PURBANCHAL UNIVERSITYaotY

B.E. (Electrical) / Fifth Semester/ FinalTime: O3:00 hrs. Full Marks: 8O /Pass Marks: 32BEGSOASH: Probabllity & Statistics

Candidates are required to giue their ansuers in their own taords as faras practicable. Assume necessary d.ata if reqtired.

All Etestions carry equal marks. Ttte marks atlotted for each sub-qttestionis specified alang ifs side.

Group A:Answer FOIJR questions. 4x14+61={Q

l(y'1 Define Standard deviation and the relative coefficient of it.

\o/rrr^the prices of shares X and Y given below, state which share

' i" *o.. stable in value?

2(a) Define Karlresults of it.

(b)

3(a)

(b)

Pearson correlation 6fr.i"nt and Interpret the

Also estimate the vafue of Xr when Xz=2.5 and X3=2

Find the multiple regression equation of Xr on Xz and Xs from the

data relating to three variables given beiow?

State and prove addition lar.v of probability.

The probability that the contractor will get a plumbing contract is

0.64 and the probability that a contractor will get an electric

contract is 0.56. If the probability that the contractor rvill get atleast one contract is 0.32, then find the probability that he willget both the contract.

4lala Define rvith exampie the random variable and its types.

-1ryzfina the value of constant K if the following function is a

pro-oability tiensity iunction. aiso iind the mean arrd var-iarrce ofrandom variabie X.

Contd....

X 55 54 52 53 56 58 52 50 5i 49Y 108 ta7 i05 105 106 ta7 to4 103 104 lol

x1 5 7 8 4 sx2 2 5 4 3 4x3 2 0 J 1 2

t?l

(5 + 2x),2 3x < 4

otherwise

5(a) Define Poisson distribution. Discuss the properties of Poisson

distribution.

{b} From the past experience it was found that the average numberof traffic accidents in an intersection of road is 3.2 accidents per

week. By using Poisson distribution find the probability that.(t) there will be no accident in next week

(ii) there will be at least 2 accidents in next week

(iii) there will be at most 2 accidents in next rveek. \/

Group B:

Answer FOUR questions. 4xl4+61=$Q

O@{O.tine Normal distribution and r.vrite down any five properties ofr' it.

(b) If marks Obtained by a group of students follow nor-rnal

distribution, 33ok of the students secure marks under 45 and 8%

of students score mark over 82. Find the mean and the standard

deviation of the Marks obtained by the students.

7(al7t Define standard error of estimator. Write down the Standard

/ error of sample mean and sample proportion.

19l Hotel's manager in Kathmandu walts to know the hotels average

t daily registration. The following table presents the numbers oft' guest registered each of 27 randotttly selected days. Calculate '\e

sample mean, standard errors of mean and 95% confid*rcelimits of population mean.

lx/(,) =

{0,

S(a) What are the steps for test of significance

,,/ ptopartion for Lrge sample.

for difference of

Contd. ...

58 63

62 63

a, 60

64

60

51

57

57

53

54

58

a

61

6t

60

57

50

e

53

59

5*

60

50

61

{31

9/ A company claims that its light bulbs are suferior to those of a/ competitor on the basis of a study which showed that a sample of

4A of its bulbs had an average life time of 628 hours ofcontinuous use with a standard deviation of 27 hours. While asample of 3O bulbs made by the competitor had an average lifetime of 619 hours of continuous use with a standard deviation of25 hours" Test at 57o level of significance, whether this claim isjustified.

9(9ll lMrite down the steps of paired t-test.

" (H ln a study of the effectiveness of physical exercise in weight" reduction, a group of 16 persons engaged in a prescribed

program of physical exercise for one month showed the followingresults of weight in pound.

Before 209 178 169 212 1A0 192 158 180 170 153 183 165 201 179 243 144

Aner 196 171 17A 2O7 177 19O 159 180 1A4 152 179 162 199 173 231 140

Use the 17o level of significance to test whether the prescribedprogram ofexercise is effective.

10(a) What are the application of chi-square distribution? Also mentionthe steps of chi-square test for independence of attributes.

(b) Mechanical engineers testing a new arc welding technique,classified welds both with respect to appearance and an X-rayinspection. Test for whether there is any association betweenappearallce and x-ray inspection at a = 5o/o.

X-rayAooearance

Bad Normal Good

Bad 20 a a

Normal 13 51 16

Good 7 12 21

- punaANcnttr, UNIvERSITYAAlry

B.tr. (Electrical) / Fifth Semester/ Final

Time: O3:00 hrs' Full Marks: 80 /Pass Marks: 32

BEG326EL: Power SYtt"- 3-tlf"k

ffiired to giue their anluters "in their oun u;ords as far

as practicable. Assui. n "it"ory data if reqtired.

