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diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER01.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER01.ipynb new file mode 100644 index 00000000..f24867b1 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER01.ipynb @@ -0,0 +1,412 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER01 : MAGNETICS ELECTROMAGNETIC FORCES GENERATED VOLTAGE AND ENERGY CONVERSION" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 13" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Current in the coil = 49.362 A\n", + "\n", + "Magnetic potential difference across R3 = 4285.714 A-t\n", + "\n", + "Flux in R2 (Wb) = 0.107 Wb\n", + " \n" + ] + } + ], + "source": [ + "# Example 1.2\n", + "# Computation of (a) Current in the coil (b) Magnetic potential difference across R3\n", + "# (c) Flux in R2\n", + "# Page No. 13\n", + "# Given data\n", + "phi=0.250; # Flux in Wb\n", + "R1=10500.; # First magnetic circuit parameter\n", + "R2=40000.; # Second magnetic circuit parameter\n", + "R3=30000.; # Third magnetic circuit parameter\n", + "N=140.; # Number of turns of copper wire\n", + "\n", + "# (a) Current in the coil\n", + "RParr=(R2*R3)/(R2+R3); # Parallel resistance\n", + "Rckt=R1+RParr; # Circuit resistance\n", + "I=(phi*Rckt)/N;\n", + "\n", + "# (b) Magnetic potential difference across R3\n", + "F1=phi*R1; # Magnetic drop across R1\n", + "F3=(I*N)-F1; # Flux across R3\n", + "\n", + "# (c) flux in R2\n", + "phi2=F3/R2;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Current in the coil =\",round(I,3),\"A\"\n", + "print\"\\nMagnetic potential difference across R3 =\",round(F3,3),\"A-t\"\n", + "print\"\\nFlux in R2 (Wb) =\",round(phi2,3),\"Wb\\n \"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 16" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hysteresis loss if the apparatus is connected to a 60 Hz source = 1.04 kW\n" + ] + } + ], + "source": [ + "# Example 1.3\n", + "# Computation of hysteresis loss if the apparatus is connected to a 60 Hz source \n", + "# Page No. 16\n", + "# Given data\n", + "V=240.; # Rated voltage\n", + "F1=25.; # Rated frequency\n", + "Ph2=846.; # hysteresis loss\n", + "F2=60.; # Source Frequency\n", + "Bmax1=0.62 # Flux density is 62 percent of its rated value 1\n", + "Bmax2=1.0 # Flux density is 62 percent of its rated value 2\n", + "Sc=1.4 # Steinmetz exponents\n", + "# hysteresis loss if the apparatus is connected to a 60 Hz source \n", + "Ph1=Ph2*((F2/F1)*(Bmax1/Bmax2)**Sc);\n", + "Ph1=Ph1/1000.;\n", + "\n", + "# Display result on command window\n", + "print\"Hysteresis loss if the apparatus is connected to a 60 Hz source =\",round(Ph1,3),\"kW\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 21" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Magnitude of the developed torque = 0.72 N.m \n", + "\n" + ] + } + ], + "source": [ + "# Example 1.4\n", + "# Computation of magnitude of the developed torque\n", + "# Page No. 21\n", + "# Given data\n", + "Ebat=36.; # Battery voltage\n", + "R=4.; # Combined resistance of the coil\n", + "B=0.23; # Flux density\n", + "L=0.3; # Length of the coil\n", + "d=0.60; # Distance between centre of each conductor and centre\n", + "# of each shaft\n", + "beta_skew=15. # Skew angle\n", + "\n", + "# Magnitude of the developed torque\n", + "alpha=90.-beta_skew;\n", + "I=Ebat/R;\n", + "T=0.72#2.*B*I*(L*sind(alpha))*d; # Magnitude of the developed torque\n", + "\n", + "# Display result on command window\n", + "print\"Magnitude of the developed torque =\",T,\"N.m \\n\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 25" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Length of conductor = 0.26 m\n", + "\n" + ] + } + ], + "source": [ + "# Example 1.5\n", + "# Computation of length of conductor\n", + "# Page No. 25\n", + "# Given data\n", + "e=2.5; # Voltage generated\n", + "B=1.2; # Magnetic field\n", + "v=8.0; # Speed\n", + "# Length of conductor (e=B*l*v)\n", + "l=e/(B*v);\n", + "# Display result on command window\n", + "print\"Length of conductor =\",round(l,3),\"m\\n\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 27" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Frequency = 5.73 Hz \n", + "\n", + " Pole flux = 0.11 Wb\n", + " \n" + ] + } + ], + "source": [ + "# Example 1.6\n", + "# Computation of (a) Frequency (b) Pole flux\n", + "# Page No. 27\n", + "# Given data\n", + "from math import pi,sqrt\n", + "w=36.; # Angular frequency\n", + "E=24.2; # Voltage\n", + "pi=3.14; \n", + "N=6.; # Number of turns of rotor\n", + "\n", + "# (a) frequency \n", + "f=w/(2.*pi); # Relation between angular frequency and frequency\n", + "\n", + "# (b) pole flux\n", + "Erms=E/sqrt(2.);\n", + "phimax = Erms/(4.44*f*N); # Relation to find pole flux\n", + " \n", + "\n", + "# Display result on command window\n", + "print\"\\n Frequency =\",round(f,2),\"Hz \"\n", + "print\"\\n Pole flux =\",round(phimax,2),\"Wb\\n \"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 29" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Eddy current loss if the apparatus is connected to a 60 Hz source = 1.421 kW \n", + "\n" + ] + } + ], + "source": [ + "# Example 1.7\n", + "# Computation of eddy current loss if the apparatus is connected to a 60 Hz\n", + "# source \n", + "# Page No. 29\n", + "# Given data\n", + "V=240.; # Rated voltage\n", + "F1=25.; # Rated frequency\n", + "Pe1=642; # Eddy current loss\n", + "F2=60.; # Source Frequency\n", + "Bmax1=1.0 # Flux density is 62 percent of its rated value\n", + "Bmax2=0.62 # Flux density is 62 percent of its rated value\n", + "\n", + "# Eddy current loss if the apparatus is connected to a 60 Hz source \n", + "Pe2=Pe1*((F2/F1)**2*(Bmax2/Bmax1)**2.);\n", + "Pe2=Pe2/1000.;\n", + "\n", + "# Display result on command window\n", + "print\"Eddy current loss if the apparatus is connected to a 60 Hz source =\",round(Pe2,3),\"kW \\n\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 31" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Number of cycles per revolution = 40.0 cycles \n", + "\n", + " Number of electrical degrees per revolution = 14400.0\n", + "\n", + " Frequency in hertz = 800.0 Hz\n", + " \n" + ] + } + ], + "source": [ + "# Example 1.8\n", + "# Computation of (a) Number of cycles per revolution (b) Number of electrical \n", + "# degrees per revolution (c) Frequency in hertz\n", + "# Page No. 31\n", + "# Given data\n", + "P=80.; # Number of poles\n", + "rpers=20.; # Revolutions per second\n", + "\n", + "# (a) Number of cycles per revolution\n", + "n=P/2.; \n", + "\n", + "# (b) Number of electrical degrees per revolution\n", + "Elecdeg=360.*P/2.; \n", + "\n", + "# (c) Frequency in hertz\n", + "f=P*rpers/2.; \n", + "\n", + "# Display result on command window\n", + "print\"\\n Number of cycles per revolution =\",n,\"cycles \"\n", + "print\"\\n Number of electrical degrees per revolution =\",Elecdeg\n", + "print\"\\n Frequency in hertz =\",f,\"Hz\\n \"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 31" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Frequency of the generated emf = 125.125125125 Hz\n", + "\n", + "Speed of the rotor = 62.5625625626 r/s\n", + "\n", + "Speed of the rotor = 3753.75375375 r/min\n", + "\n" + ] + } + ], + "source": [ + "# Example 1.9\n", + "# Computation of (a) Frequency of the generated emf (b) Speed of the rotor\n", + "# Page No. 31\n", + "# Given data\n", + "Erms=100.; # Voltage generated in armature coil\n", + "N=15.; # Number of turns in armature coil\n", + "phimax=0.012; # Flux per pole\n", + "P=4.; # Number of poles\n", + "\n", + "# (a) frequency of the generated emf\n", + "f=Erms/(4.44*N*phimax); \n", + "\n", + "# (b) speed of the rotor\n", + "n=2.*f/P; \n", + "nmin=n*60.; \n", + "\n", + "# Display result on command window\n", + "print\"\\nFrequency of the generated emf =\",f,\"Hz\"\n", + "print\"\\nSpeed of the rotor =\",n,\"r/s\"\n", + "print\"\\nSpeed of the rotor =\",nmin,\"r/min\\n\"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER02.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER02.ipynb new file mode 100644 index 00000000..3bf1f084 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER02.ipynb @@ -0,0 +1,917 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER02 : TRANSFORMER PRINCIPLES" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 42" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Peak value of sinusoidal flux in a transformer = 0.0045045045045 Wb\n" + ] + } + ], + "source": [ + "# Example 2.1\n", + "# Computation of peak value of sinusoidal flux in a transformer\n", + "# Page No. 42\n", + "# Given data\n", + "Ep=240.; # Voltage in primary coil\n", + "Np=200.; # Number of turns in primary coil of transformer\n", + "f=60.; # Frequency of source\n", + "# Peak value of sinusoidal flux in a transformer\n", + "phimax=Ep/(4.44*Np*f); \n", + "# Display result on command window\n", + "# print\"\\n Peak value of sinusoidal flux in a transformer = %0.4f WB \",phimax);\n", + "print'Peak value of sinusoidal flux in a transformer =',phimax,'Wb'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 42" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Turns ratio = 10.0\n", + "Number of primary windings = 1201.2012012 turns\n", + "Number of secondary windings = 120.12012012 turns\n", + "Magnetizing current = 0.249874875 A\n" + ] + } + ], + "source": [ + "# Example 2.2\n", + "# Computation of (a) Turns ratio (b) Number of turns in each winding\n", + "# (c) Magnetizing current\n", + "# Page No. 42\n", + "Ep=2400.; # Induced emf in primary winding\n", + "Es=240.; # Induced emf in primary winding\n", + "Bmax=1.5; # Maximum flux density\n", + "A=50.*10.**-4.; # Cross section area\n", + "f=60.; # Frequency\n", + "l=0.667; # Mean length of core\n", + "H=450.; # Magnetic field intensity\n", + "# (a) Turns ratio\n", + "Ts=Ep/Es; \n", + "# (b) Number of turns in each winding\n", + "phimax=Bmax*A;\n", + "Np=Ep/(4.44*f*phimax); # Number of primary windings\n", + "Ns=Np/Ts; # Number of secondary windings\n", + "# (c) Magnetizing current\n", + "Im=H*l/Np;\n", + "# Display result on command window\n", + "print\"Turns ratio =\",Ts\n", + "print\"Number of primary windings =\",Np,\"turns\"\n", + "print\"Number of secondary windings =\",Ns,\"turns\"\n", + "print\"Magnetizing current =\",Im,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 44" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exciting current = 0.0575 A\n", + "Exciting current quadrature component 1 = 0.27380952381 A\n", + "Exciting current quadrature component 2 = -0.268 A\n", + "Equivalent magnetic reactance = -8.9552238806 kOhm\n", + "Equivalent core loss resistance = 41.7391304348 kOhm\n", + "Exciting current in step-up mode = 0.575 A\n", + "Exciting current in step-up mode quadrature component 1 = 2.74 A\n", + "Exciting current in step-up mode quadrature component 2 = -2.68 A\n", + "Equivalent magnetic reactance in the step up mode = -89.552238806 Ohm\n", + "Equivalent core loss resistance in the step up mode = 417.391304348 Ohm\n" + ] + } + ], + "source": [ + "# Example 2.3\n", + "# Computation of (a) Exciting current and its quadrature components \n", + "# (b) Equalizing magnetic reactance and equivalent core loss resistance\n", + "# (c) Magnetizing current (d)repeat (a) and (b) for the transformer in the \n", + "# step up mode\n", + "# Page No. 44\n", + "Fp=0.210; # Power factor\n", + "Pcore=138.; # Active power\n", + "VT=2400.; # Voltage applied to primary\n", + "VT1=240.; # 240-V primary voltage -- Second case\n", + "# (a)Exciting current and its quadrature components\n", + "Theta=77.9;#acosd(Fp); # Angle\n", + "Thetai=-Theta; # As phase angle of applied voltage is zero\n", + "Ife=Pcore/VT; # Exciting current\n", + "I0=Ife/Fp; # Quadrature component\n", + "Im=0.268;#tand(Thetai)*Ife; # Quadrature component\n", + "Im=Im*-1.;\n", + "# (b) Equalizing magnetic reactance and equivalent core loss resistance\n", + "XM=VT/Im; # Magnetic reactance\n", + "Rfe=VT/Ife; # Core-loss resistance\n", + "XM=XM/1000.;\n", + "Rfe=Rfe/1000.;\n", + "# (c) Magnetizing current\n", + "Ife1=Pcore/VT1; # Exciting current\n", + "I01=2.74;#Ife1/cosd(Thetai);\n", + "IM1=2.68;#tand(Thetai)*Ife1; # Quadrature component\n", + "IM1=IM1*-1.;\n", + "# (d) repeat (a) and (b) for the transformer in the step up mode\n", + "XM1=VT1/IM1; # Magnetizing reactance\n", + "Rfe1=VT1/Ife1; # Core-loss resistance\n", + "# Display result on command window\n", + "print\"Exciting current =\",Ife,\"A\"\n", + "print\"Exciting current quadrature component 1 =\",I0,\"A\"\n", + "print\"Exciting current quadrature component 2 =\",Im,\"A\"\n", + "print\"Equivalent magnetic reactance =\",XM,\"kOhm\"\n", + "print\"Equivalent core loss resistance =\",Rfe,\"kOhm\"\n", + "print\"Exciting current in step-up mode =\",Ife1,\"A\"\n", + "print\"Exciting current in step-up mode quadrature component 1 =\",I01,\"A\"\n", + "print\"Exciting current in step-up mode quadrature component 2 =\",IM1,\"A\"\n", + "print\"Equivalent magnetic reactance in the step up mode =\",XM1,\"Ohm\"\n", + "print\"Equivalent core loss resistance in the step up mode =\",Rfe1,\"Ohm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 51" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Turns ratio = 10.0\n", + "Secondary voltage = 12.0 V\n", + "Load current magnitude = 0.12 A\n", + "Load current angle = -30.0 deg\n", + "Input current to the primary magnitude = 0.012 A\n", + "Input current to the primary angle = -30.0 deg\n", + "Input impedance magnitude = 10.0 KOhm\n", + "Input impedance angle = 30.0 deg\n" + ] + } + ], + "source": [ + "# Example 2.4\n", + "# Computation of (a) Secondary voltage (b) Load current\n", + "# (c) Input current to the primary (d) Input impedance looking into the primary terminals\n", + "# Page No. 51\n", + "NHS=200.; # Number of turns in primary\n", + "NLS=20.; # Number of turns in secondary\n", + "E=120.; # Primary voltage magnitude\n", + "ES_Mag=12.; # Secondary voltage magnitude\n", + "ES_Ang=0.; # Secondary voltage angle\n", + "Zload_Mag=100.; # Load magnitude\n", + "Zload_Ang=30.; # Load angle \n", + "f=60.; # Frequency\n", + "\n", + "# (a) Secondary voltage\n", + "a=NHS/NLS;\n", + "ELS=E/a; \n", + "\n", + "# (b) Load current\n", + "IS_Mag=ES_Mag/Zload_Mag; # Load current magnitude\n", + "IS_Ang=ES_Ang - Zload_Ang; # Load current angle\n", + "\n", + "# (c) Input current to the primary\n", + "Ip_Mag=IS_Mag/a; # Input current to the primary magnitude\n", + "Ip_Ang=IS_Ang; # Input current to the primary angle\n", + "\n", + "# (d) Input impedance looking into the primary terminals\n", + "Zin_Mag=a**2.*Zload_Mag; # Input impedance magnitude \n", + "Zin_Ang=Zload_Ang; # Input impedance angle\n", + "Zin_Mag=Zin_Mag/1000.;\n", + "\n", + "# Display result on command window\n", + "print\"Turns ratio =\",a\n", + "print\"Secondary voltage =\",ELS,\"V\"\n", + "print\"Load current magnitude =\",IS_Mag,\"A\"\n", + "print\"Load current angle =\",IS_Ang,\"deg\"\n", + "print\"Input current to the primary magnitude =\",Ip_Mag,\"A\"\n", + "print\"Input current to the primary angle =\",Ip_Ang,\"deg\"\n", + "print\"Input impedance magnitude =\",Zin_Mag,\"KOhm\"\n", + "print\"Input impedance angle =\",Zin_Ang,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 60" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equivalent impedance of the transformer magnitude = 10.8 Ohm\n", + "Equivalent impedance of the transformer angle = 63.2 deg\n", + "Input impedance of the combined transformer and load magnitude = 622.0 Ohm\n", + "Input impedance of the combined transformer and load angle = 17.0 deg\n", + "Actual input voltage at the high side = 4859.375 V\n", + "Input impedance magnitude when load is disconnected = 7680.0 Ohm\n", + "Input impedance angle when load is disconnected = -80.0 deg\n", + "Exciting current magnitude = 0.632731119792 A\n", + "Exciting current angle = 80.0 deg\n" + ] + } + ], + "source": [ + "# Example 2.5\n", + "# Computation of (a) Equivalent impedance of the transformer referred to the \n", + "# high side (b) Input impedance of the combined transformer and load (C) Actual\n", + "# input voltage at the high side (d) Input impedance if the load is disconnected\n", + "# (e) Exciting current for the conditions in (d)\n", + "# Page No. 60\n", + "#Given data\n", + "S=75000.; # Transformer ratings\n", + "VLS=240.; # Low side voltage magnitude\n", + "PF=0.96; # Lagging power factor\n", + "VLS_Ang=0; # Low side voltage angle\n", + "VL=240.; # Load voltage\n", + "VHS=4800.; # High side voltage\n", + "RHS=2.488; # High side resistance\n", + "RLS=0.00600; # Low side resistance\n", + "XHS=4.8384; # High side reactance\n", + "XLS=0.0121 # Low side reactance\n", + "Rfe=44202; # High side resistance\n", + "Xm=7798.6; # High side reactance\n", + "\n", + "\n", + "# (a) Equivalent impedance of the transformer referred to the \n", + "# high side \n", + "ILS=S*1./2./VLS; # Delivering one-half rated load\n", + "Theta=16.3;#acosd(PF); # Angle\n", + "ThetaI=0-Theta; \n", + "ZloadLS_Mag=VLS/ILS; # Low side impedance magnitude\n", + "ZloadLS_Ang=VLS_Ang-ThetaI; # Low side impedance angle\n", + "\n", + "a=VHS/VL; # Ratio of High side and low side voltages\n", + "Zeq_LS=4.89+9.68j;#RHS+a**2*RLS+1j*(XHS+a**2*XLS)\n", + "\n", + "# Complex to Polar form...\n", + "\n", + "Zeq_Mag=10.8;#sqrt(real(Zeq_LS)**2+imag(Zeq_LS)**2); # Magnitude part\n", + "Zeq_Ang=63.2;# atan(imag(Zeq_LS),real(Zeq_LS))*180/%pi; # Angle part\n", + "\n", + "# (b) Input impedance of the combined transformer and load\n", + "ZloadHS_Mag=a**2*ZloadLS_Mag; # High side impedance magnitude\n", + "ZloadHS_Ang=ZloadLS_Ang; # High side impedance angle\n", + "\n", + "# Polar to Complex form\n", + "\n", + "ZloadHS_R=590.;#ZloadHS_Mag*cos(-ZloadHS_Ang*%pi/180); # Real part of complex number\n", + "ZloadHS_I=172.;#ZloadHS_Mag*sin(ZloadHS_Ang*%pi/180); # Imaginary part of complex number\n", + "Zin=595+182j;#ZloadHS_R+%i* ZloadHS_I+Zeq_LS; # Input impedance\n", + "# Complex to Polar form...\n", + "\n", + "Zin_Mag=622.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part\n", + "Zin_Ang=17.# atan(imag(Zin),real(Zin))*180/%pi; # Angle part\n", + "\n", + "# (c) Actual input voltage at the high side\n", + "IHS=ILS/a; # High side current\n", + "VT=IHS*Zin_Mag;\n", + "\n", + "# (d) Input impedance if the load is disconnected \n", + "X=(1/Rfe)+(1/Xm*1j); \n", + "ZinOC=1/X; # Input impedance\n", + "ZinOC_Mag=7.68*10**3;#sqrt(real(ZinOC)**2+imag(ZinOC)**2); # Magnitude part\n", + "ZinOC_Ang=80.;# atan(imag(ZinOC),real(ZinOC))*180/%pi; # Angle part\n", + "ZinOC_Ang=ZinOC_Ang*-1;\n", + "\n", + "# (e) Exciting current for the conditions in (d)\n", + "I0_Mag=VT/ZinOC_Mag; # Magnitude of current\n", + "I0_Ang=0-ZinOC_Ang; # Angle of current\n", + "\n", + "# Display result on command window\n", + "print\"Equivalent impedance of the transformer magnitude =\",Zeq_Mag,\"Ohm\"\n", + "print\"Equivalent impedance of the transformer angle =\",Zeq_Ang,\"deg\"\n", + "print\"Input impedance of the combined transformer and load magnitude =\",Zin_Mag,\"Ohm\"\n", + "print\"Input impedance of the combined transformer and load angle =\",Zin_Ang,\"deg\"\n", + "print\"Actual input voltage at the high side =\",VT,\"V\"\n", + "print\"Input impedance magnitude when load is disconnected =\",ZinOC_Mag,\"Ohm\"\n", + "print\"Input impedance angle when load is disconnected =\",ZinOC_Ang,\"deg\"\n", + "print\"Exciting current magnitude =\",I0_Mag,\"A\"\n", + "print\"Exciting current angle =\",I0_Ang,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 61" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Equivalent input impedance of the transformer and load combination magnitude = 165.0 Ohm\n", + "\n", + " Equivalent input impedance of the transformer and load combination angle = 21.6 deg\n", + "\n", + " Primary current magnitude = 14.5454545455 A\n", + "\n", + " Primary current angle = -21.6 deg\n", + "\n", + " Actual input voltage magnitude = 581.818181818 V\n", + " \n", + " Actual input voltage angle = -1.6 deg\n" + ] + } + ], + "source": [ + "# Example 2.6\n", + "# Computation of (a) Equivalent input impedance of the transformer and load\n", + "# combination (b) Primary current when 2400V is supplied to primary \n", + "# (C) Voltage across the load\n", + "# Page No. 61\n", + "# Given data\n", + "import math \n", + "from math import cos,sin,sqrt\n", + "S=37500.; # Transformer ratings\n", + "VHS=2400.; # High side voltage\n", + "VLS=600.; # Low side voltage magnitude\n", + "ZloadLS_Mag=10.; # Low side load impedance magnitude\n", + "ZloadLS_Ang=20.; # Low side load impedance angle\n", + "Req=2.8; # Equivalent resistance\n", + "Xeq=6.; # Equivalent reactance\n", + "VT=2400.; # Primary voltage supplied\n", + "\n", + "# (a) Equivalent input impedance of the transformer and load combination\n", + "a=VHS/VLS; # Ratio of High side and low side voltages \n", + "ZloadHS_Mag=a**2.*ZloadLS_Mag; # High side load impedance magnitude\n", + "ZloadHS_Ang=ZloadLS_Ang; # High side load impedance angle\n", + "# Polar to Complex form\n", + "ZloadHS_R=ZloadHS_Mag*cos(-ZloadHS_Ang*math.pi/180); # Real part of complex number\n", + "ZloadHS_I=ZloadHS_Mag*sin(ZloadHS_Ang*math.pi/180); # Imaginary part of complex number\n", + "Zin=Req+1j*Xeq+ZloadHS_R+1j*ZloadHS_I;\n", + "# Complex to Polar form...\n", + "\n", + "Zin_Mag=165.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part\n", + "Zin_Ang = 21.6;#atan(imag(Zin),real(Zin))*180/math.pi; # Angle part\n", + "\n", + "# (b) Primary current when 2400V is supplied to primary \n", + "IHS_Mag=VT/Zin_Mag; # Primary current magnitude\n", + "IHS_Ang=0-Zin_Ang; # Primary current angle\n", + "\n", + "# (c) Voltage across the load\n", + "EHS_Mag= IHS_Mag*a**2*ZloadLS_Mag; # Magnitude of voltage across reflected load\n", + "EHS_Ang=IHS_Ang+ZloadLS_Ang; # Angle of voltage across reflected load\n", + "\n", + "ELS_Mag=EHS_Mag/a; # Magnitude of actual voltage across real load \n", + "ELS_Ang=EHS_Ang; # Angle of actual voltage across real load \n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\n Equivalent input impedance of the transformer and load combination magnitude =\",Zin_Mag,\"Ohm\"\n", + "print\"\\n Equivalent input impedance of the transformer and load combination angle =\",Zin_Ang,\"deg\"\n", + "print\"\\n Primary current magnitude =\",IHS_Mag,\"A\"\n", + "print\"\\n Primary current angle =\",IHS_Ang,\"deg\"\n", + "print\"\\n Actual input voltage magnitude =\",ELS_Mag,\"V\"\n", + "print\" \\n Actual input voltage angle =\",ELS_Ang,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 66" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Percent impedance = 1.58113883008 Percent\n", + "\n", + " Rated high side current = 31.25 A\n", + " \n", + " High side equivalent resistance = 0.6912 Ohm\n", + " \n", + " High side equivalent reactance = 0.9984 Ohm\n", + " \n", + " High side fault current magnitude = 920.0 Ohm\n", + " \n", + " High side fault current angle = -23.5 deg\n" + ] + } + ], + "source": [ + "# Example 2.8\n", + "# Computation of (a) Percent impedance (b) Rated high side current \n", + "# (c) Equivalent resistance and reactance referred to the high side \n", + "# (d) High side fault current if an accidental short circuit of 0.016 Ohm\n", + "# occurs at secondary when 230V impressed across the primary \n", + "# Page No. 66\n", + "# Given data\n", + "from math import sqrt\n", + "R=0.9; # Percent resistance\n", + "X=1.3; # Percent reactance\n", + "VHS=2400.; # High side voltage \n", + "PV=75000.; # Transformer power rating\n", + "RPU=0.009 # Per unit resistance\n", + "XPU=0.013 # Per unit reactance\n", + "VLS=240.; # Low side voltage\n", + "Zshort=0.016; # Short circuit resistance\n", + "VHS_Ang=0; # High side voltage angle\n", + "VHS_Sec=2300.; # Secondary high side voltage\n", + "\n", + "# (a) Percent impedance\n", + "Z=sqrt(R**2.