{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 17: POWER SYSTEM SYNCHRONOUS STABILITY"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.10: EX17_10.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// To Determine the rotor angle and angular frequency  using runga kutta and euler`s modified method\n",
"\n",
"clc\n",
"clear\n",
"Pm=3;\n",
"r1Pm=1.2;\n",
"r2Pm=2;\n",
"H=3;\n",
"f=60;\n",
"Dt=.02;\n",
"Pe=1.5;\n",
"Do=asind(1.5/3);\n",
"do=Do/57.33;\n",
"wo=0;\n",
"d=0;\n",
"K10=0;\n",
"l10=62.83*(1.5-1.2*sin(do))*.02;\n",
"K20=(377.5574-376.992)*.02;\n",
"l20=62.83*(1.5-1.2*sin(do))*.02;\n",
"K30=(377.5574-376.992)*.02;\n",
"l30=62.83*(1.5-1.2*sin(.5296547))*.02;\n",
"K40=l30*0.02;\n",
"l40=62.83*(1.5-1.2*sin(.5353094))*.02;\n",
"d1=.53528;\n",
"Dwo=(3*1.13094+2*1.123045+1.115699)/6;\n",
"w1=wo+Dwo;\n",
"d1=.53528;\n",
"mprintf('Runga-Kutta method-\n')\n",
"mprintf('w1=%.6f \nd1=%.5f\n',w1,d1);\n",
"d7=1.026;\n",
"w7=6.501;\n",
"wp=376.992+6.501;\n",
"K17=(wp-376.992)*0.02;\n",
"l17=62.83*(1.5-1.2*sin(1.026))*.02;\n",
"K27=(6.501+.297638)*0.02;\n",
"l27=62.83*(1.5-1.2*sin(1.09101))*.02;\n",
"K37=(6.501+.2736169)*0.02;\n",
"l37=62.83*(1.5-1.2*sin(1.0939863))*.02;\n",
"K47=(6.501+.545168)*0.02;\n",
"l47=62.83*(1.5-1.2*sin(1.16149))*.02;\n",
"Dd7=(K17+2*K27+2*K37+K47)/6;\n",
"d8=d7+Dd7;\n",
"Dw7=(l17+2*l27+2*l37+l47)/6;\n",
"w8=w7+Dw7;\n",
"mprintf('d8=%.5f rad.\nw8=%.4frad/sec\n\n',d8,w8)\n",
"mprintf('using Euler`s Modified Method-\n');\n",
"d0=0;\n",
"d10=.524;\n",
"w=62.83*(1.5-1.2*sin(.524));\n",
"d11=d10+0;\n",
"w11=w*.02;\n",
"d=1.13094;\n",
"dav=(0+d)/2;\n",
"wav=(56.547+56.547)/2;\n",
"d01=.524+.56547*.02;\n",
"w11=0+56.547*0.02;\n",
"mprintf('d01=%.4f\nw11=%.5f',d01,w11);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.1: EX17_1.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// To determine the acceleration . Also determine the change in torque angle and r.p.mat the end of 15 cycles\n",
"clear\n",
"clc;\n",
"H=9;\n",
"G=20;// machine Rating(MVA)\n",
"KE=H*G;\n",
"mprintf('(a)K.E stored in the rotor =%.0f MJ\n',KE);\n",
"Pi=25000*.735;\n",
"PG=15000;\n",
"Pa=(Pi-PG)/(1000);\n",
"f=50;\n",
"M=G*H/(%pi*f);\n",
"a=Pa/M;\n",
"mprintf('(b) The accelerating power =%.3f MW\n',Pa);\n",
"mprintf('Acceleration =%.3f rad/sec_2\n',a);\n",
"t=15/50;\n",
"del=sqrt(5.89)*t/2;\n",
"Del=del^2;\n",
"k=2.425*sqrt(Del)*60/4*%pi;\n",
"speed=1504.2;\n",
"mprintf('(c)Rotor speed at the end of 15 cycles =%.1f r.p.m',speed);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.2: EX17_2.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// To determine the frequency of natural oscillations if the genrator is loaded to (i)60% and (ii)75% of its maximum power transfer capacity\n",
"clear \n",
"clc;\n",
"V1=1.1;\n",
"V2=1;\n",
"X=.5;\n",
"cosdo=.8;\n",
"G=1;\n",
"H=3;\n",
"f=50;\n",
"M=G*H/(%pi*f);\n",
"dPe=V1*V2*cosdo/X;\n",
"fn=(((dPe)/M)^.5)/6.28;\n",
"sind0=.75;\n",