Atlqsestionscanuequalma*s,Themarksatlottedforeachsub.questionis sPecified along its side'

Answer FWE questions'

- . 1{a}. What do you mean by interconnected power system? Describe

\--/ the advantages and limitations of interconnected system' 1+5

(bl ,,Explain how reai pt-rwer/frequency control and reactive powerf

\y *":'- -^.^'..ol is rnaintained in interconnected power system' 1o

voltage contr

2ialrForanetworkgivenbelow'seriesimpedenceofeachlineis0+j0'12t '-/v pu. Shunt u.dmr;ttao"" of the line is negligible' Calcuiate: 12

(i) Voltage at bus-2 and bus-3 using Gauss-Seidal method (upto

two iteration)

{ii) Slack bus real and reactive power

(iii) Network real and reactive power lossIt_; - ti. jlp_ j

\b/ivrention the various load flow techniques and hence compare them

expiaining their merits' dernerits' usages and limitation' 4

Contd...-

l2l

3(a) The single line diagram of a power *y"l"ti" :notu' :-n**

below'

Compute the fault current in p'u and in {bsolute-value

if a 3 phase

to ground fault occurs at; {consider no fault impedance) 5+5

(i) the point P i'e' connection point betwden transmission line and

HV side of transformer T1

(ii) the point Q i'e' connection point betw'een transmission line

and HV side of transformer T2

a.5rr:3fK!

;{=i31i,

(b) Derive the necessary equation to determine the fault current for a

single line to ground fault' Hence d'raw the sequence network' 6

4(a)Withthehelpofsuitabiemathematicalaidverr-ffthat,foralineto line fault in a synchronous generator the zero sequence

component of current is absent and positive-sequence of current

is equal to the negative sequence component of the current' 6

(b) A signal line to earth fault occurs on a feeder' The sequence

impendence upto fault point are O'3+jO'6' g'f,+j0'55 and 1+j0'78

pu. The fault resistance is O'66pu" If voltage is 1<0 ' find fault

current and voltage of faulty phase at fault point' '\J

l5(+)Whatisequalareacriterionforassessingt]retransientstabilityJ' ofu a*o mactrine system? Explain and justify with tlle help of a

8suitable examPle.

For the system shown in figure' the numerical values for different

quantities are E=1.04 pu, V=1 pu' Xs=0'2 pu and reactances of

each line is O.4 pu. The generator is delivering a power of 1'2 Pu

:-r:-:+^ '^',- If o 1,-nr'rese short circuit far;lt occurs at thefo LIrc LlllrlrrLc uur' r! s " r------

mid.point of one the transmission lines' perform the following' 8

t (u)

Ccntd. ...

t3l

(i) If the fault is cleared (switching out of the faulted iine) when

power pngle is 60", check whether the stable or not;I ' 'itical ciearing angle'(ii) Determine the

"riti.uf ciearing angle' '

't1

:C i\'l!rAr<fx,.l,l

i

ii!

/\-L',+ I i

i _j iliie-/ ii,tlI

r..j

4x4=16

studies' Mention the

performing ioad flow

{J,

6. Answer the following questions any FOUR:

(a) Describe the importance of ioad llow

types of buses we deal with while

studies.(b) For a fault at alternative terminal' a single line to ground fauit

is generally more severe than a 3-phase fault' Give reason'

- {"t 6;;;*.* itt" different types of faults in power system?

V;;;; i""i "tea'i"g maintains better svstem stabilitv'

WhY? !,

(e) Explain how Automatic Voltage Regulator (AVR) heips in

assisting better "y*tem

stability' Draw power delta (p-6) curve

to elucidate?

.//1 -1 -. I\'l

PURBANCHAL UNIVERSITY20LV

B.E. (Electrical)/ Fifth Semester/ F)nalTime: O3:OO hrs. Full Marks: 80 /Pass Marks: 32BEG324EL: Control System Engineering

Candidates are required to giue tteir answers in their own utords as faras practicable. Assume necessary data if reqired.

All qtestions carry equal marks. Tte msrks allotted for each sub-qtestionis specified along its stde.

Answer FIIIE questioas.

*!"1 Find the transfer function X2{s)/F(s) of the mechanical systemshown in {igure below and also obtain the force-voltageanalogous circuit. 8

I of the system given below8using block reduction Technique.

6/^l hi-^---- -L^.-r !L^ ^ff^^! ^c f^^lL^^1- ^^i- ^r^L:1:+--/,lal r rrsr.rlss alrirrlL LIIE E:llELL Lrl rrerlrra(.K Irrl vdIrI. .\raltrltrv.- \--, o----,

bandwidth, noise, sensitivity, transient and frequenc;r response" I

Contd....