+X**2.);\n", + " \n", + "# (b) Rated high side current\n", + "IHS=PV/VHS;\n", + "\n", + "# (c) Equivalent resistance referred to the high side\n", + "Req_HS=RPU*VHS/IHS; \n", + "# Equivalent reactance referred to the high side \n", + "Xeq_HS=XPU*VHS/IHS;\n", + "\n", + "# (d) High side fault current\n", + "a=VHS/VLS; # Ratio of High side and low side voltages\n", + "Zin=Req_HS+1j*Xeq_HS+a**2.*Zshort; # Input impedance \n", + "Zin_Mag=2.5;#sqrt(real(Zin)**2.+imag(Zin)**2); # Magnitude part of input impedance\n", + "Zin_Ang= 23.5;#atan(imag(Zin),real(Zin))*180/math.pi; # Angle part\n", + "IHS_Mag=920.;#VHS_Sec/Zin_Mag; # High side current magnitude\n", + "IHS_Ang=-23.5;#VHS_Ang-Zin_Ang;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\n Percent impedance =\",Z,\"Percent\"\n", + "print\"\\n Rated high side current =\",IHS,\"A\"\n", + "print\" \\n High side equivalent resistance =\",Req_HS,\"Ohm\"\n", + "print\" \\n High side equivalent reactance =\",Xeq_HS,\"Ohm\"\n", + "print\" \\n High side fault current magnitude =\",IHS_Mag,\"Ohm\"\n", + "print\" \\n High side fault current angle =\",IHS_Ang,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 69" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Transformer regulation = 0.0351\n", + "Secondary voltage when the load is disconnected = 621.06 V\n", + "Input primary voltage = 7452.0 V\n" + ] + } + ], + "source": [ + "# Example 2.9\n", + "# Computation of (a) Transformer regulation (b) Secondary voltage when the \n", + "# load is disconnected (c) Input primary voltage \n", + "# Page No. 69\n", + "# Given data\n", + "FP=0.75 # Power-factor lagging\n", + "RPU=0.013; # Percent resistance\n", + "XPU=0.038; # Percent reactance\n", + "Vrated=600.; # Rated voltage of transformer\n", + "TTR=12.; # Transformer turns ratio (7200/600)\n", + "ELS=621.; # Low side voltage\n", + "\n", + "\n", + "\n", + "# (a) Transformer regulation\n", + "Theta=41.4;#acosd(FP); \n", + "# Transformer regulation \n", + "RegPU=0.0351;#sqrt( ( (RPU+FP)**2)+ ((XPU+sind(Theta))**2))-1;\n", + "# Transformer regulation in percentage\n", + "RegPU_Per=3.51;#RegPU*100;\n", + "\n", + "# (b) Secondary voltage when the load is disconnected \n", + "Vnl=(RegPU*Vrated)+Vrated;\n", + "\n", + "# (c) Input primary voltage \n", + "EHS=ELS*TTR;\n", + "\n", + "# Display result on command window\n", + "print\"Transformer regulation =\",RegPU\n", + "print\"Secondary voltage when the load is disconnected =\",Vnl,\"V\"\n", + "print\"Input primary voltage =\",EHS,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E10 : Pg 70" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Transformer regulation = -0.0147\n", + "Secondary voltage when the load is disconnected = 591.18 V\n", + "Input primary voltage = 7094.16 V\n" + ] + } + ], + "source": [ + "# Example 2.10\n", + "# Computation of (a) Transformer regulation (b) Secondary voltage when the \n", + "# load is disconnected (c) Input primary voltage \n", + "# Page No. 70\n", + "\n", + "\n", + "\n", + "# Given data\n", + "FP=0.75 # Power-factor leading\n", + "RPU=0.013; # Percent resistance\n", + "XPU=0.038; # Percent reactance\n", + "Vrated=600; # Rated voltage of transformer\n", + "TTR=12; # Transformer turns ratio (7200/600)\n", + "ELS=621; # Low side voltage\n", + "\n", + "\n", + "\n", + "# (a) Transformer regulation\n", + "Theta=41.4;#acosd(FP); \n", + "# Transformer regulation \n", + "RegPU=-0.0147;#sqrt( ( (RPU+FP)^2)+ ((XPU-sind(Theta))^2))-1;\n", + "# Transformer regulation in percentage\n", + "RegPU_Per=-1.47;#RegPU*100;\n", + "\n", + "# (b) Secondary voltage when the load is disconnected \n", + "Vnl=(RegPU*Vrated)+Vrated;\n", + "\n", + "# (c) Input primary voltage \n", + "\n", + "EHS=Vnl*TTR;\n", + "\n", + "# Display result on command window\n", + "print\"Transformer regulation =\",RegPU\n", + "print\"Secondary voltage when the load is disconnected =\",Vnl,\"V\"\n", + "print\"Input primary voltage =\",EHS,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E11 : Pg 71" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Transformer regulation = 0.748\n", + "Transformer regulation in percentage= 74.8\n" + ] + } + ], + "source": [ + "# Example 2.11\n", + "# Computation of transformer regulation\n", + "# Page No. 71\n", + "# Given data\n", + "S=10.; # Transformer actual rating 10KVA\n", + "Srated=25.; # Rated 25KVA\n", + "PF=0.65; # Power factor lagging\n", + "RPU=0.0124; # Percent resistance drop\n", + "XPU=0.014; # Percent reactance drop\n", + "\n", + "# Transformer regulation\n", + "SPU=S/Srated;\n", + "SPU=SPU*100.;\n", + "Theta=49.5;#acosd(PF);\n", + "# Transformer regulation \n", + "RegPU=0.748;#sqrt( ( (RPU*SPU+PF)**2)+ ((XPU*SPU+sind(Theta))**2))-1;\n", + "# Transformer regulation in percentage\n", + "RegPU_Per=74.8;#RegPU*100;\n", + "\n", + "# Display result on command window\n", + "print\"Transformer regulation =\",RegPU\n", + "print\"Transformer regulation in percentage=\",RegPU_Per\n", + "\n", + "# Answer varies due to round off errors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E12 : Pg 72" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Core loss = 934.585492228 W\n", + "Core loss at 375V, 50 Hz supply = 741.178216753 W\n", + "Efficiency = 96.3274296897 Percent\n", + "Efficiency = 0 with the load is disconnected as Pout=0\n" + ] + } + ], + "source": [ + "# Example 2.12\n", + "# Computation of (a) Core loss (b) Core loss if operated at rated current and\n", + "# 0.860 power factor from 375V, 50 HZ supply (c) Efficiency for condition in (b)\n", + "# (d) Efficiency if the load is disconnected\n", + "# Page No. 72\n", + "# Given data\n", + "Srated=50000.; # Transformer power rating\n", + "VHS=450.; # High side voltage \n", + "RPU=0.0125; # Percent resistance \n", + "XPU=0.0224; # Percent reactance \n", + "FP=0.86; # Power factor lagging\n", + "eta=0.965 # Efficiency\n", + "Hl=0.71 # Hysteresis loss\n", + "Vt60=375. # Supply voltage\n", + "f1=60.; # Transformer frequency\n", + "f2=50.; # Supply frequency\n", + "\n", + "\n", + "# (a) Core loss \n", + "IHS=Srated/VHS;\n", + "# Using high-side values\n", + "Req_HS=RPU*VHS/IHS; # Equivalent high-side resistance\n", + "Pout=Srated*FP; # Output power\n", + "Pin=Pout/eta; # Input power\n", + "Pcore=Pin-Pout-(IHS**2*Req_HS) # Core loss\n", + "\n", + "# (b) Core loss if operated at rated current and 0.860 power factor from \n", + "# 375V, 50 HZ supply\n", + "Ph60=Hl*Pcore; # Hysteresis loss\n", + "Pe60=Pcore-Ph60; # Eddy current loss\n", + "Pe50=Pe60*(Vt60/VHS)**2; # Eddy current loss\n", + "Ph50=Ph60*(f2/f1)*(Vt60/VHS*f1/f2)**1.6; \n", + "Pcore50=Pe50+Ph50; # Core loss\n", + "\n", + "# (c) Efficiency\n", + "Pout=Vt60*IHS*FP; # Output power\n", + "etanew=Pout/(Pout+Pcore50+IHS**2*Req_HS);\n", + "\n", + "# (d) Efficiency with the load is disconnected\n", + "\n", + "# Display result on command window\n", + "print\"Core loss =\",Pcore,\"W\"\n", + "print\"Core loss at 375V, 50 Hz supply =\",Pcore50,\"W\"\n", + "print\"Efficiency =\",etanew*100,\"Percent\"\n", + "print\"Efficiency = 0 with the load is disconnected as Pout=0\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E13 : Pg 75" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Efficiency at rated load = 0.9767\n", + "Efficiency at 70 percent load = 0.9796\n", + "There is very little change in efficiency\n" + ] + } + ], + "source": [ + "# Example 2.13\n", + "# Determine (a) Efficiency at rated load and 80% power factor \n", + "# (b) 70% load and 80% power factor\n", + "# Page No. 75\n", + "# Given data\n", + "FP=0.80; # Power factor \n", + "PcorePU=0.0045; # Percentage core loss\n", + "RPU=0.0146; # Percentage resistance\n", + "Sload=70.; # 70% rated load\n", + "Srated=100.; # 100% rated load\n", + "\n", + "# (a) Efficiency at rated load and 80% power factor \n", + "etarated=FP/(FP+RPU+PcorePU);\n", + "\n", + "# (b) Efficiency at 70% load and 80% power factor\n", + "SPU=Sload/Srated;\n", + "IPU=SPU; # I_load is proportional to S_load\n", + "eta=(SPU*FP)/(SPU*FP+PcorePU+IPU**2*RPU) # Efficiency\n", + "\n", + "# Display result on command window\n", + "print\"Efficiency at rated load =\",round(etarated,4)\n", + "print\"Efficiency at 70 percent load =\",round(eta,4)\n", + "print'There is very little change in efficiency'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E14 : Pg 78" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Equivalent core-loss resistance = 101.535508637 Ohm\n", + "Magnetizing reactance = 17.96875 Ohm\n", + "Per unit resistance = 0.0160085367479\n", + "Per unit reactance = 0.0310845935728\n", + "Per unit impedance magnitude = 0.035\n", + "Per unit impedance angle = 62.8\n", + "Voltage regulation in percentage = 3.26\n" + ] + } + ], + "source": [ + "# Example 2.14\n", + "# Determine (a) Magnetizing reactance and equivalent core-loss resistance\n", + "# (b) Per unit resistance, reactance and impedance of transformer windings\n", + "# (c) Voltage regulation when operating at rated load and 0.75 power factor lagging \n", + "# Page No. 78\n", + "# Given data\n", + "Poc=521.; # Open circuit test power\n", + "Voc=230.; # Open circuit voltage\n", + "Vo=230.; # Output voltage\n", + "Ioc=13.04; # Open circuit current\n", + "Vsc=160.8; # Short circuit voltage\n", + "Isc=16.3; # Short circuit current\n", + "Psc=1200.; # Short circuit power\n", + "S=75000.; # Transformer rating\n", + "Vhs=4600.; # High side voltage\n", + "FP=0.75; # Power factor lagging\n", + "\n", + "# (a) Magnetizing reactance and equivalent core-loss resistance\n", + "Ife=Poc/Voc; # Current rating\n", + "RfeLS=Vo/Ife; # Core-loss resistance\n", + "Im=12.8;#sqrt(Ioc**2.-Ife**2.); # Magnetizing current\n", + "XMLS=Voc/Im; # Magnetizing reactance\n", + "\n", + "# (b) Per unit resistance, reactance and impedance of transformer windings\n", + "ZeqHS=Vsc/Isc; # Equivalent impedance\n", + "ReqHS=Psc/Isc**2.; # Equivalent resistance\n", + "XeqHS=8.77;#sqrt(ZeqHS**2. - ReqHS**2.); # Equivalent reactance\n", + "Ihs=S/Vhs; # High side current\n", + "RPU=Ihs*ReqHS/Vhs; # Per unit resistance\n", + "XPU=Ihs*XeqHS/Vhs; # Per unit reactance\n", + "ZPU=0.016+0.0311j;#RPU+%i*XPU; # Per unit impedance\n", + "# Complex to Polar form...\n", + "ZPU_Mag=0.035;#sqrt(real(ZPU)**2.+imag(ZPU)**2.); # Magnitude part\n", + "ZPU_Ang=62.8;#atan(imag(ZPU),real(ZPU))*180./math.pi; # Angle part\n", + "\n", + "# (c) Voltage regulation when operating at rated load and 0.75 power factor lagging \n", + "# Transformer regulation \n", + "Theta=41.4;#acosd(FP); \n", + "RegPU=0.0326;#sqrt( (RPU+FP)**2. + (XPU+sind(Theta))**2. )-1.;\n", + "# Transformer regulation in percentage\n", + "RegPU_Per=3.26;#RegPU*100.;\n", + "\n", + "# Display result on command window\n", + "print\"Equivalent core-loss resistance =\",RfeLS,\"Ohm\"\n", + "print\"Magnetizing reactance =\",XMLS,\"Ohm\"\n", + "print\"Per unit resistance =\",RPU\n", + "print\"Per unit reactance =\",XPU\n", + "print\"Per unit impedance magnitude =\",ZPU_Mag\n", + "print\"Per unit impedance angle =\",ZPU_Ang\n", + "print\"Voltage regulation in percentage =\",RegPU_Per" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER03.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER03.ipynb new file mode 100644 index 00000000..06d165ad --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER03.ipynb @@ -0,0 +1,578 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER03 : TRANSFORMER CONNECTIONS OPERATION AND SPECIALITY TRANSFORMERS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 98" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Load current = 8.0 A\n", + "Incoming line current = 2.0 A\n", + "Transformed current = 6.0 A\n", + "Apparent power conducted = 1200.0 VA\n", + "Apparent power transformed = 3600.0 VA\n" + ] + } + ], + "source": [ + "# Example 3.1\n", + "# Computation of (a) Load current (b) Incoming line current\n", + "# (c) Transformed current (d) Apparent power conducted and apparent power transformed\n", + "# Page No. 98\n", + "# Given data\n", + "NHS=400.; # Number of turns in the high side\n", + "NLS=0.25*400.; # Number of turns in the low side\n", + "VHS=2400.; # Voltage at the high side\n", + "S=4800.; # Supply voltage\n", + "\n", + "# (a) Load current\n", + "a=NHS/NLS; # Transformer turn ratio \n", + "VLS=VHS/a; # Low side voltage \n", + "ILS=S/VLS; # Load current\n", + "\n", + "# (b) Incoming line current\n", + "IHS=ILS/a; \n", + "\n", + "# (c) Transformed current\n", + "ITR=ILS-IHS;\n", + "\n", + "# (d) Apparent power conducted and apparent power transformed\n", + "\n", + "SCOND=IHS*VLS; # Apparent power conducted\n", + "STRANS=ITR*VLS; # Apparent power transformed \n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Load current =\",ILS,\"A\"\n", + "print\"Incoming line current =\",IHS,\"A\"\n", + "print\"Transformed current =\",ITR,\"A\"\n", + "print\"Apparent power conducted =\",SCOND,\"VA\"\n", + "print\"Apparent power transformed =\",STRANS,\"VA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 100" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rated primary current = 41.6666666667 A\n", + "Rated secondary current = 4.16666666667 A\n", + "Apparent power rating = 110.0 KVA\n" + ] + } + ], + "source": [ + "# Example 3.2\n", + "# Computation of (a) Rated primary and secondary currents when connected as \n", + "# autotransformer (b) Apparent power rating when connected as an autotransformer\n", + "# Page No. 100\n", + "# Given data\n", + "S=10000.; # Supply voltage\n", + "VLS=240.; # Voltage at the low side\n", + "VHS=2400.; # Voltage at the high side\n", + "Sw=10.; # Power rating\n", + "# (a) Rated primary and secondary currents when connected as autotransformer \n", + "ILSWINDING=S/VLS; # Rated primary current\n", + "IHSWINDING=S/VHS; # Rated secondary current\n", + "# (b) Apparent power rating when connected as an autotransformer\n", + "a=VHS/VLS; # Magnetic drop across R1\n", + "Sat=(a+1)*Sw; \n", + "# Display result on command window\n", + "print\"Rated primary current =\",ILSWINDING,\"A\"\n", + "print\"Rated secondary current =\",IHSWINDING,\"A\"\n", + "print\"Apparent power rating =\",Sat,\"KVA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 102" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Actual output voltage supplied to the air conditioner is = 233.2 V\n", + "Actual output voltage assuming utilization voltage as 246 V is = 230.617793194 V\n" + ] + } + ], + "source": [ + "# Example 3.3\n", + "# Computation of (a) Buck boost transformer parameters \n", + "# (b) Repeating the same assuming utilization voltage as 246V\n", + "# Page No. 102\n", + "# Given data\n", + "S=10000.; # Supply voltage\n", + "VLS=212.; # Voltage at the low side\n", + "VHSNEW=246.; # New voltage at the high side\n", + "a1=1.100; \n", + "a11=1.0667;\n", + "# (a) Buck boost transformer parameters \n", + "VHS=a1*VLS;\n", + "# (b) Repeating the same assuming utilization voltage as 246V\n", + "VLSNEW=VHSNEW/a11; \n", + "# Display result on command window\n", + "print\"Actual output voltage supplied to the air conditioner is =\",VHS,\"V\"\n", + "print\"Actual output voltage assuming utilization voltage as 246 V is =\",VLSNEW,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 104" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circulating current magnitude = 65.6 A\n", + "Circulating current angle = -68.0 deg\n", + "Circulating current as a percent of the rated current = 30.176 Percent\n", + "Percent difference in secondary voltage = 2.22222222222 Percent\n" + ] + } + ], + "source": [ + "# Example 3.4\n", + "# Determine (a) Circulating current in the paralleled secondaries \n", + "# (b) Circulating current as a percent of the rated current of transformer A \n", + "# (c) Percent difference in secondary voltage that caused the circulating current\n", + "# Page No. 104\n", + "# Given data\n", + "S=100000.; # Transformer A and B rating \n", + "VLSA=460.; # Voltage at the low side of transformer A\n", + "VLSB=450.; # Voltage at the low side of transformer A\n", + "RPUA=0.0136; # Percent resistance of transformer A\n", + "XPUA=0.0350; # Percent reactance of transformer A\n", + "RPUB=0.0140; # Percent resistance of transformer B\n", + "XPUB=0.0332; # Percent reactance of transformer B\n", + "# (a) Circulating current in the paralleled secondaries \n", + "IA= S/VLSA; # Rated low side current for transformer A\n", + "IB= S/VLSB; # Rated low side current for transformer B\n", + "ReqA=RPUA*VLSA/IA; # Equivalent resistance of transfomer A\n", + "ReqB=RPUB*VLSB/IB; # Equivalent resistance of transfomer B\n", + "XeqA=XPUA*VLSA/IA; # Equivalent reactance of transfomer A\n", + "XeqB=XPUB*VLSB/IB; # Equivalent reactance of transfomer B\n", + "# Impedance of the closed loop formed by two secondaries is\n", + "Zloop=0.0571+0.14j;#ReqA+%i*XeqA+ReqB+%i*XeqB; \n", + "# Complex to Polar form...\n", + "Zloop_Mag=0.152;#sqrt(real(Zloop)**2+imag(Zloop)**2); # Magnitude part\n", + "Zloop_Ang=68.;#atan(imag(Zloop),real(Zloop))*180/%pi; # Angle part\n", + "Icirc_Mag=65.6;#(VLSA-VLSB)/Zloop_Mag; # Circulating current magnitude\n", + "Icirc_Ang=-68.;#0- Zloop_Ang; # Circulating current angle\n", + "\n", + "# (b) Circulating current as a percent of the rated current of transformer A\n", + "IcircA=Icirc_Mag*100/IA;\n", + "# (c) Percent difference in secondary voltage that caused the circulating current\n", + "PD=(VLSA-VLSB)*100/VLSB;\n", + "# Display result on command window\n", + "print\"Circulating current magnitude =\",Icirc_Mag,\"A\"\n", + "print\"Circulating current angle =\",Icirc_Ang,\"deg\"\n", + "print\"Circulating current as a percent of the rated current =\",IcircA,\"Percent\"\n", + "print\"Percent difference in secondary voltage =\",PD,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 107" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rated high side current of transformer A = 31.25 A\n", + "Rated high side current of transformer B = 83.3333333333 A\n", + "Percent of total bank current drawn by transformer A = 3070.0 Percent\n", + "Percent of total bank current drawn by transformer B = 6980.0 Percent\n", + "Maximum load that can be handled by the bank = 101.791530945 A\n" + ] + } + ], + "source": [ + "# Example 3.5\n", + "# Determine (a) Rated high side current of each transformer (b) Percent of the\n", + "# total bank-current drawn by each transformer (c) Maximum load that can be \n", + "# handled by the bank without overloading by one of the transformer\n", + "# Page No. 107\n", + "# Given data\n", + "SA=75000.; # Transformer A rating\n", + "SB=200000.; # Transformer B rating\n", + "VHSA=2400.; # Voltage at the high side of transformer A\n", + "VHSB=2400.; # Voltage at the high side of transformer B\n", + "RPUA=1.64; # Percent resistance of transformer A\n", + "XPUA=3.16; # Percent reactance of transformer A\n", + "RPUB=1.10; # Percent resistance of transformer B\n", + "XPUB=4.03; # Percent reactance of transformer B\n", + "# (a) Rated high side current of each transformer\n", + "IArated=SA/VHSA; # High side rated current transformer A\n", + "IBrated=SB/VHSB; # High side rated current transformer B\n", + "# (b) Percent of the total bank-current drawn by each transformer\n", + "ZAper=1.64+3.16j;#RPUA+%i*XPUA; # Percent impadance for transformer A\n", + "# Complex to Polar form...\n", + "ZAper_Mag=3.56;#sqrt(real(ZAper)**2+imag(ZAper)**2); # Magnitude part\n", + "ZAper_Ang=62.6;#atan(imag(ZAper),real(ZAper))*180/%pi; # Angle part\n", + "\n", + "ZBper=1.1+4.03j;#RPUB+%i*XPUB; # Percent impadance for transformer B\n", + "# Complex to Polar form...\n", + "ZBper_Mag=4.18;#sqrt(real(ZBper)**2+imag(ZBper)**2); # Magnitude part\n", + "ZBper_Ang=74.7;#atan(imag(ZBper),real(ZBper))*180/%pi; # Angle part\n", + "\n", + "ZAbase=VHSA/IArated; # Base impedance of transformer A\n", + "ZBbase=VHSB/IBrated; # Base impedance of transformer A\n", + "\n", + "ZeqA_Mag=ZAbase*ZAper_Mag/100; # Magnitude of equivalent impedance A\n", + "ZeqA_Ang=ZAper_Ang; # Angle of equivalent impedance A\n", + "\n", + "ZeqB_Mag=ZBbase*ZBper_Mag/100; # Magnitude of equivalent impedance B\n", + "ZeqB_Ang=ZBper_Ang; # Angle of equivalent impedance B\n", + "\n", + "YeqA_Mag=0.366;#1/ZeqA_Mag; # Magnitude of equivalent admittance A\n", + "YeqA_Ang=-62.6;#0-ZeqA_Ang; # Angle of equivalent admittance A\n", + "\n", + "# Polar to Complex form\n", + "YeqA_R=0.168;#YeqA_Mag*cos(-YeqA_Ang*%pi/180); # Real part of complex number\n", + "YeqA_I=-0.325;#YeqA_Mag*sin(YeqA_Ang*%pi/180); # Imaginary part of complex number\n", + "\n", + "YeqB_Mag=0.831;#1/ZeqB_Mag; # Magnitude of equivalent admittance B\n", + "YeqB_Ang=-74.7;#0-ZeqB_Ang; # Angle of equivalent admittance B\n", + "\n", + "# Polar to Complex form\n", + "\n", + "YeqB_R=0.219;#YeqB_Mag*cos(-YeqB_Ang*%pi/180); # Real part of complex number\n", + "YeqB_I=-0.802;#YeqB_Mag*sin(YeqB_Ang*%pi/180); # Imaginary part of complex number\n", + "YP=0.387+1.13j;#(YeqA_R - %i* YeqA_I)+(YeqB_R - %i* YeqB_I); # Parallel admittance\n", + "\n", + " # Complex to Polar form...\n", + "YP_Mag=1.19;#sqrt(real(YP)**2+imag(YP)**2); # Magnitude part\n", + "YP_Ang=71.;#atan(imag(YP),real(YP))*180/%pi; # Angle part\n", + "\n", + "IA=30.7;#YeqA_Mag/YP_Mag; # Transformer A load\n", + "IB=69.8;#YeqB_Mag/YP_Mag; # Transformer A load\n", + "IA=IA*100.;\n", + "IB=IB*100.;\n", + "\n", + "# (c) Maximum load that can be handled by the bank without overloading by \n", + "# one of the transformer\n", + "Ibank=IArated/0.307;\n", + "\n", + "# Display result on command window\n", + "\n", + "print\"Rated high side current of transformer A =\",IArated,\"A\"\n", + "print\"Rated high side current of transformer B =\",IBrated,\"A\"\n", + "print\"Percent of total bank current drawn by transformer A =\",IA,\"Percent\"\n", + "print\"Percent of total bank current drawn by transformer B =\",IB,\"Percent\"\n", + "print\"Maximum load that can be handled by the bank =\", Ibank,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 109" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Percent of total bank current drawn by transformer A = 55.1594746717 Percent\n", + "Percent of total bank current drawn by transformer B = 44.8405253283 Percent\n" + ] + } + ], + "source": [ + "# Example 3.6\n", + "# Determine the percent of the total bank-current drawn by each transformer \n", + "# Page No. 109\n", + "# Given data\n", + "ZaPU_R=0.0158; # Transformer A impedance real part\n", + "ZaPU_I=0.0301; # Transformer A impedance imaginary part\n", + "ZbPU_R=0.0109; # Transformer B impedance real part\n", + "ZbPU_I=0.0398; # Transformer B impedance imaginary part\n", + "SB=200000.; # Transformer B rating\n", + "VHSA=2400.; # Voltage at the high side of transformer A\n", + "VHSB=2400.; # Voltage at the high side of transformer B\n", + "RPUA=1.64; # Percent resistance of transformer A\n", + "XPUA=3.16; # Percent reactance of transformer A\n", + "RPUB=1.10; # Percent resistance of transformer B\n", + "XPUB=4.03; # Percent reactance of transformer B\n", + "\n", + "\n", + "\n", + "# Base impedance of transformer A\n", + "ZaPU=0.0158 + 0.0301j;#ZaPU_R+%i*ZaPU_I;\n", + "# Complex to Polar form...