Electrical Machine Design_A. K. Sawhney

Scilab Textbook Companion for Electrical Machine Design by A. K. Sawhney1 Created by Shiv Singh Meena B.Tech Electrical Engineering National Institute of Technology,Kurukshetra College Teacher None Cross-Checked by None September 29, 2016

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Funded by a grant from the National Mission on Education through ICT, http://spoken-tutorial.org/NMEICT-Intro. This Textbook Companion and Scilab codes written in it can be downloaded from the ”Textbook Companion Project” section at the website http://scilab.in

Book Description Title: Electrical Machine Design Author: A. K. Sawhney Publisher: Dhanpat Rai Edition: 6 Year: 2014 ISBN: 9788177001013

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Scilab numbering policy used in this document and the relation to the above book. Exa Example (Solved example) Eqn Equation (Particular equation of the above book) AP Appendix to Example(Scilab Code that is an Appednix to a particular

Example of the above book) For example, Exa 3.51 means solved example 3.51 of this book. Sec 2.3 means a scilab code whose theory is explained in Section 2.3 of the book.

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Contents Listt of Scilab Codes Lis

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3 Pri Princi nciple pless of Mageneti Magenetic c Circuit Circuit Design Design

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4 The Therma rmall Design Design Aspects of Electri Electrical cal Machin Machines es

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5 Des Design ign of Trans Transfor former merss

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6 Gene General ral Co Conc ncept eptss and Co Cons nstr trai aint ntss in De Desi sign gn of Ro Rota tati ting ng Machines

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7 Ar Arma matu ture re Win Windi ding ngss

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8 Aspec Aspects ts of Design Design of of Mechani Mechanical cal Part Partss

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9 DC Ma Mac chi hine ness

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10 Three Phase Induction Motors

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11 Design of Synchronous Machines

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15 Design of Magnetic Circuits

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16 D Des esig ign n of He Heat atin ing g El Elem emen ents ts and In Indu duct ctor orss an and d Wel eldi ding ng Transformers

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18 Design of Starters and Field Regulators

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List of Scilab Codes Exa 3.1 Exa 3.2 Exa 3.3 Exa 3.4 Exa 3.7 Exa 3.8 Exa 3.1 3.111 Exa 3.1 3.122 Exa 3.1 3.133 Exa 3.15 Exaa 4.1 Ex 4.1 Exaa 4.2 Ex 4.2 Exa 4.3 Exa 4.4 Exa 4.6 Exa 4.7 Exaa 4. Ex 4.88 Exa 4.9

Exa 4.11 4.11 Exa 4.12 4.12

Calculati Calcul ating ng effe effecti ctive ve len length gth of air gap . . . . . . . . . Calculatin Calcu latingg the the mmf requ required ired for the air gap of a mac machine hine Estima Est imatin tingg the the effe effecti ctive ve air gap are areaa per per pole pole . . . . . Estima Est imatin tingg the the ave averag ragee flux flux densi density ty in the the air air gap gap . . . Calcul Cal culati ating ng the app appare arent nt flux den densit sity y. . . . . . . . . . Calcul Cal culati ating ng the app appare arent nt flux den densit sity y. . . . . . . . . . Calcul Cal culati ating ng the the specifi specificc iron iron loss loss . . . . . . . . . . . . Calcul Cal culati ating ng the spec specific ific iro iron n los losss . . . . . . . . . . . . Calcul Cal culati ating ng the the hyst hystere eresis sis loss . . . . . . . . . . . . . . Calculatin Calcu latingg the magnet magnetic ic pull pull and and unbalanc unbalanced ed magnet magnetic ic pull and ratio of unbalanced magnetic pull to useful force Calc Ca lcul ulat atin ingg the loss loss that that will will pass pass thro throug ugh h copper copper bar bar to iron . . . . . . . . . . . . . . . . . . . . . . . . . . . Calc Ca lcul ulat atin ingg the loss loss that that will will be co cond nduc ucte ted d acros acrosss the the laminations . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the hea heatt radi radiate ated d from from the body . . . . . . Calcul Cal culati ating ng the len length gth and wid width th of str strip ip . . . . . . . Estima Est imatin tingg the the tem tempera peratur turee of of the hot spot . . . . . . Estima Est imatin tingg the hot spot tem tempera peratur turee . . . . . . . . . . Calc Ca lcul ulat atin ingg th thee ma maxi ximu mum m te tempe mpera ratu ture re differ differen ence ce between the coil surface and the winding . . . . . . . . . Calculatin Calcu latingg the temper temperature ature differ difference ence beetw beetween een the centre of the embedded portion of a conductor and the overhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the heat condu conduct cted ed across across the former former from from winding to core . . . . . . . . . . . . . . . . . . . . . . Estimating Estim ating the final steady steady temper temperature ature rise of coil coil and and its time constant . . . . . . . . . . . . . . . . . . . . . 4

5 6 7 8 9 10 11 11 12 13 15 16 17 17 18 19 20

21 22 23

Exa 4.13 Exa 4.15 Exa 4.17 4.17 Exa 4.19 4.19 Exa 4.2 4.222 Exaa 4. Ex 4.23 23 Exa 4.24 Exa 4.25 4.25 Exa 4.26 4.26 Exa 4.2 4.277 Exa 4.35 Exa 4.37 4.37 Exa 4.4 4.433 Exa 5.3 Exa 5.6 Exa 5.9 Exa 5.12 Exa 5.13 Exa 5.14 Exa 5.1 5.166

Exa 5.17

Exa 5.1 5.188 Exa 5.20 5.20 Exaa 6.1 Ex 6.1

Calculatingg the final steady Calculatin steady temper temperature ature rise of coil coil sursurface and hot spot temperature rise . . . . . . . . . . . Calculatin Calcu latingg the temper temperature ature rise and therma thermall time time conconstant and rating of the machine . . . . . . . . . . . . . Calcul Cal culati ating ng the tempera temperatur turee of machine machine after after one one hour of its final steady temperature rise . . . . . . . . . . . Calcul Cal culati ating ng the rate rate of chan change ge of temper temperatu ature re . . . . . Calcul Cal culati ating ng the volum volumee of air requir required ed per second second and fan power . . . . . . . . . . . . . . . . . . . . . . . . . Calc Ca lcul ulat atin ingg th thee effi effici cien ency cy of ma macchi hine ne an and d am amou oun nt of cooling water . . . . . . . . . . . . . . . . . . . . . . . Calculatin Calcu latingg the temper temperature ature rise of hydroge hydrogen n . . . . . Calcul Cal culati ating ng the amoun amountt of oil and amoun amountt of water water . . Calcul Cal culati ating ng the tempe temperat rature ure rise rise of of tank tank . . . . . . . . Calcul Cal culati ating ng the amount amount of water water requir required ed and area of water duct and pumping power . . . . . . . . . . . . . Calculatin Calcu latingg the con contin tinuous uous ratin ratingg of motor . . . . . . Calcul Cal culati ating ng the the mean mean temper temperatu ature re rise rise . . . . . . . . . Calcul Cal culati ating ng the the temper temperatu ature re rise rise . . . . . . . . . . . . Calculatin Calcu latingg the the kV kVA A outpu outputt of a single single phase trans transforme formerr Calcul Cal culati ating ng the the net net iron iron are areaa and and windo window w area area and and full full load mmf mmf . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the the net iro iron n area area and and win windo dow w area area . . . . Calculatin Calcu latingg the resis resistance tance of second secondary ary windi winding ng . . . . Calculatin Calcu latingg the leak leakage age reacta reactance nce of of the trans transforme formerr referred to the HV side . . . . . . . . . . . . . . . . . . Calculatin Calcu latingg the per unit unit leak leakage age react reactance ance . . . . . . . Calcul Cal culati ating ng the instant instantane aneous ous radial radial force force on the HV winding if a short circuit occurs at the terminals of the LV winding with HV energised and the force at full load Calculatin Calcu latingg the instan instantaneou taneouss radial radial force force and instan instantataneous axial force on the HV winding under short circuit conditions . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the maxim maximum um flux and no load load curren currentt of the transformer . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the num number ber of turns turns and no load load curren currentt . Calc Ca lcul ulat atin ingg th thee spe speci cific fic elect electri ricc an and d spe speci cific fic magne magneti ticc loading . . . . . . . . . . . . . . . . . . . . . . . . . . 5

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

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44 45 46 48

Exa 6.5 Exa 6.6 6.6 Exa 6.8 Exa 6.9 Exa 7.33 7.33 Exa 7.41 Exa 8.2 Exa 8.2 Exa 8.4 Exa 8.5 Exaa 9. Ex 9.77 Exaa 9. Ex 9.88 Exaa 9. Ex 9.99 Exa 9.1 9.100 Exa 9.12 9.12 Exa 9.26 9.26 Exa 9.2 9.277 Exa 9.32 9.32 Exa 9.33 Exa 9.34 9.34 Exa 10.2 Exa 10.1 10.133 Exa 10.15 Exa 10.16 Exa 10.19 Exa 11.4

Calculatingg the pow Calculatin power er dev developed eloped by the armatu armature re of motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the the limi limitin tingg valu valuee of spec specific ific mag magnet netic ic load load-ing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the maxi maximu mum m permissi permissible ble specifi specificc electr electric ic loading . . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the spec specific ific ele electr ctric ic loa loadin dingg . . . . . . . . . Calculatin Calcu latingg the rms rms line vol voltage tage and and circulat circulating ing curren currentt Calculatin Calcu latingg the eddy eddy curren currentt loss ratio and aver average age loss loss ratio and critical depth for minimum loss . . . . . . . Calc Ca lcul ulat atin ingg the the st stre ress ss on th thee rin ringg . . . . . . . . . . . . Calcul Cal culati ating ng the the tens tensile ile str stress ess and fac factor tor of safe safety ty . . . Calcul Cal culati ating ng the the iner inertia tia con consta stant nt of the the gene generat rator or . . . Calc Ca lcul ulat atin ingg th thee maxim maximum permis permissi sibl blee core leng length th for the machine . . . . . . . . . . . . . . . . . . . . . . . . Calc Ca lcul ulat atin ingg th thee ma maxi ximu mum m per permi miss ssib ible le outpu outputt from a machine . . . . . . . . . . . . . . . . . . . . . . . . . . Calc Ca lcul ulat atin ingg the number number of extra extra shun shuntt field turn turnss to neutralize the demagnetization . . . . . . . . . . . . . Calcul Cal culati ating ng the demagne demagnetiz tizing ing and cro cross ss magnetizi magnetizing ng mmf per pole . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the arma armatur turee volta voltage ge drop drop . . . . . . . . . Calcul Cal culati ating ng the number number of turns on each each commuta commutatin tingg pole . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the reactanc reactancee voltage voltage for a mac machin hinee with straight line and sinusoidal commutation . . . . . . . . Calcul Cal culati ating ng the mini minimu mum m numbe numberr of poles poles . . . . . . . Calculatin Calcu latingg the the maxim maximum um armatu armature re vol voltage tage . . . . . . Calcul Cal culati ating ng the tota totall commuta commutator tor losse lossess . . . . . . . . Calculatin Calcu latingg the main dimen dimentions tions of squirre squirrell cage induc induc-tion motor . . . . . . . . . . . . . . . . . . . . . . . . Calcul Cal culati ating ng the number number of sta stator tor and rot rotor or tur turns ns and rotor voltage between slip rings at standstill . . . . . . Calculatin Calcu latingg the number number of stator turns per phase . . . Calculatin Calcu latingg the magnetizing magnetizing current current per phase . . . . Calculatin Calcu latingg the current current in rotor bars and in end rings Calculatin Calcu latingg the suitab suitable le number number of slots slots and and conduct conductors ors per slot . . . . . . . . . . . . . . . . . . . . . . . . . . 6

49 50 50 52 54 55 57 58 59 60 61 61 63 64 64 65 66 67 67 69 70 71 72 73 75

Exa 11.10 11.10 Calcul Calculati ating ng the size of arm armatu ature re wire and the ac res resisistance of each pahase . . . . . . . . . . . . . . . . . . . Exa 11.11 11.11 Calcu Calculatin latingg the length length of air gap . . . . . . . . . . . . Exa 11.13 11.13 Calcu Calculatin latingg the stator bore and stator core length length and turns per phase and armature mmf per pole and mmf for air gap and field current . . . . . . . . . . . . . . . Exa 11.1 11.144 Cal Calcul culati ating ng the flux per pole and len length gth and width width of pole and winding height and pole height . . . . . . . . Exa 11.18 Calcu Calculatin latingg the direct and quadrature quadrature axis synchronou synchronouss reactances . . . . . . . . . . . . . . . . . . . . . . . . . Exa 11.20 Calcu Calculatin latingg the kVA kVA output of the machine . . . . . . Exa 11.32 Calcu Calculatin latingg the number of stator slots slots and average average flux density . . . . . . . . . . . . . . . . . . . . . . . . . . Exa 15.1 15.1 Cal Calcul culati ating ng the curr curren entt in exciti exciting ng coil coil . . . . . . . . . Exa 15. 15.44 Cal Calcul culati ating ng the windin windingg depth and and winding winding space space and space factor and the number of turns . . . . . . . . . . Exa 16. 16.22 Cal Calcul culati ating ng the the ind induct uctanc ancee . . . . . . . . . . . . . . . Exa 18.1 Calcu Calculatin latingg the upper and and lowe lowerr limits limits of curr current ent during starting and resistance of each section . . . . . . . . .

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76 77

79 80 82 83 85 87 88 90 92

Chapter 3 Principles of Magenetic Circuit Design

Scilab code Exa 3.1 Calculating effective length of air gap

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

// / / C a l c u l a t i n g e f f e c t i v e l en en gt h o f a i r gap clc ; x a mp mp l e 3 . 1 , P ag ag e No . = 3 . 1 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a i d th t h i n mm mm W s = 1 2 ; / / S l o t w id oo th t h w i dt d t h i n mm mm W t = 1 2 ; / / T oo e n gt g t h o f a i r g a p i n mm l g = 2 ; / / L en K cs cs = 1 / (1 (1 + (5 (5 * l g / Ws Ws ) ) ; / / C a r t e r ’ s c o− e f f i c i e n t f o r slots // / / C a l c u l a t i o n o f e f f e c t i v e l en en gt h o f a i r gap c h i n mm mm ys=Ws+Wt; / / S l o t P i t ch Kgs=ys/(ys-(Kcs*Ws)); / / Gap c o n t r a c t i o n f o r s l o t s Gap c o n t r a c i o n f a c t o r f o r d u ct c t s / / S i n ce ce t h e r e Kgd=1; / / Ga a r e n o d u ct ct s o t al al gap c o n t r a c i o n f a c t o r Kg=Kgs*Kgd; / / T ot t h i n mm mm lgs=Kg*lg; / / E f f e c t i v e g a p l e n g th a p l e n g t h (mm) = ’ ) ; disp (lgs, ’ E f f e c t i v e g ap 8

16 / / i n b oo oo k a ns n s we we r i s

2 . 7 4 mm mm . to round o f f e r r o r

T h e a n sw s w er e r s v ar ar y due

Scilab code Exa 3.2 Calculating the mmf required for the air gap of a

machine 1 / / C a l c u l a t i n g t he h e mm mmf r e q u i r e d

f o r t h e a i r gap o f a

machine 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

clc ; x a mp mp l e 3 . 2 , P ag ag e No . = 3 . 1 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e t er er L = 0 . 32 32 ; / / C o r e l e n g t h i n m et n d = 4 ; / / Nu m b er o f d u c t s uc t w id i d t h i n mm mm W d = 1 0 ; / / D uc ol e a rc i n meter P a = 0 .1 .1 9; 9; / / P ol c h i n mm mm ys=65.4; / / S l o t P i t ch e n gt g t h o f a i r g a p i n mm l g = 5 ; / / L en p e ni n i ng n g i n mm mm W o = 5 ; / / S l o t o pe l u x p e r p o l e i n mW mWb F pp p p = 5 2 ; / / F lu K c s = 0 .1 . 1 8; 8; / / C a r t e r ’ s c o− e f f i c i e n t f o r s l o t s K c d = 0 .2 . 2 8; 8; / / C a r t e r ’ s c o− e f f i c i e n t f o r d u c t s / / C a l c u l a t i o n o f mm mmf r e q u i r e d f o r t he he a i r ga p Kgs=ys/(ys-(Kcs*Wo)); / / Gap c o n t r a c t i o n f o r s l o t s Kgd=L/(L-(Kcd*nd*Wd*10^(-3))); / / Gap c o n t r a c t i o n f o r ducts o t al al gap c o n t r a c i o n f a c t o r Kg=Kgs*Kgd; / / T ot l u x d e n s i t y a t t he h e c e n tr tr e Bg=Fpp*10^(-3)/(Pa*L); / / F lu o f p o l e i n Wb Wb pe p e r m et e t er e r s q ua ua r e ATg=800000*Kg*Bg*lg*10^(-3); / / mmf r e q u i r e d f o r a i r gap i n A mmf r e q u i r e d f o r a i r g a p (A ( A)= ’ ) ; disp (ATg, ’ mm / / i n b o o k a ns n s we w e r i s 3 58 5 8 7 A . T h e a ns n s we w e rs r s v ar ar y du e t o round o f f e r r or 9

Scilab code Exa 3.3 Estimating the effective air gap area per pole

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// / / E st s t im i m at a t in in g t h e e f f e c t i v e

a i r g a p a re r e a p er er p o l e


/ / G iv i v en e n D at at a um b er o f p o l e P = 1 0 ; / / N um or e i n meter S b = 0 .6 .6 5; 5; / / S t a t o r b or e t er er L = 0 . 25 25 ; / / C o r e l e n g t h i n m et N umber o f s t a t o r s l o t s N ss s s = 9 0 ; / / Nu p e ni n i ng n g i n mm W os o s = 3 ; / / S t a t o r s l o t o pe N u m b er o f r o t o r s l o t s N rs r s = 1 20 20 ; / / Nu o t or o r s l o t o p en e n in i n g i n mm W or o r = 3 ; / / R ot e n gt g t h o f a i r g a p i n mm l g = 0 .9 .9 5; 5; / / L en K c s = 0 .4 . 4 6; 6; / / C a r t e r ’ s c o− e f f i c i e n t f o r s l o t s K c d = 0 .6 . 6 8; 8; / / C a r t e r ’ s c o− e f f i c i e n t f o r d u c t s N u m b er o f v e n t i l a t i n g d u ct ct s n d = 3 ; / / Nu a c h v e n t i l a t i n g D u c t i n mm mm W d = 1 0 ; / / W i d t h o f e ac / / E st s t i ma m a ti t i on o n o f e f f e c t i v e a i r g a p a re re a p e r p ol e y s = 3 . 1 4 15 15 9 2 6 54 5 4 * S b * 1 0 ^ ( 3) 3) / N s s ; / / S t a t o r s l o t p i t c h Kgss=ys/(ys-(Kcs*Wos)); / / Gap c o n t r a c t i o n f a c t o r f o r s ta to r s l o t s o t or o r d i am a m et e t e r i n m et e t er er R d = S b - 2 * l g *1 * 1 0^ 0 ^ ( - 3) 3 ) ; / / R ot tc h y r = 3 . 1 4 15 15 9 2 6 54 5 4 * R d * 1 0 ^ ( 3) 3 ) / N r s ; / / R o t o r s l o t p i tc Kgsr=yr/(yr-(Kcs*Wor)); / / Gap c o n t r a c t i o n f a c t o r f o r r ot or s l o t s Kgs=Kgss*Kgsr; / / Gap c o n t r a c t i o n f a c t o r f o r s l o t s Kgd=L*10^(3)/(L*10^(3)-(Kcd*nd*Wd)); //Gap c o n t r a c t i o n f o r d uc u c ts ts o t al al gap c o n t r a c i o n f a c t o r Kg=Kgs*Kgd; / / T ot u a l a re re a o f a i r gap A g = 3 . 14 1 4 1 59 5 9 2 65 6 5 4 * S b *L * L / P ; / / A c t ua p er e r p o le le i n meter s qu ar e 10

27 A g e = A g / Kg re a p e r p o l e i n K g ; / / E f f e c t i v e a i r g a p a re

m et e t er er s q u a r e 28 disp (Age, ’ E f f e c t i v e a i r g a p a r ea e a p eerr p o l e ( m et e t er er s q u a r e )= )= ’ ) ; 29 / / i n b o o k a ns n s we w e r i s . 0 4 05 0 5 2 A . T h e a ns n s we w e rs r s v ar ar y d u e to round o f f e r r o r

Scilab code Exa 3.4 Estimating the average flux density in the air gap

1 / / E st s t im i m at a t in i n g t h e a ve v e ra r a ge g e f l u x d e n s i t y i n t he he a i r

gap 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

clc ; x a mp mp l e 3 . 4 , P a ge ge No . = 3 . 1 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a MVA r a t i n g M VA V A = 1 72 72 ; / / MV um b er o f p o l e P = 2 0 ; / / N um i a me m e te t e r i n m et e t er er D = 6 . 5 ; / / D ia e t er er L = 1 . 72 72 ; / / C o r e l e n g t h i n m et c h i n mm mm y s = 6 4 ; / / S l o t P i t ch i d th t h i n mm mm W s = 2 2 ; / / S t a t o r s l o t ( o p e n ) w id n g th t h o f a i r g a p i n mm l g = 3 0 ; / / L e ng N u m b e r o f v e n t i l a t i n g d u ct ct s n d = 4 1 ; / / Nu ac h v e n t i l a t i n g Duct i n m mm m W d = 6 ; / / W i d t h o f e ac o t al a l mm m mf p e r p o l e i n A m m f = 2 70 7 0 00 0 0 / / T ot K f = 0 . 7; 7; / / F i e l d f o r m f a c t o r / / E st s t i ma m a ti t i on o n o f e f f e c t i v e a i r g a p a re re a p e r p ol e a t io io f o r s l o t s y=Ws/(2*lg); / / R at K c s = ( 2/ 2 / % p i ) * ( atan ( y ) - log10 ( sqrt (1+y^2))/y); / / C a r t e r ’ s co− e f f i c i e n t f o r s l o t s 19 Kgs=ys/(ys-(Kcs*Ws)); / / Gap c o n t r a c t i o n f o r s l o t s 20 y=Wd/(2*lg); / / R a ti t i o f o r d u c ts ts 21 K c d = ( 2/ 2 / % p i ) * ( atan ( y ) - log10 ( sqrt (1+y^2))/y); / / C a r t e r ’ s co− e f f i c i e n t f o r s l o t s 11

22 Kgd=L*10^(3)/(L*10^(3)-(Kcd*nd*Wd)); //Gap 23 24 25 26 27 28

c o n t r a c t i o n f o r d uc u c ts ts o t al a l g a p e x pa p a n si si o n f a c t o r Kg=Kgs*Kgd; / / T ot The r e q u i r e d f o r t h e a i r g a p i s 8 7 A T g = 0 .8 . 8 7* 7 * m m f ; / / Th % o f t h e t o t a l mmf p er er p o l e i n A B g = A T g / ( 8 00 0 0 0 0 0* 0 * K g * l g * 1 0 ^( ^( - 3 ) ) ; // Maximum f l u x d e n s i t y i n a i r g a p i n Wb Wb pe p e r m et et e r s q u a r e g e f l u x d e n s i t y i n a i r g a p i n Wb B a v = K f * Bg Bg ; / / A v e r a ge p e r m et e t er e r s q u a re re v e ra r a ge g e f l u x d e n s i t y i n a i r g a p (Wb p er er disp (Bav, ’ A ve m e te te r s q u a r e )= ’ ) ; / / i n b o o k a ns n s we w e r i s . 6 1 5 Wb Wb p er e r m et e t er e r s q ua u a r e . Th e p r ov o v i de d e d i n t he h e t ex e x t bo bo o k i s wro ng

Scilab code Exa 3.7 Calculating the apparent flux density

1 2 3 4 5 6 7 8 9 10 11

12 13 14

// / / C a l c u l a t i n g t he h e a pp p p ar a r en en t f l u x d e n s i t y clc ; x a mp mp l e 3 . 7 , P ag ag e No . = 3 . 2 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a i d th t h i n mm mm W s = 1 0 ; / / S l o t w id oo th t h w i dt d t h i n mm mm W t = 1 2 ; / / T oo r a ss s s c o r e L en e n gt g t h i n m et e t er er L = . 3 2 ; / / G ra N u m b er o f v e n t i l a t i n g d u ct ct s n d = 4 ; / / Nu a c h v e n t i l a t i n g D u c t i n mm mm W d = 1 0 ; / / W i d t h o f e ac a l f l u x d e n s i t y i n Wb Wb p er er m e t e r B re r e al a l = 2 .2 .2 ; / / R e al square rm e ab i li t y o f t e et h p = 3 1. 1 . 4* 4 * 10 1 0 ^ ( - 6) 6 ) ; / / P e rm c o r r e s p o nd n d i n g t o r e a l f l u x d e n s i t y i n h e n r y p er er meter c k i n g F ac a c to to r K i = 0 . 9; 9; / / S t a ck / / C a l c u l a t i o n o f a pp p p ar a r en e n t f l u x d e ns ns i ty mmf p e r m et e t e r c o r r es e s p o n d i ng ng t o r e a l a t = B re r e al a l / p ; / / mm 12

f l u x d e n s i t y and p e r m e a b i l i t y 15 L i = K i *( ng t h *( L - nd n d * W d * 10 10 ^( ^ ( - 3 ) ) ; / / N e t i r o n l e ng 16 y s = W t + Ws tc h Ws ; / / S l o t p i tc 17 K s = L * ys y s / ( Li L i * W t ); ); 18 B a p p = B r ea ea l + 4 * % p i * 1 0^ 0^ ( - 7 ) * a t * ( Ks Ks - 1) 1) ; 19 disp (Bapp, ’ A pp p p ar a r en e n t f l u x d e n s i t y (Wb p e r m et e t er er s q u a r e )= ’ ) ; 20 / / i n b o o k a ns n s we w e r i s 2 . 3 1 7 Wb Wb p er e r m et e t er e r s q ua u a r e . Th e

a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 3.8 Calculating the apparent flux density

1 2 3 4 5 6 7 8 9 10 11

// / / C a l c u l a t i n g t he h e a pp p p ar a r en en t f l u x d e n s i t y clc ; x a mp mp l e 3 . 8 , P ag ag e No . = 3 . 2 3 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a i d th t h i n mm mm W s = 1 0 ; / / S l o t w id c h i n mm y s = 2 8 ; / / S l o t p i t ch r a ss s s c o r e L en e n gt g t h i n m et e t er er L = . 3 5 ; / / G ra N u m b er o f v e n t i l a t i n g d u ct ct s n d = 4 ; / / Nu a c h v e n t i l a t i n g D u c t i n mm mm W d = 1 0 ; / / W i d t h o f e ac e a l f l u x d e n s i t y i n Wb Wb pe p e r m et et e r B re r e al a l = 2 .1 . 1 5; 5 ; / / R ea square mmf p e r m et e t er e r c o r r es e s p o n d i ng ng t o r e a l a t = 5 50 5 0 00 0 0 ; / / mm f l u x d e n s i t y and p e r m e a b i l i t y c k i n g F ac a c to to r K i = 0 . 9; 9; / / S t a ck / / C a l c u l a t i o n o f a pp p p ar a r en e n t f l u x d e ns ns i ty ng t h L i = K i *( *( L - nd n d * W d * 10 10 ^( ^ ( - 3 ) ) ; / / N e t i r o n l e ng o t h w id i d th t h i n mm mm W t = y s - Ws W s ; / / T o ot

12 13 14 15 16 K s = L * ys y s / ( Li L i * W t ); ); 17 B a p p = B r ea ea l + 4 * % p i * 1 0^ 0^ ( - 7 ) * a t * ( Ks Ks - 1) 1) ; 18 disp (Bapp, ’ A pp p p ar a r en e n t f l u x d e n s i t y (Wb p e r m et e t er er s q u a r e )= ’ ) ;

13

19 / / i n b o o k a ns n s we we r i s

2 . 2 15 1 5 6 Wb Wb p er e r m et e t er e r s q ua ua r e . a ns n s we w e rrss v a rry y due t o round o f f e r r o r

The

Scilab code Exa 3.11 Calculating the specific iron loss

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

// Calculati ng the s p ec i f i c iron lo ss clc ; x a mp mp l e 3 . 1 1 , P ag ag e No . = 3 . 3 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a Maximum f l u x d e n s i t y i n Wb Wb p e r m et e t er er B m = 3 . 2; 2; / / Ma square r e qu q u en e n cy c y i n Hz f = 5 0 ; / / F re h i c kn k n e ss s s o f s h e e t i n mm t = 0 .5 . 5 *1 * 1 0^ 0 ^ ( - 3 ) ; / / T hi ohm ∗ p = . 3* 3* 10 1 0 ^( ^ ( - 6 ) ; / / R e s i s t i v i t y o f a l l o y s t e e l i n oh meter e n s it i t y i n k g p er e r m et e t er e r c ub ub e D = 7 .8 . 8 *1 * 1 0^ 0 ^ (3 ( 3 ) ; / / D en a c h c y cl cl e i n p h _ ea e a c h = 4 00 0 0 ; / / H y s t e r e s i s l o s s i n e ac J o u l e p er e r m et e t er e r c ub ub e // // C a l c u l a t i o n o f t o t a l i r o n l o s s dd y c u r r e n t p e = % p i * % pi pi * f * f * B m * B m * t *t * t / ( 6 * p * D ) ; / / E dd l o s s i n W p er e r Kg e r Kg Kg p h = p h _e _e a ch ch * f / D ; / / H y s t e r s e i s l o s s i n W p er t a l i r o n l o s s i n W p er e r Kg P i = p e + ph ph ; / / T o ta e r Kg )= )= ’ ) ; disp (Pi, ’ S p e c i f i c i r o n l o s s (W p er / / i n b o o k a ns n s we w e r i s 3 . 2 W p er e r Kg . T h e p ro r o v i de de d i n t he h e t ex e x tb t b o ok ok i s wrong