{2t

(b) Discuss on Stability anaLysis. Apply Routh criterion to determine

the range of K for which the system shown in frgure will remain

stable. 2+6

3(a) Construct the root locus of a unity feedback system with c. - tloop transfer function as G(s)H(s):Kls(sz+4s+5). 10

(b) Sketch the poiar piot for G(s) = frj" . 6

4(al Construct the Bode plots for control system havingG(S)=10i S(1+0.5S)(1+0.25S). Also determine the gain crossoverfrequency, phase crossover frequency, gain margin and phasemargin. 8

(b) -A feedback control system is described as:

G(s) = 1/S(s + 2)(S + r,H(s) = 1lS .

For a unit step input, determine the steady error constanterrors.

5(a) For the given transfer function, obtain the state model:

Y(s)/u(s) = K/(s'+5s2 +4s+3).(b) For the given signal flow graph find the ratio C(S)/R(s). 8

and8

8

6. Write short notes or any FOUR:

(a} Types of control sYstem (b), Transfer function

(c) Stability (d) NYquist Plot(e) PiD controller(*

4x4=16

PURBANCHAL UNTVERSITY20Lv

B.E. (Electricaf 1 Fifth Semester/FinalTime: 03:00 hrs. Full Marks: 8O /Pass Marks: 32

BEG33 lEC: Advanced Instrumentation

candidates are required to giue their ansuters in their oun words as faras practicable. Asiume necessary data if reqtired'

AllElestionscarryeqlalmarks.Themarksallottedforeachsub-qleshonis specified. along its side.

Answer FfVE questions.L

Yv( ora* and exPlain the closed\/ instrumentation {MEI) sYstem'

irrrPiementing an MBI sYstem'

ioop microProcessor based

Also list out advantages of8

{b) /lnterface a keyboard and a printer in mode 1.Port A is designated

i7 as input for keyboard with interrupt I/o. Port B is designated as

output for printer with status check I/O' Draw the mapping

circuit and write the control word and address map' I

2@l/ compare the standards: usB2.O and usB 3.O.Describe simplex,,J

Half Duplex and Full Duplex operation using RS 232 C port. 8

;g/Co*pare between serial and parallel data transfer' 8

3(a}DesigninterfacingcircuitinterfaceasuitableDACusing8255APPI to a microprocessor to generate square wave oscillating

between -10v and +10v having a frequency of 1 KHz with output

port address DBH' 8

/;py/oru*the block diagram and explain its operation of a Data logger' I

a@|zMrratisGroundingandShielding?Explaindifferenttypesof\Y Noise couPling mechanism' 8

. b\rr6xpla.in different types of software models used in software\Y development Process' I

5. What have you learned from case study? Draw the cornplete

blockdiagramoftheindustrialprocesscontrolinvolvedinyourcasestudy.Whatarethecriticalfactorseffectingtheproductionyou have noticed in the visited industry and what measure you

can suggest for the same? What protrlems you might face after

implementing your suggested process control s5rstem' 16

Contd. ...

l2l6. Write short notes on any FOUR:

(a) Real time softrvare

...1Plc"Utt" and connectors

-19/ Low-Power design

{d.} Filtering and smoothing

;$NFiber oPtics

4x4:16

PURBANCHAL UNIVERSITYP'oI'7

B.E. (Electrical) / Fifth Semester/ FinalTime: O3:00 hrs. Full Marks: 80 /Pass Marks: 32BEG325EL: Electric Machine Design

Candidates are reqttired to giue their ansuters in their own words as faras practicable. Assume necessary data if reqttired.

Atl questions cctry eqtal marks. The marks allotted for each sub-Etestionis specifi.ed along its srde.

Answgr FI1IE questions.

l({ Wlny CROS is known as superior magnetic material? What is ageing?.J How was it removed? Why steel of low silicon content odynamo grade

steel" is preferred in rotating electrical machine. 2+2+2+2

{b) A 500 KVA transformer has total loss of 7.5KW at fuli load. Therate of heat dissipation from tank wall is 300w/"C rise and theheat energy required to raise its temperature by loC is 450Wh,calculate (i) the final steady temperature rise and thermal timeconstant of transformer, (ii) haif hour rating of the transformer togive the same temperature rise as in {i) if the copper ioss at fuliIgad is twice the iron loss. 8

2(al,tWhat are heating time constant and cooling time constant?\-/' pxplain. g

g|,/oerive an expression for KVA output of a singie phasetransformer from design point of view. 8

3(a) Derive the expression for calculating the number of tubes to beprovided in transformer tank. B

(b) Estimate the per unit regulation at 0.Bpf. lagging for a 25KVA,50H2, 11/O.433V, three phase delta/star, core type, oilimmersed, naturally cooled distribution transformer at full ioadcondition. Il/inding Dimensions. B

H.V. winding Lv windingOuter diameter 239mm 156.2mmInside diameter 186.2rnm 138mmArea of conductor 0.312mm2 14.9mmzi,ength of coii = 253mm, Consiant Voitage per iurn = O.45,Resistivity = 0.02 1f)-mm2/m.

