# CHAPTER03:THREE PHASE CIRCUITS¶

## Example E01 : Pg 172¶

In [1]:
             # EXAMPLE 3-1 PG NO-172
import math
VL=400.;
Vp=400./math.sqrt(3.);
Z=8.-1j*10.;
IL=Vp/Z;
S=math.sqrt(3.)*(VL*IL);
P=S*(math.cos(-51.34));
Q=S*(math.sin(-51.34));
Von=230.94+1j*0;
Vbn=-115.47-1j*99.99
print 'i) RMS   =  ',S,'A'

i) RMS   =   (7804.87804878+9756.09756098j) A


## Example E02 : Pg 173¶

In [2]:
      # EXAMPLE 2-32    PG NO 173
import math
Vp=400.;     # Peak voltage
VL=400.;
Z=8.-1j*10.;     # Impedance
Ip=VL/12.81;
IL=math.sqrt(3.)*Ip;
S=math.sqrt(3.)*VL*IL;
P=S*math.cos(-51.34);
Q=S*math.sin(-51.34);
Vab=Vp+1j*0;
Vbc=-200.-1j*346.410;
Vca=-200.+1j*346.;
Iab=Vab/Z;
Ibc=Vbc/Z;
Ica=Vca/Z;
Ia=Iab-Ibc;
Ib=Ibc-Iab;
Ic=Ica-Ibc;
print 'i) Peak current   =  ',Ip,'A '
print 'i) S   =  ',S,'VA '
print 'i) Active Power   =  ',P,'W '
print 'i) Reactive power   =  ',Q,'Vars '
print 'i) Iab is in reactance form  =  ',Iab,'A '
print 'i) Ibc is in  reactance form =  ',Ibc,'A '
print 'i) Ica is in reactance   form=  ',Ica,'A '
print 'i) Ia is in  reactance form =  ',Ia,'A '
print 'i) Ib is in reactance form  =  ',Ib,'A '
print 'i) Ic is in reactance  =  ',Ic,'A '

i) Peak current   =   31.2256049961 A
i) S   =   37470.7259953 VA
i) Active Power   =   17841.9317159 W
i) Reactive power   =   -32950.2773776 Vars
i) Iab is in reactance form  =   (19.512195122+24.3902439024j) A
i) Ibc is in  reactance form =   (11.3664634146-29.0931707317j) A
i) Ica is in reactance   form=   (-30.8536585366+4.68292682927j) A
i) Ia is in  reactance form =   (8.14573170732+53.4834146341j) A
i) Ib is in reactance form  =   (-8.14573170732-53.4834146341j) A
i) Ic is in reactance  =   (-42.2201219512+33.776097561j) A


## Example E03 : Pg 174¶

In [3]:
     # EXAMPLE 3.3  PG NO 174
import math
Zy=3.+1j*5.196;
Zeq=2.55+1j*2.916;
Vp=230.94;
IL=59.61;
Ip=59.61;
VL=400.;
#cos(48.83)=0.658;
#sin(48.83)=0.7527;
S=math.sqrt(3.)*VL*IL;
P=math.sqrt(3.)*VL*IL*0.658;
Q=math.sqrt(3.)*VL*IL*0.7527;
print 'i) S   =  ',S,'VA '
print 'i) Active power   =  ',P,'W '
print 'i) Reactive power   =  ',Q,'Vars '

i) S   =   41299.0194557 VA
i) Active power   =   27174.7548018 W
i) Reactive power   =   31085.7719443 Vars


## Example E04 : Pg 174¶

In [4]:
# EXAMPLE 3-4   PG NO-174
import math
V=220.;
Im=15.75+1j*21.;
Z=5.33-1j*4.;
LI=V/(math.sqrt(3.)*Z);
TLI=LI+Im;
#math.cos(-17.16)=0.955;
PF=math.sqrt(3.)*0.955*V*32.42;
print 'i) Line current   =  ',LI,'A '
print 'i) TOTAL line current   =  ',TLI,'A '
print 'i) Power Factor   =  ',PF,'W '

i) Line current   =   (15.2447127862+11.4406850178j) A
i) TOTAL line current   =   (30.9947127862+32.4406850178j) A
i) Power Factor   =   11797.7636168 W


## Example E05 : Pg 175¶

In [5]:
   # EXAMPLE 3-5 PG NO-175
import math
Pm=6000.;
Qm=8000.;
Z=16.-1j*12.;
V=220.;
PC=V/Z;
PL=3.*V*11.*0.799;
QL=3.*V*11.*(-0.6);
P=Pm+PL;
Q=Qm+QL;
PF=math.cos(1./math.tan(Q/P));
IL=P/(math.sqrt(3.)*V*0.9555);
print 'i) Phase current   =  ',PC,'A '
print 'i) PL   =  ',PL,'W '
print 'i) QL   =  ',QL,'Vars '
print 'i) Active power   =  ',P,'W '
print 'i) Reactive Power   =  ',Q,'Vars '
print 'i) Power factor   =  ',PF,'lagging '
print 'i)  line current (IL)  =  ',IL,'A '

i) Phase current   =   (8.8+6.6j) A
i) PL   =   5800.74 W
i) QL   =   -4356.0 Vars
i) Active power   =   11800.74 W
i) Reactive Power   =   3644.0 Vars
i) Power factor   =   -0.999977005554 lagging
i)  line current (IL)  =   32.411209817 A


## Example E06 : Pg 175¶

In [6]:
                   # EXAMPLE 3-6     PG NO-175
Vac=100.+1j*0;
Vcb=-50.-1j*86.6;
Vba=-50.+1j*86.6;
Zac=6.+1j*8.;
Rcb=20.+1j*0;
Zba=4.-1j*3.;
Zcb=20.+1j*0;
Iac=Vac/Zac;
print ('i) CURRENT  (Iac) is  in rectangular form  =  ',Iac,' A ');
Icb=Vcb/Zcb;
print ('i) CURRENT  (Icb) is  in  rectangular form  =  ',Icb,' A ');
Iba=Vba/Zba;
print ('i) CURRENT  (IbA) is  in rectangular form  =  ',Iba,' A ');
Ia=Iac-Iba;
print ('i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A ');
Ic=Icb-Iac;
print ('i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A ');
Ib=Iba-Icb;
print ('i) CURRENT  (Ib) is  in  rectangular form  =  ',Ib,' A ');
Pac=Vac*Iac*0.6;
print ('iv)  Power (Pac) is  in  rectangular form   =  ',Pac,'  W ');
Pcb=Vcb*Icb;
print ('iv)  Power (Pcb) is in   rectangular form    =  ',Pcb,'  W ');
Pba=Vba*Iba*0.8;
print ('iv)  Power (Pba) is  in rectangular form  =  ',Pba,'  W ');
Qac=100.*20.*0.8;
print ('iv) Reactive Power (Qac) is in rectangular form   =  ',Qac,'  vars ');
Qba=100.*20.*-0.6
print ('iv) Reactive Power (Qba) is   in rectangular form =  ',Qba,'  vars ');
P=600.+500.+1600.;
print ('iv)  Power (P) is    =  ',P,'  W ');
Q=800.-1200.;
print ('iv)  Power (Q) is    =  ',Q,'  vars ');

('i) CURRENT  (Iac) is  in rectangular form  =  ', (6-8j), ' A ')
('i) CURRENT  (Icb) is  in  rectangular form  =  ', (-2.5-4.33j), ' A ')
('i) CURRENT  (IbA) is  in rectangular form  =  ', (-18.392+7.855999999999999j), ' A ')
('i) CURRENT  (Ia) is  in rectangular form  =  ', (24.392-15.855999999999998j), ' A ')
('i) CURRENT  (Ic) is  in rectangular form  =  ', (-8.5+3.67j), ' A ')
('i) CURRENT  (Ib) is  in  rectangular form  =  ', (-15.892+12.186j), ' A ')
('iv)  Power (Pac) is  in  rectangular form   =  ', (360-480j), '  W ')
('iv)  Power (Pcb) is in   rectangular form    =  ', (-249.978+433j), '  W ')
('iv)  Power (Pba) is  in rectangular form  =  ', (191.4163200000001-1588.4377599999998j), '  W ')
('iv) Reactive Power (Qac) is in rectangular form   =  ', 1600.0, '  vars ')
('iv) Reactive Power (Qba) is   in rectangular form =  ', -1200.0, '  vars ')
('iv)  Power (P) is    =  ', 2700.0, '  W ')
('iv)  Power (Q) is    =  ', -400.0, '  vars ')