Scilab code Exa 3.12 Calculating the specific iron loss

14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// Calculati ng the s p ec i f i c iron lo ss clc ; x a mp mp l e 3 . 1 2 , P ag ag e No . = 3 . 3 5 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a Maximum f l u x d e n s i t y i n Wb Wb p e r m et e t er er B m = 1 . 0; 0; / / Ma square r e qu q u en e n cy c y i n Hz f = 1 0 0 ; / / F re h i c kn k n e ss s s o f s h e e t i n mm t = 0 .3 . 3 *1 * 1 0^ 0 ^ ( - 3 ) ; / / T hi ohm ∗ p = . 5* 5* 10 1 0 ^( ^ ( - 6 ) ; / / R e s i s t i v i t y o f a l l o y s t e e l i n oh meter e n s it i t y i n k g p er e r m et e t er e r c u be be D = 7 6 50 50 ; / / D en e r Kg p i _q _q u ot o t e d = 1 .2 . 2 ; / / Q u o t e d i r o n l o s s i n W p er // // C a l c u l a t i o n o f t o t a l i r o n l o s s o o p i n A/m S 1 = 2 *1 *1 2; 2; / / S i d e s o f h y s t e r e s i s l oo o o p i n Wb pe pe r m e t e r S 2 = 2 * 1; 1; / / S i d e s o f h y s t e r e s i s l oo square o o p i n W−s p er er A = S 1 * S2 S2 ; / / A r e a o f h y s t e r e s i s l oo m e te t e r c u be be ach c y c l e i n p h _e _ e ac a c h = A ; / / H y s t e r e s i s l o s s i n e ac J o u l e p er e r m et e t er e r c ub ub e e r Kg Kg p h = p h _e _e a ch ch * f / D ; / / H y s t e r s e i s l o s s i n W p er dd y c u r r e n t p e = % p i * % pi pi * f * f * B m * B m * t *t * t / ( 6 * p * D ) ; / / E dd l o s s i n W p er e r Kg t a l i r o n l o s s i n W p er e r Kg p i = p e + ph ph ; / / T o ta e r Kg )= )= ’ ) ; disp (pi, ’ S p e c i f i c i r o n l o s s (W p er Th e c a l c u l a t e d i r o n l o s s i s s m a l l e r t h a n t h e disp ( ’ Th quoted . ’ ) / / i n b o o k a ns n s we w e r i s 1 . 0 1 4 W p er e r Kg . T h e a ns n s we w e rs rs v a ry due t o round o f f e r r o r

Scilab code Exa 3.13 Calculating the hysteresis loss

1 // C al cu la ti ng the

h y s t e re s i s l o s s 15

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

clc ; x a mp mp l e 3 . 1 3 , P ag ag e No . = 3 . 3 5 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a Maximum f l u x d e n s i t y i n Wb Wb p e r m et e t er er B m = 1 . 0; 0; / / Ma square r e qu q u en e n cy c y i n Hz f = 5 0 ; / / F re S Gi G i = 7 .5 .5 ; / / S p e c i f i c g r a v i t y o f i r o n Kg p h = 4 . 9; 9; / / H y s t e r s e i s l o s s i n W p e r Kg / / C a l c u l a t i o n o f co− e f f i c i e n t ’ n ’ e n si s i ty ty o f i r o n D i = 7 50 50 0; 0; / / D en n = p h /( /( D i * f *( *( B m ^ (1 ( 1 .7 .7 ) ) ) ; / / c o − e f f i c i e n t ( n )= ’ ) ; disp ( n , ’ ( a ) / / i n b oo oo k a ns n s we w e r i s 1 30 3 0 7 ∗ 1 0 ˆ ( − 6 ) . T h e a ns n s we w e rs r s v ar ar y due t o round o f f e r r o r // // C a l c u l a t i o n o f h y s t e r e s i s l o s s Maximum f l u x d e n s i t y i n Wb Wb p e r m et e t er er B m = 1 . 8; 8; / / Ma square r e qu q u en e n cy c y i n Hz f = 2 5 ; / / F re e r Kg p h = n * f * Di Di * B m ^ (1 ( 1 .7 . 7 ) ; / / H y s t e r s e i s l o s s i n W p er H y s t e r s e i s l o s s (W p er e r Kg Kg ) = ’ ) ; disp (ph, ’ ( b ) / / i n b o o k a ns n s we w e r i s 6 . 6 6 W p er e r Kg . T h e a ns n s we w e rs r s v ar ar y due t o round o f f e r r o r

Scilab code Exa 3.15 Calculating the magnetic pull and unbalanced mag-

netic pull and ratio of unbalanced magnetic pull to useful force 1 / / C a l c u l a t i n g t he h e m ag a g ne n e ti t i c p u l l , u nb n b al a l an a n ce ce d

m ag a g ne n e ti t i c p u l l a n d r a t i o o f u nb n b al a l an a n ce c e d m ag a g ne n e ti ti c p ul l to u s ef u l f o r c e 2 3 4 5


/ / G iv i v en e n D at at a P o w er e r = 7 5 00 00 0; 0; / / P o we r r a t i n g

16

in W

6 7 8 9 10 11 12

r e qu q u en e n cy c y i n Hz f = 5 0 ; / / F re N umber o f p o l e s p = 2 ; / / Nu o r e i n m et et e r D = 0 . 5 ; / / S t a t o r b or x i al al l en gt h o f c or e i n meter L = 0 . 2 ; / / A xi l g = 5; / / L e n g t h o f a i r g a p e t i z i ng n g mmf p e r p o l e A T m = 4 50 5 0 0; 0 ; / / P e a k m a g n et ue o f B m = A T m * 4* 4* % p i * 1 0 ^( ^( - 7 ) / ( l g * 1 0 ^( ^( - 3 ) ) ; / / P e a k v a l ue

f l u x d e n s i t y i n Wb Wb pe p e r m et e t er e r s q ua ua r e 13 / / C a l c u l a t i o n o f m ag a g ne n e t i c p u l l p er er p o l e 14 M P = B m * Bm g n et e t ic ic p u l l B m * D * L / ( 3 *4 * 4 * % p i * 1 0 ^( ^( - 7 ) ) ; / / M a gn p er er p o l e ( F l u x D i s t r i b u t i o n i s s i n u s o i d a l ) 15 disp (MP, ’ ( a ) M a g n e t i c p u l l p e r p o l e ( N)= ’ ) ; 16 / / i n b o o k a ns n s we w e r i s 3 3 . 9 i n kN k N T h e a ns n s we w e rs r s v ar ar y d ue t o r ou ou n d o f f e r r o r 17 // / / C a l c u l a t i o n o f u nb n b al a l an a n ce c e d m ag a g ne n e ti ti c p u l l 18 e = 1 ; / / D is i s pl p l ac a c em e m en e n t o f r o t o r a x i s i n mm 19 P p = % p i * D *L * L * B m * B m * e /( /( l g * 4 * 4* 4 * % p i * 1 0 ^( ^( - 7 ) ) ; / / U n b a la l a n c e d m ag a g ne n e t ic i c p u l l p er er p a i r o f p o l e s 20 disp (Pp, ’ ( b ) Unbalanced ma g neti c p u ll p er p a i r o f p o l e s (N)= ’ ) ; 21 / / i n b o o k a ns n s we w e r i s 1 60 6 0 00 0 0 i n N T h e a ns n s we w e rs r s v ar ar y d ue t o r ou ou n d o f f e r r o r 22 / / C a l c u l a t i o n o f R at a t io i o o f u nb n b al a l an a n ce c e d m ag a g ne n e t ic ic p u l l to u s ef u l f o r c e 23 S pe ee d i n r . p . s . p e ed e d = 2 * f /p / p ; / / S p ee 24 T = P ow u l t o rq r q u e i n Nm Nm o w er e r / ( 2* 2 * % p i * S pe pe ed e d ) ; / / U s e f ul 25 F = T /( fu l f o r c e i n N / ( D /2 / 2 ) ; / / U s e fu 26 R at a t io i o o f u nb n b al a l an a n ce c e d m ag a g ne n e ti ti c p u l l t o a t io i o = P p / F; F ; / / R at u s e fu l f o rc e 27 disp (Ratio, ’ ( c ) R a ti t i o o f u nb n b a la l a nc n c e d m a gn g n et et i c p u l l t o u s e f u l f o r c e= e= ’ ) ; 28 / / i n b o o k a ns n s we w e r i s 1 6 . 8 T h e a ns n s we w e rs r s v ar a r y d ue ue t o round o f f e r r o r

17

Chapter 4 Thermal Design Aspects of Electrical Machines

Scilab code Exa 4.1 Calculating the loss that will pass through copper bar

to iron 1 // / / C a l c u l a t i n g t he he

l o s s t ha h a t w i l l p as a s s t h r o ug ug h c op o p pe pe r ba r t o i r o n

2 3 4 5 6 7 8 9 10

clc ; x a mp mp l e 4 . 1 , P ag ag e No . = 4 . 3 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a i a me m e te t e r o f c o pp p p e r b ar a r i n mm mm D = 1 2 ; / / D ia h i c kn k n e ss s s o f m i c an a n i t e t ub u b e i n mm t = 1 . 5 ; / / T hi a c an a n it i t e t u be b e i n oh o hm ∗ m e t e r p = 8 ; / / R e s i s t i v i t y o f m ac e m pe p e r a t u r e d i f f e r e n c e i n d e g r ee ee c e l s i u s T = 2 5 ; / / T em n g th t h o f c op o p pe p e r b ar ar L = 0 . 2 ; / / L e ng / / C a l c u l a t i o n o f l o s s . t ha h a t w i l l p a s s t hr h r ou o u gh g h c op o p pe pe r bar to i r on 11 S = % pi Area o f i n s u l a t i o n i n t h e pi * ( D +t + t ) * 10 1 0 ^( ^ ( - 3 ) * L ; / / Ar p a t h o f h ea ea t f lo w 12 R = ( p * t * 10 10 ^( ^ ( - 3 ) ) / S; S; / / T h e r m a l r e s i s t a n c e o f m i c a n i t e t ub ub e 18

13 Q _c _ c on on = T / R ; / / H e a t D i s s i p a t e d 14 disp (Q_con, ’ H ea e a t D i s s i p a t e d (W) = ’ ) ; 15 / / i n b o o k a ns n s we w e r i s 1 7 . 6 7 W. T h e a ns n s we w e rs r s v ar ar y due

to round o f f e r r o r

Scilab code Exa 4.2 Calculating the loss that will be conducted across the

the laminations 1 / / C a l c u l a t i n g t he he

l o s s t ha h a t w i l l b e c o nd n d uc uc t e d across th hee t h hee l a m i n a t io io n s

2 3 4 5 6 7 8 9 10 11 12 13

14

clc ; x a mp mp l e 4 . 2 , P a ge ge No . = 4 . 3 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a Q _c _ c on o n _5 _ 5 = 2 5; 5; / / H e a t D i s s i p a t e d i c k ne n e s s o f l a m i n a t i o ns n s i n mm t _5 _ 5 = 2 0 ; / / T h ic r o ss s s − s e c t i o n a re r e a o f c on o n d u ct c t i o n i n mm S _ 5 = 2 50 5 0 0; 0 ; / / C ro

square em p e r a t u r e d i f f e r e n c e i n d e g r e e c e l s i u s T _5 _ 5 = 5 ; / / T em i c kn k n e ss s s o f l a m i n a t i o n s i n mm t _ 20 20 = 4 0; 0; / / T h ic r o s s − s e c t i o n a re r e a o f c on o n du d u ct c t io io n i n S _2 _2 0 = 6 00 0 0 0; 0; / / C ro mm s q u a r e T _ 20 20 = 2 0; 0; / / T e m p e r a t u r e d i f f e r e n c e i n d e g r e e celsius // / / C a l c u l a t i o n o f h ea e a t c on o n du d u ct c t ed e d a c r o s s t he he laminations p _ a lo lo n g = ( T _ 5 * S _5 _ 5 * 1 0 ^( ^( - 6 ) ) / ( Q _ c o n _5 _ 5 * t _ 5 * 1 0 ^( ^( - 3 ) ) ; / / T he h e rm r m al al r e s i s t i v i t y a l o n g t h e d i r e c t i o n o f laminations er m a l r e s i s t i v i t y a c r o s s p _ ac a c ro r o s s = 2 0* 0* p _ a lo l o n g ; / / T h er t h e d i r e c t i o n o f l a mi m i n at at i on s

15 Q _ c on o n _ 2 0 = S _ 20 20 * 1 0 ^ ( - 6 ) * T _2 _ 2 0 / ( p _ a c r os os s * t _ 2 0 * 1 0^ 0^ ( - 3 ) ) o n du d u ct c t ed e d a c r o s s t he h e t he he l a m i n a t i o n s ; / / H e a t c on 16 disp (Q_ con_20 , ’ H ea e a t c on o n du d u cctt ed e d a c r o s s t he h e t he he

19

laminations (W)=’ ); 17 / / i n b o o k a ns n s we w e r i s 6 W. round o f f e r r o r

T h e a ns n s we w e rs r s v ar ar y d u e t o

Scilab code Exa 4.3 Calculating the heat radiated from the body

1 2 3 4 5 6 7 8 9

/ / C a l c u l a t i n g t he h e h ea e a t r a d i a t e d f r o m t he he body clc ; x a mp mp l e 4 . 3 , P ag ag e No . = 4 . 5 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e = 0 . 8 ; / / Co− e f f i c i e n t o f p e r at a t ur ur e T 1 = 2 73 7 3 +6 + 6 0; 0 ; / / T e m pe pe r a t u r e T 0 = 2 73 7 3 +2 + 2 0; 0 ; / / T e m pe / / C a l c u l a t i o n o f t he h e h ea ea t

em is si vi ty o f b o d y i n d e g re re e k e l v i n o f w a l l s i n d eg re e k e l v i n r a d i at a t e d f r o m t he he body ea t q _ r a d = 5 . 7* 7 * 1 0^ 0^ ( - 8 ) * e * ( T 1 ^ ( 4) 4 ) - T 0 ^ ( 4 ) ) ; / / H ea r a d i a t e d f r o m t he he body 10 disp (q_rad, ’ H ea e a t r a d i a t e d f ro r o m t h e b o d y ( W at at t p e r s q u a r e m e te t e r )= ’ ) ; 11 / / i n b o o k a ns n s we w e r i s 2 2 4 . 6 i n W a t t p er e r s q ua u a r e m et e t er er . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f e r r o r

Scilab code Exa 4.4 Calculating the length and width of strip

1 2 3 4 5 6

/ / C a l c u l a t i n g t he he l e n g t h and w i d t h o f s t r i p clc ; x a mp mp l e 4 . 4 , P ag ag e No . = 4 . 5 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e = 0.9; / / E m i s s i v i t y a d ia i a ti t i ng ng R a d i a t i n g _e _ e f f i c ie i e n c y = 0 . 75 7 5 ; / / R ad 20

effic ienc y

7 8 9 10

o l ta t a ge ge i n v o l t s v = 2 5 0 ; / / V ol ow e r i n W at at ts ts P = 1 0 00 00 ; / / P ow h i ck c k ne n e ss s s o f n i c k e l ch ro me s t r i p t = 0 . 2 ; / / T hi T 1 = 2 7 3+ 3 + ( 30 3 0 0 +3 +3 0 ) ; / / T e m p e r a t u r e o f s t r i p i n d e g r e e kelvin

11 T 0 = 2 73 m p e ra r a t ur u r e o f a m bi b i e n t m ed ed i u m i n 7 3 +3 + 3 0; 0 ; / / T e mp 12 13 14 15 16 17 18 19 20 21 22 23

d eg re e k e l v i n p = 1 *1 * 1 0^ 0^ ( - 6) 6) ; / / R e s i s t i v i t y o f n i c k e l c h r o m e / / C a l c u l a t i o n o f l e n g t h and w i d t h o f s t r i p e = e * R a di d i a ti t i n g_ g _ e ff f f i ci c i e nc nc y ; / / E f f e c t i v e c o − e f f i c i e n t o f e m i ss i v it y ea t q _ r a d = 5 . 7* 7 * 1 0^ 0^ ( - 8 ) * e * ( T 1 ^ ( 4) 4 ) - T 0 ^ ( 4 ) ) ; / / H ea d i s s i p a t e d b y r a d i a t i o n i n W a t t p er er m e t e r s q u a r e ohm R = v *v * v /P / P ; / / R e s i s t a n c e o f s t r i p i n oh q u al a l t o l /w l _b _ b y _w _w = R * t *1 * 1 0^ 0 ^ ( - 3) 3 ) / p ; / / T h i s i s e qu l w = 1 00 0 0 0 /( /( q _ r ad a d * 2 ) ; / / T h i s i s e q u a l t o l ∗w l = sqrt (lw*l_by_w); / / L e n g t h o f s t r i p i n m e t e r w = ( l w /l / l ) * 1 0^ 0^ ( 3) 3) ; / / W i d t h o f s t r i p i n mm e n gt g t h o f s t r i p ( m et e t er e r )= ’ ) ; disp ( l , ’ L en id t h o f s t r i p (mm) = ’ ) ; disp ( w , ’ W id / / i n b o o k L en e n gt g t h i s 3 6 . 2 m et e t er e r a n d w id i d th t h i s 2 . 9 mm mm . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f e r r o r

Scilab code Exa 4.6 Estimating the temperature of the hot spot

1 2 3 4 5 6 7 8

/ / E s t im i m a t in i n g t he h e t em e m pe p e ra r a tu t u re r e o f t he h e h ot o t s po po t clc ; x a mp mp l e 4 . 6 , P ag ag e No . = 4 . 1 1 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a a t e w i dt d t h o f t r a n s f o r m er e r c o re r e i n m et et e r t = 0 . 5 ; / / P l at c k i ng n g F ac a c to to r K i = 0 .9 .9 4; 4; / / S t a ck er kg p _ co c o re r e = 3 ; / / C o r e l o s s i n W a t t p er t h e r m a l _ c on o n d u c t iv i v i t y = 1 5 0; 0; / / T h e r m a l c o n d u c t i v i t y 21

9 10 11 12 13 14 15 16 17 18 19

20

21

in W Waa t t p e r d e gr gr ee c e l s i u s c e t em e m pe p e ra r a tu t u re re i n d eg re e c e l s i u s T s = 4 0 ; / / S u r f a ce e n si s i ty t y o f s t e e l p l a t e i n k g p er er meter D = 7 8 00 00 ; / / D en cube // / / C a l c u l a t i o n o f t he h e t em e m pe p e ra r a tu t u re r e o f t he he h o t s p o t re l o s s p er e r u n i t v o l u m e ( Wa Wa tt q = p _c _ c or o r e * Ki K i * D ; / / C o re p e r m et e t er e r c ub ub e ) p = 1 / t h er e r m al a l _ co c o n du d u c ti t i v it i t y ; // th er ma l r e s i s t i v i t y i n ce ce h e a t i s t a k e n a l l t o one end x = t; t ; / / S in e m pe p e ra r a tu t u re r e o f t h e h ot o t s po po t , T m = ( q * p* p * x * x /2 /2 ) + Ts Ts ; / / T em i f h ea e a t i s t a ke k e n a l l t o o n e e n d ( d eg eg re e c e l s i u s ) T e m p e r a t u r e o f t he h e h o t s p ot o t , i f h ea ea t disp (Tm, ’ ( a ) i s t a ke k e n a l l t o o n e e n d ( d eg e g re r e e c e l s i u s )= ’ ) ; / / i n b o o k a ns n s we w e rs r s i s 5 8 . 3 d eg e g r e e c e l s i u s . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r e a t i s t a k en e n t o b ot oth t h e d i r e c t i o n s x = t /2 / 2 ; / / S i n c e h ea e m pe p e ra r a tu t u re r e o f t h e h ot o t s po po t , T m = ( q * p* p * x * x /2 /2 ) + Ts Ts ; / / T em i f h ea e a t i s t a ke k e n t o b o t h t he h e d i r e c t i o n s ( d eg eg re e celsi us ) T e m p e r a t u r e o f t he h e h o t s p ot o t , i f h ea ea t disp (Tm, ’ ( b ) i s t a ke k e n t o b o t h t h e d i r e c t i o n s ( d eg e g re r e e c e l s i u s )= ’ ); / / i n b o o k a ns n s we w e rs r s i s 4 4 . 6 d eg e g r e e c e l s i u s . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 4.7 Estimating the hot spot temperature

1 2 3 4 5 6

/ / E s ti t i m at a t i ng n g t he h e h ot o t s p ot o t t em e m p er e r at a t u re re clc ; x a mp mp l e 4 . 7 , P ag ag e No . = 4 . 1 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a n gt g t h o f m e a n t u rn r n i n m et e t er er l = 1 ; / / L een p a ce c e F a ct ct o r S f = 0 .5 .5 6; 6; / / S pa 22

7 8 9 10 11 12 13 14 15 16 17

Watt p = 1 2 0 ; / / T o t a l l o s s i n t h e c o i l i n Wa p i = 8 ; // Thermal r e s i s t i v i t y in ohm ∗ m e t e r mm s q u ar ar e A = 1 00 0 0 *5 * 5 0; 0 ; / / A r e a o f c r o s s − s e c t i o n i n mm h i ck c k ne n e ss ss o f c o i l i n meter t = 5 0* 0* 10 1 0 ^( ^ ( - 3 ) ; / / T hi // / / C a l c u l a t i o n o f t he h e t em e m pe p e ra r a tu t u re r e o f t he he h o t s p o t h e rm r m al al p e = p i *( *( 1 - Sf S f ^ ( 1 /2 /2 ) ) ; / / E f f e c t i v e t he r e s i s t i v i t y i n oh ohm m∗ meter e t er e r c ub ub e ) V = A *l * l * 10 1 0 ^( ^( - 6) 6 ) ; / / V o l u m e o f c o i l ( i n m et e r m et e t e r c u be be q = p / V ; / / H e a t d i s s i p a t e d i n W a t t p er s s um u m in i n g e q u a l i n wa w a r d a n d o ut u t wa w a rd rd T 0 = q * p e * t * t /8 / 8 ; / / A ss h ea ea t f l o w s m pe p e ra r a tu t u re r e o f t he h e h ot o t s p ot o t ( d e g re re e c e l s i u s disp (T0, ’ T eem )= ’ ) ; / / i n b o o k a ns n s we w e rs r s i s 1 5 d e g r e e c e l s i u s . T h e a ns n s we w e rs rs v a ry r y d u e t o r ou ound o f f e r r o r

Scilab code Exa 4.8 Calculating the maximum temperature difference be-

tween the coil surface and the winding 1 / / C a l c u l a t i n g t h e ma maximum t e mp m p e r at at u r e d i f f e r e n c e

b e t w e e n t he h e c o i l s u r f a c e a n d t he h e w in i n di d i ng ng 2 3 4 5 6 7 8


/ / G iv i v en e n D at at a h i ck c k ne n e ss ss o f c o i l ( i n meter ) t = 2 5* 5* 10 1 0 ^( ^ ( - 3 ) ; / / T hi p a ce c e F a ct ct o r S f = 0 . 7; 7; / / S pa er kg ) L os o s s_ s _ cu c u = 2 0; 0; / / C o p p e r l o s s e s ( i n W a t t p er h e rm r m al al r e s i s t i v i t y o f p a p e r i n s u l a t i o n ( i n p i = 8 ; / / T he

ohm ∗ met er ) 9 D _c e n s it i t y o f c op o p pe p e r ( i n k g p er e r m et et e r _c u = 8 90 9 0 0; 0; / / D en cub e ) 10 / / C a l c u l a t i o n o f t he h e maximum t em e m p er e r at a t u re re d i f f e r e n c e b e t w e e n t he h e c o i l s u r f a c e a n d t he h e w in i n di d i ng ng 23

11 p e = p i *( *( 1 - Sf S f ^ ( 1 /2 /2 ) ) ; / / E f f e c t i v e 12 13

14 15

t he h e rm r m al al

r e s i s t i v i t y i n (ohm (ohm ∗ met er ) e t er e r c ub ub e q = S f * Lo L o s s_ s_ c u * D_ D _ cu c u ; / / L o s s e s ( i n W a t t p e r m et ) M aximum t e m p e r at at u r e d i f f e r e n c e T = q * p e * t ^ (2 (2 ) / 2 ; / / Ma b e t w e e n t he h e c o i l s u r f a c e a n d t he h e w in i n di d i ng ng ( i n d eg e g re re e c e l s i u s ) Maximum t e m p e r a tu t u r e d i f f e r e n c e b et e t we w e en en t h e disp ( T , ’ Ma c o i l s u r f a c e a n d t he h e w in i n di di n ngg ( d e g r e e c e l s i u s ) = ’ ) ; / / i n b o o k a ns n s we w e r i s 5 1 d e g r ee e e c e l s i u s . T h e a ns n s we w e rs rs v a ry due t o round o f f e r r o r

Scilab code Exa 4.9 Calculating the temperature difference beetween the

centre of the embedded portion of a conductor and the overhang 1 / / C a l c u l a t i n g t he h e t em e m pe p e ra r a tu t u re re

d i f f e r e n c e b ee e e t we we e n t he he c e n t r e o f t h hee e m b e d d e d p o r t i o n o f a c o nd n d u ct ct o r a n d t h e o v er e r h a ng ng

2 3 4 5 6 7 8 9

10


/ / G iv i v en e n D at at a n g th t h o f t he h e m ac a c h in i n e i n m et e t er er L = 0 . 5 ; / / L e ng h e rm rm a l r e s i s t i v i t y o f c o n d u c t o r i n p c = 0 .0 . 0 02 0 2 5; 5 ; / / T he ohm ∗ m e t e r p = 0 .0 . 0 2 1* 1* 10 1 0 ^ ( - 6) 6) ; / / E l e c t r i c a l r e s i s t i v i t y o f c o n d u c t o r i n ohm ∗ m e t e r r r en e n t d e n s i t y i n t he h e c o n d u c to t o r s ( i n A p er er s = 4 ; / / C u rr mm s q u a r e ) / / C a l c u l a t i o n o f t h e t em e m pe p e ra r a tu t u re re d i f f e r e n c e b ee e e tw t w ee e e n t he h e c e n t r e o f t he h e embedd ed p o r t i o n o f a c o n du d u c to t o r a n d t h e o ve v e rh r h a ng ng h e rm r m al al T = ( s * 1 0 ^ (6 (6 ) ) ^ ( 2 ) * ( p * pc p c * L * L ) / 8; 8 ; / / E f f e c t i v e t he r e s i s t i v i t y i n oh ohm m∗ meter 24

11 disp ( T , ’ T em em p pee ra r a tu t u re re d i f f e r e n c e

b ee e e tw t w ee ee n t h e c e n t r e o f t he h e em e mbedded p o r t i o n o f a c oon n du d u ct c t or o r a n d t he he o ve v e rh r h a ng ng ( d e g r e e c e l s i u s )= ’ ) ; 12 / / i n b o o k a ns n s we w e rs r s i s 2 6 . 3 d eg e g r e e c e l s i u s . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 4.11 Calculating the heat conducted across the former

from winding to core 1 / / C a l c u l a t i n g t he h e h ea e a t c on o n du d u ct c t ed e d a c r o s s t he h e f or o r me me r

f r o m w in i n di d i ng ng t o c o r e 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