\n", + "ZaPU_Mag=0.034;#sqrt(real(ZaPU)**2+imag(ZaPU)**2); # Magnitude part\n", + "ZaPU_Ang=62.3;#atan(imag(ZaPU),real(ZaPU))*180/%pi; # Angle part\n", + "\n", + "# Base impedance of transformer B\n", + "ZbPU=0.0109+0.0398j;#ZbPU_R+%i*ZbPU_I;\n", + "# Complex to Polar form...\n", + "ZbPU_Mag=0.0413;#sqrt(real(ZbPU)**2+imag(ZbPU)**2); # Magnitude part\n", + "ZbPU_Ang=74.7;#atan(imag(ZbPU),real(ZbPU))*180/%pi; # Angle part\n", + "\n", + "# Admittance of transformer A\n", + "YaPU_Mag=29.4;#1/ZaPU_Mag; # Magnitude of equivalent admittance A\n", + "YaPU_Ang=-62.3;#0-ZaPU_Ang; # Angle of equivalent admittance A\n", + "\n", + "# Polar to Complex form\n", + "\n", + "YaPU_R=13.7;#YaPU_Mag*cos(-YaPU_Ang*%pi/180); # Real part of complex number\n", + "YaPU_I=-26;#YaPU_Mag*sin(YaPU_Ang*%pi/180); # Imaginary part of complex number\n", + "\n", + "# Admittance of transformer B\n", + "YbPU_Mag=24.2;#1/ZbPU_Mag; # Magnitude of equivalent admittance B\n", + "YbPU_Ang=-74.7;#0-ZbPU_Ang; # Angle of equivalent admittance B\n", + "# Polar to Complex form\n", + "\n", + "YbPU_R=6.4;#YbPU_Mag*cos(-YbPU_Ang*%pi/180); # Real part of complex number\n", + "YbPU_I=-23.4;#YbPU_Mag*sin(YbPU_Ang*%pi/180); # Imaginary part of complex number\n", + "\n", + "# Parallel admittance\n", + "YP=20.1+49.4j;#(YaPU_R-%i*YaPU_I)+(YbPU_R-%i*YbPU_I);\n", + "# Complex to Polar form...\n", + "YP_Mag=53.3;#sqrt(real(YP)**2+imag(YP)**2); # Magnitude part\n", + "YP_Ang=67.9;#atan(imag(YP),real(YP))*180/%pi; # Angle part\n", + "\n", + "IA=YaPU_Mag/YP_Mag*100; # Percent current drawn by transformer A \n", + "IB=100-IA; \n", + "\n", + "# Display the result on the command window\n", + "print\"Percent of total bank current drawn by transformer A =\",IA,\"Percent\"\n", + "print\"Percent of total bank current drawn by transformer B =\",IB,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 113" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Bank ratio = 17.3333333333\n", + "Transformer ratio = 10.007404666\n", + "Rated line current for the high side = 20.8179183602 A\n", + "Rated phase current for the high side = 20.8179183602 A\n", + "Rated line current for the low side = 360.843918244 A\n", + "Rated phase current for the low side = 208.333333333 A\n" + ] + } + ], + "source": [ + "# Example 3.7\n", + "# Computation of (a) Bank ratio (b) Transformer ratio (c) Rated line and phase \n", + "# currents for the high side (d) Rated line and phase currents for the low side\n", + "# Page No. 113\n", + "# Given data\n", + "import math \n", + "VLINEHS=4160.; # Number of turns in the high side\n", + "VLINELS=240.; # Number of turns in the low side\n", + "VHS=2400.; # Voltage at the high side\n", + "S=4800.; # Supply voltage\n", + "Vline=150000.; # Transformer rating\n", + "\n", + "# (a) Bank ratio\n", + "bankratio=VLINEHS/VLINELS; \n", + "\n", + "# (b) Transformer ratio\n", + "Vphasep= VLINEHS/ math.sqrt(3); # For wye primary\n", + "Vphases=VLINELS # For secondary\n", + "TR=Vphasep/Vphases; # Transformer ratio \n", + "\n", + "# (c) Rated line and phase currents for the high side \n", + "Ilinew=Vline/(math.sqrt(3)*VLINEHS);\n", + "Iphasew=Ilinew;\n", + "\n", + "# (d) Rated line and phase currents for the low side\n", + "Ilined=Vline/(math.sqrt(3)*VLINELS); \n", + "Iphased=Ilined/math.sqrt(3);\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Bank ratio =\",bankratio\n", + "print\"Transformer ratio =\",TR\n", + "print\"Rated line current for the high side =\",Ilinew,\"A\"\n", + "print\"Rated phase current for the high side =\",Iphasew,\"A\"\n", + "print\"Rated line current for the low side =\",Ilined,\"A\"\n", + "print\"Rated phase current for the low side =\",Iphased,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 117" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Capacity of the bank when operating open-delta is = 43.275 kVA\n" + ] + } + ], + "source": [ + "# Example 3.8\n", + "# Determine the maximum allowable power that the open-delta bank handle \n", + "# without overheating\n", + "# Page No. 117\n", + "# Given data\n", + "S=25.;# Transformer rating\n", + "# Capacity of the delta-delta bank is\n", + "Cddb=S*3;\n", + "# Capacity of the bank when operating open-delta is\n", + "Cob=Cddb*0.577;\n", + "# Display result on command window\n", + "print\"Capacity of the bank when operating open-delta is =\",Cob,\"kVA\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 117" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Minimum power rating required for each transformer = 32.075014955 kVA\n" + ] + } + ], + "source": [ + "# Example 3.9\n", + "# Determine the minimum power rating required for each transformer\n", + "# Page No. 117\n", + "# Given data\n", + "import math\n", + "P=50000.; # Transformer power rating\n", + "Eline=120.; # Line voltage\n", + "FP=0.9 # Power factor lagging\n", + "VL=120.;\n", + "#Line current is\n", + "Iline=P/(math.sqrt(3.)*Eline*FP);\n", + "#Minimum power rating required for each transformer\n", + "Pmin=VL*Iline/1000.;\n", + "#Display result on command window\n", + "print\"Minimum power rating required for each transformer =\",Pmin,\"kVA\"" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER04.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER04.ipynb new file mode 100644 index 00000000..02abb244 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER04.ipynb @@ -0,0 +1,396 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER04 : PRINCIPLES OF THREE PHASE INDUCTION MOTORS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 140" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Synchronous speed of a six pole induction motor = 1020.0 r/min\n" + ] + } + ], + "source": [ + "# Example 4.1\n", + "# Computation of synchronous speed of a six pole induction motor\n", + "# Page No. 140\n", + "# Given data\n", + "f=60.; # Frequency\n", + "p=6.; # Number of poles\n", + "fs=f*0.85; # Frequency is 85% of its rated value\n", + "ns=120.*fs/p; # Synchronous speed\n", + "\n", + "# Display result on command window\n", + "print\"Synchronous speed of a six pole induction motor =\",ns,\"r/min\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 143" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Synchronous speed = 1200.0 r/min\n", + "Slip = 0.0833333333333\n", + "Rotor frequency = 5.0 Hz\n", + "Rotor voltage = 8.33333333333 V\n" + ] + } + ], + "source": [ + "# Example 4.2\n", + "# Computation of (a) Frequency (b) Induced voltage of six pole induction motor\n", + "# Page No. 143\n", + "# Given data\n", + "f=60.; # Frequency\n", + "p=6.; # Number of poles\n", + "nr=1100.; # Rotor speed\n", + "Ebr=100.; # Blocked rotor voltage\n", + "\n", + "# (a) Synchronous speed\n", + "ns=120.*f/p; # Synchronous speed\n", + "\n", + "# (b) Slip\n", + "s=(ns-nr)/ns; # Slip\n", + "\n", + "# (c) Rotor frequency\n", + "fr=s*f; # Rotor frequency\n", + "\n", + "# (d) Rotor voltage\n", + "Er=s*Ebr; # Rotor voltage\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Synchronous speed =\",ns,\"r/min\"\n", + "print\"Slip =\",s\n", + "print\"Rotor frequency =\",fr,\"Hz\"\n", + "print\"Rotor voltage =\",Er,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 146" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Synchronous speed = 1200.0 r/min\n", + "Slip = 0.03\n", + "Rotor impedance magnitude = 3.38 Ohm\n", + "Rotor impedance angle = 9.2 deg\n", + "Rotor current magnitude = 44.3786982249 Ohm\n", + "Rotor current angle = -9.2 deg\n", + "Rotor current magnitude by changing the shaft load = 18.5643564356 Ohm\n", + "Rotor current angle by changing the shaft load = -3.83 deg\n", + "New rotor speed = 1185.12 r/min\n" + ] + } + ], + "source": [ + "# Example 4.3\n", + "# Determine (a) Synchronous speed (b) Slip (c) Rotor impedance (d) Rotor current\n", + "# (e) Rotor current if changing the shaft load resulted in 1.24 percenr slip \n", + "# (f) Speed for the condition in (e) \n", + "# Page No. 146\n", + "# Given data\n", + "fs=60.; # Frequency\n", + "p=6.; # Number of poles\n", + "nr=1164.; # Rotor speed\n", + "Rr=0.10; # Equivalent resistance\n", + "Xbr=0.54; # Equivalent reactance\n", + "Ebr=150.; # Blocked rotor voltage per phase\n", + "s1=0.0124; # Percent slip\n", + "\n", + "# (a) Synchronous speed\n", + "ns=120.*fs/p; # Speed \n", + "\n", + "# (b) Slip\n", + "s=(ns-nr)/ns; \n", + "\n", + "# (c) Rotor impedance \n", + "Zr=3.33+0.54j;#(Rr/s)+%i*Xbr;\n", + "# Complex to Polar form...\n", + "Zr_Mag=3.38;#sqrt(real(Zr)**2+imag(Zr)**2); # Magnitude part\n", + "Zr_Ang=9.2;#atan(imag(Zr),real(Zr))*180/%pi; # Angle part\n", + "\n", + "# (d) Rotor current\n", + "Ir_Mag=Ebr/Zr_Mag; # Magnitude\n", + "Ir_Ang=0-Zr_Ang; # Angle\n", + "\n", + "# (e) Rotor current if changing the shaft load resulted in 1.24 percent slip \n", + "Zrnew=8.06+0.54j;#Rr/s1+%i*Xbr;\n", + "# Complex to Polar form...\n", + "Zrnew_Mag=8.08;#sqrt(real(Zrnew)**2+imag(Zrnew)**2); # Magnitude part\n", + "Zrnew_Ang=3.83;#atan(imag(Zrnew),real(Zrnew))*180/%pi; # Angle part\n", + "\n", + "Irnew_Mag=Ebr/Zrnew_Mag; # Magnitude\n", + "Irnew_Ang=0-Zrnew_Ang; # Angle\n", + "\n", + "# (f) Speed for the condition in (e) \n", + "nr=ns*(1-s1); \n", + "\n", + "# Display result on command window\n", + "print\"Synchronous speed =\",ns,\"r/min\"\n", + "print\"Slip =\",s\n", + "print\"Rotor impedance magnitude =\",Zr_Mag,\"Ohm\"\n", + "print\"Rotor impedance angle =\",Zr_Ang,\"deg\"\n", + "print\"Rotor current magnitude =\",Ir_Mag,\"Ohm\"\n", + "print\"Rotor current angle =\",Ir_Ang,\"deg\"\n", + "print\"Rotor current magnitude by changing the shaft load =\",Irnew_Mag,\"Ohm\"\n", + "print\"Rotor current angle by changing the shaft load =\",Irnew_Ang,\"deg\"\n", + "print\"New rotor speed =\",nr,\"r/min\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 149" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total three phase apparent power crossing the air gap (VA) =\n", + "(19702.5958869+1.8711951419j)\n", + "Active power component = 19700.0 W\n", + "Reactive power component = 3200.0 var\n", + "Rotor power factor = 0.987\n" + ] + } + ], + "source": [ + "# Example 4.4\n", + "# Determine (a) Total three phase apparent power crossing the air gap \n", + "# (b) Active and reactive components (c) Rotor power factor\n", + "# Page No. 149\n", + "# Given data\n", + "Ebr=150.; # Blocked rotor voltage per phase\n", + "Ir_Mag=44.421; # Rotor current magnitude\n", + "Ir_Ang=-9.2; # Rotor current angle\n", + "Ir_magConj=9.2; \n", + "# (a) Total three phase apparent power crossing the air gap \n", + "Sgap_Mag=3*Ebr*Ir_Mag; # Apparent power crossing the air gap magnitude\n", + "Sgap_Ang=Ir_magConj; # Apparent power crossing the air gap angle\n", + "# Polar to Complex form\n", + "Sgap_R=1.97*10.**4.;#Sgap_Mag*cos(-Sgap_Ang*%pi/180); # Real part of complex number\n", + "Sgap_I=3.2*10.**3.;#Sgap_Mag*sin(Sgap_Ang*%pi/180); # Imaginary part of complex number\n", + "Sgap=1.97*10**4 + 3.2*10**3j;#ceil(Sgap_R)+%i*ceil(Sgap_I);\n", + "# (b) Active and reactive components \n", + "Pgap=Sgap_R; # Active power component\n", + "Qgap=Sgap_I; # Reactive power component\n", + "# (c) Rotor power factor\n", + "FP=0.987;#cosd(Ir_magConj);\n", + "# Display result on command window\n", + "print\"Total three phase apparent power crossing the air gap (VA) =\"\n", + "print Sgap\n", + "print\"Active power component =\",Pgap,\"W\"\n", + "print\"Reactive power component =\",Qgap,\"var\"\n", + "print\"Rotor power factor =\",FP" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 152" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shaft speed = 1767.5308642 r/min\n", + "Mechanical power developed in hp = 19.191689008 hp\n", + "Developed torque = 57.0257372654 lb-ft\n" + ] + } + ], + "source": [ + "# Example 4.5\n", + "# Computation of (a) Shaft speed (b) Mechanical power developed\n", + "# (c) Developed torque\n", + "# Page No. 152\n", + "# Given data\n", + "Prcl=263.; # Rotor copper loss\n", + "Pgap=14580.; # Power input to the rotor\n", + "fs=60.; # Frequency\n", + "p=4.; # Number of poles\n", + "# (a) Shaft speed\n", + "s=Prcl/Pgap; # Slip\n", + "ns=120.*fs/p; # Speed of stator\n", + "nr=ns*(1.-s); # Speed of shaft\n", + "# (b) Mechanical power developed\n", + "Pmech=Pgap-Prcl; # Mechanical power developed\n", + "Pmechhp=Pmech/746.; # Mechanical power developed in hp\n", + "# (c) Developed torque\n", + "TD=5252.*Pmechhp/nr;\n", + "# Display result on command window\n", + "print\"Shaft speed =\",nr,\"r/min\"\n", + "print\"Mechanical power developed in hp =\",Pmechhp,\"hp\"\n", + "print\"Developed torque =\",TD,\"lb-ft\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 159" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Power input = 81978.021978 W\n", + "Total losses = 7378.02197802 W\n", + "Air gap power = 77478.021978 W\n", + "Shaft speed = 1176.00868024 r/min\n", + "Power factor = 0.829769162985\n", + "Combined windage, friction and stray load loss = 1329.02197802 W\n", + "Shaft torque = 446.595343067 lb-ft\n" + ] + } + ], + "source": [ + "# Example 4.6\n", + "# Determine (a) Power input (b) Total losses (c) Air gap power (d) Shaft speed\n", + "# (e) Power factor (f) Combined windage, friction and stray load loss\n", + "# (g) Shaft torque\n", + "# Page No. 159\n", + "# Given data\n", + "import math\n", + "Pshaft=74600.; # Shaft power\n", + "eeta=0.910; # Rated efficiency\n", + "ns=1200.; # Speed of stator\n", + "Pcore=1697.; # Power in core\n", + "Pscl=2803.; # Stator copper loss\n", + "Prcl=1549.; # Rotor copper loss\n", + "fs=60.; # Synchronous frequency\n", + "p=6.; # Number of poles\n", + "Vline=230.; # Line voltage\n", + "Iline=248.; # Line current\n", + "\n", + "# (a) Power input\n", + "Pin=Pshaft/eeta; # Parallel resistance\n", + "\n", + "# (b) Total losses\n", + "Ploss=Pin-Pshaft;\n", + "\n", + "# (c) Air gap power\n", + "Pgap=Pin-Pcore-Pscl;\n", + "\n", + "# (d) Shaft speed\n", + "s=Prcl/Pgap; # Parallel resistance\n", + "ns=120.*fs/p;\n", + "nr=ns*(1-s);\n", + "\n", + "# (e) Power factor\n", + "Sin=math.sqrt(3)*Vline*Iline;\n", + "FP=Pin/Sin;\n", + "\n", + "# (f) Combined windage, friction and stray load loss\n", + "Closs=Ploss-Pcore-Pscl-Prcl;\n", + "\n", + "# (g) Shaft torque\n", + "Tshaft=5252.*100./nr;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Power input =\",Pin,\"W\"\n", + "print\"Total losses =\",Ploss,\"W\"\n", + "print\"Air gap power =\",Pgap,\"W\"\n", + "print\"Shaft speed =\",nr,\"r/min\"\n", + "print\"Power factor =\",FP\n", + "print\"Combined windage, friction and stray load loss =\",Closs,\"W\"\n", + "print\"Shaft torque =\",Tshaft,\"lb-ft\"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb new file mode 100644 index 00000000..f3b97267 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER05.ipynb @@ -0,0 +1,1480 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER05 : CLASSIFICATION PERFORMANCE APPLICATIONS AND OPERATION OF THREE PHASE INDUCTION MACHINES" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 173" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Locked rotor torque = 102.756521739 lb-ft\n", + "Breakdown torque = 86.772173913 lb-ft\n", + "Pull up torque = 75.3547826087 lb-ft\n" + ] + } + ], + "source": [ + "# Example 5.1\n", + "# Computation of minimum value of (a) Locked rotor torque (b) Breakdown torque\n", + "# (c) Pull up torque\n", + "# Page No. 173\n", + "# Given data\n", + "f=60.; # Frequency in Hz\n", + "p=6.; # Number of poles\n", + "hp=10.; # Horsepower\n", + "n=1150.; # Rated speed of machine\n", + "ns=120.*f/p;\n", + "# (a) Locked rotor torque\n", + "Trated=hp*5252./n; # Rated torque \n", + "Tlockedrotor=2.25*Trated;\n", + "# (b) Breakdown torque\n", + "Tbreakdown=1.90*Trated;\n", + "# (c) Pull up torque\n", + "Tpullup=1.65*Trated;\n", + "# Display result on command window\n", + "print\"Locked rotor torque =\",Tlockedrotor,\"lb-ft\"\n", + "print\"Breakdown torque =\",Tbreakdown,\"lb-ft\"\n", + "print\"Pull up torque =\",Tpullup,\"lb-ft\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 180" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Slip = 0.0125\n", + "\n", + "Line current magnitude = 15.0898365811 A\n", + "\n", + "Line current angle = -30.2 deg\n", + "\n", + "Apparent power = 10390.9402326 W\n", + "\n", + "Active power = 6047.67163108 var\n", + "\n", + "Reactive power = 12022.7272727 VA\n", + "\n", + "Power factor of the motor = 0.864\n", + "\n", + "Equivalent rotor curret magnitude = 12.6578934123 A\n", + "\n", + "Equivalent rotor curret angle = -6.85 deg\n", + "\n", + "Stator copper loss = 136.621900826 W\n", + "\n", + "Rotor copper loss = 120.166699229 W\n", + "\n", + "Core loss = 606.519617558 W\n", + "\n", + "Air-gap power = 9613.33593829 W\n", + "\n", + "Mechanical power developed = 9493.16923906 W\n", + "\n", + "Developed torque = 56.3982375046 lb-ft\n", + "\n", + "Shaft horsepower = 12.5491045777 hp\n", + "\n", + "Shaft torque = 55.6184786853 lb-ft\n", + "\n", + "Effiency = 0.90094176325\n" + ] + } + ], + "source": [ + "# Example 5.2\n", + "# Determine (a) Slip (b) Line current (c) Apparent power, active power, \n", + "# reactive power and power factor of the motor (d) Equivalent rotor curret\n", + "# (e) Stator copper loss (f) Rotor copper loss (g) Core loss (h) Air-gap\n", + "# power (i) Mechanical power developed (j) Developed torque (k) Shaft \n", + "# horsepower (l) Shaft torque (m) Effiency \n", + "# Page No. 180\n", + "# Given data\n", + "from math import sqrt,pi,sin,cos \n", + "f=60.; # Frequency\n", + "P=6.; # Number of poles\n", + "nr=1185.;\n", + "R1=0.200; # Motor resistance\n", + "R2=0.250;\n", + "X1=1.20; # Motor reactance\n", + "X2=1.29;\n", + "Rfe=317.; # Field resistance\n", + "XM=42.; # Motor reactance\n", + "V=460.; # Voltage rating\n", + "PFPS=166.; # Stray loss\n", + "\n", + "# (a) Slip \n", + "ns=(120.*f)/P;\n", + "s=(ns-nr)/ns; # Speed difference\n", + "\n", + "# (b) Line current\n", + "Z2=20 + 1.29j;#(R2/s)+%i*X2;\n", + "# Complex to Polar form...\n", + "Z2_Mag=20.;#sqrt(real(Z2)**2+imag(Z2)**2); # Magnitude part\n", + "Z2_Ang =3.69;#atan(imag(Z2),real(Z2))*180/%pi; # Angle part\n", + "\n", + "Z0_Num_Mag=Rfe*XM; # Z0 numerator\n", + "Z0_Num_Ang=0+90; \n", + " \n", + "Z0_Den_R=Rfe; # Z0 denominator\n", + "Z0_Den_I=XM;\n", + "Z0_Den=317 + 42j;#Z0_Den_R+%i*Z0_Den_I;\n", + "# Complex to Polar form...\n", + "Z0_Den_Mag=320.;#sqrt(real(Z0_Den)**2+imag(Z0_Den)**2); # Magnitude part\n", + "Z0_Den_Ang =7.55;#atan(imag(Z0_Den),real(Z0_Den))*180/%pi; # Angle part\n", + "\n", + "Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; # Magnitude of Z0\n", + "Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; # Angle of Z0\n", + "\n", + "# Polar to Complex form\n", + "Z0_R=Z0_Mag*cos(-Z0_Ang*pi/180); # Real part of complex number\n", + "Z0_I=Z0_Mag*sin(Z0_Ang*pi/180); # Imaginary part of complex number\n", + "\n", + "# ZP computation\n", + "ZP_Num_Mag=Z2_Mag*Z0_Mag; # ZP numerator magnitude\n", + "ZP_Num_Ang=Z2_Ang+Z0_Ang; # ZP numerator angle\n", + "\n", + "ZP_Den_R=25.5;#real(Z2)+Z0_R; # Real part of ZP denominator\n", + "ZP_Den_I=42.6;#imag(Z2)+Z0_I; \n", + "ZP_Den=25.5 + 42.6j;#lZP_Den_R+%i*ZP_Den_I; # ZP in complex form\n", + "\n", + "# Complex to Polar form...\n", + "ZP_Den_Mag=49.6;#sqrt(real(ZP_Den)**2+imag(ZP_Den)**2); # Magnitude part\n", + "ZP_Den_Ang =59.1;#atan(imag(ZP_Den),real(ZP_Den))*180/%pi; # Angle part\n", + "\n", + "ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; # Final vlaue of ZP in polar form\n", + "ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;\n", + "# Polar to Complex form\n", + "ZP_R=ZP_Mag*cos(-ZP_Ang*pi/180); # Real part of complex number\n", + "ZP_I=ZP_Mag*sin(ZP_Ang*pi/180); # Imaginary part of complex number\n", + "\n", + "# Zin computation\n", + "ZP=15 + 7.65j;#ZP_R+%i*ZP_I; # Parallel impedance\n", + "Z1=0.2 + 1.2j;#R1+%i*X1;\n", + "Zin=Z1+ZP; # Input impedance\n", + "# Complex to Polar form...\n", + "Zin_Mag=17.6;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part\n", + "Zin_Ang =30.2;#atan(imag(Zin),real(Zin))*180/%pi; # Angle part\n", + "\n", + "# I1 computation\n", + "I1_Mag=(V/sqrt(3.))/Zin_Mag; # I1 magnitude\n", + "I1_Ang=0-Zin_Ang; # I1 angle\n", + "\n", + "# (c) Apparent power, active power, reactive power and power factor of the motor\n", + "S_Mag=3.*(V/sqrt(3.))*I1_Mag; # S magnitude\n", + "S_Ang=0-(-Zin_Ang); # S angle\n", + "\n", + "# Polar to Complex form\n", + "S_R=S_Mag*cos(-S_Ang*pi/180); # Real part of complex number\n", + "S_I=S_Mag*sin(S_Ang*pi/180); # Imaginary part of complex number\n", + "\n", + "FP=0.864;#cosd(S_Ang); # Power factor\n", + "\n", + "# (d) Equivalent rotor curret\n", + "E2_Mag=I1_Mag*ZP_Mag; # E2 magnitude\n", + "E2_Ang=I1_Ang+ZP_Ang; # E2 angle\n", + "\n", + "I2_Mag=E2_Mag/Z2_Mag; # I2 magnitude\n", + "I2_Ang=E2_Ang-Z2_Ang; # I2 angle\n", + "\n", + "# (e) Stator copper loss \n", + "Pscl=3.*I1_Mag**2.*R1;\n", + "\n", + "# (f) Rotor copper loss\n", + "Prel=3.*I2_Mag**2.*R2;\n", + "\n", + "# (g) Core loss \n", + "Pcore=3.*(E2_Mag**2./Rfe);\n", + "\n", + "# (h) Air-gap power\n", + "Pgap=Prel/s;\n", + "\n", + "# (i) Mechanical power developed\n", + "Pmech=Prel*(1.-s)/s;\n", + "\n", + "# (j) Developed torque \n", + "TD=(21.12*I2_Mag**2*R2)/(s*ns);\n", + "\n", + "# (k) Shaft horsepower\n", + "LOSS=Pscl+Prel+Pcore+PFPS;\n", + "Pshaft=(S_R-LOSS)/746.;\n", + "\n", + "# (l) Shaft torque\n", + "T=5252.*Pshaft/nr;\n", + "\n", + "# (m) Effiency \n", + "eta=Pshaft/S_R*746.;\n", + "\n", + "# Display result on command window\n", + "print\"\\nSlip =\",s\n", + "print\"\\nLine current magnitude =\",I1_Mag,\"A\"\n", + "print\"\\nLine current angle =\",I1_Ang,\"deg\"\n", + "print\"\\nApparent power =\",S_R,\"W\"\n", + "print\"\\nActive power =\",S_I,\"var\"\n", + "print\"\\nReactive power =\",S_Mag,\"VA\"\n", + "print\"\\nPower factor of the motor =\",FP\n", + "print\"\\nEquivalent rotor curret magnitude =\",I2_Mag,\"A\"\n", + "print\"\\nEquivalent rotor curret angle =\",I2_Ang,\"deg\"\n", + "print\"\\nStator copper loss =\",Pscl,\"W\"\n", + "print\"\\nRotor copper loss =\",Prel,\"W\"\n", + "print\"\\nCore loss =\",Pcore,\"W\"\n", + "print\"\\nAir-gap power =\",Pgap,\"W\"\n", + "print\"\\nMechanical power developed =\",Pmech,\"W\"\n", + "print\"\\nDeveloped torque =\",TD,\"lb-ft\"\n", + "print\"\\nShaft horsepower =\",Pshaft,\"hp\"\n", + "print\"\\nShaft torque =\",T,\"lb-ft\"\n", + "print\"\\nEffiency =\",eta" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 184" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Speed at which maximum torque is developed = 1531.8 r/min\n", + "\n", + "Maximum torque that the machine can develop = 366.489979327 lb-ft\n", + "\n", + "Rated shaft torque = 119.977155911 lb-ft\n", + "\n", + "Maximum torque is developed at slip of 0.1490 and \n", + "hence machine is placed in design A category\n" + ] + } + ], + "source": [ + "# Example 5.3\n", + "# Computation of (a) Speed at which maximum torque is developed (b) Maximum \n", + "# torque that the machine can develop (c) Rated shaft torque (d) Which NEMA \n", + "# design fits this motor?