## Example E07 : Pg 176¶

In [7]:
                      # EXAMPLE 3-7  PG NO-176-177
Vab=400.+1j*0;
Vbc=-200.-1j*346.410;
R=100.;
Ica=0;
Iab=Vab/R;
print 'i) CURRENT  (Iab) is  in rectangular form  =  ',Iab,' A '
Ibc=Vbc/R;
print 'i) CURRENT  (Ibc) is  in rectangular form  =  ',Ibc,' A '
Ia=Iab-Ica;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Ibc-Iab;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Ica-Ibc;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '

i) CURRENT  (Iab) is  in rectangular form  =   (4+0j)  A
i) CURRENT  (Ibc) is  in rectangular form  =   (-2-3.4641j)  A
i) CURRENT  (Ia) is  in rectangular form  =   (4+0j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (-6-3.4641j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (2+3.4641j)  A


## Example E08 : Pg 177¶

In [8]:
                       # EXAMPLE 3-8   PG NO-177
Za=10-1j*8;
Zb=12+1j*0;
Zc=8+1j*10;
Van=230.94+1j*0;
Vbn=-115.47-1j*200;
Vcn=-115.47+1j*200;
Ia=Van/Za;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Vbn/Zb;
print 'ii) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Vcn/Zc;
print 'iii) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
In=Ia+Ib+Ic;
print 'iv) CURRENT  (In) is  in rectangular form  =  ',In,' A '

P=(230.94*18.028*0.78)+(230.94*19.245)+(230.94*18.028*0.62)

print 'v) POWER  (P) is  in rectangular form  =  ',P,' W '

i) CURRENT  (Ia) is  in rectangular form  =   (14.0817073171+11.2653658537j)  A
ii) CURRENT  (Ib) is  in rectangular form  =   (-9.6225-16.6666666667j)  A
iii) CURRENT  (Ic) is  in rectangular form  =   (6.56243902439+16.7969512195j)  A
iv) CURRENT  (In) is  in rectangular form  =   (11.0216463415+11.3956504065j)  A
v) POWER  (P) is  in rectangular form  =   10273.181148  W


## Example E09 : Pg 178¶

In [9]:
                                   # EXAMPLE 3-9     PG NO-178-179
Z1=10.+1j*0;
Z2=13.+1j*7.5;
Z3=-13.+1j*7.5;
Z4=8.66-1j*5.;
#X=[Z1+Z2 Z3;Z3 Z2+Z4];
Z5=-104.+1j*180.13;
Z6=280.+1j*0;
#Y=[Z5 Z3;Z6 Z2+Z4];
I1=-2.26 + 8.65j;#det(Y/X);
print 'i)   Current (I1) is    =  ',I1,' A  '

i)   Current (I1) is    =   (-2.26+8.65j)  A


## Example E10 : Pg 180¶

In [10]:
                     # EXAMPLE 3-10          PG NO-180
Za=6.+1j*0;
Zb=5.26+1j*3;
Zc=3.535+1j*3.535;
Van=230.94+1j*0;
Vcn=-115.47-1j*200;
Vbn=-115.47+1j*200;
Ya=1./Za;
print 'i) admittance  (Ya) is  in rectangular form  =  ',Ya,' siemens '
Yb=1./Zb;
print 'i) admittance  (Yb) is  in  rectangular form  =  ',Yb,' siemens '
Yc=1./Zc;
print 'i) admittance  (Yc) is  in rectangular form  =  ',Yc,' siemens '
Von=((Van*Ya)+(Vbn*Yb)+(Vcn*Yc))/(Ya+Yb+Yc);
print 'i) Voltage  (Von) is  in rectangular form  =  ',Von,' V'
Vao=Van-Von;
print 'i) Voltage  (Vao) is  in rectangular form  =  ',Vao,' V'
Vbo=Vbn-Von;
print 'i) Voltage  (Vbo) is  in rectangular form  =  ',Vbo,' V'
Vco=Vcn-Von;
print 'i) Voltage  (Vco) is  in rectangular form  =  ',Vco,' V'
Ia=Vao*Ya;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Vbo*Yc;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Vco*Yc;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '

i) admittance  (Ya) is  in rectangular form  =   (0.166666666667+0j)  siemens
i) admittance  (Yb) is  in  rectangular form  =   (0.143450893977-0.0818160992266j)  siemens
i) admittance  (Yc) is  in rectangular form  =   (0.1414427157-0.1414427157j)  siemens
i) Voltage  (Von) is  in rectangular form  =   (-34.3032387626+41.0196191983j)  V
i) Voltage  (Vao) is  in rectangular form  =   (265.243238763-41.0196191983j)  V
i) Voltage  (Vbo) is  in rectangular form  =   (-81.1667612374+158.980380802j)  V
i) Voltage  (Vco) is  in rectangular form  =   (-81.1667612374-241.019619198j)  V
i) CURRENT  (Ia) is  in rectangular form  =   (44.2072064604-6.83660319972j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (11.0061696696+33.9670639376j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (-45.5709166104-22.6100223424j)  A


## Example E11 : Pg 181¶

In [11]:
                       # EXAMPLE 3-11   PG NO-181

Vrn=230.94+1j*0;
Vyn=-115.47-1j*200.;
Vbn=-115.47+1j*200.;
Yr=-1j*0.05;
Yy=1j*0.05;
Yb=0.05;
Von=((Vrn*Yr)+(Vyn*Yy)+(Vbn*Yb))/(Yr+Yy+Yb);
print 'i) Voltage  (Von) is  in rectangular form  =  ',Von,' V'
Vyo=Vyn-Von;
print 'i) Voltage  (Vyo) is  in rectangular form  =  ',Vyo,' V'
Iy=Vyo*Yy;
print 'iii) CURRENT  (Iy) is  in rectangular form  =  ',Iy, ' A '

i) Voltage  (Von) is  in rectangular form  =   (84.53-146.41j)  V
i) Voltage  (Vyo) is  in rectangular form  =   (-200-53.59j)  V
iii) CURRENT  (Iy) is  in rectangular form  =   (2.6795-10j)  A


## Example E12 : Pg 181¶

In [12]:
              # EXAMPLE 3-12       PG NO-181-182
import math
Vp=400.;
Zp=10+1j*24;
Zpy=6-1j*8;
Ip=Vp/Zp;
print 'i) CURRENT  (Ip) is  in rectangular form  =  ',Ip,' A '
Ipy=(Vp/math.sqrt(3.))/Zpy;
print 'ii) CURRENT  (Ipy) is  in rectangular form  =  ',Ipy,' A '
Rp=10.;
Rpy=6.;
Xp=24.;
Xpy=-8.;
P1=3*Ip*Ip*Rp;
print 'iii)  Power (P1) is    =  ',P1,'  W '
P2=Ipy*Ipy*3*Rpy;
print 'iv)  Power (P2) is    =  ',P2,'  W '
Q1=3*Ip*Ip*Xp;
print 'v)  Power (Q1) is    =  ',Q1,'  W '
Qy=3*Ipy*Ipy*Xpy;
print 'vi)  Power (Qy) is    =  ',Qy,'  W '
P=P1+P2;
print 'vii)  Power (P) is    =  ',P,'  W '
Q=Q1+Qy;
print 'viii)  Power (Q) is    =  ',Q,'  W '
S=P+1j*Q;
print 'ix)  Power (S) is    =  ',S,'  W '
LI=S/(math.sqrt(3.)*Vp);
print 'x) CURRENT  (LI) is  in rectangular form  =  ',LI,' A '

i) CURRENT  (Ip) is  in rectangular form  =   (5.91715976331-14.201183432j)  A
ii) CURRENT  (Ipy) is  in rectangular form  =   (13.8564064606+18.4752086141j)  A
iii)  Power (P1) is    =   (-4999.8249361-5041.8402717j)   W
iv)  Power (P2) is    =   (-2688+9216j)   W
v)  Power (Q1) is    =   (-11999.5798466-12100.4166521j)   W
vi)  Power (Qy) is    =   (3584-12288j)   W
vii)  Power (P) is    =   (-7687.8249361+4174.1597283j)   W
viii)  Power (Q) is    =   (-8415.57984664-24388.4166521j)   W
ix)  Power (S) is    =   (16700.591716-4241.42011834j)   W
x) CURRENT  (LI) is  in rectangular form  =   (24.1052278071-6.12196261768j)  A


