator current is $$120$$ $$A,$$ then the load angle (in degrees) at this load is ____________.
GATE EE 2015 Set 2
11
A synchronous generator is connected to an infinite bus with excitation voltage $${E_f} = 1.3\,pu.$$ The generator has a synchronous reactance of $$1.1$$ $$pu$$ and is delivering real power $$(P)$$ of $$0.6$$ $$pu$$ to the bus. Assume the infinite bus voltage to be $$1.0$$ $$pu.$$ Neglect stator resistance. The reactive power $$(Q)$$ in $$pu$$ supplied by the generator to the bus under this condition is ____________.
GATE EE 2014 Set 2
12
A $$20$$-pole alternator is having $$180$$ identical stator slots with $$6$$ conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is $${V_1}.$$ If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is $${V_ 2}.$$ Assuming full pitch, single-layer winding, the ratio $${V_1}/{V_2}$$ is
GATE EE 2014 Set 2
13
There are two generators in a power system. No-load frequencies of the generators are $$51.5$$ $$Hz$$ and $$51$$ $$Hz,$$ respectively, and both are having droop constant of $$1$$ $$Hz/MW.$$ Total load in the system is $$2.5$$ $$MW.$$ Assuming that the generators are operating under their respective droop characteristics, the frequency of the power system in $$Hz$$ in the steady state is ____________.
GATE EE 2014 Set 2
14
A non-salient pole synchronous generator having synchronous reactance of $$0.8$$ $$pu$$ is supplying $$1$$ $$pu$$ power to a unity power factor load at a terminal voltage of $$1.1$$ $$pu$$. Neglecting the armature resistance, the angle of the voltage behind the synchronous reactance with respect to the angle of the terminal voltage in degrees is ____________.
GATE EE 2014 Set 3
15
A three phase synchronous generator is to be connected to the infinite bus. The lamps are connected as shown in the figure for the synchronization. The phase sequence of bus voltage is $$R$$-$$Y$$-$$B$$ and that of incoming generator voltage is $$R'$$ - $$Y'$$ - $$B'.$$
It was found that the lamps are becoming dark in the sequence $${L_a} - {L_b} - {L_c}.$$ It means that the phase sequence of incoming generator is
GATE EE 2014 Set 1
16
The direct axis and quadrature axis reactances of a salient pole alternator are $$1.2$$ $$p.u$$ and $$1.0$$ $$p.u$$ respectively. The armature resistance is negligible. If this alternator is delivering rated $$kVA$$ at $$upf$$ and at rated voltage then its power angle is
GATE EE 2011
17
A separately excited $$dc$$ machine is coupled to a $$50Hz,$$ three-phase, 4-pole induction machine as shown in the figure. The dc machine is energized first and the machines rotate at $$1600$$ $$rpm.$$ Subsequently the induction machine is also connected to a $$50Hz,$$ three-phase source, the phase sequence being consistent with the direction of rotation. In steady state
GATE EE 2010
18
A $$50$$ $$Hz$$ synchronous generator is initially connected to a long lossless transmission line which is open circuited at the receiving end. With the field voltage held constant, the generator is disconnected from the transmission line. Which of the following may be said about the steady state terminal voltage and field current of the generator?
GATE EE 2010
19
A field excitation of $$20A$$ in a certain alternator results in a armature current of $$400$$ $$A$$ in short circuit and a terminal voltage of $$2000$$ $$V$$ on open circuit. The magnitude of the internal voltage drop with in the machine at a load current of $$200$$ $$A.$$
GATE EE 2009
20
A synchronous motor is connected to an infinite bus at $$1.0$$ $$p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power factor. Its synchronous reactance is $$1.0$$ $$pu$$ and resistance is negligible.
The excitation voltage and load angle will respectively be
GATE EE 2008
21
A synchronous motor is connected to an infinite bus at $$1.0p.u$$ voltage and draws $$0.6$$ $$pu$$ at unity power factor. Its synchronous reactance is $$1.0$$ $$pu$$ and resistance is negligible.
