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author | priyanka | 2015-06-24 15:03:17 +0530 |
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committer | priyanka | 2015-06-24 15:03:17 +0530 |
commit | b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b (patch) | |
tree | ab291cffc65280e58ac82470ba63fbcca7805165 /1445/CH7 | |
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initial commit / add all books
Diffstat (limited to '1445/CH7')
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diff --git a/1445/CH7/EX7.1/Ex7_1.sce b/1445/CH7/EX7.1/Ex7_1.sce new file mode 100644 index 000000000..c88808117 --- /dev/null +++ b/1445/CH7/EX7.1/Ex7_1.sce @@ -0,0 +1,35 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 1 + +disp("CHAPTER 7"); +disp("EXAMPLE 1"); + +//VARIABLE INITIALIZATION +I_0=10; //no load current in Amperes +pf=0.25; //power factor +v1=400; //in Volts +f=50; //in Hertz + +//SOLUTION + +//solution (a) +//magnetizing component +//Iphi=I0.sin theta +theta=acos(pf); //taking value of theta from the given power factor +I_phi=I_0*sin(theta); +disp(sprintf("(a) The magnetizing component of no load current is %.2f A",I_phi)); + +//solution (b) +//iron loss +//Pc=V1.Ic +//Ic=I0.cos theta & also Ic=I0.pf as pf=cos theta +p_c=v1*I_0*pf; +disp(sprintf("(b) The iron loss is %d W",p_c)); + +//solution (c) +N1=500; // number of turns in primary given +phi_m=v1/(sqrt(2)*%pi*f*N1); +disp(sprintf("(c) The maximum value of flux in the core is %.2f mWb",phi_m*1000)); + +//END + diff --git a/1445/CH7/EX7.10/Ex7_10.sce b/1445/CH7/EX7.10/Ex7_10.sce new file mode 100644 index 000000000..d9018d0ec --- /dev/null +++ b/1445/CH7/EX7.10/Ex7_10.sce @@ -0,0 +1,30 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 10 + +disp("CHAPTER 7"); +disp("EXAMPLE 10"); + +//6600/220 V single phase transformer +//VARIABLE INITIALIZATION +v1=6600; //primary voltage in Volts +v2=220; //secondary voltage in Volts +coreA=0.05; //core section m^2 +fluxD=1.2; //flux density in wm/m^2 +f=50; //Hz + +//SOLUTION +//E1=sqrt(2).pi.f.N1.φm +//flux density = Phimax/core area +phiM=coreA*fluxD; +N1=v1/(4.44*f*phiM); //4.44=sqrt(2).pi +N1=round(N1); +// +//N2=N1.E2/E1 +N2=N1*(v2/v1); +N2=round(N2); +disp(sprintf("The no. of turns on HT side is %d",N1)); +disp(sprintf("The no. of turns on LT side is %d",N2)); +disp(" "); +// +//END + diff --git a/1445/CH7/EX7.11/Ex7_11.sce b/1445/CH7/EX7.11/Ex7_11.sce new file mode 100644 index 000000000..df17e61c0 --- /dev/null +++ b/1445/CH7/EX7.11/Ex7_11.sce @@ -0,0 +1,28 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 11 + +disp("CHAPTER 7"); +disp("EXAMPLE 11"); + +//2200/220 V 44 kVA transformer with 50 turns in the secondary +//VARIABLE INITIALIZATION +va=44000; // +v1=2200; //primary voltage in Volts +v2=220; //secondary voltage in Volts +N2=50; //turns in secondary coil + +//SOLUTION +// N1/N2=V1/V2 +N1=N2*(v1/v2); +disp("SOLUTION (a)"); +disp(sprintf("The no. of turns on HT side is %f",N1)); +// +//since losses are negligible, input=output, V1.I1=V2.I2 +I1=va/v1; +I2=va/v2; +disp("SOLUTION (b)"); +disp(sprintf("The primary full load current is %.0f Amp",I1)); +disp(sprintf("The secondary full load current is %.0f Amp",I2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.12/Ex7_12.sce b/1445/CH7/EX7.12/Ex7_12.sce new file mode 100644 index 000000000..980b54bd2 --- /dev/null +++ b/1445/CH7/EX7.12/Ex7_12.sce @@ -0,0 +1,40 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 12 + +disp("CHAPTER 7"); +disp("EXAMPLE 12"); + +//no load cuurent of transformer ia 10A at pf of 0.25 lagging when connected to 400V, 50 Hz supply +//VARIABLE INITIALIZATION +v1=400; //primary voltage in Volts +f=50; //Hz +Io=10; //in Amp no load current +pf =0.25; //lagging +N1=500; //given + +//SOLUTION +//magnetizing component of no load current +// N1/N2=V1/V2 +//Iphi=Io.sin phi0 +//pf=cos phi0 +phi0=acos(pf); +Iphi=Io*sin(phi0); +disp("SOLUTION (a)"); +disp(sprintf("The magnetic component of no load current is %f Amp",Iphi)); +// +//iron loss +//Pi=ironloss=power input on no load +//Pi=Wo=V1.Io.cos phi0 +ironLoss=v1*Io*pf; +disp("SOLUTION (b)"); +disp(sprintf("The iron loss on no load is %.0f W",ironLoss)); +// +//maximum flux in the core +//E1=sqrt(2).pi.f.N1.φm +//E1=V1 +phiM=v1/(4.44*f*N1); +disp("SOLUTION (c)"); +disp(sprintf("The value of flux in the core is %5.4f mWb",phiM*1000)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.13/Ex7_13.sce b/1445/CH7/EX7.13/Ex7_13.sce new file mode 100644 index 000000000..047444eca --- /dev/null +++ b/1445/CH7/EX7.13/Ex7_13.sce @@ -0,0 +1,34 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 13 + +disp("CHAPTER 7"); +disp("EXAMPLE 13"); +//230/115 V single phase transformer +//VARIABLE INITIALIZATION +v1=230; //primary voltage in Volts +v2=115; +f=50; //Hz +Io=2; //in Amp no load current +pf0 =0.28; //lagging +I2=20; // +pf2=0.8; //lagging + +//SOLUTION +// +//given power factors in primary and secondary +// I1.N1=I2.N2 +phi0=acos(pf0); +phi2=acos(pf2); +//let Ix and Iy be the components of I0 and I'1 along X and Y axes +//then +//Ix=Io.sin phi0 + I'2.sin phi2 +// +//Ix=Io.cos phi0 + I'2.cos phi2 +I_dash_2=I2*v2/v1; +Ix=Io*sin(phi0)+I_dash_2*sin(phi2); +Iy=Io*cos(phi0)+I_dash_2*cos(phi2); +I1=sqrt(Ix^2+Iy^2); +disp(sprintf("The current taken by primary is %.1f Amp",I1)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.14/Ex7_14.sce b/1445/CH7/EX7.14/Ex7_14.sce new file mode 100644 index 000000000..4f635a60b --- /dev/null +++ b/1445/CH7/EX7.14/Ex7_14.sce @@ -0,0 +1,51 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 14 + +disp("CHAPTER 7"); +disp("EXAMPLE 14"); + +//1100/110 V 22 kVA single phase transformer +//VARIABLE INITIALIZATION +va=22000; //apparent power +v1=1100; //primary voltage in Volts +v2=110; //secondary voltage in Volts +R1=2; //in Ohms +R2=0.02; //in Ohms +X1=5; //in Ohms +X2=0.045; //in Ohms + +//SOLUTION +//N1/N2=v1/v2; + +R_dash_2=R2*((v1/v2)^2); +X_dash_2=X2*((v1/v2)^2); +disp("SOLUTION (a)"); +disp(sprintf("The equivalent resistance of secondary referred to primary is %.1fΩ",R_dash_2)); +disp(sprintf("The equivalent reactance of secondary referred to primary is %.1f Ω",X_dash_2)); +// +R_e1=R_dash_2+R1; +X_e1=X_dash_2+X1; +disp("SOLUTION (b)"); +disp(sprintf("The total resistance referred to primary is %.1f Ω",R_e1)); +disp(sprintf("The total reactance referred to primary is %.1f Ω",X_e1)); +// +R_dash_1=R1*((v2/v1)^2); +X_dash_1=X1*((v2/v1)^2); +disp("SOLUTION (c)"); +disp(sprintf("The equivalent resistance of secondary referred to secondary is %.2f Ω",R_dash_1)); +disp(sprintf("The equivalent reactance of secondary referred to secondary is %.2f Ω",X_dash_1)); +// +R_e2=R_dash_1+R2; +X_e2=X_dash_1+X2; +disp("SOLUTION (d)"); +disp(sprintf("The total resistance referred to secondary is %.3f Ω",R_e2)); +disp(sprintf("The total reactance referred to secondary is %.3f Ω",X_e2)); +// +I1=va/v1; +I2=va/v2; +copperLoss=R1*I1^2+R2*I2^2; +disp("SOLUTION (e)"); +disp(sprintf("The total copper loss is %4.0f W",copperLoss)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.15/Ex7_15.sce