\n", + "# Page No. 184\n", + "# Given data\n", + "from math import sqrt\n", + "f=60.; # Frequency in Hz\n", + "p=4.; # Number of poles\n", + "hp=40.; # Horsepower\n", + "n=1751.; # Rated speed of machine\n", + "v=460./sqrt(3.); # Voltage\n", + "s=0.1490; # Slip\n", + "R2=0.153; # Rotor resistance \n", + "R1=0.102;\n", + "X1=0.409; # Rotor reactance\n", + "X2=0.613;\n", + "\n", + "# (a) Speed at which maximum torque is developed \n", + "STDmax=R2/(sqrt(R1**2.+(X1+X2)**2.));\n", + "ns=120.*f/p; #stator spped\n", + "nr=ns*(1.-s);\n", + "\n", + "# (b) Maximum torque that the machine can develop\n", + "TDmax=(21.12*v**2.)/(2.*ns*(sqrt(R1**2.+(X1+X2)**2.)+R1));\n", + "\n", + "# (c) Rated shaft torque\n", + "TDshaft=hp*5252./n;\n", + "\n", + "# Display result on command window\n", + "print\"\\nSpeed at which maximum torque is developed =\",nr,\"r/min\"\n", + "print\"\\nMaximum torque that the machine can develop =\",TDmax,\"lb-ft\"\n", + "print\"\\nRated shaft torque =\",TDshaft,\"lb-ft\"\n", + "print\"\\nMaximum torque is developed at slip of 0.1490 and \\nhence machine is placed in design A category\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 185" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Amount of torque that must be removed from the motor shaft = 28.3488636364 lb-ft\n", + "\n", + " Expected minimum starting torque for the lower voltage = 169.197954545 lb-ft\n", + "\n", + " Percent change in developed torque = -19.0 Percent\n" + ] + } + ], + "source": [ + "# Example 5.4\n", + "# Computation of (a) Amount of torque that must be removed from the motor \n", + "# shaft to maintain 1760r/min (b) Expected minimum startimg torque for the \n", + "# lower voltage (c) Percent change in developed torque caused by 10% drop in \n", + "# system voltage.\n", + "# Page No. 185\n", + "# Given data\n", + "hp=50.; # Horsepower\n", + "n=1760.; # Rated speed of machine\n", + "v1=460.;\n", + "# (a) Amount of torque that must be removed from the motor shaft to maintain \n", + "# 1760r/min\n", + "v2=v1*0.90;\n", + "Trated=hp*5252./n; #Rated torque \n", + "TD2=Trated*(v2/v1)**2.;\n", + "Treduction=Trated-TD2;\n", + "# (b) Expected minimum startimg torque for the lower voltage\n", + "Tlr=1.40*Trated;\n", + "Tlr2=Tlr*(v2/v1)**2;\n", + "# (c) Percent change in developed torque caused by 10% drop in system voltage\n", + "Tchange=(TD2-Trated)/Trated;\n", + "Tchanger=(Tlr2-Tlr)/Tlr;\n", + "# Display result on command window\n", + "print\"\\n Amount of torque that must be removed from the motor shaft =\",Treduction,\"lb-ft\"\n", + "print\"\\n Expected minimum starting torque for the lower voltage =\",Tlr2,\"lb-ft\"\n", + "print\"\\n Percent change in developed torque =\",Tchanger*100,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 187" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Shaft speed = 588.875 r/min\n", + "\n", + "Rotor current referred to the stator = 111.916287976 A\n" + ] + } + ], + "source": [ + "# Example 5.5\n", + "# Computation of minimum value of (a) Shaft speed (b) Rotor current referred \n", + "# to the stator\n", + "# Page No. 187\n", + "# Given data\n", + "from math import sqrt\n", + "f=60.; # Frequency in Hz\n", + "p=12.; # Number of poles\n", + "nr=591.1; # Rated speed of machine\n", + "v=575.; # Voltage rating of the machine\n", + "R2=0.055;\n", + "\n", + "# (a) Shaft speed\n", + "ns=120.*f/p; # Speed (r/min)\n", + "s1=(ns-nr)/ns; # Slip 1\n", + "s2=1.25*s1; # Slip 2\n", + "nr1=ns*(1.-s2);\n", + "\n", + "# (b) Rotor current referred to the stator\n", + "V=v/sqrt(3.);\n", + "I2=V*s2/R2;\n", + "\n", + "# Display result on command window\n", + "print\"\\nShaft speed =\",nr1,\"r/min\"\n", + "print\"\\nRotor current referred to the stator =\",I2,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 190" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "New operating speed in case of voltage and frequency drop = 1100.72839506 r/min\n", + "\n", + "New shaft horsepower = 18.7358024691 hp\n" + ] + } + ], + "source": [ + "# Example 5.6\n", + "# Determine (a) New operating speed if a system disturbance causes a 10% drop\n", + "# in voltage and 6% drop in frequency (b) New shaft horsepower.\n", + "# Page No. 190\n", + "# Given data\n", + "etaV=0.90; # Efficiency related to voltage\n", + "V=230.; # Voltage\n", + "etaF=0.94; # Efficiency related to voltage\n", + "f=60.; # Frequency\n", + "N=6.; # Number of poles\n", + "nr1=1175.; # Speed of motor\n", + "P=20.; # Horsepower of motor\n", + "\n", + "# (a) New operating speed if a system disturbance causes a 10% drop in \n", + "# voltage and 6% drop in frequency\n", + "V2=etaV*V; # New voltage after 10% drop\n", + "f2=etaF*f; # New frequency after 6% drop\n", + "ns1=120.*f/N;\n", + "ns2=120.*0.94*f/N;\n", + "s1=(ns1-nr1)/ns1; # Speed difference\n", + "\n", + "s2=s1*((V/V2)**2.)*(f2/f); \n", + "nr2=ns2*(1.-s2); # New speed\n", + "\n", + "# (b) New shaft horsepower\n", + "P2=P*(nr2/nr1); # With a constant torque load T2=T1\n", + "\n", + "# Display result on command window\n", + "print\"\\nNew operating speed in case of voltage and frequency drop =\",nr2,\"r/min\"\n", + "print\"\\nNew shaft horsepower =\",P2,\"hp\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 192" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Expected locked-rotor line current = 173.32173913 A\n" + ] + } + ], + "source": [ + "# Example 5.7\n", + "# Determine expected locked-rotor line current\n", + "# Page No. 192\n", + "# Given data\n", + "Ir1=151.; # Rated current\n", + "V1=230.; # Rated voltage\n", + "V2=220.; # Motor starting voltage\n", + "F1=60.; # Rated frequency\n", + "F2=50.; # Motor starting frequency\n", + "# Expected locked-rotor line current\n", + "Ir2=Ir1*((V2/F2)/(V1/F1));\n", + "# Display result on command window\n", + "print\"\\n Expected locked-rotor line current =\",Ir2,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 193" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Expected minimum locked-rotor torque = 270.102857143 lb-ft\n", + "\n", + "Expected minimum locked-rotor torque after drop = 265.465984372 lb-ft\n" + ] + } + ], + "source": [ + "# Example 5.8\n", + "# Determine (a) Expected minimum locked-rotor torque (b) Repeat (a) when \n", + "# voltage and frequency dropped to 230V and 58Hz \n", + "# Page No. 193\n", + "# Given data\n", + "HPrated=75.; # Rated horsepower\n", + "nrated=1750.; # Rated speed\n", + "V1=240.; # Rated voltage\n", + "V2=230.; # Voltage after drop\n", + "F1=60.; # Rated frequency\n", + "F2=58.; # Frequency after drop\n", + "\n", + "# (a) Expected minimum locked-rotor torque\n", + "Trated=5252.*HPrated/nrated; # Rated torque\n", + "Tlr=Trated*1.2; # Minimum locked-rotor torque is 120% rated \n", + "\n", + "# (b) Expected minimum locked-rotor torque when voltage and frequency dropped \n", + "# to 230V and 58Hz \n", + "Tlr2=Tlr*((V2/F2)**2.)*((F1/V1)**2.);\n", + "\n", + "# Display result on command window\n", + "print\"\\nExpected minimum locked-rotor torque =\",Tlr,\"lb-ft\"\n", + "print\"\\nExpected minimum locked-rotor torque after drop =\",Tlr2,\"lb-ft\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 194" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Shaft speed = 1470.15519161 r/min\n", + "\n", + "Slip = 0.019896538928\n" + ] + } + ], + "source": [ + "# Example 5.9\n", + "# Determine (a) Shaft r/min (b) Slip \n", + "# Page No. 194\n", + "# Given data\n", + "from math import sqrt\n", + "F1=60.; # Rated frequency\n", + "N=4.; # Number of poles\n", + "F2=50.; # New frequency\n", + "ns=1770.; # Rated speed\n", + "\n", + "# (a) Shaft r/min\n", + "ns60=120.*F1/N; # Speed at rated ferquency \n", + "ns50=120.*F2/N; # Speed at 50 Hz frequency\n", + "s60=(ns60-ns)/ns60; # Slip at 60 Hz frequency\n", + "\n", + "# Using eq. (5.16) and by solving..s50=29.251/nr50\n", + "# Using eq. (4.3) and solving for nr50 we get the quadratic equation..\n", + "# Using various values of quadratic equations, we have\n", + "a=1.;\n", + "b=-1500.;\n", + "c=43876.5;\n", + "r1=(-b+sqrt(b**2-4*a*c))/(2.*a); # Root 1\n", + "\n", + "r2=(-b-sqrt(b**2-4*a*c))/(2.*a); # Root 2\n", + "# Answer 'r2' is not valid\n", + "\n", + "# (b) Slip \n", + "s50=(ns50-r1)/ns50;\n", + "\n", + "# Display result on command window\n", + "print\"\\nShaft speed =\",r1,\"r/min\"\n", + "print\"\\nSlip =\",s50" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E10 : Pg 198" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Low range of rotor speed = 311.142857143 r/min\n", + "\n", + " High range of rotor speed = 504.0 r/min\n", + "\n", + " Required rheostat resistance = 0.114905179241 Ohm/phase\n" + ] + } + ], + "source": [ + "# Example 5.10\n", + "# Determine (a) Range of rotor speed (b) Required rheostat resistance\n", + "# Page No. 198\n", + "# Given data\n", + "from math import sqrt\n", + "F=60.; # Frequency of motor\n", + "P=14.; # Number of poles\n", + "SL=0.395; # Low speed point\n", + "SH=0.02; # High speed point\n", + "Stdmax=0.74; # Value at which TD is maximum (from curve B)\n", + "R1=0.403; # Motor resistance\n", + "R2=0.317;\n", + "X1=1.32; # Motor reactance\n", + "X2=1.32;\n", + "a=3.8; # Ratio of stator turns/phase to rotor turns/phase\n", + "\n", + "# (a) Range of rotor speed\n", + "ns=120.*F/P; # Speed\n", + "nrl=ns*(1.-SL); # Rotor low speed\n", + "nrh=ns*(1.-SH); # Rotor high speed\n", + "\n", + "# (b) Required rheostat resistance\n", + "Rrhe=Stdmax*(sqrt(R1**2.+(X1+X2)**2.))-R2;\n", + "Rehereq=Rrhe/a**2.;\n", + "\n", + "# Display result on command window\n", + "print\"\\n Low range of rotor speed =\",nrl,\"r/min\"\n", + "print\"\\n High range of rotor speed =\",nrh,\"r/min\"\n", + "print\"\\n Required rheostat resistance =\",Rehereq,\"Ohm/phase\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E11 : Pg 201" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Rotor frequency = 0.795 Hz\n", + "\n", + " Slip at which TDmax occurs = 0.079830908464\n", + "\n", + " Rotor speed at 1/2 rated torque = 1488.075 r/min\n", + "\n", + " Required rheostat resistance = 0.0627232651992 Ohm/phase\n", + "\n", + " Rated torque = 1423.16160282 lb-ft\n" + ] + } + ], + "source": [ + "# Example 5.11\n", + "# Determine (a) Rotor frequency (b) Slip at which TDmax occurs (c) Rotor speed\n", + "# at 1/2 rated torque load (d) Required rheostat resistance (e) Rated torque\n", + "# Page No. 201\n", + "# Given data\n", + "from math import sqrt\n", + "S=0.0159; # Slip\n", + "Fbr=50.; # Rated frequency\n", + "R1=0.00536; # Motor resistance\n", + "R2=0.00613;\n", + "X1=0.0383; # Motor reactance\n", + "X2=0.0383;\n", + "Rrhe=0; # Initial rheostat resistance\n", + "P=4.; # Number of poles\n", + "NR=1000.; # Rated speed\n", + "s1=0.0159; # Slip of rheostat\n", + "a=2.; # Stator to rotor turns ratio\n", + "hp=400.; # Motor horsepower\n", + "\n", + "# (a) Rotor frequency\n", + "fr=S*Fbr;\n", + "\n", + "# (b) Slip at which TDmax occurs\n", + "Stdmax=(R2+Rrhe)/(sqrt(R1**2.+(X1+X2)**2.));\n", + "\n", + "# (c) Rotor speed at 1/2 rated torque load \n", + "s=S*(0.5)*(R2/R2); # Rotor speed at 1/2 rated torque\n", + "ns=120.*Fbr/P; \n", + "nr=ns*(1.-s); # Rotor speed\n", + "\n", + "# (d) Required rheostat resistance\n", + "s2=(ns-NR)/ns;\n", + "Rrhe2=((s2/s1)*(1./0.5)*(R2+Rrhe))-R2; # rheostat resistance\n", + "Rrheostat=Rrhe2/a**2.;\n", + "\n", + "# (e) Rated torque\n", + "nr1=ns*(1.-s1); # Rated speed\n", + "T=hp*5252./nr1;\n", + "\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\n Rotor frequency =\",fr,\"Hz\"\n", + "print\"\\n Slip at which TDmax occurs =\",Stdmax\n", + "print\"\\n Rotor speed at 1/2 rated torque =\",nr,\"r/min\"\n", + "print\"\\n Required rheostat resistance =\",Rrheostat,\"Ohm/phase\"\n", + "print\"\\n Rated torque =\",T,\"lb-ft\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E12 : Pg 202" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Percent change in rotor circuit resistance = 77.7777777778 Percent increase\n" + ] + } + ], + "source": [ + "# Example 5.12\n", + "# Determine the percent increase or decrease in rotor circuit resistance\n", + "# Page No. 202\n", + "# Given data\n", + "Stdmax1=0.45; # Maximum torque condition 1\n", + "Stdmax2=0.80; # Maximum torque condition 2\n", + "# Percent increase or decrease in rotor circuit resistance\n", + "PerCh=1/(Stdmax1/Stdmax2);\n", + "PerCh=PerCh-1;\n", + "# Display result on command window\n", + "print\"\\nPercent change in rotor circuit resistance =\",PerCh*100,\"Percent increase\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E13 : Pg 208" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Lower limit of expected range of in-rush current = 1054.29179591 A\n", + "\n", + " Upper limit of expected range of in-rush current = 1186.0782704 A\n" + ] + } + ], + "source": [ + "# Example 5.13\n", + "# Determine the expected in-rush current\n", + "# Page No. 208\n", + "# Given data\n", + "from math import sqrt\n", + "kva1=5.6; # KVA/hp lower limit from table 5.9\n", + "hp=150.; # Motor horsepower\n", + "Vline=460.; # Line voltage\n", + "kva2=6.3; # KVA/hp upper limit from table 5.9\n", + "# Expected in-rush current\n", + "# Lower limit of expected range of in-rush current is\n", + "Ilrss=(kva1*hp*1000)/(sqrt(3)*Vline); \n", + "# Upper limit of expected range of in-rush current is\n", + "Iulss=(kva2*hp*1000)/(sqrt(3)*Vline); \n", + "# Display result on command window\n", + "print\"\\n Lower limit of expected range of in-rush current =\",Ilrss,\"A\"\n", + "print\"\\n Upper limit of expected range of in-rush current =\",Iulss,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E14 : Pg 211" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Percent voltage unbalance = 2.58\n", + "\n", + "Expected approximate temperature rise = 124.64408 deg C\n", + "\n", + " Expected insulation life = 7.2476842001 years\n", + "\n", + " Required derating of motor = 27.6 hp\n" + ] + } + ], + "source": [ + "# Example 5.14\n", + "# Determine (a) Percent voltage unbalance (b) Expected approximate temp. rise\n", + "# if operating at rated load in a 40 deg ambient (c) Expected insulation life \n", + "# (d) Required derating of motor to prevent shortening isulation life.\n", + "# Page No. 211\n", + "# Given data\n", + "from math import sqrt\n", + "VL1=460.; # Line voltage 1\n", + "VL2=455.; # Line voltage 2\n", + "VL3=440.; # Line voltage 3 \n", + "Trated=110.; # Rated temp. (from table 5.8)\n", + "hp=30.; # Motor horsepower\n", + "\n", + "# (a) Percent voltage unbalance \n", + "Vavg=(VL1+VL2+VL3)/3.; # Average line voltage\n", + "\n", + "#VD1=abs(VL1-Vavg); # Voltage deviation from the average \n", + "#VD2=abs(VL2-Vavg); \n", + "#VD3=abs(VL3-Vavg); \n", + "#VD=[VD1 VD2 VD3]; \n", + "#VDMax=max(VD); # Choose maximum value of voltage deviation\n", + "PerUBV=2.58;#(VDMax/Vavg)*100;\n", + "\n", + "# (b) Expected approximate temp. rise if operating at rated load in a 40 deg\n", + "PerDeltaT=2.*PerUBV**2.; # Percent change in temp.\n", + "Tubv=Trated*(1.+(PerDeltaT/100.));\n", + "\n", + "# (c) Expected insulation life \n", + "DeltaT=Tubv-Trated; # Percent increase in motor temp.\n", + "RL=1./(2.**(DeltaT/10.)); # Relative life on insulation\n", + "EL=RL*20;\n", + "\n", + "# (d) Required derating of motor to prevent shortening isulation life\n", + "ReqDer=hp*0.92;\n", + "\n", + "# Display result on command window\n", + "print\"\\nPercent voltage unbalance =\",PerUBV\n", + "print\"\\nExpected approximate temperature rise =\",Tubv,\"deg C\"\n", + "print\"\\n Expected insulation life =\",EL,\"years\"\n", + "print\"\\n Required derating of motor =\",ReqDer,\"hp\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E15 : Pg 213" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Motor resistance 1 = 0.119131367292 Ohm\n", + "\n", + " Motor reactance 1 = 0.567292225201 Ohm\n", + "\n", + " Motor resistance 2 = 0.11345844504 Ohm\n", + "\n", + " Motor reactance 2 = 0.100978016086 Ohm\n", + "\n", + " Field resistance = 113.45844504 Ohm\n", + "\n", + " Reactance of motor = 20.8763538874 Ohm\n" + ] + } + ], + "source": [ + "# Example 5.15\n", + "# Determine the machine parameters in ohms\n", + "# Page No. 213\n", + "# Given data\n", + "from math import sqrt \n", + "V=460.; # Motor voltage\n", + "hp=50.; # Motor horsepower\n", + "r1=0.021; # Resistance\n", + "r2=0.020;\n", + "x1=0.100; # Reactance\n", + "x2=0.0178;\n", + "rfe=20.; \n", + "Xm=3.68; # Motor reactance\n", + "\n", + "# Machine parameters in ohms\n", + "Vbase=V/sqrt(3.); # Base voltage\n", + "Pbase=hp*746./3.; # Base power\n", + "Zbase=Vbase**2./Pbase; # Base impedance\n", + "\n", + "R1=r1*Zbase;\n", + "X1=x1*Zbase;\n", + "R2=r2*Zbase;\n", + "X2=x2*Zbase;\n", + "Rfe=rfe*Zbase;\n", + "XM=Xm*Zbase;\n", + "\n", + "# Display result on command window\n", + "print\"\\n Motor resistance 1 =\",R1,\"Ohm\"\n", + "print\"\\n Motor reactance 1 =\",X1,\"Ohm\"\n", + "print\"\\n Motor resistance 2 =\",R2,\"Ohm\"\n", + "print\"\\n Motor reactance 2 =\",X2,\"Ohm\"\n", + "print\"\\n Field resistance =\",Rfe,\"Ohm\"\n", + "print\"\\n Reactance of motor =\",XM,\"Ohm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E16 : Pg 218" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Motor resistance 1 = 0.101694915254 Ohm/phase\n", + "\n", + " Motor reactance 1 = 0.407379662436 Ohm/phase\n", + "\n", + " Motor resistance 2 = 0.153299139443 Ohm/phase\n", + "\n", + " Motor reactance 2 = 0.611069493654 Ohm/phase\n", + "\n", + " Reactance of motor = 7.58314688225 Ohm/phase\n", + "\n", + " Combined friction, windage and core loss = 1446.05864407 W/phase\n", + "\n", + " No-load current as a percent of rated current = 56.5743944637 Percent\n" + ] + } + ], + "source": [ + "# Example 5.16\n", + "# Determine (a) R1, R2, X1, X2, XM and the combined core, friction and windage \n", + "# loss (b) Express the no-load current as a percent of rated current\n", + "# Page No. 218\n", + "# Given data\n", + "from math import sqrt\n", + "P3ph=2573.4; # 3-ph power of induction motor\n", + "Vline=36.2; # Line voltage\n", + "Iline=58; # Line current\n", + "P3phnl=4664.4; # No load power\n", + "Vlinenl=460.; # No load line volatge\n", + "Ilinenl=32.7; # No load line current\n", + "Vdc=12.; # DC voltage\n", + "Idc=59.; # DC current\n", + "F1=60.; # Rated frequency\n", + "F2=15.; # Test frequency\n", + "Irated=57.8; # Rated current\n", + " \n", + "# (a) R1, R2, X1, X2, XM and the combined core, friction and windage loss\n", + "Pbr15=P3ph/3.; # Power/phase\n", + "Vbr15=Vline/sqrt(3.); # Voltage/phase\n", + "Ibr15=Iline;\n", + "PNL=P3phnl/3.; # No load power/phase\n", + "VNL=Vlinenl/sqrt(3.); # No load voltage/phase\n", + "INL=Ilinenl; # No load current/phase\n", + "\n", + "# Determination of R1\n", + "Rdc=Vdc/Idc;\n", + "R1=Rdc/2.;\n", + "\n", + "# Determination of R2\n", + "Zbr15=Vbr15/Ibr15; # Impedance\n", + "Rbr15=Pbr15/Ibr15**2.;\n", + "R2=Rbr15-R1;\n", + "\n", + "# Determination of X1 and X2\n", + "Xbr15=sqrt(Zbr15**2.-Rbr15**2.);\n", + "Xbr60=Xbr15*(F1/F2);\n", + "X1=0.4*Xbr60; # From Table 5.10\n", + "X2=0.6*Xbr60;\n", + "\n", + "# Determination of XM\n", + "SNL=VNL*INL;\n", + "QNL=sqrt(SNL**2.-PNL**2.);\n", + "XNL=QNL/INL**2.;\n", + "XM=XNL-X1;\n", + "\n", + "# Determination of combined friction, windage and core loss\n", + "Ploss=PNL-(INL**2.*R1);\n", + "\n", + "# (b) No-load current as a percent of rated current\n", + "PerINL=INL*100./Irated;\n", + "\n", + "# Display result on command window\n", + "print\"\\n Motor resistance 1 =\",R1,\"Ohm/phase\"\n", + "print\"\\n Motor reactance 1 =\",X1,\"Ohm/phase\"\n", + "print\"\\n Motor resistance 2 = \",R2,\"Ohm/phase\"\n", + "print\"\\n Motor reactance 2 =\",X2,\"Ohm/phase\"\n", + "print\"\\n Reactance of motor =\",XM,\"Ohm/phase\"\n", + "print\"\\n Combined friction, windage and core loss =\",Ploss,\"W/phase\"\n", + "print\"\\n No-load current as a percent of rated current =\",PerINL,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E17 : Pg 223" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Active power of the motor = -9232.86054488 W\n" + ] + } + ], + "source": [ + "# Example 5.17\n", + "# Determine the active power that the motor, driven as an induction generator\n", + "# delivers to the system.\n", + "# Page No. 223\n", + "# Given data\n", + "from math import sqrt,pi,sin,cos\n", + "ns=1200.; # Speed\n", + "nr=1215.;\n", + "R1=0.200; # Motor resistance\n", + "R2=0.250;\n", + "X1=1.20; # Motor reactance\n", + "X2=1.29;\n", + "Rfe=317.; # Field resistance\n", + "XM=42.; # Motor reactance\n", + "V=460.; # Voltage rating\n", + "\n", + "# Active power of the motor computation\n", + "s=(ns-nr)/ns; # Speed difference\n", + "Z2=-20 + 1.29j;#(R2/s)+%i*X2;\n", + "\n", + "# Complex to Polar form...\n", + "Z2_Mag=20.;#sqrt(real(Z2)**2+imag(Z2)**2); # Magnitude part\n", + "Z2_Ang =176.;#atan(imag(Z2),real(Z2))*180/%pi; # Angle part\n", + "\n", + "Z0_Num_Mag=Rfe*XM; # Z0 numerator\n", + "Z0_Num_Ang=0+90; \n", + " \n", + "Z0_Den_R=Rfe; # Z0 denominator\n", + "Z0_Den_I=XM;\n", + "Z0_Den=317 + 42j;#Z0_Den_R+%i*Z0_Den_I;\n", + "# Complex to Polar form...\n", + "Z0_Den_Mag=320.;#sqrt(real(Z0_Den)**2+imag(Z0_Den)**2); # Magnitude part\n", + "Z0_Den_Ang =7.55;#atan(imag(Z0_Den),real(Z0_Den))*180/%pi; # Angle part\n", + "\n", + "Z0_Mag=Z0_Num_Mag/Z0_Den_Mag; # Magnitude of Z0\n", + "Z0_Ang=Z0_Num_Ang-Z0_Den_Ang; # Angle of Z0\n", + "\n", + "# Polar to Complex form\n", + "Z0_R=Z0_Mag*cos(-Z0_Ang*pi/180); # Real part of complex number\n", + "Z0_I=Z0_Mag*sin(Z0_Ang*pi/180); # Imaginary part of complex number\n", + "\n", + "# ZP computation\n", + "ZP_Num_Mag=Z2_Mag*Z0_Mag; # ZP numerator magnitude\n", + "ZP_Num_Ang=Z2_Ang+Z0_Ang; # ZP numerator angle\n", + "\n", + "ZP_Den_R=-14.5;#real(Z2)+Z0_R; # Real part of ZP denominator\n", + "ZP_Den_I=42.6;#imag(Z2)+Z0_I; \n", + "ZP_Den=-14.5 + 42.6j;#ZP_Den_R+%i*ZP_Den_I; # ZP in complex form\n", + "\n", + "# Complex to Polar form...\n", + "ZP_Den_Mag=45.;#sqrt(real(ZP_Den)**2+imag(ZP_Den)**2); # Magnitude part\n", + "ZP_Den_Ang =109.;# atan(imag(ZP_Den),real(ZP_Den))*180/%pi; # Angle part\n", + "\n", + "ZP_Mag=ZP_Num_Mag/ZP_Den_Mag; # Final vlaue of ZP in polar form\n", + "ZP_Ang=ZP_Num_Ang-ZP_Den_Ang;\n", + "# Polar to Complex form\n", + "ZP_R=ZP_Mag*cos(-ZP_Ang*pi/180); # Real part of complex number\n", + "ZP_I=ZP_Mag*sin(ZP_Ang*pi/180); # Imaginary part of complex number\n", + "\n", + "# Zin computation\n", + "ZP=-16.1 + 9.3j;#ZP_R+%i*ZP_I; # Parallel impedance\n", + "Z1=0.2 + 1.2j;#R1+%i*X1;\n", + "Zin=Z1+ZP; # Input impedance\n", + "# Complex to Polar form...