Quiz1 Ac Otplusbook-1

Examp le 5.1 (page 1)

Determine the pitch (or coil span) factors for the following windings: (i) 36 stator slots, 4 poles, coil span 1 to 8. (ii) 96 stator slots, 6 poles, coil span 1 to 12. Sketch the two coil spans.


What are the effects of the coil and distribution span factors on the output and waveform of an alternator? Determine their values for a 3-phase winding with 4 slots per pole per phase, the coil span being 10 slot pitches. Calculate the percentage increase in R.M.S. value of the phase voltage due to a 25 percent third harmonic.

Examp le 5.3 (page 1-2)

What are the causes of harmonics in the voltage and current waves of electrical machinery and what means are taken in design to reduce them? The phase voltage of a 750 kW, 2200 V, 3-phase, 50 Hz alternator has a 5 percent third harmonic. What is the circulating current on normal voltage if the machine is delta connected? The resistance and reactance per phase are 0.25ohms and 0.7ohms respectively. Express the loss due to the circulating current as a percentage of full-load output.


A 3-phase, 3-phase, 16-pole alternator has the following data: Number of slots = 192 ; conductors/slot = 8 (conductors of each phase are connected in series) coil span = 160 electrical degrees; speed of the alternator = 375 r.p.m.; flux/pole = 55 mWb. Calculate the phase and line voltages.


A 3-phase, 3-phase, star-connected star-connected alternator has the following f ollowing data: voltage voltage required to be generated on open-circuit = 4000 V (at 50 Hz); speed = 500 r.p.m.; stator slots/pole/phase = 3; conductors/slot = 12. Calculate: (i) Number of poles, and

(ii) useful flux pole.


A 3-phase, 10-pole alternator has 2 slots per pole per phase on its stator with conductors per slot. The air gap flux is sinusoidally distributed and equals to 0.05 Wb. The _____ double layer winding with a coil span of 150 electrical degrees. If the alternator is running _____ r.p.m., calculate the e.m.f. generated per phase at no load.


Calculate the speed and open-circuit line and phase voltages of a 4-pole, 3phase, 50 Hz star-connected alternator with 36 slots and 30 conductors per slot. The flux per pole is 0.05 Wb sinusoidally distributed.


A 4-pole, 50 Hz star-connected star-connected alternator alternator has has a flux per pole of 0.12 0.12 Wb. It has 4 slots per pole per phase, conductors per slot being 4. If the winding coil span is 150degress, find the e.m.f.


A 3-phase, 3-phase, 4-pole, 50 Hz star-connected star-connected alternator alternator has 60 slots with 2 conductors per slot and having armature winding of the double layer type. Coils are short-pitched, that is, if one coil side lies in slot number 1, the other coil side lies in slot number 13. Find the useful flux per pole required to induce a line voltage of 6.6 kV.

Examp le 5.10 (page (page 4)

An 8-pole, 3-phase, 60degrees 60degrees spread, double layer winding has 72 coils in 72 slots. The coils are short-pitched by two slots. Calculate the winding factor for the fundamental and third harmonic.


Calculate the r.m.s. value of the induced e.m.f. per phase of a 10-pole, 3-phase, 50 Hz alternator with 2 slots per pole per phase and 4 conductors per slot in two layers. The coil span is 150degrees. The flux per pole hass a fundamental component of 0.12 Wb and a 20% third harmonic component.


A 3-phase, 10-pole alternator has 2 slots per pole per phase on its stator with conductors per slot. The air gap flux is sinusoidally distributed and equals to 0.05 Wb. The _____ double layer winding with a coil span of 150 electrical degrees. If the alternator is running _____ r.p.m., calculate the e.m.f. generated per phase at no load.


Calculate the speed and open-circuit line and phase voltages of a 4-pole, 3phase, 50 Hz star-connected alternator with 36 slots and 30 conductors per slot. The flux per pole is 0.05 Wb sinusoidally distributed.


A 4-pole, 50 Hz star-connected star-connected alternator alternator has has a flux per pole of 0.12 0.12 Wb. It has 4 slots per pole per phase, conductors per slot being 4. If the winding coil span is 150degress, find the e.m.f.