b/1445/CH7/EX7.15/Ex7_15.sce new file mode 100644 index 000000000..62b09f20e --- /dev/null +++ b/1445/CH7/EX7.15/Ex7_15.sce @@ -0,0 +1,38 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 15 + +disp("CHAPTER 7"); +disp("EXAMPLE 15"); +//20kVA single phase transformer +//VARIABLE INITIALIZATION +va=20000; //apparent power +v1=2000; //primary voltage in Volts +v2=200; //secondary voltage in Volts +R1=2.5; //in Ohms +R2=0.04; //in Ohms +X1=8; //in Ohms +X2=0.07; //in Ohms +pf2=0.8; + +//SOLUTION +//N1b/N2=v1/v2; +I2=va/v2; +phi2=acos(pf2); +// +R_dash_1=R1*((v2/v1)^2); +X_dash_1=X1*((v2/v1)^2); +// +R_e2=R_dash_1+R2; +X_e2=X_dash_1+X2; +//disp(sprintf("The total resistance referred to secondary is %f Ω",R_e2)); +//disp(sprintf("The total reactance referred to secondary is %f Ω",X_e2)); +// +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +V2=v2-(I2*R_e2*pf2+I2*X_e2*sin(phi2)); +%reg=(v2-V2)*100/v2; +disp(sprintf("The secondary terminal voltage is %.2f V",V2)); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.16/Ex7_16.sce b/1445/CH7/EX7.16/Ex7_16.sce new file mode 100644 index 000000000..99cf22818 --- /dev/null +++ b/1445/CH7/EX7.16/Ex7_16.sce @@ -0,0 +1,47 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 16 + +disp("CHAPTER 7"); +disp("EXAMPLE 16"); + +//Values from the previous example. +//VARIABLE INITIALIZATION +va=20000; //apparent power +v1=2000; //primary voltage in Volts +v2=200; //secondary voltage in Volts +R1=2.5; //in Ohms +R2=0.04; //in Ohms +X1=8; //in Ohms +X2=0.07; //in Ohms +pf2=0.8; + +//SOLUTION +//N1/N2=v1/v2; +I2=va/v2; +phi2=acos(pf2); + +// +R_dash_1=R1*((v2/v1)^2); +X_dash_1=X1*((v2/v1)^2); +// +R_e2=R_dash_1+R2; +X_e2=X_dash_1+X2; +//disp(sprintf("The total resistance referred to secondary is %f Ω",R_e2)); +//disp(sprintf("The total reactance referred to secondary is %f Ω",X_e2)); +// +//power factor angle at which regulation is zero is given by tan.phi2=-Re2/Xe2 +phi2=atan(-R_e2/X_e2); +disp(sprintf("The PF at which the regulation is zero is %.3f",cos(phi2))); +// +//power factor angle at which regulation is maximum is given by tan.phi2=Xe2/Re2 +phi2=atan(X_e2/R_e2); +disp(sprintf("The PF at which the regulation is maximum is %.3f",cos(phi2))); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R + +V2=v2-(I2*R_e2*cos(phi2)+I2*X_e2*sin(phi2)); +%reg=(v2-V2)*100/v2; +disp(sprintf("The maximum value of percent regulation is %.2f ",%reg)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.17/Ex7_17.sce b/1445/CH7/EX7.17/Ex7_17.sce new file mode 100644 index 000000000..7ae2f47e6 --- /dev/null +++ b/1445/CH7/EX7.17/Ex7_17.sce @@ -0,0 +1,43 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 17 + +disp("CHAPTER 7"); +disp("EXAMPLE 17"); + +//200kVA single phase transformer +//VARIABLE INITIALIZATION +va=200000; // +ironLoss=1000; // Watts +cuLoss=2000; //Watts +pf=0.8; +// +//SOLUTION +// +Pout=va*pf; //Full load output +loss=ironLoss+cuLoss; +Pin=Pout+loss; //INPUT=OUTPUT+LOSS +eff=Pout*100/Pin; +disp("SOLUTION (a)"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +// +//at half load +Pout=va*pf/2; +loss=ironLoss+cuLoss*(1/2)^2; // ironloss is independent of output +Pin=Pout+loss; +eff=Pout*100/Pin; +disp("SOLUTION (b)"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +// +//fraction x of copperloss=ironloss for maximum efficiency +//x^2.cuLoss=ironLoss +x=sqrt(ironLoss/cuLoss); +Pout=x*va*pf; +loss=ironLoss+cuLoss*x^2; +Pin=Pout+loss; +eff=Pout*100/Pin; +disp("SOLUTION (c)"); +disp(sprintf("The percent efficiency at %f load is %.2f ",x,eff)); + +disp(" "); +// +//END diff --git a/1445/CH7/EX7.18/Ex7_18.sce b/1445/CH7/EX7.18/Ex7_18.sce new file mode 100644 index 000000000..5d9e22bf4 --- /dev/null +++ b/1445/CH7/EX7.18/Ex7_18.sce @@ -0,0 +1,47 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 18 + +disp("CHAPTER 7"); +disp("EXAMPLE 18"); + +//400kVA distribution transformer variously loaded during day +//VARIABLE INITIALIZATION +va=400000; // +ironLoss=1500; // Watts +cuLoss=4000; //Watts +//during the day frommidnight to midnight is as below: +h1=6; //first 6 hours from midnight to 6 hrs +load1=0; +pf1=0; +h2=6; //next 6 hours from 6 am to noon +load2=100000; //kVA converted to VA +pf2=0.8; +h3=5; //next from noon to 5 pm +load3=400000; +pf3=0.8; +h4=3; //next from 5 pm to 8 pm +load4=300000; +pf4=0.7; +h5=4; //next from 8 pm to midnight +load5=200000; +pf5=0.85; +// +//SOLUTION +// +//energy loss at any load=(VA output/VA rated)^2 .Full load cuLoss +loss1=h1*load1; +loss2=h2*(load2/va)^2*cuLoss; +loss3=h3*(load3/va)^2*cuLoss; +loss4=h4*(load4/va)^2*cuLoss; +loss5=h5*(load5/va)^2*cuLoss; +//loss in 24 hours +loss24=loss1+loss2+loss3+loss4+loss5; +//disp(sprintf("The all day loss is %f ",loss24)); +Pout=h1*load1*pf1+h2*load2*pf2+h3*load3*pf3+h4*load4*pf4+h5*load5*pf5; +//disp(sprintf("The all day energy output is %f ",Pout)); +Pin=Pout+ironLoss*24+loss24; +eff=Pout*100/Pin; +disp(sprintf("The all day percent efficiency is %.2f ",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.19/Ex7_19.sce b/1445/CH7/EX7.19/Ex7_19.sce new file mode 100644 index 000000000..5673a8c80 --- /dev/null +++ b/1445/CH7/EX7.19/Ex7_19.sce @@ -0,0 +1,70 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 19 + +disp("CHAPTER 7"); +disp("EXAMPLE 19"); + +//Open circuit and short circuit test on 10 kVA transformer 500/250 V 50 Hz single phase transformer +//VARIABLE INITIALIZATION +va=10000; //apparent power +v1=500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +f=50; +//open circuit parameters +Voc=500; +Io=2; +Wi=100; // watts HT side +Woc=Wi; //just another nomenclature +//short circuit test +Vsc=25; +Isc=20; +Wc=90; // watts HT side +// +pf=0.8; +//SOLUTION +//open circuit +phi0=acos(Woc/(v1*Io)); +Ic=Io*cos(phi0); +Iphi=Io*sin(phi0); +Rc=v1/Ic; +X=v1/Iphi; +disp("SOLUTION (a)"); +disp(sprintf("The value of Ic is %.2f Amp",Ic)); +disp(sprintf("The value of IΦ is %.2f Amp",Iphi)); +disp(sprintf("The value of Rc is %.0f Ohm",Rc)); +disp(sprintf("The value of X is %.0fΩ",X)); +// +//short circuit +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of Power factor is %.3f",pf1)); +disp(sprintf("The value of Re1 is %.3f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.3f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.3fΩ",X_e1)); +// +//Regulation and efficiency +//% Regulation +I1=va/v1; +phi=acos(pf); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +%reg=(Isc*R_e1*pf+Isc*X_e1*sin(phi))*100/v1; +disp("SOLUTION (c(i))"); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +// +//Efficiency +//full load output at pf=0.8 +Pout=va*pf; +ironLoss=Wi; +cuLoss=Wc; +loss=ironLoss+cuLoss; +Pin=Pout+loss; +eff=Pout*100/Pin; +disp("SOLUTION (c(ii))"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.2/Ex7_2.sce b/1445/CH7/EX7.2/Ex7_2.sce new file mode 100644 index 000000000..df6d083dd --- /dev/null +++ b/1445/CH7/EX7.2/Ex7_2.sce @@ -0,0 +1,42 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 2 + +disp("CHAPTER 7"); +disp("EXAMPLE 2"); +// +//400/200V transformer +//VARIABLE INITIALIZATION +v1=400; //primary