/ / G iv i v en e n D at at a c k n e ss s s o f f o r me m e r ( i n mm mm) t = 2 . 5 ; / / T h i ck i c kn k n e ss s s o f a i r s p ac a c e ( i n mm mm) t _a _a ir ir = 1 ; / / T h ic T h e i n n e r d i me m e n ti t i o ns n s o f t he h e f o rm r m er er l w = 1 50 5 0 *2 * 2 50 5 0 ; / / Th o f f i e l d c o i l ( i n mm s q u a r e ) i n di d i ng n g h e i g h t ( i n mm) h = 2 0 0 ; / / W in r m er er ( s _ fo f o rm r m e r = 0 .1 . 1 66 6 6 ; / / T h e r m a l c o n d u c t i v i t y o f f o rm i n W p er e r m et e t e r p er e r d e g r ee ee c e l s i u s ) ct i v i ty o f a i r ( i n W s _a _ a ir i r = 0 .0 . 0 5; 5 ; / / T h e r m a l c o n d u ct p er e r m et e t e r p er e r d e g r ee ee c e l s i u s ) p e r a t u r e r i s e ( i n d e g r ee ee c e l s i u s ) T = 4 0 ; / / T e m pe // / / C a l c u l a t i o n o f t he h e h ea e a t c on o n du d u ct c t ed e d a c r o s s t he he f or o r me m e r f r o m w in i n di d i ng ng t o c o r e ea t S = 2 * (1 ( 1 5 0+ 0 + 2 50 5 0 ) * h * 10 1 0 ^( ^ ( - 6 ) ; / / A r e a o f p a t h o f h ea f l o w ( i n m et e t er e r s q u a re re ) h e rm rm a l R _ f o r me m e r = t * 1 0 ^( ^( - 3 ) / ( S * s _ f o r me m e r ) ; / / T he r e s i s t a n c e o f f or o r me m e r ( i n ohm ) h e rm rm a l R _ a i r = t _ ai a i r * 1 0 ^( ^( - 3 ) / ( S * s _ a i r ) ; / / T he r e s i s t a n c e o f f or o r me m e r ( i n ohm ) n c e R f or o r me me r and R a i r a r e R 0 = R _f _ f o rm rm e r + R _a _a ir i r ; / / S i nc 25

i n s e r i e s . T o ta t a l t he h e r ma m a l r e s i s t a n c e t o h ea e a t f lo lo w ( in ohm) 17 Q _c e a t c o n du d u c t ed e d ( i n W a tt tt s ) _ c on o n = T / R0 R0 ; / / H ea 18 disp (Q_con, ’ H ea e a t c on o n du d u cctt ed e d a c r o s s t he h e f or o r me me r fro m w in i n d iin n g t o c o r e ( i n W a t t s )= )= ’ ); 19 / / i n b o o k a ns n s we w e rs r s i s 1 8 2 .6 . 6 W a t t s . T h e a ns n s we w e rs r s v ar ar y due t o round o f f e r r o r

Scilab code Exa 4.12 Estimating the final steady temperature rise of coil

and its time constant 1 / / E st s t im i m at a t in in g t h e f i n a l

s te t e ad a d y t em e m pe p e ra r a tu t u re re r i s e o f c o i l and i t s t i m e c o n s t a n t

2 3 4 5 6 7 8 9 10 11 12 13 14 15


/ / G iv i v en e n D at at a et e r S = 0 . 15 15 ; / / H e a t d i s s i p a t i n g s u r f a c e ( i n m et squ are ) e n gt g t h o f m e a n t u rn r n i n m et e t er er l = 1 ; / / L en p a ce c e F a ct ct o r S f = 0 .5 .5 6; 6; / / S pa A = 1 00 0 0 *5 * 5 0; 0 ; / / A r e a o f c r o s s − s e c t i o n ( i n mm s q u a r e ) Q = 150; / / D i s s i p a t i n g l o s s ( i n Watts ) t y ( i n W a t t p er e r d e g re re e e m is is s iv i v i ty t y = 3 4; 4 ; / / E m i s s i v i ty c e l s i u s p er e r m et et e r s q u a r e ) e a t o f c o pp p p er e r ( i n J p er er k g p e r h = 3 9 0 ; / / S p e c i f i c h ea d eg e g re re e c e l s i u s ) // / / C a l c u l a t i o n o f t h e f i n a l s te t e ad a d y t em e m pe p e ra r a tu t u re re r i s e o f c o i l a n d i t s t i m e c on o n st s t an an t p p e r ( i n m et e t er er V = l * A * Sf Sf * 1 0^ 0^ ( - 6) 6 ) ; / / V o l u m e o f c o pp cub e ) c e c op o p pe p e r w ei e i g he h e s 8 90 9 0 0 k g p er e r m et e t er er G = V *8 * 8 90 9 0 0; 0; / / S i n ce c ub u b e . W e i g ht ht o f c o pp pp e r ( i n kg ) e a d y t em e m p er e r a tu t u re re T m = Q / ( S* S * e m is i s s iv i v i ty t y ) ; / / F i n a l s t ea 26

16 17 18 19

r i s e ( i n d eg e g re re e c e l s i u s ) e a ti t i ng n g t im i m e c o n st st a n t ( i n T h = G * h /( /( S * e m is i s s iv i v i ty t y ) ; / / H ea seconds ) a l s t ea e a d y t em e m p er e r at a t u re r e r i s e ( d e g re re e disp (Tm, ’ F i n al c e l s i u s ) )= ’ ) ; t i n g t i me m e c o n s t a n t ( s e c o n d s )= ’ ) ; disp (Th, ’ H e a ti / / i n b o o k f i n a l s te t e a d y t em e m pe p e ra r a tu t u re re r i s e ( i n d eg r e e c e l s i u s ) i s e qu qu a l t o 2 9 . 4 and h e a t i n g t i m e c o n s t a n t ( i n s ec e c on o n ds d s ) i s e qu q u al a l t o 1 9 0 6 . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 4.13 Calculating Calculating the final steady temperature temperature rise of coil

surface and hot spot temperature rise 1 // / / C a l c u l a t i n g t he he

coil 2 3 4 5 6 7 8 9 10 11 12 13 14

f i n a l s te t e ad a d y t em e m pe p e r at a t ur ur e r i s e o f s u r f a c e a n d h o t s po p o t t em e m pe p e ra r a tu t u re re r i s e


/ / G iv i v en e n D at at a o l i ng n g s u r f a c e ( i n m et e t er e r s q ua ua r e ) S = 0 .1 .1 25 25 ; / / C o ol e n gt g t h o f m e a n t u rn r n i n m et e t er er l = 0 . 8 ; / / L en p a ce c e F a ct ct o r S f = 0 .5 .5 6; 6; / / S pa A = 1 20 2 0 *5 * 5 0; 0 ; / / A r e a o f c r o s s − s e c t i o n ( i n mm s q u a r e ) Q = 150; / / D i s s i p a t i n g l o s s ( i n Watts ) e m is is s iv i v i ty t y = 3 0; 0; / / S p e c i f i c h e a t d i s s i p a t i o n ( i n W a t t p er e r d e g re r e e c e l s i u s p er e r m et e t er e r s q ua ua r e ) he rm rm al al r e s i s t i v i t y o f i n s u l a t i n g m a t e r i a l p i = 8 ; / / T he ( in ohm ∗ met er ) // / / C a l c u l a t i o n o f t h e f i n a l s te t e ad a d y t em e m pe p e ra r a tu t u re re r i s e o f c o i l s u r f a c e a n d h ot o t s po p o t t em e m pe p e ra r a tu t u re re r i s e e a d y t em e m p er e r a tu t u re re T m = Q / ( S* S * e m is i s s iv i v i ty t y ) ; / / F i n a l s t ea r i s e ( i n d eg e g re re e c e l s i u s ) h e rm r m al al p 0 = p i *( *( 1 - Sf S f ^ ( 1 /2 /2 ) ) ; / / E f f e c t i v e t he 27

15 16

17 18 19

r e s i s t i v i t y ( in ohm ohm ∗ met er ) s s ( i n W a t t s p e r m et e t er e r c ub ub e q = Q / ( l* l * A * 10 1 0 ^( ^ ( - 6 ) ) ; / / L o ss ) e r a t u re re T 0 = q * p 0 * ( 5 0* 0* 1 0 ^( ^( - 3 ) ) ^ ( 2) 2) / 8 ; / / T e m p er d i f f e r e n c e b e t w e e n c o i l s u r t f a c e a n d h o t s po po t ( i n d eg eg re e c e l s i u s ) a l s t ea e a d y t em e m p er e r at a t u re r e r i s e ( d e g re re e disp (Tm, ’ F i n al c e l s i u s )= ’ ) ; m pe p e ra r a tu t u re r e r i s e o f h ot o t s p ot o t ( d e gr gr e e disp (Tm+T0, ’ T eem c e l s i u s )= ’ ) ; / / i n b o o k f i n a l s te t e a d y t em e m pe p e ra r a tu t u re re r i s e ( i n d eg r e e c e l s i u s ) i s e qu q u a l t o 4 0 a n d h ot o t s po p o t t em e m pe p e ra r a tu t u re re r i s e ( i n d eg e g re r e e c e l s i u s ) i s e qu q u al a l t o 5 9 . 5 . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 4.15 Calculating the temperature rise and thermal time

constant and rating of the machine 1 / / C a l c u l a t i n g t he h e t em e m pe p e ra r a tu t u re re

r i s e a n d t he h e rm r m al a l t i me me c o n st st a n t a n nd d rating of th hee m ac a c h i ne ne

2 3 4 5 6 7 8 9 10 11


/ / G iv i v en e n D at at a i a me m e te t e r o f i n d u c t i o n m o to to r ( i n m et e t er er ) D = 0 . 6 ; / / D ia e n gt g t h o f i n d u c t i o n m o to t o r ( i n m et e t er er ) L = 0 . 9 ; / / L en o t o r ( i n W) W) o u t = 7 50 5 0 0; 0 ; / / O u t p u t o f i n d u c t i o n m ot e = 0.9; / / E f f i c i e n c y G = 375; / / Weight o f m a t e r i a l ( i n kg ) e a t ( i n J / kg k g d e g re re e c e l s i u s ) h = 7 2 5 ; / / S p e c i f i c h ea e a t d i s s i p a t i o n ( i n W a t t p er er L em e m = 1 2 ; / / S p e c i f i c h ea m e t e r s qu qu ar e d eg re e c e l s i u s ) 12 / / C a l c u l a t i o n o f t he h e t em e m pe p e ra r a tu t u re r e r i s e a n d t he h e rm r m al al t im i m e c o n st s t a n t o f t he h e m ac a c h i ne ne 28

13 S = ( % p i * D * L ) +( o t al a l h ea ea t + ( 2 * % pi p i / 4 * D ^ ( 2 ) ) ; / / T ot

dissi pating

14 15 16 17 18 19 20 21 22 23 24

s u r f a c e ( i n m et et e r s q u a r e ) Q = ( ou o u t /e / e ) -o - o ut ut ; / / L o s s e s ( i n W a t t s ) n a l t em e m pe p e ra r a tu t u re re r i s e ( i n d eg re e T m = Q /( / ( S * Le Le m ); ) ; / / F i na celsi us ) nd s ) T h = G * h /( /( S * L em em ) ; / / T i m e c o n s t a n t ( i n s e c o nd n a l t em e m pe p e ra r a tu t u re re r i s e ( d eg re e c e l s i u s ) disp (Tm, ’ ( a ) F i na = ’ ); T i m e c o n s t a n t ( s ec e c on o n ds ds ) = ’ ); disp (Th, ’ / / C a l c u l a t i o n o f t h e r a t i n g o f t he he m a c h i n e e a t d i s s i p a t i o n ( i n Wa tt L em e m _n _ n ew e w = 2 5; 5; / / S p e c i f i c h ea p er e r m et et e r s q u a r e d e g r e e c e l s i u s ) Q = T m *S * S * L e m_ m_ ne ne w ; / / L o s s e s ( i n W a t t s ) to r ( i n W o u t = ( e * Q) Q ) / (1 (1 - e ) ; / / O u t p u t o f i n d u c t i o n m o to ) a t in i n g o f t h e m ac a c hi h i ne n e ( Wa Watt ) = ’ ) ; disp (out, ’ ( b ) R at / / i n b o o k a ns n s we w e rs r s a r e 3 0 .8 . 8 5 d e g r ee e e c e l s i u s , 1 0 02 02 5 s e co c o n d s a n d 1 56 5 6 87 8 7 w at a t ts t s . T h e a ns n s we w e rs r s v ar ar y d u e t o round o f f e r r or

Scilab code Exa 4.17 Calculating the temperature of machine after one

hour of its final steady temperature rise 1 / / C a l c u l a t i n g t he h e t em e m pe p e ra r a tu t u re re o f machine a f t e r one

hour o f i t s 2 3 4 5 6

f i n a l s te t e a dy d y t e m p er e r a t u re re r i s e


/ / G iv i v en e n D at at a m p e ra r a t u re re ( i n d e g r e e c e l s i u s ) T i = 4 0 ; / / I n i t i a l t e mp bi en en t t e m p e r a tu tu r e ( i n d e g r e e T _ a m bi bi e nt n t = 3 0; 0; / / A m bi celsi us ) 7 T m = 8 0 ; / / F i n a l s t e ad a d y t em e m pe p e ra r a tu t u re re r i s e ( i n d eg re e celsi us ) 29

8 T h = 2 ; / / H e at a t i ng n g t im i m e c o n s t a n t ( i n h o ur ur s ) 9 t = 1 ; / / S i nc n c e we w e h aav v e t o c a l c u l a t e t em e m pe p e ra r a tu t u re re o f

10 11 12

13 14

m a c h i n e a f t e r o n e h o u r o f i t s f i n a l s te t e ad ad y t em e m p er e r tu t u re r e r i s e ( i n h ou o u rs rs ) // / / C a l c u l a t i o n o f t h e f i n a l s te t e ad a d y t em e m pe p e ra r a tu t u re re r i s e o f c o i l s u r f a c e a n d h ot o t s po p o t t em e m pe p e ra r a tu t u re re r i s e m p e ra r a t u re re r i s e ( T i _r _r i se se = T i - T _ a m bi bi e nt n t ; / / I n i t i a l t e mp i n d eg e g re re e c e l s i u s ) T = T m * (1 (1 - % e ^ ( - t / T h ) ) +( + ( T i _ r i se se * % e ^ ( - t / T h ) ) ; / / T em e m pe p e ra r a tu t u re r e r i s e a f t e r o ne n e h ou o u r ( i n d e g re re e celsi us ) e m pe p e ra r a tu t u re r e o f m ac a c hi h i ne n e a f t e r o ne ne disp (T+ T_ambient , ’ T em h ou o u r ( d e g re r e e c e l s i u s )= ’ ) ; / / i n b o o k a ns n s we w e r i s 6 7 .5 . 5 4 ( d e g r e e c e l s i u s ) . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 4.19 Calculating the rate of change of temperature

1 // / / C a l c u l a t i n g t he h e r a t e o f c h an a n ge g e o f t em e m pe p e ra r a tu t u re re a t

t =0 2 3 4 5 6 7 8


/ / G iv i v en e n D at at a r r e n t ( i n A m pe pe r e s ) I = 2 . 5 ; / / C u rr l t ag ag e ( i n v o l t s ) V = 2 3 0 ; / / V o lt o p pe p e r ( i n kg ) G = 6 0 ; / / W e i g h t o f c op e a t o f c o pp p p er e r ( i n J p er er k g p e r h = 3 9 0 ; / / S p e c i f i c h ea d eg e g re re e c e l s i u s ) 9 // / / C a l c u l a t i o n o f t he h e r a t e o f c h an a n g e o f t em e m pe p e ra r a tu t u re re a t t =0 =0 10 Q = I * V ; / / L o ss ss ( i n Watts ) 11 T _ r at h a ng n g e o f t em e m p er e r a tu t u re re a t a t e = Q / ( G* G * h ) ; / / R a t e o f c ha t =0 =0 ( i n d e g r ee e e c e l s i u s p er e r s ec e c on on d ) 30

12 disp (T_rate , ’ R at a t e o f c h an a n ge g e o f t em e m p er e r a tu t u re r e a t t =0 =0 ( d e g r e e c e l s i u s p er e r s ec e c oon n d )= ’ ) ; 13 / / i n b o o k a ns n s we w e r i s 0 . 02 0 2 4 6 ( i n d e g r ee e e c e l s i u s p eerr

s ec e c on on d ) .

T h e a ns n s we w e rs r s v ar a r y d u e t o r o u nd nd o f f

error

Scilab code Exa 4.22 Calculating the volume of air required per second

and fan power 1 // / / C a l c u l a t i n g t he he vo lu m e o f a i r

r e q u i r e d p er e r s ec e c on on d

a n d f a n p ow o w er er 2 3 4 5 6 7 8 9 10 11 12 13 14 15


/ / G iv i v en e n D at at a rb o − a l t e r n a t o r M VA V A = 5 0 ; / / MVA r a t i n g o f t u rb o t al a l l o s s ( i n kW kW) Q = 1 5 00 00 ; / / T ot e m pe p e r at a t ur u r e o f a i r ( i n d eg eg re e T i = 2 5 ; / / I n l e t t em celsi us ) pe r a t u r e l i m i t ( i n d e g r e e c e l s i u s ) T = 3 0 ; / / T e m pe m a t r i c h e i g h t ( i n mm mm o f m er e r cu c u ry ry ) H = 7 6 0 ; / / B a r o ma s u r e ( i n N p er e r m et e t er e r s q ua ua r e ) P = 2 0 00 00 ; / / P r e s su F an e f f i c i e n c y n f = 0 . 4; 4; / / Fa / / A s s um u m p t io io n o n s t an an t c p = 9 9 5; 5; / / S p e c i f i c h e a t o f a i r a t c on p r e s s u r e ( i n J p er e r k g p er e r d eg eg re e c e l s i u s ) N . T. T. P . ( i n V = 0 .7 .7 75 75 ; / / V o l u m e o f 1 k g o f a i r a t N. meter cube ) / / C a l c u l a t i o n o f t h e v ol o l u m e o f a i r r e qu q u i r e d p er er s e co c o n d a n d f a n p ow ow e r

16 V a = ( V * Q * 1 0 ^( ^ ( 3 ) / ( c p * T ) ) *( * ( ( T i + 2 73 7 3 ) / 2 7 3 ) * ( 7 60 60 / H ) ; / /

V o l u m e o f a i r ( i n m et e t er e r c ub u b e p e r s e co co n d ) 17 P f = ( P * Va w e r ( i n kW) Va / n f ) *1 * 1 0^ 0 ^ ( - 3) 3 ) ; / / F a n p o we 18 disp (Va, ’ Vo V o l u m e o f a i r ( m et e t er e r c ub u b e p e r s e co c o n d )= ’ ) ; 19 disp (Pf, ’ Fan Fan power (kW)=’ ) ; 31

20 / / i n b o o k Va i s

e q ua u a l t o 4 2 . 6 ( m et e t er e r c ub u b e p er e r s ec e c on on d ) a n d P f i s e q u a l t o 2 1 2. 2 . 5 (kW) . T h e a ns n s we w e rs rs v a ry due t o round o f f e r r o r

Scilab code Exa 4.23 Calculating the efficiency of machine and amount of

cooling water 1 / / C a l c u l a t i n g t he he

e f f i c i e n c y o f m a c h i n e and amount

o f c o o l i n g w a te te r 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19


/ / G iv i v en e n D at at a rb o − a l t e r n a t o r M VA V A = 3 0 ; / / MVA r a t i n g o f t u rb e m pe p e r at a t ur u r e o f a i r ( i n d eg eg re e T i = 1 5 ; / / I n l e t t em celsi us ) u t le l e t t em e m pe p e ra r a tu t u re r e o f a i r ( i n d e g r ee ee T o = 4 5 ; / / O ut celsi us ) m a t r i c h e i g h t ( i n mm mm o f m er e r cu c u ry ry ) H = 7 5 0 ; / / B a r o ma e t er e r c ub u b e p e r s e co co n d ) V a = 3 0 ; / / V o l u m e o f a i r ( i n m et F an e f f i c i e n c y n f = 0 . 4; 4; / / Fa o n st s t an an t c p = 1 00 00 0; 0; / / S p e c i f i c h e a t o f a i r a t c on p r e s s u r e ( i n J p er e r k g p er e r d eg eg re e c e l s i u s ) N . T. T. P . ( i n V = 0 . 78 78 ; / / V o l u m e o f 1 k g o f a i r a t N. meter cube ) p f = 0 . 8; 8; / / P o w e r f a c t o r // // C a lc u la t io n o f t h e e f f i c i e n c y o f machine ee T = T o - Ti T i ; / / T e m p e r a t u r e r i s e l i m i t ( i n d e g r ee celsi us ) Q = V a / (( ( ( V * 1 0 ^ ( 3) 3) / ( c p * T ) ) * ( ( Ti T i + 2 7 3 ) / 2 7 3) 3) * ( 7 6 0 / H ) ) ; / / T ot o t al a l l o s s e s ( i n kW kW) u t pu p u t p o we we r ( i n kW) P _o _ o ut u t = 3 0 *1 *1 0 ^( ^ ( 3 ) * pf pf ; / / O ut we r ( i n kW) n = P _o _ o ut u t / ( P _ ou ou t + Q ) *1 * 1 00 0 0 ; / / F a n p o we c h iin n e ( i n p e r ce c e n t a ge g e )= ’ ) disp ( n , ’ ( a ) E f f i c i e n c y o f m a ch 32

; 20 / / C a l c u l a t i o n o f t he h e a m o u n t o f c o o l i n g w a te te r 21 T = 8 ; / / T em e m pe p e ra r a tu t u re r e r i s e o f w aatt er e r ( i n d e gr gr e e

celsi us ) 22 V w = 0 .2 . 2 4* 4 * Q / T; T ; / / Amo un t o f

c o o l i n g w a te te r ( i n l i t r e

p e r s e c o nd nd ) 23 disp (Vw, ’ ( b ) Am ou nt o f c o o l i n g w a te te r ( l i t r e p e r seco nd )=’ ); 24 / / i n b o o k e f f i c i e n c y i s e qu q u a l t o 9 5 .7 . 7% and amount o f c o o l i n g w at a t er e r 3 2 . 4 ( l i t r e p e r s e co c o n d ) . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 4.24 Calculating the temperature rise of hydrogen

1 2 3 4 5 6 7 8 9 10 11 12 13

/ / C a l c u l a t i n g t he h e t em e m pe p e ra r a tu t u re r e r i s e o f h yd y d r og o g en en clc ; x a mp mp l e 4 . 2 4 , P ag ag e No . = 4 . 5 1 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a Q = 7 5 0 ; / / L o s s e s ( i n kW) e m pe p e r at a t ur u r e o f a i r ( i n d eg eg re e T i = 2 5 ; / / I n l e t t em celsi us ) r o m at a t r ic i c h e i g h t ( i n mm mm o f H = ( 20 2 0 00 0 0 +7 + 7 60 6 0 ) ; / / B a ro merc ury ) d r og o g en e n l e a v i n g t he he c o o l e r s ( V H = 1 0 ; / / V o l u m e o f h y dr i n m et e t er e r c ub u b e p e r s e co co n d ) o n st s t an an t c p = 1 25 2 5 40 4 0 ; / / S p e c i f i c h e a t o f a i r a t c on p r e s s u r e ( i n J p er e r k g p er e r d eg eg re e c e l s i u s ) N . T. T. P . ( i n V = 1 1 .2 .2 ; / / V o l u m e o f 1 k g o f a i r a t N. meter cube ) // / / C a l c u l a t i o n o f t he h e t em e m pe p e ra r a tu t u re r e r i s e o f h yd y d ro r o ge ge n T = ( V * Q * 1 0 ^( ^ ( 3 ) / ( c p * VH V H ) ) * ( ( T i + 2 73 73 ) / 2 7 3 ) * ( 7 60 60 / H ) ; / / T em e m pe p e ra r a tu t u re r e r i s e o f h yd y d ro r o ge g e n ( i n d e gr gr e e c e l s i u s ) m p eerr at a t ur ur e r i s e o f h y yd d ro r o ggee n ( d e g re re e c e l s i u s disp ( T , ’ T e mp 33

)= ’ ) ; 14 / / i n b o o k a ns n s i s 2 0 ( d e g r ee ee c e l s i u s ) . v a ry due t o round o f f e r r o r

T h e a ns n s we w e rs rs

Scilab code Exa 4.25 Calculating the amount of oil and amount of water

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

/ / C a l c u l a t i n g t he h e a m o u n t o f o i l a n d a mo mo u n t o f w at a t er er clc ; x a mp mp l e 4 . 2 5 , P ag ag e No . = 4 . 5 1 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a MVA r a t i n g o f t r a n s f o r m e r M VA V A = 4 0 ; / / MV o t al a l l o s s e s ( i n kW kW) Q = 2 0 0 ; / / T ot i n ce c e 2 0% o f l o s s e s a re re d i s s i p a t e d Q _o _ o il i l = 0 .8 .8 * Q; Q ; / / S in b y t a nk n k w a l l s H e a t t ak a k en e n u p b y o i l ( i n kW kW) / / C a l c u l a t i o n o f t h e a mount o f o i l eg re e c e l s i u s T = 2 0 ; / / T e m p e r a t u r e r i s e o f o i l ( i n d eg ) s u m in in g c p = 0 . 4; 4; / / b y a s su V o = 0 .2 . 2 4* 4 * Q _ o il il / ( c p *T * T ) ; / / Am ou nt o f o i l ( i n l i t r e p e r s e c o nd nd ) A mo unt o f o i l ( l i t r e p e r s e c o n d ) = ’ ) ; disp (Vo, ’ Am // / / C a l c u l a t i o n o f t he h e a m o u n t o f w at a t er er p e r at a t ur u r e r i s e o f w at a t er e r ( i n d e g re re e T = 1 0 ; / / T e m pe celsi us ) V w = 0 .2 . 2 4* 4 * Q _ o il il / T ; / / Am ou nt o f w a t e r ( i n l i t r e p e r seco nd ) A mo unt o f w a t e r ( l i t r e p e r s e c o n d ) = ’ ) ; disp (Vw, ’ Am / / i n b oo oo k Vo i s e q u a l t o 4 . 8 ( l i t r e p e r s e co co n d ) and Vw i s e q ua u a l t o 3 . 8 4 ( l i t r e p er e r s ec e c on o n d ) . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

34

Scilab code Exa 4.26 Calculating the temperature rise of tank

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

// / / C a l c u l a t i n g t he h e t em e m pe p e ra r a tu t u re re r i s e o f tan k clc ; x a mp mp l e 4 . 2 6 , P ag ag e No . = 4 . 5 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a MVA r a t i n g o f t r a n s f o r m e r M VA V A = 1 5 ; / / MV kW) Q _i _ i ro r o n = 8 0; 0; / / I r o n l o s s e s ( i n kW pp er er l o s s e s ( i n kW kW) Q _ c op o p p er er = 1 20 2 0 ; / / C o pp m p er e r at a t ur u r e r i s e o f w at a t er e r ( i n d e g re re e T _w _ w at a t er e r = 1 5; 5; / / T e mp celsi us ) t e r ( i n l i t r e p e r s e c o nd nd ) V w = 3 ; / / Amo un t o f w a te D i m e n s io i o n s = 3 . 5 * 3. 3 . 0 * 1. 1. 4 ; / / Ta n k d i m e n s i o n s ( i n met er ) l = 10; // S p e c i f i c l o s s d i s s i p a t i o n f r o m t a n k w a l l s ( i n W a t t p er e r d e gr g r e e c e l s i u s p er e r m et e t e r s q ua ua r e ) / / C a l c u l a t i o n o f t h e t em e m pe p e ra r a tu t u re re r i s e o f ta nk o t al a l l o s s e s ( i n kW kW) Q _ t o ta t a l = Q _ i ro ro n + Q _ c o p pe p e r ; / / T ot ea t t a k en e n a w a y b y w a te te r ( i n Q = V w * T_ T _ w at at e r / 0. 0 . 24 2 4 ; / / H ea kW) os s d i s s i p a t e d by w a l l s ( i n Q _ w al al l s = Q _ to to ta t a l - Q ; / / L os kW) nk w a l l s by S = 2 * 3. 3 . 5 *( * ( 3 +1 + 1 . 14 1 4 ) ; / / A r e a o f t a nk n e g l e c t i n g t op o p a n d b ot otto m s u r f a c e s m p er e r at a t ur u r e r i s e o f t an an k T = Q _w _ w a ll ll s * 1 0 ^( ^( 3) 3 ) / ( S * l) l ) ; / / T e mp ( i n d eg re e c e l s i u s ) m p eerr at a t ur u r e r i s e o f t an a n k ( d e g re r e e c e l s i u s )= ’ ) disp ( T , ’ T e mp ;

19 / / i n b o o k a ns n s we we r i s

4 0 . 6 ( d e g r ee ee c e l s i u s ) . p r ov o v i de de d i n t h hee t ex e x t bo bo o k i s wro ng

35

The

Scilab code Exa 4.27 Calculating the amount of water required and area

of water duct and pumping power 1 // / / C a l c u l a t i n g t he h e a m o u n t o f w at a t er e r r e q u i r e d p er er

s ec e c o nd n d , a r e a o f w a te t e r d u ct c t a n d p u m pi pi n g p ow o w er er 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18


