Sunday, May 17, 2020

100 MCQ OF Synchronous Generator or Alternator with Explanation Part-9


100 MCQ OF Synchronous Generator or Alternator with Explanation


81.A 4-pole, 50 Hz, the synchronous generator has 48 slots in which a double layer winding is housed. Each coil has 10 turns and is short pitched by an angle of 36 to electrical. The fundamental flux per pole is 0.25 Wb. The line to line induced emf, for a three-phase star connection is approximately


Given Data

The number of Poles P = 4
No of slots = 48
Flux φ = 0.25 Wb
Number of turns = 10

For double layer winding,

No of coils = No of slots = 48
Total number of Turns = 48 × 10 = 480
Hence turns per phase = 480 ⁄ 3 = 160

Pitch factor KP is

\begin{array}{l}{K_P} = \cos \dfrac{\alpha }{2}\\\\{K_P} = \cos \dfrac{{36^\circ }}{2}\\\\{K_P} = \cos 18^\circ \\\\{K_P} = 0.951\end{array}

Now distribution factor Kd is given as

\begin{array}{l}{K_d} = \dfrac{{\sin (m\alpha /2)}}{{m\sin \alpha /2}}\\\\{\text{where alpha is slot angle = }}\dfrac{{{\text{180 electrical}}}}{{{\text{No of slots/pole}}}}\\{\rm{\alpha }} = \dfrac{{180 \times 4}}{{48}} = 15^\circ \\\\{\text{m = no of slots per pole per phase}}\\\\m = \dfrac{{48}}{{4 \times 3}} = 4\\\\\therefore {K_d} = \dfrac{{\sin (60^\circ /2)}}{{4\sin (15^\circ /2)}}\\\\{K_d} = 0.9576\end{array}

∴ EMF per phase Eph of an alternator is

Eph = 4.44.Kp.Kd.φ.f.Tph
Eph = 4.44 × 0.951 × 0.9576 × 0.25 × 50 × 160
Eph = 808.68

Line to Line induced EMF

EL = √3EPH
EL = √3 × 808.68
EL = 1400.67 V

82.A 3 phase, 4-pole alternator has 48 stator slots carrying a 3 phase distributed winding. Each coil of the winding in short chorded by one slot-pitch.The winding factor (Kw) is


Given Data

The number of Poles P = 4
No of slots = 48
Phase  = 3

Distribution factor Kd is given as

\begin{array}{l}{K_d} = \dfrac{{\sin (m\alpha /2)}}{{m\sin \alpha /2}}\\\\{\text{where alpha is slot angle = }}\dfrac{{{\text{180 electrical}}}}{{{\text{No of slots/pole}}}}\\{\rm{\alpha }} = \dfrac{{180 \times 4}}{{48}} = 15^\circ \\\\{\text{m = no of slots per pole per phase}}\\\\m = \dfrac{{48}}{{4 \times 3}} = 4\\\\\therefore {K_d} = \dfrac{{\sin (60^\circ /2)}}{{4\sin (15^\circ /2)}}\\\\{K_d} = 0.9576\end{array}

Pitch factor KP is

\begin{array}{l}{K_P} = \cos \dfrac{\alpha }{2}\\\\{K_P} = \cos \dfrac{{15^\circ }}{2}\\\\{K_P} = 0.9914\end{array}

Sometimes distribution factor (Kd) and pitch factor (Kp) of an alternator are combined into a single factor called winding factor (Kw). The winding factor is the product of Kd and Kp i.e.


Kw = Kp × Kd

Kw = 0.9576 × 0.9914
Kw = 0.9494

83.A 6 pole alternator with 36 slots carries a 3-phase distributed winding. Each coil is short-pitched by one slot. The winding factor is given by


Distribution factor Kd is given as

\begin{array}{l}{K_d} = \dfrac{{\sin (m\alpha /2)}}{{m\sin \alpha /2}}\\\\{\text{where alpha is slot angle = }}\dfrac{{{\text{180 electrical}}}}{{{\text{No of slots/pole}}}}\\{\rm{\alpha }} = \dfrac{{180 \times 6}}{{36}} = 30^\circ \\\\{\rm{m = no of slots per pole per phase}}\\\\m = \dfrac{{36}}{{6 \times 3}} = 2\\\\\therefore {K_d} = \dfrac{{\sin (2 \times 15^\circ /2)}}{{4\sin (30^\circ /2)}}\\\\{K_d} = \dfrac{1}{{4\sin 15^\circ }}\end{array}

Also the Pitch factor KP is

\begin{array}{l}{K_P} = \cos \dfrac{\alpha }{2}\\\\{K_P} = \cos \dfrac{{30^\circ }}{2}\\\\{K_P} = \cos 15^\circ \end{array}

The winding factor is the product of Kd and Kp i.e.