"d0=asind(sind0);\n",
"dPe2=V1*V2*cosd(d0)/X;\n",
"fn2=(((dPe2)/M)^.5)/6.28;\n",
"mprintf('(i)fn=%.2f Hz\n',fn);\n",
"mprintf('(i)fn(Hz)=%.2f Hz',fn2);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.3: EX17_3.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//To calculate the maximum value of d during the swinging of the rotor around its new equilibrium position\n",
"clc\n",
"clear\n",
"a=.25;//sindo=.25\n",
"do=asind(a);//\n",
"b=.5//sindc=.5\n",
"dc=asind(b);\n",
"c=cosd(do)+.5*do*%pi/180;\n",
"dm=dc;\n",
"e=1;\n",
"while(e>.0001)\n",
"    dm=dm+.1;\n",
"    e=abs(c-(((.5*dm*%pi)/180)+cosd(dm)));\n",
"end\n",
"printf('dm approximately found to be %d degree',dm);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.4: To_calculate_the_critical_clearing_angle_for_the_condition_described.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// To calculate the critical clearing angle for the condition described.\n",
"clear \n",
"clc;\n",
"sindo=.5;\n",
"d0=asind(sindo)*%pi/180;\n",
"r1=.2;\n",
"r2=.75;\n",
"sindm=.5/.75;\n",
"d=asind(sindm);\n",
"cosdm=cosd(d);\n",
"dm=%pi*(180-(asind(sindm)))/180;\n",
"Dc=((.5*(dm-d0))-(r2*cosdm)-(r1*cosd(d0)))/(r2-r1);\n",
"dc=acosd(Dc);// critical angle\n",
"mprintf('The critical clearing angle  is given by=%.2f degrees',dc);//Answers don't match due to difference in rounding off of digits"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.5: To_calculate_the_critical_clearing_angle_for_the_generator_for_a_3phase_fault.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// To calculate the critical clearing angle for the generator for a 3-phase fault\n",
"clear \n",
"clc;\n",
"ZA=.375;\n",
"ZB=.35;\n",
"ZC=.0545;\n",
"ZAB=((ZA*ZB)+(ZB*ZC)+(ZC*ZA))/ZC;//Reactance between the generator and infinite bus during the fault(p.u)\n",
"Zgbf=%i*.3+ %i*(.55/2) +%i*.15;//Reactance between the generator and infinite bus before the fault(p.u)\n",
"Zgb=%i*.3+ %i*(.55) +%i*.15;//Reactance between the generator and infinite bus after the fault is cleared (p.u)\n",
"Pmaxo=1.2*1/abs(Zgbf);// Maximum power output Before the fault(p.u)\n",
"Pmax1=1.2*1/abs(ZAB);// Maximum power output during the fault(p.u)\n",
"Pmax2=1.2*1/abs(Zgb);// Maximum power output after the fault(p.u)\n",
"r1=Pmax1/Pmaxo;\n",
"r2=Pmax2/Pmaxo;\n",
"Ps=1;\n",
"sindo=Ps/Pmaxo;\n",
"do=asind(sindo);\n",
"d0=asind(sindo)*%pi/180;\n",
"sindm=1/Pmax2;\n",
"cosdm=cosd(asind(sindm));\n",
"Dm=%pi*(180-(asind(sindm)))/180;\n",
"Dc=(((sindo*(Dm-d0))-(r2*cosdm))-(r1*cosd(do)))/(r2-r1);\n",
"dc=acosd(Dc);// critical angle\n",
"mprintf('The critical clearing angle is given by= %.1f ',dc);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.6: determine_the_critical_clearing_angle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//(A) determine the critical clearing angle \n",
"clear \n",
"clc;\n",
"Pm=%i*.12 + %i*.035 + ((%i*.25*%i*.3)/%i*.55);\n",
"Pm1=0;\n",
"Pm2=1.1*1/.405;\n",
"r1=0;\n",
"r2=2.716/3.775;\n",