## Example E13 : Pg 182¶

In [13]:
                                     # EXAMPLE 3-13    PG NO 182
VRY=375.877+1j*136.80;
print 'i)   LINE VOLTAGE (VRY) is in rectangular form   =  ',VRY,' V  '
VYB=-69.45-1j*393.923;
print 'ii)   LINE VOLTAGE (VYB) is in rectangular form   =  ',VYB,' V  '
VBR=-306.41+1j*257.11;
print 'iii)   LINE VOLTAGE (VBR) is in rectangular form   =  ',VBR,' V  '
VYR=-VRY;
print 'i)   LINE VOLTAGE (VYR) is in rectangular form   =  ',VYR,' V  '
VRB=69.45+1j*393.923;
print 'i)   LINE VOLTAGE (VRB) is in rectangular form   =  ',VRB,' V  '
VBY=306.41-1j*257.11;
print 'i)   LINE VOLTAGE (VBY) is in rectangular form   =  ',VBY,' V  '

i)   LINE VOLTAGE (VRY) is in rectangular form   =   (375.877+136.8j)  V
ii)   LINE VOLTAGE (VYB) is in rectangular form   =   (-69.45-393.923j)  V
iii)   LINE VOLTAGE (VBR) is in rectangular form   =   (-306.41+257.11j)  V
i)   LINE VOLTAGE (VYR) is in rectangular form   =   (-375.877-136.8j)  V
i)   LINE VOLTAGE (VRB) is in rectangular form   =   (69.45+393.923j)  V
i)   LINE VOLTAGE (VBY) is in rectangular form   =   (306.41-257.11j)  V


## Example E14 : Pg 182¶

In [14]:
                     # EXAMPLE 3-14   PG NO 182-183
X=[[400+1j*0, -6+1j*0],[-200-1j*346.410,  6-1j*0]];
Y=[[12+1j*0, -6+1j*0],[-6+1j*0, 6-1j*8]];
I1=52.31-1j*7.120;
I2=37.957-1j*14.23;
Ia=I1;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=I2-I1;
print 'i) CURRENT  (Ib) is  in  rectangular form  =  ',Ib,' A '
IC=-I2;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',IC,' A '
Z1=6+1j*0;
Vao=Ia*Z1;
print 'i) VOLTAGE  (Vao) is  in rectangular form  =  ',Vao,' V '
Vbo=Ib*Z1;
print 'i) VOLTAGE  (Vbo) is  in rectangular form  =  ',Vbo,' V '
Vco=IC*(-1j*8);
print 'i) VOLTAGE  (Vco) is  in rectangular form  =  ',Vco,' V '

i) CURRENT  (Ia) is  in rectangular form  =   (52.31-7.12j)  A
i) CURRENT  (Ib) is  in  rectangular form  =   (-14.353-7.11j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (-37.957+14.23j)  A
i) VOLTAGE  (Vao) is  in rectangular form  =   (313.86-42.72j)  V
i) VOLTAGE  (Vbo) is  in rectangular form  =   (-86.118-42.66j)  V
i) VOLTAGE  (Vco) is  in rectangular form  =   (113.84+303.656j)  V


## Example E15 : Pg 185¶

In [15]:
                       # EXAMPLE 3-15  PG NO-185-186
Van=230.94+1j*0;
Vbn=-115.47-1j*200.;
Vcn=-115.47+1j*200.;
V1=10.*10.**3.;
Ia=V1/Van;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
V2=4.*10.**3.;
Ic=V2/Van;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
V3=6.*10.**3.;
Ib=V3/Van;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
In=(Ia+Ib+Ic);
print 'i) CURRENT  (In) is  in rectangular form  =  ',In,' A '
W1=(V1+V2+V3)/2.;
print 'iv)  Power (W1) is in rectangular form    =  ',W1,'  W '

i) CURRENT  (Ia) is  in rectangular form  =   (43.3012903785+0j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (17.3205161514+0j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (25.9807742271+0j)  A
i) CURRENT  (In) is  in rectangular form  =   (86.6025807569+0j)  A
iv)  Power (W1) is in rectangular form    =   10000.0   W


## Example E16 : Pg 186¶

In [16]:
        # example-3.16   pg no-186
W1=5920.;
W2=2610.;
P=8530.;
tanQ=(1.732*(W2-W1))/(W1+W2);
cosQ=0.83;
PF=cosQ;
print 'i) tanQ  = ',tanQ
print 'ii) POWER FACTOR  = ',PF

i) tanQ  =  -0.672089097304
ii) POWER FACTOR  =  0.83


## Example E18 : Pg 186¶

In [17]:
  # Example 3.18      pg no-186-187
cosQ=0.8;
sinQ=0.6;
VL=10000.;
V=5000.*10.**3.;               # VOLTAGE
PF=0.9;                 # POWER FACTOR
IL=V/(1.732*VL*cosQ) ;
I1=IL*cosQ;    # ACTIVE  COMPONENT
I2=IL*sinQ;    # REACTIVE  COMPONENT
P=1.732*(VL*IL*PF)
print 'i) IL = ',IL,' A'
print 'i) ACTIVE COMPONENT = ',I1,' A'
print 'i)  REACTIVE COMPONENT = ',I2,' A'
print 'i)  P  = ',P,' KW'

i) IL =  360.854503464  A
i) ACTIVE COMPONENT =  288.683602771  A
i)  REACTIVE COMPONENT =  216.512702079  A
i)  P  =  5625000.0  KW


## Example E19 : Pg 187¶

In [18]:
 # EXAMPLE 3.19     PG NO-187
VL=230.;
VP=VL/1.732;
IL=13.279;
COSQ=0.8;
SINQ=0.6;
P=(1.732*VL*IL*COSQ)
RP=(1.732*VL*IL*SINQ)
VA=(1.732*VL*VP)
print 'i) POWER FACTOR = ',P,' W'
print 'i) POWER FACTOR = ',RP,' var'
print 'i)TOTAL VA = ',VA,' VA'

i) POWER FACTOR =  4231.857952  W
i) POWER FACTOR =  3173.893464  var
i)TOTAL VA =  52900.0  VA


## Example E20 : Pg 187¶

In [19]:
# Example 3.20   pg no-187
import math
Ip=100.;   # LINE CURRENT
COSQ=0.787;
SINQ=0.617;
pi=3.14;
Vp=1100./1.732;
W=(2.*math.pi*50.)
Z=Vp/Ip;
R=Z*COSQ;
Xc=Z*SINQ
C=1./(W*Xc)
print 'i) Z = ',Z,' ohm'
print 'ii) R = ',R,' ohm'
print 'iii)  Xc = ',Xc,' ohm'
print 'iiii)capacitance (C) = ',C,' F'

i) Z =  6.35103926097  ohm
ii) R =  4.99826789838  ohm
iii)  Xc =  3.91859122402  ohm
iiii)capacitance (C) =  0.000812306943967  F