\n", + "Zin_Mag=19.;#sqrt(real(Zin)**2+imag(Zin)**2); # Magnitude part\n", + "Zin_Ang =146.;#atan(imag(Zin),real(Zin))*180/%pi; # Angle part\n", + "\n", + "# I1 computation\n", + "I1_Mag=(V/sqrt(3))/Zin_Mag; # I1 magnitude\n", + "I1_Ang=0-Zin_Ang; # I1 angle\n", + "\n", + "# S computation\n", + "S_Mag=3*(V/sqrt(3))*I1_Mag; # S magnitude\n", + "S_Ang=0-(-Zin_Ang); # S angle\n", + "\n", + "# Polar to Complex form\n", + "S_R=S_Mag*cos(-S_Ang*pi/180); # Real part of complex number\n", + "S_I=S_Mag*sin(S_Ang*pi/180); # Imaginary part of complex number\n", + "\n", + "# Display result on command window\n", + "print\"Active power of the motor =\",S_R,\"W\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E18 : Pg 231" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Locked rotor torque = 719.215600351 lb-ft\n", + "\n", + "Expected average in-rush current = 1051.15402271 A\n", + "\n", + "Locked rotor torque when motor is started at reduced voltage = 303.868591148 lb-ft\n", + "\n", + "In-rush line current = 443.95 A\n" + ] + } + ], + "source": [ + "# Example 5.18\n", + "# Computation of (a) Locked rotor torque and the expected average in rush \n", + "# current (b) Repeat part (a) assuming motor is started at reduced voltage \n", + "# with 65% tap (c) In rush line current line current when starting at reduced \n", + "# voltage\n", + "# Page No. 231\n", + "# Given data\n", + "from math import sqrt\n", + "P=125.; # Rated Voltage\n", + "n=1141.; # Speed of machine\n", + "hp=125.; # Horsepower rating of device \n", + "Vline=460.; # Line voltage\n", + "ns=1200.; # Stator speed\n", + "s=0.125; # Slip\n", + "ILS=683.; # Current at low side\n", + "# (a) Locked rotor torque and the expected average in rush current\n", + "Trated=P*5252./(n); # Rated torque\n", + "Tlr=1.25*Trated; # Locked rotor torque\n", + "kVA=(6.3+7.1)/2.;\n", + "Ilr=(kVA*1000.*hp)/(Vline*sqrt(3.)); # In-rush current\n", + "# (b) Locked rotor torque and the expected average in rush current when motor \n", + "# is started at reduced voltage\n", + "V2=0.65*Vline; # Voltage impressed across the stator\n", + "I=Ilr*0.65; # Average in-rush current\n", + "T2=Tlr*(V2/Vline)**2.; # Locked rotor toreque\n", + "nr=ns*(1.-s);\n", + "# (c) In rush line current line current when starting at reduced voltage\n", + "a=1./0.65; # Bank ratio of autotransformer\n", + "IHS=ILS/a;\n", + "# Display result on command window\n", + "print\"\\nLocked rotor torque =\",Tlr,\"lb-ft\"\n", + "print\"\\nExpected average in-rush current =\",Ilr,\"A\"\n", + "print\"\\nLocked rotor torque when motor is started at reduced voltage =\",T2,\"lb-ft\"\n", + "print\"\\nIn-rush line current =\",IHS,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E19 : Pg 233" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Locked rotor current per phase = 485.523078295 A\n", + "\n", + " Minimum locked rotor torque = 84.032 lb-ft\n", + "\n", + " Locked rotor current per phase when motor is delta connected = 1456.56923488 A\n", + "\n", + " Code letter = 19.3418647166\n" + ] + } + ], + "source": [ + "# Example 5.19\n", + "# Computation of (a) Locked rotor current per phase and minimum locked rotor \n", + "# torque when starting (b) Locked rotor current per phase when motor is delta \n", + "# connected (c) Code letter \n", + "# Page No.233\n", + "# Given data\n", + "from math import sqrt\n", + "V=460.; # Rated Voltage\n", + "Z=0.547; # Locked rotor impedance\n", + "n=1750.; # Speed of machine\n", + "hp=60.; # Horsepower rating of device\n", + "f=60.; # Frequency of motor \n", + "# (a) Locked rotor current per phase and minimum locked rotor torque \n", + "Vphase=V/sqrt(3.); # Voltage/phase\n", + "Ilr1=Vphase/Z; # Locked rotor current/phase\n", + "Trated=hp*5252./(n); # Rated torque\n", + "Tlr=1.4*Trated; # Locked rotor torque\n", + "T2=Tlr*(Vphase/V)**2.;\n", + "# (b) Locked rotor current per phase when motor is delta connected \n", + "Ilr=V/Z; # Locked rotor current/phase\n", + "Il=Ilr*sqrt(3.); # Line current\n", + "# (c) Code letter\n", + "Slr=sqrt(3.)*V*Il/1000.; # Code letter at rated voltage\n", + "kVA=Slr/f;\n", + "# Display result on command window\n", + "print\"\\n Locked rotor current per phase =\",Ilr1,\"A\"\n", + "print\"\\n Minimum locked rotor torque =\",T2,\"lb-ft\"\n", + "print\"\\n Locked rotor current per phase when motor is delta connected =\",Il,\"A\"\n", + "print\"\\n Code letter =\",kVA" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E20 : Pg 235" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Resistance of the resistors required = 0.409208864143 Ohm\n", + "\n", + "Stator voltage per phase at locked rotor = 63.882 V\n", + "\n", + "Expected minimum locked rotor torque = 1.5 Trated\n" + ] + } + ], + "source": [ + "# Example 5.20\n", + "# Computation of (a) Resistance of the resistors required to limit the locked \n", + "# rotor current to 3 times rated current (b) Stator voltage per phase at \n", + "# locked rotor (c) Expected minimum locked rotor torque when starting as a \n", + "# percent of rated torque\n", + "# Page No. 235\n", + "# Given data\n", + "from math import sqrt\n", + "Ilr=3.*78.; # Locked rotor current\n", + "Vbranch=132.79; # Branch voltage\n", + "Rlr=0.2549; #Locked rotor resistance\n", + "Xlr=0.0978; #Locked rotor impedance\n", + "f=60.; #Frequency of motor \n", + "Zlr=0.273;\n", + "\n", + "# (a) Resistance of the resistors required to limit the locked rotor current \n", + "# to 3 times rated current\n", + "Rex=sqrt((Vbranch**2./Ilr**2.)-(Rlr**2.))-Xlr;\n", + "\n", + "# (b) Stator voltage per phase at locked rotor \n", + "IZlr=Ilr*Zlr;\n", + "VT1_N=IZlr;\n", + "\n", + "# (c) Expected minimum locked rotor torque when starting as a percent of \n", + "# rated torque\n", + "# From table 5.1 --> Minimum locked rotor torque = 150% rated torque\n", + "\n", + "# Display result on command window\n", + "\n", + "print\"\\nResistance of the resistors required =\",Rex,\"Ohm\"\n", + "print\"\\nStator voltage per phase at locked rotor =\",VT1_N,\"V\"\n", + "print'\\nExpected minimum locked rotor torque = 1.5 Trated'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E21 : Pg 236" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The inductance of each series connected inductor = 4.44444609821 mH\n", + "\n", + "The voltage rating of each series connected inductor = 80.4248018577 V\n" + ] + } + ], + "source": [ + "# Example 5.21\n", + "# Computation of Inductance and voltage rating of each series connected \n", + "# inductor required to limit the starting current to approximately 2*Irated. \n", + "# Page No. 236\n", + "# Given data\n", + "from math import sqrt,pi\n", + "KVA=6.7; # Average locked rotor KVA/hp\n", + "hp=7.5; # Motor horsepower\n", + "Vline=208.; # Line voltage\n", + "I=48.; # Total current\n", + "Rlr=0.294; # Locked rotor resistance\n", + "Xlr=0.809; # Locked rotor impedance\n", + "f=60.; # Frequency of motor\n", + "\n", + "# Corresponding approximate load current\n", + "Ilr=KVA*1000.*hp/(sqrt(3.)*Vline); \n", + "Vphase=Vline/sqrt(3.); # Voltage/phase\n", + "\n", + "# Applying ohm's law to one phase\n", + "Zlr=Vphase/Ilr; # Impedance\n", + "Xex=sqrt((Vphase**2./I**2.)-(Rlr**2.))-Xlr;\n", + "L=Xex/(2.*pi*f);\n", + "L=L*10.**03;\n", + "VXl=I*Xex;\n", + "\n", + "# Display result on command window\n", + "print\"\\nThe inductance of each series connected inductor =\",L,\"mH\"\n", + "print\"\\nThe voltage rating of each series connected inductor =\",VXl,\"V\"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER06.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER06.ipynb new file mode 100644 index 00000000..91939ce1 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER06.ipynb @@ -0,0 +1,350 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER06 : SINGLE PHASE INDUCTION MOTORS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 257" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Main winding current magnitude = 29.8 A\n", + "\n", + " Main winding current angle = -60.3 deg\n", + "\n", + " Auxillary winding current magnitude = 9.66 A\n", + "\n", + " Auxillary winding current angle = -42.6 deg\n", + "\n", + " Phase displacement angle = 17.7 deg\n", + "\n", + " Locked rotor torque in terms of the machine constant = 87.4 .Ksp\n", + "\n", + " External resistance required = 5.25 Ohm\n", + "\n", + " Locked rotor torque = 22.5 .Ksp\n", + "\n", + " Percent increase in locked rotor torque = -74.2562929062 Percent increase\n" + ] + } + ], + "source": [ + "# Example 6.1\n", + "# Determine (a) Locked rotor current in each winding (b) Phase displacement\n", + "# angle between the two currents (c) Locked rotor torque in terms of the\n", + "# machine constant (d) External resistance required in series with the auxillary\n", + "# winding in order to obtain a 30 degree phase displacement between the currents\n", + "# in the two windings (e) Locked rotor torque for the conditions in (d) \n", + "# (f) Percent increase in locked rotor torque due to the addition of external\n", + "# resistance \n", + "# Page No. 257\n", + "# Given data\n", + "Zmw=2.00+1j*3.50 # Main winding impedance\n", + "Zaw=9.15+1j*8.40 # Auxillary winding impedance\n", + "VT=120.; # Transformer voltage\n", + "Xaw=8.40; # Auxillary winding reactance\n", + "Raw=9.15; # Auxillary winding resistance\n", + "# (a) Locked rotor current in each winding\n", + "# Main winding impedance in polar form\n", + "# Complex to Polar form...\n", + "Zmw_Mag=4.03;#sqrt(real(Zmw)**2+imag(Zmw)**2); # Magnitude part\n", + "Zmw_Ang=60.3;#atan(imag(Zmw),real(Zmw))*180/%pi; # Angle part\n", + "\n", + "# Auxillary winding impedance in polar form\n", + "# Complex to Polar form...\n", + "Zaw_Mag=12.4;#sqrt(real(Zaw)**2+imag(Zaw)**2); # Magnitude part\n", + "Zaw_Ang=42.6;#atan(imag(Zaw),real(Zaw))*180/%pi; # Angle part\n", + "\n", + "# Main winding current\n", + "Imw_Mag=29.8;#VT/Zmw_Mag; # Main winding current magnitude\n", + "Imw_Ang=-60.3;#0-Zmw_Ang; # Main winding current angle\n", + "\n", + "# Auxillary winding current\n", + "Iaw_Mag=9.66;#VT/Zaw_Mag; # Auxillary winding current magnitude\n", + "Iaw_Ang=-42.6;#0-Zaw_Ang; # Auxillary winding current angle\n", + "\n", + "# (b) Phase displacement angle between the two currents\n", + "Alpha=17.7;#abs(Imw_Ang-Iaw_Ang);\n", + "\n", + "# (c) Locked rotor torque in terms of the machine constant \n", + "Tlr=87.4;#Imw_Mag*Iaw_Mag*sind(Alpha);\n", + "\n", + "# (d) External resistance required in seris with the auxillary winding in \n", + "# order to obtain a 30 degree phase displacement between the currents in the\n", + "# two windings \n", + "Theta_awi=-30.3;#Imw_Ang+30; # Required phase angle\n", + "Theta_awz=30.3;#-Theta_awi;\n", + "Rx=5.25;#(Xaw/tand(Theta_awz))-Raw;\n", + "\n", + "# (e) Locked rotor torque for the conditions in (d)\n", + "Zawnew=14.4 + 8.4j;#Raw+Rx+1j*Xaw; # Auxillary winding impedance\n", + "# Complex to Polar form...\n", + "Zmwnew_Mag=16.7;#sqrt(real(Zawnew)**2+imag(Zawnew)**2); # Magnitude part\n", + "Zmwnew_Ang=30.3;#atan(imag(Zawnew),real(Zawnew))*180/%pi; # Angle part\n", + "\n", + "Iawnew_Mag=7.2;#VT/Zmwnew_Mag; # Auxillary winding current magnitude\n", + "Iawnew_Ang=-30.3;#0-Zmwnew_Ang; # Auxillary winding current magnitude\n", + "Tlenew=22.5;#107;#Imw_Mag*Iawnew_Mag*sind(30);\n", + "\n", + "# (f) Percent increase in locked rotor torque due to the addition of external\n", + "# resistance\n", + "PI=(Tlenew-Tlr)/Tlr*100.;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\n Main winding current magnitude =\",Imw_Mag,\"A\"\n", + "print\"\\n Main winding current angle =\",Imw_Ang,\"deg\"\n", + "print\"\\n Auxillary winding current magnitude =\",Iaw_Mag,\"A\"\n", + "print\"\\n Auxillary winding current angle =\",Iaw_Ang,\"deg\"\n", + "print\"\\n Phase displacement angle =\",Alpha,\"deg\"\n", + "print\"\\n Locked rotor torque in terms of the machine constant =\",Tlr,\".Ksp\"\n", + "print\"\\n External resistance required =\",Rx,\"Ohm\"\n", + "print\"\\n Locked rotor torque =\",Tlenew,\".Ksp\"\n", + "print\"\\n Percent increase in locked rotor torque =\",PI,\"Percent increase\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 265" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Required capacitance = 1281.76980266 microF\n", + "\n", + " Percent increase in locked rotor torque = 216.526610644 Percent\n" + ] + } + ], + "source": [ + "# Example 6.2\n", + "# Determine (a) Capacitance required in series with the auxillary winding \n", + "# in order to obtain a 90 degree phase displacement between the current in \n", + "# the main winding and the current in the auxillary winding at locked rotor \n", + "# (b) Locked rotor torque in terms of the machine constant \n", + "# Page No. 265\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Zmw=2.00+1j*3.50 # Main winding impedance\n", + "Zaw=9.15+1j*8.40 # Auxillary winding impedance\n", + "VT=120.; # Transformer voltage\n", + "Xaw=8.40; # Auxillary winding reactance\n", + "Raw=9.15; # Auxillary winding resistance\n", + "f=60.; # Frequency\n", + "Tlr=107.1; # Original torque\n", + "\n", + "# (a) Capacitance required in series with the auxillary winding \n", + "# Main winding impedance in polar form\n", + "# Complex to Polar form...\n", + "Zmw_Mag=4.03;#sqrt(real(Zmw)**2.+imag(Zmw)**2.); # Magnitude part\n", + "Zmw_Ang=60.3;#atan(imag(Zmw),real(Zmw))*180./pi; # Angle part\n", + "\n", + "# Auxillary winding impedance in polar form\n", + "# Complex to Polar form...\n", + "Zaw_Mag=12.4;#sqrt(real(Zaw)**2.+imag(Zaw)**2.); # Magnitude part\n", + "Zaw_Ang=42.6;#atan(imag(Zaw),real(Zaw))*180/pi; # Angle part\n", + "\n", + "# Main winding current\n", + "Imw_Mag=29.8;#VT/Zmw_Mag; # Main winding current magnitude\n", + "Imw_Ang=-60.3;#0-Zmw_Ang; # Main winding current angle\n", + "\n", + "# Auxillary winding current\n", + "Iaw_Mag=9.66;#VT/Zaw_Mag; # Auxillary winding current magnitude\n", + "Iaw_Ang=-42.6;#0-Zaw_Ang; # Auxillary winding current angle\n", + "\n", + "Theta_awi=90-60.26; # Required phase angle\n", + "Theta_awz=-Theta_awi;\n", + "\n", + "Xc=13.6;#Xaw-Raw*tand(Theta_awz); # Capacitive reactance\n", + "\n", + "C=1./2.*pi*f*Xc; # Required capacitance\n", + "\n", + "\n", + "# (b) Locked rotor torque in terms of the machine constant \n", + "Zawnew=9.15 + -5.23j;#Raw+1j*Xaw-1j*Xc; # Auxillary winding impedance\n", + "# Complex to Polar form...\n", + "Zawnew_Mag=10.5;#sqrt(real(Zawnew)**2+imag(Zawnew)**2); # Magnitude part\n", + "Zawnew_Ang=-29.7;#atan(imag(Zawnew),real(Zawnew))*180/%pi; # Angle part\n", + "\n", + "Iawnew_Mag=11.4;#VT/Zawnew_Mag; # Auxillary winding current magnitude\n", + "Iawnew_Ang=29.7;#0-Zawnew_Ang; # Auxillary winding current magnitude\n", + "\n", + "Tlenew=339.;#Imw_Mag*Iawnew_Mag*sind(90);\n", + "\n", + "# Percent change increase in locked rotor torque \n", + "PI=(Tlenew-Tlr)/Tlr*100;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\n Required capacitance =\",C,\"microF\"\n", + "print\"\\n Percent increase in locked rotor torque =\",PI,\"Percent\"\n", + "\n", + "#Note: Capacitor computation is wrong in the book" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 271" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " NEMA standard horsepower rating of machine = 52.5 hp\n", + "\n", + " Required running capacitance = 1590.0 microF\n", + "\n", + " Additional capacitance required for starting = 12210.0 microF\n" + ] + } + ], + "source": [ + "# Example 6.3\n", + "# Determine (a) NEMA standard horsepower rating of machine (b) Required \n", + "# running capacitance (c) Additional capacitance required for starting\n", + "# Page No. 271\n", + "# Given data\n", + "hp=35.; # Power in hp\n", + "p=3.; # Number of phase\n", + "f=60.; # Frequency\n", + "# (a) NEMA standard horsepower rating of machine\n", + "Prated3ph=hp*p/2.;\n", + "# (b)Required running capacitance\n", + "C1=26.5*f;\n", + "# (c) Additional capacitance required for starting.\n", + "C2=230.*f-C1;\n", + "# Display result on command window\n", + "print\"\\n NEMA standard horsepower rating of machine =\",Prated3ph,\"hp\"\n", + "print\"\\n Required running capacitance =\",C1,\"microF\"\n", + "print\"\\n Additional capacitance required for starting =\",C2,\"microF\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 274" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Motor line current = 41.4829962669 A\n", + "\n", + " Motor phase current = 41.4829962669 A\n", + "\n", + " Motor line current if one line opens = 71.8506571845 A\n", + "\n", + " Motor phase current if one line opens = 71.8506571845 A\n", + "\n", + " Line current if the power factor is 82.0 percent = 73.9536032484 A\n", + "\n", + " Phase current if the power factor is 82.0 percent = 73.9536032484 A\n" + ] + } + ], + "source": [ + "# Example 6.4\n", + "# Computation of (a) Motor line current and motor phase current (b) Motor line \n", + "# current and motor phase current if one line opens (c) Line and phase \n", + "# currents if the power factor when single phasing is 82.0 percent.\n", + "# Page No. 274\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Vline=2300.; # Line voltage\n", + "Fp3ph=3.; # Frequency of three phase\n", + "PF=0.844; # Power factor\n", + "PF1=0.820; # 82.2 percent power factor\n", + "Pin=350.*746./(0.936*2); # Input power\n", + "# (a) Motor line current and motor phase current\n", + "Iline3ph=Pin/(sqrt(3)*Vline*PF);\n", + "Iphase3ph=Iline3ph;\n", + "#(b) Motor line current and motor phase current if one line opens\n", + "Iline1ph=(sqrt(3)*Iline3ph*PF)/PF;\n", + "Iphase1ph=Iline1ph;\n", + "# (c) Line and phase currents if the power factoe when single phasing is 82.0 percent.\n", + "Iline=(Iline1ph*PF)/PF1;\n", + "Iphase=Iline;\n", + "# Display result on command window\n", + "print\"\\n Motor line current =\",Iline3ph,\"A\"\n", + "print\"\\n Motor phase current =\",Iphase3ph,\"A\"\n", + "print\"\\n Motor line current if one line opens =\",Iline1ph,\"A\"\n", + "print\"\\n Motor phase current if one line opens =\",Iphase1ph,\"A\"\n", + "print\"\\n Line current if the power factor is 82.0 percent =\",Iline,\"A\"\n", + "print\"\\n Phase current if the power factor is 82.0 percent =\",Iphase,\"A\"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER07.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER07.ipynb new file mode 100644 index 00000000..dc70cc29 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER07.ipynb @@ -0,0 +1,174 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER07 : SPECIALITY MACHINES " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 282" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Torque load on the shaft = 29.1777777778 lb-ft \n", + "\n", + " Torque angle if the voltage drops to 224V = 41.9 deg\n", + "\n", + " Because torque angle is less than 45 degree, \n", + " the rotor will not pull out of synchronism \n" + ] + } + ], + "source": [ + "# Example 7.1\n", + "# Determine (a) Torque load on the shaft (b) Torque angle if the voltage \n", + "# drops to 224V (c) Will the rotor pull out of synchronism?\n", + "# Page No. 282\n", + "# Given data\n", + "f=60.; # Frequency\n", + "P=4.; # Number of poles\n", + "Pshaft=10.; # Shaft power in hp\n", + "V1=240.; # Rated voltage\n", + "V2=224.; # New voltage\n", + "phirel1=30.; # Torque angle\n", + "# (a) Torque load on the shaft\n", + "ns=120.*f/P; # speed of machine\n", + "Trel=Pshaft*5252./ns;\n", + "# (b) Torque angle if the voltage drops to 224V\n", + "phirel2=41.9;#asind((V1**2./V2**2.)*sind(2.*phirel1))/2.\n", + "# Display result on command window\n", + "print\"\\n Torque load on the shaft =\",Trel,\"lb-ft \"\n", + "print\"\\n Torque angle if the voltage drops to 224V =\",phirel2,\"deg\"\n", + "print\"\\n Because torque angle is less than 45 degree, \\n the rotor will not pull out of synchronism \"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 287" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Resolution = 180.0\n", + "\n", + " Number of steps required for the rotor to make 20.6 revolutions = 3708.0\n", + "\n", + " Shaft speed if the stepping frequency is 1800 pulses/s = 10.0 r/s\n" + ] + } + ], + "source": [ + "# Example 7.2\n", + "# Determine (a) Resolution (b) Number of steps required for the rotor to make \n", + "# 20.6 revolutions (c) Shaft speed if the stepping frequency is 1800 pulses/s\n", + "# Page No. 287\n", + "# Given data\n", + "betaa=2.; # Step angle\n", + "theta=20.6; # Number of revolutions\n", + "fp=1800.; # Stepping frequency\n", + "# (a) Resolution\n", + "stepsperrev=360./betaa; # Speed of machine\n", + "# (b) Number of steps required for the rotor to make 20.6 revolutions\n", + "steps=theta*360./betaa;\n", + "# (c) Shaft speed if the stepping frequency is 1800 pulses/s.\n", + "n=betaa*fp/360.;\n", + "# Display result on command window\n", + "print\"\\n Resolution =\",stepsperrev\n", + "print\"\\n Number of steps required for the rotor to make 20.6 revolutions =\",steps\n", + "print\"\\n Shaft speed if the stepping frequency is 1800 pulses/s =\",n,\"r/s\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 299" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The synchronous speed = 24.0 m/s\n", + "\n", + "Rail speed assuming slip of 16.7 percent = 19.992 m/s\n" + ] + } + ], + "source": [ + "# Example 7.3\n", + "# Determine (a) Synchronous speed (b) Rail speed assuming slip of 16.7%\n", + "# Page No. 299\n", + "# Given data\n", + "f=50.; # Frequency of machine\n", + "tau=0.24; # Pole pitch\n", + "s=0.167; # Slip\n", + "# (a) The synchronous speed \n", + "Us=2*tau*f;\n", + "# (b) Rail speed assuming slip of 16.7 percent\n", + "U=Us*(1-s);\n", + "# Display result on command window\n", + "print\"\\nThe synchronous speed =\",Us,\"m/s\"\n", + "print\"\\nRail speed assuming slip of 16.7 percent =\",U,\"m/s\"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER08.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER08.ipynb new file mode 100644 index 00000000..adecb6cf --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER08.ipynb @@ -0,0 +1,405 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER08 : SYNCHRONOUS MOTORS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 317" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Developed torque = 303.935185185 lb-ft\n", + "\n", + "Armature current magnitude= 122.0 A\n", + "\n", + "Armature current angle= -36.9 deg\n", + "\n", + "Excitation voltage magnitude = 535.0 V\n", + "\n", + "Excitation voltage angle = -29.7 deg\n", + "\n", + "Power angle = -29.7 deg\n", + "\n", + "Maximum torque = 614.063151623 lb-ft\n" + ] + } + ], + "source": [ + "# Example 8.1\n", + "# Determine (a) Developed torque (b) Armature current (c) Excitation voltage\n", + "# (d) Power angle (e) Maximum torque \n", + "# Page No. 317\n", + "# Given data\n", + "from math import sqrt,pi\n", + "f=60.; # Operating frequency\n", + "P=4.; # Number of poles\n", + "Pmech=100.; # Mechanical power\n", + "eta=0.96; # Efficiency\n", + "FP=0.80; # Power factor leading\n", + "V=460.; # Motor voltage\n", + "Xs_Mag=2.72; # Synchronous reactnace magnitude\n", + "Xs_Ang=90.; # Synchronous reactnace magnitude\n", + "deltaPull=-90.; # Pullout power angle\n", + "# (a) Developed torque\n", + "ns=120.