"d0=(asind(1/3.775));\n",
"dM=(180-asind(1/2.716));\n",
"do=d0*%pi/180;\n",
"dm=dM*%pi/180;\n",
"dc=acosd((((dm-do)*sind(d0))-(r1*cosd(d0))+(r2*cosd(dM)))/(r2-r1));\n",
"mprintf('dc=%.2f',dc);\n",
""
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.7: EX17_7.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// To determine the centre and radius for the pull out curve ans also minimum output vars when the output powers are (i)0 (ii).25p.u (iii) .5p.u\n",
"clear \n",
"clc;\n",
"Pc=0;\n",
"V=.98;\n",
"Qc=V^2*((1/.4)-(1/1.1))/2;\n",
"R=V^2*((1/.4)+(1/1.1))/2;\n",
"Q=-(.98^2*((1.1-.4)/.44)/2) + (.98^2)*1.5/(2*.44);\n",
"mprintf('(i)Q=%.2f MVAr\n',abs(Q)*100);\n",
"P=.25;\n",
"Q2=-((1.637^2)-(.25^2))^.5 + .7639;\n",
"mprintf('(ii)Q=%.4f p.u\n',Q2);\n",
"Q3=-((1.637^2)-(.5^2))^.5 + .7639;\n",
"mprintf('(iii)Q=%.4f p.u',Q3);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.8: Compute_the_prefault_faulted_and_post_fault_reduced_Y_matrices.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Compute the prefault, faulted and post fault reduced Y matrices\n",
"clear \n",
"clc;\n",
"y=[-%i*5 0 %i*5 ; 0 -%i*5 %i*5;%i*5 %i*5 -%i*10 ];\n",
"YAA=[-%i*5 0;0 -%i*5];\n",
"YAB=[%i*5;%i*5];\n",
"YBA=[%i*5 %i*5];\n",
"YBB=[%i*10];\n",
"Y=YAA-YAB*(inv(YBB))*YBA;\n",
"Yfull=[-%i*5 0 %i*5;0 -%i*7.5 %i*2.5;%i*5 %i*2.5 -%i*12.5];\n",
"disp(Yfull,'(i)faulted case, full matrix(admittance)=');\n",
"Y=[-%i*3 %i*1;%i*1 -%i*7];\n",
"disp(Y,'(ii)Pre-fault case, reduced admittance matrix=');\n",
"Y=[-%i*5 0 %i*5;0 -%i*2.5 %i*2.5;%i*5 %i*2.5 -%i*7.5];\n",
"disp(Y,'(iii)Post-fault case, full matrix(admittance)=');\n",
"Y=[-%i*1.667 %i*1.667;%i*1.667 -%i*1.667];\n",
"disp(Y,' reduced admittance matrix=');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 17.9: EX17_9.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"//Determine the reduced admittance matrices for prefault, fault and post fault conditions and determine the power angle characterstics for three conditions.\n",
"clear \n",
"clc;\n",
"Y=[-%i*8.33 0 %i*8.33 0;0 -%i*28.57 0 %i*28.75;%i*8.33 0 -%i*15.67 %i*7.33;0 %i*28.57 %i*7.33 -%i*35.9];\n",
"YBB=[-%i*15.67 %i*7.33;%i*7.33 -%i*35.9];\n",
"YAA=[-%i*8.33 0;0 -%i*28.57];\n",
"YAB=[%i*8.33 0;0 %i*28.57];\n",
"YBA=YAB;\n",
"Y=YAA-(YAB*(inv(YBB))*YBA);\n",
"Y1=([-%i*8.33 0;0 -%i*28.57])-(([0;(%i*28.57/-%i*35.9)]*[0 %i*28.57]));\n",
"disp(Y1,'Reduced admittance matrix during fault=');\n",
"Yfull=[-%i*8.33 0 %i*8.33 0;0 -%i*28.57 0 %i*28.75;%i*8.33 0 -%i*12.33 %i*4;0 %i*28.57 %i*4 -%i*32.57];\n",
"YBB=[-%i*12.33 %i*4;%i*4 -%i*32.57];\n",
"Y=YAA-(YAB*(inv(YBB))*YBA);\n",
"disp(Y,'(i) Post fault condition ,reduced matrix=');\n",
"Y12=Y(1,2);\n",
"E1=1.1;\n",
"E2=1;\n",
"printf('\n Power angle characterstics , Pe= %fsind',abs(Y12)*E1*E2);"
   ]
   }
],
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			{
			 "text": "MetaKernel Magics",
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