1 2
3 P=50D+3 //p ow er per pha se 4 Power_rating=3*P
5 Vpp=2300 //pr im ar y phas e voltage 6 Vsp=230 // seco ndar y ph as e voltage
7 Vpl= sqrt(3)*Vpp //pri ma ry no rm al lin e voltage 8 Vsl=Vsp // se con dar y no rma l li ne voltage
9 mprintf (”Ra ti ng of 3 − ph as e tra nsf orm er will be −\n3−
pha se , %d k VA, %d/%d V, st ar / de lt a conn ecti on \n ”,
Power_rating/1D+3, round (Vpl), round (Vsl)) 10 Ipp=P/Vpp
11 Ipl=Ipp 12 Isp=P/Vsp 13 Isl= sqrt(3)*Isp
14 mprintf (”Pri ma ry phas e curren t=%f A \ nP ri ma ry li ne
current=%f A \ nSe con dar y pha se curren t=%f A \
nS ec on da ry li ne current =%f A \n ”,Ipp,Ipl,Isp,Isl)
15 // calculating vol tag e regul ation
16 Rp_dash=1.2 // equ iva len t resistance referred t o primary
17 Xp_dash=1.6 // equiv alent reac tanc e referred to primary
18 VR=Ipp*(Rp_dash*.8+Xp_dash*.6)*100/Vpp
19 mprintf (”Voltage Regulation= %f percent ” , VR)
Scilab code Exa 15.2 Example on three phase transformer
1
2 // calculat ing no . of tur ns pe r ph as e 3 Vsp=440/ sqrt (3) // seco ndar y ph ase voltage 4 Et=8 //e mf per tur n in volt
5 Ts =round (Vsp/Et)
6 Vpp=1100 //pr im ar y phas e voltage 7 Tp=Ts*Vpp/Vsp
8 mprintf (”No. of turn s pe r ph as e on pr im ar y wi nd in g=
%d\nNo. of turn s pe r ph as e on sec ond ary wi nd in g=
%d\ n ”, Tp, Ts)
9 // calculat ing ne t cro ss −section al ar ea of co re 10 f=50 // frequ ency
11 Bm=1.3 // flux density 12 Ai=Et/(4.44*f*Bm)
13 mprintf (”N et cross −se ct io na l area of cor e , Ai=%d cm
ˆ2 ”, round (Ai*1D+4))
Scilab code Exa 15.3 Example on three phase transformer
1
2 // calculat ing curre nts in th e main and teaser transformer
3 P2=600D+3 //output 4 V2=110 // applied voltage
5 pf=.707 // lagging power facto r 6 I2=P2/(pf*V2)
7 I1t=1.15*I2*110/6600 8 I1m=I2*110/6600
9 mprintf (”Curren ts in pr im ar y wi ndi ng of main and
tease r tr ans fo rm er is %f A a nd %f A respectively \
n ”, I1 m,I1t)
10 // calculating line cur ren ts 11 Ic=I1t
12 Ib =sqrt(I1m^2+(I1t/2)^2) 13 Ia=Ib
14 mprintf (”Lin e currents are %f A , %f A a nd %f A ” , Ia,
Ib,Ic)
Scilab code Exa 15.4 Example on three phase transformer
1
2 function [r, the ta]=rect2p ol(x,y)
3 r =sqrt(x^2+y^2) 4 theta=atand(y/x)
5 endfunction
6 Q=750 // total lo ad to be sh ar ed 7 pf=.8 // lagging power facto r 8 theta=-acosd(.8)
9 Q=rect2pol(Q* cos(theta),Q* sin(theta))
10 Zb=rect2pol(.35,3.3) // per pha se im pe dan ce of transformer B
11 Za=rect2pol(.2,1.8) // per pha se im pe da nc e of transformer A
12 Qa=Zb*Q/(Za+Zb) 13 Qb=Za*Q/(Za+Zb)
14 mprintf (”Tra ns fo rm er A of 50 0 k VA rating shares a
load of %f k VA wh er eas transformer B of 25 0 k VA
Chapter 16
Electromechanical Energy
Conversion
Scilab code Exa 16.2 Example on Electromechanical Energy Conversion Devices