/ / G iv i v en e n D at at a o p pe p e r l o s s e s ( i n kW kW) Q = 8 0 0 ; / / S t a t o r c op m p er e r at a t ur u r e o f w at a t er e r i n l e t ( i n d e gr gr e e T i = 3 8 ; / / T e mp celsi us ) m p er e r at a t ur u r e o f w at a t er e r o u t l e t ( i n d e g re re e T o = 6 8 ; / / T e mp celsi us ) Number o f s l o t s N s = 4 8 ; / / Nu e t er e r p er e r s ec e c on on d ) v = 1 ; / / v e l o c i t y ( i n m et e t er er p = 3 00 0 0 *1 * 1 0^ 0 ^ (3 ( 3 ) ; / / P u m p i n g p r e s s u r e ( i n N p e r m et squ are ) n = 0.6; / / E f f i c i e n c y / / C a l c u l a t i o n o f t he h e v o l u m e o f w at a t er e r r e q u i r e d p er er second m p er e r at a t ur u r e r i s e o f w at a t er e r ( i n d e g re re e T = T o - Ti T i ; / / T e mp celsi us ) V w l = 0 .2 . 2 4* 4 * Q / T ; / / Am ou nt o f w a t e r ( i n l i t r e p e r seco nd ) t e r ( i n m et e t er e r c ub ub e V w m = V wl wl * 1 0^ 0 ^ ( - 3) 3 ) ; / / Am ou nt o f w a te p e r s e c o nd nd ) n c e e a ch c h s l o t h as a s t w o c o nd nd uc to r s N _ c on o n d = 2 * Ns Ns ; / / S i nc T ot o t al a l n u m b e r o f s t a t o r c o n du d u c to to r s n c e e ac a c h c on o n du d u ct c t or or i s N _ su su b _c _ c o nd n d = 3 2* 2 * N _ c on on d ; / / S i nc s u b di d i v i de d e d i n t o 3 2 su b−c o n d u c t o r s te r V w _ s u b _c _c o n d = V wl w l / N _ s u b _ c on o n d ; / / V o l u m e o f w a te r e q u i r e d f o r e ac a c h s u b −c o n d u c t o r s ( i n l i t r e p e r 36

seco nd ) 19 disp (Vw_sub_cond , ’ Vo V o l u m e o f w at a t er e r r e q u i r e d f o r e ac ac h s u b − c o n d u c t o r s ( l i t r e p e r s e c o n d )= ’ ) ; 20 A = V w _s a c h d uc uc t ( i n _ s u b_ b _ c on o n d * 1 0^ 0 ^ ( - 3) 3 ) / v ; / / A r e a o f e ac 21 22 23 24 25 26

m e te te r s q u a r e ) re a o f e ac a c h d uc u c t ( i n mm mm s q u a r e ) A = A * 10 1 0 ^( ^ ( 6) 6 ) ; / / A re ea o f e a ch c h d u ct c t (mm s q u a r e ) = ’ ) ; disp ( A , ’ A r ea ed Q = 8 00 00 - 5 00 00 ; / / S i n c e i t i a a 5 0 0 KW d i r e c t c o o l ed t u r b o − a l t e r n a t o r ( i n kW) um pi pi ng ng p o w er e r ( i n kW P = ( Q * 10 1 0 ^ (3 (3 ) * V wm wm / n ) * 10 10 ^( ^ ( - 3 ) ; / / P um ) Pump mpin ingg power (kW)=’ ) ; disp ( P , ’ Pu / / i n b oo oo k V w l i s e q u a l t o 0 . 0 0 2 0 8 ( l i t r e p e r s e co co n d ) , A i s 2 (mm s q u a r e ) a n d p u m p i n g p ow o w e r i s 3 . 2 (kW ) . T h e a n sw s w er e r s v a ry ry d u e t o r o u n d o f f e r r o r

Scilab code Exa 4.35 Calculating the continuous rating of motor

1 2 3 4 5 6 7 8 9 10 11 12 13 14

/ / C a l c u l a t i n g t he h e c o nt n t i n u ou ou s r a t i n g o f motor clc ; x a mp mp l e 4 . 3 5 , P ag ag e No . = 4 . 6 7 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a o t o r ( i n kW kW) P s h = 3 7. 7 . 5; 5 ; / / P o w e r r a t i n g o f m ot ut s ) t h = 3 0 ; / / T i m e ( i n m i n ut e a t in i n g t im i m e c o n s t a n t ( i n m in i n ut ut s ) T h = 9 0 ; / / H ea // / / C a l c u l a t i o n o f t he h e c o n t i n uo uo u s r a t i n g o f motor e a ti t i ng n g o v er e r l oa oa d r a t i o p h = 1 /( /( 1 - % e ^( ^( - t h / Th Th ) ) ; / / H ea 0% f u l l K = 0 .7 . 7 ^( ^ ( 2) 2 ) ; / / Maximum e f f i c i e n c y o c c u r s a t 7 0% load e c ha h a ni n i ca c a l o v e rl rl o a d r a t i o p m = ( ( K +1 +1 ) * ph ph - K ) ^ ( 1/ 1/ 2 ) ; / / M ec o n ti t i n uo u o us u s r a t i n g o f m o to to r ( i n kW kW) P no no m = P sh sh / pm p m ; / / C on n t i nu n u o u s r a t i n g o f m ot o t or o r (kW) = ’ ) ; disp (Pnom, ’ C o nt / / i n b o o k a ns n s we w e r i s 1 7 . 2 kW kW . T h e a ns n s we w e rs r s v ar ar y due 37

to round o f f e r r o r

Scilab code Exa 4.37 Calculating the mean temperature rise

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

16 17 18

/ / C a l c u l a t i n g t he h e m e a n t em e m pe p e ra r a t ur ur e r i s e clc ; x a mp mp l e 4 . 3 7 , P ag ag e No . = 4 . 7 3 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e a t in i n g t im i m e ( i n m in i n ut ut s ) t h = 2 0 ; / / H ea a t i ng n g t im i m e c o n s t a n t ( i n m in i n ut ut s ) T h = 1 2 0; 0; / / H e at i n g t im i m e ( i n m in i n ut ut s ) t c = 1 5 ; / / C o o l in l i n g t im i m e c o n s t a n t ( i n m in i n ut ut s ) T c = 1 8 0; 0; / / C o o li e m pe p e ra r a tu t u re r e r i s e o n t he h e c o nt n t i n u ou ou s T m = 5 0 ; / / F i n a l t em f u l l l o ad a d ( i n d e g re re e c e l s i u s ) pp er er l o s s a t f u l l l o a d ( i n W a t t ) L o s s_ s _ f l = 5 00 0 0 ; / / C o pp a d ( i n Wa tt ) L o s s_ s _ n l = 3 00 0 0 ; / / C o p p e r l o s s a t n o l o ad / / C a l c u l a t i o n o f t he h e m ea n t em e m pe p e ra r a tu t u re re r i s e T o t a l _ L os o s s _ f l = L o s s_ s_ f l + L o s s _n _n l ; / / T o t a l l o s s a t f u l l l o a d ( i n Wa tt ) o t a l l o s s a t n o l oa oa d ( i n T o t a l _L _ L o s s _n _ n l = L o s s_ s_ n l ; / / T ot Watt) na l T n = T o t a l_ l _ L o s s_ s_ n l / T o t a l _ L o ss ss _ f l * T m ; / / F i na t em e m p er e r a tu t u r e r i s e w h e n r un u n ni n i ng n g o n n o l o ad ad ( i n d eg e g re re e c e l s i u s ) T = ( ( T m * th th / T h ) + ( T n * tc t c / T c ) ) / ( t h / Th Th + t c / T c ) ; // Mean t em e m pe p e ra r a tu t u re r e r i s e ( i n d e g r ee ee c e l s i u s ) Mean t em e m p er e r a tu t u re r e r i s e ( d e g re r e e c e l s i u s )= ’ ) ; disp ( T , ’ Me / / i n b o o k a n s w e r i s 3 9 . 5 8 d eg e g r e e c e l s i u s . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

38

Scilab code Exa 4.43 Calculating the temperature rise

1 2 3 4 5

/ / C a l c u l a t i n g t he h e t em e m pe p e ra r a tu t u re re r i s e clc ; x a mp mp l e 4 . 4 3 , P ag ag e No . = 4 . 7 7 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a ro s s− s e c t i o n a l a z = 3 0* 0 * 10 1 0 ^( ^ ( - 6 ) ; / / C ro

a re a ( i n meter

squ are ) 6 I z = 2 0* n t ( i n Ampere ) 0 * 10 1 0 ^( ^ ( 3) 3 ) ; / / C u r r e nt 7 t = 5 0 ; / / T i m e ( i n m i l i s e co co n d ) 8 p = 0 .0 n d uc u c to to r ( i n . 0 2 1* 1* 10 1 0 ^ ( - 6) 6 ) ; / / R e s i s t i v i t y o f c o nd 9 10 11 12 13 14

ohm ∗ met er ) e a t ( i n J / kg k g d e g re re e c e l s i u s ) h = 4 1 8 ; / / S p e c i f i c h ea n s i t y ( i n k g p e r m et e t er e r c ub ub e ) g = 8 9 00 00 ; / / D e ns // / / C a l c u l a t i o n o f t he h e t em e m pe p e ra r a tu t u re re r i s e e r a t u re re T = I z ^ ( 2) 2) * p * t * 1 0 ^( ^( - 3 ) / ( g * a z ^ ( 2) 2 ) * h ) ; / / T e m p er r i s e ( i n d eg e g re re e c e l s i u s ) em p pee ra r a tu t u re re r i s e ( d e g r e e c e l s i u s )= ’ ) ; disp ( T , ’ T em / / i n b o o k a ns n s we w e r i s 1 2 5 d e gr g r e e c e l s i u s . T h e a ns n s we w e rs rs v a ry r y d u e t o r ou ound o f f e r r o r

39

Chapter 5 Design of Transformers

Scilab code Exa 5.3 Calculating the kVA output of a single phase trans-

former 1 / / C a l c u l a t i n g t he h e kV kVA o ut u t pu p u t o f a s i n g l e p ha h a se se

transformer 2 3 4 5 6 7 8 9 10 11 12 13


/ / G iv i v en e n D at at a t a n ce c e b et e t w ee e e n c o r e c e n t r e s ( i n m et e t er er ) D = 0 . 4 ; / / D i s ta e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq u x d e n s i t y o f c o r e ( i n Wb Wb p er e r m et et e r B m = 1 . 2; 2; / / F l ux squ are ) W i nd o w s p a c e f a c t o r K w = 0 .2 .2 7; 7; / / Wi r r e n t d e n s i t y ( i n A m p e r e p e r mm mm s q u a r e ) s = 2 . 3 ; / / C u rr t i o o f c o r e h e i g ht h t and d i s t a n c e R 1 = 2 . 8; 8; / / R a ti b et e t we we e n c o r e c e n t r e s ti o o f c i r c u m s c r i b i n g c i r c l e and R 2 = 0 .5 .5 6; 6; / / R a ti d i s t a n c e b e t w e e n c o re re c e n t r es t i o o f n e t i r o n a re r e a a nd nd a re re a o f R 3 = 0 . 7; 7; / / R a ti ci rcu ms cri bi ng c i r c l e / / C a l c u l a t i o n o f t he h e kV kVA o ut u t pu p u t o f a s i n g l e p ha h a se se 40

14 15 16 17 18 19 20 21 22

transformer r e h e i g h t o r w i n d o w h e i g h t ( i n m et e t er er ) H w = R 1 *D * D ; / / C o re i a me m e te te r o f c i r c u m s c r i b i n g c i r c l e ( i n d = R 2 *D * D ; / / D ia met er ) nd ow ow ( i n m e te te r ) W w = D -d - d ; / / W i d t h o f w i nd re a o f w i n d o w ( i n m et e t er er s q u a r e ) A w = H w * Ww Ww ; / / A re A = ( %p % p i /4 / 4 )* ) * d *d *d ; / / A r e a o f c i r c u m s c r i b i n g c i r c l e ( i n m e te te r s q u a r e ) e a ( i n m et e t er e r s q ua ua r e ) A i = R 3 *A * A ; / / N e t i r o n a r ea Q = 2 . 22 22 * f * B m * K w * s * 1 0^ 0^ ( 6 ) * A w * Ai A i * 1 0 ^( ^( - 3 ) ; // kVA o ut u t pu p u t o f a s i n g l e p ha h a se se t r a n s f o r m e r t p ut u t o f a s i n g l e p ha h a se se t r a n s f o r m e r ( disp ( Q , ’ kVA o u tp kVA)=’ ) ; / / i n b oo oo k a ns n s we w e r i s 4 50 5 0 kV kVA . T h e a n sw s w er e r s v ar ar y due to round o f f e r r o r

Scilab code Exa 5.6 Calculating the net iron area and window area and

full load mmf 1 / / C a l c u l a t i n g t he h e n et e t i r o n a r ea e a a n d w in in d o w a r ea ea and

f u l l l o a d mmf 2 3 4 5 6 7 8


/ / G iv i v en e n D at at a kVA r a t i n g Q = 4 0 0 ; / / kV a t io i o o f f l u x t o f u l l l o a d mmf R = 2 .4 . 4 *1 * 1 0^ 0 ^ ( - 6 ) ; / / R at e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq Wb p e r B m = 1 . 3; 3; / / Maximum f l u x d e n s i t y o f c o r e ( i n Wb m e te te r s q u a r e ) 9 K w = 0 .2 W i nd o w s p a c e f a c t o r .2 6; 6; / / Wi 10 s = 2 . 7 ; / / C u rr r r e n t d e n s i t y ( i n A m p e r e p e r mm mm s q u a r e ) 11 // / / C a l c u l a t i o n o f t h e n e t i r o n a re re a 12 K = ( 4 .4 . 4 4 * f * R * 1 0 ^( ^ ( 3 ) ) ^ ( 1 /2 /2 ) ;

41

13 14 15 16 17 18

l t ag a g e p er e r t ur u r n ( i n V o lt lt s ) E t = K * Q ^( ^ ( 1/ 1 / 2) 2 ) ; / / V o lt F lu l u x = E t / (4 ( 4 .4 . 4 4 * f ); ) ; / / F l u x ( i n Wb) e a ( i n m et e t er e r s q ua ua r e ) A i = F lu lu x /B / B m; m ; / / N e t i r o n a r ea e t i r o n a r e a ( m et e t er er s q u a r e )= ’ ) ; disp (Ai, ’ N et // / / C a l c u l a t i o n o f t he h e n et e t w i n d o w a r ea ea Wind ndow ow A w = Q / ( 2 . 22 22 * f * B m * K w * s * 1 0^ 0 ^ ( 6 ) * A i * 10 1 0 ^ ( - 3 ) ) ; // Wi

19 20 21 22 23

a r e a ( i n m et e t er e r s q u a re re ) W i n do w a r e a ( m e t e r s q u a r e ) = ’ ) ; disp (Aw, ’ Wi / / C a l c u l a t i o n o f t he h e f u l l l o ad a d mmf A T = F lu lu x /R / R ; / / F u l l l o a d mmf ( i n A ) disp (AT, ’ F u l l l o a d mmf ( A ) = ’ ) ; / / i n b oo oo k a n sw s w e rs r s a r e 0 . 0 5 0 7 ( m et e t er e r s q u a re re ) , 0 . 0 7 7 7 ( m et e t er e r s q ua u a r e ) a n d 2 75 7 5 00 0 0 ( A ) r e s p e c t i v e l y . The a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 5.9 Calculating the net iron area and window area

1 2 3 4 5 6 7 8 9 10 11 12

/ / C a l c u l a t i n g t he h e n et e t i r o n a r ea e a a n d w in in d o w a r ea ea clc ; x a mp mp l e 5 . 9 , P ag ag e No . = 5 . 8 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a kVA r a t i n g Q = 4 0 0 ; / / kV e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq Wb p e r B m = 1 . 5; 5; / / Maximum f l u x d e n s i t y o f c o r e ( i n Wb m e te te r s q u a r e ) ac e f a c t o r K w = 0 .1 .1 2; 2; / / C o p p e r s p ac r r e n t d e n s i t y ( i n A m p e r e p e r mm mm s q u a r e ) s = 2 . 2 ; / / C u rr e n si s i ty t y o f c op o p pe p e r ( i n k g p er er g c = 8 . 9* 9* 1 0^ 0 ^ ( 3) 3 ) ; / / D en meter cube ) e n si s i ty t y o f i r o n ( i n k g p er e r m et et e r g i = 7 . 8* 8* 1 0^ 0 ^ ( 3) 3 ) ; / / D en cub e ) a t io i o o f l e ng n g t h o f m e a n t ur u r n o f c op o p pe pe r R 1 = 0 . 5; 5; / / R at t o l e ng n g t h o f m ea n f l u x p a th th 42

13 R 2 = 4 ; / / R at a t io i o o f w e ig i g ht h t o f i r o n t o w ei e i gh gh t o f

copper 14 / /// C a l c u l a t i o n o f t h e n e t i r o n a re re a 15 C = ( 1 / 2. 2 . 2 2 * R 1 * gc g c / g i * 1 0 ^ (3 ( 3 ) ) ^ ( 1 / 2) 2 ) ; / / F l u x ( i n Wb) 16 A i = C * ( Q * R 2 /( re a / ( f * B m * s * 1 0 ^( ^( 6 ) ) ) ^ ( 1 /2 / 2 ) ; / / N e t i r o n a re

( i n m et e t er er s q u a r e ) 17 disp (Ai, ’ N et e t i r o n a r e a ( m et e t er er s q u a r e )= ’ ) ; 18 // / / C a l c u l a t i o n o f t he h e n et e t w i n d o w a r ea ea 19 A w = Q / ( 2 . 22 Wind ndow ow 22 * f * B m * K w * s * 1 0^ 0 ^ ( 6 ) * A i * 10 1 0 ^ ( - 3 ) ) ; // Wi

a r e a ( i n m et e t er e r s q u a re re ) 20 disp (Aw, ’ Wi W i n do w a r e a ( m e t e r s q u a r e ) = ’ ) ; 21 / / i n b oo oo k a n sw s w e rs r s a r e 0 . 0 4 7 8 ( m et e t er e r s q u a re re ) and 0 . 1 8 3 ( m et e t er e r s q ua u a r e ) r e s p e c t i v e l y . T h e a ns n s we w e rs rs v a ry due t o round o f f e r r o r

Scilab code Exa 5.12 Calculating the resistance of secondary winding

1 2 3 4 5 6 7 8 9 10 11

// / / C a l c u l a t i n g t he h e r e s i s t a n c e o f s ec e c on o n d a ry r y w in i n di d i ng ng clc ; x a mp mp l e 5 . 1 2 , P ag ag e No . = 5 . 8 9 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a u r re r e nt n t d e n s i t y o f p ri r i ma m a ry r y w in i n d in in g ( i n s p = 2 . 2; 2; / / C ur A mp mp er er e p e r mm s q u a r e ) u r re r e nt n t d e n s i t y o f s e c on o n d a ry r y w i nd n d i ng ng ( i n s s = 2 . 1; 1; / / C ur A mp mp er er e p e r mm s q u a r e ) c e o f p ri r i ma m a ry r y i n d i n g ( i n ohm ) r p = 8 ; / / R e s i s t a n ce n c e l e ng n g t h o f m ea n t ur u r n o f p ri r i ma m a ry ry R 1 = 1 /1 / 1 .1 . 1 ; / / S i nc i s 1 0% th t h a n t ha h a t o f t he h e s ec e c on o n da d a ry ry i n ce ce r a t i o o f t ra ns fo rm at io n i s 1 0: 1 R 2 = 1 /1 /1 0; 0; / / S in // / / C a l c u l a t i o n o f t h e r e s i s t a n c e o f s ec e c on o n da d a ry ry winding i s t a n c e o f s ec e c on o n da da ry r s = R 2 * R2 R2 * ( ss s s / s p )* ) * R 1 * rp rp ; / / R e s is w i n d i n g ( oh ohm ) 43

12 disp (rs, ’ R e s i s t a n c e 13 / / i n b o o k a ns n s we we r i s

o f s e c on o n d a r y w in i n d iin n g ( oh ohm )= )= ’ ) ; 0 . 0 69 6 9 4 ohm . T h e a ns n s we w e rs r s v ar ar y due t o round o f f e r r o r

Scilab code Exa 5.13 Calculating the leakage leakage reactance of the transformer

referred to the HV side 1 / / C a l c u l a t i n g t he h e l e a k a g e r e a c t a nc n c e o f t he he

t r a n s f o r m e r r e f e r r e d t o t he he h . v . s i d e 2 3 4 5


/ / G iv i v en e n D at at a / / 6 60 6 0 0/ 0 / 4 00 0 0 V , d e l t a / s t a r 3− p ha h a se s e c o r e t yp yp e transformer 6 Q = 3 0 0 ; / / kV kVA r a t i n g 7 f = 5 0 ; / / F r eq e q u en e n c y ( i n Hz ) 8 9 10 11 12

u 0 = 4 * %p % p i * 10 1 0 ^( ^( - 7 ) ; di n g t u r n s T p = 8 3 0; 0; / / h . v w i n di e n gt g t h o f m e a n t u r n ( i n m et e t er er ) L mt m t = 0 .9 .9 ; / / L en e i gh g h t o f c o i l s ( i n m et e t er er ) L c = 0 . 5; 5; / / H ei t w e en e n h . v a nd nd l . v . a = 0 .0 .0 15 15 ; / / W i d t h o f d u c t b e tw

w i n d i n g s ( i n m et e t er er ) 13 b p = 0 .0 te r ) . 0 25 2 5 ; / / W i d t h o f h . v . w i n d i n g ( i n m e te 14 b s = 0 .0 d i n g ( i n m eett er er ) . 0 16 1 6 ; / / W i d t h o f l . v . w i n di 15 / / C a l c u l a t i o n o f t h e l e a k a g e r e a c t a nc nc e o f th e t r a n s f o r m e r r e f e r r e d t o t he he h . v . s i d e 16 X p = 2 * % pi p i * f * u 0 * T p * Tp T p * L m t / L c * ( a +( +( b p + b s ) / 3) 3) ; / / L e a k a ge g e r e a c t a nc n c e r e f e r r e d t o t he h e p ri r i ma m a ry ry s i d e ( ohm) 17 disp (Xp, ’ ( a ) L e a ka k a g e r e a ct c t a n ce c e r e f e r r e d t o t he he p r im i m a ry r y s i d e ( oh ohm )= )= ’ ) ; 18 / / I f t he h e l . v . w in i n di d i ng n g d i v i d ed e d i n t o t w o p ar a r ts ts , one o n e ac a c h s i d e o f h . v . w in i n di d i ng ng 44

19 X p = % p i * f * u0 ak a g e u0 * T p * T p * L mt m t / L c * ( a + ( bp b p + b s ) / 6 ) ; / / L e ak

r e a c t a nc n c e r e f e r r e d t o t he h e p ri r i ma m a ry r y s i d e ( oh ohm ) 20 disp (Xp, ’ ( b ) L e a ka k a g e r e a ct c t a n ce c e r e f e r r e d t o t he he p r im i m a ry r y s i d e ( oh ohm )= )= ’ ) ; 21 / / i n b oo o o k a n s w er e r s a r e 1 4 oh o hm a nd n d 5 . 3 6 ohm r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error

Scilab code Exa 5.14 Calculating the per unit leakage reactance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

/ / C a l c u l a t i n g t he h e p er e r u n i t l e a k a g e r e a c ta t a n ce ce clc ; x a mp mp l e 5 . 1 4 , P ag ag e No . = 5 . 9 0 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a // / / 2 00 0 0 0/ 0 / 40 4 0 0 V , s i n g l e p ha h a se s e s h e l l t yp y p e t r a n s f or or m er kVA r a t i n g Q = 1 0 0 ; / / kV e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq

u 0 = 4 * %p % p i * 10 1 0 ^( ^( - 7 ) ; di n g t u r n s T p = 2 0 0; 0; / / h . v w i n di e n gt g t h o f m e a n t u r n ( i n m et e t er er ) L mt m t = 1 .5 .5 ; / / L en d i n g ( i n m et e t er er ) W = 0 . 12 12 ; / / W i d t h o f w i n di t w e en e n h . v a nd nd l . v . a = 0 .0 .0 16 16 ; / / W i d t h o f d u c t b e tw

w i n d i n g s ( i n m et e t er er ) te r ) b p = 0 .0 .0 4; 4; / / W i d t h o f h . v . w i n d i n g ( i n m e te d i n g ( i n m et e t er er ) b s = 0 .0 . 0 36 3 6 ; / / W i d t h o f l . v . w i n di / / C a l c u l a t i o n o f t h e p er e r u n i t l e a k a g e r e a c ta t a n ce ce ka g e X p = % p i * f * u0 u0 * T p * T p / 2* 2 * L m t / W * ( a + ( bp b p + b s ) / 6 ) ; / / L e a ka r e a ct c t a n ce c e r e f e r r e d t o t he h e p ri r i ma m a ry r y s i d e ( oh ohm ) V . w in i n d in in g c u r r e n t a t f u l l I _h _ h v = Q * 1 0^ 0 ^ ( 3) 3) / 2 0 00 0 0 ; / / H . V. l o a d ( i n a mp m p er er e ) i t l e a k a g e r e a ct c t a n ce ce X p_ p _ pu p u = X p * I_ I _ hv h v / 2 0 00 0 0 ; / / P e r u n it g e r e a c t a nc n c e= e= ’ ) ; disp (Xp_pu, ’ P e r u n i t l e a k a ge / / i n b o o k a ns n s we w e r i s 0 . 0 3 5 3 . T h e a ns n s we w e rs r s v a ry ry d u e t o 45

round o f f e r r or

Scilab code Exa 5.16 Calculating the instantaneous radial force on the

HV winding if a short circuit occurs at the terminals of the LV winding with HV energised and the force at full load 1 / / C a l c u l a t i n g t he h e i n s t a n t a n eo eo u s r a d i a l

f o r c e on t h e h . v . w i n di d i n g i f a s h or o r t c i r c u i t o c c u r s a t t he he t e r m i n a l s o f t he h e l . v . w in i n di d i ng n g w it it h h . v . e n e r g i s e d a n d t he he f o r c e a t f u l l l o a d

2 3 4 5


/ / G iv i v en e n D at at a / / 6 60 6 0 0/ 0 / 4 00 0 0 V , d e l t a / s t a r 3− p ha h a se s e c o r e t yp yp e transformer 6 Q = 1 0 00 kVA r a t i n g 00 ; / / kV 7 f = 5 0 ; / / F r eq e q u en e n c y ( i n Hz ) 8 9 10 11 12 13 14 15 16 17 18

u 0 = 4 * %p % p i * 10 1 0 ^( ^( - 7 ) ; nd i n g t u r n s T = 5 0 0 ; / / h . v w i nd e n gt g t h o f m e a n t u r n ( i n m et e t er er ) L mt m t = 1 .3 .3 ; / / L en e i g ht h t o f w in i n d in i n g ( i n m et e t er er ) L c = 0 . 6; 6; / / H ei in g e f f e c t m u l t i p l i e r m = 1 . 8 ; / / D o u b l in

/ / C a l c u l a t i o n o f t h e p er e r u n i t l e a k a g e r e a c ta t a n ce ce o a d c u rr r r e n t p er er I _f _ f l = Q * 1 0 00 0 0 / (3 ( 3 * 66 6 6 0 0) 0 ) ; / / F u l l l oa p h a se se o n h . v . s i d e ( i n Ampere ) a n t a n eo e o u s p ea ea k i = m * 2 ^( ^ ( 1/ 1 / 2 ) * ( 1/ 1 / 0 .0 . 0 5 ) * I _f _f l ; / / I n s t an v a lu l u e o f s h o rt r t c i r c u i t c u r r e n t ( i n Ampere ) o t al a l i n s t a n t a n eo eo u s F r = u 0 / 2* 2* ( i *T * T ) ^ (2 ( 2 ) * Lm L m t / Lc L c ; / / T ot r a d i a l f o r c e on t h e h . v . c o i l ( i n N) o t al a l i n s ta t a n t a n e o us u s r a d i a l f o r c e o n t he he h . v disp (Fr, ’ T ot . c o i l (N)= ’ ) ; o r ce c e a t f u l l l o ad ad F r = u 0 / 2 *( *( I _ f l * T ) ^ ( 2) 2 ) * L m t / L c ; / / F or ( in N) 46

19 disp (Fr, ’ F o r ce ce a t f u l l l o a d (N)= ’ ) ; 20 disp ( ’ T h is i s s h o w s t ha h a t t he h e f o r c e s u n de d e r s h o rt rt

cir cui t c o n d i t i o n s a r e c o n s i d er e r a b l y l a r g e a s c om omp a r ed w i th th f o r c e s a t f u l l l o a d ’ ) 21 / / i n b oo oo k a n sw s w e rs r s a r e 2 33 3 3 00 0 0 00 0 0 ( N ) a n d 8 66 6 6 ( N ) . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 5.17 Calculating the instantaneous radial force and in-

stantaneous axial force on the HV winding under short circuit conditions 1 / / C a l c u l a t i n g t he h e i n s t a n t a n eo eo u s r a d i a l

f o r c e and i n s t a n t a ne n e o u s a x i a l f o r c e on t h hee h . v . w in i n di d i ng ng u n d e r s h or or t c i r c u i t c o n di t i on s