*f/P; # Synchronous speed\n", + "Td=5252.*Pmech/(ns*eta); \n", + "\n", + "\n", + "# (b) Armature current\n", + "S=Pmech*746./(eta*FP);\n", + "Theta=-36.9;#-acosd(FP); # Power factor angle (negative as FP is leading)\n", + "V1phi=V/sqrt(3.); # Single line voltage\n", + "S1phi_Mag=S/3.; # Magnitude \n", + "S1phi_Ang=Theta; # Angle\n", + "VT_Mag=V1phi;\n", + "VT_Ang=0;\n", + "Ia_Mag=122.;#S1phi_Mag/VT_Mag; # Armature current magnitude\n", + "Ia_Ang=36.9;#S1phi_Ang-VT_Ang; # Armature current angle\n", + "Ia_Ang=-Ia_Ang; # Complex conjugate of Ia\n", + "# (c) Excitation voltage\n", + "Var1_Mag=Ia_Mag*Xs_Mag;\n", + "Var1_Ang=Ia_Ang+Xs_Ang;\n", + "\n", + "####/\n", + "N01=266 + 0j;#VT_Mag+1j*VT_Ang;\n", + "N02=332 + 127j;#Var1_Mag+1j*Var1_Ang;\n", + "# Polar to Complex form\n", + "\n", + "N01_R=266.;#VT_Mag*cos(-VT_Ang*%pi/180); # Real part of complex number 1\n", + "N01_I=0;#VT_Mag*sin(VT_Ang*%pi/180); #Imaginary part of complex number 1\n", + "\n", + "N02_R=-199.;#Var1_Mag*cos(-Var1_Ang*%pi/180); # Real part of complex number 2\n", + "N02_I=265.;#Var1_Mag*sin(Var1_Ang*%pi/180); #Imaginary part of complex number 2\n", + "\n", + "FinalNo_R=N01_R-N02_R;\n", + "FinalNo_I=N01_I-N02_I;\n", + "FinNum=465 + -265j;#FinalNo_R+1j*FinalNo_I;\n", + "# Complex to Polar form...\n", + "FN_M=535.;#sqrt(real(FinNum)**2+imag(FinNum)**2); # Magnitude part\n", + "FN_A =-29.7;# atan(imag(FinNum),real(FinNum))*180/%pi;# Angle part\n", + "###\n", + "Ef_Mag=FN_M;\n", + "Ef_Ang=FN_A;\n", + "# (d) Power angle\n", + "delta=Ef_Ang;\n", + "# (e) Maximum torque \n", + "Pin=1.57*10**05;#3.*(-VT_Mag*Ef_Mag/Xs_Mag)*sind(deltaPull); # Active power input\n", + "Tpull=5252.*Pin/(746.*ns);\n", + "# Display result on command window\n", + "print\"\\nDeveloped torque =\",Td,\"lb-ft\"\n", + "print\"\\nArmature current magnitude=\",Ia_Mag,\"A\"\n", + "print\"\\nArmature current angle=\",Ia_Ang,\"deg\"\n", + "print\"\\nExcitation voltage magnitude =\",Ef_Mag,\"V\"\n", + "print\"\\nExcitation voltage angle =\",Ef_Ang,\"deg\"\n", + "print\"\\nPower angle =\",delta,\"deg\"\n", + "print\"\\nMaximum torque =\",Tpull,\"lb-ft\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 322" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "The minimum value of excitation = 98.0 V\n", + "\n", + "The minimum value of excitation using eq.(8.16) = 99.5 V\n", + "\n", + "The minimum value of excitation using eq.(8.21) = 99.4533076428 V\n", + "\n", + "Power angle = -34.8 deg\n" + ] + } + ], + "source": [ + "# Example 8.2\n", + "# Determine (a) The minimum value of excitation that will maintain \n", + "# synchronism (b) Repeat (a) using eq.(8.16) (c) Repeat (a) using eq.(8.21)\n", + "# (d) Power angle if the field excitation voltage is increased to 175% of the\n", + "# stability limit determined in (c)\n", + "# Page No. 322\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Pin=40.; # Input power\n", + "Pin1phase=40./3.; # Single phase power\n", + "Xs=1.27; # Synchronous reactnace \n", + "VT=220./sqrt(3.); # Voltage\n", + "delta=-90.; # Power angle\n", + "\n", + "f=60.; # Operating frequency\n", + "P=4.; # Number of poles\n", + "Pmech=100.; # Mechanical power\n", + "eta=0.96; # Efficiency\n", + "FP=0.80; # Power factor leading\n", + "V=460.; # Motor voltage\n", + "Xs_Mag=2.72; # Synchronous reactnace magnitude\n", + "Xs_Ang=90.; # Synchronous reactnace magnitude\n", + "deltaPull=-90.; # Pullout power angle\n", + "\n", + "# (a) The minimum value of excitation that will maintain synchronism\n", + "Ef=98.; # From the graph (Figure 8.13)\n", + "\n", + "# (b) The minimum value of excitation using eq.(8.16)\n", + "Ef816=99.5;#-Pin*Xs*746/(3*VT*sind(delta));\n", + "\n", + "\n", + "# (c) The minimum value of excitation using eq.(8.21)\n", + "Ef821=Xs*Pin1phase*746/(VT);\n", + "\n", + "# (d) Power angle if the field excitation voltage is increased to 175%\n", + "#delta2=Ef816*sind(delta)/(1.75*Ef816);\n", + "delta2=-34.8;#asind(delta2);\n", + "\n", + "# Display result on command window\n", + "print\"\\nThe minimum value of excitation =\",Ef,\"V\"\n", + "print\"\\nThe minimum value of excitation using eq.(8.16) =\",Ef816,\"V\"\n", + "print\"\\nThe minimum value of excitation using eq.(8.21) =\",Ef821,\"V\"\n", + "print\"\\nPower angle =\",delta2,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 324" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "System active power = 400.174191023 kW\n", + "\n", + "Power factor of the synchronous motor = 0.828 leading\n", + "\n", + "System power factor = 0.995 lagging\n", + "\n", + "Percent change in synchronous field current = 9.24855491329 Percent\n", + "\n", + "Power angle of the synchronous motor = -15 deg\n" + ] + } + ], + "source": [ + "# Example 8.3\n", + "# Determine (a) System active power (b) Power factor of the synchronous motor\n", + "# (c) System power factor (d) Percent change in synchronous field current \n", + "# required to adjust the system power factor to unity (e) Power angle of the \n", + "# synchronous motor for the conditions in (d) \n", + "# Page No. 324\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Php=400.; # Power in hp\n", + "eta=0.958; # Efficiency\n", + "Pheater=50000.; # Resistance heater power \n", + "Vs=300.; # Synchronous motor voltage\n", + "eta2=0.96; # Synchronous motor efficiency\n", + "Xs=0.667; # Synchronous reactnace\n", + "VT=460.; # 3-Phase supply voltage\n", + "delta=-16.4; # Power angle\n", + "# (a) System active power \n", + "Pindmot=Php*0.75*746./(eta); # Motor operating at three quarter rated load\n", + "Psynmot=Vs*0.5*746./(eta2); # Synchronous motor power \n", + "Psys=Pindmot+Pheater+Psynmot;\n", + "Psysk=Psys/1000.;\n", + "# (b) Power factor of the synchronous motor\n", + "Pin=Psynmot; # Power input\n", + "Vtph=VT/sqrt(3); # Voltage per phase\n", + "Ef=346.;#-(Pin*Xs)/(3*Vtph*sind(delta));\n", + "# Complex to Polar form...\n", + "Ef_Mag=Ef; # Magnitude part \n", + "Ef_Ang=delta; # Angle part\n", + "Vtph_Mag=Vtph; \n", + "Vtph_Ang=0;\n", + "######\n", + "N01=346 + -16.4j;#Ef_Mag+1j*Ef_Ang; # Ef in polar form \n", + "N02=266 + 0j;#Vtph_Mag+1j*Vtph_Ang; # Vt in polar for\n", + "\n", + "N01_R=332.;#Ef_Mag*cos(-Ef_Ang*%pi/180); # Real part of complex number Ef\n", + "N01_I=-97.6;#Ef_Mag*sin(Ef_Ang*%pi/180); #Imaginary part of complex number Ef\n", + "\n", + "N02_R=266.;#Vtph_Mag*cos(-Vtph_Ang*%pi/180); # Real part of complex number Vt\n", + "N02_I=0;#Vtph_Mag*sin(Vtph_Ang*%pi/180); #Imaginary part of complex number Vt\n", + "FinalNo_R=N01_R-N02_R;\n", + "FinalNo_I=N01_I-N02_I;\n", + "FinNum=66 + -97.6j;#FinalNo_R+1j*FinalNo_I;\n", + "# Complex to Polar form...\n", + "FN_M=118.;#sqrt(real(FinNum)**2+imag(FinNum)**2); # Magnitude part\n", + "FN_A =-55.9;#tan(imag(FinNum),real(FinNum))*180/%pi;# Angle part\n", + "Ia_Mag=FN_M/Xs; # Magnitude of Ia\n", + "Ia_Ang=FN_A-(-90); # Angle of Ia\n", + "Theta=0-Ia_Ang;\n", + "FP=0.828;#cosd(Theta); # Power factor\n", + "# (c) System power factor\n", + "ThetaIndMot=27.;#acosd(0.891); # Induction motor power factor\n", + "Thetaheat=0;#acosd(1); # Heater power factor\n", + "ThetaSyncMot=-34.06; # Synchronous motor power factor\n", + "Qindmot=1.19*10**05;#tand(27)*Pindmot; \n", + "Qsynmot=-7.88*10**04;#tand(ThetaSyncMot)*Psynmot;\n", + "Qsys=Qindmot+Qsynmot;\n", + "Ssys=Psys+1j*Qsys; # System variable in complex form\n", + "# Complex to Polar form...\n", + "Ssys_Mag=4.02*10**05;#sqrt(real(Ssys)**2+imag(Ssys)**2); # Magnitude part\n", + "Ssys_Ang =5.74;# atan(imag(Ssys),real(Ssys))*180/%pi; # Angle part\n", + "FPsys=0.995;#cosd(Ssys_Ang); # System power factor \n", + "# (d) Percent change in synchronous field current required to adjust the \n", + "# system power factor to unity\n", + "Ssynmot=Psynmot-(1j*(-Qsynmot+Qsys)); # Synchronous motor system\n", + "# Complex to Polar form...\n", + "Ssynmot_Mag=1.67e+05;#sqrt(real(Ssynmot)**2+imag(Ssynmot)**2); # Magnitude part\n", + "Ssynmot_Ang=-45.6;#atan(imag(Ssynmot),real(Ssynmot))*180/%pi; # Angle part\n", + "Ssynmot1ph_Mag=5.55e+04;#Ssynmot_Mag/3; # For single phase magnitude\n", + "Ssynmot1ph_Ang=-45.6;#Ssynmot_Ang; # For single phase angle\n", + "Iastar_Mag=209.;#Ssynmot1ph_Mag/Vtph; # Current magnitude\n", + "Iastar_Ang=-45.6;#Ssynmot1ph_Ang-0; # Current angle\n", + "IaNew_Mag=209.;#Iastar_Mag;\n", + "IaNew_Ang=45.6;#-Iastar_Ang;\n", + "IaXs_Mag=IaNew_Mag*Xs;\n", + "IaXs_Ang=IaNew_Ang-90;\n", + "# Convert these number into complex and then perform addition\n", + "# Polar to Complex form\n", + "# Y=29.416<-62.3043 #Polar form number\n", + "IaXs_R=99.6;#IaXs_Mag*cos(-IaXs_Ang*%pi/180); # Real part of complex number\n", + "IaXs_I=-97.6;#IaXs_Mag*sin(IaXs_Ang*%pi/180); # Imaginary part of complex number\n", + "Efnew=Vtph+IaXs_R+1j*IaXs_I;\n", + "# Complex to Polar form...\n", + "\n", + "Efnew_Mag=378.;#sqrt(real(Efnew)**2+imag(Efnew)**2); # Magnitude part\n", + "Efnew_Ang=-15;#atan(imag(Efnew),real(Efnew))*180/%pi; # Angle part\n", + "\n", + "DeltaEf=(Efnew_Mag-Ef)/Ef; \n", + "\n", + "# (e) Power angle of the synchronous motor\n", + "deltasynmot=Efnew_Ang;\n", + "\n", + "# Display result on command window\n", + "print\"\\nSystem active power =\",Psysk,\"kW\"\n", + "print\"\\nPower factor of the synchronous motor =\",FP,\"leading\"\n", + "print\"\\nSystem power factor =\",FPsys,\"lagging\"\n", + "print\"\\nPercent change in synchronous field current =\",DeltaEf*100,\"Percent\"\n", + "print\"\\nPower angle of the synchronous motor =\",deltasynmot,\"deg\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 328" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Developed torque = 887.004444444 lb-ft\n", + "\n", + "Developed torque in percent of rated torque = 164.27613941 Percent\n" + ] + } + ], + "source": [ + "# Example 8.4\n", + "# Determine (a) Developed torque if the field current is adjusted so that the\n", + "# excitation voltage is equal to two times the applied stator voltage, and the\n", + "# power angle is -18 degrees (b) Developed torque in percent of rated torque, \n", + "# if the load is increased until maximum reluctance torque occurs.\n", + "# Page No. 328\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Vt1ph=2300./sqrt(3.); # Applied voltage/phase\n", + "Ef1ph=2300./sqrt(3.); # Excitation voltage/phase\n", + "Xd=36.66; # Direct axis reactance/phase\n", + "delta=-18.; # Power angle\n", + "Xq=23.33; # Quadrature-axis reactance/phase\n", + "n=900.; # Speed of motor\n", + "deltanew=-45.;\n", + "RatTor=200.; # Rated torque of motor\n", + "# (a) Developed torque\n", + "Pmag1ph=2.97e+04;#-((Vt1ph*2.*Ef1ph)/Xd)*sind(delta); # Power \n", + "Prel1ph=8.08e+03;#-Vt1ph**2.*( (Xd-Xq) / (2.*Xd*Xq)) *sind(2.*delta); # Reluctance power\n", + "Psal3ph=1.13e+05;#3*(Pmag1ph+Prel1ph); # Salient power of motor\n", + "Psal3phHP=152.;#Psal3ph/746;\n", + "T=(5252*Psal3phHP)/n; # Developed torque\n", + "# (b) Developed torque in percent of rated torque\n", + "# The reluctance torque has its maximum value at delta= -45 degrees\n", + "Pmag1phnew=6.8e+04;#-((Vt1ph*2*Ef1ph)/Xd)*sind(deltanew); # Power\n", + "Prel1phnew=1.37e+04;#-Vt1ph**2*( (Xd-Xq) / (2*Xd*Xq)) *sind(2*deltanew); # Reluctance power\n", + "Psal3phnew=3*(Pmag1phnew+Prel1phnew); # Salient power of motor\n", + "Psal3phHPnew=Psal3phnew/746;\n", + "PerRatTorq=Psal3phHPnew*100/RatTor;\n", + "# Display result on command window\n", + "print\"\\nDeveloped torque =\",T,\"lb-ft\"\n", + "print\"\\nDeveloped torque in percent of rated torque =\",PerRatTorq,\"Percent\"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER09.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER09.ipynb new file mode 100644 index 00000000..2315abd4 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER09.ipynb @@ -0,0 +1,782 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER09 : SYNCHRONOUS GENERATORS " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 342" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Turbine torque supplied to the alternator = 219.028894847 lb-ft\n", + "\n", + " Excitation voltage = 419.0 V/phase\n", + "\n", + " Active components of apparent power= 112.0 kW\n", + "\n", + " Reactive components of apparent power= 72.2 kvar lagging\n", + "\n", + " Power factor = 0.84 lagging\n", + "\n", + " Excitation voltage new = 356.15 V/phase\n", + "\n", + " Turbine speed = 3600.0 r/min\n" + ] + } + ], + "source": [ + "# Example 9.1\n", + "# Determine (a) Turbine torque supplied to the alternator (b) Excitation \n", + "# voltage (c) Active and reactive components of apparent power (d) Power \n", + "# factor (e) Neglecting saturation effects, excitation voltage if the field \n", + "# current is reduced to 85% of its voltage in (a) (f) Turbine speed.\n", + "# Page No. 342\n", + "# Given data\n", + "from math import sqrt,pi\n", + "hp=112000.; # Power input\n", + "n=746.*3600.; # Speed\n", + "VT=460.; # 3-Phase supply voltage\n", + "Pout=112000.; # Power\n", + "Xs=1.26; # Synchronous reactnace\n", + "delta=25.; # Power angle\n", + "eta=0.85; # Percent reduction factor\n", + "P=2.; # Number of poles\n", + "f=60.; # Frequnecy\n", + "# (a) Turbine torque supplied to the alternator\n", + "T=(hp*5252.)/n;\n", + "# (b) Excitation voltage\n", + "Vt=VT/sqrt(3); # Voltage/phase\n", + "Ef=419.;#(Pout*Xs)/(3*Vt*sind(delta));\n", + "# (c) Active and reactive components of apparent power\n", + "# Vt=Ef-Ia*j*Xs\n", + "# Solving for Vt-Ef\n", + "Vt_Mag=Vt;\n", + "Vt_Ang=0;\n", + "Ef_Mag=Ef;\n", + "Ef_Ang=delta;\n", + "# \n", + "N01=419 + 25j;#Ef_Mag+1j*Ef_Ang; # Ef in polar form \n", + "N02=266 + 0j;#Vt_Mag+1j*Vt_Ang; # Vt in polar for\n", + "\n", + "N01_R=380.;#Ef_Mag*cos(-Ef_Ang*%pi/180); # Real part of complex number Ef\n", + "N01_I=177.;#Ef_Mag*sin(Ef_Ang*%pi/180); #Imaginary part of complex number Ef\n", + "\n", + "N02_R=266.;#Vt_Mag*cos(-Vt_Ang*%pi/180); # Real part of complex number Vt\n", + "N02_I=0;#Vt_Mag*sin(Vt_Ang*%pi/180); #Imaginary part of complex number Vt\n", + "\n", + "FinalNo_R=N01_R-N02_R;\n", + "FinalNo_I=N01_I-N02_I;\n", + "FinNum=FinalNo_R+1j*FinalNo_I;\n", + "\n", + "# Now FinNum/Xs in polar form\n", + "FinNum_Mag=211.;#sqrt(real(FinNum)**2+imag(FinNum)**2); # Magnitude part\n", + "FinNum_Ang =57.2;# atan(imag(FinNum),real(FinNum))*180/%pi; # Angle part\n", + "Ia_Mag=FinNum_Mag/Xs;\n", + "Ia_Ang=FinNum_Ang-90;\n", + "\n", + "# Computation of S=3*Vt*Ia*\n", + "S_Mag=3*Vt_Mag*Ia_Mag;\n", + "S_Ang=Vt_Ang+-Ia_Ang;\n", + "\n", + "# Polar to complex form\n", + "S_R=1.12e+05;#S_Mag*cos(-S_Ang*%pi/180); # Real part of complex number S\n", + "S_I=7.22e+04;#S_Mag*sin(S_Ang*%pi/180); # Imaginary part of complex number S\n", + "\n", + "# (d) Power factor\n", + "Fp=0.84;#cosd(Ia_Ang);\n", + "\n", + "# (e) Excitation voltage\n", + "Efnew=eta*Ef_Mag;\n", + "\n", + "# (f) Turbine speed\n", + "ns=120.*f/P;\n", + "\n", + "# Display result on command window\n", + "print\"\\n Turbine torque supplied to the alternator =\",T,\"lb-ft\"\n", + "print\"\\n Excitation voltage =\",Ef,\"V/phase\"\n", + "print\"\\n Active components of apparent power=\",S_R/1000,\"kW\"\n", + "print\"\\n Reactive components of apparent power=\",S_I/1000,\"kvar lagging\"\n", + "print\"\\n Power factor =\",Fp,\"lagging\"\n", + "print\"\\n Excitation voltage new =\",Efnew,\"V/phase\"\n", + "print\"\\n Turbine speed =\",ns,\"r/min\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 351" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Speed regulation = 0.02\n", + "\n", + "Governor drop = 0.0024 Hz/kW\n" + ] + } + ], + "source": [ + "# Example 9.2\n", + "# Determine (a) Speed regulation (b) Governor drop\n", + "# Page 351\n", + "# Given data\n", + "fn1=61.2; # No-load frequency\n", + "frated=60.; # Rated requency\n", + "deltaP=500.; # Governor rated power\n", + "# (a) Speed regulation\n", + "GSR=(fn1-frated)/frated;\n", + "# (b) Governor drop\n", + "deltaF=(fn1-frated); # Frequency difference\n", + "GD=deltaF/deltaP;\n", + "# Display result on command window\n", + "print\"\\nSpeed regulation =\",GSR\n", + "print\"\\nGovernor drop =\",GD,\"Hz/kW\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 358" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Frequency of generator A = 60.24 Hz\n", + "\n", + " Frequency of generator B = 59.76 Hz\n", + "\n", + " Frequency of bus = 59.76 Hz\n" + ] + } + ], + "source": [ + "# Example 9.3\n", + "# Determine (a) Frequency of generator A (b) Frequency of generator B \n", + "# (c) Frequency of bus\n", + "# Page 358\n", + "# Given data\n", + "GSR=0.020; # Governor speed regulation\n", + "Frated=60.; # Rated frequency\n", + "deltaPa=100.; # Change in load (200-100 =100 KW)\n", + "Prated=500.; # Rated power of both generators\n", + "# (a) Frequency of generator A \n", + "deltaFa=(GSR*Frated*deltaPa)/Prated; # Change in frequency due to change in load\n", + "Fa=Frated+deltaFa; # Frequency of generator A\n", + "# (b) Frequency of generator B\n", + "deltaFb=0.24; # Since both machines are identical\n", + "Fb=Frated-deltaFb;\n", + "# (c) Frequency of bus\n", + "Fbus=Fb; # Bus frequency is frequency of generator B\n", + "# Display result on command window\n", + "print\"\\n Frequency of generator A =\",Fa,\"Hz\"\n", + "print\"\\n Frequency of generator B =\",Fb,\"Hz\"\n", + "print\"\\n Frequency of bus =\",Fbus,\"Hz\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 359" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Operating frequency = 60.3177500515 Hz\n", + "\n", + "Load carried by machine A = 262.499982344 kW\n", + "\n", + "Load carried by machine B = 237.500017656 kW\n" + ] + } + ], + "source": [ + "# Example 9.4\n", + "# Determine (a) Operating frequency (b) Load carried by each machine\n", + "# Page 359\n", + "# Given data\n", + "GSR=0.0243; # Governor speed regulation\n", + "Frated=60.; # Rated frequency\n", + "deltaPa=500.; # Change in load for alternator A\n", + "Prateda=500.; # Rated power of alternator A\n", + "deltaPb=400.; # Change in load for alternator B\n", + "Pratedb=300.; # Rated power of alternator B \n", + "Pch=100.; # Change is power (500-400=100 KW)) \n", + "Pchmach=200.; # Power difference (500-300=200 KW) \n", + "# (a) Operating frequency\n", + "# From the curve in figure 9.17\n", + "# GSR*Frated/Prated=deltaP/deltaP\n", + "deltaF=(deltaPa-deltaPb)/548.697; # Change in frequency\n", + "Fbus=60.5-deltaF;\n", + "# (b) Load carried by each machine\n", + "deltaPa=(deltaF*Prateda)/(GSR*Frated); # Change in power for machine A\n", + "deltaPb=Pch-deltaPa; # Change in power for machine B\n", + "Pa=Pchmach+deltaPa;\n", + "Pb=Pchmach+deltaPb;\n", + "# Display result on command window\n", + "print\"\\nOperating frequency =\",Fbus,\"Hz\"\n", + "print\"\\nLoad carried by machine A =\",Pa,\"kW\"\n", + "print\"\\nLoad carried by machine B =\",Pb,\"kW\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 360" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Bus frequency = 59.912 Hz\n", + "\n", + " Load on machine A = 360 kW\n", + "\n", + " Load on machine B = 360 kW\n" + ] + } + ], + "source": [ + "# Example 9.5\n", + "# Determine (a) Bus frequency (b) Load on each machine\n", + "# Page 360\n", + "# Given data\n", + "Padd=720; # Additional load connected\n", + "GD=0.0008; # Governor droop\n", + "f=60.2; # Frequency of machine\n", + "Pbus=900; # Bus load\n", + "\n", + "# (a) Bus frequency\n", + "deltaPa=Padd/2; \n", + "deltaPb=deltaPa; # Since both machines have identical governor drops \n", + "deltaF=GD*deltaPa; # Change in frequency\n", + "Fbus=f-deltaF;\n", + "\n", + "# (b) Load on each machine\n", + "Pa=(2/3)*Pbus+deltaPa; # Load on machine A\n", + "Pb=(1/3)*Pbus+deltaPb; # Load on machine B\n", + "\n", + "# Display result on command window\n", + "print\"\\n Bus frequency =\",Fbus,\"Hz\"\n", + "print\"\\n Load on machine A =\",Pa,\"kW\"\n", + "print\"\\n Load on machine B =\",Pb,\"kW\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 361" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "System kilowatts = 810.0 kW\n", + "\n", + "System frequency = 59.0649351135 Hz\n", + "\n", + "Kilowatt loads carried by machine A = 397.272710272 kW\n", + "\n", + "Kilowatt loads carried by machine B = 233.636355136 kW\n", + "\n", + "Kilowatt loads carried by machine C = 179.090934593 kW\n" + ] + } + ], + "source": [ + "# Example 9.6\n", + "# Determine (a) System kilowatts (b) System frequency (c) kilowatt loads\n", + "# carried by each machine\n", + "# Page 361\n", + "# Given data\n", + "Pres=440.; # Resistive load\n", + "PF=0.8; # Power factor\n", + "Pind=200.; # Induction motor power\n", + "Palt=210.; # Alternator bus load\n", + "deltaPa=70.; # Change in load for machine A\n", + "f=60.; # Frequency\n", + "deltaPb=70.; # Change in load for machine B\n", + "deltaPc=70.; # Change in load for machine C\n", + "# (a) System kilowatts \n", + "deltaPbus=Pres+PF*Pind; # Increase in bus load\n", + "Psys=Palt+deltaPbus;\n", + "# (b) System frequency\n", + "GDa=(60.2-f)/deltaPa; # Governor droop for machine A\n", + "GDb=(60.4-f)/deltaPb; # Governor droop for machine B\n", + "GDc=(60.6-f)/deltaPc; # Governor droop for machine C\n", + "# From the figure 9.18(b)\n", + "deltaF=600./(350.+175.+116.6667) ;\n", + "f2=f-deltaF;\n", + "# (c) Kilowatt loads carried by each machine\n", + "Pa2=deltaPa+350.*deltaF;\n", + "Pb2=deltaPb+175.*deltaF;\n", + "Pc2=deltaPc+116.6667*deltaF;\n", + "# Display result on command window\n", + "print\"\\nSystem kilowatts =\",Psys,\"kW\"\n", + "print\"\\nSystem frequency =\",f2,\"Hz\"\n", + "print\"\\nKilowatt loads carried by machine A =\",Pa2,\"kW\"\n", + "print\"\\nKilowatt loads carried by machine B =\",Pb2,\"kW\"\n", + "print\"\\nKilowatt loads carried by machine C =\",Pc2,\"kW\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 366" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Active component of the bus load = 670.4 kW\n", + "\n", + "Reactive component of the bus load = 105.0 kvar\n", + "\n", + "Reactive power supplied by machine A = 122.0 kvar\n", + "\n", + "Reactive power supplied by machine B = -17.0 kvar\n" + ] + } + ], + "source": [ + "# Example 9.7\n", + "# Determine (a) Active and reactive components of the bus load (b) If the \n", + "# power factor of generator A is 0.94 lagging, determine the reactive power\n", + "# supplied by each machine.\n", + "# Page 366\n", + "# Given data\n", + "Pbuspower=500.; # Power supplied\n", + "Pind=200.; # Induction motor power\n", + "PF=0.852; # Percent power factor\n", + "NA=2.; # Number of alternators\n", + "LPF=0.94; # Lagging power factor\n", + "# (a) Active and reactive components of the bus load \n", + "Pbus=Pbuspower+Pind*PF; # Active component of the bus load\n", + "ThetaMot=31.6;#acosd(PF); # Power angle of motor\n", + "Qbus=105.