A 3-phase, 3-phase, 4-pole, 50 Hz star-connected star-connected alternator alternator has 60 slots with 2 conductors per slot and having armature winding of the double layer type. Coils are short-pitched, that is, if one coil side lies in slot number 1, the other coil side lies in slot number 13. Find the useful flux per pole required to induce a line voltage of 6.6 kV.


An 8-pole, 3-phase, 60degrees 60degrees spread, double layer winding has 72 coils in 72 slots. The coils are short-pitched by two slots. Calculate the winding factor for the fundamental and third harmonic.


Calculate the r.m.s. value of the induced e.m.f. per phase of a 10-pole, 3-phase, 50 Hz alternator with 2 slots per pole per phase and 4 conductors per slot in two layers. The coil span is 150degrees. The flux per pole hass a fundamental component of 0.12 Wb and a 20% third harmonic component.


The flux distribution curve of a smooth-core, 50 Hz generator is B = 10sin theta + 2 sin3*theta + 2 sin5*theta + 2 sin7*theta kilo-gauss when theta is measured from the neutral axis. The pole ____ 35 cm, the core length 32 cm, and stator coil span four-fifths of the pole pitch. Determine the ____ for the e.m.f. induced in one turn, and its r.m.s. value.


A 3-phase water-wheel generator generator is rated at 100 MVA, unity power factor, ___ star-connected 50 Hz, 120 r.p.m. Determine: (i) the number of poles; (ii) the kW rating; (iii) the current rating; (iv) the input at rated kW load if the efficiency is 97% (excluding the field loss); (v) prime mover torque applied to the generator shaft.


(a) Compare the constructional features of hydel and turbo-generators. (b) A 200 kVA, 480 V, 50 Hz, Y-connected synchronous generator with a rated field current of 5 A was tested, and the following data were obtained: - Open circuit terminal voltage 540 V (line-to-line) - short circuit current 300 A When a d.c. voltage of 10 V was applied to two of its terminals, a current of 25 A was measured. Find the value of the synchronous reactance.


A 600 V, 60 kVA, single-phase alternator alternator has an effective effective resistance resistance of 0.2ohms. A field current of 10 A produces an armature current of 210 A on short-circuit short-circuit and an e.m.f. of 480 V on open-circuit. Calculate: (i) Synchronous impedance and reactance (ii) Full-load regulation with 0.8 p.f. lagging

Example 5.16 (page 8)

A 3-phase star-connected alternator is rated at 1500 kVA, 12000 V. The armature effective resistance and synchronous reactance are 2ohms and 35ohms respectively per phase. Calculate the percentage regulation for a load of 1200 kW at power factor of: (i) 0.8 lagging (ii) 0.8 leading

Example 5.17 (page 8-9)

A 3300 V, 3-phase star-connected alternator has a full load current of 100 A. On short-circuit a field current of 5 amperes was necessary to produce full-load current. The e.m.f. on open-circuit for the same excitation was 900 volts. The armature resistance was 0.8ohms/phase. Determine the full-load voltage regulation for: (i) 0.8 p.f. lagging (ii) 0.8 p.f. leading


A 3.3 kV, 3-phase star-connected alternator has a full-load current of 100 A. Under short-circuit condition it takes 5 A field current to produce full-load short circuit current. The e.m.f. on open circuit for the same excitation is 900 V (line-to-line). The armature resistance is 0.9ohms/phase. Determine the synchronous reactance per phase and regulation for (i) 0.8 p.f. lagging, (ii) 0.8 p.f. leading.


A 3-phase, star-connected, 1000 kVA, 11000 V alternator has rated current of 52.5 A. The A.C. resistance of the winding per phase is 0.45ohms. The test results are given below: O.C. test: Field current = 12.5 A, voltage between lines = 422 V S.C. test: Field current = 12.5 A, line current = 52.5 A Determine the full-load voltage regulation of the alternator (a) 0.8 p.f. lagging and (b) 0.8 p.f. leading.


(a) Develop the terms generally used for reducing harmonic voltages from the induced e.m.f. (b) A 3-phase, 50 Hz, 6000 kVA, 6000 V star-connected alternator has an effective resistance of 0.2ohms. A field current of 10 A produces 480 V on open-circuit and a field current of 5 A given armature current of 105 A. Calculate the voltage regulation of this alternator at 0.8 power for lagging.