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17


/ / G iv i v en e n D at at a / / 7 50 5 0 0/ 0 / 43 4 3 5 V, V , s i n g l e p ha h a se s e c o re r e t yp y p e t r a n s f o r m er er kVA r a t i n g Q = 5 7 5 ; / / kV e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq

u 0 = 4 * %p % p i * 10 1 0 ^( ^( - 7 ) ; er u n i t i mp m p ed e d an a n ce ce Z _ pu p u = 0 .0 . 0 36 3 6 ; / / P er nd i n g t u r n s T = 1 9 0 ; / / h . v w i nd e n gt g t h o f m ea n t u r n ( i n m et e t er er ) L m t = 1 .2 . 2 5; 5 ; / / L en e i gh g h t o f c o i l s ( i n m et e t er er ) L c = 0 .3 .3 5; 5; / / H ei in g e f f e c t m u l t i p l i e r m = 1 . 8 ; / / D o u b l in c t ( i n m et e t er er ) a = 0 .0 .0 15 15 ; / / W i d t h o f d u ct te r ) b p = 0 .0 . 0 27 2 7 ; / / W i d t h o f h . v . w i n d i n g ( i n m e te d i n g ( i n m et e t er er ) b s = 0 .0 . 0 23 2 3 ; / / W i d t h o f l . v . w i n di c e t he h e h . v . w in i n di d i ng n g i s 5% s h o r t e r k = 0 . 05 05 ; / / S i n ce

t ha h a n t h e l . v . w i nd n d i ng n g a t o ne ne e n d 18 // / / C a l c u l a t i o n o f t h e i n st s t a nt n t a ne n e o us us r a d i a l f o r c e 19 I _f l u e o f f u l l l o ad a d c u r r e nt nt _ f l = Q * 1 0 00 0 0 / 75 7 5 0 0; 0; / / Rms v a lu ( in Am Ampe pere) re) 47

20 i = m * 2 ^( a n t a n eo e o u s p ea ea k ^ ( 1/ 1 / 2 ) * (1 ( 1 / Z _p _ p u ) * I_ I _ fl f l ; / / I n s t an 21 22

23 24

25 26 27

v a lu l u e o f s h o rt r t c i r c u i t c u r r e n t ( i n Ampere ) ne o us r a d i a l F r = u 0 /2 / 2 *( * ( i * T ) ^( ^ ( 2) 2 ) * L m t / Lc Lc ; / / I n s t a n t a ne f o r c e o n t he he h . v . c o i l ( i n N) n t a n e o us u s r a d i a l f o r c e o n t he he h . v . disp (Fr, ’ ( a ) I n s t a nt w i n d i n g ( N ) = ’ ) ; / / i n b o ok o k a ns n s we w e r i s 2 38 3 8 00 0 0 00 0 0 (N) . T h e a ns n s we w e rs r s v ar a r y d ue u e t o r o u nd nd o f f e r r o r // / / C a l c u l a t i o n o f t h e i n st s t a nt n t a ne n e o us us a x i a l f o r c e ta l F a = u 0 / 2* 2* k * ( i * T ) ^ ( 2) 2) * L m t / ( 2 * ( a + bp b p + b s ) ) ; / / T o ta i n st s t a nt n t a ne n e o us u s r a d i a l f o r c e o n t he he h . v . c o i l ( i n N ) a n t a n eo e o u s a x i a l f o r c e o n t he he h . v . disp (Fa, ’ ( b ) I n s t an w i n d i n g ( N )= ’ ) ; / / i n b o o k a ns n s we w e r i s 3 20 2 0 00 0 0 00 0 0 ( N ) . T h e p r ov o v i de de d i n t he h e t ex e x tb t b o ok ok i s wrong ha t t h e r e i s a v e r y l a r g e a x i a l disp ( ’ T h i s s h o w s t ha f o r c e , e v e n t h o u g h o n e o f t he h e w in i n di di n ngg i s o nl n l y 5% s h o r t e r t h a n t he h e o t he he r a t o n e end ’ )

Scilab code Exa 5.18 Calculating the maximum flux and no load current

of the transformer 1 / / C a l c u l a t i n g t h e ma maximum f l u x a n d n o l o a d c u r r e n t

o f t he h e t r a n s f or or m er 2 3 4 5 6 7


/ / G iv i v en e n D at at a r i ma m a ry r y w in i n di d i ng ng v o l t a g e ( i n v o l t s ) E p = 4 0 0; 0; / / P ri e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq A = 2 .5 . 5 *1 * 1 0^ 0^ ( - 3 ) ; / / A r e a o f c r o s s s e c t i o n ( i n m e t e r squ are ) 8 S f = 0 . 9; ng f a c t o r 9; / / S t a c k i ng 9 T p = 8 0 0; r i ma m a ry r y w in i n d in in g t u r n s 0; / / P ri 48

10 11 12 13

e n gt g t h o f t he h e f l u x p at a t h ( i n m et e t er er ) l i = 2 . 5; 5; / / L en p a ce ce u 0 = 4 * %p % p i * 10 1 0 ^( ^ ( - 7 ) ; / / P e r m e a b i l i t y o f f r e e s pa u r = 1 00 00 0; 0; / / R e l a t i v e e r m e a b i l i t y e n si s i ty t y o f i r o n ( i n k g p er er m e t e r D = 7 .8 . 8 *1 * 1 0^ 0 ^ (3 ( 3 ) ; / / D en cub e )

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

F D_ D_ w = 2 .6 .6 ; / / W o r k i n g f l u x

d e n s i t y ( i n W p er er kg ) / / C a l c u l a t i o n o f t h e ma maximum f l u x e a ( i n m et e t er e r s q ua ua r e ) A i = S f *A * A ; / / N e t i r o n a r ea Maximum f l u x d e n s i t y o f B m = E p / (4 ( 4 .4 . 4 4 * f * Ai Ai * T p ); ) ; / / Ma c o r e ( i n Wb p e r m et e t er er s q u a r e ) Wb) F m = B m * Ai Ai ; / / Maximum f l u x i n t h e c o r e ( i n Wb Maximum f l u x i n t h e c o r e (Wb) = ’ ) ; disp (Fm, ’ Ma / / C a l c u l a t i o n o f t h e n o l oa oa d c ur re nt e t i c mmf ( i n A ) A T0 T0 = l i /( /( u r * u0 u0 ) * Bm B m ; / / M a g n et g n et e t i si s i n g c u r r e nt n t ( i n A) I m = A T0 T 0 / ( 2 ^( ^ ( 1 /2 /2 ) * T p ); ) ; / / M a gn e t er e r c ub ub e ) V = A i * li li ; / / V o l u m e o f t h e c o r e ( i n m et W = V * D ;/ / Weight o f c o r e ( i n kg ) P i = W * FD F D _w _w ; / / I r o n l o s s ( i n W) o s s c o m p o n e n t o f n o l o ad a d c u r r e nt nt ( i n I l = P i / Ep Ep ; / / L os A) a d c u r r e nt n t ( i n A) I 0 = ( I m * Im Im + I l * I l ) ^ ( 1/ 1 / 2 ) ; / / No l o ad No l o a d c u r r e n t ( A mp mp e r e )= )= ’ ) ; disp (I0, ’ No / / i n b oo o o k a n s w er e r s a r e 0 . 0 0 2 2 5 (Wb) a n d 1 . 7 7 ( Am A mpere ) r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f error

Scilab code Exa 5.20 Calculating the number of turns and no load current

1 / / C a l c u l a t i n g t he h e n u m b e r o f t u rn r n s a n d n o l o ad ad

current 2 clc ; 3 disp ( ’ E xa x a mp mp l e 5 . 2 0 , P ag ag e No . = 5 . 1 0 1 ’ ) 4 / / G iv i v en e n D at at a

49

5 E = 6 6 00 r i ma m a ry r y w in i n di d i ng ng v o l t a g e ( i n v o l t s ) 00 ; / / P ri 6 f = 6 0 ; / / F r eq e q u en e n c y ( i n Hz ) 7 A i = 2 2. 2 . 6 *1 *1 0^ 0^ ( - 3 ) ; / / A r e a o f c r o s s s e c t i o n ( i n m e t e r 8 9 10 11 12 13 14 15 16 17 18 19 20 21

22 23 24 25 26 27 28 29 30

squa re ) Wb p e r B m = 1 . 1; 1; / / Maximum f l u x d e n s i t y o f c o r e ( i n Wb m e te te r s q u a r e ) m p li l i tu t u de de f a c t o r A f = 1 .5 .5 2; 2; / / A mp r i ma m a ry r y w in i n d in in g t u r n s T p = 8 0 0; 0; / / P ri e t er er ) l = 2 . 23 23 ; / / Mean l e n g t h ( i n m et e t er e r ( i n A p e r m et e t er er ) m m f = 2 32 32 ; / / mmf p e r m et N umber o f l a p j o i n t s n = 4 ; / / Nu G s = 7 . 5* 5* 1 0^ 0 ^ ( 3) 3) ; / / S p e c i f i c g r a v i t y o f p l a t e s L s = 1 .7 .7 6; 6; / / S p e c i f i c l o s s ( i n W p e r k g ) / / C a l c u l a t i o n o f t he he number o f t u r n s T p = E / ( 4. 4 . 44 4 4 * f * Ai A i * B m ); ) ; / / Nu m b er o f t u r n s disp (Tp, ’ ( a ) N u m b er o f t u r n s = ’ ) ; / / C a l c u l a t i o n o f t h e n o l oa oa d c ur re nt Mmf r e q u i r e d f o r i r o n p a r t s m m f _ ir ir o n = m mf mf * l ; / / Mm Mmf r e q u i r e d f o r j o i n t s . m m f _ j oi oi n t s = 4 * (1 ( 1 / 4 ) * m mf m f ; / / Mm S i n ce c e l ap a p j o i n t s t a k e s 1 / 4 t im i m es e s r e a c t i v e mm mmf a s r e q u i r e d p er er m e t e r o f c o r e t a l m a g n e ti t i s i n g mmf ( A T 0 = m m f _i _i r o n + m m f _ j oi oi n t s ; / / T o ta in A) K p k = A f * 2^ 2 ^ (1 ( 1 / 2) 2) ; / / P e a k f a c t o r a g n et e t i si si n g c u r r e n t ( i n A) I m = A T0 T 0 / ( K pk pk * T p ); ) ; / / M ag W = A i * l* l * Gs Gs ; / / W e i g h t o f c o r e ( i n k g ) P i = L s *W * W ; / / I r o n l o s s ( i n W) o s s c o m p o n e n t o f n o l o ad a d c u r r e nt nt ( i n A I l = P i /E / E ; / / L os ) a d c u r r e nt n t ( i n A) I 0 = ( I m * Im Im + I l * I l ) ^ ( 1/ 1 / 2 ) ; / / No l o ad mp e r e )= )= ’ ) ; disp (I0, ’ ( b ) No l o a d c u r r e n t ( A mp / / i n b oo oo k a n sw s w e rs r s a r e 1 10 10 0 a nd 0 . 3 3 3 (A) r e s p e c t i v e l y . T h e p ro r o vi v i de d e d i n t h e t ex e x tb t b oo oo k i s wrong

50

Chapter 6 General Concepts and Constraints in Design of Rotating Machines

Scilab code Exa 6.1 Calculating the specific electric and specific magnetic

loading 1 // Ca lc ul at in g the

specific

e l e c t r i c and s p e c i f i c

m a gn g n et et i c l o a d i n g 2 3 4 5 6 7 8 9 10 11 12 13


/ / G iv i v en e n D at at a P = 3 5 0 ; / / P o w e r r a t i n g ( i n kW) t a g e ( i n V) E = 5 0 0 ; / / V o l ta

r pm pm p = a = Z = L = D =

= 4 50 50 ; N umber o f p o l e s 6 ; / / Nu c e a=p f o r l a p w in i n di d i ng ng 6 ; / / S i n ce 6 6 0 ; / / Number o f c o n d u c t o r s o r e l e n g t h ( i n m et e t er er ) 0 . 32 32 ; / / C or rm at a t ur ur e d i a m e t e r ( i n m et e t er er ) 0 . 87 87 ; / / A rm

// Calc ula tion of the s p e c i f i c 51

e l e c t r i c load ing

14 15 16 17

at u r e c u r r e n t ( i n A ) I a = P * 10 1 0 00 0 0 / E; E ; / / A r m at u r re r e nt n t i n e ac a c h c on o n d uc u c to to r ( i n A ) I z = I a /a / a ; / / C ur a c = I z *Z * Z / ( %p % p i * D) D) ; / / S p e c i f i c e l e c t r i c l o a d i n g p e re re disp (ac, ’ S p e c i f i c e l e c t r i c l o a d i n g ( a m pe c o n d u c t o r s p e r m et e t er e r )= ’ ) ;

/ / C a l c u l a t i o n o f t h e s p e c i f i c m a gn g n e ti ti c l o a d i n g l u x p e r p o l e ( i n Wb Wb) F = E * a /( /( Z * r pm pm / 6 0* 0 * p ) ; / / F lu B ac ac = p * F /( /( % p i *D * D * L ); ); / / s p e c i f i c m a g n e t i c l o a d i n g a g ne n e ti t i c l o a d i n g (Wb p eerr m et e t er er disp (Bac, ’ S p e c i f i c m ag s q u a r e )= )= ’ ) ; 22 / / i n b oo oo k a n sw s w e rs r s a r e 2 82 8 2 00 0 0 ( a mp m p e r e c o n d u c to to r s p e r m et e t er e r ) a n d 0 . 6 9 3 (Wb p e r m et e t er er s q u a r e ) r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error 18 19 20 21

Scilab code Exa 6.5 Calculating the power developed by the armature of

motor 1 / / C a l c u l a t i n g t he h e p o w e r d e ve v e lo l o p ed e d b y t he h e a rm r m at a t ur ur e

o f m ot o t or or 2 3 4 5 6 7 8


/ / G iv i v en e n D at at a W) P = 1 2 5 ; / / P o w e r r a t i n g ( i n W) t a g e ( i n V) E = 2 3 0 ; / / V o l ta r p m = 5 00 0 0 0; 0;

/ / C a l c u l a t i o n o f t he h e p o w e r d ev e v el e l o p ed e d b y t he he armature 9 L o ss o t al a l l o s s e s ( i n W) s s e s_ s _ t ot o t a l = P ; / / T ot 10 L o ss o n st s t an a n t l o s s e s ( i n W) W) . s s e s_ s _ c on o n s ta t a n t = P / 3; 3 ; / / C on S i n c e t h e sum o f i r o n , f r i c t i o n a nd nd w i nd nd a g e l o s s e s i s a pp p p ro r o xi x i ma m a te t e l y 1 /3 /3 o f t o t a l l o s s e s 11 P a = L o s s es es _ t o ta ta l + L o s s e s _ c o ns ns t a n t ; / / P o w e r d e v e l o p e d 52

b y t h e a r ma m a t ur u r e ( i n W) W) 12 disp (Pa, ’ P o we we r d e v e l o p e d b y t h e a r m a t ur u r e (W) = ’ ) ; 13 / / i n b oo oo k a ns n s we w e r i s 1 67 6 7 (W) . T h e a n sw s w e rs r s v ar ar y due to round o f f e r r o r

Scilab code Exa 6.6 Calculating the limiting value of specific magnetic

loading 1 / / C a l c u l a t i n g t he he l i m i t i n g

v a lu lu e o f s p e c i f i c

m a gn g n et et i c l o a d i n g 2 3 4 5 6 7 8 9 10 11


/ / G iv i v en e n D at at a r m at a t ur ur e ( i n B t = 2 . 0; 0; / / Maximum f l u x d e n s i t y i n t h e a rm Wb p e r m et e t er er s q u a r e ) rc t o p o l e p i t c h R = 0 . 7 ; / / R a t i o o f p o l e a rc t i o o f mi n im um w id i d th t h o f t o o th th t o W t_ t _ ys y s = 0 .4 .4 ; / / R a ti s l o t p it ch / / C a l c u l a t i o n o f t he h e l i m i t i n g v a lu lu e o f s p e c i f i c m a gn g n et et i c l o a d i n g B a v = R * W t_ t _ ys ys * B t ; / / L i m i t i n g v a l u e o f s p e c i f i c m a gn g n et e t i c l o a d i n g ( i n W pe p e r m et e t er e r s q u a re re ) disp (Bav, ’ L i m i t i n g v a l u e o f s p e c i f i c m a g n e t i c l o a d i n g (W pe p e r m et e t er e r s q u a r e )= ’ ) ; / / i n b o o k a ns n s we w e r i s 0 . 5 6 (W p er e r m et e t er e r s q ua u a r e ) . Th e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Scilab code Exa 6.8 Calculating the maximum permissible specific elec-

tric loading 53

1 // Calc ula ting

t h e maximum p e r m i s s i b l e e l e c t r i c l oa di ng

2 3 4 5 6

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

s p ec i f i c


/ / G iv i v en e n D at at a p _2 _ 2 0 = 1 . 73 73 4* 4 * 10 1 0 ^ ( - 8) 8) ; / / R e s i s t i v i t y o f c o p p e r a t 2 0

d e g r e e c e l s i u s ( i n ohm ∗ met er ) n c e t em e m p er e r at a t u re re co − a lp l p ha h a = 0 .0 . 0 0 39 3 9 3; 3 ; / / R e s i s t a nc e f f i c i e n t o f c op o p pe p e r a t 2 0 d e g re r e e c e l s i u s ( i n p er er d eg e g re re e c e l s i u s ) u r r en e n t d e n s i t y ( i n A p e r mm mm s q u a re re ) s = 3 . 5 ; / / C ur o l i ng ng co− e f f i c i e n t c = 0 . 03 03 ; / / C o ol nt t e m p e r a t u r e ( i n T m _a _a m bi b i e nt n t = 4 0; 0 ; / / Maximum a m b i e nt d eg e g re re e c e l s i u s ) Maximum t e m pe p e r a tu tu r e r i s e f o r C l a s s T m _ r is is e _A _ A = 5 0; 0; / / Ma A i n s u l a t i o n ( i n d eg e g re re e c e l s i u s ) Maximum t e m pe p e r a tu tu r e r i s e f o r C l a s s T m _ r is is e _E _ E = 6 5; 5; / / Ma E i n s u l a t i o n ( i n d eg e g re re e c e l s i u s ) / / C a l c u l a t i o n o f t h e maximum p e r m i s s i b l e s p e c i f i c e l e c t r i c l oa di ng // f o r C la s s A i n s u l a t i o n e r a ti t i n g t e mp m p e r at at u r e T _ A = T m _ am a m b i e nt nt + T m _ ri r i s e _A _ A ; / / O p er o f c op o p pe p e r c o n d u c to to r s ( i n d e g r e e c e l s i u s ) p = p _ 20 20 * ( 1 + a l p ha h a * ( T _A _ A - 2 0) 0) ) ; / / R e s i s t i v i t y a t o p e r a t i n g t e mp m p e r at a t u r e ( i n ohm ∗ met er ) a c = T m _ ri r i s e _A _ A / ( p * s * 1 0 ^ (6 ( 6 ) * c ) ; / / Maximum p e r m i s s i b l e s p e c i f i c e l e c t r i c l oa di ng Maximum a l l o w a b l e s p e c i f i c e l e c t r i c l o a d i n g disp (ac, ’ Ma ( a mp m p er er e c o n d u c t o r s p e r m et e t er e r )= ’ ) ; e r a ti t i n g t e mp m p e r at at u r e T _ E = T m _ am a m b i e nt nt + T m _ ri r i s e _E _ E ; / / O p er o f c op o p pe p e r c o n d u c to to r s ( i n d e g r e e c e l s i u s ) / / f o r C la la ss E i n s u l a t i o n p = p _ 20 20 * ( 1 + a l p ha h a * ( T _E _ E - 2 0) 0) ) ; / / R e s i s t i v i t y a t o p e r a t i n g t e mp m p e r at a t u r e ( i n ohm ∗ met er ) a c = T m _ ri r i s e _E _ E / ( p * s * 1 0 ^ (6 ( 6 ) * c ) ; / / Maximum p e r m i s s i b l e s p e c i f i c e l e c t r i c l oa di ng Maximum a l l o w a b l e s p e c i f i c e l e c t r i c l o a d i n g disp (ac, ’ Ma ( a mp m p er er e c o n d u c t o r s p e r m et e t er e r )= ’ ) ; 54

23 / / i n b oo oo k a n sw s w e rs r s a r e 2 16 1 6 00 0 0 ( a mp m p e r e c o n d u c to to r s p e r

m et e t er e r ) a n d 2 6 70 7 0 0 ( a m pe p e re re c o n d u c t o r s p e r m et e t er er ) r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error

Scilab code Exa 6.9 Calculating the specific electric loading

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

// Cal cul ati ng the s p e c i f i c

e l e c t r i c loa din g


/ / G iv i v en e n D at at a W) P c = 1 00 00 0; 0; / / C o r e l o s s ( i n W) rm a tu tu re re r e s i s t a n c e ( i n ohm ) R = 0 .0 .0 25 25 ; / / A rm l = 230; / / S p e c i f i c l o s s d i s s i p a t i o n ( i n W p e r d e g r e e c e l s i u s p er e r m et et e r s q u a r e ) n c e a=z f o r l a p w in i n di d i ng ng a = 2 ; / / S i nc Z = 2 7 0 ; / / Number o f c o n d u c t o r s o r e l e n g t h ( i n m et e t er er ) L = 0 . 25 25 ; / / C or rm at a t ur ur e d i a m e t e r ( i n m et e t er er ) D = 0 . 25 25 ; / / A rm p e r at a t ur u r e r i s e ( d e g re re e c e l s i u s ) T = 4 0 ; / / T e m pe // Calc ula tion of the s p e c i f i c e l e c t r i c load ing o l i ng ng co− e f f i c i e n t c = 1 / l; l ; / / C o ol qu ar e ) S = % pi pi * D *L * L ; / / D i s s i p a t i o n s u r f a c e ( i n m e t e r s qu Maximum a l l o w a b l e p w e r d i s s i p a t i o n f ro ro m Q = S *T * T /c / c ; / / Ma a rm r m at a t ur ur e s u r f a c e r m at a t ur u r e c u r r e n t ( i n A m p er e I a = ( (Q ( Q - P c )/ ) / R ) ^ (1 (1 / 2) 2) ; / / A rm ) u r re r e nt n t i n e ac a c h c on o n d uc u c to to r ( i n A ) I z = I a /a / a ; / / C ur a c = I z *Z * Z / ( %p % p i * D) D) ; / / S p e c i f i c e l e c t r i c l o a d i n g p e re re disp (ac, ’ S p e c i f i c e l e c t r i c l o a d i n g ( a m pe c o n d u c t o r s p e r m et e t er e r )= ’ ) ; / / i n b oo oo k a ns n s we w e r i s 3 10 1 0 00 0 0 ( a mp m p er er e c o n d u c to to r s p e r m et e t er e r ) . Th e a ns n s we w e rs r s v ar a r y d u e t o r o un un d o f f e r r o r 55

56

Chapter 7 Armature Windings

Scilab code Exa 7.33 Calculating the rms line voltage and circulating cur-

rent 1 / / C a l c u l a t i n g t he he rms l i n e

v o l t a g e and c i r c u l a t i n g

current 2 3 4 5 6 7 8 9 10 11 12


/ / G iv i v en e n D at at a m p li l i tu t u de d e o f f u n da d a m e nt nt a l em f ( i n V) E = 1 0 00 00 ; / / A mp e a ct c t a nc n c e p e r p ha h a s e ( i n ohm ) R = 1 0 ; / / R ea / / C a l c u l a t i o n o f t h e rm r ms l i n e v o l t a g e and c i r c u l a t i n g c ur re nt R ms v a l u e o f f u nd n d a me m e nt nt a l emf p e r E p h1 h 1 = E / 2 ^( ^ ( 1 /2 /2 ) ; / / Rm phase Rms v a l u e o f 3 r d h ar a r mo m o ni ni c E p h3 h 3 = 0 .2 . 2 * E ph p h 1 ; / / Rm c o mp m p o ne n e n t o f p ha h a se s e v o l t a g e ( i n V) V ) G iv i v en en 2 0% 0% Rms v a l u e o f 5 t h h ar a r mo m o ni ni c E p h5 h 5 = 0 .1 . 1 * E ph p h 1 ; / / Rm c o mp m p o ne n e n t o f p ha h a se s e v o l t a g e ( i n V) V ) G iv i v en en 1 0% 0% E p h = ( E p h 1 * E p h1 h1 + E p h 5 * E p h5 h5 ) ^ ( 1 / 2 ) ; / / P h a s e v o l t a g e c o n s i d e r i n g n o 3 r d h ar a r mo m o ni ni c disp (3^(1/2)*Eph, ’ ( a ) r m s l i n e v o l t a g e w h e n s t a r 57

c o n n e c t e d ( V )= ’ ) ; 13 disp (Eph, ’ ( b ) r m s l i n e v o l t a g e w h e n d e l t a c o n nn n eecc t ed ed (V)=’ ) ; 14 I _ c i r c u la l a t i n g = 3 * E p h3 h3 / ( 3 * 3 * 1 0) 0) ; / / C i r c u l a t i n g c u r r e n t t a ki k i n g r e a c t a nc n c e c o r r e sp s p o n di di n g t o 3 r d harmonic 15 disp (I_circu lating , ’ C i r c u l a t i n g c u r r e nt n t ( a mp m p e r e )= )= ’ ); 16 / / i n b o o k a ns n s we w e rs r s a r e 1 2 3 0. 0 . 8 V , 7 1 0 . 6 v and 4 . 7 1 a m p e r e r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar a r y d ue ue t o round o f f e r r o r

Scilab code Exa 7.41 Calculating the eddy current loss ratio and average

loss ratio and critical depth for minimum loss 1 / / C a l c u l a t i n g t he he e d d y c u r r e n t

average lo ss loss 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

l o s s r a t i o and r a t i o a n d c r i t i c a l d ep e p th t h f o r mi n im um

clc ; x a mp mp l e 7 . 4 1 , P ag ag e No . = 7 . 1 0 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a i d t h ( i n mm mm) W s = 2 0 ; / / S l o t w id e r c o n d u c t o r s ( i n mm mm) b = 1 4 ; / / W i d t h o f c o p p er ep th th o f c o p p er e r c o n d u c t o r s ( i n mm mm) h = 8 ; / / D ep r e q ue u e n cy c y ( i n Hz ) f = 5 0 / / F re N umber o f l a y e r s N = 5 ; / / Nu // // C a l c u l a t i o n o f e ddy l o s s f a c t o r f o r d i f f e r e n t layers

a = 1 00 0 0 *( * ( b / W s ) ^( ^ ( 1/ 1 / 2) 2) ; a h = a * h *1 * 1 0^ 0 ^ ( - 3) 3) ; a h 4 = a h ^ (4 (4 ) ; K e1 e1 = 1; / / 1 s t l a y e r nd l a y e r K e2 e2 = 1 + ah a h 4 * 2* 2* (2 ( 2 - 1 ) / 3; 3 ; / / 2 nd d l a y er K e3 e3 = 1 + ah a h 4 * 3* 3* (3 ( 3 - 1 ) / 3; 3 ; / / 3 rrd

58

17 18 19 20 21 22 23 24

th l a y er K e4 e4 = 1 + ah a h 4 * 4* 4* (4 ( 4 - 1 ) / 3; 3 ; / / 4 th th l a y er K e5 e5 = 1 + ah a h 4 * 5* 5* (5 ( 5 - 1 ) / 3; 3 ; / / 5 th Ke1 = ’ ) ; disp (Ke1, ’ 1 s t l a y e r Ke2 = ’ ) ; disp (Ke2, ’ 2 n d l a y e r K e3 = ’ ) ; disp (Ke3, ’ 3 r d l a y e r K e4 = ’ ) ; disp (Ke4, ’ 4 t h l a y e r K e5 = ’ ) ; disp (Ke5, ’ 5 t h l a y e r

/ / C a l c u l a t i o n o f a ve v e ra r a ge g e e d d y c u rr rr en t l o s s f a c t o r f or a l l the f iv e l ay er s

25 K e_ e _ av a v = 1 + ah a h 4 * N* N * N / 9; 9; 26 disp (Ke_av, ’ A v e r a g e e d d y c u r r e n t l o s s f a c t o r f o r a l l the f i v e l a ye rs = ’ ); 27 / / C a l c u l a t i o n o f c r i t i c a l d ep e p th t h f o r m in im u m l o s s 28 h c = 1 / ( a * (3 ( 3 * N * N / 9) 9) ^ ( 1 / 4 ) ) * 1 0 00 00 ; / / C r i t i c a l d e p t h (

i n mm) 29 disp (hc, ’ C r i t i c a l d ep e p th t h (mm) = ’ ) ; 30 / / C a l c u l a t i o n o f a ve v e ra r a ge g e e d d y c u rr rr en t l o s s f a c t o r f o r a l l t he he f i v e l a y e r s f o r t h i s c r i t i c a l d e p t h 31 32 33 34

a h c = a * hc h c * 1 0^ 0^ ( - 3) 3) ; a h c4 c 4 = a hc hc ^ ( 4) 4) ; K e_ e _ av a v = 1 + ah a h c4 c 4 * N * N /9 /9 ; disp (Ke_av, ’ A v e r a g e e d d y c u r r e n t t h i s c r i t i c a l d e p t h= h= ’ ) ;

35 / / i n b o o k a ns n s we w e rs rs a r e 1 , 1 . 1 3 ,

loss

factor for

1.4 , 1.8 , 2.33 , 1.55 , 7 mm a n d 1 . 3 3 r e s p e c t i v e l y . T h e a n nss we w e rs r s v ar ar y due t o round o f f e r r o r

59

Chapter 8 Aspects of Design of Mechanical Parts

Scilab code Exa 8.2 Calculating the stress on the ring

1 2 3 4 5 6 7 8 9

// / / C a l c u l a t i n g t he h e s t r e s s o n t h e r i ng ng clc ; x a mp mp l e 8 . 2 , P ag ag e No . = 8 . 8 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e e d i n r . p . m. m. r p m = 3 00 0 0 0; 0 ; / / S p ee a d iu i u s o f o ve v e rh r h an a n g ( i n m et e t er er ) R m = 0 .3 .3 5; 5; / / R ad a d iu i u s o f r i n g ( i n m et e t er er ) R m r = 0 .4 . 4 9; 9 ; / / R ad o p pe p e r w in i n di d i ng ng ( i n kg ) G = 3 0 0 ; / / W e i g h t o f c op e n si s i ty t y o f r i n g m a t e r i a l ( i n k g p er er g r = 7 80 80 0; 0; / / D en meter cube ) re a o f r e t a i n i n g r i n g t b = 3 5 0* 0* 4 5* 5* 1 0^ 0^ ( - 6 ) ; / / A re / / C a l c u l a t i o n o f t h e s t r e s s on t h e r i n g ee d i n r . p . s n = r p m / 60 6 0 ; / / S p ee i a me m e te t e r o f o ve v e rh r h a ng n g ( i n m et e t er er ) D m = 2 * Rm R m ; / / D ia i a me m e te t e r o f r i n g ( i n m et e t er er ) D m r = 2 * R mr m r ; / / D ia

10 11 12 13 14 15 f t = ( % p i * n * n * G* G * D m / t b ) +( +( % p i * % p i * n * n* n * g r * D mr mr * D m r ) ; / /

S t r e s s o n r i n g ( i n N e w t o n p er e r m et e t er e r s q ua ua r e ) 60

16 disp (ft, ’ S t r e s s o n r i n g ( Ne N e w t o n p e r m et e t er e r s q u a re r e )= ’ ) ; 17 / / i n b oo oo k a ns n s we w e r i s 2 8 9 . 5 (MN p e r m et e t er e r s q u a re re ) .