1
2 i =3// cur ren t in coi l 3 x=5D-2 // len gth of air gap 4 lambda= sqrt(i/(121*x^2)) 5 // cal cul at in g f i e l d ene rgy W f
6 W_f= integrate (”121 ∗ lambda ˆ2 ∗ .05ˆ2” ,”lambda” , 0 , lambda)
7 mprintf (” Field energy stor ed= %f wa tt −s e c \n ”, W_f )
8 // calc ulat ing coe ner gy
9 W_f_dash= integrate (” i ˆ.5/ (11 ∗ .0 5) ”,” i ”,0, i)
10 mprintf (”Co−ener gy= %f wat t −s e c \n ”, W_ f_d as h)
11 // calc ulat ing me ch ani cal force on moving pa rt − keeping la mb da constant
12 function y=f(x)
13 y=121*x^2*lambda^3/3
14 endfunction
15 F_f=-1* derivative (f,x)
round (F_f))
Scilab code Exa 16.3 Example on Electromechanical Energy Conversion Devices
1
2 mu_not=4D-7*%pi
3 i=120/6 // cur re nt flo wi ng in coil 4 N=300 //n o . of turn s
5 x=.005 // len gth of air gap
6 Ag=36D-4 // cro ss − sectional ar ea at g ap 7 // calc ulat ing stored f i e l d en er gy
8 W_f=mu_not*N^2*Ag*i^2/(4*x)
9 mprintf (” Stor ed f i e l d energy= %f wa tt −s e c \n ”, W_f )
10 // calc ulat ing me ch ani cal force dev elo ped 11 F_f=mu_not*N^2*i^2*Ag/(4*x^2)
Chapter 17
Fundamentals of DC Machines
Scilab code Exa 17.1 Example on DC Winding
1
2 P =6//n o . of poles
3 a = P//n o . of parallel circuits 4 n=150 //n o . of slots
5 c =8//n o . of co nd uc tor s pe r slot 6 Z=n*c // tota l no . of con duct ors 7 T=Z/2 //n o . of tur ns
8 Lmt=250D-2 // mean length of on e tur n 9 S=10*2.5*1D-6 // cross sectional ar ea 10 rho=2.1D-8 // r e s i s t i v i t y at 80 de gr ee C 11 R=(rho*Lmt*T)/(a^2*S)
12 mprintf (” Re si st an ce= %f ohm \ n”,R )
Scilab code Exa 17.2 Example on DC Winding
1
2 P =4//n o . of poles 3 n=24 //n o . of slots
4 c =2// con duct ors pe r slo t 5 Z=n*c // tota l no . of con duct ors 6 p=Z/4 // pole pitch
7 Ybp=p+1 //bac k pitch 8 Yfp=p-1 // front pitch 9 Y=Ybp-Yfp
10 mprintf (” Resultant pitch= %f”,Y )
Scilab code Exa 17.3 Example on EMF Equation
1
2 P =6//n o . of poles
3 A = P//n o . of paral lel pa t hs 4 phi=.018 // flux pe r pole
5 N=600 // sp ee d of rotation in rpm 6 Z=840 // tota l no . of con duct ors 7 Eg=P*phi*N*Z/(60*A)
8 mprintf (”E mf gen era ted= %f V \ n ”,Eg)
Scilab code Exa 17.4 Example on EMF Equation
1
2 P =6//n o . of poles
3 A =2//n o . of paral lel pa t hs
4 Z=300 //n o . of conduct ors on ar ma tu re 5 N=1000 // sp ee d of rotation in rpm 6 Eg=400 //e mf gene rate d on open ci rc ui t 7 phi=60*Eg*A/(P*N*Z)
Scilab code Exa 17.5 Example on EMF Equation
1
2 Eg=400 //e mf generated
3 n=80 //n o . of slo ts on ar ma tu r e 4 c=10 // cond uct ors pe r sl ot
5 Z=n*c // tota l no . of con duct ors on ar ma tu re 6 N=1000 // speed in rpm
7 phi=60*Eg/(N*Z)
8 Eg=220 // desired va lu e of gen er ate d volta ge 9 N=60*Eg/(phi*Z)