Kw = Kp × Kd

\begin{array}{l}{K_w} = \dfrac{1}{{4\sin 15^\circ }} \times \cos 15^\circ \\\\\dfrac{{Cos\theta }}{{Sin\theta }} = Cot\theta \\\\\therefore {K_w} = \dfrac{{Cot15^\circ }}{4}\end{array}

84.For eliminating 7th harmonic from the emf ware of an alternator, what is the fractional pitch Winding


For eliminating 7th harmonic

Kp7 = 0

\begin{array}{l}\cos \dfrac{{7\alpha }}{2} = 0\\\\ = \dfrac{{7\alpha }}{2} = \dfrac{\pi }{2}\\\\\alpha = \dfrac{\pi }{7}\end{array}

85.A part of an alternator winding consists of 8 coils in series, each coil having an emf of 80V (rms) induced in it. Coils are placed in successive slots and having electrical phase displacement of 30°. Then the emf of right coils in series is.


Given

Phase displacement angle α = 30°

No of slots per pole per phase (n) = Number of coil = 8

Distribution factor Kd is

\begin{array}{l}\therefore {K_d} = \dfrac{{\sin (8 \times 30^\circ /2)}}{{8\sin (30^\circ /2)}}\\\\{K_d} = 0.4182\end{array}

Airthmetic sum of voltage = Total Number of coils x Given voltage

= 8 x 80 = 640 V

The EMF of right coils in series is

Vector sum of voltage = Distribution factor x Airthmetic sum of voltage

= 0.4182 × 640

= 267. 6 V

86.If a 3 phase, 25 kV, 50Hz Star connected synchronous generator runs at 1000 rpm. Then the number of poles and voltage per phase is _______ & ________ respectively


Given data

Frequency f = 50 Hz
Line voltage VL = 25 kV = 25 x 103 V
Speed Ns = 1000 RPM

The synchronous speed of an alternator is given as

Ns = 120f/P

P = 120f/N

P = 120 x 50/1000

P = 6

In star connection Voltage per phase is given by

VPH = VL⁄√3

VPH = 25 x 103 ⁄ √3
VPH = 14433.7 V

87.A 3 phase Star connected synchronous generator is rated at 15 kVA, 400V, 50Hz. If rated load at 0.8 pf lagging is supplied where resistance is 0.5Ω and synchronous reactance is 10Ω. Then the voltage regulation of an alternator is.


Given Data,

Line voltage VL = 400 V
Alternator Rating = 15 KVA = 15 x 103 VA
Resistance Ra = 0.5 Ω
Synchronous Reactance XL = 10 Ω

Full Load current IL =  VA ⁄ √3 VL
IL = 15 x 103 ⁄ √3 x 400
IL = 21.6 A

For star connection Voltage per phase is given by
VPH = VL ⁄ √3
VPH = 400 ⁄ √3
VPH = 230.9 V

Generated voltage per phase of an alternator is given as


EPH = VPH + ILRa + ILXL

= 230 + 21.6 × 0.5 + 21.6 × 10
= 457.7 V

The voltage regulation of an alternator is defined as the change in its terminal voltage when the full load is removed, keeping field excitation and speed constant, divided by the rated terminal Voltage.

So if Vph = Rated terminal voltage
Eph = No load induced e.m.f

Voltage Regulation = (Eph − Vph)/Vph
= (457.7 − 400) ⁄ 400
= 0.144

88.A 30 MVA, 15 kV alternator will have a per phase nominal impedance of ...............


The Nominal impedance of a synchronous machine is also called as the base Impedance. The nominal impedance of an alternator is the ratio of the rated line-to-neutral voltage divided by the rated line current. The nominal impedance is used as a base of comparison for other impedances that the alternator possesses.


Zbase = Vbase ⁄ Ibase

Apparent Power (S) = V x I


Zbase = V2base ⁄ Sbase

∴ Nominal Impedance
Zbase = (15000)2 ⁄ 30 × 106
Zbase = 7.5Ω

89.For the same power rating, an alternator is .................... that of a d.c. generator


The efficiency of alternator increase with the increase in size because losses to heat are reduced. 

The coefficient of efficiency can be increased by designing the machine to have reduced losses windings (copper losses) and magnetic circuit (iron losses). By increasing the cross-section of conductors, the resistance of copper conductors is decreased which leads to reduced copper losses. By increasing the cross-section of the magnetic circuit, the magnetic induction decreases for the same flux. Consequently, iron losses are smaller. On the other hand, this approach to reducing the current density and magnetic induction leads to an increased volume and mass of the machine.

The efficiency of an alternator automatically improves as the power rating increases. For example, if an alternator of 1 kVA has an efficiency of 50%, a larger but similar model having a capacity of 10 MVA will have an efficiency of about 90%.