voltage in Volts +v2=200; //secondary voltage in Volts +I0=1; //in Amperes +pf1=0.4; //power factor in degrees on no load +I2=50; //secondary current in Amperes +pf2=0.8; //secondary supplies lagging power factor in degrees + +//SOLUTION +//primary current is given by +//I1=I0+I2 +//function to convert from polar to rectangular form +function [x,y]=pol2rect(mag,angle1); +x=mag*cos(angle1); +y=mag*sin(angle1); +endfunction; +// +phi_0=acos(pf1); // cosine inverse of the power factor which is given +phi=acos(pf2); // cosine inverse of the power factor which is given +I2_dash=(v2*I2)/v1; //v1.i1=v2.i2 +//I0=1 < phi_0 in polar format +[x0,y0]=pol2rect(I0,-phi_0); +[x2_dash,y2_dash]=pol2rect(I2_dash,-phi); +I1_x=x0+x2_dash; //x-component of I1 +I1_y=y0+y2_dash; //y-component of I1 +disp(sprintf("The primary current in reactangular form is (%.3f-j%.2f) A",I1_x,-I1_y)); +// +//function to convert from rectangular form to polar form +function [I,angle]=rect2pol(x,y); +I=sqrt((x^2)+(y^2)); +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[I,angle]=rect2pol(I1_x,I1_y); // converting current from rectangular to polar form +disp(sprintf("The primary current in polar form is (%.3f <%.2f) A",I,angle)); +//END diff --git a/1445/CH7/EX7.20/Ex7_20.sce b/1445/CH7/EX7.20/Ex7_20.sce new file mode 100644 index 000000000..0c5f59379 --- /dev/null +++ b/1445/CH7/EX7.20/Ex7_20.sce @@ -0,0 +1,44 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 20 + +disp("CHAPTER 7"); +disp("EXAMPLE 20"); + +//4 kVA 200/400 V 50 hz single phase transformer +//VARIABLE INITIALIZATION +va=4000; //apparent power +v1=200; //primary voltage in Volts +v2=400; //secondary voltage in Volts +f=50; +R_e1=0.15; +Pi=60; //core losses iron core +pf1=0.9; //power factor of primary +pf2=0.8; //power factor of secondary + +//SOLUTION +//Copper loss on full load +R_e2=(v2/v1)^2*R_e1; +I1=va/v1; +I2=va/v2; +Pcu=I2^2*R_e2; //cu losses +disp("SOLUTION (i)"); +disp(sprintf("The value of Copper Losses at full load is %.0f W",Pcu)); +// +//efficiency +Pout=va*pf1; +Pin=Pout+Pi+Pcu; +eff=Pout*100/Pin; +disp("SOLUTION (ii)"); +disp(sprintf("The percent efficiency at full load %f PF is %.2f",pf1,eff)); +// +// +//efficiency at half load +Pout=va*pf2/2; +Pin=Pout+Pi+Pcu*(1/2)^2; +eff=Pout*100/Pin; +disp("SOLUTION (ii)"); +disp(sprintf("The percent efficiency at half load %f PF is %.2f",pf2,eff)); + +disp(" "); +// +//END diff --git a/1445/CH7/EX7.21/Ex7_21.sce b/1445/CH7/EX7.21/Ex7_21.sce new file mode 100644 index 000000000..7135f11c4 --- /dev/null +++ b/1445/CH7/EX7.21/Ex7_21.sce @@ -0,0 +1,36 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 21 + +disp("CHAPTER 7"); +disp("EXAMPLE 21"); + +//250/125 V 5kVA single phase transformer +//VARIABLE INITIALIZATION +va=5000; //apparent power +v1=250; //primary voltage in Volts +v2=125; //secondary voltage in Volts +R1=0.2; //resistance of primary +X1=0.75; //leakage reactance of primary +R2=0.05; //resistance of secondary +X2=0.2; //leakage reactance of secondary +pf=0.8; //power factor (leading) + +//SOLUTION +R_e2=(v2/v1)^2*R1+R2; +X_e2=(v2/v1)^2*X1+X2; +I1=va/v1; +I2=va/v2; +// +//at full load leading +phi=acos(pf); +%reg=(I2*R_e2*pf-I2*X_e2*sin(phi))*100/v2; +disp("SOLUTION (i)"); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +// +//%R=(E2-V2).100/E2 +V2=v2-%reg*v2/100; +disp("SOLUTION (ii)"); +disp(sprintf("The secondary terminal voltage at full load is %.2f V",V2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.22/Ex7_22.sce b/1445/CH7/EX7.22/Ex7_22.sce new file mode 100644 index 000000000..8262bd109 --- /dev/null +++ b/1445/CH7/EX7.22/Ex7_22.sce @@ -0,0 +1,29 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 22 + +disp("CHAPTER 7"); +disp("EXAMPLE 22"); + +//6600/400 V single phase transformer +//VARIABLE INITIALIZATION +v1=6600; //primary voltage in Volts +v2=400; //secondary voltage in Volts +R1=2.5; //primary resistance +R2=0.01; //secondary resistance + +//SOLUTION +//while finding equivalent resistance referrd to primary +//transfer R2 resistance to R'2 +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +// +//to find total equivalent resistance referred to secondary +//first calculate R'1 +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +// +disp(sprintf("The total equivalent resistance referred to primary is %.6f Ω",R_e1)); +disp(sprintf("The total equivalent resistance referred to secondary is %.6f Ω",R_e2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.23/Ex7_23.sce b/1445/CH7/EX7.23/Ex7_23.sce new file mode 100644 index 000000000..c794f2e98 --- /dev/null +++ b/1445/CH7/EX7.23/Ex7_23.sce @@ -0,0 +1,79 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 23 + +disp("CHAPTER 7"); +disp("EXAMPLE 23"); + +//33kVA 2200/220 V 50Hz single phase transformer +//VARIABLE INITIALIZATION +va=33000; +v1=2200; //primary voltage in Volts +v2=220; //secondary voltage in Volts +f=50; // frequency in Hz +R1=2.4; //primary winding (High Voltage side) resistance +X1=6; //primary winding (High Voltage side)leakage reactance +R2=0.03; //secondary winding (Low Voltage side) resistance +X2=0.07; //secondary winding (Low Voltage side)leakage reactance + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; + +disp("SOLUTION (a)"); +disp(sprintf("The primary resistance referred to secondary %.2f Ω",R_dash_1)); +disp(sprintf("The primary leakage reactance referred to secondary %.2f Ω",X_dash_1)); +// +disp("SOLUTION (b)"); +disp(sprintf("The secondary resistance referred to secondary %.2f Ω",R_dash_2)); +disp(sprintf("The secondary leakage reactance referred to secondary %.2f Ω",X_dash_2)); +// +disp("SOLUTION (C(i))"); +disp(sprintf("The equivalent resistance referred to primary %.2f Ω",R_e1)); +disp(sprintf("The equivalent leakage reactance referred to primary %.2f Ω",X_e1)); +// +disp("SOLUTION (C(ii))"); +disp(sprintf("The equivalent resistance referred to secondaryy %.2f Ω",R_e2)); +disp(sprintf("The equivalent leakage reactance referred to secondary %.2f Ω",X_e2)); +// +//Ohmic load +I1=va/v1; // primary full load current +I2=va/v2; // secondary full load current +oLoss=I2^2*R_e2; //ohmic loss +disp("SOLUTION (d)"); +disp(sprintf("The ohmic loss at full load %.0f W",oLoss)); +// +//Voltage to be applied on the HV side +//to obtain short circuit currnet of 160 A in L.V side winding +Z_e1=sqrt(R_e1^2+X_e1^2); // equivalent leakage impedance +//voltage to be applied on HV side is equivalent leakage reactance x primary current +//relationship between current and voltage in transformer +//I1/I2=V2/V1 +//Given V2=220 V, V1=2200 V, I2=160 Amp +//Therefore, I1=I2.