10 mprintf (”Sp ee d of rota tion to generate 22 0 V=%f r pm \
n ”, round (N))
Scilab code Exa 17.6 Example on EMF Equation
1
2 n=60 //n o . of slo ts on ar ma tu r e 3 c =6// con duct ors pe r slo t 4 Z=n*c // tota l no . of con duct ors
5 A =2//n o . of par all el pa th s in ar ma tu r e w in di ng 6 N=750 // sp ee d of rotation
7 P =4//n o . of poles
8 Eg=230 //e mf gene rate d on open ci rc ui t 9 phi=60*Eg*A/(P*N*Z)
10 mprintf (” Useful fux per pole= %f Wb \ n ”,phi)
11 Eg=115 //e mf to be gen er ate d at no lo ad
12 A=P*N*Z*phi/(60*Eg) // requ ired no . of par all el pa th s in arm atu re win ding
13 mprintf (”A s the ma ch in e ha s equal number of poles
and par all el pa th s in ar ma t ur e w i n d in g , th e
ar ma tu r e will be la p co nn ec te d to gen era te 1 15 V
Scilab code Exa 17.7 Example on Types of DC Machines
1
2 // calculat ing ter mina l volta ge 3 P=10D+3 // load supplied
4 Vl=220 // volta ge at lo ad term inals 5 Il=P/Vl
6 R=.1 // resistance of feeder s 7 Vd=Il*R // voltage dr op on feeder s 8 V=Vd+Vl
9 mprintf (”Te rm in al voltage across th e ar ma tu re
terminals=%f V \ n”,V )
10 // Calculat ing sh un t f i e l d current 11 Rsh=100 //sh un t resist ance 12 Ish=V/Rsh
13 mprintf (”Shunt f i e l d cu rre nt= %f A \n ”,Ish)
14 // Calculat ing generat ed emf 15 Ra=.05 // res ist anc e of ar ma tu re 16 Eg=V+Il*Ra
17 mprintf (” Generate d em f Eg=%f V ”,Eg)
Scilab code Exa 17.8 Example on Types of DC Machines
1
2 // calculat ing total ar ma tu r e cur ren t 3 V=200 // termin al voltage across ar ma tu re 4 Rsh=80 //sh un t f i e l d res is ta nc e
5 Ish=V/Rsh //shun t f i e l d curren t 6 Il=100 // load current
7 Ia=Il+Ish
8 mprintf (”Arma tur e cu rr en t=%f A \n ”,Ia)
10 A =4//n o . of paral lel pa t hs
11 mprintf (” Curre nt per armat ure pat h=%f A \ n ”,Ia/A)
12 // calc ulat ing emf gene rate d 13 Ra=.1 //arm at ur e res ist anc e 14 e =2//br us h contact dr op 15 Eg=V+Ia*Ra+e
16 mprintf (”E mf gen era ted= %f V \ n ”,Eg)
Scilab code Exa 17.9 Example on Types of DC Machines
1
2 V=100 // terminal voltage 3 Il=200 // load current
4 Rse=.03 // resis tance of ser ies f i e l d wi nd in g 5 Ra=.04 // res ist anc e of ar ma tu re wi nd in g 6 Rsh=60 // resist ance of sh un t
7 Vd=Il*Rse // voltage dr op in se ri es f i e l d wi nd in g 8 V_dash=V+Il*Rse // termin al voltage across ar ma tu re 9 Ish=V_dash/Rsh
10 Ia=Il+Ish
11 Eg=V+Il*Rse+Ia*Ra
12 mprintf (” Generate d em f=%f V ”,Eg)
Scilab code Exa 17.10 Example on Types of DC Machines
1
2 V=250 // terminal voltage 3 Il=450 // load current
4 Rsh=50 //sh un t f i e l d res is ta nc e 5 Ish=V/Rsh
6 Ia=Ish+Il
7 Ra=.05 //arm at ur e resi sta nce 8 Eg=V+Ia*Ra
9 P =4//n o . of poles