Contd. ...

l2lI

$@l/Prove that the output of a three phase induction machine can be\'/ expressed in terms of its main dimension, specific loading and

speed. 8

(b) ,Find the main dimension of 3.7kw, 3-phase, 40OV, SOHz,V/ 2810r.p.m. squirrel cage ind.uction motor having on efficiency of

0.85 and full load power factor of 0.84. Assume: 8

Specific magnetic loading = 0.45 wb/rn2

Specific electric loading = 23000 A/m.

Take the rotor peripheral speed as approximately 2O urls ^+

synchronous speed.

5(a) For a dc machine design show that the minimum nurnberof coilor commutator segments required is EP/ i5. 8

(b) A 500 kw, 375r.p.m., 8 pole, dc generator has a flux per pole of0.0885 wb. Determine the armature demagnetizing and cross

magnetizing mrnf per pole if the brushes are given a load of 5percent of pole pitch. Assume power developed by armature to be

equal to rating of machine.

6. Answer the following questions any FOUR:

t,

4x4=16

1$lzDistribution transformer should have low value of leakage

reactance.(b) Stepping of core decreases the copper loss.(c) The size of the machine will be small if it is designed with

\/ higher speed for the same output

.(1ffitate the elasses of insulating material.

;$f,Describe the construction of rotating field synchronor-'machine. Mention its advantage over rotating armature

machine.

PURBANCHAL UNIVERSITYaOLry

B.E. (Electrical) I Fifth Semester/FinalTime: 01:30 hrs. Full Marks: 4O /Pass Marks: 16

BPG323EL: Synchronous & Special Machioe

Candidates are required. to giue their ansuters in their oun utords as faras practicable. Assume necessary data if reqrired.

All qtesttons carrg eqtat marks. The marks allottedfor each sub-qtesfionis specified along its side.

Answer FIVE questions.

What is meant by armature reaction in synchronous generator?

Discuss the effect of armature reaction on its emf when load isresistive, capacitive andrinductive. I

6./ Answer in short any TWO;./ fic^puritor start and run motor

/ (p) wortdng of schrage motor(c) Stepper motor. A

4+4

2. A 50 Hz, 3-phase, 480V connected salient pole synchronousgenerator has )fu = 0.01O and \ = 0.0750. Armature winding

. resistance is 0-01C) per phase. The generator supplies a 12OOA atO.8pf lagging. Catcuiate the excitation ernf' 8

/S/' Wny synchronous motor is not a self starting motor. Describe the

"/ ' various methods to start the synchronous motor. 8/

4.,/ "Power angle characteristics of non salient pole s5':rchronous/ machine is not valid for salient pole Synchronous machine",

Explain in detail. 8

5. TThe main winding and starting winding of a 50 Hz capaci-tor start

/ sing,le-phase induction motor have impedances as follow: 8L

Main winding: (3+3j) ohm

Starting winding: (7.5+3j) ohm

calculate the value of capacitor to be connected in series withthe starting winding to produce a phase difference of 90" between

main winding current and starting winding current at starting.

AOLry

B.E. (Electrical) / Fifth Semester/ Final

Time: 01:3O hrs' Fuli Marks: 40 /Pass Marks: 16

BEG396MS: Research M*{"dol:gl

Answer FIVE questlons'

. r-/ What is scientific research? Describe the process of scientific

:z 2+6research Process'

2."AProblemwell-statedishalftheresearchsoived"'lntheiightofthis statement, define research problem and explain the different

steps considered vrhile formuiating the research problems in

research design' 2+6

z.r/ wnuris data? Why data is taken as the building block of any

\J/ research? ExPlain'

2+6

+. ,,z(vnat is research report? Explain the

"'-/ research report.

5.,/ The owner of the Ches Tahoe restaurant is interested in how

\J '--' "^ --' es 1o randomlYmuch people spend at the restaurant' He examrn

selected """ipt* for parties of four and writes down the following

!, data. 44,50, gg' 96' 42' 47 ' 40' 39;46' 50

Calculate the variance and Standard deviation' 8

What do you understand by the following terminologies? Give

your clear views on them (anY TWO):

(a) Research proposai 1pp&e"earch Hypcthesis

(c)validity (llP/obabilitY*

6.t

procedures of writing2+6

2x4=B