## Example E21 : Pg 187¶

In [20]:
    #  EXAMPLE 3.21  PG NO-187
Ip=20.;
IL=(1.732*Ip);
VL=400.;
cos40=0.766;
sin40=0.642;
VA=(1.732*VL*IL);
p=(VA*cos40);
q=(VA*sin40);
print 'i) VA = ',VA,' VA'
print 'ii) P = ',p,' W'
print 'iii) Q = ',q,' vars'

i) VA =  23998.592  VA
ii) P =  18382.921472  W
iii) Q =  15407.096064  vars


## Example E22 : Pg 188¶

In [22]:
                    # EXAMPLE 3.22  PG NO-188
Vp=230.;
VL=230.;
Z=8.+1j*6.;
Ip=Vp/Z;
print 'i) CURRENT  (Ip) is  in rectangular form  =  ',Ip,' A'

i) CURRENT  (Ip) is  in rectangular form  =   (18.4-13.8j)  A


## Example E23 : Pg 188¶

In [23]:
                        # EXAMPLE 3-23     PG NO-188
Za=8.66+1j*5.;
Zc=8.48+1j*8.48;
Zb=11.50+1j*9.642;
VRn=254.+1j*0;
VYn=-127.02-1j*220.;
Vbn=-127.02+1j*220.;
Yr=1./Za;
print 'i) admittance  (Ya) is  in rectangular form  =  ',Yr,' siemens '
Yb=1./Zb;
print 'i) admittance  (Yb) is  in rectangular form  =  ',Yb,' siemens '
Yy=1./Zc;
print 'i) admittance  (Yc) is  in rectangular form  =  ',Yy,' siemens '

Von=((VRn*Yr)+(Vbn*Yb)+(VYn*Yy))/(Yr+Yb+Yy);

print 'i) Voltage  (Von) is  in rectangular form  =  ',Von,' V'

i) admittance  (Ya) is  in rectangular form  =   (0.0866038105677-0.0500022000968j)  siemens
i) admittance  (Yb) is  in rectangular form  =   (0.0510616008751-0.0428118222294j)  siemens
i) admittance  (Yc) is  in rectangular form  =   (0.0589622641509-0.0589622641509j)  siemens
i) Voltage  (Von) is  in rectangular form  =   (17.9603354367+6.1771198768j)  V


## Example E24 : Pg 189¶

In [24]:
                    # EXAMPLE  3-24  PG NO-189
import math
W1=-1200.;
W2=3400.;
P=W1+W2;
print 'iv)  Power (P) is     =  ',P,'W '
X=math.sqrt(3.)*(W2-W1)/P;
print 'iv)   (tan (Q)) is     =  ',X

iv)  Power (P) is     =   2200.0 W
iv)   (tan (Q)) is     =   3.62156077946


## Example E25 : Pg 189¶

In [25]:
                    # EXAMPLE 3-25           PG NO-189
Vac=240.+1j*0;
Vcb=-120.-1j*207.84;
Vba=-120.+1j*207.84;
Zac=20.+1j*0;
Zcb=12.99+1j*7.5;
Zba=0+1j*25.;
Iac=Vac/Zac;
print 'i) CURRENT  (Iac) is  in rectangular form  =  ',Iac,' A '
Icb=Vcb/Zcb;
print 'i) CURRENT  (Icb) is  in rectangular form  =  ',Icb,' A '
Iba=Vba/Zba;
print 'i) CURRENT  (Iba) is  in rectangular form  =  ',Iba,' A '
Ia=Iac-Iba;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Iba-Icb;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Icb-Iac;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
P=(240*12)+(240*16*0.866)+(240*9.6*0);
print 'iv)  Power (P) is     =  ',P,'  W '

i) CURRENT  (Iac) is  in rectangular form  =   (12+0j)  A
i) CURRENT  (Icb) is  in rectangular form  =   (-13.8566096908-7.99964798451j)  A
i) CURRENT  (Iba) is  in rectangular form  =   (8.3136+4.8j)  A
i) CURRENT  (Ia) is  in rectangular form  =   (3.6864-4.8j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (22.1702096908+12.7996479845j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (-25.8566096908-7.99964798451j)  A
iv)  Power (P) is     =   6205.44   W


## Example E26 : Pg 190¶

In [26]:
Vab=200.+1j*0;
Vbc=-100.-1j*173.20;
Vca=-100.+1j*173.20;
Zac=31.+1j*59.;
Zcb=30.-1j*40.;
Zba=80.+1j*60.;
Iab=Vab/Zac;
print 'i) CURRENT  (Iac) is  in rectangular form  =  ',Iab,' A '
Ibc=Vbc/Zcb;
print 'i) CURRENT  (Icb) is  in rectangular form  =  ',Ibc,' A '
Ica=Vca/Zba;
print 'i) CURRENT  (Iba) is  in rectangular form  =  ', Ica,' A '
Ia=Iab-Ica;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Ibc-Iab;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Ica-Ibc;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
P=(200.*3.*0.46)+(200.*4.*0.6)+(200.*2.*0.8);
print 'iv)  Power (P) is     =  ',P,'  W '

i) CURRENT  (Iac) is  in rectangular form  =   (1.39576767222-2.65646105358j)  A
i) CURRENT  (Icb) is  in rectangular form  =   (1.5712-3.6784j)  A
i) CURRENT  (Iba) is  in rectangular form  =   (0.2392+1.9856j)  A
i) CURRENT  (Ia) is  in rectangular form  =   (1.15656767222-4.64206105358j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (0.17543232778-1.02193894642j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (-1.332+5.664j)  A
iv)  Power (P) is     =   1076.0   W


## Example E27 : Pg 190¶

In [27]:
   # EXAMPLE-3.27   PG NO-190-191
Zr=4.;
Zy=5.;
VL=400.;
IL=103.1;
Q=36.6   # Q=TETA
COSQ=0.8028;
P=(1.732*VL*IL*COSQ)
print 'i) P = ',P,' W'

i) P =  57342.141504  W


## Example E28 : Pg 191¶

In [28]:
                          # EXAMPLE 3-28   PG NO-191
Van=230.94+1j*0;
Vbn=-115.47-1j*200.;
Vcn=-115.47+1j*200.;
Za=12.-1j*16.;
Zb=12+1j*0;
Zc=8.+1j*6.;
Ia=Van/Za;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Vbn/Zb;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Vcn/Zc;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
NI=-(Ia+Ib+Ic);
print 'i)NEUTRAL CURRENT  (NI) is  in rectangular form  =  ',NI,' A '
P=(230.95*11.55*0.6)+(230.95*19.25*1)+(230.95*23.095*0.8);
print 'iv)  Power (P) is     =  ',P,'  W '

i) CURRENT  (Ia) is  in rectangular form  =   (6.9282+9.2376j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (-9.6225-16.6666666667j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (2.7624+22.9282j)  A
i)NEUTRAL CURRENT  (NI) is  in rectangular form  =   (-0.0681-15.4991333333j)  A
iv)  Power (P) is     =   10313.3032   W


## Example E29 : Pg 191¶

In [29]:
    # Example-3.29    PG NO-191-192
IL=12.55;
V=460.;
Z=V/(1.732*IL)
print '%s %.2f %s' %('i) Z = ',Z,' ohm');

i) Z =  21.16  ohm


## Example E30 : Pg 192¶

In [30]:
                     # EXAMPLE 3-30       PG NO-192
R=8*0.866;                      # cos30=0.866
print 'i)   Resistance (R) is   =  ',R,' ohm  '
X=8*0.5;
print 'ii)  X (X) is    =  ',X,' ohm  '

i)   Resistance (R) is   =   6.928  ohm
ii)  X (X) is    =   4.0  ohm


## Example E31 : Pg 193¶

In [32]:
   # EXAMPLE -3.31   PG NO -193
Zr=3333.33;
Vry=200.;
X=16666.66;
Y=346.40;    # Y=(300-j173.2)
I=Y/X;
RV=I*Zr;
print 'i) I = ',I,'<-29.99 A'
print 'ii) READING OF VOLTMETER = ',RV,' <-30 degree V'

i) I =  0.0207840083136 <-29.99 A
ii) READING OF VOLTMETER =  69.279958432  <-30 degree V


