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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Ch-12, Parallel Operation of alternators"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.1 Page 243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a\n",
+ " load on 1 alternator 2666.67kW \n",
+ " load on 2 alternator 3333.33kW\n",
+ "b\n",
+ " load supplied by machine 1 with full load on machine2 3200kW \n",
+ " total load is 2666kW\n"
+ ]
+ }
+ ],
+ "source": [
+ "p=4000 #given kva of alternator\n",
+ "fnl1=50 #frequency on no load\n",
+ "fl1=47.5 #frequency on load\n",
+ "fnl2=50 #frequency on no load on second alternator\n",
+ "fl2=48 #frequency on load on second alternator\n",
+ "l=6000 #load given two to alternator\n",
+ "df1=fnl1-fl1 #change in 1 alternator frequency\n",
+ "df2=fnl2-fl2 #change in 2 alternator frequency\n",
+ "l1=df2*(l)/(df2+df1) #load on 1 alternator\n",
+ "print 'a'\n",
+ "l2=l-l1\n",
+ "print \" load on 1 alternator %.2fkW \\n load on 2 alternator %.2fkW\"%(l1,l2)\n",
+ "ml1=df2*p/df1 #load on 1 machine when machine 2 on full load\n",
+ "ll=ml1+p \n",
+ "print 'b'\n",
+ "print \" load supplied by machine 1 with full load on machine2 %dkW \\n total load is %dkW\"%(ml1,l1) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.2 page 243"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "induced emf of a machine a 5.35+1.52i =5.565708kV per phase\n",
+ "\n",
+ "induced emf of a machine b 4.60+1.28i =4.776461kV per phase\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, atan, acos, pi, sin\n",
+ "l1=3000 #load on 1 machine\n",
+ "pf1=0.8 #pf on 1 machine\n",
+ "i2=150 #current on 2 machine\n",
+ "z1=0.4+12*1J #synchronour impedence\n",
+ "z2=0.5+10*1J\n",
+ "vt=6.6 #terminal voltage\n",
+ "al=l1/2 #active load on each machine\n",
+ "cosdb=al/(vt*i2*sqrt(3)) #cos db\n",
+ "db=acos(cosdb)*180/pi #angle in digree\n",
+ "ib=i2*complex(cosdb,-sin(db*pi/180)) #current in complex number\n",
+ "it=l1/(vt*pf1*sqrt(3)) #total current\n",
+ "itc=complex(it*pf1,-it*sin(acos(pf1))) #total current in complex\n",
+ "ia=itc-ib \n",
+ "pfa=atan(ia.imag/ia.real) #pf of current a\n",
+ "ea=(vt/sqrt(3))+ia*(z1)/1000 #voltage a\n",
+ "pha=atan(ea.imag/ea.real)*180/pi #phase angle of unit a\n",
+ "print \"induced emf of a machine a %.2f+%.2fi =%fkV per phase\"%(ea.real,ea.imag,abs(ea))\n",
+ "eb=(vt/sqrt(3))+ib*(z2)/1000 #voltage b\n",
+ "phb=atan(eb.imag/eb.real)*180/pi #phase angle of unit b\n",
+ "print \"\\ninduced emf of a machine b %.2f+%.2fi =%fkV per phase\"%(eb.real,eb.imag,abs(eb))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.3 Page 244"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "current is 10.37-4.56iA =11.33A\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import cos,pi\n",
+ "e1=3000 ;ph1=20 ;e2=2900; ph2=0 #given induced emf of two machines\n",
+ "z1=2+20*1J ;z2=2.5+30*1J #impedence of two synchronous machine\n",
+ "zl=10+4*1J #load impedence\n",
+ "e11=e1*(cos(ph1*pi/180)+sin(ph1*pi/180)*1J)\n",
+ "e22=e2*(cos(ph2*pi/180)+sin(ph2*pi/180)*1J)\n",
+ "Is=(e11-e22)*zl/(z1*z2+(z1+z2)*zl)\n",
+ "print \"current is %.2f%.2fiA =%.2fA\"%((Is).real,(Is).imag,abs(Is))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.4 Page 244"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "terminal voltage 239.68V \n",
+ "current supplied by each 10.72A \n",
+ "power factor of each 0.894 lagging \n",
+ "power delivered by each 2297.7941KW\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, atan, acos, pi, sin\n",
+ "z=10+5*1J #load\n",
+ "e1=250 ;e2=250 #emf of generator\n",
+ "z1=2*1J; z2=2*1J #synchronous impedence\n",
+ "v=(e1*z2+z1*e2)/((z1*z2/z)+z1+z2) \n",
+ "vph=atan(v.imag/v.real)*180/pi #substitution the value in equation 12.10\n",
+ "i1=(z2*e1+(e1-e2)*z)/(z1*z2+(z1+z2)*z); iph=atan((i1).imag/(i1).real)*180/pi #substitution the value in equation 12.7\n",
+ "pf1=cos(pi/180*(vph-iph))\n",
+ "pd=v*i1*pf1\n",