10 phi=.05 // flux pe r pole in W b 11 n=120 //n o . of slo ts on ar ma tu re 12 c =4// con duct ors pe r slo t 13 Z=n*c // tota l no . of con duct ors 14 A = P//n o . of paral lel pa t hs 15 N=60*Eg*A/(P*phi*Z)
16 mprintf (”Spe ed of ro tat io n=%f r pm” , round (N))
Scilab code Exa 17.11 Example on Types of DC Machines
1
2 //w hen the dc sh un t ma ch in e wo rk s as a generator 3 V=250 // terminal voltage
4 Il=80 // load current 5 Rsh=100 // f i e l d re si st an ce 6 Ra=.12 //arm at ur e resi sta nce 7 Ish=V/Rsh
8 Ia=Il+Ish 9 Eg=V+Ia*Ra 10
11 // when the dc sh un t ma ch in e wo rk s as a mo tor 12 V=250 // applied voltage to motor
13 Il=80 // li ne current drawn by the mot or 14 Ia=Il-Ish
15 Eb=V-Ia*Ra
16 // fo r a ma ch in e , P ∗ p h i ∗Z/(60 ∗A) is a co ns ta nt 17 x=Eg/Eb
18 mprintf (”speed as gener ator /speed as mo to r=%f” ,x )
Scilab code Exa 17.12 Example on Types of DC Machines
2 // calc ulat ing bac k emf 3 V=120 // applied voltage 4 Il=200 // li ne curren t
5 Rsh=30 //sh un t f i e l d res is ta nc e 6 Ra=.02 //arm at ur e wi nd in g resi sta nce 7 Ish=V/Rsh
8 Ia=Il-Ish 9 Eb=V-Ia*Ra
10 mprintf (”Back emf =%f V \ n ”,Eb)
11 n=90 //n o . of slo ts on ar ma tu r e 12 c =4// con duct ors pe r slo t
13 Z=n*c // tota l no . of con duct ors on ar ma tu re 14 phi=.04
15 N=60*Eb/(phi*Z)
16 mprintf (”Sp eed at whi ch motor wil l run when flux pe r
po le i s .0 4 Wb=%d r pm” ,round (N))
Scilab code Exa 17.13 Example on Types of DC Machines
1
2 // calculat ing lo ad cur ren t
3 i=30 // curren t drawn by eac h mo to r 4 I=5*i // curren t drawn by 5 mot ors 5 P=150*60 // total lighting lo ad 6 V=110 // applied voltage
7 I1=P/V // cur ren t ta ke n by light ing lo ad 8 I=I1+I
9 mprintf (”Total load curren t=%d A \ n ”,round (I))
10 // calculat ing ter mina l volta ge
11 V_dash=110 // volt age at term inals of lo ad 12 R=.04 // resistance of feeder s
13 Vd=I*R // volta ge d rop in feeders 14 V=V_dash+Vd
15 mprintf (”Te r mi na l volta ge across th e gene rat or
16 // calc ulat ing emf gene rate d 17 Rsh=55 // res is ta nc e of shu nt f i e l d 18 Ish=V/Rsh
19 Ia=I+Ish 20 Ise=Ia
21 Rse=.04 // se ri es f i e l d resi sta nce 22 Ra=.03 //arm at ur e resi sta nce 23 Eg=V+Ia*(Ra+Rse)
24 mprintf (” Generate d em f , Eg=%f V” ,Eg)
Scilab code Exa 17.14 Example on Types of DC Machines
1
2 // when the ma ch in e is wo rk in g as generator 3 V=240 // ter mina l volt age across th e lo ad 4 P=40D+3 // load on generator
5 Il=P/V // load current
6 Rsh=60 // res is ta nc e of shu nt f i e l d 7 Ish=V/Rsh
8 Ia=Il+Ish
9 Ra=.03 //arm at ur e resi sta nce 10 e=2*1 // voltage dr op at bru she s 11 Eg=V+Ia*Ra+e
12 N=450 // sp e e d as a gen er ato r at this lo ad 13 // l e t k=P ∗ p h i ∗Z/(60 ∗A)