(V2/V1) +I1=160*(v2/v1); +V=I1*Z_e1; //160*(v2/v1)*Z_e1; +//Power Input +P=(I1)^2*R_e1 //P=I^2.R +disp("SOLUTION (e)"); +disp(sprintf("The voltage to be applied on HV side is %.2f V",V)); +disp(sprintf("The power input is %.1f W",P)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.24/Ex7_24.sce b/1445/CH7/EX7.24/Ex7_24.sce new file mode 100644 index 000000000..6a74149b1 --- /dev/null +++ b/1445/CH7/EX7.24/Ex7_24.sce @@ -0,0 +1,61 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 24 + +disp("CHAPTER 7"); +disp("EXAMPLE 24"); + +//10kVA 2500/250 V single phase transformer +//VARIABLE INITIALIZATION +va=10000; +v1=2500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +R1=4.8; //primary HV side winding resistance +X1=11.2; //primary HV side winding leakage reactance +R2=0.048; //secondary LV side winding resistance +X2=0.112; //secondary LV side winding leakage reactaance + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; +//leakage impedence +//The transformer leakage impedance=z0=Re2+j.Xe2 +//Therefore: +z0=R_e2+X_e2*%i; +//Further Given +//the LV winding side is connected to load impedance of 5+j.3.5 Ohm +//The power factor 0.8 lagging on LV side +//applied load is +Zl=5+3.5*%i; +//total impedence in series +//The leakage impedance and load impedance are in series, therefore, total impedance is sum of the two +// +Z=z0+Zl; +magZ=sqrt(real(Z)^2+imag(Z)^2); +magZl=sqrt(real(Zl)^2+imag(Zl)^2); +//V2=I2.Zl +I2=v2/magZ; +V2=I2*magZl +disp("SOLUTION (a)"); +disp(sprintf("The secondary terminal voltage is %.0f V",V2)); +// +//part (b) and (c) of the problem cannot be solved mathematically alone. +disp(" "); +// +//END diff --git a/1445/CH7/EX7.25/Ex7_25.sce b/1445/CH7/EX7.25/Ex7_25.sce new file mode 100644 index 000000000..acb81a060 --- /dev/null +++ b/1445/CH7/EX7.25/Ex7_25.sce @@ -0,0 +1,66 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 25 + +disp("CHAPTER 7"); +disp("EXAMPLE 25"); + +//15kVA 2200/110 V transformer +//VARIABLE INITIALIZATION +va=25000; //power rating +v1=2200; //primary voltage in Volts +v2=110; //secondary voltage in Volts +f=50; +R1=1.75; +X1=2.6; +R2=0.0045; +X2=0.0075; + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; +// +Z_e1=R_e1+X_e1*%i; +Z_e2=R_e2+X_e2*%i; +magZ_e1=sqrt(real(Z_e1)^2+imag(Z_e1)^2); +magZ_e2=sqrt(real(Z_e2)^2+imag(Z_e2)^2); +// +// +disp("SOLUTION (a)"); +disp(sprintf("The equivalent resistance referred to primary %.2f Ω",R_e1)); +disp("SOLUTION (b)"); +disp(sprintf("The equivalent resistance referred to secondaryy %.5f Ω",R_e2)); +disp("SOLUTION (c)"); +disp(sprintf("The equivalent leakage reactance referred to primary %.1f Ω",X_e1)); +disp("SOLUTION (d)"); +disp(sprintf("The equivalent leakage reactance referred to secondary %.3f Ω",X_e2)); +disp("SOLUTION (e)"); +disp(sprintf("The equivalent impedance referred to primary %.5f Ω",magZ_e1)); +disp("SOLUTION (f)"); +disp(sprintf("The equivalent impedance referred to secondary %.5f Ω",magZ_e2)); +// +//primary and secondary full load current and voltage relationship with power rating +I1=va/v1; //primary current +I2=va/v2; //secondary current +cuLoss=I2^2*R_e2; //copper loss or also as I1^2.R1 + I2^2.R2 +disp("SOLUTION (d)"); +disp(sprintf("The copper loss at full load %f W",cuLoss)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.26/Ex7_26.sce b/1445/CH7/EX7.26/Ex7_26.sce new file mode 100644 index 000000000..7fed48bc9 --- /dev/null +++ b/1445/CH7/EX7.26/Ex7_26.sce @@ -0,0 +1,68 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 26 + +disp("CHAPTER 7"); +disp("EXAMPLE 26"); + +//open circuit & short circuit test +//10 kVA 500/250 V 50 Hz single phase +//VARIABLE INITIALIZATION +va=10000; //apparent power +v1=500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +f=50; // frequency +//open circuit parameters +Voc=500; +Io=2; +Wi=100; // watts HT side +Woc=Wi; //just to keep symbology +//short circuit test +Vsc=25; +Isc=20; +Wc=90; // watts HT side +// +pf=0.8; +//SOLUTION +//open circuit +phi0=acos(Woc/(v1*Io)); +Ic=Io*cos(phi0); +Iphi=Io*sin(phi0); +Rc=v1/Ic; +X=v1/Iphi; +disp("SOLUTION (a)"); +disp(sprintf("The value of Ic is %.2f Amp",Ic)); +disp(sprintf("The value of IΦ is %.2f Amp",Iphi)); +disp(sprintf("The value of Rc is %.2f Ohm",Rc)); +disp(sprintf("The value of X is %.2fΩ",X)); +// +//short circuit +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of Power factor is %f",pf1)); +disp(sprintf("The value of Re1 is %f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %fΩ",X_e1)); +// +I1=va/v1; +phi=acos(pf); +//R=er.cos phi2+vx.sin phi2 +//E2=V2+I2.R +%reg=(Isc*R_e1*pf+Isc*X_e1*sin(phi))*100/v1; +disp("SOLUTION (c(i))"); +disp(sprintf("The percent regulation at full load is %.2f",%reg)); +// +//full load output at pf=0.8 +Pout=va*pf; // Output Power +ironLoss=Wi; +cuLoss=Wc; +loss=ironLoss+cuLoss; +Pin=Pout+loss; //Input Power +eff=Pout*100/Pin; //efficiency +disp("SOLUTION (c(ii))"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.27/Ex7_27.sce b/1445/CH7/EX7.27/Ex7_27.sce new file mode 100644 index 000000000..b72abacee --- /dev/null +++ b/1445/CH7/EX7.27/Ex7_27.sce @@ -0,0 +1,73 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 27 + +disp("CHAPTER 7"); +disp("EXAMPLE 27"); + +//200kVA 1100/400 V delta star distribution transformer +//three phase +//VARIABLE INITIALIZATION +va=200000; //apparent power +v1=11000; //primary voltage in Volts +v2=400; //secondary voltage in Volts +f=50; // frequency +//open circuit test parameters +V3=400; +I3=9; +W3=1500; //load in watts HT side +//short circuit test parameters +Vsc=350; +Isc=20; +Wc=2100; //load in watts HT side +// +pf=0.8; +//SOLUTION +Voc=V3/sqrt(3); //per phase applied voltage in open circiut +Io=9; //per phase exciting current.= I3 +Wi=W3/3; // per phase core loss in watts HT side +Pc=Wi; //core losses +//power factor Pc=V1.Io.cos phi0 //v1=Voc +//open circuit test performed on LV side +phi0=acos(Wi/(Voc*Io)); +Ic=Io*cos(phi0); //core loss current +Iphi=Io*sin(phi0); //magnetising current +Rc=Voc/Ic; //Core loss resistance +X=Voc/Iphi; // +disp("SOLUTION (a)"); +disp(sprintf("The value of Ic is %.0f Amp",Ic)); +disp(sprintf("The value of IΦ is %.2f Amp",Iphi)); +disp(sprintf("The value of Rc is %.2f Ohm",Rc)); +disp(sprintf("The value of X is %.2fΩ",X)); +// +//core loss resistance referred to hv side +Rch=Rc*(v1/Voc)^2; +XphiH=X*(v1/Voc)^2; +disp(sprintf("The value of Rch is %.2f kΩ",Rch/1000)); +disp(sprintf("The value of XΦh is %.2f KΩ",XphiH/1000)); +//short circuit +//This test performed on HV side +//first find rated current +Isc=va/(3*v1); +Psc=Wc/3; //ohmic loss per phase +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Psc/Isc^2; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of ohmic loss per phase is %.0f W",Psc)); +disp(sprintf("The value of Re1 is %.2f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.2f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.2fΩ",X_e1)); +// +//efficiency at half load +pf=1; //unity power factor +Pout=(va/3)*(1/2)*pf; +//core losses=Pc +//cuLosses ohmic loss =Psc +Pin=Pout+Pc+(1/2)^2*Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at half load is %.2f",eff)); + +disp(" "); +// +//END diff --git a/1445/CH7/EX7.28/Ex7_28.sce b/1445/CH7/EX7.28/Ex7_28.sce new file mode 100644 index 000000000..022c5502e --- /dev/null +++ b/1445/CH7/EX7.28/Ex7_28.sce @@ -0,0 +1,97 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 28 + +disp("CHAPTER 7"); +disp("EXAMPLE 28"); + +//10 kVA 2500/250 V single phase transformer +//open circuit and short circuit tests +//VARIABLE INITIALIZATION +va=10000; //apparent