90.Electrical fault between two windings of the same phase of a generator having double star winding can be detected by the following protection in the generator


The Merz-Price protection system gives protection against phase to phase faults and earth faults. It does not give protection against inter-turn faults. The inter-turn fault is a short circuit between the turns of the same phase winding. Thus the current produced due to such fault is a local circuit current and it does not affect the currents entering and leaving the winding at the two ends, where C.T.s are located. Hence Merz-Price protection cannot give protection against inter-turn faults.

In single turn generator, there is no question of inter-turn faults but in multiturn generators, the inter-turn fault protection is necessary. So such inter-turn protection is provided for multiturn generators such as hydroelectric generators. These generators have double winding armatures. This means each phase winding is divided into two halves, due to the very heavy currents which they have to carry. This splitting of the single-phase winding into two is advantageous in providing inter-turn fault protection to such hydroelectric generators.



The scheme uses cross differential principle. Each phase of the generator is doubly wound and split into two parts S1 and S2 as shown in the Fig. The current transformers are connected in the two parallel paths of each phase winding.

The secondaries of the current transformers are cross-connected. The current transformers work on circulating current principle. The relay is connected across the cross-connected secondaries of the current transformers.

Under normal operating conditions, when the two paths are sound then currents In the two parallel paths S1 and S2 are equal. Hence currents in the secondaries of the current transformers are also equal. The secondary current flows around the loop and Is same at all the points. Hence no current flows through the relay and the relay inoperative.

If the short circuit is developed between the adjacent turns of the part Sit of the winding say then currents through S1 and S2 no longer remain same. Thus unequal currents will be induced in the secondaries of the current transformers. The difference of these currents flows through the relay R. Relay then closes its contacts to trip the circuit breaker which isolates the generator from the system.

Such an inter-turn fault protection system is extremely sensitive but it can be applied to the generators having doubly wound armatures.


https://www.youtube.com/channel/UC4_D50vMu1wbQrPaLFYo6Eg https://www.youtube.com/channel/UC4_D50vMu1wbQrPaLFYo6Eg RRB JE, SSC AE/JE UPSSSC JE, SSC JE, CIVIL ENGINEERING MCQs, ELECTICAL ENGINEERING MCQs, preavious year quesion papers, dmrc, lmrc, drdo,rrb ntpc, ntpc, pgcil, dsssb, states board, GATE IES EE, ESE, ECE, ME, CE, IT & CS EXAM MATERIALS & OLD PAPERS Electrical Engineering https://t.me/pravendrarajpoot Daily news & current affairs in hindi & english fully updated Daily current affairs https://t.me/newsdailypkr Engineering Discussion group for your upcoming exams, you can ask your any query regarding your problem,👇👇👇 https://t.me/joinchat/JObxeA7n6S4qvnegrGhTgA PKR ELECTRICAL ENGINEERING I am sure this is the best place for you guys subscribe and get success IF YOU WANT TO JOIN ME ON TELEGRAM FOR PDF @newsdailypkr AE/JE EE, ESE, ECE, ME, CE, IT & CS EXAM MATERIALS & OLD PAPERS Electrical Engineering https://t.me/pravendrarajpoot facebook page:- Pravendra Kumar Rajpoot https://t.me/newsdailypkr https://chat.whatsapp.com/5AS7dNFTP4H4vVsiWsqHrT https://t.me/srk50 https://t.me/pravendrarajpoot https://t.me/joinchat/JObxeA7n6S4qvnegrGhTgA https://t.me/pravendrarajpoot Daily news & current affairs in hindi & english fully updated Daily current affairs https://t.me/newsdailypkr Engineering Discussion group for your upcoming exams, you can ask your any query regarding your problem,👇👇👇 https://t.me/joinchat/JObxeA7n6S4qvnegrGhTgA PKR ELECTRICAL ENGINEERING I am sure this is the best place for you guys subscribe and get success IF YOU WANT TO JOIN ME ON TELEGRAM FOR PDF @newsdailypkr AE/JE EE, ESE, ECE, ME, CE, IT & CS EXAM MATERIALS & OLD PAPERS Electrical Engineering https://t.me/pravendrarajpoot facebook page:- Pravendra Kumar Rajpoot https://t.me/newsdailypkr https://chat.whatsapp.com/5AS7dNFTP4H4vVsiWsqHrT https://t.me/srk50 https://t.me/pravendrarajpoot https://t.me/joinchat/JObxeA7n6S4qvnegrGhTgA
at

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)

Featured Post

MAJOR 10 PANDEMICS (MAHAMARI) IN HISTORY

OUTBREAK: 10 OF THE WORST PANDEMICS IN HISTORY BY PRAVENDRA KUMAR RAJPOOT Scientists and medical researchers have for years have dif...