(a) Why the modern alternators are designed with a high-ratio of armature synchronous reactance to resistance ratio? Why in addition external reactors are provided in series with each phase of an alternator? (b) A 3-phase, Y-connected, 11 kV, 165 MVA alternator has a synchronous reactance of 1 ohm and armature resistance of 0.1 ohm per phase. Calculate short circuit current at the instant of short circuit and sustained short circuit current.


A 1500 kVA, 6600 V, 3-phase star connected alternator with a resistance of 0.4 ohm and reactance of 6 ohms per phase, delivers full-load current at power factor 0.8 lagging and normal rated voltage. Estimate the terminal voltage for the same excitation and load current ____ 0.8 power factor leading.


(a) A 3-phase, star-connected, 5 kVA, 400 V, 50 Hz, 4-pole alternator has the following test data at rated speed: (i) Table given (ii) Exciting current (amperes)

1.0

2.0

S.C. line current

7.2

10.8

3.6

3.0

(iii) Armature resistance per phase 2.0 ohms. Draw O.C. and S. C. (long given)


A 3-phase star-connected synchronous generator is rated at 1.5 MVA, 11 kV. The armature effective resistance and synchronous reactance are 1.2 ohms and 25

ohms respectively per phase. Calculate the percentage regulation for a load of 1.4375 MVA at (i) 0.8 p.f. lagging and (ii) 0.8 p.f. leading.


The no-load excitation of an alternator required to give rated voltage is 90 A. In a short-circuit test with full-load current flowing in the armature., the field excitation was 70 A. Determine the approximate excitation that will be required to give full-load current at 0.8 p.f. lag and at the rated terminal voltage.


A 3-phase star-connected, 1000 kVA, 2000 V, 50 Hz, alternator gave the following: Field current, A:

10

20

Open-circuit voltage, V:

800

1500 1760 2000 2350 2600

Short-circuit armature current, A: -----

200

25

250

30

300

40

-----

50

-----

Draw the characteristic curves and estimate the full-load percentage regulation at: (i) 0.8 power factor lagging; and

(ii) 0.8 power factor leading.


A 6600 V alternator gave the following test results: O.C. voltage, V:

3100

4900

6600

7500

8300

Field current, A:

16

25

37.5

50

70

A field current of 22 A is found necessary to circulate full-load current on shortcircuit of the armature. Calculate the full-load regulation at 0.8 power factor lagging by: (i) the ampere-turn method; (ii) The synchronous impedance method. Comment on the two values of regulation obtained by the above methods.


The following O.C.C. was obtained in case of a 3-phase, 6000 B alternator running at normal speed: Field current, A:

14

18

23

30

43

Terminal voltage, V:

4000

5000

6000

7000

8000

The field current is 17 A when armature is short-circuited and the full-load current is ___. Using synchronous impedance method, determine the voltage regulation of the alternator ___ the full-load of 200 kVA at 0.707 lagging. Neglect armature resistance.


A 275 kW, 3-phase, 6600 V non-salient pole type alternator gave the following test results: O.C.C.: Exciting amperes, A:

46.5

58

67.5

96

Volts, V:

5600

6600

7240

8100

S.C.C.: Stator current 35 amperes with an exciting current of 50 amperes. Leakage reactance on full-load: 8 percent. Calculate as accurately as possible the exciting current (for full-load) at 0.8 p.f. lagging. Neglect armature resistance.


The following are the no-load characteristics of a 3300 B, 1500 kVA, starconnected, 8-pole, 3-phase alternator running at 750 r.p.m.: Terminal voltage

Field AT/poles

1500

2000

2200

3000

2700

4000

3200

5000

3550

6000

3800

7000

4000

8000

4100

9000

4150

10000

The resistance measured between terminals is 0.5ohms and its true reactance per phase is 1.4 ohms. The number of turns per phase is 60. Assuming that the armature reaction ampere turns per pole are equal to 1.6 times amperes turns/pole/phase and the ratio of effective to the measured ohmic resistance is 1.5, determine the percentage regulation, when full-load at normal voltage and at p.f. 0.8 lag is thrown off and the speed of the alternator increases to 790 r.p.m.