14 k=Eg/N
15 //w hen the ma ch in e is wo rk in g as mo tor 16 Ia=Il-Ish
17 Eb=V-Ia*Ra-e 18 N=Eb/k
Chapter 18
DC Generators
Scilab code Exa 18.1 Example on Magnetization Characteristics
1
2 i =linspace (0,1.6,9)
3 V=[ 0 40 66 86 101 11 2 121 128 133 ]
4 plot (i, V,re ct=[ 0 0 1. 6 13 3] )
5 xtitle (”Magnetiz ation cur ve for ex am pl e 18.1 ” ,” Fie ld
Current” ,”Generate d em f”)
6
7 // refe r F ig . 18. 4 in th e te xt bo ok
8 Rsh=94 // res is ta nc e of shu nt f i e l d wi ndi ng 9 //OA is th e f i e l d resistance line for this
resistance
10 Voc=126 // volt age cor res pond ing to poi nt A
11 mprintf (”O pen ci rc ui t voltage when th e f i e l d ci rc ui t
res is ta nc e is 94 ohm=%d V \n ”,Voc)
12 // D is point on OCC corresponding to 11 0 V. O D repr esent s t he f i e l d resistance line t o ge ne ra te this vol tag e
13 R=70/.6 // total resist ance of sh un t f i e l d cir cui t
Figure 18.2: Example on Magnetization Characteristics
circu it is %f o hm \ n ”, R-R sh)
15 // lin e OE represents th e c r i t i c a l res ist anc e of shu nt f i e l d
16 Rc=40/.2
17 mprintf (” Cr it ic al res is ta nc e=%d o hm” ,Rc)
Scilab code Exa 18.2 Example on Magnetization Characteristics
1
2 i =linspace (0,3.5,8)
4 plot2d (i,V)
5 xtitle (”Magnetiz ation cur ve for ex am pl e 18.2 ” ,” Fie ld
Current” ,”Generate d em f”)
6
7 // refe r F ig . 18. 5 in th e te xt bo ok 8 Rsh=60 //sh un t f i e l d res is ta nc e 9 // line OA is f i e l d resis tance line
10 Voc=149 // volt age cor res pond ing to poi nt A
11 mprintf (”O pen ci r cu i t volt age= %d V \ n ”,Voc)
12 // re si st an ce repr esen ted by OE is c r i t i c a l resistance
13 Rc=120
14 mprintf (” Cr it ic al res is ta nc e of shu nt f i e l d=%d o hm \n
”,Rc)
15 // when th e lo ad ha s a resist ance of 4 o hm 16 R =4
17 // load cur ren t I=V/4 18 // I s h=V/60
19 // Ia=I+Is h 20 Eg=Voc
21 Ra=.1 //arm at ur e res ist anc e 22 //V=Eg−I a ∗Ra
23 V=Eg/(1+(1/R+1/Rsh)*Ra)
24 mprintf (”Terminal voltag e , V=%f V \n ”,V )
25 // when th e ter mina l volt age is 1 0 0 V 26 V=100 // terminal voltage
27 Ia=(Eg-V)/Ra 28 Ish=V/Rsh 29 I=Ia-Ish
30 mprintf (”Lo ad cu rr en t=%f A ”,I )
1
2 i =linspace (0,2.5,6) 3 V=[ 0 50 84 105 120 13 1]
4 plot (i,V)
5 xtitle (”Magnetiz ation cur ve for ex am pl e 18.3 ” ,” Fie ld
Current” ,”Generate d em f”) 6 7 // refe r F ig .18.6 in th e te xt bo ok 8 // OE is the f i e l d res is ta nc e li ne of c r i t i c a l resistance 9 Rc=100 10 // so lvi ng ( i i i ) 11 Rsh=70 // f i e l d re si st an ce 12 N=750 // speed in rpm 13 Nc=Rsh/Rc*N
14 mprintf (”When the f i e l d re si st an ce is 70 ohm,
c r i t i c a l s p ee d=%d rpm \n ”,round (Nc))
15 // so lvi ng ( iv )