T h e a ns n s we w e rs r s v ar a r y d ue u e t o r o u nd nd o f f

error

Scilab code Exa 8.4 Calculating the tensile stress and factor of safety

1 // // C a l c u l a t i n g t h e

tensile

s t r e s s and f a c t o r o f

safety 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


/ / G iv i v en e n D at at a e e d i n r . p . m. m. r p m = 3 00 0 0 0; 0 ; / / S p ee i a me m e te te r o f r o t o r ( i n meter ) D r 1 = 1 .1 . 1 5; 5 ; / / O u t e r d ia N umber o f r o t o r s l o t N rs r s = 3 9 ; / / Nu mm) D rs r s = 1 40 40 ; / / D e p t h o f r o t o r s l o t ( i n mm mm) W rs r s = 4 5 ; / / W i d t h o f r o t o r s l o t ( i n mm e n si s i ty t y o f s t e e l ( i n k g p er e r m et et e r c u b e ) g s = 7 80 80 0; 0; / / D en y i e l d _ st s t r e s s = 5 2 0 *1 * 1 0 ^ (6 (6 ) ; / / Y i e l d s t r e s s o f r o t o r s t e e l ( i n N e w t o n p e r m et e t er e r s q u a re re ) / / C a l c u l a t i o n o f t h e t e n s i l e s t r e s s and f a c t o r o f safety ee d i n r . p . s n = r p m / 60 6 0 ; / / S p ee a m e t e r o f r o t o r a t t he he D r2 r2 = D r1 r1 - 2* 2* D r s * 10 10 ^( ^ ( - 3 ) ; / / D i am b o t t o m o f s l o t s ( i n m et e t er er ) ot h a t t = ( % pi p i * D r2 r 2 * 1 0 ^( ^ ( 3 ) / Nr N r s ) - Wr Wr s ; / / W i d t h o f t o ot t h e b ot o t t o m o f s l o t ( i n mm mm) n g le l e s ub u b te t e nd n d ed e d b y e ac ac h s l o t ( i n a l p ha h a = 3 60 6 0 / N rs rs ; / / A ng deg ree )

17 f = % pi pi ^ ( 3 ) / ( 3 * t * 10 1 0 ^ ( - 3 ) ) * gs g s * n * n * ( a l ph p h a / 3 6 0 ) * ( D r1 r1 er ^(3)-Dr2^(3)); / / T e n s i l e s t r e s s ( i n N e w t o n p er

m e te te r s q u a r e ) 18 disp ( f , ’ T e n s i l e s t r e s s a t t h e r o o t o f t h e t ee ee th a t 61

n or o r ma m a l o p e r a t i n g s p e ed e d ( N ew ew t o n p e r m et e t er e r s q u a r e )= ’ ); 19 f _ 20 o v er e r s pe pe e d 2 0 = 1 . 2^ 2^ (2 ( 2 ) * f ; / / T e n s i l e s t r e s s a t 2 0% ov . S i n c e c e n t ri f u g a l f or ce i s p ro pa rt io na l o f s q u a r e o f s pe p e ed ed 20 disp (yield_stress/f_20, ’ F ac a c to t o r o f s a f e t y a t 2 0% o v er er s p e e d = ’ ); 21 / / i n b oo o o k a n s w er e r s a r e 1 78 7 8 ( Me M eg a N e w t o n p e r m et e t er er s q u a r e ) a n d 2 . 0 3 r e s p e c t i v e l y . T h e a ns n s we w e rs r s v a ry ry due t o round o f f e r r o r

Scilab code Exa 8.5 Calculating the inertia constant of the generator

1 2 3 4 5 6 7 8 9 10 11 12 13 14

// / / C a l c u l a t i n g t he h e i n e r t i a c o n s t a n t o f t h e g e ne n e r a t or or clc ; x a mp mp l e 8 . 5 , P ag ag e No . = 8 . 1 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a ow er er r a t i n g ( i n MW) P = 5 0 0 ; / / P ow e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq J = 5 0* 0 * 10 1 0 ^( ^ ( 3) 3 ) ; / / Mo me nt o f i n e r t i a ( i n k g − m e t e r squ are ) ow e r f a c t o r p f = 0 .8 .8 5; 5; / / P ow / / C a l c u l a t i o n o f t h e i n e r t i a c on o n st s t an an t o f t he generator n g ul u l ar a r s p ee e e d ( i n r ad ad / s ) w = 2 * % pi p i * f; f ; / / A ng kVA r a t i n g Q = 5 0 0* 0 * 1 0^ 0 ^ ( 3) 3) / p f ; / / kV H = ( 1/ 1 / 2) 2 ) * J * w *w * w / ( Q *1 * 1 0^ 0 ^ ( 3) 3) ) ; / / I n e r t i a c o n s t a n t ( i n second s ) n d s )= ’ ) ; disp ( H , ’ I n e r t i a c o n s t a n t ( s e c o nd / / i n b o o k a ns n s we w e r i s 4 . 2 s e co c o n d s . T h e a ns n s we w e rs r s v ar ar y due t o round o f f e r r o r

62

Chapter 9 DC Machines

Scilab code Exa 9.7 Calculating the maximum permissible core length for

the machine 1 / / C a l c u l a t i n g t he h e maximum p e r m i s s i b l e

core length

f o r t h e m ac a c h in in e 2 3 4 5 6 7 8 9 10 11 12


/ / G iv i v en e n D at at a F o rm f a c t o r K f = 0 .6 .6 7; 7; / / Fo a p d e n s i t y ( i n Wb p e r m e te te r B g = 1 ; / / Maximum g ap squ are ) tu re re p e r i p h e r a l s p ee e e d ( i n m et e t er er ) V a = 4 0 ; / / A r m a tu Maximum p e r m i s s i b l e v a l u e o f e m f i n du d u c ed ed i n E = 7 ; / / Ma a c o nd n d u ct c t o r a t n o l o ad a d ( i n V o lt lt s ) / / C a l c u l a t i o n o f t he h e ma m aximum p e r m i s s i b l e c o r e l e n g t h f o r t he h e m a ch c h in in e v e ra r a ge g e g a p d e n s i t y ( i n Wb Wb p e r m et e t er er B a v = K f * Bg B g ; / / A ve squ are ) Maximum p e r m i s s i b l e c o r e l e n g t h ( L = E /( / ( B av av * Va V a ) ; / / Ma i n m e te te r ) Maximum p e r m i s s i b l e c o r e l e n g t h ( m et e t er e r )= ’ ) ; disp ( L , ’ Ma 63

13 / / i n b oo oo k a ns n s we we r i s

0 . 2 6 ( m et e t er er ) . due t o round o f f e r r o r

T h e a n sw s w er e r s v ar ar y

Scilab code Exa 9.8 Calculating the maximum permissible output from a

machine 1 / / C a l c u l a t i n g t h e ma maximum p e r m i s s i b l e o ut u t pu p u t f ro ro m a

machine 2 3 4 5 6 7 8 9 10 11


/ / G iv i v en e n D at at a a m et e t er e r ( i n m et e t er er ) D = 2 ; / / D i am a c = 5 00 0 0 00 00 ; / / S p e c i f i c e l e c t r i c l o a d i n g n e r a t ed e d i n a c on o n du d u ct c t or or a t no l o a d e z = 7 . 5; 5; / / e m f g e ne ( in Volts ) / / C a l c u l a t i o n o f t h e ma maximum p e r m i s s i b l e o ut u t p ut ut f ro r o m a m ac a c hi h i ne ne P = % pi pi * D * ac a c * e z *1 * 1 0^ 0 ^ ( - 3) 3 ) ; / / Maximum p e r m i s s i b l e o u t p u t ( i n kW) Maximum p e r m i s s i b l e o u t p u t (kW) = ’ ) ; disp ( P , ’ Ma / / i n b oo oo k a ns n s we w e r i s 2 35 3 5 0 (kW) . T h e a n sw s w er e r s v ar a r y d ue ue t o r ou ou n d o f f e r r o r

Scilab code Exa 9.9 Calculating the number of extra shunt field turns to

neutralize the demagnetization 1 / / C a l c u l a t i n g t he h e n u m b e r o f e x t ra r a s hu h u nt nt

t o n e u t r a l i z e t he h e d e m a gn g n e ti t i z a t io io n 2 clc ;

64

f i e l d t u rn rn s

3 4 5 6 7 8 9 10

11 12 13 14 15 16 17

18 19 20 21 22 23 24

25

x a mp mp l e 9 . 9 , P ag ag e No . = 9 . 3 8 ’ ) disp ( ’ E xa / / G iv i v en e n D at at a N umber o f p o l e s p = 4 ; / / Nu u r re r e nt n t s u p p l i e d b y g e n e r a to to r ( i n ampere I s = 1 4 0; 0; / / C ur ) um b e r o f a r ma m a t ur ur e c o n d u c t o r s Z = 4 8 0 ; / / N um n c e b r u s h e s a r e g i v e n an m e ch c h _ de d e g re r e e = 1 0; 0; / / S i nc a c tu t u a l l e a d o f 1 0 d eg e g re re e / / C a l c u l a t i o n o f t he h e e x tr t r a s hu h u nt n t f i e l d t u rn rn s t o n e u t r a l i z e t he h e d e m a g n et e t i z a t i on on at ur ur e c u r r e n t ( A ) . Since f i e l d I a = I s + 10 1 0 ; / / A r m at w in i n di d i ng n g i s s hu h u nt n t c on o n ne n e ct c t ed e d a n d t a ke k e s a c u r re re n t o f 1 0 a m pe p e re re ad ( i n a lp l p ha h a = p / 2* 2 * m e c h _d _ d e gr g r e e ; / / A n g l e o f l e ad e l e c t r i c a l d e g r ee ) disp ( ’ ( a ) Wave c o n n e c t e d ’ ) / / W i t h w av av e w in i n d in i n g n u m b e r o f p a r a l l e l p a th th s a = 2 // r m at a t ur u r e mm mmf p e r p o l e ( A ) A T a = I a *Z * Z / ( a *2 *2 * p ); ) ; / / A rm t i z i n g mmf p e r A T a d = A Ta Ta * 2 * a l p h a / 1 8 0; 0; ; / / D e m a g n e ti p o l e (A) r o s s m a g n et e t i z i ng n g mm m mf p e r p o l e ( A A T aq a q = A T a - A Ta T a d ; / / C ro ) t r a t u rn r n s r e q u i r e d o n t he he E x t r a _ tu tu r n s = A T ad ad / 1 0 ; / / E x tr s hu h u nt nt f i e l d . S i n c e f i e l d w in i n d in i n g i s s hu h u nt nt c on o n n ec e c te t e d a n d t a k es e s a c u r r e nt nt o f 10 ampere xtt ra r a t u rn r n s r e q u i r e d o n t he he s h hu u nt nt disp (Extra_turns , ’ E x f i e l d = ’ ); te d ’ ) disp ( ’ ( b ) L a p c o n n e c te / / W i t h l a p w in i n di d i ng n g n u m b e r o f p a r a l l e l p at a t hs hs a = p // r m at a t ur u r e mm mmf p e r p o l e ( A ) A T a = I a *Z * Z / ( a *2 *2 * p ); ) ; / / A rm t i z i n g mmf p e r A T a d = A Ta Ta * 2 * a l p h a / 1 8 0; 0; ; / / D e m a g n e ti p o l e (A) r o s s m a g n et e t i z i ng n g mm m mf p e r p o l e ( A A T aq a q = A T a - A Ta T a d ; / / C ro ) t r a t u rn r n s r e q u i r e d o n t he he E x t r a _ tu tu r n s = A T ad ad / 1 0 ; / / E x tr s hu h u nt nt f i e l d . S i n c e f i e l d w in i n d in i n g i s s hu h u nt nt c on o n n ec e c te t e d a n d t a k es e s a c u r r e nt nt o f 10 ampere xtt ra r a t u rn r n s r e q u i r e d o n t he he s h hu u nt nt disp (Extra_turns , ’ E x 65

f i e l d = ’ ); 26 / / i n b o o k a ns n s we w e rs rs a r e 1 0 0 and 5 0 r e s p e c t i v e l y . a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f e r r o r

Th e

Scilab code Exa 9.10 Calculating the demagnetizing and cross magnetiz-

ing mmf per pole 1 / / C a l c u l a t i n g t he h e d em e m a g ne n e ti t i zi z i ng n g and c r o s s

m a g n e t i z i n g mm mmf p e r p o l e 2 3 4 5 6 7 8 9 10 11

12 13 14 15 16 17


/ / G iv i v en e n D at at a P = 5 0 0 ; / / P o w e r r a t i n g ( i n kW) e e d i n r . p . m. m. r pm p m = 3 75 75 ; / / S p ee N umber o f p o l e s p = 8 ; / / Nu l u x p e r p o l e ( i n Wb Wb p e r m et e t er er ) f l ux u x = 0 . 08 08 85 8 5 ; / / F lu / / C a l c u l a t i o n o f t he h e d em e m a g ne n e ti t i zi z i n g and c r o s s m a g n e t i z i n g mm mmf p e r p o l e ee d i n r . p . s . n = r p m / 60 6 0 ; / / S p ee us h s h i f t ( i n e l e c t r i c a l a lp l p ha h a = 5 / 10 1 0 0 *1 *1 8 0; 0 ; / / B r us d eg e g re re e ) . S i n ce c e t h e b ru r u sh s h es e s a re r e g i v en e n a l e a d by o f 5% o f p o l e p i tc tc h r m a tu t u re r e mmf p e r A T a = P / ( 2 * f l ux ux * n * p * p * 1 0^ 0 ^ ( - 3 ) ) ; / / A rm p o l e (A) t i z i n g mmf p e r A T a d = A Ta Ta * 2 * a l p h a / 1 8 0; 0; ; / / D e m a g n e ti p o l e (A) r o s s m a g n et e t i z i ng n g mm m mf p e r p o l e ( A A T aq a q = A T a - A Ta T a d ; / / C ro ) a g n e ti t i z i ng n g mmf p e r p o l e ( A ) = ’ ) ; disp (ATad, ’ D e m ag r o s s m a g n et e t i z i ng n g mmf p er e r p o l e (A) = ’ ) ; disp (ATaq, ’ C ro / / i n b oo oo k a n sw s w e rs r s a r e 7 06 0 6 ( A ) a n d 6 35 35 4 (A) r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error 66

Scilab code Exa 9.12 Calculating the armature voltage drop

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

/ / C a l c u l a t i n g t he h e a rm r m at a t u re re v o l t a g e d r o p clc ; x a mp mp l e 9 . 1 2 , P ag ag e No . = 9 . 4 9 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a P = 3 0 0 ; / / P o w e r r a t i n g ( i n kW) o l ta t a ge ge r a t i n g ( i n v o l t s ) V = 5 0 0 ; / / V ol a t hs h s ( S i n ce c e l a p w in i n di d i ng ng a = 6 ; / / N u m b e r o f p a r a l l e l p at ) p = 0 .0 .0 21 21 ; // r e s i s t i v i t y ( in ohm mm sq ua re ) um b e r o f s l o t s N s = 1 5 0; 0; / / N um e n gt g t h o f m e a n t u r n ( i n m et e t er er ) L mt m t = 2 .5 .5 ; / / L en re a o f e ac a c h c o n d u c t ro r o r ( i n mm mm s q u a r e ) a z = 2 5 ; / / A re / / C a l c u l a t i o n o f t he h e a rm r m at a t ur ur e v o l t a g e d r o p r m at a t ur u r e c o n du d u c to to r s . S i n ce ce 8 Z = N s *8 * 8 ; / / N u m b e r o f a rm c o n d u c t o rs r s p er er s l o t r m at a t u re re ( r a = Z * p * Lm Lm t / (2 ( 2 * a *a * a * az a z ) ; / / R e s i s t a n c e o f a rm i n ohm ) rm at a t ur ur e c u r r e n t I a = P * 10 1 0 ^( ^ ( 3) 3 ) / V ; / / A rm rm at a t ur ur e v o l t a g e d ro ro p ( V o l t s ) = ’ ) ; disp (Ia*ra, ’ A rm / / i n b oo oo k a ns n s we w e r i s 2 1 ( V ol o l t ) . T h e a n sw s w er e r s v ar a r y d ue ue t o r ou ou n d o f f e r r o r

Scilab code Exa 9.26 Calculating the number of turns on each commu-

tating pole

67

1 / / C a l c u l a t i n g t he h e n u m b e r o f t u rn r n s o n e ac ac h

c om o m mu m u ta t a t in in g p o l e 2 3 4 5 6 7 8 9 10 11 12 13 14 15

16 17 18 19


/ / G iv i v en e n D at at a N umber o f p o l e s p = 6 ; / / Nu l u x d e n s i t y ( i n Wb Wb p e r m et e t er e r s q u a re re ) B gi g i = 0 .5 .5 ; / / F lu a t u r e f u l l l o a d c u r r e n t ( i n a mp mp e r e ) I a = 5 0 0; 0; / / A r m at Z = 5 4 0 ; / / Number o f c o n d u c t o r s K gi gi = 1; / / I n e r p o l e i n t e r a c t i o n f a c t o r en g t h o f a i r gap l gi g i = 4 ; / / E f f e c t i v e l en / / C a l c u l a t i o n o f t he h e n u m b e r o f t u r n s o n e a ch ch c om o m mu m u ta t a t in in g p o l e N u m b e r o f p a r a l l e l p at a t hs hs . S i nc n c e a rm r m at a t ur ur e a = p ; / / Nu i s l a p wo u nd r m at a t ur u r e mm mmf p e r p o l e A T a = I a /a / a * Z /( / ( 2* 2 * p ) ; / / A rm m m f _ a i r ga ga p = 8 0 00 0 0 0 0 * B g i * K gi gi * l g i * 1 0 ^( ^( - 3 ) ; // Mmf r e q u i r e d f o r a i r g a p ( i n A) A) Mmf r e q u i r e d f o r i r o n m m f _ ir i r o n = 0 . 1* 1* m m f _a _ a i r ga g a p ; / / Mm p a r t s ( i n A) A) . S i nc n c e mm mmf r e q u i r e d i s o n e − t e n t h t ha ha t f o r a i r gap t a l mm m mf p e r p o l e A T i = A Ta T a + m m f _ a i r ga ga p + m m f _ i r on o n ; / / T o ta o n e ac a c h i n t e r p o l e ( i n A) A) n s o n e ac ac h i n t e r p o l e T i = A Ti Ti / Ia I a ; / / Nu m b er o f t u r ns Nu m b e r o f t u rn r n s o n e ac ac h i n t e r p o l e = ’ ) ; disp (Ti, ’ Nu / / i n b o o k a ns n s we w e r i s 1 1 . T h e a ns n s we w e rs r s v ar ar y d u e t o round o f f e r r o r

Scilab code Exa 9.27 Calculating the reactance voltage for a machine machine with

straight line and sinusoidal commutation 1 // / / C a l c u l a t i n g t he h e r e a c t a nc n c e v o l t a g e f o r a m ac achine

w i th th s t r a i g h t

l i n e and s i n u s o i d a l c o m m u t a t i o n 68

2 3 4 5 6 7 8 9 10

11 12 13 14 15


/ / G iv i v en e n D at at a N s = 6 0 ; / / Number o f s e g m e n t s e r s ec e c on on d r ev e v = 1 0 ; / / N u m b e r o f r e v o l u t i o n p er ru sh s h w id i d th t h i n s e gm g m en en t s W = 1 . 5 ; / / B ru L = 0 . 2 ; / / Co− e f f i c i e n t o f s e l f − i n d u c t i o n ( i n mH) u r re r e nt n t p er er c o i l I = 2 0 ; / / C ur // / / C a l c u l a t i o n o f t h e r e a c t a nc nc e v o lt a ge f o r a m a c h i n e w i t h s t r a i g h t l i n e and s i n u s o i d a l commutation o m mu m u ta t a t io io n T c = W /( / ( N s* s * r ev ev ) ; / / T i m e o f c om e r ag a g e r e a c t a nc nc e v o l t a g e E ra r a v = L * 10 1 0 ^( ^ ( - 3 ) * 2* 2 * I / Tc T c ; / / A v er e a ct c t an a n ce c e v o l t a g e w i th th s t r a i g h t l i n e disp (Erav, ’ R ea c o m m u ta ta t i o n ( V o l t s ) = ’ ) ; e a ct c t an a n ccee v o l t a g e w it it h s i n u s o i d a l disp (%pi/2*Erav, ’ R ea c o m m u ta ta t i o n ( V o l t s ) = ’ ) ; / / i n b o o k a ns n s we w e rs r s a r e 3 . 2 V o lt l t s a n d 5 V o lt lt s r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error

Scilab code Exa 9.32 Calculating the minimum number of poles

1 2 3 4 5 6

/ / C a l c u l a t i n g t h e mi n im um n u m b e r o f p o l e s clc ; x a mp mp l e 9 . 3 2 , P ag ag e No . = 9 . 9 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a P = 1 2 00 00 ; / / P o w e r r a t i n g ( i n kW) v e ra r a g e v o l t a g e b et e t we w e en e n c om o m mu m u ta t a to to r E c = 1 5 ; / / A ve s e g me m e n ts ts ( i n V o l t s ) 7 A Ta r m at a t ur u r e mm mmf p e r p o l e Ta = 1 00 0 0 00 0 0 ; / / A rm 8 / / C a l c u l a t i o n o f t h e mi m i n im u m n um um b e r o f p o l e s 9 a = P * 1 0^ M i n im u m n u m b e r o f p a r a l l e l 0 ^ ( 3) 3) / ( A Ta T a * E c ); ) ; / / Mi 69

paths 10 p = a ; / / Mi Minimum n um um b e r o f p o l e s . Since these p a r a l l e l p at a t h s c a n b e o b t ai a i ne n e d b y u s i n g a s im i m pl p l ex ex winding 11 disp ( p , ’ Mi Minimum n um um be be r o f p o l e s = ’ ) ; 12 / / i n b o o k a ns n s we w e r i s 8 p o l e s . T h e a ns n s we w e rs r s v ar ar y due to round o f f e r r o r

Scilab code Exa 9.33 Calculating the maximum armature voltage

1 2 3 4 5 6 7 8 9 10 11 12

/ / C a l c u l a t i n g t h e ma m aximum a r m a t ur ur e v o l t a g e clc ; x a mp mp l e 9 . 3 3 , P ag ag e No . = 9 . 9 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e e d o f c o mm m m u ta ta to to r ( i n m et e t er er V c = 4 0 ; / / P e r i p h e r a l s p ee p e r s e c o nd nd ) v e ra r a ge g e e m f b et e t we w e en e n a d j a c e n t s eg e g m en e n ts ts ( i n E c = 2 0 ; / / A ve Vol ts ) o m mu m u ta t a to t o r s e g m e n ts ts ( i n B c = 4 ; / / Minimum p i t c h o f c om mm) e q u en e n c y ( i n Hz ) f = 4 0 ; / / F r eq / / C a l c u l a t i o n o f t h e ma maximum a rm r m at a t ur ur e v o l t a g e E = V c * Ec Ec / ( 2* 2* f * B c *1 * 1 0^ 0 ^ ( - 3) 3 ) ) ; / / Maximum a r m a t u r e v o l t a g e ( i n V o lt lt s ) Maximum a r m a t u r e v o l t a g e ( V o l t s ) = ’ ) ; disp ( E , ’ Ma / / i n b o o k a ns n s we w e r i s 2 50 5 0 0 V o lt l t s . T h e a ns n s we w e rs r s v ar ar y due t o round o f f e r r o r

Scilab code Exa 9.34 Calculating the total commutator losses

70

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

/ / C a l c u l a t i n g t he he t o t a l co mm ut at or l o s s e s clc ; x a mp mp l e 9 . 3 4 , P ag ag e No . = 9 . 9 2 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a P = 8 0 0 ; / / P o w e r r a t i n g ( i n kW) l t ag a g e r a t i n g ( i n V o lt lt s ) V = 4 0 0 ; / / V o lt r pm p m = 3 00 00 ; // r . p .m. N u m b er o f p o l e s p = 1 0 ; / / Nu e t er er ) . S i n c e 1 00 00 D c = 1 ; / / C o m m u t a t o r d i a m e t e r ( i n m et cm = 1 m et e t er er u = 0 . 23 23 ; / / Co− e f f i c i e n t o f f r i c t i o n ru sh s h p r e s s u r e ( i n kN p e r m et e t er e r s q u a re re ) P b = 1 4. 4. 7; 7; / / B ru u r re r e nt n t d e n s i t y i n b r us u s h es e s ( i n A p er e r mm mm J = 0 .0 .0 75 75 ; / / C ur squa re ) o t al a l b ru r u sh s h c o n t ac a c t d ro r o p ( i n V o l ts ts ) V cb c b = 2 .2 .2 ; / / T ot // / / C a l c u l a t i o n o f t he he t o t a l co m mu ta to r l o s s e s n = r p m / 60 6 0 ; // r . p . s . ma tu tu re re c u r r e n t ( i n A m p e r e ) I a = P * 10 1 0 ^( ^ ( 3) 3 ) / V ; / / A r ma r r e nt n t p e r b r us u s h a rm ( i n A m p er e ) I b = 2 * Ia Ia / p; p ; / / C u rr r u sh s h a r e a p e r b r us u s h a r m ( i n mm mm s q u a r e ) A b = I b /J / J ; / / B ru o t al a l b ru r u sh s h a re r e a o n t he he A B = p * Ab A b * 1 0^ 0^ ( - 6) 6 ) ; / / T ot c om o m mu m u ta t a to t o r ( i n m e te te r s q u a r e ) p e ed e d ( i n m et e t er e r p er er V c = % pi pi * Dc D c * n; n ; / / P e r i p h e r a l s pe seco nd ) r u sh sh f r i c t i o n l o s s ( i n W cf cf = u * Pb P b * 1 0 ^( ^( 3 ) * AB AB * V c ; / / B ru Watts) t a c t l o s s ( i n Watts ) W c b = I a * Vc V c b ; / / B r u s h c o n ta o m mu m u ta t a to t o r l o s s e s ( W at a t ts ts ) = ’ ) ; disp (Wcf+Wcb, ’ T o t a l c om / / i n b oo oo k a ns n s we w e r i s 7 23 2 3 0 W a t t s . T h e a n sw s w e rs r s v ar ar y due t o round o f f e r r o r