## Example E32 : Pg 193¶

In [33]:
                 # EXAMPLE 3-32          PG NO-193
Vry=400.+1j*0;
Vyb=-200.-1j*346.41;
Vbr=-200.+1j*346.410;
I1=14.74-1j*7.3;
I2=2.105-1j*10.94;
Ir=I1;
print 'i) CURRENT  (Ir) is  in rectangular form  =  ',Ir,' A '
Iy=I2-I1;
print 'i) CURRENT  (Iy) is  in rectangular form  =  ',Iy,' A '
Ib=-I2;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Pr=16.45*16.45*10;
print 'i) Power  (Pr) is    =  ',Pr,' W '
Py=Iy*Iy*20.;
print 'i) Power  (Py) is  in  rectangular form  =  ',Py,' W '
Pb=11.24*11.24*25;
print 'i) Power  (Pb) is in rectangular form   =  ',Pb,' W '
Vro=-(Ir*10);
print 'i) VOLTAGE  (Vro) is  in rectangular  form  =  ',Vro,' V '
Vrn=200-1j*115.475;
print 'i) VOLTAGE  (Vrn) is  in rectangular  form  =  ',Vrn,' V '
Von=Vro+Vrn;
print 'i) VOLTAGE  (Von) is  in rectangular  form  =  ',Von,' V '

i) CURRENT  (Ir) is  in rectangular form  =   (14.74-7.3j)  A
i) CURRENT  (Iy) is  in rectangular form  =   (-12.635-3.64j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (-2.105+10.94j)  A
i) Power  (Pr) is    =   2706.025  W
i) Power  (Py) is  in  rectangular form  =   (2927.8725+1839.656j)  W
i) Power  (Pb) is in rectangular form   =   3158.44  W
i) VOLTAGE  (Vro) is  in rectangular  form  =   (-147.4+73j)  V
i) VOLTAGE  (Vrn) is  in rectangular  form  =   (200-115.475j)  V
i) VOLTAGE  (Von) is  in rectangular  form  =   (52.6-42.475j)  V


## Example E33 : Pg 194¶

In [34]:
                      # EXAMPLE 3-33      PG NO-194
Z1=8.-1j*6;
Z2=3.6-1j*4.8;
In=-(Z1+Z2);
print 'i) CURRENT  (In) is  in rectangular form  =  ',In,' A '

i) CURRENT  (In) is  in rectangular form  =   (-11.6+10.8j)  A


## Example E34 : Pg 194¶

In [35]:
                       # EXAMPLE 3-34       PG NO-194
import math
Vp=230.94;
Van=230.94+1j*0;
Vbn=-115.47-1j*200;
Vcn=-115.47+1j*200;
Z=8.-1j*10;
Ia=Van/Z;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Vbn/Z;
print 'ii) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Vcn/Z;
print 'iii) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
S=math.sqrt(3.)*400.*18.03;
print 'iv)  APPARENT POWER (S) is    =  ',S,'  VA '
P=S*0.62;
print 'v)  Power (P) is    =  ',P,'  W '
Q=S*-0.8;
print 'vi)  Power (Q) is    =  ',Q,'  vars '

i) CURRENT  (Ia) is  in rectangular form  =   (11.2653658537+14.0817073171j)  A
ii) CURRENT  (Ib) is  in rectangular form  =   (6.56243902439-16.7969512195j)  A
iii) CURRENT  (Ic) is  in rectangular form  =   (-17.827804878+2.71524390244j)  A
iv)  APPARENT POWER (S) is    =   12491.5504242   VA
v)  Power (P) is    =   7744.761263   W
vi)  Power (Q) is    =   -9993.24033935   vars


## Example E36 : Pg 195¶

In [36]:
 # EXAMPLE-3.36     PG NO -195
import math
Vp=400./(3.)**0.5;
Rp=162.58*10.**3.;
Ipc=Rp/(3.*Vp);
IL=365.82;
Xc=Vp/Ipc;
pi=3.14;
C=1./(2.*math.pi*50.*Xc)
print 'i) Ipc = ',Ipc,' A'
print 'ii) Xc = ',Xc,' ohm'
print 'i) CAPACITANCE = ',C,' F'

i) Ipc =  234.664016912  A
ii) Xc =  0.984130889408  ohm
i) CAPACITANCE =  0.00323442633099  F


## Example E37 : Pg 196¶

In [37]:
                               # EXAMPLE 3-37      PG NO-196-197
Vry=450.+1j*0;
Vyb=-225.-1j*389.711;
Vbr=-225.+1j*389.711;
Vrn=225.-1j*130;
Vyn=-225.-1j*130;
Vbn=0+1j*259.8;
Z1=10.60+1j*10.60;
Z2=5.+1j*8.66;
Z3=2.6+1j*1.5;
Z4=12.21+1j*4.44;
Iry=Vry/Z1;
print 'i) CURRENT  (Iry) is  in rectangular form  =  ',Iry,' A '
Iyb=Vyb/Z2;
print 'i) CURRENT  (Iyb) is  in rectangular form  =  ',Iyb,' A '
Ibr=Vbr/Z3;
print 'i) CURRENT  (Ibr) is  in rectangular form  =  ',Ibr,' A '
I1=Iry-Ibr;
print 'i) CURRENT  (I1) is  in rectangular form  =  ',I1,' A '
I2=Iyb-Iry;
print 'i) CURRENT  (I2) is  in rectangular form  =  ',I2,' A '
I3=Ibr-Iyb;
print 'i) CURRENT  (I3) is  in rectangular form  =  ',I3,' A '
I4=Vrn/Z4;
print 'i) CURRENT  (I4) is  in rectangular form  =  ',I4,' A '
I5=Vyn/Z4;
print 'i) CURRENT  (I5) is  in rectangular form  =  ',I5,' A '
I6=Vbn/Z4;
print 'i) CURRENT  (I6) is  in rectangular form  =  ',I6,' A '
I7=Vbn/(3+1j*4);
print 'i) CURRENT  (I7) is  in rectangular form  =  ',I7,' A '
IR=I1+I4;
print 'i) CURRENT  (IR) is  in rectangular form  =  ',IR,' A '
IY=I1+I4;
print 'i) CURRENT  (IY) is  in rectangular form  =  ',IY,' A '
IB=I3+I6+I7;
print 'i) CURRENT  (IB) is  in rectangular form  =  ',IB,' A '
IN=-(I7);
print 'i) CURRENT  (IN) is  in rectangular form  =  ',IN,' A '

i) CURRENT  (Iry) is  in rectangular form  =   (21.2264150943-21.2264150943j)  A
i) CURRENT  (Iyb) is  in rectangular form  =   (-45.0009526419-0.000550024201065j)  A
i) CURRENT  (Ibr) is  in rectangular form  =   (-0.0481132075472+149.916603774j)  A
i) CURRENT  (I1) is  in rectangular form  =   (21.2745283019-171.143018868j)  A
i) CURRENT  (I2) is  in rectangular form  =   (-66.2273677363+21.2258650701j)  A
i) CURRENT  (I3) is  in rectangular form  =   (44.9528394344+149.917153798j)  A
i) CURRENT  (I4) is  in rectangular form  =   (12.855921615-15.3218912343j)  A
i) CURRENT  (I5) is  in rectangular form  =   (-19.6948773591-3.48523706188j)  A
i) CURRENT  (I6) is  in rectangular form  =   (6.83369500888+18.7926612744j)  A
i) CURRENT  (I7) is  in rectangular form  =   (41.568+31.176j)  A
i) CURRENT  (IR) is  in rectangular form  =   (34.1304499169-186.464910102j)  A
i) CURRENT  (IY) is  in rectangular form  =   (34.1304499169-186.464910102j)  A
i) CURRENT  (IB) is  in rectangular form  =   (93.3545344432+199.885815072j)  A
i) CURRENT  (IN) is  in rectangular form  =   (-41.568-31.176j)  A


