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diff --git a/Power_System_Engineering_by_S_Chakraborthy/17-POWER_SYSTEM_STABILITY.ipynb b/Power_System_Engineering_by_S_Chakraborthy/17-POWER_SYSTEM_STABILITY.ipynb new file mode 100644 index 0000000..5c3a3a0 --- /dev/null +++ b/Power_System_Engineering_by_S_Chakraborthy/17-POWER_SYSTEM_STABILITY.ipynb @@ -0,0 +1,1426 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 17: POWER SYSTEM STABILITY" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.10: EX17_10.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.10 :\n", +"// Page number 275-276\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"E_1 = 1.1 // Sending end voltage(p.u)\n", +"x_d1 = 1.0 // Reactance(p.u)\n", +"x_T1 = 0.1 // Reactance(p.u)\n", +"x_l1 = 0.4 // Reactance(p.u)\n", +"x_l2 = 0.4 // Reactance(p.u)\n", +"x_T2 = 0.1 // Reactance(p.u)\n", +"E_2 = 1.0 // Receiving end voltage(p.u)\n", +"x_d2 = 1.0 // Reactance(p.u)\n", +"x_L = 1.0 // Shunt inductor reactance(p.u)\n", +"x_C = 1.0 // Static capacitor reactance(p.u)\n", +"delta = 30.0 // δ(°)\n", +"\n", +"// Calculations\n", +"// Case(a)\n", +"Z_1_a = x_d1+x_T1+(x_l1/2.0) // Reactance(p.u)\n", +"X_1_a = %i*Z_1_a\n", +"Z_2_a = x_T2+x_d2 // Reactance(p.u)\n", +"X_2_a = %i*Z_2_a\n", +"Z_3_a = -x_C // Reactance(p.u)\n", +"X_3_a = %i*Z_3_a\n", +"X_a = X_1_a+X_2_a+(X_1_a*X_2_a/X_3_a) // Transfer reactance(p.u)\n", +"P_max_a = E_1*E_2/abs(X_a) // Maximum steady state power if static capacitor is connected(p.u)\n", +"P_a = P_max_a*sind(delta) // Value of P(p.u)\n", +"Q_a = (E_1*E_2/abs(X_a))*cosd(delta)-(E_2**2/abs(X_a)) // Value of Q(p.u)\n", +"// Case(b)\n", +"Z_1_b = x_d1+x_T1+(x_l1/2.0) // Reactance(p.u)\n", +"X_1_b = %i*Z_1_b\n", +"Z_2_b = x_T2+x_d2 // Reactance(p.u)\n", +"X_2_b = %i*Z_2_b\n", +"Z_3_b = x_L // Reactance(p.u)\n", +"X_3_b = %i*Z_3_b\n", +"X_b = X_1_b+X_2_b+(X_1_b*X_2_b/X_3_b) // Transfer reactance(p.u)\n", +"P_max_b = E_1*E_2/abs(X_b) // Maximum steady state power if static capacitor is replaced by an inductive reactor(p.u)\n", +"P_b = P_max_b*sind(delta) // Value of P(p.u)\n", +"Q_b = (E_1*E_2/abs(X_b))*cosd(delta)-(E_2**2/abs(X_b)) // Value of Q(p.u)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.10 : SOLUTION :-')\n", +"printf('\nCase(a): Maximum steady state power if static capacitor is connected, P_max = %.3f p.u', P_max_a)\n", +"printf('\n Value of P = %.3f p.u', P_a)\n", +"printf('\n Value of Q = %.3f p.u', Q_a)\n", +"printf('\nCase(b): Maximum steady state power if static capacitor is replaced by an inductive reactor, P_max = %.3f p.u', P_max_b)\n", +"printf('\n Value of P = %.3f p.u', P_b)\n", +"printf('\n Value of Q = %.4f p.u', Q_b)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.11: Kinetic_energy_stored_in_the_rotor_at_synchronous_speed_and_Acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.11 :\n", +"// Page number 303\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 50.0 // Frequency(Hz)\n", +"G = 100.0 // Rating of generator(MVA)\n", +"H = 5.0 // Inertia constant(MJ/MVA)\n", +"P_a = 20.0 // Acceleration power(MVA)\n", +"\n", +"// Calculations\n", +"GH = G*H // Energy stored in rotor at synchronous speed(MJ)\n", +"M = GH/(180*f) // Angular momentum\n", +"acceleration = P_a/M // Acceleration(°/sec^2)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.11 : SOLUTION :-')\n", +"printf('\nKinetic energy stored in the rotor at synchronous speed, GH = %.f MJ', GH)\n", +"printf('\nAcceleration = %.f°/sec^2', acceleration)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.12: Kinetic_energy_stored_in_the_rotor_at_synchronous_speed_and_Acceleration.