power +v1=2500; //primary voltage in Volts +v2=250; //secondary voltage in Volts +f=50; +//open circuit parameters +Voc=250; +Io=0.8; +Wi=50; // watts HT side +//short circuit test +Vsc=60; +Isc=3; +Wc=45; // watts HT side +// +//loads +pf=0.8; +//SOLUTION +//Open circuit test conducted on lv because 250 V during this test is equal to rated voltage on lv side. +I1=va/v1; //full rated current on hv side +Psc0=Wc*(I1/Isc)^2; //ohmic loss/ cu loss at full load rated current +Pc=Wi; // core losses +// 1/4 load +Psc=(1/4)^2*Psc0; +Pout=va*pf*(1/4); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp("SOLUTION (a)"); +disp(sprintf("The efficiency at 1/4 load is %.2f",eff)); +// +// 1/2 load +Psc=(1/2)^2*Psc0; +Pout=va*pf*(1/2); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at 1/2 load is %.2f",eff)); +// +// full load +Psc=(1/1)^2*Psc0; +Pout=va*pf*(1/1); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at full load is %.2f",eff)); +// +// 1 1/4 = 5/4 load +Psc=(5/4)^2*Psc0; +Pout=va*pf*(5/4); +Pin=Pout+Pc+Psc; +eff=Pout*100/Pin; +disp(sprintf("The efficiency at 1 1/4 or 5/4 load is %.2f",eff)); +// +//maximum efficiency at x, but then ohmic loss=core loss +x=sqrt(Pc/Psc0); +Pout=va*x*pf; +Pin=Pout+Pc+Pc; //Ohmic losses = core losses at max efficiency +eff=Pout*100/Pin; +disp("SOLUTION (b)"); +disp(sprintf("The maximum efficiency is %.2f",eff)); +// +//short circuit test performed on lv side +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp("SOLUTION (c)"); +disp(sprintf("The value of Re1 is %.2f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.2f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.2fΩ",X_e1)); +// +//ee, ex; +er=I1*R_e1/v1; +ex=I1*X_e1/v1; +disp(sprintf("The value of Er is %.3f pu",er)); +disp(sprintf("The value of Ex is %.3f",ex)); +// +phi=acos(pf); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +%reg=(I1*R_e1*pf+I1*X_e1*sin(phi))*100/v1; //same as using er and ex +disp(sprintf("The percent regulation at full load lagging is %.2f",%reg)); +%reg1=(I1*R_e1*pf-I1*X_e1*sin(phi))*100/v1; //same as using er and ex +disp(sprintf("The percent regulation at full load leading is %.2f",%reg1)); +V21=(1-%reg/100)*v2; +V22=(1-%reg1/100)*v2; +disp(sprintf("The secondary terminal voltage at full load lagging is %.2f",V21)); +disp(sprintf("The secondary terminal voltage at full load leading is %.2f",V22)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.29/Ex7_29.sce b/1445/CH7/EX7.29/Ex7_29.sce new file mode 100644 index 000000000..5e8b2f759 --- /dev/null +++ b/1445/CH7/EX7.29/Ex7_29.sce @@ -0,0 +1,59 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 29 + +disp("CHAPTER 7"); +disp("EXAMPLE 29"); + +//20kVA 4000/1000 V single phase transformer +//VARIABLE INITIALIZATION +va=200000; //apparent power +v1=4000; //primary voltage in Volts +v2=1000; //secondary voltage in Volts +f=50; // frequency in Hz +//loads +pf=1; //power factor is unity +eff=0.97; // at full load and at 60% of full load +nlpf=0.5; //no load pf +lpf=0.8 //lagging pf +reg=0.05; //%regulation at 0.8 pf +// +//SOLUTION +loss=(1-eff)*va/eff; //=Pc+Pcu losses +//simultaneous equation to be solved +//eq 1: Pc+Pcu=loss; +//fractipon of copper/ ohmic losses +f=(0.6)^2; // 60% of full load +//the 2nd equation is Pc+f*Pcu=loss +//now the matrix +M=[1,1;1,f]; +A=[loss,loss*0.6]; +Mi=inv(M); +Ans=A*inv(M); +Pc=Ans(1,1); +Pcu=Ans(1,2); +//disp(sprintf("The Pc is %f",Pc)); +//disp(sprintf("The Pcu is %f",Pcu)); +//LV side +R_e2=Pcu/va; +//from %reg find X_e2 +phi=acos(lpf); +X_e2=(reg-R_e2*cos(phi))/sin(phi); +//in oms units +R_e2=R_e2*v2^2/va; // in ohms +X_e2=X_e2*v2^2/va; // in ohms +disp(sprintf("The Re2 is %.3f Ω",R_e2)); +disp(sprintf("The Xe2 is %.3f Ω",X_e2)); +// +Rc=v2^2/Pc; +Ie2=Pc/(v2*0.25); +Ic=Pc/v2; +Iphi=sqrt(Ie2^2-Ic^2); +Xphi=v2/Iphi; +disp(sprintf("The Rc is %.2f Ω",Rc)); +disp(sprintf("The Ie2 is %.3f A",Ie2)); +disp(sprintf("The Ic is %.3f A",Ic)); +disp(sprintf("The Iphi is %.4f A",Iphi)); +disp(sprintf("The Xphi is %.2f Ω",Xphi)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.3/Ex7_3.sce b/1445/CH7/EX7.3/Ex7_3.sce new file mode 100644 index 000000000..870db87c8 --- /dev/null +++ b/1445/CH7/EX7.3/Ex7_3.sce @@ -0,0 +1,72 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 3 + +disp("CHAPTER 7"); +disp("EXAMPLE 3"); +// +//2300/230 V 50 Hz transformer +//VARIABLE INITIALIZATION +v1=2300; //primary voltage in Volts +v2=230; //secondary voltage in Volts +f=50; +R1=0.286; +X1=0.73; +R_dash_2=0.319; +X_dash_2=0.73; +Rc=250; +Xphi=1250; +Zl=0.387+0.29*%i; +// +//SOLUTION +Z_e1=(R1+R_dash_2)+(X1+X_dash_2)*%i; +Z_dash_l=(v1/v2)^2*Zl; +// +I_dash_1=v1/(Z_dash_l+Z_e1); +//[mag,angle]=rect2pol(real(I_dash_1),imag(I_dash_1)); +//disp(sprintf("The current is %f <%f A",mag,angle)); +//impedance of shunt branch +Zm=Rc*(Xphi*%i)/(Rc+Xphi*%i); +//[mag,angle]=rect2pol(real(Zm),imag(Zm)); +//disp(sprintf("The Zm is %f <%f A",mag,angle)); +I0=v1/Zm; +//[mag,angle]=rect2pol(real(I0),imag(I0)); +//disp(sprintf("The I0 is %f <%f A",mag,angle)); +// +//primary current +I1=I0+I_dash_1; +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +[mag,angle]=rect2pol(real(I1),imag(I1)); +theta1=angle; +disp("SOLUTION (i)"); +disp(sprintf("The primay current in rectangulr form is %.3f -j%.2f A",real(I1),-imag(I1))); +disp(sprintf("The primay current in polar form is %.3f <%.2f A",mag,angle)); +// +//input power +Pin=v1*I1; ; //=I1.cos(theta1) +//disp(sprintf("The input power is %.3f kW",Pin/1000)); +//output power +V_dash_2=I_dash_1*Z_dash_l; +[mag,angle]=rect2pol(real(V_dash_2),imag(V_dash_2)); +theta2=angle; +//disp(sprintf("The V_dash_2 is %.2f <%.2f A",mag,angle)); +// +Pout= V_dash_2*I_dash_1; //I_dash_1.cos(theta1) +//disp(sprintf("The output power is %.3f kW",real(Pout)/1000)); +//Efficiency +disp("SOLUTION (ii)"); +disp(sprintf("The Efficiency is %.2f kW",Pout*100/Pin));// text Book answer is 78.75% +//Losses +Pc=v1*I0; //core loss +loss=Pin-Pout; +Pcu=loss-Pc; //copper loss +disp(sprintf("The core loss is %.2f kW",Pc/1000));//text book answer is 0.8 kW +disp(sprintf("The copper loss is %.2f kW",Pcu/1000));//text book answer is 1..38 kW +//efficiency +//eff=Pout*100/Pin; +//disp(sprintf("The percent efficiency is %f W",eff)); +disp(" "); +// The answers from V_dash_2 calculation onward do not match with the book on page 7.21 and 7.22 +//END diff --git a/1445/CH7/EX7.30/Ex7_30.sce b/1445/CH7/EX7.30/Ex7_30.sce new file mode 100644 index 000000000..7d78d4b84 --- /dev/null +++ b/1445/CH7/EX7.30/Ex7_30.sce @@ -0,0 +1,23 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 30 + +disp("CHAPTER 7"); +disp("EXAMPLE 30"); + +//6600/440 V single phase transformer +//VARIABLE INITIALIZATION +v1=6600; //primary voltage in Volts +v2=440; //secondary voltage in Volts +e_r=0.02; //equivalent resistance +e_x=0.05; //equivalent reactance +pf=0.8; //power factor +// +//SOLUTION +//worked out differently a bit from the text book in terms of the steps +phi=acos(pf); //phase angle +reg=e_r*cos(phi)+e_x*sin(phi); //voltage regulation +V2=v2*(1-reg); //secondary terminal voltage +disp(sprintf("The secondary terminal voltage is %.2f V",V2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.31/Ex7_31.sce b/1445/CH7/EX7.31/Ex7_31.sce new file mode 100644 index 000000000..0150a59be --- /dev/null +++ b/1445/CH7/EX7.31/Ex7_31.sce @@ -0,0 +1,29 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 31 + +disp("CHAPTER 7"); +disp("EXAMPLE 31"); + +//single phase transformer having 400 primary and 1000 secondary turns +//VARIABLE INITIALIZATION +N1=400; +N2=1000; +coreA=60; //net core area in cm^2 +v1=500; //primary voltage in Volts +f=50; //frequency + +// +//SOLUTION +//v1=E1=4.44.