71

Chapter 10 Three Phase Induction Motors

Scilab code Exa 10.2 Calculating the main dimentions of squirrel cage in-

duction motor 1 // / / C a l c u l a t i n g t he h e m a i n d i m en e n ti ti on s o f

s q u i r r e l c ag ag e

i n d u c t i o n m ot ot o r 2 3 4 5 6 7 8 9 10 11

clc ; x a mp mp l e 1 0 . 2 , P ag ag e No . = 1 0 . 1 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a P = 1 5 ; / / P o w e r r a t i n g ( i n kW) l t ag a g e r a t i n g ( i n V o lt lt s ) V = 4 0 0 ; / / V o lt r p m = 2 81 8 1 0; 0 ; // r . p .m. e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq e = 0 . 88 88 ; / / E f f i c i e n c y p f = 0 . 9; 9; / / F u l l l o a d p o w e r f a c t o r a c = 2 50 5 0 00 00 ; / / S p e c i f i c e l e c t r i c a l l o a d i n g ( i n A p e r met er ) 12 B av a g ne n e ti t i c l o a d i n g ( i n Wb Wb p eerr a v = 0 .5 .5 ; / / S p e c i f i c m ag m e te te r s q u a r e ) 13 K w = 0 .9 . 9 55 55 ; 14 / / t h e r o t o r

p e r i p h e r a l s pe p e e d i s a pp p p ro r o xi x i ma m a te t e ly ly 20 m et e t eerr p eerr s e co c o n d a t s y nc n c h ro r o n o us u s s p ee ee d 72

15 / / C a l c u l a t i o n o f t h e m a i n d im i m en e n ti t i on on s o f s q u i r r e l

c a ge g e i n d u c t i o n m ot ot o r 16 Q = P /( / ( e * pf pf ) ; / / kVA i n p u t 17 C o = 1 1* u t pu pu t c o− e f f i c i e n t 1 * K w * Ba B a v * ac ac * 1 0^ 0^ ( - 3) 3 ) ; / / O ut 18 n s = 3 00 y n ch c h ro r o no n o us u s s pe p e ed e d c o r r es e s p o n d i ng ng t o 0 0 0/ 0 / 60 6 0 ; / / S yn

5 0 Hz ( i n r . p . s . ) 19 D 2 L = Q / ( Co r o du d u ct c t o f D ˆ ( 2 ) ∗L Co * n s ); ) ; / / P ro 20 D = 2 0/ c e t he h e r o t o r d ia i a me m e te te r i n an 0/ ( %p % p i* i * ns n s ) ; / / S i n ce i n d uc u c t i on o n m o t o r i s a lm l m os o s t e qu q u a l t o s t a t o r b or or e 21 L = D 2L 2L / ( D* D * D ); ); 22 disp ( ’ Ma M a i n d i m en e n ti t i o n s o f s q u i r r e l c aagg e i n d uc u c t i on on motor ’ ) 23 disp ( D , ’D ’D ( meter )=’ ) ; 24 disp ( L , ’ L ( m e t e r ) = ’ ) ; 25 / / i n b o o k a ns n s we w e rs r s a r e 0 . 1 25 2 5 7 m et e t er e r a n d 0 . 1 77 7 7 m et e t er er

respecti vely . error

T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f

Scilab code Exa 10.13 Calculating the number of stator and rotor turns

and rotor voltage between slip rings at standstill 1 / / C a l c u l a t i n g t he h e n u m b e r o f s t a t o r a n d r o t o r t u rn rn s

a nd r o t o r v o l t a g e b e t w e e n s l i p standstill 2 3 4 5 6 7 8

rings at

clc ; x a mp mp l e 1 0 . 1 3 , P a ge ge No . = 1 0 . 3 5 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a / / 3 p ha h a se se i n d u c t i o n mo t o r N umber o f s t a t o r s l o t s N ss s s = 5 4 ; / / Nu N umber o f r o t o r s l o t s N rs r s = 7 2 ; / / Nu p l ie ie d v o l t a g e a c r o s s t h e s t a t o r V = 4 0 0 ; / / A p pl terminals 9 / / C a l c u l a t i o n o f t he he number o f s t a t o r and r o t o r 73

10 11 12 13 14 15 16 17

t ur u r n s and r o t o r v o l t a g e b e t w e e n s l i p r i n g s a t standstill n s p er er p h a s e . S i n ce ce 8 T s = N ss ss * 8/ 8 / 6; 6 ; / / S t a t o r t u r ns c o n d u c to t o r s p er er s l o t u r n s p e r p h a se se . S in ce 4 T r = N rs rs * 4/ 4 / 6; 6 ; / / R o t o r t ur c o n d u c to t o r s p er er s l o t a t o r v o l t a g e p er e r p ha h a se se E s = 4 0 0/ 0 / 3 ^( ^ ( 1 /2 / 2 ) ; / / S t at a g e p er e r p ha h a se se a t E r = E s * Tr T r / Ts T s ; / / R o t o r v o l t ag standstill n s p eerr p ha h a se se = ’ ) ; disp (Ts, ’ S t a t o r t u r ns o t or o r t u r n s p e r p ha h a se se = ’ ); disp (Tr, ’ R ot disp (3^(1/2)*Er, ’ R o t o r v o l t a g e b e t w e e n s l i p r i n g s a t s t a n d s t i l l ( V o l ts t s )= ’ ) ; / / i n b o o k a ns n s we w e rs r s a r e 7 2 , 4 8 a n d 2 6 6 . 7 V o lt lt s r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error

Scilab code Exa 10.15 Calculating the number of stator turns per phase

1 2 3 4 5 6 7 8 9 10

/ / C a l c u l a t i n g t he h e n u m b e r o f s t a t o r t u rn r n s p er e r p ha h a se se clc ; x a mp mp l e 1 0 . 1 5 , P a ge ge No . = 1 0 . 4 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a // / / 3 p ha h a se s e s t a r c o nn n n ec e c te te d i n d u c t i o n motor P = 7 5 ; / / P o w e r r a t i n g ( i n kw ) o l ta t a ge ge r a t i n g V = 3 0 00 00 ; / / V ol e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq N umber o f p o l e s p = 8 ; / / Nu mmf r e q u i r e d f o r f l u x d e n s i t y a t 3 0 A T6 T6 0 = 5 00 0 0 ; / / mm d e g r e e f r o m p o le le a x i s 11 K w s = 0 .9 . 9 5; 5; / / W i n d i n g f a c t o r 12 e = 0 . 94 oa d e f f i c i e n c y 94 ; / / F u l l l oa 13 p f = 0 .8 l l l oa oa d power f a c t o r .8 6; 6; / / F u ll 74

14 // / / C a l c u l a t i o n o f t he he number o f s t a t o r

t u r n s p er er

phase 15 I = P * 1 0 ^ (3 oa d c u r r e n t ( ( 3 ) / ( 3 ^ ( 1 /2 / 2 ) * V * e * p f ) ; / / F u l l l oa 16

17 18 19

i n a mp m p er er e ) t i z i n g c u r r e n t ( i n Ampere ) . I m = 0 .3 . 3 5* 5 * I ; / / M a g n e ti S i n ce c e m a gn g n e ti t i z in i n g c u r r e nt n t i s 3 5% o f f u l l l o ad ad current a t o r t u r n s p er e r p ha h a se se T s = 0 .4 . 4 2 7* 7* p * A T6 T 6 0 / ( Kw K w s * Im Im ) ; / / S t at n s p eerr p ha h a se se = ’ ) ; disp (Ts, ’ S t a t o r t u r ns / / i n b o o k a ns n s we w e r i s 2 8 8 . T h e a ns n s we w e rs r s v ar a r y d ue ue t o round o f f e r r o r

Scilab code Exa 10.16 Calculating the magnetizing current per phase

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

/ / C a l c u l a t i n g t he h e m a g n e ti t i zi z i ng n g c u r re r e n t p er e r p ha h a se se clc ; x a mp mp l e 1 0 . 1 6 , P a ge ge No . = 1 0 . 4 4 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a / / 3 p ha h a se s e d e l t a c on o n n ec e c te t e d i n d u c t i on on motor P = 7 5 ; / / P o w e r r a t i n g ( i n kw ) o l ta t a ge ge r a t i n g V = 4 0 0 ; / / V ol e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq N umber o f p o l e s p = 6 ; / / Nu i a me m e te t e r o f m ot o t o r c o r e ( i n m et e t er er ) D = 0 . 3 ; / / D ia e n gt g t h o f m ot o t o r c o r e ( i n m et e t er er ) L = 0 . 12 12 ; / / L en N umber o f s t a t o r s l o t s N ss s s = 7 2 ; / / Nu d u c to t o r s p er er s l o t N c = 2 0 ; / / N u m b e r o f c o n du e n gt g t h o f a i r g a p ( i n m et e t er er ) l g = 0 .5 .5 5; 5; / / L en G ap c o n s t r a c t i o n f a c t o r K g = 1 . 2 / / Ga il span ( s l o t s ) C o i l _S _S p an a n = 1 1; 1; / / C o il / / C a l c u l a t i o n o f t he h e m a g n e ti t i zi z i n g c u r r e n t p er e r p ha h a se se er p h a s e q = N ss ss / (3 ( 3 * p) p ) ; / / S l o t s p e r p o l e p er K d = s i n (60/2*%pi/180)/(q* s i n (60/(2*4)*%pi/180)); / / 75

20 21

22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

D i s t ri b u ti o n f a c t o r N s _ po p o l e = N ss ss / p ; / / S l o t s p e r p o l e n g le l e o f c h or o r d in in g ( i n a l p h a = 1 / N s _ po po l e * 1 8 0; 0 ; / / A ng d eg e g re re e ) . S i n ce c e t h e w i n d in i n g i s c h o rd rd e d by 1 s l o t pitch i t ch ch f a c t o r K p = c o s (alpha/2*%pi/180); / / P it a t o r w i nd n d in in g f a c t o r K w s = K d * Kp K p ; / / S t at o t al a l s t a t o r c o n d uc uc to rs N s = N ss ss * Nc N c ; / / T ot e r p ha h a se se T s = N s / (3 ( 3 *2 * 2 ) ; / / S t a t o r t u r n s p er a t o r v o l t a g e p er e r p ha h a se se . S i nc nc e machine E b = V ; / / S t at i s d e l t a c on o n ne n e ct c t ed ed l u x p e r p o l e ( i n Wb Wb) F m = E b / (4 ( 4 .4 . 4 4 * f * Ts Ts * K ws w s ) ; / / F lu e r p o l e ( i n m et e t er e r s q ua ua r e ) A = % pi pi * D *L * L / p; p ; / / A r e a p er v e ra r a ge g e a i r g a p d e n s i t y ( i n Wb Wb p er er B a v = F m / A; A ; / / A ve m e te te r s q u a r e ) G ap f l u x d e n s i t y a t 3 0 d e g r e e B g 60 6 0 = 1 .3 . 3 6* 6 * B a v ; / / Ga from p o le a x i s Mmf r e q u i r e d f o r A T g = 8 0 0 00 00 0 * B g 6 0 * Kg K g * l g * 1 0 ^( ^( - 3 ) ; / / Mm a i r g a p ( i n A) Mmf f o r i r o n p a r ts t s ( i n A) A) . S i nc nc e A Ti Ti = 0 .3 . 3 5* 5 * A Tg T g ; / / Mm mmf r e q u i r e d f o r i r o n p a r ts t s i s 3 5% o f a i r g a p mm mmf A T 60 6 0 = A Tg Tg + A Ti T i ; / / T o t a l mmf ( i n A ) g n e ti t i z in in g c u r r e n t I m = 0 .4 . 4 2 7* 7* p * A T6 T 6 0 / ( Kw K w s * Ts Ts ) ; / / M a gn p e r p ha h a se s e ( i n a mp mp e r e ) n e t iz i z i ng n g c u r r e n t p e r p ha h a se s e ( Am A mpere ) = ’ ) ; disp (Im, ’ M a g ne / / i n b oo oo k a ns n s we w e r i s 4 . 5 6 A m p e r e . T h e a n sw s w er e r s v ar ar y due t o round o f f e r r o r

Scilab code Exa 10.19 Calculating the current in rotor bars and in end

rings 1 / / C a l c u l a t i n g t he h e c u r r e n t i n r o t o r b ar a r s a nd nd i n e n d

rings 76

2 3 4 5 6 7 8 9 10 11 12 13


/ / G iv i v en e n D at at a N umber o f p o l e s p = 6 ; / / Nu a s es es o f s t a t o r m s = 3 ; / / Nu m b er o f p h as N umber o f s t a t o r s l o t s N ss s s = 7 2 ; / / Nu d u c to t o r s p er er s l o t N c = 1 5 ; / / N u m b e r o f c o n du N umber o f s t a t o r s l o t s S r = 5 5 ; / / Nu I s = 2 4. 4. 1; 1; / / S t a t o r c u r r e n t ( i n A m p e r e ) il span ( s l o t s ) C o i l _S _S p an a n = 1 1; 1; / / C o il ow e r f a c t o r p f = 0 .8 .8 3; 3; / / P ow // / / C a l c u l a t i o n o f t h e c u r r e n t i n r o t o r b ar a r s aan nd i n end r i n g s 14 q = N ss e r p h a se se ss / ( ms ms * p) p ) ; / / S t a t o r s l o t s p e r p o l e p er 15 K d = s i n (60/2*%pi/180)/(q* s i n (60/(2*4)*%pi/180)); / / D i s t ri b u ti o n f a c t o r 16 N s _ po p o l e = N ss ss / p ; / / S l o t s p e r p o l e 17 a l p h a = 1 / N s _ po n g le l e o f c h or o r d in in g ( i n po l e * 1 8 0; 0 ; / / A ng d eg e g re re e ) . S i n ce c e t h e w i n d in i n g i s c h o rd rd e d by 1 s l o t pitch 18 K p = c o s (alpha/2*%pi/180); / / P it i t ch ch f a c t o r 19 K w s = K d * Kp n d in in g f a c t o r K p ; / / S t a t o r w i nd 20 I r _ = I s * pf pf ; / / S t a t o r c u r r e n t e q u i v a l e n t t o r o t o r c u r r e n t ( i n Ampere ) 21 N s = N ss o t al a l s t a t o r c o n d uc uc to rs ss * Nc N c ; / / T ot 22 T s = N s / ( ms r n s p er e r p ha h a se se ms * 2) 2 ) ; / / S t a t o r t u rn 23 I b = 2 * ms r r en e n t i n e a ch ch r o t o r b a r ms * K ws w s * T s * Ir Ir _ / Sr Sr ; / / C u rr ( in Am Ampe pere) re) 24 I e = S r * Ib r r en e n t i n e a ch ch e n d r i n g ( i n Ib / ( % pi pi * p ) ; / / C u rr Ampere) 25 disp (Ib, ’ C ur u r re r e nt n t i n e ac a c h r o t o r b ar a r ( Am A m p er e ) = ’ ) ; 26 disp (Ie, ’ C ur u r re r e nt n t i n e ac a c h e n d r i n g ( Am A mpere ) = ’ ) ; 27 / / i n b oo o o k a n s w er e r s a r e 3 7 5 . 4 A m p e r e a n d 1 0 9 5 . 3 A m p er e r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar a r y d ue ue t o r o u n d o f f error

77

Chapter 11 Design of Synchronous Machines

Scilab code Exa 11.4 Calculating the suitable number of slots and con-

ductors per slot 1 / / C a l c u l a t i n g t he he s u i t a b l e number o f s l o t s

and

c o n d u c to t o r s p er er s l o t 2 3 4 5 6 7 8 9 10 11 12

clc ; x a mp mp l e 1 1 . 4 , P ag ag e No . = 1 1 . 2 8 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a / / 3 p h a s e s t a r c on o n ne n e ct c t ed ed a l t e r a t o r ( S i n g l e l a y e r windi ng ) r pm p m = 3 00 00 ; // R. p .m. o l ta t a ge ge r a t i n g ( i n v o l t s ) E = 3 3 00 00 ; / / V ol e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq i a me m e te t e r o f c o r e ( i n m et e t er er ) D = 2 . 3 ; / / D ia e n gt g t h o f c o r e ( i n m et e t er er ) L = 0 . 35 35 ; / / L en he a i r gap ( i n B m = 0 . 9; 9; / / Maximum f l u x d e n s i t y i n t he Wb p e r m e te te r s q u a r e ) / / C a l c u l a t i o n o f t h e s u i t a b l e number o f s l o t s a nd c o n d u c to t o r s p er er s l o t 78

13 n s = r pm pm / 60 60 ; / / S y n c h r o n o u s s p e e d ( r . p . s ) 14 p = 2 * f /n N umber o f p o l e s / n s ; / / Nu 15 B av he a i r av = 2 / % pi p i * Bm B m ; / / A v e r a g e f l u x d e n s i t y i n t he 16 17 18 19 20 21 22 23 24 25 26

g ap ap ( i n Wb p e r m et e t er er s q u a r e ) l u x p e r p o l e ( i n Wb Wb) F l u x _ po p o l e = B av av * % p i * D * L / p ; / / F lu l t a ge g e p er e r p ha h a se se ( i n v o l t s ) E p h = E / 3 ^( ^ ( 1 /2 / 2 ) ; / / V o lt c h ( i n mm) . T h e s l o t p i t ch ch y s = 4 0 ; / / S l o t p i t ch s h ou o u l d b e n e a r l y 4 0 mm mm f o r 3 . 3 kV m ac a c hi h i ne ne s i n g w in i n di d i ng ng f a c t o r K w = 0 .9 . 9 55 5 5 ; / / T a k in u r ns ns p e r T ph p h = i n t (Eph/(4.44*f*Flux_pole*Kw)); / / T ur phase q = i n t (%pi*D/(3*p*ys*10^(-3))); / / S l o t s p e r p o l e p e r p ha h a se se o t al a l nu mb er o f s t a t o r s l o t s S = 3 * p *q * q ; / / T ot o t al a l n u m b e r o f s t a t o r c o n du d u c to to r s T ph ph 6 = 6 * Tp Tp h ; / / T ot o n du d u ct c t or o r s p er er s l o t Z s = i n t (Tph6/S); / / C on o t al a l s t a t o r c o n du d u c to t o r s u ssee d = ’ ) ; disp (Zs*S, ’ T ot u r n s p e r p ha h a se s e u se s e d= d= ’ ) ; disp (Zs*S/6, ’ T ur

Scilab code Exa 11.10 Calculating the size of armature wire and the ac

resistance of each pahase 1 / / C a l c u l a t i n g t he he

s i z e o f a rm r m at a t ur u r e w ir i r e a n d t he he a . c . r e s i s ta n c e o f each pahase

2 3 4 5 6 7 8 9 10


/ / G iv i v en e n D at at a / / 3 p ha h a se s e s t a r c o nn n n ec e c te t e d s yn y n ch c h ro r o no n o u s g e n e r a t or or N umber o f p o l e s p = 8 ; / / Nu e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq o l e p i t c h ( i n m et e t er er ) y s = 0 . 3; 3; / / P ol n e c u r r e n t ( i n Ampere ) I z = 1 0 0; 0; / / L i ne r o ss s s a x i a l l e n g th t h ( i n m et et e r ) L = 0 . 3 ; / / G ro 79

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

e r p o l e p er e r p h a se se S p p = 3; 3; / / S l o t s p er o n du d u ct c t or o r s p er er s l o t C s = 6 ; / / C on dd y c u r r e n t K c_ c _ av a v = 1 .3 .3 ; / / A v e r a g e e dd

loss factor / / C a l c u l a t i o n o f t h e s u i t a b l e number o f s l o t s a nd c o n d u c to t o r s p er er s l o t rm at a t ur u r e d i a m e t e r ( i n m et e t er er ) D = y s * p/ p / % pi pi ; / / A rm hr o n o u s s p e e d ( i n r . p . s . ) n s = 2 * f/ f / p; p ; / / S y n c hr p e ed e d ( i n m et e t er e r p er er V a = % pi pi * D* D * ns n s ; / / P e r i p h e r a l s pe seco nd ) o t al a l number o f s l o t s S = S pp pp * 3* 3 * p ; / / T ot t a l n u m b e r o f c o n d u c to to r s Z = S * C s ; / / T o ta rn s p e r p ha h a se se T p h = Z /6 / 6 ; / / T u rn te r ) a c = I z *Z * Z / ( %p % p i * D) D ) ; / / ( i n A m p e r e p e r m e te u r r en e n t d e n s i t y ( i n A m p er e J = ( 43 4 3 0 00 00 / a c ) +( +( V a / 16 16 ) ; / / C ur p e r mm s q u a r e ) r m at a t ur u r e c o n du d u c t or or a s = 1 0 0/ 0/ J ; / / A r e a o f a rm r e a o f a r ma m a t ur u r e c o n d u c t o r (mm s q u a r e ) = disp (as, ’ ( a ) A re ’ ); c t iv i v e l e ng n g t h o f e ac a c h t ur ur n ( i n L _ a ct c t i ve ve = 2 * L; L ; / / A ct met er ) i n ce ce To t a l l en gt h o f a t ur n i s L m t = 2 * L _a _ a ct c t i ve ve ; / / S in t w i c e t he he a c t i v e l e n g t h ( i n m e t e r ) r e s i s t iv iv i t y = 0 . 02 02 1 ; / / R e s i s t i v i t y o f c o p p e r a t 7 5 d e gr g r e e c e l s i u s ( i n ohm p er e r m et e t er er ) D . C. C. r e s i s t a n c e o f r _ d c = r e s is i s t i v it it y * T p h * L m t / a s ; / / D. e ac a c h p ha h a se s e a t 7 5 d e g r e e c e l s i u s ( i n ohm ) A . C. C. r e s i s t a n c e o f e a c h p h a s e r _a _ a c = K c_ c _ av a v * r _ dc d c ; / / A. C . r e s i s t a n c e o f e ac a c h p ha h a se s e ( oh ohm )= )= ’ disp (r_ac, ’ ( b ) A . C. );

31 / / i n b oo oo k a n sw s w e rs r s a r e 2 3 . 8 mm mm s q u a r e a n d 0 . 0 9 9 ohm

respecti vely . error

T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f

80

Scilab code Exa 11.11 Calculating the length of air gap

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

// / / C a l c u l a t i n g t he he l e n g t h o f a i r g a p clc ; x a mp mp l e 1 1 . 1 1 , P a ge ge No . = 1 1 . 3 5 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a / / 3 p ha h a se se s i l i e n t p o l e a l t e r n a t o r kVA r a t i n g k VA V A = 5 00 00 ; / / kV l t ag a g e r a t i n g ( i n kV ) V = 3 . 3 ; / / V o lt e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq r pm p m = 6 00 00 ; // R. p .m. rn s p e r p ha h a se se T ph p h = 1 80 80 ; / / T u rn v e ra r a ge g e f l u x d e n s i t y ( i n Wb Wb p e r m et e t er er B a v = 0 .5 . 5 4; 4 ; / / A ve squ are ) rt c i r c u i t r a t i o S CR C R = 1 .2 .2 ; / / S h o rt K w = 0 .9 . 9 55 55 ; / / W i n d i n g f a c t o r G ap c o n s t r a c t i o n f a c t o r K g = 1 .1 .1 5; 5; / / Ga n c e f i e l d f o r m f a c t o r i s e qu q u a l t o t he he K f = 0 .6 .6 5; 5; / / S i nc r a t i o o f p ol o l e a rc r c t o p ol o l e p it i t ch ch / / C a l c u l a t i o n o f t h e l en gt h o f a i r gap hr o n o u s s p e e d ( i n r . p . s . ) n s = r pm pm / 60 6 0 ; / / S y n c hr N umber o f p o l e s p = 2 * f /n / n s ; / / Nu r m at a t ur ur e d i a m e t e r I p h = k VA VA * 1 0 0 0 / ( 3 ^ (1 ( 1 / 2 ) * V * 1 0 00 0 0 ) ; / / A rm ( in meter ) rm at a t ur u r e mm m mf p e r p o l e ( i n A Ta Ta = 2 .7 . 7 * I ph p h * T ph p h * K w /p / p ; / / A rm A) A T _ f0 f 0 = S CR C R * A Ta T a ; / / No l o a d f i e l d mmf p e r p o l e M aximum f l u x d e n s i t y i n a i r g a p ( i n B g = B av av / Kf K f ; / / Ma Wb p e r m e te te r s q u a r e ) l g = 0 . 8* 8* A T _f _f 0 / ( 8 0 0 0 00 00 * B g * K g ) ; / / L e n g t h o f a i r g a p / / S i n ce c e mm mmf r e q u i r e d f o r g a p i s 8 0% o f n o l oa oa d f i e l d mm mmf f n g t h o f a i r g ap a p (mm) = ’ ) ; disp (lg*1000, ’ L e ng / / i n b o o k a ns n s we w e r i s 5 . 2 mm mm . T h e a ns n s we w e rs r s v ar ar y du e t o round o f f e r r or

81

Scilab code Exa 11.13 Calculating the stator bore and stator core length

and turns per phase and armature mmf per pole and mmf for air gap and field current 1 / / C a l c u l a t i n g t he h e s t a t o r b or or e and s t a t o r

c or e l e n g t h a n d t u r n s p e r p ha h a se s e a n d a rm r m at a t ur u r e mm mmf p e r p o l e a n d mmf f o r a i r g a p a n d f i e l d c u r r e n t

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

18 19 20 21 22


/ / G iv i v en e n D at at a / / 3 p ha h a se s e s yn y n ch c h ro r o no n o u s g e n e r a t or or kVA r a t i n g Q = 1 2 50 50 ; / / kV o l ta t a g e r a t i n g ( i n kV ) E = 3 3 00 00 ; / / V ol e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq r pm p m = 3 00 00 ; // R. p .m. a g ne n e ti t i c l o a d i n g ( i n Wb Wb p er er B a v = 0 .5 . 5 8; 8 ; / / S p e c i f i c m ag m e te te r s q u a r e ) a c = 3 30 3 0 00 00 ; / / S p e c i f i c e l e c t r i c l o a d i n g ( i n Ampere p e r m e te te r ) l g = 5 . 5; 5; / / Gap l e n g t h ( i n mm) e l d t ur ur ns per p ol e T _f _ f ie i e ld l d = 6 0; 0; / / F i el rt c i r c u i t r a t i o S CR C R = 1 .2 .2 ; / / S h o rt K w = 0 .9 . 9 55 55 ; / / W i n d i n g f a c t o r p e ed e d ( i n m et e t er e r p er e r s ec e c on on d ) V a = 3 0 ; / / P e r i p h e r a l s pe // / / C a l c u l a t i o n o f t h e s t a t o r b or or e and s t a t o r c o r e l e n g t h a n d t u r n s p e r p ha h a se s e a n d a rm r m at a t ur u r e mm mmf p e r p o l e a n d mmf f o r a i r g a p a n d f i e l d c u r r e n t hr o n o u s s p e e d ( i n r . p . s . ) n s = r pm pm / 60 6 0 ; / / S y n c hr N umber o f p o l e s p = 2 * f /n / n s ; / / Nu u t pu pu t c o− e f f i c i e n t C o = 1 1* 1 * K w * Ba B a v * ac ac * 1 0^ 0^ ( - 3) 3 ) ; / / O ut r o du d u ct c t o f D∗D∗ L D 2 L = Q / ( Co Co * n s ); ) ; / / P ro o r e ( i n m et e t er er ) D = V a / ( %p % p i* i * ns n s ) ; / / S t a t o r b or 82

23 24 25 26 27 28 29 30 31 32

e t er er ) = ’ ) ; disp ( D , ’ S t a t o r b o r e ( m et e t er er ) L = D 2L 2L / D ^( ^ ( 2) 2) ; / / S t a t o r c o r e l e n g t h ( i n m et e t er er )= ’ ) ; disp ( L , ’ S t a t o r c o r e l e n g t h ( m et er p o l e A _p _ p o le le = % pi pi * D * L/ L / p ; / / A r e a p er er p o l e F _p _ p o le le = B av av * A _ po p o le l e ; / / F l u x p er l t a ge g e p er e r p ha h a se se E p h = E / 3 ^( ^ ( 1 /2 / 2 ) ; / / V o lt rn s p e r p h as as e T ph p h = i n t (Eph/(4.44*f*F_pole*Kw)); / / T u rn u r n s p e r p ha h a se se = ’ ); disp (Tph, ’ T ur u r re r e n t p e r p ha h a se se I ph ph = Q * 1 0 00 0 0 / (3 ( 3 ^ (1 ( 1 / 2) 2 ) * E ) ; / / C ur rm at a t ur u r e mm m mf p e r p o l e ( i n A Ta Ta = 2 .7 . 7 * I ph p h * T ph p h * K w /p / p ; / / A rm A)

33 disp (ATa, ’ A rm r m at a t ur u r e mmf p e r p o l e ( A mp mp e r e ) = ’ ) ; 34 A _ e f f ec re a e c t i ve v e = 0 . 6* 6* A _ p o l e ; / / E f f e c t i v e g a p a re

is

0 . 6 t im i m es e s t he h e a c tu t u a l a re re a 35 K g Bg B g = F _ po p o l e / A _ e f f ec ec t i v e ; / / E f f e c t i v e g a p d e n s i t y ( i n Wb p e r m et e t er er s q u a r e ) 36 m m f _ a i r ga Mmf f o r a i r ga p = 8 0 00 0 0 0 0 * K g Bg Bg * l g * 1 0 ^( ^ ( - 3 ) ; / / Mm g ap ap ( i n A ) 37 disp (mmf_airgap , ’ Mm Mmf f o r a i r g ap a p ( A mp mp e r e )= )= ’ ) ; 38 A T_ T _ f0 f 0 = S CR C R * m m f _a _ a i rg r g a p ; / / No l o a d f i e l d mmf p e r p o l e 39 I f = A T_ e l d c u r r e n t a t n o l oa oa d T _ f0 f 0 / T _f _ f ie i e ld l d ; / / F i el 40 disp (If, ’ F i e l d c u r r e n t a t n o l o a d ( Am A m p e r e )= )= ’ ) ; 41 / / i n b oo oo k a n sw s w e rs r s a r e 1 . 9 m et et er er , 0 . 3 4 5 m et et e r , 1 5 0 , 4 2 4 0 a mp mp er er e , 4 2 5 0 a mp m p er e r e a nd nd 8 5 a mp m p er er e r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f error

