1
2 E1=400 //e ddy cur ren t los ses
3 // for a machine , eddy cu rr en t losses is directly pro por tio nal to Bmaxˆ2 and f ˆ2
4 // Bmax is proporti onal to flux 5 // f is prop orti onal t o sp ee d
6 //w hen sp ee d and flux increased by 10%
7 E2=1.1^2*1.1^2*E1 //E ddy curren t lo ss es un de r ch an ge d conditi on
8 mprintf (” Increase in eddy current lo ss es= %f W” , E2-
E1 )
Scilab code Exa 20.2 Example on losses in DC Machine
1
2 N=1500 // speed in rpm 3 E1=300 // hysteresis losses 4 //E1=k1 ∗N
5 k1=E1/N
6 E2=150 //e ddy cur ren t los ses 7 //E2=k2 ∗Nˆ 2
8 k2=E2/N^2
9 E=E1+E2 // tota l ir on losses
10 // when iro n losses ar e r ed uc ed t o half 11 //k1 ∗N1+k2 ∗N1ˆ2=.5 ∗E
12 // solving for N1
13 N1=(-k1+ sqrt(k1^2-4*k2*(-.5*E)))/(2*k2)
14 mprintf (”T o t a l ir on losses will be h al v e d i f s p e e d
is red uce d to % d r pm” , round (N1))
Scilab code Exa 20.3 Example on losses in DC Machine
1
2 // calculating effic ienc y at f u l l lo ad 3 Il=200 // current supplied
4 Rsh=100 //shun t f i e l d res is ta nc e 5 V=500 // terminal voltage
6 Ish=V/Rsh 7 Ia=Il+Ish
8 Wcu=Ia^2*.1 //arm at ur e co pp er lo ss es
9 Wc=4000 // cons tant lo ss es including f i e l d co pp er losses
10 Wt=Wcu+Wc // total losses 11 Po=V*Il //output pow er 12 e=Po*100/(Po+Wt)
13 mprintf (” Eff ici enc y at f u l l load =%f percent \n ”, e )
14 / / Cal cul ati ng effic ienc y at half lo ad 15 Il=200/2 16 Ia=Il+Ish 17 Wcu=Ia^2*.1 18 Wt=Wc+Wcu 19 Po=V*Il 20 e=Po*100/(Po+Wt)
21 mprintf (” Efficienc y at half lo ad =%f per cen t \n ”, e ) 22 // Cal cul ati ng effic ienc y at 1.5 ti me s t he f u l l lo ad 23 Il=1.5*200 24 Ia=Il+Ish 25 Wcu=Ia^2*.1 26 Wt=Wc+Wcu 27 Po=V*Il 28 e=Po*100/(Po+Wt)
29 mprintf (” Effi cien cy at 1.5 tim es th e f u l l loa d=%f
perc ent ”, e )
Scilab code Exa 20.4 Example on losses in DC Machine
1
2 Po=10D+3 //ou tpu t po we r of ea ch mot or at f u l l load 3 e=.85 // eff ici enc y at f u l l lo ad
4 Pi=Po/e
5 W=Pi-Po // total los ses at f u l l lo ad for e ac h motor 6 // calcu lating half lo ad efficiency for motor A 7 Wc=500 // cons tant lo ss es
8 Wcu1=(W-Wc)/2^2 // co pp er lo ss es 9 W1=Wc+Wcu1 // total losses
10 P1=Po/2 //output 11 e1=P1/(P1+W1)*100
12 mprintf (” Effi cien cy at half loa d for motor A=%f
percent \ n ”, e1)
13 // calcu lating half lo ad efficiency for motor B 14 Wc=600 // cons tant lo ss es
15 Wcu2=(W-Wc)/2^2 // co pp er lo ss es 16 W2=Wc+Wcu2 // total losses
17 P2=Po/2 //output 18 e2=P2/(P2+W2)*100
19 mprintf (” Effi cien cy at half loa d for motor B=%f
Scilab code Exa 20.5 Example on losses in DC Machine
1
2 // calculating power re qui red at th e driv ing shaf t at f u l l load
3 Po=30D+3 //out pu t power of dc sh un t generat or 4 Wi=1300 // mec han ica l and iron lo ss es
5 Rsh=125 //shun t f i e l d res is ta nc e 6 V=250 // terminal voltage
7 Ra=.13 //arm at ur e r esi sta nce 8 Ish=V/Rsh
9 Wcu=V*Ish //sh un t f i e l d cop per lo ss es 10 Wc=Wi+Wcu // con st ant los ses of gene rat or 11 Il=Po/V
12 Ia=Il+Ish
13 Wcu=Ia^2*Ra //arm at ur e co pp er lo ss 14 Wt=Wc+Wcu // total losses
15 Pi=Po+Wt
16 mprintf (”P ower requi red at th e driving shaft at f u l l
load=%f kW \n ”, Pi/1 0^3 )
17 // calculating effic ienc y at f u l l lo ad 18 e=Po/Pi*100
19 mprintf (” Eff ici enc y at f u l l load =%f percent \n ”, e )
20 // calcu lating efficiency a t half l oa d 21 Il=(Po/2)/V
22 Ia=Il+Ish