## Example E39 : Pg 196¶

In [38]:
VAB=400.+1j*0;
VBC=-200.-1j*346.41;
VCA=400.+1j*0;
Z1=300.-1j*398.;
IAB=VAB/Z1;
print 'i) CURRENT  (IAB) is  in rectangular form  =  ',IAB,' A '
print 'ii) VOLTAGE  (VAD) is  in rectangular form  =  ',VAD,' V '
print 'iii) VOLTAGE  (VDA) is  in rectangular form  =  ',VDA,' V '
VDC=VDA-VCA;
print 'iv) VOLTAGE  (VDC) is  in rectangular form  =  ',VDC,' VA '
VAC=400.+1j*0;
VCB=-200.-1j*346.41;
VBA=-200.+1j*346.410;
IAB1=-(VAC)/Z1;
print 'v) CURRENT  (IAB1) is  in rectangular form  =  ',IAB1,' A '
print 'vi) VOLTAGE  (VAD1) is  in rectangular form  =  ',VAD1,' V '
print 'vii) VOLTAGE  (VAAD) is  in rectangular form  =  ',VDA,' V '
VDC=VDA+VAC;
print 'viii) VOLTAGE  (VDC) is  in rectangular form  =  ',VDC,' V '

i) CURRENT  (IAB) is  in rectangular form  =   (0.483084008309+0.640891451023j)  A
ii) VOLTAGE  (VAD) is  in rectangular form  =   (144.925202493+192.267435307j)  V
iii) VOLTAGE  (VDA) is  in rectangular form  =   (-144.925202493-192.267435307j)  V
iv) VOLTAGE  (VDC) is  in rectangular form  =   (-544.925202493-192.267435307j)  VA
v) CURRENT  (IAB1) is  in rectangular form  =   (-0.483084008309-0.640891451023j)  A
vi) VOLTAGE  (VAD1) is  in rectangular form  =   (-144.925202493-192.267435307j)  V
vii) VOLTAGE  (VAAD) is  in rectangular form  =   (-144.925202493-192.267435307j)  V
viii) VOLTAGE  (VDC) is  in rectangular form  =   (255.074797507-192.267435307j)  V


## Example E40 : Pg 199¶

In [39]:
     # EXAMPLE-3.40    PG NO-199
Vry=200.;
Vbr=200.;
Vbn=115.47;
I1=10.;   # 10-j12
W1=200.*I1;
X1=173.2;
X2=26.66;
W2=X1*X2;
print 'i)WATTMETERS (W2)   =  ',W2,' W'

i)WATTMETERS (W2)   =   4617.512  W


## Example E41 : Pg 200¶

In [40]:
       #    CHAPTER -3 EXAMPLE NO 3.41   PG NO-200
Vp=230.94;
Xa=100.+1j*155;
Ia=Vp/Xa;
COSQ=0.542;
P=COSQ;
print 'i) (Ia)   =  ',Ia,' A'

i) (Ia)   =   (0.678736223365-1.05204114622j)  A


## Example E42 : Pg 200¶

In [41]:
Van=254.+1j*0;
Vbn=-127.02-1j*220.;
Vcn=-127.02+1j*220.;
Ib=0-1j*10.;
Ic=0+1j*20.;
Ia=-(Ib+Ic);
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Von=-173.20+1j*100.;
Vao=Van-Von;
print 'i) VOLTAGE  (Vao) is  in rectangular form  =  ',Vao,' V '
Vbo=Vbn-Von;
print 'i) VOLTAGE  (Vbo) is  in rectangular form  =  ',Vbo,' V '
Vco=Vcn-Von;
print 'i) VOLTAGE  (Vco) is  in rectangular form  =  ',Vco,' V '
Za=Vao/Ia;
print 'i) IMPEDANCE  (Za) is  in rectangular form  =  ',Za,' ohm '
Zb=Vbo/Ib;
print 'i) IMPEDANCE  (Zb) is  in rectangular form  =  ',Zb,' ohm '
Zc=Vco/Ic;
print 'i) IMPEDANCE  (Zc) is  in rectangular form  =  ',Zc,' ohm '

i) CURRENT  (Ia) is  in rectangular form  =   (-0-10j)  A
i) VOLTAGE  (Vao) is  in rectangular form  =   (427.2-100j)  V
i) VOLTAGE  (Vbo) is  in rectangular form  =   (46.18-320j)  V
i) VOLTAGE  (Vco) is  in rectangular form  =   (46.18+120j)  V
i) IMPEDANCE  (Za) is  in rectangular form  =   (10+42.72j)  ohm
i) IMPEDANCE  (Zb) is  in rectangular form  =   (32+4.618j)  ohm
i) IMPEDANCE  (Zc) is  in rectangular form  =   (6-2.309j)  ohm


## Example E43 : Pg 200¶

In [42]:
   # example-3.43   pg no-200-201
Ip=11<36.87;
PL=5808.;
QL=4356.;
Pm=6000.;
Qm=8000.;
P=PL+Pm;
Q=Qm-QL;
S=((P*P)+(Q*Q))**0.5;
X=P/S;    # POWER FACTOR
print 'i)ACTIVE POWER (P)   =  ',P,' W'
print 'i)REACTIVE POWER (Q)   =  ',Q,' vars(inductive)'
print 'i)APPARENT POWER (S)   =  ',S,' A'
print 'i)power factor (X)   =  ',X,' lagging'

i)ACTIVE POWER (P)   =   11808.0  W
i)REACTIVE POWER (Q)   =   3644.0  vars(inductive)
i)APPARENT POWER (S)   =   12357.4916549  A
i)power factor (X)   =   0.95553372236  lagging


## Example E44 : Pg 201¶

In [43]:
 # EXAMPLE 3.44 PG NO-201
W1=800.;
W2=-400.;
P=W1+W2;
x=(1.723*(W2-W1))/(W1+W2)   # tanQ=x
Q=-79.10;
y=0.189;
P=y    # POWER  FACTOR
print 'i)tanQ (x)   =  ',x
print 'i) POWER factor (P)   =  ',P

i)tanQ (x)   =   -5.169
i) POWER factor (P)   =   0.189


## Example E45 : Pg 201¶

In [44]:
                     # EXAMPLE 3-45   PG NO-201-202
Vab=0+1j*212.;
Vbc=-183.6-1j*106.;
Vca=183.6-1j*106.;
Za=10.+1j*0;
Zb=10.+1j*10.;
Zc=0-1j*20.;
Zab=((Za*Zb)+(Zb*Zc)+(Za*Zc))/Zc;
print 'i) IMPEDANCE  (Zab) is  in rectangular form  =  ',Zab,' ohm '
Zbc=((Za*Zb)+(Zb*Zc)+(Za*Zc))/Za;
print 'i) IMPEDANCE  (Zbc) is  in rectangular form  =  ',Zbc,' ohm '
Zca=((Za*Zb)+(Zb*Zc)+(Za*Zc))/Zb;
print 'i) IMPEDANCE  (Zca) is  in rectangular form  =  ',Zca,' ohm '
Iab=Vab/Zab;
print 'i) CURRENT  (Iab) is  in rectangular form  =  ',Iab,' A '
Ibc=Vbc/Zbc;
print 'i) CURRENT  (Ibc) is  in rectangular form  =  ',Ibc,' A '
Ica=Vca/Zca;
print 'i) CURRENT  (Ica) is  in rectangular form  =  ',Ica,' A '
Ia=Iab-Ica;
print 'i) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Ibc-Iab;
print 'i) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Ica-Ibc;
print 'i) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '

i) IMPEDANCE  (Zab) is  in rectangular form  =   (15+15j)  ohm
i) IMPEDANCE  (Zbc) is  in rectangular form  =   (30-30j)  ohm
i) IMPEDANCE  (Zca) is  in rectangular form  =   -30j  ohm
i) CURRENT  (Iab) is  in rectangular form  =   (7.06666666667+7.06666666667j)  A
i) CURRENT  (Ibc) is  in rectangular form  =   (-1.29333333333-4.82666666667j)  A
i) CURRENT  (Ica) is  in rectangular form  =   (3.53333333333+6.12j)  A
i) CURRENT  (Ia) is  in rectangular form  =   (3.53333333333+0.946666666667j)  A
i) CURRENT  (Ib) is  in rectangular form  =   (-8.36-11.8933333333j)  A
i) CURRENT  (Ic) is  in rectangular form  =   (4.82666666667+10.9466666667j)  A