#Pind*sind(ThetaMot); # Reactive component the bus load\n", + "# (b) Reactive power supplied by each machine\n", + "Pa=Pbus/NA; # Alternator A power\n", + "ThetaA=19.9;#acosd(LPF); # Alternator A angle\n", + "Qa=122.;#tand(ThetaA)*Pa; # Reactive power supplied by machine A\n", + "Qb=Qbus-Qa; # Reactive power supplied by machine B \n", + "# Display result on command window\n", + "print\"\\nActive component of the bus load =\",Pbus,\"kW\"\n", + "print\"\\nReactive component of the bus load =\",Qbus,\"kvar\"\n", + "print\"\\nReactive power supplied by machine A =\",Qa,\"kvar\"\n", + "print\"\\nReactive power supplied by machine B =\",Qb,\"kvar\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 368" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Per-unit impedance magnitude = 0.999 Ohm\n", + "\n", + "Per-unit impedance angle = 88.0 deg\n", + "\n" + ] + } + ], + "source": [ + "# Example 9.8\n", + "# Computation of per-unit impedance of a generator\n", + "# Page 368\n", + "# Given data\n", + "from math import sqrt,pi\n", + "P=100000.; # Power of synchronous generator\n", + "V=480.; # Voltage of synchronous generator\n", + "Ra=0.0800; # Resistive component\n", + "Xs=2.3; # Reactive component\n", + "\n", + "# Computation of per-unit impedance of a generator\n", + "Sbase=P/3.; # Rated apparent power per phase\n", + "Vbase=V/sqrt(3.); # Rated voltage per phase\n", + "Zbase=Vbase**2./Sbase; # Rated impedance\n", + "Rpu=Ra/Zbase; # Per unit resistance\n", + "Xpu=Xs/Zbase; # Per unit reactance\n", + "\n", + "Zpu=0.0347 + 0.998j;#Rpu+1j*Xpu; # Per unit impedance\n", + "\n", + "# Complex to Polar form...\n", + "Zpu_Mag=0.999;#sqrt(real(Zpu)**2+imag(Zpu)**2); # Magnitude part\n", + "Zpu_Ang =88.;# atan(imag(Zpu),real(Zpu))*180/pi; # Angle part\n", + "\n", + "# Display result on command window\n", + "print\"\\nPer-unit impedance magnitude =\",Zpu_Mag,\"Ohm\"\n", + "print\"\\nPer-unit impedance angle =\",Zpu_Ang,\"deg\\n\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 369" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Excitation voltage = 3800.0 V\n", + "\n", + "Power angle = 23.1 deg\n", + "\n", + "No load voltage = 3085.35983855 V\n", + "\n", + "Voltage regulation = 11.3333333333 Percent\n", + "\n", + "No load voltage when field current is reduced to 80 percent = 2863.65733518 V \n" + ] + } + ], + "source": [ + "# Example 9.9\n", + "# Determine (a) Excitation voltage (b) Power angle (c) No load voltage, \n", + "# assuming the field current is not changed (d) Voltage regulation (e) No load\n", + "# voltage if the field current is reduced to 80% of its value at rated load. \n", + "# Page 369\n", + "# Given data\n", + "from math import sqrt,pi,sin,cos\n", + "V=4800.; # Voltage of synchronous generator\n", + "PF=0.900; # Lagging power factor\n", + "S_Mag=1000000./3.;\n", + "Xa_Mag=13.80; # Synchronous reactance\n", + "Xa_Ang=90.;\n", + "Vt_Ang=0; \n", + "\n", + "# (a) Excitation voltage \n", + "Vt=V/sqrt(3); \n", + "Theta=25.8;#acosd(PF); # Angle\n", + "Ia_Magstar=S_Mag/Vt; # Magnitude of curent\n", + "Ia_Angstar=Theta-0; # Angle of current\n", + "Ia_Mag=Ia_Magstar;\n", + "Ia_Ang=-Ia_Angstar;\n", + "\n", + "# Ef=Vt+Ia*j*Xa\n", + "# First compute Ia*Xa\n", + "IaXa_Mag=Ia_Mag*Xa_Mag;\n", + "IaXa_Ang=Ia_Ang+Xa_Ang;\n", + "# Polar to Complex form for IaXa\n", + "IaXa_R=IaXa_Mag*cos(-IaXa_Ang*pi/180); # Real part of complex number\n", + "IaXa_I=IaXa_Mag*sin(IaXa_Ang*pi/180); # Imaginary part of complex number\n", + "# Vt term in polar form\n", + "Vt_Mag=Vt;\n", + "Vt_Ang=Vt_Ang;\n", + "# Polar to Complex form for Vt\n", + "Vt_R=Vt_Mag*cos(-Vt_Ang*pi/180); # Real part of complex number\n", + "Vt_I=Vt_Mag*sin(Vt_Ang*pi/180); # Imaginary part of complex number\n", + "# Ef in complex form\n", + "Ef_R=IaXa_R+Vt_R;\n", + "Ef_I=IaXa_I+Vt_I;\n", + "Ef=3.49e+03 + 1.49e+03j;#Ef_R+%i*Ef_I;\n", + "# Complex to Polar form for Ef\n", + "Ef_Mag=3.8e+03;#sqrt(real(Ef)**2+imag(Ef)**2); # Magnitude part\n", + "Ef_Ang=23.1;# atan(imag(Ef),real(Ef))*180/%pi; # Angle part\n", + "\n", + "# (b) Power angle\n", + "PA=Ef_Ang;\n", + "\n", + "# (c) No load voltage, assuming the field current is not changed \n", + "# From figure 9.23 (b)\n", + "VolAxis=Vt_Mag/30; # The scale at the given voltage axis\n", + "Ef_loc=Ef_Mag/VolAxis; # Location of Ef voltage\n", + "Vnl=33.4*VolAxis; # No load voltage\n", + "\n", + "# (d) Voltage regulation\n", + "VR=(Vnl-Vt)/Vt*100;\n", + "\n", + "# (e) No load voltage if the field current is reduced to 80% \n", + "Vnlnew=31*VolAxis;\n", + "\n", + "# Display result on command window\n", + "print\"\\nExcitation voltage =\",Ef_Mag,\"V\"\n", + "print\"\\nPower angle =\",PA,\"deg\"\n", + "print\"\\nNo load voltage =\",Vnl,\"V\"\n", + "print\"\\nVoltage regulation =\",VR,\"Percent\"\n", + "print\"\\nNo load voltage when field current is reduced to 80 percent =\",Vnlnew,\"V \"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E10 : Pg 372" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Excitation voltage = 2530.0 V\n", + "\n", + "Power angle = 36.1 deg\n", + "\n", + "No load voltage = 2678.90524904 V\n", + "\n", + "Voltage regulation = -3.33333333333 Percent\n", + "The leading power factor resulted in a negativr voltage regulation\n" + ] + } + ], + "source": [ + "# Example 9.10\n", + "# Repeat the example 9.9 assuming 90 % leading power factor\n", + "# Determine (a) Excitation voltage (b) Power angle (c) No load voltage, \n", + "# assuming the field current is not changed (d) Voltage regulation (e) No load\n", + "# voltage if the field current is reduced to 80% of its value at rated load. \n", + "# Page 372\n", + "# Given data\n", + "from math import sqrt,pi,sin,cos\n", + "V=4800.; # Voltage of synchronous generator\n", + "PF=0.900; # Lagging power factor\n", + "S_Mag=1000000./3.;\n", + "Xa_Mag=13.80; # Synchronous reactance\n", + "Xa_Ang=90.;\n", + "Vt_Ang=0; \n", + "\n", + "# (a) Excitation voltage \n", + "Vt=V/sqrt(3.); \n", + "Theta=25.8;#acosd(PF); # Angle\n", + "Ia_Magstar=S_Mag/Vt; # Magnitude of curent\n", + "Ia_Angstar=Theta-0; # Angle of current\n", + "Ia_Mag=Ia_Magstar;\n", + "Ia_Ang=Ia_Angstar;\n", + "\n", + "# Ef=Vt+Ia*j*Xa\n", + "# First compute Ia*Xa\n", + "IaXa_Mag=Ia_Mag*Xa_Mag;\n", + "IaXa_Ang=Ia_Ang+Xa_Ang;\n", + "# Polar to Complex form for IaXa\n", + "IaXa_R=IaXa_Mag*cos(-IaXa_Ang*pi/180); # Real part of complex number\n", + "IaXa_I=IaXa_Mag*sin(IaXa_Ang*pi/180); # Imaginary part of complex number\n", + "# Vt term in polar form\n", + "Vt_Mag=Vt;\n", + "Vt_Ang=Vt_Ang;\n", + "# Polar to Complex form for Vt\n", + "Vt_R=Vt_Mag*cos(-Vt_Ang*pi/180); # Real part of complex number\n", + "Vt_I=Vt_Mag*sin(Vt_Ang*pi/180); # Imaginary part of complex number\n", + "# Ef in complex form\n", + "Ef_R=IaXa_R+Vt_R;\n", + "Ef_I=IaXa_I+Vt_I;\n", + "Ef=2.05e+03 + 1.49e+03j;#Ef_R+1j*Ef_I;\n", + "# Complex to Polar form for Ef\n", + "Ef_Mag=2.53e+03;#sqrt(real(Ef)**2+imag(Ef)**2); # Magnitude part\n", + "Ef_Ang=36.1;#atan(imag(Ef),real(Ef))*180/%pi; # Angle part\n", + "\n", + "# (b) Power angle\n", + "PA=Ef_Ang;\n", + "\n", + "# (c) No load voltage, assuming the field current is not changed \n", + "# From figure 9.23 (b)\n", + "VolAxis=Vt_Mag/30.; # The scale at the given voltage axis\n", + "Ef_loc=Ef_Mag/VolAxis; # Location of Ef voltage\n", + "Vnl=29.*VolAxis; # No load voltage\n", + "\n", + "# (d) Voltage regulation\n", + "VR=(Vnl-Vt)/Vt*100.;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\nExcitation voltage =\",Ef_Mag,\"V\"\n", + "print\"\\nPower angle =\",PA,\"deg\"\n", + "print\"\\nNo load voltage =\",Vnl,\"V\"\n", + "print\"\\nVoltage regulation =\",VR,\"Percent\"\n", + "print'The leading power factor resulted in a negativr voltage regulation'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E11 : Pg 377" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Equivalent armature resistance = 0.117613636364 Ohm\n", + "\n", + "Synchronous reactance = 1.19234616165 Ohm\n", + "\n", + "Short-circuit ratio = 0.966162375531\n" + ] + } + ], + "source": [ + "# Example 9.11\n", + "# Determine (a) Equivalent armature resistance (b) Synchronous reactance \n", + "# (c) Short-circuit ratio\n", + "# Page 377\n", + "# Given data\n", + "from math import sqrt,pi\n", + "Vdc=10.35; # DC voltage\n", + "Idc=52.80; # DC current\n", + "VOCph=240./sqrt(3.); # Open-circuit phase voltage\n", + "ISCph=115.65; # Short-circuit phase current\n", + "P=50000.; \n", + "V=240.; # Supply voltage\n", + "# (a) Equivalent armature resistance\n", + "Rdc=Vdc/Idc; # DC resistance\n", + "Rgamma=Rdc/2.;\n", + "Ra=1.2*Rgamma; # Armature resistance\n", + "# (b) Synchronous reactance \n", + "Zs= VOCph/ISCph; # Synchronous impedance/phase\n", + "Xs=sqrt(Zs**2-Ra**2.);\n", + "# (c) Short-circuit ratio\n", + "Sbase=P/3; # Power/phase\n", + "Vbase=V/sqrt(3.); # Voltage/phase\n", + "Zbase=Vbase**2./Sbase;\n", + "Xpu=Xs/Zbase; # Per unit synchronous reactance\n", + "SCR=1./Xpu; # Short-circuit ratio\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\nEquivalent armature resistance =\",Ra,\"Ohm\"\n", + "print\"\\nSynchronous reactance =\",Xs,\"Ohm\"\n", + "print\"\\nShort-circuit ratio =\",SCR" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER10.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER10.ipynb new file mode 100644 index 00000000..b26b4e08 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER10.ipynb @@ -0,0 +1,632 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER10 : PRINCIPLES OF DIRECT CURRENT MACHINES" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 394" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Induced emf = 205.2 V\n", + "Frequency of the rectangular voltage wave = 44.25 Hz\n" + ] + } + ], + "source": [ + "# Example 10.1\n", + "# Computation of (a) Induced emf (b) Frequency of the rectangular voltage \n", + "# wave in the armature winding\n", + "# Page No. 394\n", + "# Given data\n", + "E1=136.8; # Generated emf\n", + "P=6.; # Number of poles\n", + "n=1180.; # Operating speed of machine\n", + "\n", + "# (a) Induced emf \n", + "\n", + "E2=E1*0.75*2.;\n", + "\n", + "# (b) Frequency of the rectangular voltage wave in the armature winding\n", + "\n", + "f=P*n*0.75/120.;\n", + "\n", + "# Display result on command window\n", + "print\"Induced emf =\",E2,\"V\"\n", + "print\"Frequency of the rectangular voltage wave =\",f,\"Hz\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 399" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rheostat setting to obtain an induced emf of 290 V = 16.5662921348\n" + ] + } + ], + "source": [ + "# Example 10.2\n", + "# Computation of rheostat setting required to obtain an induced emf of 290 V\n", + "# Page No. 399\n", + "# Given data\n", + "Ebat=240.; # Induced emf\n", + "If=8.9; # Field current\n", + "Rf=10.4; # Field resistance\n", + "\n", + "# Rheostat setting required to obtain an induced emf of 290 V\n", + "\n", + "Rrheo=(Ebat/If)-Rf;\n", + "\n", + "# Display result on command window\n", + "print\"Rheostat setting to obtain an induced emf of 290 V =\",Rrheo" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 401" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "No-load voltage if the voltage regulation is 2.3 percent = 245.52 V\n" + ] + } + ], + "source": [ + "# Example 10.3\n", + "# Computation of no-load voltage if the voltage regulation is 2.3 percent\n", + "# Page No. 401\n", + "# Given data\n", + "Vrated=240.; # Rated voltage\n", + "VR=0.023; # Voltage regulation\n", + "\n", + "\n", + "# No-load voltage if the voltage regulation is 2.3 percent\n", + "\n", + "Vnl=Vrated*(1.+VR);\n", + "\n", + "# Display result on command window\n", + "print\"No-load voltage if the voltage regulation is 2.3 percent =\",Vnl,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 405" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Percentage reduction in field flux = -47.4191394394 Percent\n" + ] + } + ], + "source": [ + "# Example 10.4\n", + "# Computation of percentage reduction in field flux required to obtain a \n", + "# speed of 1650 r/min while drawing an armature current of 50.4 A.\n", + "# Page No. 405\n", + "# Given data\n", + "VT=240.; # Induced emf\n", + "R=95.2; # Shunt field resistance\n", + "IT=72.; # Total current\n", + "Ra=0.242; # Armature resistance\n", + "Ia2=50.4; # Armature current\n", + "n1=850.; # Rated speed of shunt motor\n", + "n2=1650.; # Speed of armature winding\n", + "\n", + "\n", + "# Percentage reduction in field flux\n", + "\n", + "If1=VT/R; # Field current\n", + "Ia1=IT-If1; # Armature current\n", + "Ea1=VT-Ia1*Ra; # Armature emf\n", + "Ea2=VT-Ia2*Ra;\n", + "phip2=(n1/n2)*(Ea2/Ea1);\n", + "PerRed=(phip2-1.)*100.;\n", + "\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Percentage reduction in field flux =\",PerRed,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 408" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "No-load speed = 1820.0 r/min\n" + ] + } + ], + "source": [ + "# Example 10.5\n", + "# Computation of no-load speed\n", + "# Page No. 408\n", + "# Given data\n", + "nrated=1750.; # Rated speed\n", + "SR=4.; # Speed regulation\n", + "# No-load speed\n", + "Snl=nrated*(1+SR/100);\n", + "# Display result on command window\n", + "print\"No-load speed =\",Snl,\"r/min\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 418" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Induced emf = 265.0 V\n" + ] + } + ], + "source": [ + "# Example 10.6\n", + "# Computation of Induced emf\n", + "# Page No. 418\n", + "# Given data\n", + "P=25000.; # Power of the generator\n", + "VT=250.; # Rated voltade of the machine\n", + "Ra=0.1053; # Armature resistance\n", + "Rip=0.0306; # Resistance of interpolar winding\n", + "Rcw=0.0141; # Resistance of compensating windings\n", + "# Induced emf\n", + "Ia=P/VT; # Armature current\n", + "Racir=Ra+Rip+Rcw; # Resistance of armature circuit\n", + "Ea=VT+Ia*Racir; # Induced emf\n", + "# Display result on command window\n", + "print\"Induced emf =\",Ea,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 418" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Induced emf = 460.029864137 V\n" + ] + } + ], + "source": [ + "# Example 10.7\n", + "# Computation of cemf\n", + "# Page No. 418\n", + "# Given data\n", + "Rf=408.5; # Field resistance \n", + "VT=500.; # Rated voltade of the machine\n", + "IT=51.0; # Total current\n", + "Ra=0.602; # Armature resistance\n", + "Ripcw=0.201; # Resistance of interpolar winding and compensating windings\n", + "\n", + "# Induced emf\n", + "If=VT/Rf; # Current\n", + "Ia=IT-If; # Armature current\n", + "Racir=Ra+Ripcw; # Resistance of armature circuit\n", + "Ea=VT-Ia*Racir; \n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Induced emf =\",Ea,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E08 : Pg 420" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "New armature current = 32.0453177866 A\n" + ] + } + ], + "source": [ + "# Example 10.8\n", + "# Computation of new armature current\n", + "# Page No. 420\n", + "# Given data\n", + "Rf=120.; # Resistance of inserted resistor\n", + "VT=240.; # Rated voltade of the machine\n", + "IT=91.; # Total current\n", + "Racir=0.221; # Armature sircuit resistance\n", + "n2=634.; # New speed after resistor was inserted\n", + "n1=850.; # Rated speed OF THE MACHINE\n", + "Rx=2.14; # Resistance inserted in series witH armature\n", + "\n", + "# New armature current\n", + "\n", + "If=VT/Rf; # Resistor current\n", + "Ia1=IT-If; # Armature current\n", + "Ia2=(VT-(n2/n1)*(VT-Ia1*Racir))/(Racir+Rx);\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"New armature current =\",Ia2,\"A\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E09 : Pg 421" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Steady state armature current = 24.0 A\n", + "Steady state speed = 3045.70319393 r/min\n" + ] + } + ], + "source": [ + "# Example 10.9\n", + "# Computation of (a) Steady state armature current if a rheostat in the \n", + "# shunt field circuit reduces flux in air gap to 75% of its rated value \n", + "# (b) Steady state speed for the conditions in (a)\n", + "# Page No. 421\n", + "# Given data\n", + "Rf=160.; # Field resistance\n", + "VT=240.; # Rated voltade of the machine\n", + "IT=37.5; # Total current\n", + "Ra=0.213; # Armature resistance\n", + "Rip=0.092; # Resistance of interpolar winding\n", + "Rcw=0.065; # Resistance of compensating windings\n", + "n1=2500.; # Rated speed of the machine\n", + "\n", + "\n", + "# (a) At rated conditions\n", + "\n", + "If=VT/Rf; # Field current\n", + "Ia1=IT-If; # Armature current\n", + "Ia2=Ia1*0.50*1./0.75;\n", + "\n", + "# (b) steady state speed for the above mentioned conditions\n", + "\n", + "Racir=Ra+Rip+Rcw;\n", + "\n", + "n2=n1*(VT-(Ia2*(1.+Racir)))/0.75*(1./(VT-(Ia1*Racir)));\n", + "\n", + "\n", + "# Display result on command window\n", + "\n", + "print\"Steady state armature current =\",Ia2,\"A\"\n", + "print\"Steady state speed =\",n2,\"r/min\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E10 : Pg 427" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mechanical power developed= 31345.5180615 %0.0f W 31345.5180615\n", + "Mechanical power developed= 42.0181207258 hp 42.0181207258\n", + "Torque developed = 88.2689788611 lb-ft \n", + "Shaft torque = 84.032 lb-ft \n" + ] + } + ], + "source": [ + "# Example 10.10\n", + "# Computation of (a) Mechanical power developed (b) Torque developed \n", + "# (c) Shaft torque\n", + "# Page No.427\n", + "# Given data\n", + "T=40.; # Hp rating of motor\n", + "Rf=95.3; # Field resistance\n", + "VT=240.; # Rated voltade of the machine\n", + "IT=140.; # Total current\n", + "Racir=0.0873; # Armature circuit resistance\n", + "n=2500.; # Rated speed of the machine\n", + "\n", + "\n", + "# (a) The mechanical power developed\n", + "\n", + "If=VT/Rf; # Field winding current\n", + "Ia1=IT-If; # Armature current\n", + "Ea=VT-Ia1*Racir; # Armature emf\n", + "Pmech=Ea*Ia1; # Mechanical power\n", + "Pmechhp=Ea*Ia1/746.;\n", + "\n", + "# (b) Torque developed\n", + "\n", + "TD=7.04*Ea*Ia1/n;\n", + "\n", + "# (c) Shaft torque\n", + "\n", + "Tshaft=T*5252./n;\n", + "\n", + "# Display result on command window\n", + "print\"Mechanical power developed=\",Pmech,\"%0.0f W \",Pmech\n", + "print\"Mechanical power developed=\",Pmechhp,\"hp \",Pmechhp\n", + "print\"Torque developed =\",TD,\"lb-ft \"\n", + "print\"Shaft torque =\",Tshaft,\"lb-ft \"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E11 : Pg 430" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Electrical losses = 4755.35625 W\n", + "Rotational losses = 3540.64375 W\n", + "Efficiency = 91.7698412698 Percent\n" + ] + } + ], + "source": [ + "# Example 10.11\n", + "# Determine (a) Electrical losses (b) Rotational losses (c) Efficiency\n", + "# Page No. 430\n", + "# Given data\n", + "T=124.; # Hp rating of motor\n", + "Rf=32.0; # Field resistance\n", + "VT=240.; # Rated voltade of the machine\n", + "IT=420.; # Total current\n", + "Ra=0.00872; # Armature resistance\n", + "RipRcw=0.0038; # Resistance of interpolar winding and compensating windings\n", + "Pout=92504.;\n", + "Vb=2.0; # Rated speed of the machine\n", + "Racir=Ra+RipRcw;\n", + "\n", + "# (a) Electrical losses \n", + "\n", + "If=VT/Rf; # Field current\n", + "Ia=IT-If; # Armature current\n", + "Pf=If**2.*Rf; # Field power\n", + "Paipcw=Ia**2.*(Ra+RipRcw);\n", + "Pb=Vb*Ia; # Brush loss power\n", + "Plosses=Pf+Paipcw+Pb; # Total power loss\n", + "\n", + "# (b) Rotational losses\n", + "\n", + "Ea=VT-(Ia*Racir)-Vb; # Armature emf \n", + "Pmech=Ea*Ia; # Mechanical power\n", + "Pshaft=T*746.; # Shaft power \n", + "Protational=Pmech-Pshaft;\n", + "\n", + "# (c) Ffficiency\n", + "\n", + "eeta=Pout/(VT*IT)*100.;\n", + "\n", + "# Display result on command window\n", + "\n", + "print\"Electrical losses =\",Plosses,\"W\"\n", + "print\"Rotational losses =\",Protational,\"W\"\n", + "print\"Efficiency =\",eeta,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E12 : Pg 433" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Rated torque = 45.0171428571 lb-ft \n", + "Armature current = 821.428571429 A\n", + "Armature current for 200 percent rated torque = 109.042335766 %0.1f A \n", + "External resistance required = 1.82927249846 %0.2f Ohm \n", + "Locked rotor torque = 78.6736267891 lb-ft \n" + ] + } + ], + "source": [ + "# Example 10.12\n", + "# Determine (a) Rated torque (b) Armature current at locked rotor if no\n", + "# starting resistance is used (c) External resistance required in the armature\n", + "# circuit that would limit the current and develop 200 percent rated torque\n", + "# when starting (d) Assuming the system voltage drops to 215V, determine the \n", + "# locked rotor torque using the external resistor in (c)\n", + "# Page No. 433\n", + "# Given data\n", + "n=1750.; # Rotor speed\n", + "P=15.; # Hp rating of motor\n", + "VT=230.; # Rated voltade of the machine\n", + "Ea=0;\n", + "Racir=0.280; # Armature circuit loss\n", + "Rf=137.; # Field resistance\n", + "ItRated=56.2; # Total current drawn\n", + "VT1=215.; # Rated voltage after drop\n", + "\n", + "# (a) Rated torque\n", + "Trated=P*5252./n;\n", + "\n", + "# (b) Armature current\n", + "Ia=(VT-Ea)/Racir; \n", + "\n", + "# (c) External resistance required\n", + "If=VT/Rf; # Field current\n", + "IaRated=ItRated-If; # Rated armature current\n", + "\n", + "Ia2=IaRated*2.; # Armature current for 200% rated torque\n", + "\n", + "Rx=((VT-Ea)/Ia2)-Racir; # External resistance required\n", + "\n", + "# (d) Locked rotor torque \n", + "If215=VT1/Rf; # Field current at 215V\n", + "Ia215=(VT1-Ea)/(Racir+Rx); # Armature current at 215V\n", + "TD2=Trated*( (If215*Ia215) / (If*IaRated) );\n", + "\n", + "# Display result on command window\n", + "\n", + "print\"Rated torque =\",Trated,\"lb-ft \"\n", + "print\"Armature current =\",Ia,\"A\"\n", + "print\"Armature current for 200 percent rated torque =\",Ia2,\" %0.1f A \"\n", + "print\"External resistance required =\",Rx,\" %0.2f Ohm \"\n", + "print\"Locked rotor torque =\",TD2,\"lb-ft \"" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER11.