The following data pertains to a 3.3 kV, 1200 kVA, 3-phase star-connected ___ pole alternator: Exciting AT/pole

Generated Voltage (line)

2000

1500

3600

2500

5000

3150

6000

3450

7000

3680

8000

3850

9000

4000

10000

4050

Resistance per phase = 0.5ohms Leakage reactance per phase = 1.3ohms Equivalent armature reaction (AT/pole) = 15 times the line current Reluctance to cross flux = 2 times direct flux Determine the regulation at full-load at 0.8 power factor lag.


The following data pertains to a 15000 kVA, 11 kV, 3-phas, 50 Hz star-connected turbo alternator:

O.C. line kV Field AT in 10^3 Zero p.f. full load line kV Determine: (i) Armature reaction (ii) Armature reactance (iii) Synchronous reactance (iv) Percentage regulation for full-load at 0.8 p.f. lagging.


A 10 kVA, 440 V, 50 Hz, 3-phase alternator has the open-circuit characteristics below: Field current, A:

1.5

3.0

5.0

8.0

11.0

15.0

Terminal voltage, V:

150

300

440

550

600

635

With full-load zero power factor applied an excitation of 14 A produced a terminal voltage 500 V on short-circuit, 4 A excitation was required to give full-load current. Determine as accurately as possible, the percentage regulation for full-load 0.8 p.f. (i) lagging (ii) leading.


The following data pertains to a 5000 kVA, 6600 V, 3-phase, 50 Hz ___ nected alternator: Field current, A:

32

50

75

100

140

O.C. terminal voltage, V:

3100 4900 6600 7500 8300

Full-load current Zero p.f. test line p.d., V:

0

1850 4250 5800 7000

Determine the regulation by zero power factor method at full-load unity power factor. Neglect armature resistance.


A 2200 V, 50 Hz, 3-phase, star-connected alternator has an effective resistance of 0.5ohms per phase. A field current of 30 A produced the full-load current of 200 A on short-circuit and a line-to-line e.m.f. of 1100 V on open-circuit. Determine: (i) the power angel of the alternator when it delivers full-load at 0.8 p.f. (lag) (ii) the SCR of the alternator.


A 3-phase synchronous generator has per phase a direct axis ____ reactance of 1.0 per unit and a quadrature axis synchronous reactance of 0.65 per unit. Draw ____ diagram of the machine when operating at full-load at a power factor of 0.8 lagging and ____ there: (i) the load angle;

(ii) per unit no-load e.m.f.

Neglect armature resistance.


A 5 kVA, 220 V, star-connected 3-phase salient pole alternator with ______ quadrature axes reactances of 12 ohms and 7 ohms respectively, delivers full-load current at unity power factor. Calculate the excitation voltage, neglecting resistance.


A 10 kVA, 380 V, 50 Hz, 3-phase, star-connected salient pole alternator has direct axis and quadrature axis reactances of 12 ohms and 8 ohms respectively. The armature has a resistance of 1 ohm per phase. The generator delivers rated load at 0.8 power factor lagging with the terminal voltage being maintained at rated value. If the load angle is 16.15degrees determine: (i) the direct axis and quadrature axis components of armature current. (ii) excitation voltage of the generator.


A 3-phase star-connected alternator is delivering 20 MW and 8 MVA to an infinite bus at 11 kV. The alternator has synchronous impedance of 0+j3 ohms. Determine the load angle and the excitation emf of the alternator.


A 3.5 MVA, slow speed, 3-phase synchronous generator rated at 6.6 kV _____ poles. Its direct and quadrature axes synchronous reactances as measured by the slip test are ______ and 6 ohms respectively. (i) Neglecting armature resistance, determine the regulation and excitation e.m.f. ______ maintain 6.6 kV at the terminals when supplying a load of 2.5 MW at 0.8 power factor lagging. (ii) What maximum power can generator supply at the rated terminal voltage, if the ______ becomes open-circuited?


A 3-phase, 17.32 kVA, 400 V, star-connected alternator is delivering rated load at 400 V and at p.f. 0.8 lag. Its synchronous impedance is 0.2+j2 ohms per phase. Find the load angle at which it is operating. Now, with the magnitude of excitation voltage held constant, the nature of rated load p.f. is altered to p.f. 0.8 leading. Determine the new value of terminal voltage and the load angle.