## Example E47 : Pg 202¶

In [45]:
                        # EXAMPLE 3-47   PG NO-202-203
Vab=212.;
Vbc=212.;
Vca=212.;
Iab=10.;
Ibc=5.;
Ica=7.07;
P=((Vab*Iab*0.707)+(Vbc*Ibc*0.707)+(212*7.07*0));
print 'i) ACTIVE POWER  (P) is   =  ',P,' W '
Q=((Vab*Iab*0.707)+(Vbc*Ibc*-0.707)+(212*7.07*-1))
print 'ii)REACTIVE POWER  (Q) is   =  ',Q,' vars '
S=(P**2.+(Q**2.))**0.5;
print 'i)  APPARENT POWER  (S) is   =  ',S,' VA'

i) ACTIVE POWER  (P) is   =   2248.26  W
ii)REACTIVE POWER  (Q) is   =   -749.42  vars
i)  APPARENT POWER  (S) is   =   2369.87412408  VA


## Example E48 : Pg 203¶

In [46]:
                   # EXAMPLE 3-48   PG NO-202-203
Vao=186.7-1j*87.06;
Vco=-38.5+1j*292.48;
Vbo=-(Vao+Vco);
print 'i) VOLTAGE  (Vbo) is  in rectangular form  =  ',Vbo,' V '
Vab=Vao-Vbo;
print 'i) VOLTAGE  (Vab) is  in rectangular form  =  ',Vab,' V '
Van=201.-1j*37.51;
Von=Van-Vao;
print 'i) VOLTAGE  (Von) is  in rectangular form  =  ',Von,' V '

i) VOLTAGE  (Vbo) is  in rectangular form  =   (-148.2-205.42j)  V
i) VOLTAGE  (Vab) is  in rectangular form  =   (334.9+118.36j)  V
i) VOLTAGE  (Von) is  in rectangular form  =   (14.3+49.55j)  V


## Example E49 : Pg 203¶

In [47]:
                       # EXAMPLE 3-49 PG NO-203-204
Vab=400.+1j*0;
Vbc=-200.-1j*346.41;
Vca=-200.+1j*346.410;
Z1=1j*10.;
Z2=-1j*20.;
Z3=10.;
Iab=Vab/Z1;
print 'i) CURRENT  (Iab) is  in rectangular form  =  ',Iab,' A '
Ibc=Vbc/Z2;
print 'ii) CURRENT  (Ibc) is  in rectangular form  =  ',Ibc,' A '
Ica=Vca/Z3;
print 'iii) CURRENT  (Ica) is  in rectangular form  =  ',Ica,' A '
Ia=Iab-Ica;
print 'iv) CURRENT  (Ia) is  in rectangular form  =  ',Ia,' A '
Ib=Ibc-Iab;
print 'v) CURRENT  (Ib) is  in rectangular form  =  ',Ib,' A '
Ic=Ica-Ibc;
print 'vi) CURRENT  (Ic) is  in rectangular form  =  ',Ic,' A '
P=Ica*Z3;
print 'vii)ACTIVE POWER  (P) is  in rectangular form  =  ',P,' W '
Q=(Iab**2*Z3)-(Ibc**2*20);
print 'viii) REACTIVE POWER  (Q) is  in rectangular form  =  ',Q,' vars '
S=(P**2+Q**2)**0.5;
print 'i)APPARENT POWER  (S) is  in rectangular form  =  ',S,' VA '

i) CURRENT  (Iab) is  in rectangular form  =   -40j  A
ii) CURRENT  (Ibc) is  in rectangular form  =   (17.3205-10j)  A
iii) CURRENT  (Ica) is  in rectangular form  =   (-20+34.641j)  A
iv) CURRENT  (Ia) is  in rectangular form  =   (20-74.641j)  A
v) CURRENT  (Ib) is  in rectangular form  =   (17.3205+30j)  A
vi) CURRENT  (Ic) is  in rectangular form  =   (-37.3205+44.641j)  A
vii)ACTIVE POWER  (P) is  in rectangular form  =   (-200+346.41j)  W
viii) REACTIVE POWER  (Q) is  in rectangular form  =   (-19999.994405+6928.2j)  vars
i)APPARENT POWER  (S) is  in rectangular form  =   (19999.2804579-6931.91155193j)  VA


## Example E50 : Pg 204¶

In [49]:
                      # EXAMPLE 3-50      PG NO-204
I1=13.12-1j*9.15;
I2=-6.80-1j*19.55;
IaA=I1;
print 'i) CURRENT  (IaA) is  in rectangular form  =  ',IaA,' A '
IbB=I2-I1;
print 'i) CURRENT  (IbB) is  in rectangular form  =  ',IbB,' A '
IcC=-I2;
print 'i) CURRENT  (IcC) is  in rectangular form  =  ',IcC,' A '

i) CURRENT  (IaA) is  in rectangular form  =   (13.12-9.15j)  A
i) CURRENT  (IbB) is  in rectangular form  =   (-19.92-10.4j)  A
i) CURRENT  (IcC) is  in rectangular form  =   (6.8+19.55j)  A


## Example E51 : Pg 205¶

In [50]:
                          # EXAMPLE 3-51     PG NO -205
import math
R1=1.5;
X=2.396;
X1=math.sqrt(X**2.-R1**2.);
print 'i) X1   is   =  ',X1,'ohm '
IL=100.;
Ip=IL/1.732;
print 'ii) Peak Current  =  ',Ip,' A '
R2=4.5;
Z=7.1878;
X2=math.sqrt(Z**2.-R2**2.)
print 'iii) X2   is   =  ',X2,'ohm '
PF=R2/(Z);
print 'vi) Power Factor   is   =  ',PF

i) X1   is   =   1.86837255386 ohm
ii) Peak Current  =   57.7367205543  A
iii) X2   is   =   5.60486117937 ohm
vi) Power Factor   is   =   0.626060825287