23 Wcu=Ia^2*Ra // co pp er lo ss es 24 Wt=Wc+Wcu // total losses 25 e=(Po/2)/(Po/2+Wt)*100
26 mprintf (” Efficienc y at half lo ad =%f per cen t \n ”, e )
27 // at maximum e f f i c i e n c y 28 Wcu=Wc // co pp er lo ss es 29 Ia =sqrt(Wcu/Ra)
31 mprintf (”P ower out put at max ef f ic i en c y=%f kW \n ”,Il* V/10^3)
32 // calculat ing max eff ici enc y 33 e_max=Il*V/(Il*V+2*Wc)*100
34 mprintf (”Max ef fi ci en cy= %f percent ” , e_ ma x)
35 //an sw er va ry fro m th e te xtb ook due to rou nd of f error
Scilab code Exa 20.6 Example on losses in DC Machine
1
2 V=500 // voltage applied to motor 3 Ra=.2 //arm at ur e r esi sta nce
4 Il0=4 //n o loa d curren t ta ke n by mo tor 5 Ish=1 //shun t current
6 Pi=V*Il0 //po wer inp ut at no load 7 Ia0=Il0-Ish
8 Wcu=Ia0^2*Ra //ar m at ur e co pp er los ses at n o lo ad 9 Wc=Pi-Wcu // cons tant lo ss es
10 //w hen input curren t= 20 A 11 Il=20
12 Ia=Il-Ish
13 Wcu=Ia^2*Ra //arm at ur e co pp er lo ss es 14 Wt=Wc+Wcu // total losses
15 Pi=V*Il //po wer input to mot or 16 Po=Pi-Wt
17 e=Po/Pi*100
18 mprintf (”When input curren t= 20 A, outp ut is %f W and
effic ienc y of motor is %f per ce nt \ n”,P o, e)
19 //w hen input curren t =100 A 20 Il=100
21 Ia=Il-Ish
22 Wcu=Ia^2*Ra //arm at ur e co pp er lo ss es 23 Wt=Wc+Wcu // total losses
25 Po=Pi-Wt 26 e=Po/Pi*100
27 mprintf (”When input curren t =100 A , out put is %f W
and effic ienc y of motor is %f pe rc en t \ n ”, Po,e)
Scilab code Exa 20.7 Example on losses in DC Machine
1
2 //sh un t generato r was run as a sh un t motor at no load
3 I0=5 // cur ren t dr aw n
4 Ish=1.5 //shun t f i e l d curren t 5 Ia0=I0-Ish
6 Ra=.15 //ar m a t u r e circu it resistance 7 V=440 // terminal voltage
8 Wcu=Ia0^2*Ra //arm at ur e co pp er los s 9 Pi=V*I0 //p ow er input
10 Wc=Pi-Wcu // cons tant lo ss es
11 // calculating effic ienc y of s h u n t ge ne rat or at f u l l load
12 Po=50D+3 //out pu t of generat or 13 Il=Po/V // load current
14 Ia=Il+Ish
15 Wcu=Ia^2*Ra // co pp er lo ss es 16 Wt=Wc+Wcu // total losses 17 e=Po/(Po+Wt)*100
18 mprintf (” Efficienc y of sh un t gen erat or at f u l l lo ad =
%f percent \ n ”, e )
19 // calculating effic ienc y at 3 /4th lo ad 20 I1=3/4*Il // load current
21 Ia=I1+Ish
22 Wcu=Ia^2*Ra // co pp er lo ss es 23 Wt=Wc+Wcu // total losses 24 e=(3/4*Po)/(3/4*Po+Wt)*100
26 // calcu lating efficiency a t half l oa d 27 I2=.5*Il // load current
28 Ia=I2+Ish
29 Wcu=Ia^2*.15 // co pp er lo ss es 30 Wt=Wc+Wcu // total losses 31 e=(.5*Po)/(.5*Po+Wt)*100
32 mprintf (” Effi cien cy at half loa d=%f perc ent ” , e )
Scilab code Exa 20.8 Example on losses in DC Machine
1
2 I1=50 // input current fr om ma in s
3 Po=100D+3 //ou tp ut of gene rato r on f u l l lo ad in W 4 V=500 // terminal voltage
5 I2=Po/V // lo ad curr ent of gene rat or 6 Rg=.1 //ar ma t ur e resist ance of gene rat or 7 Rm=.1 //arm at ur e res ist anc e of mo tor 8 Pi=25D+3 // input po we r fr om mai ns
9 Pr=(Pi-I2^2*Rg-(I1+I2)^2*Rm)/2 // iro n an d me ch ani cal lo ss es in ea ch ma chin e 10 I3=4 //sh un t f i e l d current of generator 11 I4=3 //shun t f i e l d curren t of mo to r 12 / / calculating effic ienc y of gen er ato r 13 Wt=Pr+V*I3+I2^2*Rg // total losses 14 e=Po/(Po+Wt)*100
15 mprintf (” Effi cien cy of generato r=%f perc ent \n ”, e )
16 // calculating effic ienc y of motor 17 Pi=V*(I1+I2+I4) //po we r input
18 Wt=Pr+V*I4+(I1+I2)^2*Rm // total losses 19 e=(Pi-Wt)/Pi*100