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.12 :\n", +"// Page number 303-304\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 50.0 // Frequency(Hz)\n", +"P = 4.0 // Number of poles\n", +"G = 20.0 // Rating of generator(MVA)\n", +"H = 9.0 // Inertia constant(kWsec/MVA)\n", +"P_m = 26800.0 // Rotational loss(hp)\n", +"P_e = 16000.0 // Electric power developed(kW)\n", +"\n", +"// Calculations\n", +"GH = G*H // Energy stored in rotor at synchronous speed(MJ)\n", +"P_m_kW = P_m*0.746 // Rotational loss(kW)\n", +"P_a = P_m_kW-P_e // Acceleration power(kW)\n", +"P_a1 = P_a/1000.0 // Acceleration power(MW)\n", +"M = GH/(180*f) // Angular momentum\n", +"acceleration = P_a1/M // Acceleration(°/sec^2)\n", +"acceleration_1 = acceleration*%pi/180.0 // Acceleration(rad/sec^2)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.12 : SOLUTION :-')\n", +"printf('\nKinetic energy stored in the rotor at synchronous speed, GH = %.f MJ', GH)\n", +"printf('\nAcceleration = %.f°/sec^2 = %.2f rad/sec^2 \n', acceleration,acceleration_1)\n", +"printf('\nNOTE: ERROR: H = 9 kW-sec/MVA, not 9 kW-sec/kVA as mentioned in the textbook statement')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.13: Change_in_torque_angle_in_that_period_and_RPM_at_the_end_of_10_cycles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.13 :\n", +"// Page number 304\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 50.0 // Frequency(Hz)\n", +"P = 4.0 // Number of poles\n", +"alpha = 200.0 // Acceleration(°/sec^2)\n", +"alpha_rad = 3.49 // Acceleration(rad/sec^2)\n", +"n = 10.0 // Number of cycle\n", +"\n", +"// Calculations\n", +"t = 1/f*n // Time(sec)\n", +"delta_rel = ((alpha_rad*2)**0.5*0.5)**2 // Relation of change in rotor angle with time(rad)\n", +"delta = delta_rel*t**2 // Change in torque angle(rad)\n", +"delta_deg = delta*180/%pi // Change in torque angle in that period(°)\n", +"rpm_rad = (alpha_rad*2*delta)**0.5 // r.p.m(rad/sec)\n", +"rpm = rpm_rad*60.0/(%pi*P) // r.p.m\n", +"speed_rotor = (120*f/P)+rpm // Rotor speed at the end of 10 cycles(r.p.m)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.13 : SOLUTION :-')\n", +"printf('\nChange in torque angle in that period, δ = %.4f rad = %.f elect degree', delta,delta_deg)\n", +"printf('\nRotor speed at the end of 10 cycles = %.2f r.p.m', speed_rotor)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.14: Accelerating_torque_at_the_time_the_fault_occurs.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.14 :\n", +"// Page number 304\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"Power = 20.0*10**3 // Rating of generator(kVA)\n", +"PF = 0.8 // Lagging power factor\n", +"fault = 0.5 // Reduction in output under fault\n", +"P = 4.0 // Number of poles\n", +"f = 50.0 // Frequency(Hz)\n", +"\n", +"// Calculations\n", +"P_m = Power*PF // Output power before fault(kW)\n", +"P_e = fault*P_m // Output after fault(kW)\n", +"P_a = P_m-P_e // Accelerating power(kW)\n", +"w_s = 4.0*%pi*f/P // Speed\n", +"T_a = P_a*10**3/w_s // Accelerating torque at the time the fault occurs(N-m)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.14 : SOLUTION :-')\n", +"printf('\nAccelerating torque at the time the fault occurs, T_a = %.2f N-m', T_a)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.16: Value_of_H_and_in_100_MVA_base.