Φm.N1.f Volts +phiM=v1/(4.44*N1*f); +//flux density Bm=Φm/area +Bm=phiM/coreA; //lines per cm +//voltage per turn +vpt=v1/N1; +v2=N2*vpt; +// +disp(sprintf("The maximum flux density is %.3fx10^-5 Wb per cm^2",Bm*10^5));//text book anser is 9383 lines per cm^2 +disp(sprintf("The secondary voltage is %.0f V",v2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.32/Ex7_32.sce b/1445/CH7/EX7.32/Ex7_32.sce new file mode 100644 index 000000000..05a91a7ea --- /dev/null +++ b/1445/CH7/EX7.32/Ex7_32.sce @@ -0,0 +1,62 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 32 + +disp("CHAPTER 7"); +disp("EXAMPLE 32"); + +//50 kVA 4400/220 V single phase transformer +//VARIABLE INITIALIZATION +va=50000; +v1=4400; //primary voltage in Volts +v2=220; //secondary voltage in Volts +f=50; +R1=3.45; +X1=5.2; +R2=0.0009; +X2=0.015; + +//SOLUTION +// +//Primary resistance and leakage reactance referred to secondary +//R'1 & X'1 +//Secondary resistance and leakage reactance referred to primary +//R'2 & X'2 +//Equivalent resistance & leakage reactance referred to primary +//Re1 & Xe1 +//Equivalent resistance & leakage reactance referred to secondary +//Re2 & Xe2 +// +R_dash_2=R2*(v1/v2)^2; +R_e1=R1+R_dash_2; +X_dash_2=X2*(v1/v2)^2; +X_e1=X1+X_dash_2; +// +R_dash_1=R1*(v2/v1)^2; +R_e2=R2+R_dash_1; +X_dash_1=X1*(v2/v1)^2; +X_e2=X2+X_dash_1; +// +Z_e1=R_e1+X_e1*%i; +Z_e2=R_e2+X_e2*%i; +magZ_e1=sqrt(real(Z_e1)^2+imag(Z_e1)^2); +magZ_e2=sqrt(real(Z_e2)^2+imag(Z_e2)^2); +// +disp("SOLUTION (i)"); +disp(sprintf("The equivalent resistance referred to primary %.4f Ω",R_e1));//text book answer is 7.05 ohm +disp("SOLUTION (ii)"); +disp(sprintf("The equivalent resistance referred to secondaryy %.4f Ω",R_e2)); +disp("SOLUTION (iii)"); +disp(sprintf("The equivalent leakage reactance referred to primary %.4f Ω",X_e1)); +disp(sprintf("The equivalent leakage reactance referred to secondary %.4f Ω",X_e2)); +disp("SOLUTION (iv)"); +disp(sprintf("The equivalent impedance referred to primary %.4f Ω",magZ_e1)); // text book answer is 13.23 ohm +disp(sprintf("The equivalent impedance referred to secondary %.4f Ω",magZ_e2));//text book answer is 0.0331 ohm +// +I1=va/v1; +I2=va/v2; +Pcu=I2^2*R_e2; +disp("SOLUTION (d)"); +disp(sprintf("The copper loss at full load %.0f W",Pcu)); +disp(" "); +//The answers in the book on page 7.77 are wrong for all but Xe1 and Xe2 values. +//END diff --git a/1445/CH7/EX7.33/Ex7_33.sce b/1445/CH7/EX7.33/Ex7_33.sce new file mode 100644 index 000000000..35ea4a24d --- /dev/null +++ b/1445/CH7/EX7.33/Ex7_33.sce @@ -0,0 +1,66 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 33 + +disp("CHAPTER 7"); +disp("EXAMPLE 33"); + +// 5kVA 400/200 V 50 Hz single phase transformer +//open ciruit and short circuit tests +//VARIABLE INITIALIZATION +va=5000; //apparent power +v1=400; //primary voltage in Volts +v2=200; //secondary voltage in Volts +f=50; +//no load parameters +Voc=400; +Io=1; +Woc=50; // watts HT side +//short circuit test +Vsc=12; +Isc=10; +Wc=40; // watts HT side +// +pf=0.8; +//SOLUTION +//no load condition +phi0=acos(Woc/(v1*Io)); +Ic=Io*cos(phi0); +Iphi=Io*sin(phi0); +Rc=v1/Ic; +X=v1/Iphi; +disp("SOLUTION (i)"); +disp(sprintf("The value of Ic is %f Amp",Ic)); +disp(sprintf("The value of IΦ is %f Amp",Iphi)); +//disp(sprintf("The value of Rc is %f Ohm",Rc)); +//disp(sprintf("The value of X is %fΩ",X)); +// +//short circuit +phisc=acos(Wc/(Vsc*Isc)); +pf1=cos(phisc); +R_e1=Vsc*pf1/Isc; +Z_e1=Vsc/Isc; +X_e1=sqrt(Z_e1^2-R_e1^2); +disp(sprintf("The value of Re1 is %.2f Ohm",R_e1)); +disp(sprintf("The value of Ze1 is %.2f Ohm",Z_e1)); +disp(sprintf("The value of Xe1 is %.2fΩ",X_e1)); +// +I1=va/v1; +phi=acos(pf); +//R=ercosphi2+vx.sinphi2 +//E2=V2+I2.R +%reg=(I1*R_e1*pf+I1*X_e1*sin(phi))*100/v1; +disp("SOLUTION (c(i))"); +disp(sprintf("The percent regulation at full load is %.3f",%reg)); +// +//full load output at pf=0.8 +Pout=va*pf; //output power +ironLoss=Woc; +cuLoss=Wc; +loss=ironLoss+cuLoss; +Pin=Pout+loss; // input power +eff=Pout*100/Pin; +disp("SOLUTION (c(ii))"); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); // not calculated in the text book +disp(" "); +// +//END diff --git a/1445/CH7/EX7.34/Ex7_34.sce b/1445/CH7/EX7.34/Ex7_34.sce new file mode 100644 index 000000000..eaf48effe --- /dev/null +++ b/1445/CH7/EX7.34/Ex7_34.sce @@ -0,0 +1,41 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 35 + +disp("CHAPTER 7"); +disp("EXAMPLE 35"); + +//single phase 50 hz, 200kVA, 11kVA/230 V +//open circuit and short circuit tests +//VARIABLE INITIALIZATION +va=200000; //apparent power +v1=11000; //primary voltage in Volts +v2=230; //secondary voltage in Volts +Woc=1600; //watts also equals core losses +Wc=2600; //watts, also equals cu losses +f=50; +//no load parameters +//day cycle given +h1=8; // hours +load1=160000; //load in watts +pf1=0.8; //power factor +h2=6; +load2=100000; +pf2=1; +h3=10; +load3=0; +pf3=0; +//SOLUTION +//24 hr energy output +Pout=load1*h1*pf1+load2*h2*pf2+load3*h3*pf3; +Pc24=Woc*24; // 24 hours Pc loss +//cu loss= hours.(kva output/kva rated)^2.Full load Cu loss +Pcu24=h1*(load1/va)^2*Wc+h2*(load2/va)^2*Wc+h3*(load3/va)^2*Wc; +Pin=Pout+Pc24+Pcu24; +eff=Pout*100/Pin; +//disp(sprintf("The value Pout is %f",Pout)); +//disp(sprintf("The value Pc is %f",Pc24)); +//disp(sprintf("The value Pcu is %f",Pcu24)); +disp(sprintf("The percent efficiency at full load is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.35/Ex7_35.sce b/1445/CH7/EX7.35/Ex7_35.sce new file mode 100644 index 000000000..1d5f68a38 --- /dev/null +++ b/1445/CH7/EX7.35/Ex7_35.sce @@ -0,0 +1,46 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 36 + +disp("CHAPTER 7"); +disp("EXAMPLE 36"); + +// 100kVA 50 Hz 440/11000 V single phase transformer +//VARIABLE INITIALIZATION +va=100000; //apparent power +v1=440; //primary voltage in Volts +v2=11000; //secondary voltage in Volts +f=50; // efficiency +//loads +pf=1; //power factor at half load current +eff1=0.985; // at full load at 0.8pf +eff2=0.99; //at half full load at unity pf +pf1=0.8; // power factor at full load current +pf2=1; // +// +//SOLUTION +loss1=(1-eff1)*va*pf1/eff1; //=Pc+Pcu losses +loss2=(1-eff2)*va*(1/2)*pf2/eff2; //=Pc+Pcu losses +//simultaneous equation to be solved +//eq 1: Pc+Pcu=loss; +//fractipon of copper/ ohmic losses +f=(1/2)^2; // 60% of full load +//the 2nd equation is Pc+f*Pcu=loss +//now the matrix +M=[1,1;1,f]; //Pc+Pcu=loss1; Pc+(1/2)^2*Pcu=loss2: 1,1,; 1,f +A=[loss1,loss2]; +Mi=inv(M); +Ans=A*inv(M); +Pc=Ans(1,1); +Pcu=Ans(1,2); +disp(sprintf("The Pc is %.1f W",Pc)); +disp(sprintf("The Pcu is %.1f W",Pcu)); +// +//maximumefficiency at farction x times the full load;and then f.Pcu=Pc +x=sqrt(Pc/Pcu); +disp(sprintf("The maximum efficiency would occur at a load of %.0f kVA",x*va/1000)); +I1=va/v1; +I1maxEff=I1*x; +disp(sprintf("The current at maximum efficeincy is %.0f A",I1maxEff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.36/Ex7_36.sce b/1445/CH7/EX7.36/Ex7_36.sce new file mode 100644 index 000000000..860243a80 --- /dev/null +++ b/1445/CH7/EX7.36/Ex7_36.sce @@ -0,0 +1,46 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 36 + +disp("CHAPTER 7"); +disp("EXAMPLE 36"); + +//100kVA 50 Hz 440/1100 V single phase transformer +//VARIABLE INITIALIZATION +va=100000; //apparent power +v1=440; //primary voltage in Volts +v2=11000; //secondary voltage in Volts +f=50; // frequency +//loads +pf=1; //power factor unity +eff1=0.985; // at full load at 0.8pf +eff2=0.99; //at half full load at unity pf +pf1=0.8; // power factor +pf2=1; //power factor +// +//SOLUTION +loss1=(1-eff1)*va*pf1/eff1; //=Pc+Pcu losses +loss2=(1-eff2)*va*(1/2)*pf2/eff2; //=Pc+Pcu losses +//simultaneous equation to be solved +//eq 1: Pc+Pcu=loss; +//fractipon of copper/ ohmic losses +f=(1/2)^2; // 60% of full load +//the 2nd equation is Pc+f*Pcu=loss +//now the matrix +M=[1,1;1,f]; //Pc+Pcu=loss1; Pc+(1/2)^2*Pcu=loss2: 1,1,; 1,f +A=[loss1,loss2]; +Mi=inv(M); +Ans=A*inv(M); +Pc=Ans(1,1); +Pcu=Ans(1,2); +disp(sprintf("The Pc is %.1f W",Pc)); +disp(sprintf("The Pcu is %.1f W",Pcu)); +// +//maximumefficiency at farction x times the full load;and then f.Pcu=Pc +x=sqrt(Pc/Pcu); +disp(sprintf("The maximum efficiency would occur at a load of %.0f kVA",x*va/1000)); +I1=va/v1; +I1maxEff=I1*x; +disp(sprintf("The current at maximum efficeincy is %.0f A",I1maxEff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.37/Ex7_37.sce b/1445/CH7/EX7.37/Ex7_37.sce new file mode 100644 index 000000000..b4d21103f --- /dev/null +++ b/1445/CH7/EX7.37/Ex7_37.sce @@ -0,0 +1,40 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 37 + +disp("CHAPTER 7"); +disp("EXAMPLE 37"); + +//500 kVA 3300/500 V 50 hz single phase transformer +//VARIABLE INITIALIZATION +va=500000; //apparent power +v1=3300; //primary voltage in Volts +v2=500; //secondary voltage in Volts +f=50; +//loads +pf=1; //power factor unity +eff=0.97; // at 3/4 full load at unity pf +pf2=0.8; //power factor +// +//SOLUTION +I1=va/v1; +loss=(1-eff)*va*(3/4)*pf/eff; //=Pc+Pcu losses at 3/4 load +//since the eff value is maximum, Pcu=Pc; therefore, 2*Pc=loss +Pc=loss/2; +//(3/4)^2*Pcu=Pc; +f=(3/4)^2; //3/4 load +//Pcu=Pc/f +Pcu=Pc/f; +//disp(sprintf("The Pc is %f W",Pc)); +//disp(sprintf("The Pcu is %f W",Pcu)); +// +R_e1=Pcu/I1^2; +disp(sprintf("The value of Re1 is %.3f W",R_e1)); +//10% impedance +Z_e1=v1*0.1/I1; +X_e1=sqrt(Z_e1^2-R_e1^2); +phi=acos(0.8); +%reg=(I1*R_e1*cos(phi)+I1*X_e1*sin(phi))*100/v1; +disp(sprintf("The percent regulation at full load 0.8 pf is %.2f W",%reg)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.38/Ex7_38.sce b/1445/CH7/EX7.38/Ex7_38.sce new file mode 100644 index 000000000..080504a42 --- /dev/null +++ b/1445/CH7/EX7.38/Ex7_38.sce @@ -0,0 +1,31 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 38 + +disp("CHAPTER 7"); +disp("EXAMPLE 38"); + +//220/115 V 25 Hz single phase transformer +//VARIABLE INITIALIZATION +v1=220; //primary voltage in Volts +v2=115; //secondary voltage in Volts +f1=25; //frequency rating of the transformer in Hz +f2=50; //frequency of the connected load +//loads +V=440 // i Volts +We1=100; //in Watts at 220 V, eddy losses +Pc1=2*We1; //Total iron losses which equals We+Wh due to eddy and hysteresis +Wh1=Pc1-We1; +// +//SOLUTION +//since we know that We=kh.f.B^1.6 and Wh=Ke.Kf^2.f^2.B^2 +//since all being constant exept frequency, we may take We2/We1=f2^2/f1^2 +//and Wh2/Wh1=f2/f1 +//flux density in both cases is same as in second case voltage and frquency both are doubled +//find values for We2 and Wh2, whence Pc2=We2+Wh2 +We2=f2^2*We1/f1^2; +Wh2=f2*Wh1/f1; +Pc2=We2+Wh2; +disp(sprintf("The total no load losses at 400 V is %.0f W",Pc2)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.39/Ex7_39.sce b/1445/CH7/EX7.39/Ex7_39.sce new file mode 100644 index 000000000..0d9677643 --- /dev/null +++ b/1445/CH7/EX7.39/Ex7_39.sce @@ -0,0 +1,41 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 39 + +disp("CHAPTER 7"); +disp("EXAMPLE 39"); + +//220/440 v 50 Hz transformer +//VARIABLE INITIALIZATION +v1=220; //primary voltage in Volts +v2=440; //secondary voltage in Volts +f1=50; //rated frequency in Hz + +//loads +V=110; +f2=25; //frquency of the applied load +//say, else computation may not be possible using computer +Pout1=100; //in watt, just assumed for computational purposes for the 220V supply +We1=0.01*Pout1; //in Watts at 220 V, eddy losses which are 1% of the output at 220V +Wh1=0.01*Pout1; //in Watts at 220 V, hysteresis losses which are 1% of the output at 220V +//Pc1=We1+Wh1; //Total iron losses which equals We+Wh due to eddy and hysteresis +Pcu1=0.01*Pout1; //copper losses +// +//SOLUTION +//since on connecting to half the power ie 110V, the output would get halved +Pout2=Pout1/2; +xPcu=Pcu1/Pout2; +disp(sprintf("The copper losses at 110 V would be %.0f percent of the output",xPcu*100)); +//now coming to frequency dependant losses ie eddy and hysteresis +//since we know that We=kh.f.B^1.6 and Wh=Ke.Kf^2.f^2.B^2 +//since all being constant exept frequency, we may take We2/We1=f2^2/f1^2 +//and Wh2/Wh1=f2/f1 +//find values for We2 and Wh2, whence Pc2=We2+Wh2 +We2=f2^2*We1/f1^2; +Wh2=f2*Wh1/f1; +xWe=We2/Pout2; +xWh=Wh2/Pout2; +disp(sprintf("The eddy losses at 110 V would be %.2f percent of the output",xWe*100)); +disp(sprintf("The hysteresis losses at 110 V would be %.2f percent of the output",xWh*100)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.4/Ex7_4.sce b/1445/CH7/EX7.4/Ex7_4.sce new file mode 100644 index 000000000..4f6586072 --- /dev/null +++ b/1445/CH7/EX7.4/Ex7_4.sce @@ -0,0 +1,38 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 4 + +disp("CHAPTER 7"); +disp("EXAMPLE 4"); + +//10kVA Transformer with 50 turns on primary and 10 turns on secondary +//connected to 440 V 50Haz supply +//VARIABLE INITIALIZATION +va=10*1000; //apparent power, converting kVA to VA +N1=50; //number of turns on primary side +N2=10; //number of turns on secondary side +v1=440; //primary voltage in Volts +f=50; //in Hertz + +//SOLUTION + +//solution (a) +//K=N2/N1=V2/V1 +v2=v1*(N2/N1); +disp(sprintf("(a) The secondary voltage on no load is %d V",v2)); + +//solution (b) +//Current on Full load +//primary side I1=VA/V1 +//secondary side I2=VA/V2 +I1=va/v1; +disp(sprintf("(b) The full load primary current is %.4f A",I1)); +I2=va/v2; +disp(sprintf("The full load secondary current is %.4f A",I2)); + +//solution (c) +//As per EMF equation +//E2=sqrt(2).pi.f.phimax.N2 +phi_m=v2/(sqrt(2)*%pi*f*N2); +disp(sprintf("(c) The maximum value of the flux is %.3f mWb",phi_m*1000)); + +//END diff --git a/1445/CH7/EX7.40/Ex7_40.sce b/1445/CH7/EX7.40/Ex7_40.sce new file mode 100644 index 000000000..a78c44b1d --- /dev/null +++ b/1445/CH7/EX7.40/Ex7_40.sce @@ -0,0 +1,22 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 40 + +disp("CHAPTER 7"); +disp("EXAMPLE 40"); + +//Given +//transformer on no load has a core loss 50W, draws a current of 2 A (RMS) and induced emf 220 V(RMS) +//VARIABLE INITIALIZATION +loss=50; //core loss in Watts +I0=2; //no load current in Amperes +v0=220; //induced emf in Volts + +//SOLUTION +pf=loss/(v0*I0); +I_c=I0*pf; //core loss component +I_phi=I0*sin(acos(pf)); //magnetizing component +disp(sprintf("The magnetizing component, I_c= %.4f A,",I_phi)); +disp(sprintf("The core loss component, I_Φ= %.4f A,",I_c)); + +//END + diff --git a/1445/CH7/EX7.41/Ex7_41.sce b/1445/CH7/EX7.41/Ex7_41.sce new file mode 100644 index 000000000..ffab26d2c --- /dev/null +++ b/1445/CH7/EX7.41/Ex7_41.sce @@ -0,0 +1,32 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 41 + +disp("CHAPTER 7"); +disp("EXAMPLE 41"); + +//3-phase 550/440 V star connected transformer supplies a load of 400kW +//VARIABLE INITIALIZATION +v1=550; //primary voltage in Volts +v2=440; //secondary voltage in Volts +p=400*1000; //load in Watts +pf=0.8; //power factor(lagging) + +//SOLUTION + +//solution (a) +I2=p/(sqrt(3)*v2*pf); //current on secondary side +I1=I2*(v2/v1); //since I1:I2=N2:N1 +I=I2-I1; //in sections Oa, Ob and Oc +disp(sprintf("(a) The current flowing in sections Oa, Ob and Oc is %.0f A",I)); +disp(sprintf("The current flowing in sections aA, bB and cC is %.0f A",I1)); + +//solution (b) +//power transferred by transformer action = Pin.(1-k) +p_o=p*(1-(v2/v1)); //k=v2/v1 +disp(sprintf("(b) The power transferred by transformer action %.0f kW",p_o/1000)); + +//solution (c) +p_d=p-p_o; +disp(sprintf("(c) The power conducted directly %d kW",p_d/1000)); + +//END diff --git a/1445/CH7/EX7.5/Ex7_5.sce b/1445/CH7/EX7.5/Ex7_5.sce new file mode 100644 index 000000000..cd6b7f3b3 --- /dev/null +++ b/1445/CH7/EX7.5/Ex7_5.sce @@ -0,0 +1,31 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 5 + +disp("CHAPTER 7"); +disp("EXAMPLE 5"); + +//single phase transformer +//350 primary and 1050 secondary turns +//VARIABLE INITIALIZATION +N1=350; //number of turns on primary side +N2=1050; //number of turns on secondary side +v1=400; //primary voltage in Volts +f=50; //in Hertz +ar=50/10000; //cross-sectional area of core in m^2 + +//SOLUTION + +//solution (i) +//emf1=sqrt(2).pi.f.Phimax.N1 +//Phimax=Bm.Area, Bm=flux density +//Bm=e1/sqrt(2).pi.A.f.N1 +Bm=v1/(sqrt(2)*%pi*ar*f*N1); +disp(sprintf("(i) The maximum flux density is %.4f Wb/m^2",Bm)); + +//solution (ii) +//e2/e1=n2/n1=K +K=N2/N1; +e2=K*v1; +disp(sprintf("(ii) The induced emf in the secondary winding is %d V",e2)); + +//END diff --git a/1445/CH7/EX7.6/Ex7_6.sce b/1445/CH7/EX7.6/Ex7_6.sce new file mode 100644 index 000000000..2abcb8cf9 --- /dev/null +++ b/1445/CH7/EX7.6/Ex7_6.sce @@ -0,0 +1,37 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 6 + +disp("CHAPTER 7"); +disp("EXAMPLE 6"); + +//2200/20V 50Hz single phase transformer +//VARIABLE INITIALIZATION +v1=2200; //primary voltage in Volts +v2=220; //secondary voltage in Volts +I=0.6; //exciting current in Amperes +p_c=361; //core loss in Watts +I2=60; //load current in Amperes +pf=0.8; //power factor + +//SOLUTION + +//solution (a) +//core loss components +I1=p_c/v1; //vertical component of I0 +I_phi=sqrt((I^2)-(I1^2)); //horizontal component of I0 +disp(sprintf("(a) The core loss component is %.3f A",I1)); +disp(sprintf("And the magnetising component is %.3f A",I_phi)); + +//solution (b) +//I1.N1=I2.N2 +I1_dash=(v2/v1)*I2; +theta=acos(pf); +I1_x=I1_dash*sin(theta)+I_phi; //horizontal component of I0 +I1_y=I1_dash*pf+I1; //vertical component of I0 +I1_res=sqrt((I1_x^2)+(I1_y^2)); //primary current +pf_p=I1_y/I1_res; //primary power factor +disp(sprintf("(b) The primary current is %.3f A",I1_res)); +disp(sprintf("And the power factor is %.3f A",pf_p)); + +//END + diff --git a/1445/CH7/EX7.8/Ex7_8.sce b/1445/CH7/EX7.8/Ex7_8.sce new file mode 100644 index 000000000..e53aed921 --- /dev/null +++ b/1445/CH7/EX7.8/Ex7_8.sce @@ -0,0 +1,66 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 8 + +disp("CHAPTER 7"); +disp("EXAMPLE 8"); + +//23 kVA 2300/230 V 60 Hz step down transformer + +//VARIABLE INITIALIZATION +va=23000; //apparent power +v1=2300; //primary voltage in Volts +v2=230; //secondary voltage in Volts +r1=4; //primary resistance in Ohms +r2=0.04; //secondary resistance in Ohms +X1=12; //leakage reactance primary in Ohms +X2=0.12; //leake reactance in secondary in Ohms +pf=0.866; //power factor(leading) + +//SOLUTION +//assume voltage across load be 230 V +//V'1=I2.(Re2+jXe2)+V2 +//Re2=R'1+R2 +//R'1=R1.(N2/N1)^2 +//Xe2=X'1+X2 +//X'1=X1.(N2/N1)^2 +//Ze2=Re2+j.Xe2 +r1_dash=r1*((v2/v1)^2); +r_e2=r1_dash+r2; +X1_dash=X1*((v2/v1)^2); +X_e2=X1_dash+X2; +// +//disp(sprintf("The value of Re2 %f and Xe2 %f",r_e2,X_e2)); +I2=0.75*(va/v2); //since transformer operates at 75% of its rated load +// +function [x,y]=pol2rect(mag,angle); +x=mag*cos(angle*(%pi/180)); //to convert the angle from degrees to radians +y=mag*sin(angle*(%pi/180)); +endfunction; +[x,y]=pol2rect(I2,-30); +I_dash_2=x+y*%i; +//disp(sprintf("The value %f %f",real(I_dash_2),imag(I_dash_2))); +// +Z_e2=r_e2+X_e2*%i; //in rect coordinates +//disp(sprintf("The value %f %f",real(Z_e2),imag(Z_e2))); +// +V_dash_1=v2+I_dash_2*Z_e2; +//disp(sprintf("The value %f %f",real(V_dash_1),imag(V_dash_1))); +// +function [mag,angle]=rect2pol(x,y); +mag=sqrt((x^2)+(y^2)); //z is impedance & the resultant of x and y +angle=atan(y/x)*(180/%pi); //to convert the angle from radians to degrees +endfunction; +// +[magV1,angleV1]=rect2pol(real(V_dash_1),imag(V_dash_1)); +//disp(sprintf("The value %f <%f",magV1,angleV1)); +// +//Pin=V'1.I2.cos theta1 +//Pout=V2.I2.cos theta2 +Pin=magV1*I2*cos((30+angleV1)*%pi/180); +Pout=v2*I2*cos(30*%pi/180); +eff=Pout*100/Pin; +// +disp(sprintf("The efficiency of the transformer is %.2f",eff)); +disp(" "); +// +//END diff --git a/1445/CH7/EX7.9/Ex7_9.sce b/1445/CH7/EX7.9/Ex7_9.sce new file mode 100644 index 000000000..4a53d3b70 --- /dev/null +++ b/1445/CH7/EX7.9/Ex7_9.sce @@ -0,0 +1,36 @@ +//CHAPTER 7- SINGLE PHASE TRANSFORMER +//Example 9 + +disp("CHAPTER 7"); +disp("EXAMPLE 9"); + +//11000/400 V distribution transformer +//VARIABLE INITIALIZATION +v1=11000; //primary voltage in Volts +v2=400; //secondary voltage in Volts +Io=1; //primary current in Amp +pf=0.24 //power factor lagging + +//SOLUTION +//core loss current +//Ic=Io.cos phi +//Ic=Io.pf +Ic=Io*pf; +disp("SOLUTION (a)"); +disp(sprintf("The value of core loss current is %.2f Amp",Ic)); +// +//magnetizing current +//Iphi=sqrt(Io^2-Ic^2) +Iphi=sqrt(Io^2-Ic^2); +disp("SOLUTION (b)"); +disp(sprintf("The value ofmagnetizing current is %.3f Amp",Iphi)); +// +//Iron Loss +//Iron loss=primary voltage X core loss current +IronLoss=v1*Ic; +disp("SOLUTION (c)"); +disp(sprintf("The iron loss is %.0f W",IronLoss)); +disp(" "); +// +//END + |