Keeping the excitation voltage same, the load on the motor is increased such that the motor current increases by $$20\% $$. The operating power factor will become
GATE EE 2008
22
A $$100$$ $$kVA$$, $$415V,$$ star connected synchronous machine generates rated open circuit voltage $$415V$$ at a field current of $$15A.$$ The short circuit armature current at a field current of $$10A$$ is equal to the rated armature current. The per unit saturated synchronous reactance is
GATE EE 2007
23
A $$3$$ phase, $$3$$ stack, variable reluctance stepper motor has $$20$$ poles on each rotor and stator stack. The step angle of this stepper motor is
GATE EE 2007
24
A $$3$$-phase $$4000$$ $$V,$$ $$5$$ $$kW,$$ star connected synchronous motor having an internal reactance of $$10$$ $$ohms$$ is operating at $$50\% $$ load, unity power factor. Now, the excitation is increased by $$1\% $$, what will be the new load in percent, if the power factor is to be kept same? Neglect all losses and consider linear magnetic circuit.
GATE EE 2006
25
A $$4$$ pole, $$50$$ $$Hz,$$ synchronous generator has $$48$$ slots in which a double layer winding is house. Each coil has $$10$$ turns and is short pitched by an angle to $$36$$ degrees electrical. The fundamental flux per pole is $$0.025$$ $$Wb$$
The line to line induced $$emf$$, for a three phase star connection is approximately
GATE EE 2006
26
A $$4$$ pole, $$50$$ $$Hz,$$ synchronous generator has $$48$$ slots in which a double layer winding is house. Each coil has $$10$$ turns and is short pitched by an angle to $$36$$ degrees electrical. The fundamental flux per pole is $$0.025$$ $$Wb$$
The line to line induced $$emf,$$ for two phase connection is
GATE EE 2006
27
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.
The induced $$emf$$ is close to (line to line)
GATE EE 2005
28
A $$1000$$ $$kVA,$$ $$6.6$$ $$kV,$$ $$3$$-phase star connected cylindrical pole synchronous generator has a synchronous reactance of $$20\Omega .$$ Neglect the armature resistance and consider operation at full load and unity power factor.
The power angle is close to
GATE EE 2005
29
The synchronous speed for the seventh space harmonic $$mmf$$ wave of a $$3$$-phase, $$8$$ pole, $$50$$ $$Hz$$ induction machine is
GATE EE 2004
30
A hydraulic turbine having rated speed of $$250$$ $$rpm$$ is connected to a synchronous generator. In order to produce power at $$50$$ $$Hz,$$ the number of poles required in the generator are
GATE EE 2004
31
A $$500$$ $$MW$$ $$3$$-phase $$Y$$-connected synchronous generator has a rated voltage of $$21.5kV$$ at $$0.85$$ $$pf.$$ The line current when operating at full load rated conditions will be
GATE EE 2004
32
For a $$1.8$$ degree, $$2$$-phase bipolar stepper motor, the stepping rate is $$100$$ steps/second. The rotational speed of the motor in $$rpm$$ is
GATE EE 2004
33
A $$400$$ $$V,$$ $$50$$ $$kVA,$$ $$0.8$$ $$pf$$ leading delta connected, $$50$$ $$Hz$$ synchronous machine has a synchronous reactance of $$2$$ $$ohm$$ and negligible armature resistance. The friction and windage losses are $$2$$ $$kW$$ and the core loss is $$0.8$$ $$kW.$$ The shaft is supplying $$9$$ $$kW$$ load at a power factor of $$0.8$$ leading. The line current drawn is
GATE EE 2004
34
Two $$3$$-phase, $$Y$$-connected alternators are to be paralleled to a set of common bus bars. The armature has a per phase synchronous reactance of $$1.7\Omega $$ and negligible armature resistance. The line voltage of the first machines is adjusted to $$3300$$ $$V$$ and that of the second machine is adjusted to $$3200$$ $$V.$$ the machine voltages are in phase at the instant they are paralleled. Under this condition, the synchronizing current per phase will be
GATE EE 2004
35
A $$4$$-pole, $$3$$-phase, double layer winding is housed in a $$36$$-slot stator for an $$ac$$ machine with $$60$$ degree phase spread. Coil span is $$7$$ slot pitches. Number of slots in which top and bottom layers belong to different phases is.