+ "z=10+5*1J #load\n",
+ "e1=250 ;e2=250 #emf of generator\n",
+ "z1=2*1J; z2=2*1J #synchronous impedence\n",
+ "v=(e1*z2+z1*e2)/((z1*z2/z)+z1+z2) \n",
+ "vph=atan(v.imag/v.real)*180/pi #substitution the value in equation 12.10\n",
+ "i1=(z2*e1+(e1-e2)*z)/(z1*z2+(z1+z2)*z) \n",
+ "iph=atan(i1.imag/i1.real)*180/pi #substitution the value in equation 12.7\n",
+ "pf1=cos(pi/180*(vph-iph))\n",
+ "pd=v*i1*pf1\n",
+ "print \"terminal voltage %.2fV \\ncurrent supplied by each %.2fA \\npower factor of each %.3f lagging \\npower delivered by each %.4fKW\"%(abs(v),abs(i1),abs(pf1),abs(pd))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.5 Page 247"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(a)\n",
+ " synchronous power 872kW \n",
+ " synchronous torque for 0.5 displacement 2777N-M\n",
+ "(b) full load\n",
+ " synchronous power 977kW \n",
+ " synchronous torque for 0.5 displacement 3111N-M\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, atan, acos, pi, sin\n",
+ "po=5 #mva rating\n",
+ "v=10 #voltage in kv\n",
+ "n=1500 ;ns=n/60 #speed\n",
+ "f=50 #freaquency\n",
+ "pfb=0.8#power factor in b\n",
+ "x=0.2*1J #reactance of machine\n",
+ "md=0.5 #machanical displacement\n",
+ "#no load\n",
+ "v=1 ;e=1 \n",
+ "p=4\n",
+ "spu=v*e/abs(x); sp=spu*po*1000 ;mt=(pi*p)/(180*2)\n",
+ "spm=sp*mt #synchronous power in per mech.deree\n",
+ "st=spm*md*1000/(2*ns*pi)\n",
+ "print '(a)'\n",
+ "print \" synchronous power %dkW \\n synchronous torque for %.1f displacement %dN-M\"%(spm,md,st)\n",
+ "print '(b) full load'\n",
+ "ee=e+x*(pfb-sin(acos(pfb))*1J)\n",
+ "spb=v*abs(ee)*cos(atan(ee.imag/ee.real))/abs(x) #synchronous power \n",
+ "sppm=spb*po*1000*mt #synchronous power per mech.degree\n",
+ "stp=sppm*md*1000/(2*pi*ns)#synchrounous torque under load\n",
+ "print \" synchronous power %dkW \\n synchronous torque for %.1f displacement %dN-M\"%(sppm,md,stp)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.6 page 248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ " synchronous power 502.7kW per mech.degree \n",
+ " synchrounous torque 6666N-m\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, atan, acos, pi, sin\n",
+ "po=2*10**6 ;p=8 ;n=750; v=6000 ;x=6*1J ;pf=0.8 #given \n",
+ "i=po/(v*sqrt(3))\n",
+ "e=(v/sqrt(3))+i*x*(pf-sin(acos(pf))*1J)\n",
+ "mt=p*pi/(2*180)\n",
+ "cs=cos(atan(e.imag/e.real))\n",
+ "ps=abs(e)*v*sqrt(3)*cs*mt/(1000*abs(x))\n",
+ "ns=n/60\n",
+ "ts=ps*1000/(2*pi*ns)\n",
+ "print \" synchronous power %.1fkW per mech.degree \\n synchrounous torque %dN-m\"%(ps,ts)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## example 12.7 page 248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "a\n",
+ " open circuit emf 6598volts per phase and -2.78 degree\n",
+ "b.\n",
+ " current 365.6A \n",
+ " power factor 0.998\n",
+ "c.\n",
+ "current 456.25A\n",
+ "current 456.25A\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import sqrt, atan, acos, pi, sin\n",
+ "i=100 ;pf=-0.8 ;v=11*1000 ;x=4*1J ;ds=10; pfc=-0.8 #given,currents,power factor,voltage,reactance,delta w.r.t steem supply,pf of alternator\n",
+ "e=(v/sqrt(3))+(i*x*(pf-sin(acos(pf))*1J))\n",
+ "print 'a'\n",
+ "ph=atan(e.imag/e.real)*180/pi\n",
+ "print \" open circuit emf %dvolts per phase and %.2f degree\"%(abs(e),ph)\n",
+ "d=ds-ph\n",
+ "eee=round(abs(e)/100)*100\n",
+ "ic=round(abs(eee)*sin(d*pi/180)/abs(x))\n",
+ "iis=(eee**2-(abs(x)*ic)**2)**(0.5)\n",
+ "Is=(iis-v/sqrt(3))/abs(x)\n",
+ "tad=Is/ic\n",
+ "d=atan(tad)*180/pi\n",
+ "ii=ic/cos(d*pi/180)\n",
+ "pff=cos(d*pi/180)\n",
+ "print 'b.'\n",
+ "print \" current %.1fA \\n power factor %.3f\"%(ii,pff)\n",
+ "print 'c.'\n",
+ "ia=ii*pff/abs(pfc)\n",
+ "print \"current %.2fA\"%(ia)\n",
+ "\n",
+ "ia=ii*pff/abs(pfc)\n",
+ "print \"current %.2fA\"%(ia)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.9"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
generated by cgit (git 2.34.1) at 2024-12-20 10:10:28 +0000