16 Eg=100 //open − circuit vo lt ag e 17 Rsh=55 //sh un t f i e l d res is ta nc e
18 // now , th e oper atin g poi nt is M inste ad of A 19 //LM/LN=N1/N
20 // from the graph , LM/LN=10 0/115 21 N1=100/115*N // desir ed spe ed
22 mprintf (”W ith sh un t f i e l d re si st an ce of 55 ohm,
red uct ion in sp ee d to m ake th e open cir cui t
vol tag e equal to 100 V =%d r pm” ,round (N-N1))
Scilab code Exa 18.4 Example on Magnetization Characteristics
1
2 // ge ner ate d emf is direc tly proportio nal to sp ee d 3 // read ings for OCC at 100 0 rpm are
4 Eg 2 =[10* (1000/ 800) 112*( 1000/ 800) 198*( 1000/ 800) 232*( 1000/ 800) 252*( 1000/ 800) 266*( 1000/ 800)] 5 i =linspace (0,5,6)
6 plot2d (i,Eg2)
7 xtitle (”Magnetiz ation cur ve for ex am pl e 18.4 ” ,” Fie ld
cur ren t ”,”Generate d em f”)
8
9 // refe r F ig .18.7 in th e te xt bo ok 10 Rsh=70 // resist ance of f i e l d cir cui t 11 // line OA is f i e l d resis tance line
12 V=330 // volt age cor res pon din g to poi nt A
13 mprintf (”No lo ad ter min al volt age is %d V \ n”,V )
14 // now , no lo ad ter min al volt age is 2 70 V 15 V=270
16 // th e oper atin g poi nt is D
17 // line OD is cor res pon ding f i e l d resist ance line 18 R=V/2.4 // resis tance repr esen ted by line OD
19 mprintf (” Add iti ona l resist ance requ ired in th e f i e l d
ci rc ui t to re duc e th e voltage to 27 0 V=%f o hm \n ”
,R-Rsh)
Scilab code Exa 18.5 Example on Parallel Operation
1
2 // for generato r A
3 V1=240 // i n i t i a l term ina l vol tag e 4 V2=225 // fin al ter mina l volta ge 5 Ia=120 //ar ma tu re current
6 Ra=(V1-V2)/Ia //arm at ur e res ist anc e 7 // for generato r B
8 V1=230 // i n i t i a l term ina l vol tag e 9 V2=215 // fin al ter mina l volta ge 10 Ib=100 //ar ma tu re current
11 Rb=(V1-V2)/Ib //arm at ur e res ist anc e 12 I=200 // total lo ad cur ren t
13 // I1+I 2=I , V=240 − I 1 ∗Ra , V=230 − I 2 ∗Rb 14 // solvi ng for V, I1 and I2
15 a=[ 1 1 0;R a 0 1;0 Rb 1] 16 b=[200;240;230] 17 x =inv(a)*b 18 I1=x(1,1) 19 I2=x(2,1) 20 V=x(3,1)
21 mprintf (”Bus −bar volt age= %f V, \ nG ene rat or A sup pli es
%f A, \ nGe ne rat or B sup pli es %f A ” , V,I 1,I2)
Scilab code Exa 18.6 Example on Parallel Operation
1
2 Ra=.03 //ar ma tu r e resist ance of e ac h gene rato r 3 Rsh=60 // f i e l d res ist anc e of ea ch generato r 4 I=4500 // total lo ad cur ren t
5 // I1+I2 =4500 , Is h=V/60 6 // Ia 1=I1+ V/60
7 // Ia 2=I2+ V/60
8 Ea1=500 // in du ce d emf in generat or 1 9 //500=V+Ia1 ∗ . 0 3
10 Ea2=510 // in du ce d emf in generat or 2 11 //510=V+Ia2 ∗ . 0 3
12 // solving for V, I1 and I2
13 a=[ 1 1 0; .0 3 0 1+ .0 3/ 60 ;0 .0 3 1+ .0 3/ 60 ] 14 b=[4500;500;510] 15 x =inv(a)*b 16 I1=x(1,1) 17 I2=x(2,1) 18 V=x(3,1)
