{
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"source": [
"# Chapter 4 - AC to AC Converters"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4.1 page 158"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" rms load voltage = 101.70 V\n",
"\n",
" rms load current = 20.34 A\n",
"\n",
" rms thyristor current = 14.38 A\n",
"\n",
" input power factor = 0.442 \n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin\n",
"R=5 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 120 # degree\n",
"\n",
"Vor=Vs*sqrt(1/pi*(pi-alpha*pi/180+sin(2*alpha*pi/180)/2)) # V\n",
"print '\\n rms load voltage = %.2f V'%( Vor)\n",
"Ior=Vor/R # A\n",
"print '\\n rms load current = %.2f A'%( Ior)\n",
"Irms=Ior/sqrt(2) # A\n",
"print '\\n rms thyristor current = %.2f A'%( Irms)\n",
"pf=sqrt(1/pi*((pi-alpha*pi/180)+sin(2*alpha*pi/180)/2)) # power factor\n",
"print '\\n input power factor = %.3f '%(pf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4.2 page 158"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" (a) rms output voltage = 138 V\n",
"\n",
" (b) Power output to load = 1904.4 W\n",
"\n",
" (c) Power input to regulator = 1904.4 W\n",
"\n",
" (d) input power factor = 0.6 \n",
"\n",
" (e) average scr current = 3.727 A\n",
"\n",
" rms scr current = 9.758 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin\n",
"R=10 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"nc=18 # conducting cycles\n",
"noff=32 # off cycles\n",
"\n",
"k=nc/(nc+noff) # duty ratio\n",
"Vor=Vs*sqrt(k) # V\n",
"Po=Vor**2/R # W\n",
"Pi=Po # W (losses are negligble)\n",
"Ior=Vor/R # A\n",
"pf=Po/Vs/Ior # W\n",
"Im=Vs*sqrt(2)/R # A\n",
"Irms=Im*sqrt(k)/2 # A\n",
"Iav=k*Im/pi # A\n",
"print '\\n (a) rms output voltage = %.0f V'%( Vor)\n",
"print '\\n (b) Power output to load = %.1f W'%( Po)\n",
"print '\\n (c) Power input to regulator = %.1f W'%( Pi)\n",
"print '\\n (d) input power factor = %.1f '%(pf)\n",
"print '\\n (e) average scr current = %.3f A'%( Iav)\n",
"print '\\n rms scr current = %.3f A'%( Irms)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4.3 page 159"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" rms load voltage = 162.63 V\n",
"\n",
" rms load current = 16.26 A\n",
"\n",
" power input = 2645.00 W\n",
"\n",
" load power factor = 0.7 \n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin\n",
"R=10 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 90 # degree\n",
"\n",
"Vor=Vs*sqrt(1/pi*(pi-alpha*pi/180+sin(2*alpha*pi/180)/2)) # V\n",
"Ior=Vor/R # A\n",
"P=Ior**2*R # W\n",
"pf=Vor/Vs # power factor\n",
"print '\\n rms load voltage = %.2f V'%( Vor)\n",
"print '\\n rms load current = %.2f A'%( Ior)\n",
"print '\\n power input = %.2f W'%( P)\n",
"print '\\n load power factor = %.1f '%(pf)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4.4 page 160"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" rms load voltage = 219.30 V\n",
"\n",
" rms load current = 7.31 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin\n",
"\n",
"R=30 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"alpha = 45 # degree\n",
"\n",
"Vor=Vs*sqrt(1/pi*(pi-alpha*pi/180+sin(2*alpha*pi/180)/2)) # V\n",
"Ior=Vor/R # A\n",
"print '\\n rms load voltage = %.2f V'%( Vor)\n",
"print '\\n rms load current = %.2f A'%( Ior)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4.5 page 160"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" max load voltage = 230.00 V\n",
"\n",
" max load current = 16.263 A\n",
"\n",
" range of delay angle = 0 to 45\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin,tan\n",
"\n",
"R=10 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"fi = 45 # degree\n",
"\n",
"Vmax=Vs # V(max supply voltage)\n",
"XL=R*tan(fi*pi/180) # ohm\n",
"Z=XL*sqrt(2) # ohm\n",
"Imax=Vs/Z # A\n",
"\n",
"print '\\n max load voltage = %.2f V'%( Vmax)\n",
"print '\\n max load current = %.3f A'%( Imax)\n",
"print '\\n range of delay angle = %d to %d'%(0,fi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex 4.7 page 161"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
" (i) control range of firing angle = 53.13 to pi\n",
"\n",
" (ii) max rms load current = 46 A\n",
"\n",
" (iii) max power input to load = 6348 W\n",
"\n",
" (iv) max power factor = 0.6 \n",
"\n",
" (v) max rms thyristor current = 32.527 A\n",
"\n",
" max average thyristor current = 20.718 A\n"
]
}
],
"source": [
"from __future__ import division\n",
"from math import sqrt,pi,sin,atan\n",
"\n",
"R=3 # ohm\n",
"wL=4 # ohm\n",
"Vs=230 # V\n",
"f=50 # Hz\n",
"\n",
"fi=atan(wL/R)*180/pi # degree\n",
"print '\\n (i) control range of firing angle = %.2f to pi'%(fi)\n",
"Imax=Vs/sqrt(R**2+wL**2) # A\n",
"print '\\n (ii) max rms load current = %.f A'%( Imax)\n",
"Pmax=Imax**2*R # W\n",
"print '\\n (iii) max power input to load = %.f W'%( Pmax)\n",
"pf_max=Pmax/Vs/Imax # power factor\n",
"print '\\n (iv) max power factor = %.1f '%( pf_max)\n",
"Ithrms=Imax/sqrt(2) # A\n",
"Ithav=Ithrms/1.57 # A\n",
"print '\\n (v) max rms thyristor current = %.3f A'%( Ithrms)\n",
"print '\\n max average thyristor current = %.3f A'%( Ithav)"
]
}
],
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