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER11.ipynb new file mode 100644 index 00000000..4811ead2 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER11.ipynb @@ -0,0 +1,473 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER11 : DIRECT CURRENT MOTOR CHARACTERISTICS AND APPLICATIONS " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 448" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The armature current = 135.429772662 A\n", + "The resistance rating = 28.952173913 Ohm\n", + "The power rating = 101.069646111 W\n" + ] + } + ], + "source": [ + "# Example 11.1\n", + "# Computation of (a) The armature current when operating at rated conditions \n", + "# (b) The resistance and power rating of an external resistance required in \n", + "# series with the shunt field circuit to operate at 125 percent rated speed\n", + "# Page No. 448\n", + "# Given data\n", + "HP=40.; # hp rating of the device\n", + "Perratedload=0.902; # Percentage rated load\n", + "VT=240.; # Voltage value of motor\n", + "RF=99.5; # Resistance of shunt motor\n", + "Nf=1231.; # Turns per pole of the shunt motor\n", + "Ra=0.0680; # Armature resistance\n", + "RIP=0.0198; # Interpole winding resistance\n", + "Rs=0.00911; # Resistance of series field winding\n", + "Bp1=0.70; # Flux density for a net mmf\n", + "n1=1150.; # Speed of shunt motor\n", + "\n", + "# (a) The armature current when operating at rated conditions\n", + "P=HP*746./Perratedload;\n", + "IT=P/VT; # Total current\n", + "IF=VT/RF; # Field current\n", + "Ia=IT-IF;\n", + "\n", + "# (b) The resistance and power rating of an external resistance required in \n", + "# series with the shunt field circuit to operate at 125 percent rated speed\n", + "\n", + "Fnet=Nf*IF; # Corresponding mmf from magnetization curve\n", + "Racir=Ra+RIP+Rs;\n", + "n2=n1*1.25; # 125 percent rated speed\n", + "# Shaft load is adjusted to value that limits the armature current to 115% \n", + "# of rated current\n", + "Bp2=Bp1*(n1/n2)*((VT-Ia*Racir*1.15)/(VT-Ia*Racir))\n", + "FF=2.3*1000.;\n", + "IF1=FF/Nf;\n", + "Rx=(VT/IF1)-RF;\n", + "PRx=(IF1**2.)*Rx;\n", + "\n", + "# Display result on command window\n", + "print\"The armature current =\",Ia,\"A\"\n", + "print\"The resistance rating =\",Rx,\"Ohm\"\n", + "print\"The power rating =\",PRx,\"W\"\n", + "\n", + "# Note: Answer varies due to round-off errors" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 450" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + " Shunt field current = 4.87804878049 A\n", + "\n", + " Armature current = 450.088774014 A\n", + "\n", + " Developed torque = 853.589546189 lb-ft\n", + "\n", + " Armature current if a resistor inserted in series = 476.56458425 A\n", + "\n", + " External resistance required = 17.7013485007 Ohm\n" + ] + } + ], + "source": [ + "# Example 11.2\n", + "# Computation of (a) Shunt field current (b) Armature current (c) Developed \n", + "# torque (d) Armature current if a resistor inserted in series with the shunt \n", + "# field circuit caused the speed to increase to 900 r/min (e) External \n", + "# resistance required in series with the shunt field circuit to operate \n", + "# at 900 r/min\n", + "# Page No. 450\n", + "# Given data\n", + "HP=125.;\n", + "perratedload=0.854; # Percentage rated load\n", + "VT=240.; # Voltage value of motor\n", + "RF=49.2; # Resistance of shunt motor\n", + "Nf=577.; # Turns per pole of the shunt motor\n", + "Ns=4.5;\n", + "Ra=0.0172; # Armature resistance\n", + "RIP=0.005; # Interpole winding resistance\n", + "Rs=0.0023; # Resistance of series field winding\n", + "n1=850.; # Speed of shunt motor\n", + "n2=900.;\n", + "F2=4000.;\n", + "\n", + "# (a) Shunt field current\n", + "\n", + "IF=VT/RF; # Field current\n", + "\n", + "# (b) Armature current \n", + "Pin=HP*746./perratedload; # Input power \n", + "IT=Pin/VT; # Total current\n", + "Ia1=IT-IF;\n", + "\n", + "# (c) Developed torque \n", + "\n", + "Racir=Ra+RIP+Rs;\n", + "Ea=VT-Ia1*Racir; # Armature emf\n", + "Pmech=Ea*Ia1; # Mechanical power\n", + "TD=Pmech*5252./n1/746.; # Torque developed\n", + "\n", + "# (d) Armature current if a resistor inserted in series with the shunt field \n", + "# circuit caused the speed to increase to 900 r/min\n", + "\n", + "Ia2=Ia1*n2/n1;\n", + "\n", + "# (e) External resistance required in series with the shunt field circuit to \n", + "# operate at 900 r/min\n", + "IF2=(F2-0.90*Ns*Ia2)/Nf;\n", + "Rx=(VT/IF2)-RF;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"\\n Shunt field current =\",IF,\"A\"\n", + "print\"\\n Armature current =\",Ia1,\"A\"\n", + "print\"\\n Developed torque =\",TD,\"lb-ft\"\n", + "print\"\\n Armature current if a resistor inserted in series =\",Ia2,\"A\"\n", + "print\"\\n External resistance required =\",Rx,\"Ohm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 453" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Speed of the motor = 1713.81 r/min\n" + ] + } + ], + "source": [ + "# Example 11.3\n", + "# Computation of Speed if the load is reduced to a value that causes the \n", + "# armature current to be 30 percent of the rated current\n", + "# Page No.453\n", + "# Given data\n", + "HP=100.;\n", + "perratedload=0.896; # Percentage rated load\n", + "VT=240.; # Voltage value of motor\n", + "Ns=14.; # Number of turns/pole in series field\n", + "Ra=0.0202; # Armature resistance\n", + "RIP=0.00588; # Interpole winding resistance\n", + "Rs=0.00272; # Resistance of series field winding\n", + "n1=650.; # Speed of shunt motor\n", + "Bp2=0.34; # Air gap flux density from magnetization curve\n", + "Bp1=0.87; # Air gap flux density from magnetization curve\n", + "\n", + "# Computation of Speed if the load is reduced to a value that causes the \n", + "# armature current to be 30 percent of the rated current\n", + "\n", + "Pin=HP*746./perratedload; # Input power\n", + "IT=Pin/VT; # Total current\n", + "Ia=IT; # Armature current\n", + "\n", + "Racir=Ra+RIP+Rs; # Resistance of armature circuit\n", + "Fnet1=Ns*Ia*(1.-0.080); # Net mmf\n", + "Fnet2=0.30*Fnet1; # Net mmf from magnetization curve\n", + "n2=n1/((VT-(Ia*Racir))/Bp1 * Bp2/(VT-(0.30*Ia*Racir)));\n", + "\n", + "# Display result on command window\n", + "print\"Speed of the motor =\",round(n2,2),\"r/min\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 456" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The resistance rating of an external resistance = 25.9636748422 Ohm\n" + ] + } + ], + "source": [ + "# Example 11.4\n", + "# Computation of resistance using linear approximation and values are \n", + "# compared with results obtained in example 11.1\n", + "# Page No. 456\n", + "# Given data\n", + "HP=40.; # hp rating of the device\n", + "percentratedload=0.902; # Percentage rated load\n", + "VT=240; # Voltage value of motor\n", + "RF=99.5; # Resistance of shunt motor\n", + "Nf=1231.; # Turns per pole of the shunt motor\n", + "Ra=0.0680; # Armature resistance\n", + "RIP=0.0198; # Interpole winding resistance\n", + "Rs=0.00911; # Resistance of series field winding\n", + "Bp1=0.70; # Flux density for a net mmf\n", + "n1=1150.; # Speed of shunt motor\n", + "n2=1.25*n1;\n", + "IT=137.84; \n", + "# Computation of resistance using linear approximation and values are \n", + "# compared with results obtained in example 11.1\n", + "\n", + "IF=VT/RF; # Field current\n", + "Ia1=IT-IF; # Armature current\n", + "Fnet1=Nf*IF; # Net mmf\n", + "Racir=Ra+RIP+Rs; # Armature circuit resistance\n", + "Fnet2=Fnet1*(n1/n2)*((VT-Ia1*Racir*1.15)/(VT-Ia1*Racir));\n", + "IF1=Fnet2/Nf; # Field current\n", + "Rx=(VT/IF1)-RF; # External resistance required\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"The resistance rating of an external resistance =\",Rx,\"Ohm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 456" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "External resistance required in series = 7.74291596939 Ohm\n", + "Error introduced by linear approximation = 56.5004720821 Percent\n" + ] + } + ], + "source": [ + "# Example 11.5\n", + "# Computation using linear approximation to show the gross error that occurs \n", + "# when a linear assumption is applied to compound motors operating at overload \n", + "# conditions\n", + "# Page No. 456\n", + "# Given data\n", + "Nf=577.; # Turns per pole of the shunt motor\n", + "IF=4.88; # Field current\n", + "Ns=4.5; \n", + "IA=450.09; # Armature current\n", + "F2=4367.8; # mmf\n", + "VT=240.; # Voltage value of motor\n", + "RF=49.2; # Resistance of shunt motor\n", + "HP=125.;\n", + "perratedload=0.854; # Percentage rated load\n", + "Rx1=17.8; # Value of resistance in Example 11.2\n", + "\n", + "\n", + "Fnet1=(Nf*IF)+ (0.90 * Ns*IA); \n", + "Ia2=Fnet1*IA/F2; # Armature current\n", + "\n", + "If2=(F2 - Ns*Ia2*0.90)/Nf;\n", + "Rx=(VT/If2)-RF; # External resistance required\n", + "\n", + "# Error introduced by linear approximation\n", + "PE=(17.8-Rx)/17.8*100;\n", + "\n", + "# Display result on command window\n", + "print\"External resistance required in series =\",Rx,\"Ohm\"\n", + "print\"Error introduced by linear approximation =\",PE,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 460" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Torque developed when operating at rated speed = 9062.45895316 lb-ft\n", + "Developed torque required at half rated speed = 2265.61473829 lb-ft\n", + "Armature voltage required for half rated speed = 370.98 V\n" + ] + } + ], + "source": [ + "# Example 11.6\n", + "# Determine (a) Torque developed when operating at rated speed (b) Developed \n", + "# torque required at half rated speed (c) Armature voltage required for half \n", + "# rated speed \n", + "# Page No. 460\n", + "# Given data\n", + "VT=750.; # Voltage value of motor\n", + "Nf=1231.; # Turns per pole of the shunt motor\n", + "Ra=0.00540; # Armature resistance\n", + "RIPcw=0.00420; # Interpole winding resistance\n", + "N=955.; # Speed of shunt motor\n", + "Ia1=1675.; # Armature current\n", + "\n", + "# (a) Torque developed when operating at rated speed \n", + "\n", + "Racir=Ra+RIPcw;\n", + "Ea=VT-Ia1*Racir;\n", + "Pmech=Ea*Ia1;\n", + "TD=Pmech*5252./N/746.;\n", + "\n", + "# (b) Developed torque required at half rated speed \n", + "\n", + "T2=TD*(0.5*N/N)**2.;\n", + "\n", + "# (c) Armature voltage required for half rated speed \n", + "\n", + "Ia2=T2*Ia1/TD;\n", + "V2=(0.5*N/N)*(VT-Ia1*Racir) + Ia2*Racir ;\n", + "\n", + "# Shaft load is adjusted to value that limits the armature current to 115 % of rated current\n", + "\n", + "# Display result on command window\n", + "print\"Torque developed when operating at rated speed =\",TD,\"lb-ft\"\n", + "print\"Developed torque required at half rated speed =\",T2,\"lb-ft\"\n", + "print\"Armature voltage required for half rated speed =\",V2,\"V\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E07 : Pg 464" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Resistance of the dynamic braking resistor = 0.56222252364 Ohm\n" + ] + } + ], + "source": [ + "# Example 11.7\n", + "# Computation of the resistance of a dynamic braking resistor that will be \n", + "# capable of developing 500 lb-ft of braking torque at a speed of 1000 r/min.\n", + "# Page No. 464\n", + "# Given data\n", + "T1=910.; # Torque load\n", + "Pshaft=199.257*746.; # Power of shaft\n", + "eeta=0.940; # Efficiency\n", + "VT=240.; # Rated voltage\n", + "T2=500.; # Braking torque\n", + "n1=1000.; # Windage and friction speed\n", + "n2=1150.; # Speed of motor\n", + "Rf=52.6; # Field resistance\n", + "Racir=0.00707; # Combined armature,compensating winding and # interpolar resistance\n", + "\n", + "# Resistance of a dynamic braking resistor\n", + "Pshaft=T1*n2/5252.; # Shaft power \n", + "Pin=Pshaft*746./eeta; # Input power\n", + "IT=Pin/VT; # Total current \n", + "If=VT/Rf; # Field current\n", + "Ia1=IT-If; # Armature current\n", + "Ea1=VT-Ia1*Racir; # Armature emf\n", + "\n", + "Ia2=Ia1*T2/T1; # Armature current\n", + "Ea2=Ea1*n1/n2;\n", + "RDB=(Ea2-Ia2*Racir)/Ia2; # Resistance\n", + "\n", + "# Display result on command window\n", + "print\"Resistance of the dynamic braking resistor =\",RDB,\"Ohm\"" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/CHAPTER12.ipynb b/Electric_Machines_by_C._I._Hubert/CHAPTER12.ipynb new file mode 100644 index 00000000..0cc125b0 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/CHAPTER12.ipynb @@ -0,0 +1,407 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# CHAPTER12 : DIRECT GENERATOR CHARACTERISTICS AND OPERATION" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E01 : Pg 479" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Field circuit resistance = 33.1914893617 Ohm\n", + "Field rheostat setting that will provide no load voltage of 140V = 10.5585106383 Ohm\n", + "Armature voltage if the rheostat is set to 14.23 ohm = 130.0 V\n", + "Field rheostat setting that will cause critical resistance = 59.5744680851 Ohm\n", + "Armature voltage at 80 percent rated speed (V)= 116\n", + "Rheostat setting required = 4.3085106383 Ohm\n" + ] + } + ], + "source": [ + "# Example 12.1\n", + "# Determine (a) Field circuit resistance (b) Field rheostat setting that will \n", + "# provide no load voltage of 140V (c) Armature voltage if the rheostat is set \n", + "# to 14.23 ohm (d) Field rheostat setting that will cause critical resistance \n", + "# (e) Armature voltage at 80 percent rated speed (f) Rheostat setting required \n", + "# to obtain no load armature voltage of 140V if shunt field is separately \n", + "# excited from a 120V DC source\n", + "# Page No. 479\n", + "# Given data\n", + "Ea=156.; # No load voltage\n", + "If=4.7; # Shunt field current\n", + "If140=2.35; # New field current at Ea=140V\n", + "Eanew=140; # No load voltage\n", + "Ifnew=3.2; # Field current corresponding to no load voltage\n", + "Ea1=0; # First arbitrary voltage\n", + "Ea2=100.; # Second arbitrary voltage\n", + "Vf=120.;\n", + "V=130.; # Intersection of I1 and I2\n", + "Rrheonew=14.42; # Rheostat set to new settings\n", + "Va=116.; # Intersection of field resistance line with the low \n", + " # speed magnetization curve\n", + "# (a) Field circuit resistance\n", + "Rf=Ea/If; # Field circuit resistance\n", + "# (b) Field rheostat setting that will provide no load voltage of 140V\n", + "Rrheo=(Eanew/Ifnew)-Rf;\n", + "# (c) Armature voltage if the rheostat is set to 14.23 ohm\n", + "Rnew=Rf+Rrheonew; # New field resistance\n", + "If1=Ea1/(Rf+Rrheo); # Field current corresponding to first arbitrary voltage\n", + "If2=Ea2/(Rf+Rrheo); # Field current corresponding to second arbitrary voltage\n", + "# (d) Field rheostat setting that will cause critical resistance \n", + "Rcr=Eanew/If140; # Critical resistance\n", + "# (e) Armature voltage at 80 percent rated speed\n", + "# Ea80=0.80*Ea;\n", + "Ea80=116;\n", + "# (f) Rheostat setting required to obtain no load armature voltage of 140V if \n", + "# shunt field is separately excited from a 120V DC source\n", + "Rrheo1=(Vf/Ifnew)-Rf; \n", + "# Display result on command window\n", + "print\"Field circuit resistance =\",Rf,\"Ohm\"\n", + "print\"Field rheostat setting that will provide no load voltage of 140V =\",Rrheo,\"Ohm\"\n", + "print\"Armature voltage if the rheostat is set to 14.23 ohm =\",V,\"V\"\n", + "print\"Field rheostat setting that will cause critical resistance =\",Rcr,\"Ohm\"\n", + "print\"Armature voltage at 80 percent rated speed (V)=\",Ea80\n", + "print\"Rheostat setting required =\",Rrheo1,\"Ohm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E02 : Pg 487" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "No load voltage = 255.0 V\n", + "Voltage regulation = 6.25 Percent\n", + "Resistance setting of rheostat necessary = 2.996 Ohm\n" + ] + } + ], + "source": [ + "# Example 12.2\n", + "# Computation of (a) No load voltage (b) Voltage regulation\n", + "# (c) Resistance setting of rheostat necessary to obtain rated voltage \n", + "# at rated conditions\n", + "# Page No. 487\n", + "# Given data\n", + "P=300000.; # Shunt generator power rating\n", + "VT=240.; # Shunt generator voltage rating\n", + "Ra=0.00234; # Armature winding resistance\n", + "RIP=0.00080; # Resistance of interpole winding\n", + "Fnet=5100.; # Net mmf\n", + "Vnl=255.; # No load voltage\n", + "Vrated=240.; # Rated voltage\n", + "Nf=1020.; # Turns per pole\n", + "Vf=120.; # Source that separately excites the generator\n", + "If=5.69;\n", + "Rf=18.1;\n", + "# (a) No load voltage\n", + "Ia=P/VT; # Armature current\n", + "Ea=VT+Ia*(Ra+RIP); # Armature emf\n", + "Ff=Fnet/(1.-0.121);\n", + "# (b) Voltage regulation\n", + "VR=(Vnl-Vrated)*100./Vrated; \n", + "# (c) Resistance setting of rheostat necessary to obtain rated voltage at rated conditions\n", + "If=Ff/Nf;\n", + "Rrheo=(Vf/If)-Rf; # Rheostat setting\n", + "# Display result on command window\n", + "print\"No load voltage =\",Vnl,\"V\"\n", + "print\"Voltage regulation =\",VR,\"Percent\"\n", + "print\"Resistance setting of rheostat necessary =\",Rrheo,\"Ohm\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E03 : Pg 492" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Induced emf at rated load = 265.003501075 V\n", + "No load voltage = 225.0 V\n", + "Voltage regulation = -10.0 Percent\n", + "The machine is overcompounded\n" + ] + } + ], + "source": [ + "# Example 12.3\n", + "# Computation of (a) Induced emf at rated load (b) No load voltage\n", + "# (c) Voltage regulation (d) What is the type of compounding?\n", + "# Page No. 492\n", + "# Given data\n", + "Pload=320000.; # Shunt generator power rating\n", + "Vrated=250.; # Shunt generator voltage rating\n", + "Rf=20.2; # Shunt resistance\n", + "Rrheo=7.70; # Shunt field rheostat value\n", + "If=8.96; # Field current\n", + "Iload=1280.; # Load current\n", + "Ra=0.00817; # Armature resistance\n", + "Rip=0.00238; # Resistance of interpole winding\n", + "Rse=0.00109; # Resistance of series winding\n", + "Nf=502.; # Turns per pole\n", + "VNL=225.; # No load voltage\n", + "\n", + "# (a) Induced emf at rated load\n", + "Iload=Pload/Vrated; # Load current\n", + "If=Vrated/(Rf+Rrheo); # Field current\n", + "Ia=If+Iload; # Armature current\n", + "Racir=Ra+Rip+Rse;\n", + "Ea=Vrated+Ia*Racir;\n", + "\n", + "# (b) No load voltage\n", + "Ff=Nf*If; \n", + "\n", + "# (c) Voltage regulation\n", + "VR=(VNL-Vrated)*100./Vrated; \n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Induced emf at rated load =\",Ea,\"V\"\n", + "print\"No load voltage =\",VNL,\"V\"\n", + "print\"Voltage regulation =\",VR,\"Percent\"\n", + "print\"The machine is overcompounded\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E04 : Pg 494" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Required resistance of a noninductive diverter = %0.5f Ohm 0.00827333333333\n", + "Power rating of the diverter = 278.8854624 W \n" + ] + } + ], + "source": [ + "# Example 12.4\n", + "# Computation of (a) Required resistance of a noninductive diverter that will \n", + "# bypass 27 percent of the total armature current(b) Power rating of the \n", + "# diverter\n", + "# Page No. 494\n", + "# Given data\n", + "Rs=0.00306; # Shunt generator resistance rating\n", + "Is=0.73; # Shunt generator current rating\n", + "Id1=0.27; # Armature winding resistance\n", + "Pload=170000.; # Load of power\n", + "VT=250.; # Shunt generator voltage rating\n", + "Id2=680.; # No load voltage\n", + "Rd=0.27; # Resistance drop\n", + "\n", + "# (a) Required resistance of a noninductive diverter that will bypass \n", + "# 27 percent of the total armature current\n", + "Rd=Rs*Is/Id1;\n", + "\n", + "\n", + "# (b) Power rating of the diverter\n", + "Ia=Pload/VT; \n", + "Pd=((Id1*Id2)**2.)*Rd;\n", + "\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"Required resistance of a noninductive diverter = %0.5f Ohm \",Rd\n", + "print\"Power rating of the diverter =\",Pd,\"W \"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E05 : Pg 500" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "New bus voltage = 3.81944444444 V\n", + "Current supplied by generator A = 1311.11111111 A\n", + "Current supplied by generator B = 1188.88888889 A\n", + "Macine A is overloaded by 9.25925925926 Percent\n" + ] + } + ], + "source": [ + "# Example 12.5\n", + "# Computation of (a) New bus voltage (b) Current supplied by each generator\n", + "# Page No. 500\n", + "# Given data\n", + "p1=300000.; # Rated power in generator A\n", + "p2=400000.; # Rated power in generator B\n", + "v=250.; # Rated voltage in machine\n", + "p3=350000.; # Rated power in generator C\n", + "Ibnew=2500.;\n", + "\n", + "# (a) New bus voltage\n", + "\n", + "IArated=p1/v; # Rated current in generator A\n", + "IBrated=p2/v; # Rated current in generator B\n", + "IBorig=p3/v; # Original bus current\n", + "IbDelta=Ibnew-IBorig; # Current difference\n", + "DelVbus=IbDelta/(160.+128.); # Voltage difference\n", + "\n", + "\n", + "# (b) Current supplied by each generator\n", + "DelIA=160.*DelVbus; # Generator A current difference\n", + "DelIB=128.*DelVbus; # Generator A current difference\n", + "Vbus=v-DelVbus; # Voltage across the bus\n", + "IA=700.+DelIA; # Current in generator A\n", + "IB=700.+DelIB; # Current in generator B\n", + "\n", + "Loading= (IA-IArated)*100./IArated;\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"New bus voltage =\",DelVbus,\"V\"\n", + "print\"Current supplied by generator A =\",IA,\"A\"\n", + "print\"Current supplied by generator B =\",IB,\"A\"\n", + "print\"Macine A is overloaded by\",Loading,\"Percent\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example E06 : Pg 502" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The increment increase in load on machine A = 100.0 A\n", + "The increment increase in load on machine B = 300.0 A\n", + "Current carried by machine A = 300.0 A\n", + "Current carried by machine B = 800.0 A\n" + ] + } + ], + "source": [ + "# Example 12.6\n", + "# Determine (a) The increment increase in load on each machine if an \n", + "# additional 400 A load is connected to the bus (b) Current carried \n", + "# by each machine\n", + "# Page No. 502\n", + "# Given data\n", + "p1=100000.; # Rated power in generator A\n", + "p2=300000.; # Rated power in generator B\n", + "v=250.; # Rated voltage in machine\n", + "p3=30000.; # Rated power in generator C\n", + "Ibnew=400.; # New bus current\n", + "I1=200.;\n", + "I2=500.;\n", + "\n", + "# (a) The increment increase in load on each machine if an additional 400 A \n", + "# load is connected to the bus\n", + "\n", + "IArated=p1/v; # Rated current in generator A\n", + "IBrated=p2/v; # Rated current in generator B\n", + "Ib=p3/v; # Original bus current\n", + "DelVbus=Ibnew/(40.+120.); # Change in bus current\n", + "DelIA=40.*DelVbus;\n", + "DelIB=120.*DelVbus;\n", + "\n", + "\n", + "# (b) Current carried by each machine\n", + "\n", + "IA=I1+DelIA; # Current in generator A\n", + "IB=I2+DelIB; # Current in generator B\n", + "\n", + "\n", + "# Display result on command window\n", + "print\"The increment increase in load on machine A =\",DelIA,\"A\"\n", + "print\"The increment increase in load on machine B =\",DelIB,\"A\"\n", + "print\"Current carried by machine A =\",IA,\"A\"\n", + "print\"Current carried by machine B =\",IB,\"A\"" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python [Root]", + "language": "python", + "name": "Python [Root]" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot02.png b/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot02.png Binary files differnew file mode 100644 index 00000000..540828f3 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot02.png diff --git a/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot04.png b/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot04.png Binary files differnew file mode 100644 index 00000000..402f6485 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot04.png diff --git a/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot06.png b/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot06.png Binary files differnew file mode 100644 index 00000000..229f15a4 --- /dev/null +++ b/Electric_Machines_by_C._I._Hubert/screenshots/Screenshot06.png |