19 mprintf (”Bus −bar volt age= %f V, \ nLoad shared by
gen era tor 1=%f A, \ nLoad shared by gener ator 2=%f
Scilab code Exa 18.7 Example on Parallel Operation
1
2 //Le t V be bus −ba r volt age and I1 , I2 be th e cur ren ts sup pli ed by gen era tor s 1 and 2 respectively
3 Il=3000 // total lo ad cur ren t 4 // I1+I2 =I l
5 // for gene rato r 1
6 Rsh1=30 // f i e l d re si st an ce 7 Ra1=.05 //arm at ur e res ist anc e 8 Eg1=400 // induced em f
9 // for gene rato r 2
10 Rsh2=25 // f i e l d re si st an ce 11 Ra2=.03 //arm at ur e res ist anc e 12 Eg2=380 // induced em f
13 // I s h 1=V/ Rsh1 14 // I s h 2=V/ Rsh2 15 // Ia 1= I1+Is h1 16 // Ia 2= I2+Is h2
17 //Eg1=V+Ia1 ∗ Ra1 ; E g2=V+I a 2 ∗Ra2 18 // solving for I1 , I2 and V
19 a=[ 1 1 0;R a1 0 1+R a1/R sh 1;0 Ra 2 1+R a2/R sh 2] 20 b=[Il;Eg1;Eg2] 21 x =inv(a)*b 22 I1=x(1,1) 23 I2=x(2,1) 24 V=x(3,1) 25 P1=V*I1 26 P2=V*I2
27 mprintf (”Ou tp ut of gen era tor 1=%f kW \ nO ut pu t of
ge ne ra to r 2=%f kW”, P1/1 00 0, P2/10 00)
28 // an sw er s va ry from th e te xt boo k due to rou nd off error
Chapter 19
DC Motors
Scilab code Exa 19.1 Example on Torque and Speed
1
2 // calc ulat ing tor que de ve op ed 3 P =6//n o . of poles
4 A =6//n o . of parallel circuits 5 Ia=300 //ar ma tu re current 6 n=500 //n o . of ar ma tu re turns 7 Z=2*500 // tota l no . of con duc tors 8 phi=75D-3 // flux pe r pole
9 Ta=.159*P*phi*Ia*Z/A
10 mprintf (”Torq ue devel oped= %f N −m\ n ”,Ta)
11 // calculat ing shaft to rq ue
12 T=2.5*Ta/100 // torque l o st in wi nd age , f r i c t i o n an d ir on losses
13 Tsh=Ta-T
14 mprintf (” Shaft torque =%f N −m\n ”,Tsh)
15 // calc ulat ing shaft power 16 N=400 // speed in rpm 17 Psh=2*%pi*N*Tsh/60
18 mprintf (” Sh af t power =%f kW”,Psh/1000)
19 //an sw er va ry fro m th e te xtb ook due to rou nd of f error
Scilab code Exa 19.2 Example on Torque and Speed
12 // calc ulat ing tor que dev elo ped by ar ma tu re 3 V=200 // voltage applied across th e motor 4 Rsh=40 // res is ta nc e of shu nt f i e l d wi ndi ng 5 Ish=V/Rsh
6 I=100 // tot al current drawn by mo tor 7 Ia=I-Ish
8 Ra=.1 //arm at ur e res ist anc e 9 Eb=V-Ia*Ra
10 P=Eb*Ia // mechanic al po we r developed 11 N=750 // speed in rpm
12 Ta=60*P/(2*%pi*N)
13 mprintf (”Tor qu e developed by armat ure =%f N −m\ n ”,Ta)
14 // calculat ing co pp er los ses
15 Wcu1=V*Ia-Eb*Ia //arm at ur e co pp er lo ss es 16 Wcu2=Ish^2*Rsh // f i e l d coppe r lo ss es
17 mprintf (”Total cop per lo ss es= %f W \n ”,Wcu1+Wcu2)
18 // calc ulat ing shaft power
19 Wc=1500 // f r i c t i o n an d iro n l o s s e s 20 Pi=200*100 // input to mo to r 21 Psh=Pi-(Wc+Wcu1+Wcu2)
22 mprintf (” Sh af t powe r=%f kW \ n”,Psh/1000)
23 // calculat ing shaft to rq ue 24 Tsh=60*Psh/(2*%pi*N)