A 10000 kVA, 3-phase, star-connected 11000 V, 2-pole turbo-generator has a synchronous impedance of (0.0145+j0.5) ohms per phase. The various losses in this generator are as follows: Open-circuit core loss at 11000V

= 90 kW;

Windage and friction loss

= 50 kW;

Short-circuit load loss at 525 A

= 220 kW;

Field winding resistance

= 3 ohms;

Field current

= 175 A.

Ignoring the change in field current, compute the efficiency at: (i) rated load, 0.8 power factor leading; (ii) half rated load, 0.9 power factor lagging.


A 2MVA, 3.3 kV, 3-phase, star-connected alternator delivers rated load at a p.f. 0.8 lagging. The effective resistance between armature winding terminals is 0.12 ohms. The field takes 70 A at 130 V. Friction and windage loss is 15 kW and the core losses are 32 kW. Determine the full-load efficiency of the alternator.


A 3 MVA, 6-pole alternator runs at 1000 r.p.m. in parallel with other _____ on 3.3 kV bus-bars. The synchronous reactance is 20%. Calculate the synchronizing power ____ mechanical degree of displacement and the corresponding synchronizing torque.


A 4 MVA, 10 kV, 1500 r.p.m., 50 Hz alternator runs in parallel with _____ machines. Its synchronous reactance is 25%. Find for (i) no-load, (ii) full-load, at p.f. 0.8 lagging synchronizing power per unit mechanical angle of phase displacement, and calculate its synchronizing torque if the mechanical displacement is 0.7.


A 4500 kVA, 50 Hz, 3-phase, synchronous generator having a _____ reactance of 0.3 p.u. is running at 1500 r.p.m. and is excited to give 11000 V. If the rotor _____ slightly from its equilibrium position, what is the synchronizing torque in N-m per degree ______ displacement.


A 2-pole, 50-Hz, 3-phase, turbo-alternator is excited to generate the bus-bar voltage of 11 kV on no-load. The machine is star-connected and the short-circuit current for this excitation is 1000 A.


3 MVA, 6-pole alternator runs at 1000 r.p.m. on 3.3 kV bus-bars. The synchronous reactance is 25%. Calculate the synchronizing power and torque per mechanical degree of displacement when the alternator is supplying full-load at 0.8 power factor lagging.


A number of alternators are working in parallel with their terminal voltage equal to the rated value. one of the machines, which has a synchronous reactance of 50% and a resistance of 1%, delivers a power output in kW equal to 70% of its rated kVA. if the emf of the equals 1.2 times the terminal voltage, find out the power factor at which the machine is operating. Example 5.50 (page 33-34)

Two 1-phase alternators operate in parallel and supply a load impedance (3+j4) ohm. if the impedance of each machine is (0.2+j2) and e.m.fs. are (200+j0) and (222+j0) respectively, determine for each machine: Example 5.51 (page 34)

Two alternators working in parallel supply a lighting load of 3000 kW and motor load aggregating to 5000kW at a p.f. 0.72. One machine is loaded up to 5000kW at 0.8 pf lagging. what is the load and power factor of the other machine? Example 5.52 (page 34)

The following loads are supplied by two alternators running in parallel. (i) 1400 kW at p.f. 0.86 lagging,

(ii) 900 kW at p.f. 0.8 lagging.

(iii) 800 kW at p.f. unity

(iv) 500 kW at p.f. 0.8 leading.

if the load on one machine is adjustedto 2100 kW at p.f. 0.92, find the load and p.f. of the other machine. Example 5.53 (page 34-35)

the following data pertains to two similar alternators: 3-phase, 6600V , 60-Hz, 1200 kVA, star-connected. Example 5.54 (page 35-36)

two identical 3-phase alternators work in parallel and supply a total load 1600 kW at 11000 V at a power factor of 0.92. each machine supplies half the total power. the synchronous reactance of each is 50ohm/phase and resistance is 2.5ohm/phase. the field excitation of the first machine is adjusted so that the armature current is 50 A lagging. determine the armature current of the second alternator, the power factor at which each machine is working and generated voltage of the first alternator. Example 5.55 (page 36-37)

a 6600 V, 1200 kVA, 3-phase alternator is delivering full load at 0.8 p.f. lagging. its reactance is 25% and resistance negligible. by changing the excitation, the emf increased by 30%, at this load, calculate:

(i) new current

(ii) power factor.

the machine is connected to infinite bus-bars.


a turbo-alternator having a reactance of 10 ohm has an armature current of 220 Amperes at unitypower factor when running an 11000V constant frequency bus bars. if the admissions be unchanged and the e.m.f. raised by 25 per cent determine graphically or otherwise new value of machine current and power factor. Example 5.57 (page 38)

A 6600 V, 1200 kVA alternator has a reactance of 25% and is delivering full-load at 0.8 p.f. lagging. it is connected to constant frequency bus-bar. if the steam supply is gradually increased, calculate: Example 5.58 (page 38-39)

two 3-phase synchronous mechanically coupled generators operate in parallel on the same load. determine the kW output and power factor of each machine under the following conditions. Synchronous impedance of each generator: 02+j2 ohm/phase. equivalent impedance of the load: 03+j4 ohm/phase. induced e.m.f./phase, 2000+j0 volts for machine 1 and 2200+j100 for machine 2. Example 5.59 (page 39)

two exactly similar turbo-alternators are rated at 25MW each. they are running in parallel. the speed-load characteristics of the driving turbines are such that the frequency of alternator 1 drops uniformly from 50-Hz on no-load to 48-Hz on full-load, and that of alternator from 50-Hz to 48.5-Hz. how will the two machines share a load of 30MW? Example 5.60 (page 39-40)

two 800 kW alternators operate in parallel. the speed regulation of one set is 100%to 103% from full-load to no-load and that of the other is 100% to 104%. how will the two alternators share a load of 1200 kW and at what load will one machine cease to supply any portion of the load? Example 5.61 (page 40-41)

two 60 MVA, 3-phase alternative operate in parallel. the settings of the governors are such that the rise in speed from full-load to no-load is 2% in one machine and 3% in the other, the characteristics being straight lines in both cases. if each machine is fully loaded when the total load is 120 MW, what will be the load on each machine when the total load is reduced to 80 MW?


the following two synchronous machines are operating in parallel machine A: 50 MW

6% speed regulation


two synchronous generators are supplying a common load. generator no-load frequency of 51.5-Hz and regulation of 1 MW/Hz. generator 2 has no-load frequency Example 5.64 (page 43)

A 12MVA, 5000 V, 3-phase, 4-pole, 50-Hz alternator is connected to bus-bars. the short-circuit current is 4.0 time the normal full-load current and the moment of increase of the rotating system is 22000 kg m^2. determine the normal period of oscillation. Example 5.65 (page 43)

the following figures pertain to a 2-pole, 50-Hz, 3-phase turbo-alternator connected to the infinite bus. Example 5.66 (page 43-44)

a 10000 kVA, 4-pole, 6600 V, 50 Hz, 3-phase star-connected alternator has a synchronous reactance of 25% and operates on constant voltage, constant frequency bus-bars. if the natural period of oscillation while operating at full-load and unity power factor is to be limited to 1.5 seconds, calculate the moment of inertia of the rotating system. Example 5.67 (page 44)

A 100MVA synchronous generator operates on full-load at frequency if 50 Hz the load is suddenly reduced to 50MW. due to time log in governor system the steam value begins to close after 0.4 seconds. determine the change in frequency that occurs in this time. given, H=5 Example 5.68 (page 45)

a 3-phase, 11 kV, 5 MVA, star-connected alternator has a synchronous impedance of (1+j12) per phase. its excitation is such that the generated line e.m.f. is 12kV. if the alternator is connected to infinite bus bars, determine the maximum output at the given excitation. Example 5.69 (page 45)

a 3-phase, 11 kV, 10 MW, star-connected synchronous generator has a synchronous impedance of (0.6+j10.0) per phase. if the excitation is such that the open-circuit voltage is 12 kV, determine: (i) maximum output of the generator,

(ii) current and p.f. at the maximum output,

Quiz # 1 1. A 3-phase, 50 Hz, 8 pole, star-connected alternator has 120 stator slots and each slot has 10 conductors. The coil span is 12 slots. If the flux pole is 0.12 W b, calculate the induced emf between lines.