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.16 :\n", +"// Page number 304-305\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"S = 1000.0 // Rating of generator(MVA)\n", +"N = 1500.0 // Speed of alternator(r.p.m)\n", +"WR_sq = 5.0*10**6 // WR^2(lb.ft^2)\n", +"\n", +"// Calculations\n", +"H = 2.31*10**-10*WR_sq*N**2/S // Inertia constant(MJ/MVA)\n", +"H_100 = H*1000.0/100 // Inertia constant on 100 MVA(MJ/MVA)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.16 : SOLUTION :-')\n", +"printf('\nValue of inertia constant, H = %.1f MJ/MVA', H)\n", +"printf('\nValue of inertia constant in 100 MVA base, H = %.f MJ/MVA', H_100)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.17: Equivalent_H_for_the_two_to_common_100_MVA_base.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.17 :\n", +"// Page number 305\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"MVA_1 = 500.0 // Rating of generator(MVA)\n", +"H_1 = 4.0 // Inertia constant(MJ/VA)\n", +"MVA_2 = 1000.0 // Rating of generator(MVA)\n", +"H_2 = 3.5 // Inertia constant(MJ/VA)\n", +"MVA = 100.0 // Base MVA\n", +"\n", +"// Calculations\n", +"KE_T = H_1*MVA_1+H_2*MVA_2 // Total KE of the system(MJ)\n", +"H_total = KE_T/MVA // Equivalent H for the two to common 100MVA base(MJ/MVA)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.17 : SOLUTION :-')\n", +"printf('\nEquivalent H for the two to common 100 MVA base, H = %.f MJ/MVA', H_total)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.18: Energy_stored_in_the_rotor_at_the_rated_speed_Value_of_H_and_Angular_momentum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.18 :\n", +"// Page number 305\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"MVA = 210.0 // Rating of generator(MVA)\n", +"P = 2.0 // Number of poles\n", +"f = 50.0 // Frequency(Hz)\n", +"MI = 60.0*10**3 // Moment of inertia(kg-mt^2)\n", +"\n", +"// Calculations\n", +"N = 120.0*f/P // Speed(r.p.m)\n", +"KE = 1.0/2*MI*(2*%pi*N/f)**2/10**6 // Energy stored in the rotor at rated speed(MJ)\n", +"H = KE/MVA // Inertia constant(MJ/MVA)\n", +"G = MVA\n", +"M = G*H/(180*f) // Angular momentum(MJ-sec/elect.degree)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.18 : SOLUTION :-')\n", +"printf('\nEnergy stored in the rotor at the rated speed, KE = %.2e MJ', KE)\n", +"printf('\nValue of inertia constant, H = %.2f MJ/MVA', H)\n", +"printf('\nAngular momentum, M = %.3f MJ-sec/elect.degree', M)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.19: Acceleration_of_the_rotor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.19 :\n", +"// Page number 305\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"P_accl = 30.0 // Acceleration power(MVA)\n", +"M = 0.474 // Angular momentum(MJ-sec/elect.degree). From Example 10.18\n", +"\n", +"// Calculations\n", +"acceleration = P_accl/M // Acceleration of the rotor(elect.degree/sec^2)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.19 : SOLUTION :-')\n", +"printf('\nAcceleration of the rotor = %.2f elect.degree/sec^2', acceleration)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.1: Operating_power_angle_and_Magnitude_of_P0.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.1 :\n", +"// Page number 270\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"Z = 0.1 // Impedance of transmission line(p.u)\n", +"M = 0.3 // Stability margin\n", +"X = 1.0 // Constant(p.u)\n", +"\n", +"// Calculations\n", +"sin_delta_0 = 1-M // Sin(δ_0)\n", +"delta_0 = asind(sin_delta_0) // δ_0(°)\n", +"P_0 = X/Z*sin_delta_0 // Magnitude of P_0(p.u)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.1 : SOLUTION :-')\n", +"printf('\nOperating power angle, δ_0 = %.2f° ', delta_0)\n", +"printf('\nP_0 = %.2f p.u', P_0)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.20: Accelerating_power_and_New_power_angle_after_10_cycles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.20 :\n", +"// Page number 305\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"MVA = 50.0 // Rating of alternator(MVA)\n", +"P = 4.0 // Number of poles\n", +"f = 50.0 // Frequency(Hz)\n", +"KE = 150.0 // Kinetic energy stored in rotor(MJ)\n", +"P_m = 25.0 // Machine input(MW)\n", +"P_e = 22.5 // Developed power(MW)\n", +"n = 10.0 // Number of cycles\n", +"\n", +"// Calculations\n", +"P_a = P_m-P_e // Accelerating power(MW)\n", +"H = KE/MVA // Inertia constant(MJ/MVA)\n", +"G = MVA\n", +"M_deg = G*H/(180*f) // Angular momentum(MJ-sec/elect.degree)\n", +"M = G*H/(%pi*f) // Angular momentum(MJ-sec/rad)\n", +"acceleration = P_a/M // Accelerating power(rad/sec^2)\n", +"t = 1/f*n // Time(sec)\n", +"delta = 1.309*t**2 // Term in δ\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.20 : SOLUTION :-')\n", +"printf('\nAccelerating power = %.3f rad/sec^2', acceleration)\n", +"printf('\nNew power angle after 10 cycles, δ = (%.3f + δ_0) rad', delta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.21: Kinetic_energy_stored_by_rotor_at_synchronous_speed_and_Acceleration_in.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.21 :\n", +"// Page number 305-306\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 50.0 // Frequency(Hz)\n", +"P = 4.0 // Number of poles\n", +"G = 20.0 // Rating of turbo-generator(MVA)\n", +"V = 13.2 // Voltage(kV)\n", +"H = 9.0 // Inertia constant(kW-sec/kVA)\n", +"P_s = 20.0 // Input power less rotational loss(MW)\n", +"P_e = 15.0 // Output power(MW)\n", +"\n", +"// Calculations\n", +"KE = G*H // Kinetic energy stored(MJ)\n", +"M = G*H/(180*f) // Angular momentum(MJ-sec/elect.degree)\n", +"P_a = P_s-P_e // Accelerating power(MW)\n", +"alpha = P_a/M // Acceleration(elect.degree/sec^2)\n", +"alpha_deg = alpha/2.0 // Acceleration(degree/sec^2)\n", +"alpha_rpm = 60.0*alpha_deg/360 // Acceleration(rpm/sec)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.21 : SOLUTION :-')\n", +"printf('\nCase(a): Kinetic energy stored by rotor at synchronous speed, GH = %.f MJ', KE)\n", +"printf('\nCase(b): Acceleration, α = %.f degree/sec^2', alpha_deg)\n", +"printf('\n Acceleration, α = %.2f rpm/sec', alpha_rpm)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.22: Change_in_torque_angle_and_Speed_in_rpm_at_the_end_of_10_cycles.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.22 :\n", +"// Page number 306\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 50.0 // Frequency(Hz)\n", +"P = 4.0 // Number of poles\n", +"G = 20.0 // Rating of turbo-generator(MVA)\n", +"V = 13.2 // Voltage(kV)\n", +"H = 9.0 // Inertia constant(kW-sec/kVA)\n", +"P_s = 20.0 // Input power less rotational loss(MW)\n", +"P_e = 15.0 // Output power(MW)\n", +"n = 10.0 // Number of cycles\n", +"\n", +"// Calculations\n", +"KE = G*H // Kinetic energy stored(MJ)\n", +"M = G*H/(180*f) // Angular momentum(MJ-sec/elect.degree)\n", +"P_a = P_s-P_e // Accelerating power(MW)\n", +"alpha = P_a/M // Acceleration(elect.degree/sec^2)\n", +"alpha_deg = alpha/2.0 // Acceleration(degree/sec^2)\n", +"alpha_rpm = 60.0*alpha_deg/360 // Acceleration(rpm/sec)\n", +"t = 1.0/f*n // Time(sec)\n", +"delta = 1.0/2*alpha*t**2 // Change in torque angle(elect.degree)\n", +"N_s = 120*f/P // Synchronous speed(rpm)\n", +"speed = N_s+alpha_rpm*t // Speed at the end of 10 cycles(rpm)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.22 : SOLUTION :-')\n", +"printf('\nChange in torque angle in that period, δ = %.f elect degrees.', delta)\n", +"printf('\nSpeed in rpm at the end of 10 cycles = %.2f rpm', speed)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.23: Accelerating_torque_at_the_time_of_fault_occurrence.