25 mprintf (” Shaft torque =%f N −m\n ”,Tsh)
26 // calculating effic ienc y 27 e=Psh/Pi*100
28 mprintf (” Ef fi ci en cy= %f percent ” ,e )
1
2 Po=60D+3 // f u l l load out put of the mo tor 3 e=0.905 // eff ici enc y of th e motor 4 Pin=Po/e
5 V=400 // applied voltage
6 I=Pin/V // li ne current drawn by the mo tor 7 Rsh=200 // res ist anc e of th e sh un t f i e l d wi nd in g 8 Ish=V/Rsh
9 Ia=I-Ish
10 Ra=0.1 //arm at ur e resi sta nce 11 Eb=V-Ia*Ra
12 A =2//n o . of par all el pa th s in ar ma tu r e w in di ng 13 P =4//n o . of poles
14 phi=45D-3 // flux pe r pole
15 Z=450 // tot al number of conduct ors 16 N =round (60*Eb*A/(P*phi*Z))
17 mprintf (” Fu ll loa d speed= %d rpm \ n”,N )
18 // calc ulat ing ar ma tu re tor que 19 Ta=0.159*P*phi*Ia*Z/A
20 mprintf (”To rq ue deve loped by the ar ma tu re of the D C
moto r=%f N−m\ n ”,Ta)
21 // calculat ing useful to rq ue 22 Psh=60D+3 // sh af t po we r 23 Tsh=60*Psh/(2*%pi*N)
24 mprintf (” Usef ul torque= %f N −m”,Tsh)
25 // error in th e te xt bo ok a ns we r for useful to rq ue
Scilab code Exa 19.4 Example on Torque and Speed
1
2 V=220 // voltage applied to motor 3 Rsh=157 //shun t f i e l d re si st an ce 4 Ra=0.3 //arm at ur e resi sta nce 5 Ish=V/Rsh
7 Ia0=I0-Ish 8 Eb0=V-Ia0*Ra
9 //un de r loade d conditions , 10 I=30 // cur ren t dr aw n by mo to r 11 Ia=I-Ish
12 Eb=V-Ia*Ra 13 // ph i =.97 ∗ phi0
14 / /b a ck e mf is directly prop ort iona l t o flux an d speed
15 N0=1000 // spe ed at no load 16 N=Eb*N0/(Eb0*.97)
17 mprintf (”Spee d unde r loaded con di tio n=%d rpm” , round
(N))
Scilab code Exa 19.5 Example on Torque and Speed
1
2 // calc ulat ing shaft power
3 V=100 // volt age appl ied to ser ies motor 4 Ra=.22 //arm at ur e resi sta nce
5 Rse=.13 // se ri es f i e l d resi sta nce 6 Rm=Ra+Rse // total resistance
7 Ia=45 // cur ren t in ar ma tu re cir cui t 8 Eb=V-Ia*Rm
9 Pm=Eb*Ia // mechanic al po we r developed 10 Wc=750 // ir on an d f r i c t i o n l o s s es 11 Psh=Pm-Wc
12 mprintf (” Sh af t powe r=%f kW \ n”,Psh/1000)
13 // calc ulat ing tor que dev elo ped 14 N=750 // speed in rpm
15 Ta=60*Pm/(2*%pi*N)
16 mprintf (” Total torque= %f N −m\n ”,Ta)
17 // calculat ing shaft to rq ue 18 Tsh=60*Psh/(2*%pi*N)
Scilab code Exa 19.6 Example on Torque and Speed
1
2 // calc ulat ing sp ee d 3 P =4//n o . of poles 4 V=220 // applied voltage
5 Ia=46 // cur ren t in ar ma tu re cir cui t 6 Ra=.25 // f i e l d re si st an ce
7 Rse=.15 // se ri es f i e l d resi sta nce 8 Rm=Ra+Rse
9 Eb=V-Ia*Rm
10 A =2//n o . of parallel circuits 11 phi=20D-3 // flux pe r pole
12 Z=1200 // to tal conduct ors on ar ma tu re 13 N =round (60*Eb*A/(P*phi*Z))
14 mprintf (” Spe ed , N=%d rpm \ n ”, N )
15 // calculating total to rq ue