Scilab code Exa 11.14 Calculating the flux per pole and length and width

of pole and winding height and pole height 1 / / C a l c u l a t i n g t he h e f l u x p er er p o l e and l e n g t h and

w i dt d t h o f p o le l e a n d w in i n di d i ng n g h e ig i g h t and p o l e h e i g h t 2 clc ;

83

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

x a mp mp l e 1 1 . 1 4 , P a ge ge No . = 1 1 . 4 0 ’ ) disp ( ’ E xa / / G iv i v en e n D at at a // / / 3 p h a s e s t a r c on o n ne n e ct c t ed ed s e l i e n t p o l e a l t e r n a t o r kVA r a t i n g Q = 2 5 00 00 ; / / kV o l ta t a g e r a t i n g ( i n kV ) E = 2 4 00 00 ; / / V ol e q u en e n c y ( i n Hz ) f = 6 0 ; / / F r eq r pm p m = 2 25 25 ; // R. p .m. o r e ( i n m et e t er er ) D = 2 . 5 ; / / S t a t o r b or o r e l e n g t h ( i n m et e t er er ) L = 0 . 44 44 ; / / C or N u m b e r o f s l o t p er e r p o le l e p er e r p ha h a se se N sp s p p = 3 ; / / Nu d u c to t o r s p er er s l o t N cs c s = 4 ; / / N u m b e r o f c o n du se a = 2 ; / / C i r c u i t s p e r p h a se l e c o re r e ( i n Wb Wb p er er B p = 1 . 5; 5; / / F l u x d e n s i t y i n p o le m e te te r s q u a r e ) ep th th o f w i n d i n g ( i n mm mm) d f = 3 0 ; / / D ep l d w id i d in i n d s pa p a ce ce f a c t o r S f = 0 .8 .8 4; 4; / / F i e ld e a ka k a ge ge f a c t o r C l = 1 . 2; 2; / / L ea K w = 0 .9 .9 5; 5; / / W i n d i n g f a c t o r o s s d i s s i p a t e d b y f i e l d w in i n di d i ng ng q f = 1 80 80 0; 0 ; / / L os gh t o f i n s u l a t i o n h _ in i n s ul u l a ti t i o n = 3 0; 0 ; / / H e i gh / / C a l c u l a t i o n o f t h e f l u x p er er p o l e and l e n g t h a nd w i dt d t h o f p o le l e a n d w in i n di d i ng n g h e ig i g h t and p o l e h e i g h t hr o n o u s s p e e d ( i n r . p . s . ) n s = r pm pm / 60 6 0 ; / / S y n c hr N umber o f p o l e s p = 2 * f /n / n s ; / / Nu o t al a l number o f s l o t s S = 3 * p * 3. 3 . 5; 5; / / T ot t a l n u m b e r o f c o n d u ct ct o r s Z = N c s * S; S ; / / T o ta rn s p e r p ha h a se se T ph p h = i n t (Z/6); / / T u rn l t ag a g e p er e r p ha h a se se E p h = E / 3 ^ ( 1/ 1 / 2 ) ; / / V o lt e r p o le le ( i n F _ p o le l e = E ph p h * a / ( 4 . 4 4* 4 * T p h * f * K w ) ; / / F l u x p er Wb) l u x p e r p o l e (Wb) = ’ ) ; disp (F_pole , ’ ( a ) F lu l u x i n p o l e b o d y ( i n Wb Wb) F p = C l * F _p _ p ol o l e ; / / F lu e t er e r s q ua ua r e ) A p = F p / Bp Bp ; / / A r e a o f p o l e b o d y ( i n m et e n gt g t h o f p o l e b o d y = L en e n gt g t h o f a rm r m at a t ur ur e L p = L ; / / L en core id t h o f p o l e b o d y b p = A p / Lp Lp ; / / W id e n gt g t h o f p o l e b o d y ( m et e t er er ) = ’ ) ; disp (Lp, ’ ( b ) L en Width o f p o l e b o d y ( m e t e r ) = ’ ) ; disp (bp, ’ 84

37 I ph u r re r e nt n t i n e ac a c h p ha h a se se ph = Q * 1 0 00 0 0 / (3 ( 3 ^ (1 ( 1 / 2) 2 ) * E ) ; / / C ur 38 I z = I p h/ u r re r e nt n t i n e ac a c h c o nd n d u ct ct o r h / a; a ; / / C ur 39 A Ta r m at a t ur u r e mm mmf p e r p o l e ( i n A Ta = 2 .7 . 7 * I z * Tp Tp h * Kw Kw / p ; / / A rm

) 40 A T_ T _ fl f l = 2 * A Ta T a ; / / F i e l d mmf a t f u l l l o a d ( i n A ) 41 h f = A T _f _ f l / ( 1 0 ^ (4 (4 ) * ( S f * d f * 1 0^ 0^ ( - 3 ) * q f ) ^ ( 1 /2 /2 ) ) ; / /

H e i gh g h t o f f i e l d w i n di d i n g ( i n m et e t er er ) 42 disp (hf, ’ ( c ) H e i g h t o f f i e l d w i n d i n g ( m e te te r ) = ’ ) ; 43 disp (hf+h_insulation*10^(-3), ’ ( d ) H e i gh gh t o f p o l e ( meter ) =’ ); 44 / / i n b oo oo k a n sw s w e rs r s a r e 0 . 0 4 9 Wb Wb, 0 . 4 4 m et et e r , 0 . 0 8 9 m e t e r , 0 . 1 6 m et e t e r a n d 0 . 1 9 m et et e r r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar a r y d ue u e t o r o u nd nd o f f e r r o r

Scilab code Exa 11.18 Calculating the direct and quadrature axis syn-

chronous reactances 1 // / / C a l c u l a t i n g t he h e d i r e c t a n d q ua u a d r at a t ur ur e a x i s

s y nc n c h ro r o n o us us r e a c t a n c e s 2 3 4 5 6 7 8 9 10 11 12 13 14 15


/ / G iv i v en e n D at at a // / / 3 p h a s e s t a r c on o n ne n e ct c t ed ed s e l i e n t p o l e a l t e r n a t o r kVA r a t i n g Q = 2 5 00 00 ; / / kV o l ta t a g e r a t i n g ( i n kV ) E = 2 4 00 00 ; / / V ol e q u en e n c y ( i n Hz ) f = 6 0 ; / / F r eq N u m b er o f p o l e s p = 3 2 ; / / Nu o r e ( i n m et e t er er ) D = 2 . 5 ; / / S t a t o r b or o r e l e n g t h ( i n m et e t er er ) L = 0 . 44 44 ; / / C or rn s p e r p ha h a se se T ph p h = 2 24 24 ; / / T u rn i r g a p l e n g th t h ( i n m et e t er er ) l g = 1 0 ; / / A ir K g = 1 .1 .1 1; 1; / / A i r g a p c o n s t r a c t i o n f a c t o r K w = 0 .9 .9 5; 5; / / W i n d i n g f a c t o r 85

16 R = 0 . 69 r c t o p ol o l e p i t ch ch 69 ; / / R a t i o o f p o l e a rc 17 A 1 = 1 .0 a t io i o o f a mp m p li l i tu t u de d e o f f un u n da d a me m e nt n t al al o f . 0 68 6 8 ; / / R at

g a p f l u x d e n s i t y t o ma m aximum g ap ap d e n s i t y 18 X l = 0 .1 i t l e a k a g e r e a c t a nc nc e .1 4; 4; / / P e r u n it 19 / / C a l c u l a t i o n o f t h e d i r e c t a n d q ua u a dr d r at a t ur ur e a x i s s y nc n c h ro r o n o us us r e a c t a n c e s 20 x m = 7 . 54 5 4 * f * T p h * T ph ph * K w * K w * D * L /( / ( p * p * l g * 1 0^ 0^ ( - 3 ) * K g ) a g ne n e ti t i c r e a c t a n c e p e r p h as a s e ( i n ohm ) *10^(-6); / / M ag 21 E p h = E / 3 ^ ( 1/ l t ag a g e p er e r p ha h a se se 1 / 2 ) ; / / V o lt 22 I ph u r re r e nt n t i n e ac a c h p ha h a se se ph = Q * 1 0 00 0 0 / (3 ( 3 ^ (1 ( 1 / 2) 2 ) * E ) ; / / C ur 23 X m = I ph n e t is i s i n g r e a c t a nc nc e p h * x m / Ep Ep h ; / / P e r u n i t m a g ne 24 a = R *% n g le l e e m br b r ac a c ed e d b y p o l e a r c ( i n r ad ad ) * % p i ; / / A ng 25 p d = ( a +s e d uc u c ti t i on on f a c t o r f o r + s i n (a))/(4* s i n (a/2)); / / R ed 26 27 28 29 30 31 32 33 34

d i r e c t a x i s a rm r m at a t ur u r e mm mmf lu x d i s t r i b u t i o n f a c t o r f o r d i r e c t A d 1 = p d * A1 A 1 ; / / F lu axis e r u n i t d i r e c t a x i s a rm r m at a t ur ur e X a d = A d1 d1 * Xm X m ; / / P er r e a c t i o n r e a ct c t a n ce ce lu x A q 1 = ( (4 ( 4 * R + 1) 1) / 5 ) -( - ( s i n (R*%pi)/%pi); / / F lu d i s t r i b u t i o n co− e f f i c i e n t f o r q u a d r a t u r e a x i s a d r at a t u re r e a x i s a rm r m at a t ur ur e X a q = A q1 q1 * Xm X m ; / / P e r u n i t q u ad r e a c t i o n r e a ct c t a n ce ce i t d i r e c t a x i s s yn y n ch c h ro r o no n o us us X d = X l + Xa X a d; d ; / / P e r u n it reactance a d r at a t u re r e a x i s s yn y n ch c h ro r o no no u s X q = X l + Xa X a q; q ; / / P e r u n i t q u ad reactance i t d i r e c t a x i s s yn y n ch c h ro r o no n o us u s r e a c t a nc nc e disp (Xd, ’ P e r u n it = ’ ); a d r at a t u re r e a x i s s yn y n cch h ro r o n ou ou s disp (Xq, ’ P e r u n i t q u ad r e a c t a n c e = ’ ); / / i n b o o k a ns n s we w e rs r s a r e 0 . 91 9 1 6 a n d 0 . 53 53 3 r e s p e c t i v e l y . T h e a ns n s we w e rs r s v ar ar y d u e t o r o u n d o f f e r r o r

86

Scilab code Exa 11.20 Calculating the kVA output of the machine

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

/ / C a l c u l a t i n g t he h e kV kVA o u tp t p ut u t o f t he h e m ac a c h in in e clc ; x a mp mp l e 1 1 . 2 0 , P a ge ge No . = 1 1 . 5 6 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a / / 3 p ha h a se s e t ur u r bo bo − a l t e r n a t o r r p m = 3 00 0 0 0; 0 ; // R. p .m. e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq o r e l e n g t h ( i n m et e t er er ) L = 0 . 94 94 ; / / C or v e ra r a ge g e g a p d e n s i t y ( i n Wb Wb p e r m et e t er er B a v = 0 .4 . 4 5; 5 ; / / A ve sqa ure ) mp e r e c o n d u c t o r s p e r m et e t er er a c = 2 50 5 0 00 0 0 ; / / A mp p e ed e d o f r o t o r ( i n m e t e r p er er V a = 1 0 0; 0; / / P e r i p h e r a l s pe seco nd ) e n gt g t h o f a i r g a p ( i n mm mm) l g = 2 0 ; / / L en K w = 0 .9 .9 5; 5; / / W i n d i n g f a c t o r / / W in in di di ng ng i s i n f i n i t e l y d i s t r i b u t e d w i th t h a p h a se se s pr p r ea ea d o f 60 d eg re e / / C a l c u l a t i o n o f t he h e kV kVA o u tp t p ut u t o f t he h e m ac a c h i ne ne n s = r pm pm / 60 6 0 ; // R. p . s i a me m e te t e r o f r o t o r ( i n m et e t er er ) D r = V a /( /( % pi p i * n s ); ) ; / / D ia o r b or o r e ( i n m et e t er er ) D = D r + (2 (2 * l g *1 * 1 0^ 0 ^ ( - 3) 3 ) ) ; / / S t a t or // f o r f u l l p i t c h K d = 0 .9 . 9 55 55 ; / / D i s t r i b u t i o n f a c t o r i t ch ch f a c t o r K p = 1 ; / / P it K w = K d * Kp Kp ; / / W i n d i n g f a c t o r Q = 1 1* 1* K w * B a v * a c * D * D* D * L * n s * 1 0^ 0^ ( - 3 ) ; / / kVA o u t p u t c h i ne n e ( kV kVA )= )= ’ ) ; disp ( Q , ’ ( a ) kVA o u t p u t o f m a ch / / f o r c ho h o rd r d ed e d b y 1 /3 /3 p o le p i tc h n g le l e o f c h or o r d in in g a l p ha h a = 1 8 0/ 0/ 3; 3 ; / / A ng i t ch ch f a c t o r K p = c o s (alpha*%pi/180/2); / / P it K d = 0 .9 . 9 55 55 ; / / D i s t r i b u t i o n f a c t o r K w = K d * Kp Kp ; / / W i n d i n g f a c t o r Q = 1 1* 1* K w * B a v * a c * D * D* D * L * n s * 1 0^ 0^ ( - 3 ) ; / / kVA o u t p u t h i n e ( kV kVA )= )= ’ ) ; disp ( Q , ’ ( b ) kVA o u t p u t o f m a c hi / / i n b oo o o k a n s w e r s a r e 2 4 8 0 kV kVA a nd n d 2 1 47 4 7 kVA r e s p e c t i v e l y . T h e p ro r o vi v i de d e d i n t h e t ex e x tb t b oo oo k i s 87

wrong

Scilab code Exa 11.32 Calculating the number of stator slots and average

flux density 1 // / / C a l c u l a t i n g t he he number o f s t a t o r

s l o t s and

a v e ra ra ge f l u x d e n si t y 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23


/ / G iv i v en e n D at at a / / 3 p ha h a se s e s t a r c on o n ne n e ct c t ed e d d i r e c t w a te t e r c o ol ol e d generator MVA r a t i n g Q = 5 8 8 ; / / MV o l ta t a ge ge r a t i n g E = 2 20 20 00 00 ; / / V ol N u m b er o f p o l e s p = 2 ; / / Nu r p m = 2 50 5 0 0; 0 ; // R. p .m. e q u en e n c y ( i n Hz ) f = 5 0 ; / / F r eq o r e ( i n m et e t er er ) D = 1 . 3 ; / / S t a t o r b or r e l e n g t h ( i n m et e t er er ) L = 6 ; / / C o re d u c to t o r s p er er s l o t N c = 2; 2; / / N u m b e r o f c o n du se a = 2 ; / / C i r c u i t s p e r p h a se mp e r e c o n d u c t o r s p e r m et e t er er a c = 2 00 0 0 00 0 0 0; 0 ; / / A mp K w = 0 .9 .9 2; 2; / / W i n d i n g f a c t o r / / W in in di di ng ng i s i n f i n i t e l y d i s t r i b u t e d w i th t h a p h a se se s pr p r ea ea d o f 60 d eg re e / / C a l c u l a t i o n o f t h e nu n umber o f s t a t o r s l o t s and a v e ra ra ge f l u x d e n si t y n s = r pm pm / 60 6 0 ; // Speed ( r . p . s ) l t a ge g e p er e r p ha h a se se E p h = E / 3 ^( ^ ( 1 /2 / 2 ) ; / / V o lt u r re r e nt n t p e r p h as as e I p h = Q * 1 0 ^ ( 6) 6) / ( 3 ^( ^ ( 1 / 2) 2 ) * E ) ; / / C ur u r re r e nt n t i n e ac a c h c o n du d u c to t o r ( i n a m pe pe r e ) I s = I p h/ h / a; a ; / / C ur m a t ur ur e Z = % pi pi * D *a * a c/ c / Is I s ; / / T o t a l n u m b e r o f a r ma conductors 88

24 T ph e r p ha h a se se f o r a t h r e e p h = i n t (Z/6+1); / / T u r n s p er

p h a s e m a ch c h i ne ne 25 Z = 6 * T ph t u a l n u m b e r o f c o n d u c to t o r s u se se d ph ; / / A c tu 26 S = Z / N c ; / / N um um b e r o f s l o t s 27 disp ( S , ’ ( a ) N u m b e r o f s l o t s = ’ ) ; 28 F _ p o le e r p o le le ( i n l e = a * E p h / ( 4 .4 .4 4 * f * T p h * Kw K w ) ; / / F l u x p er Wb) 29 p o le e t er er ) le _ pi p i t ch c h = % pi p i * D / p; p ; / / P o l e p i t c h ( i n m et 30 B a v = F _ po ge f l u x d e n s i t y p o l e / ( p o l e _p _ p i t ch c h * L ) ; / / A v e r a ge ( i n Wb p e r m e te te r s q u a r e ) 31 disp (Bav, ’ ( b ) A ve v e ra r a ge g e f l u x d e n s i t y (Wb p e r m et e t er er s q u a r e ) = ’ ); 32 / / i n b oo oo k a n sw s w e rs r s a r e 5 4 a n d 0 . 5 6 5 Wb Wb p e r m et e t er er s q u a r e r e s p e c t i v e l y . T h e a ns n s we w e rs r s v a ry ry d u e t o round o f f e r r o r

89

Chapter 15 Design of Magnetic Circuits

Scilab code Exa 15.1 Calculating the current in exciting coil

1 2 3 4 5 6 7 8 9 10 11 12 13

14 15

// C al cu la ti ng the c ur re nt i n e x ci t i ng c o i l clc ; x a mp mp l e 1 5 . 1 , P ag ag e No . = 1 5 . 7 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a F = 2 00 ; / / Mass ( i n kg ) l g = 5 ; / / D i s t a n c e ( i n mm) qu ar e ) A = 5 *1 * 1 0^ 0^ ( - 3) 3) ; / / A r e a o f p o l e f a c e ( i n m e t e r s qu ns T = 3 0 00 00 ; / / E x c i t i n g c o i l t u r ns p a ce ce u 0 = 4 * %p % p i * 10 1 0 ^( ^ ( - 7 ) ; / / P e r m e a b i l i t y o f f r e e s pa // // C al cu l a ti o n o f th e c ur re nt i n e x c i t i n g c o i l B = ( F * u0 u0 / ( 0 .0 . 0 51 5 1 * A ) ) ^ (1 (1 / 2) 2) ; / / f l u x d e n s i t y i n a i r g ap ap ( i n Wb p e r m et e t er er s q u a r e ) Mmf r e q u i r e d f o r m m f _ ai a i r = 8 0 0 00 00 0 * B * l g * 1 0^ 0^ ( - 3 ) ; / / Mm a i r ( i n A) Mmf r e q u i r e d f o r i r o n m m f_ f _ ir i r o n = 0 .1 . 1 * m m f_ f _ a ir ir ; / / Mm p a r t s ( i n A) A) . S i n ce c e mmf r e q u i r e d f o r i r o n p a rt rt s i s 1 0% o f a i r g a p mm mmf A T = m m f_ f_ a ir ir + m m f _i _ i r on on ; / / T o t a l mmf r r en e n t i n e x c i t i n g c o i l ( i n A m p er e ) I = A T /T / T ; / / C u rr 90

16 disp ( I , ’ C ur u r re r e nt n t i n e x c i t i n g c o i l ( Am A mp ere ) = ’ ) ; 17 / / i n b oo oo k a ns n s we w e r i s 1 . 4 5 6 A m p e r e . T h e a n sw s w er e r s v ar ar y

due t o round o f f e r r o r

Scilab code Exa 15.4 Calculating the winding depth and winding space

and space factor and the number of turns 1 / / C a l c u l a t i n g t he h e w in i n di d i ng n g d ep e p th t h a n d w in i n di d i ng n g s p ac ac e

a n d s p ac a c e f a c t o r a n d t he h e n u m b e r o f t u rn rn s 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

clc ; x a mp mp l e 1 5 . 4 , P ag ag e No . = 1 5 . 9 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a e t we w e en e n f l a n g e s ( i n mm mm) h f = 8 0 ; / / i n b et a m e te t e r ( i n mm mm) D o = 7 5 ; / / i n f l a n g e d i am a m et e t e r t ub u b e ( i n mm mm) D i = 3 0 ; / / i n g r o s s d i am o p pe p e r w i re re a = 0 .0 . 0 35 3 5 7; 7 ; / / A r e a o f c op a m e te t e r o f b a r e c o n d u c t o r ( i n mm mm) d = 0 .2 .2 13 13 ; / / D i am i a me m e te t e r o f i n s u l a t e d c o nd n d u ct ct o r d 1 = 0 . 21 2 1 3 +2 + 2 * 0. 0 . 0 5; 5 ; / / D ia ( i n mm) / / C a l c u l a t i o n o f t he h e w in i n di d i ng n g d ep e p th t h a n d w in i n di d i ng ng s p ac a c e a n d s p ac a c e f a c t o r a n d t he h e n u m b e r o f t u r ns ns i n di d i ng n g d e p t h ( i n mm) d f = ( Do Do - D i) i ) / 2; 2; / / W in n d in in g s p a c e A w = h f *1 * 1 0^ 0 ^ ( - 3) 3 ) * d f * 10 10 ^( ^ ( - 3 ) ; / / W i nd in di di ng ng d ep ep t h = ’ ) ; disp (df, ’ ( a ) W in W i n d i n g s pa pa c e = ’ ); disp (Aw, ’ t o r s w h e n t he he y bed ’ ) disp ( ’ ( b ) f o r c o n d u c to ac e f a c t o r S f = 0 .9 . 9 *( * ( d / d 1 ) ^( ^( 2) 2 ) ; / / S p ac um b e r o f t u r n s T = S f * Aw Aw / a * 10 1 0 ^ (6 (6 ) ; / / N um Space fa c t o r = ’ ); disp (Sf, ’ Number o f t u r n s = ’ ) ; disp ( T , ’ f o r c on o n d u ct c t or o r s when t h e y d o n o t b e d ’ ) disp ( ’ ce f a c t o r S f = 0 .7 . 7 8 *( *( d / d 1 ) ^( ^ ( 2) 2 ) ; / / S p a ce um b e r o f t u r n s T = S f * Aw Aw / a * 10 1 0 ^ (6 (6 ) ; / / N um 91

24 disp (Sf, ’ Space fa c t o r = ’ ); 25 disp ( T , ’ Number o f t u r n s = ’ ) ; 26 / / i n b oo o o k a n s w er e r s a r e 2 2 . 5 mm, 0 . 0 0 1 8 mm s q u a re re ,

0 . 4 1 7 , 2 10 1 0 25 2 5 , 0 . 3 6 1 a n d 1 8 2 00 00 . due t o round o f f e r r o r

92

T h e a ns n s we w e rs r s v ar ar y

Chapter 16 Design of Heating Elements and Inductors and Welding Transformers

Scilab code Exa 16.2 Calculating the inductance

1 2 3 4 5 6 7 8 9 10 11 12 13

/ / C a l c u l a t i n g t he h e i n du du ct an ce clc ; x a mp mp l e 1 6 . 2 , P ag ag e No . = 1 6 . 6 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a N = 2 5 ; / / Nu m b er o f t u r n s o s s s e c t i o n a l a re r e a o f t h e c o r e ( i n cm cm A c = 1 ; / / C r os squ are ) paa ce ce u 0 = 4 * %p % p i * 10 1 0 ^( ^( - 7 ) ; / / P e r m e a b i l i t y o f f r e e s p ti v e p e r me a b i li t y u r = 2 0 0; 0; / / R e l a ti l c = 1 5 ; / / ( i n cm ) // / / C a l c u l a t i o n o f t he h e i n d u ct ct an c e L = u 0 * u r * Ac Ac * 1 0 ^( ^( - 4 ) * N ^ ( 2 ) / ( l c * 10 1 0 ^ ( - 2 ) ) * 1 0 ^( ^( 6 ) ; / / I n d u ct c t a n ce c e ( i n m ic i c ro ro H) cr o H) = ’ ) ; disp ( L , ’ I n d u c t a n c e ( m i cr / / i n b o o k a ns n s we w e r i s 1 0 5 m ic i c ro r o H . T h e a ns n s we w e rs r s v ar ar y 93

due t o round o f f e r r o r

94

Chapter 18 Design of Starters and Field Regulators

Scilab code Exa 18.1 Calculating the upper and lower limits of current

during starting and resistance of each section 1 / / C a l c u l a t i n g t he h e u p p e r a n d l ow o w er er

l i m i t s o f c ur re nt d ur u r in in g s t a r t i n g and r e s i s t a n c e o f e a c h s e c t i o n

2 3 4 5 6 7 8 9 10 11 12

clc ; x a mp mp l e 1 8 . 1 , P ag ag e No . = 1 8 . 3 ’ ) disp ( ’ E xa

/ / G iv i v en e n D at at a / / d . c . s h u n t m ot o t or or P = 3 7 ; / / P o w e r r a t i n g ( i n kW) l t ag a g e r a t i n g ( i n V o lt lt s ) V = 2 5 0 ; / / V o lt oa d e f f i c i e n c y e = 0 . 84 84 ; / / F u l l l oa r m = 0 . 2; 2; / / A r m a t u r e c i r c u i t r e s i s t a n c e ( i n ohm ) n s = 8 ; / / Nu m b er o f s t u d s / / Maximum t o r q u e i s 1 50 5 0% o f f u l l l o a d t o r q u e / / C a l c u l a t i o n o f t h e u p p e r a n d l ow o w er er l i m i t s o f c u r r e n t d ur u r in in g s t a r t i n g 13 I fl a d c u r r e nt n t ( i n A m p er e fl = P * 1 0^ 0 ^ ( 3) 3) / ( V * e) e ) ; / / F u l l l o ad ) 95

14 I 1 = 1 .5 M aximum c u r r e n t ( i n A m p e r e ) . .5 * If I f l ; / / Ma

Since

t or o r qu qu e i s p r o p o r t i o n a l t o c u r r e n t 15 n = n s - 1; um b e r o f s e c t i o n s 1; / / N um 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

a lp l p ha h a = ( r m * I1 I1 / V ) ^( ^ ( 1/ 1/ n ) ; n t ( i n Ampere ) I 2 = a lp l p ha h a * I1 I 1 ; / / L o w e r l i m i t o f c u r r e nt pp e r l i m i t o f c u r r en e n t ( Am Am pere ) = ’ ) ; disp (I1, ’ U pp o w e r l i m i t o f c u r r e nt n t ( Am Am pere ) = ’ ) ; disp (I2, ’ L ow

// C al cu la ti on o f the r e s i s ta n c e o f each s e ct i o n t a l r e s i s t a n c e a t s t a r t i n g ( i n oh o hm ) R 1 = V /I / I 1 ; / / T o ta

r 1 = ( 1 - al a l ph p h a ) * R1 R1 ; r 2 = a lp l p ha h a * r1 r1 ; r 3 = a lp l p ha h a * r2 r2 ; r 4 = a lp l p ha h a * r3 r3 ; r 5 = a lp l p ha h a * r4 r4 ; r 6 = a lp l p ha h a * r5 r5 ; r 7 = a lp l p ha h a * r6 r6 ; o t al al r e s i s t a n c e a t s t a r t i n g disp (R1, ’ T ot i s t a n c e o f e aacc h s e c t i o n ’ ) disp ( ’ R e s is ohm ) = ’ ) ; disp (r1, ’ r 1 ( oh ohm ) = ’ ) ; disp (r2, ’ r 2 ( oh ohm ) = ’ ) ; disp (r3, ’ r 3 ( oh ohm ) = ’ ) ; disp (r4, ’ r 4 ( oh ohm ) = ’ ) ; disp (r5, ’ r 5 ( oh ohm ) = ’ ) ; disp (r6, ’ r 6 ( oh ohm ) = ’ ) ; disp (r7, ’ r 7 ( oh

( oh ohm ) = ’ ) ;

/ / i n b oo oo k a n sw s w e rs r s a r e I 1 = 2 64 6 4 a m p e r e , I 2 = 2 11 11 a m p e r e , R1 = 0 . 9 4 7 ohm , r 1 = 0 . 1 8 9 ohm , , r 2 = 0 . 1 5 1 oh o hm , r 3 = 0 . 1 2 1 ohm , r 4 = 0 . 0 9 7 ohm , r 5 = 0 . 0 7 7 oh ohm , r 6 = 0 . 0 6 2 oh ohm , r 7 = 0. 0 . 0 5 0 oh ohm . Th e a ns n s we w e rs r s v a ry ry d u e t o r o u n d o f f e r r o r

96

Electrical Machine Design_A. K. Sawhney

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