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.23 :\n", +"// Page number 306\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"G = 20.0 // Rating of turbo-generator(MVA)\n", +"PF = 0.75 // Lagging power factor\n", +"fault = 0.5 // Fault reduces output power\n", +"N_s = 1500.0 // Synchronous speed(rpm). From Example 10.22\n", +"\n", +"// Calculations\n", +"P_prefault = PF*G // Pre-fault output power(MW)\n", +"P_a = P_prefault*fault // Post-fault output power(MW)\n", +"w = 2.0*%pi*N_s/60 // ω(rad/sec)\n", +"T_a = P_a*10**6/w // Accelerating torque at the time of fault occurrence(N-m)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.23 : SOLUTION :-')\n", +"printf('\nAccelerating torque at the time of fault occurrence, T_a = %.f N-m', T_a)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.24: Swing_equation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.24 :\n", +"// Page number 306-307\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"x_d = %i*0.2 // Transient reactance of generator(p.u)\n", +"P_e = 0.8 // Power delivered(p.u)\n", +"V_t = 1.05 // Terminal voltage(p.u)\n", +"H = 4.0 // Inertia constant(kW-sec/kVA)\n", +"x_t = %i*0.1 // Transformer reactance(p.u)\n", +"x_l = %i*0.4 // Transmission line reactance(p.u)\n", +"V = 1.0 // Infinite bus voltage(p.u)\n", +"f = 50.0 // Frequency(Hz)\n", +"\n", +"// Calculations\n", +"x_12 = x_d+x_t+(x_l/2) // Reactance b/w bus 1 & 2(p.u)\n", +"y_12 = 1/x_12 // Admittance b/w bus 1 & 2(p.u)\n", +"y_21 = y_12 // Admittance b/w bus 2 & 1(p.u)\n", +"y_10 = 0.0 // Admittance b/w bus 1 & 0(p.u)\n", +"y_20 = 0.0 // Admittance b/w bus 2 & 0(p.u)\n", +"Y_11 = y_12+y_10 // Admittance at bus 1(p.u)\n", +"Y_12 = -y_12 // Admittance b/w bus 1 & 2(p.u)\n", +"Y_21 = -y_12 // Admittance b/w bus 2 & 1(p.u)\n", +"Y_22 = y_21+y_20 // Admittance at bus 2(p.u)\n", +"x_32 = x_t+(x_l/2) // Reactance b/w bus 3 & 1(p.u)\n", +"theta_t = asind(P_e*abs(x_32)/V_t) // Angle(°)\n", +"V_t1 = V_t*exp(%i*theta_t*%pi/180) // Terminal voltage(p.u)\n", +"I = (V_t1-V)/x_32 // Current(p.u)\n", +"E = V_t1+I*x_d // Alternator voltage(p.u)\n", +"sine = poly(0,'sin')\n", +"P_e1 = 2.0*abs(E) // Developed power(p.u) in terms of sin δ\n", +"P_m_P_e = P_e-P_e1*sine\n", +"M = 2*H/(2*%pi*f) // Angular momentum\n", +"acc = (P_e-P_e1*sine)*2*%pi*f/(2*H) // Acceleration = α (rad/sec^2)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.24 : SOLUTION :-')\n", +"printf('\nSwing equation is, %.4f*α = %.1f - %.3fsin δ\n', M,P_e,P_e1)\n", +"printf('\nNOTE: Swing equation is simplified and represented here')\n", +"printf('\n ERROR: x_d = 0.2 p.u, not 0.1 p.u as mentioned in textbook statement')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.26: Critical_clearing_angle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.26 :\n", +"// Page number 308-309\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"X_d = 0.25 // Transient reactance of generator(p.u)\n", +"X_t1 = 0.15 // Reactance of transformer(p.u)\n", +"X_t2 = 0.15 // Reactance of transformer(p.u)\n", +"X_t3 = 0.15 // Reactance of transformer(p.u)\n", +"X_t4 = 0.15 // Reactance of transformer(p.u)\n", +"X_l1 = 0.20 // Reactance of line(p.u)\n", +"X_l2 = 0.20 // Reactance of line(p.u)\n", +"X_tr = 0.15 // Reactance of transformer(p.u)\n", +"P_m = 1.0 // Power delivered(p.u)\n", +"E = 1.20 // Voltage behind transient reactance(p.u)\n", +"V = 1.0 // Infinite bus