GATE EE 2003
36
The flux per pole in a synchronous motor with the field circuit ON and the stator disconnected from the supply is found to be $$25$$ $$mWb.$$ When the stator is connected to the rated supply with the field excitation unchanged, the flux per pole in the achine is found to be $$20$$ $$mWb$$ while the motor is running on no load. Assuming no load losses to be zero, the no load current down by the motor from the supply
GATE EE 2002
37
A star-connected 440 V, 50 Hz alternators has per phase synchronous reactance
of 10 Ω. It supplies a balanced capacitive load current of 20 A, as shown in the
per phase equivalent circuit of Figure. It is desirable to have zero voltage
regulation. The load power factor should be
GATE EE 2001
38
A single-phase, 2000 V alternator has armature resistance and reactance of 0.8
ohms and 4.94 ohms respectively. The voltage regulation of the alternator at
100 A load at 0.8 leading power-factor is:
GATE EE 2000
39
A three phase alternator is wound with a 60 degree phase-spread armature
windings and develops 300 kVA. If the armature is reconnected utilizing all the
coils for single phase operation with a phase spread of 180 degrees, the new
rating of the machine is
GATE EE 1999
40
The armature of a single phase alternator is completely wound with T single turn
coils distributed uniformly. The induced voltage in each turn is 2 Volts (rms). The emf
of the whole winding is
GATE EE 1998
41
A single-phase alternator has a synchronous reactance of $$2$$ $$ohms$$ and negligible resistance. If it supplies $$10$$ $$A$$ to a purely capacitive load at $$200V,$$ then generated $$e.m.f$$ will be ... $$V$$ and the regulation will be ...... $$\% $$
GATE EE 1997
42
A synchronous motor operates at $$0.8$$ $$p.f.$$ lagging. If the field current of the motor is continuously increased
$$(1)$$ the power factor decreases upto a certain value of field current and thereafter it increases
$$(2)$$ the armature current increases upto a certain value of field current and thereafter it decreases
$$(3)$$ the power factor increases upto a certain value of field current and thereafter it decreases
$$(4)$$ the armature current decreases upto a certain value of field current and thereafter it increases. From these the correct one is
GATE EE 1993
43
Two $$550$$ $$kVA$$ alternators operate in parallel to supply the following loads
$$(i)$$ $$250$$ $$kW$$ at $$0.95$$ power factor lag
$$(ii)$$ $$100$$ $$kW$$ at $$0.8$$ power factor lead one machine is supplying $$200kW$$ at $$0.9$$ power factor lag. The power factor of the other machine must be
$$(i)$$ $$250$$ $$kW$$ at $$0.95$$ power factor lag
$$(ii)$$ $$100$$ $$kW$$ at $$0.8$$ power factor lead one machine is supplying $$200kW$$ at $$0.9$$ power factor lag. The power factor of the other machine must be
GATE EE 1993
44
A three phase alternator has negligible stator resistance. A short circuit test is conducted on this alternator. At a particular speed a field current of $${{\rm I}_f}$$ is required to drive the rated armature current. If the speed of the alternator is reduced to half, the field current required to maintain rated armature current
GATE EE 1993
Marks 5
1
A $$415$$ $$V,$$ $$2$$ pole, $$3$$ phase, $$50$$ $$Hz,$$ star connected, non-salient pole synchronous motor has synchronous reactance of $$2\,\Omega $$ per phase and negligible stator resistance. At a particular field excitation, it draws 20 A at unity power factor from a $$415$$ $$V,$$ $$3$$ phase, $$50$$ $$Hz$$ supply. The mechanical load on the motor is now increased till the stator current is equal to $$50$$ $$A.$$ The field excitation remains unchanged. Determine:
$$(a)$$ the per phase open circuit voltage $${E_0}$$
$$(b)$$ the developed power for the new operating condition and corresponding power factor.
$$(a)$$ the per phase open circuit voltage $${E_0}$$
$$(b)$$ the developed power for the new operating condition and corresponding power factor.