2. A 3-phase, star connected alternator has the following data: voltage required to be generated on open circuit = 4,000 V at 50 Hz; speed = 500 rpm; stator slots/pole/phase = 3, conductors/slot= 12. Calculate useful flux per pole.

3. A 3-phase star connected with synchronous impedance of j5 ohms per phase is connected to an 11kV system. The alternator power output is found to be 10 MW and reactive power as 3 MVAR. Compute (a) the magnitude of excitation voltage, (b) line current, (c) and power factor.

4. A 200 KVA, 480 V, 50 Hz, star-connected synchronous generator with a rated field current of 5 A was tested and the following data were obtained: Open circuit terminal voltage = 540 V(line to line) Short circuit current

= 300 A

When a dc voltage of 10 V was applied to two of its terminals, a current of 25 A was measured. Determine the full-load voltage regulation at 0.8 pf lagging.

5. A 3-phase, 50 Hz, 6000 kVA, 6,000 V star-connected alternator has an effective resistance of 0.2 ohm. A field current of 10 A produces 480 V on open-circuit and a field current of 5 A gives armature current 105 A on short circuit. Calculate the voltage regulation of this alternator at 0.8 pf lagging.

‘

6. A 3.5 MVA, slow speed, 3-phase synchronous generator rated at 6.6kV has 32 poles. It’s direct and quadrature axes synchronous reactance are measured by the slip test are 9.6 ohms and 6 ohms, respectively. Neglecting armature reactance, determine (a) the regulation and (b) magnitude of excitation emf needed to maintain 6.6 kV at the terminals when sup plying a load of 2.5 MW at 0.8 power factor lagging.

7.A 150 kVA, 500 V, 3-phase, star conn ected alternator has the following data: Friction and windage loss

= 350 watts

Open circuit core loss

= 500 watts

Field winding resistance at 75 deg Celsius = 200 ohms Effective armature resistance/ phase

= 0.03 ohms

The voltage applied to the field winding is 250 V. Calculate the alternator efficiency at 0.8 pf and the at half full-load.

8. A 2-pole, 50 Hz, 3-phase, turbo alternator is excited to generate the busbar voltage at 11kV on no-load. The machine is star connected and the short-circuit current for this excitation is

1,000A. Calculate (a) the synchronizing power per degree of mechanical displacement of the rotor and (b) the corresponding synchronizing torque.

9. A 2,000-kVA, 3-phase, star-connected, 5,000V, 10-pole alternator has a synchronous reactance of 10% and is running in parallel with infinite bus. Calculate (a) the synchronizing

power and (b) the corresponding synchronizing torque per mechanical degree of phase displacement at full-load, 0.8 power factor. Use exact method.

10. Two-identical 3-phase alternators work in parallel and supply a total load of 1,600 kW at 11,000 V at a power factor of 0.92. Each machine supplies half the total power. The synchronous reactance of each is 50 ohms/phase and the resistance is 2.5 ohms/phase. The field excitation of the first machine is adjusted so that armature current is 50 A lagging. Determine (a) the armature current of the second alternator, (b) the power factor at which each machine is working and (c) generated voltage of the first alternator.

11. Two generators rated at 500MW and 600MW are operating in parallel. The drop characteristics of their governors are 4% and 5 %, respectively from no-load to full-load. Assuming that the generators are operating at 60 Hz at no-load, how would a load of 11,000 MW be shared between them? What would be the system frequency at this load? Assuming linear governor operation

12. A 10,000 kVA, 4 pole, 6,600 V, 50-Hz, 3-phase star-connected alternator has synchronous reactance of 25% and operated on constant voltage, constant frequency bus-bars. If the natural period of oscillation while operating at full-load and unity power factor is to be limited to 1.5 seconds, calculate the moment of inertia of the rotating system.

13. A 3-phase, 11Kv, 5MVA, star-connected alternator has synchronous impedance of (1+j12) ohms per phase. It’s excitation is such that the generated line emf is 12Kv. If the alternator is connected to infinite bus-bars, determine (a) th e maximum output at the given excitation.

14. A 3-phase, 11kV, 10-MW, star-connected synchronous generator has synchronous impedance of j10 ohms per phase. If the excitation is such that the open circuit voltage is 12kV, determine (a) the maximum output of the generator (b) the current and p.f. at the maximum output.

Quiz1 Ac Otplusbook-1

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