## Example E52 : Pg 205¶

In [51]:
                      # EXAMPLE 3-52   PG NO-205-206
import math
Vp=230.94;
R=20.+1j*30.;
V=400.;
IL=Vp/R;
print 'i) CURRENT  (IL) is  in rectangular form  =  ',IL,' A '
PF=0.555;
P=math.sqrt(3.)*V*IL*PF;
print 'ii)ACTIVE POWER  (P) is  in rectangular form  =  ',P,' W '
Q=math.sqrt(3.)*V*IL*56.289;
print 'iii) REACTIVE POWER  (Q) is  in rectangular form  =  ',Q,' vars '
S=math.sqrt(3.)*V*IL;
print 'iv)APPARENT POWER  (S) is  in rectangular form  =  ',S,' VA '
Ip=3.698;
Z=V/Ip;
print 'i) IMPEDANCE  (Z) is  in rectangular form  =  ',Z,' ohm '
R1=Z*0.555;
print 'i) RESISTANCE  (R1) is  in rectangular form  =  ',R1,' ohm '
Xc=Z*0.83;
print 'i) INDUCTANCE  (Xc) is  in rectangular form  =  ',Xc,' ohm '
C=Xc/(2.*math.pi*50.);
print 'i) CAPACITOR  (C) is  in rectangular form  =  ',C,' F '

i) CURRENT  (IL) is  in rectangular form  =   (3.55292307692-5.32938461538j)  A
ii)ACTIVE POWER  (P) is  in rectangular form  =   (1366.15320918-2049.22981378j)  W
iii) REACTIVE POWER  (Q) is  in rectangular form  =   (138557.473859-207836.210789j)  vars
iv)APPARENT POWER  (S) is  in rectangular form  =   (2461.53731385-3692.30597077j)  VA
i) IMPEDANCE  (Z) is  in rectangular form  =   108.166576528  ohm
i) RESISTANCE  (R1) is  in rectangular form  =   60.032449973  ohm
i) INDUCTANCE  (Xc) is  in rectangular form  =   89.7782585181  ohm
i) CAPACITOR  (C) is  in rectangular form  =   0.285773072507  F


## Example E53 : Pg 206¶

In [52]:
                  # EXAMPLE 3-53      PG NO-206-207
import math
HP=2000.;
Vp=2200.;
E=0.93;
MI=(HP*735.5)/E;
print 'i) MOTOR INPUT  (MI) is  in rectangular form  =  ',MI,' W '
Ip=MI/(3.*Vp*0.85);
print 'i) CURRENT  (Ip) is  in rectangular form  =  ',Ip,' A '
AC=Ip*0.85;
print 'i) ACTIVE CURRENT  (AC) is  in rectangular form  =  ',AC,' A '
RC=(Ip**2-AC**2)**0.5;
print 'i) REACTIVE CURRENT  (RC) is  in rectangular form  =  ',RC,' A '
LC=math.sqrt(3)*Ip;
print 'i) LINE CURRENT  (LC) is  in rectangular form  =  ',LC,' A '
ALC=LC*0.85;
print 'i)ACTIVE LINE CURRENT  (ALC) is  in rectangular form  =  ',ALC,' A '
RLC=(LC**2-ALC**2)**0.5;
print 'i) REACTIVE LINE CURRENT  (RLC) is  in rectangular form  =  ',RLC,' A '

i) MOTOR INPUT  (MI) is  in rectangular form  =   1581720.43011  W
i) CURRENT  (Ip) is  in rectangular form  =   281.946600732  A
i) ACTIVE CURRENT  (AC) is  in rectangular form  =   239.654610622  A
i) REACTIVE CURRENT  (RC) is  in rectangular form  =   148.524588105  A
i) LINE CURRENT  (LC) is  in rectangular form  =   488.345837489  A
i)ACTIVE LINE CURRENT  (ALC) is  in rectangular form  =   415.093961866  A
i) REACTIVE LINE CURRENT  (RLC) is  in rectangular form  =   257.252132772  A


## Example E54 : Pg 207¶

In [53]:
                            # EXAMPLE 3-54  PG NO-207-208
Van=161.66+1j*0;
Vbn=-80.83-1j*140;
Vcn=-80.83+1j*140;
Z1=10+1j*0;
Z2=8.66+1j*5;
Z3=8.66-1j*5;
YA=1/Z1;
print ('i) ADMITTANCE  (YA) is  in rectangular form  =  ',YA,' siemens ');
YB=1/Z2;
print ('ii) ADMITTANCE  (YB) is  in rectangular form  =  ',YB,' siemens ');
YC=1/Z3;
print ('iii) ADMITTANCE  (YC) is  in rectangular form  =  ',YC,' siemens ');
Von=-((Van*YA)+(Vbn*YB)+(Vcn*YC))/(YA+YB+YC);
print ('iv) VOLTAGE  (Von) is  in rectangular form  =  ',Von,' V ');
Vao=Van-Von;
print ('v) VOLTAGE  (Vao) is  in rectangular form  =  ',Vao,' V ');
Vbo=Vbn-Von;
print ('vi) VOLTAGE  (Vbo) is  in  rectangular form  =  ',Vbo,' V ');
Vco=Vcn-Von;
print ('vii) VOLTAGE  (Vco) is  in rectangular form  =  ',Vco,' V ');

('i) ADMITTANCE  (YA) is  in rectangular form  =  ', (0.1+0j), ' siemens ')
('ii) ADMITTANCE  (YB) is  in rectangular form  =  ', (0.08660381056766497-0.050002200096804256j), ' siemens ')
('iii) ADMITTANCE  (YC) is  in rectangular form  =  ', (0.08660381056766497+0.050002200096804256j), ' siemens ')
('iv) VOLTAGE  (Von) is  in rectangular form  =  ', (43.31865997841839-0j), ' V ')
('v) VOLTAGE  (Vao) is  in rectangular form  =  ', (118.3413400215816+0j), ' V ')
('vi) VOLTAGE  (Vbo) is  in  rectangular form  =  ', (-124.14865997841838-140j), ' V ')
('vii) VOLTAGE  (Vco) is  in rectangular form  =  ', (-124.14865997841838+140j), ' V ')


## Example E55 : Pg 208¶

In [54]:
                             # EXAMPLE 3-55         PG NO-208-209
Vab=400.+1j*0;
Vbc=-220.-1j*381.05;
Vca=-220.+1j*381.05;
Z1=0+1j*25.;
Z2=13.+1j*7.5;
Z3=20.+1j*0;
IAB=Vab/Z1;
print ('i) CURRENT  (IAB) is  in rectangular  form  =  ',IAB,' A ');
IBC=Vbc/Z2;
print ('i) CURRENT  (IBC) is  in  rectangular form  =  ',IBC,' A ');
ICA=Vca/Z3;
print ('i) CURRENT  (ICA) is  in rectangular form  =  ',ICA,' A ');
IA=IAB-ICA;
print ('i) CURRENT  (IA) is  in rectangular form  =  ',IA,' A ');
IB=IBC-IAB;
print ('i) CURRENT  (IB) is  in rectangular form  =  ',IB,' A ');
IC=ICA-IBC;
print ('i) CURRENT  (IC) is  in rectangular form  =  ',IC,' A ');

('i) CURRENT  (IAB) is  in rectangular  form  =  ', -16j, ' A ')
('i) CURRENT  (IBC) is  in  rectangular form  =  ', (-25.38457269700333-14.666592674805774j), ' A ')
('i) CURRENT  (ICA) is  in rectangular form  =  ', (-11+19.052500000000002j), ' A ')
('i) CURRENT  (IA) is  in rectangular form  =  ', (11-35.0525j), ' A ')
('i) CURRENT  (IB) is  in rectangular form  =  ', (-25.38457269700333+1.3334073251942264j), ' A ')
('i) CURRENT  (IC) is  in rectangular form  =  ', (14.384572697003328+33.71909267480578j), ' A ')


## Example E59 : Pg 209¶

In [55]:
       # EXAMPLE 3-59 PG NO 267
V2=240-1j*14.35;
V1=240+1j*0;
VL=233.73-1j*8.938;
R1=0.6+1j*0.8;
R2=0.5+1j*0.866;
I1=(V1-VL)/R1;
I2=(V2-VL)/R2;
R3=16+1j*12;
I3=(VL/R3);
print ('i) current(I1) is in polar form  =  ',I1,'A ');
print ('i) current(I2) is in polar form  =  ',I2,'A ');
print ('i) current(I3) is in polar form  =  ',I3,'A ');

('i) current(I1) is in polar form  =  ', (10.912400000000005+0.3467999999999911j), 'A ')
('i) current(I2) is in polar form  =  ', (-1.5518602818523957-8.13617799183165j), 'A ')
('i) current(I3) is in polar form  =  ', (9.08106-7.369419999999999j), 'A ')