GATE EE 2002
2
A $$50$$ $$kW$$ synchronous motor is tested by driving it by another motor. When the excitation is not switched on, the driving motor takes $$800$$ $$W.$$ When the armature is short-circuited and the rated armature current of $$10$$ $$A$$ is passed through it, the driving motor requires $$2500$$ $$W.$$ On open-circuiting the armature with rated excitation, the driving motor takes $$1800$$ $$W.$$ Calculate the efficiency of the synchronous motor at $$50\% $$ load. Neglect the losses in the driving motor.
GATE EE 2001
3
Two identical synchronous generators, each of $$100$$ $$MVA,$$ are working in parallel supplying $$100$$ $$MVA$$ at $$0.8$$ lagging $$p.f.$$ at rated voltage. Initially the machines are sharing load equally. If the field current of first generator is reduced by $$5\% $$ and of the second generator increased by $$5\% ,$$ find the sharing of load ($$MW$$ and $$MVAR$$) between the generators.
Assume$${X_d} = {X_q} = 0.8\,\,p.u.$$ no field saturation and rated voltage across load. Reasonable approximations may be made.
Assume$${X_d} = {X_q} = 0.8\,\,p.u.$$ no field saturation and rated voltage across load. Reasonable approximations may be made.
GATE EE 2001
4
A $$2300$$ $$V,$$ $$3$$-phase synchronous motor driving a pump is provided with a line ammeter and a field rheostat. When the rheostat is adjusted such that the $$ac$$ line current is minimum. The ammeter reads $$8.8$$ $$A.$$ What is the power being delivered to the pump, neglecting losses? How should the rheostat be adjusted so that the motor operates at $$0.8$$ leading power factor? How many $$kVARs$$ is the motor supplying to the system at this new power factor?
GATE EE 2000
5
A $$5MVA$$, $$11kV$$, $$3$$-phase star connected alternator is synchronized to the bus bars and is operating with an induced $$EMF$$ of $$125\% $$ of the rated voltage. If the load current is $$500$$ $$A,$$ what is the power factor of operation? The machine has a synchronous reactance of $$5\,\,\Omega $$ and negligible resistance per phase.
GATE EE 1997
6
The per unit voltage of two synchronous machines connected through a lossless line are $$0.95\,\,\angle \,{10^0}\,\,$$ and $$1.0\,\,\angle \,{0^0}\,\,$$. Match the two sides in the following
$$(a)$$ Real power of Machine $$1$$
$$(b)$$ Reactive power of machine $$1$$
$$(c)$$ Power factor of Machine $$1$$
$$(a)$$ Real power of Machine $$1$$
$$(b)$$ Reactive power of machine $$1$$
$$(c)$$ Power factor of Machine $$1$$
$$(P)$$ Positive real power
$$(Q)$$ Positive reactive power
$$(R)$$ Negative real power
$$(S)$$ Negative reactive power
$$(T)$$ Leading power factor
$$(U)$$ Lagging power factor
GATE EE 1996
7
The distribution factor for a $$36$$ slot stator with three-phase, $$8$$-pole winding, having $${120^ \circ }$$ phase Spread, is _________
GATE EE 1995
8
Figure depicts the load characteristics of an constant speed. Match the following sets of operating conditions with the given characteristics. Disregard the effects of saliency, saturation and stator resistance.
$$(a)$$ Constant excitation and non-zero leading power-factor
$$(b)$$ Constant excitation and zero power-factor, leading
$$(c)$$ Constant terminal voltage and zero power-factor, leading
$$(d)$$ Constant terminal voltage and non-zero leading power-factor
GATE EE 1992