voltage(p.u)\n", +"\n", +"// Calculations\n", +"X_14 = X_d+((X_t1+X_t2+X_l1)/2)+X_tr // Reactance before fault(p.u)\n", +"x_1_b = X_t1+X_t2+X_l1 // Reactance(p.u). From figure (b)\n", +"x_2_b = X_l2+X_t4 // Reactance(p.u). From figure (b)\n", +"x_1 = x_1_b*X_t3/(x_1_b+x_2_b+X_t3) // Reactance(p.u). From figure (c)\n", +"x_2 = x_1_b*x_2_b/(x_1_b+x_2_b+X_t3) // Reactance(p.u). From figure (c)\n", +"x_3 = X_t3*x_2_b/(x_1_b+x_2_b+X_t3) // Reactance(p.u). From figure (c)\n", +"X_14_fault = x_1+X_d+x_2+X_tr+((x_1+X_d)*(x_2+X_tr)/x_3) // Reactance under fault(p.u)\n", +"X_14_after_fault = X_d+X_t1+X_l1+X_t2+X_tr // Reactance after fault is cleared(p.u)\n", +"P_max = V*E/X_14 // Maximum power transfer(p.u)\n", +"gamma_1 = (V*E/X_14_fault)/P_max // γ_1\n", +"gamma_2 = (V*E/X_14_after_fault)/P_max // γ_2\n", +"delta_0 = asin(P_m/P_max) // δ_0(radians)\n", +"delta_0_degree = delta_0*180/%pi // δ_0(°)\n", +"delta_m = %pi-asin(P_m/(gamma_2*P_max)) // δ_1(radians)\n", +"delta_m_degree = delta_m*180/%pi // δ_1(°)\n", +"delta_c = acosd((P_m/P_max*(delta_m-delta_0)+gamma_2*cos(delta_m)-gamma_1*cos(delta_0))/(gamma_2-gamma_1)) // Clearing angle(°)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.26 : SOLUTION :-')\n", +"printf('\nCritical clearing angle, δ_c = %.2f° ', delta_c)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.27: Critical_angle_using_equal_area_criterion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.27 :\n", +"// Page number 309-310\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 50.0 // Frequency(Hz)\n", +"P_m = 1.0 // Power delivered(p.u)\n", +"P_max = 1.8 // Maximum power(p.u)\n", +"gamma_1_P_max = 0.4 // Reduced maximum power after fault(p.u)\n", +"gamma_2_P_max = 1.30 // Maximum power after fault clearance(p.u)\n", +"\n", +"// Calculations\n", +"delta_0 = asin(P_m/P_max) // δ_0(radians)\n", +"delta_0_degree = delta_0*180/%pi // δ_0(°)\n", +"delta_f = %pi-asin(P_m/(gamma_2_P_max)) // δ_1(radians)\n", +"delta_f_degree = delta_f*180/%pi // δ_1(°)\n", +"gamma_1 = gamma_1_P_max/P_max // γ_1\n", +"gamma_2 = gamma_2_P_max/P_max // γ_2\n", +"delta_c = acosd(1.0/(gamma_2-gamma_1)*((delta_f-delta_0)*sin(delta_0)+(gamma_2*cos(delta_f)-gamma_1*cos(delta_0)))) // Clearing angle(°)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.27 : SOLUTION :-')\n", +"printf('\nCritical angle, δ_c = %.2f° ', delta_c)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.28: Critical_clearing_angle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.28 :\n", +"// Page number 310\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"sin_delta_0 = 0.45 // Supplying percent of peak power capacity before fault\n", +"x = 4.0 // Reactance under fault increased\n", +"gamma_2 = 0.7 // Peak power delivered after fault clearance\n", +"\n", +"// Calculations\n", +"delta_0 = asin(sin_delta_0) // δ_0(radians)\n", +"delta_0_degree = delta_0*180/%pi // δ_0(°)\n", +"gamma_1 = 1.0/x // γ_1\n", +"delta_m = %pi-asin(sin_delta_0/(gamma_2)) // δ_m(radians)\n", +"delta_m_degree = delta_m*180/%pi // δ_m(°)\n", +"delta_c = acosd(1.0/(gamma_2-gamma_1)*((delta_m-delta_0)*sin(delta_0)+(gamma_2*cos(delta_m)-gamma_1*cos(delta_0)))) // Clearing angle(°)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.28 : SOLUTION :-')\n", +"printf('\nCritical clearing angle, δ_c = %.f° ', delta_c)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.2: Minimum_value_of_E_and_VL_Maximum_power_limit_and_Steady_state_stability_margin.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.2 :\n", +"// Page number 270\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"x_s = 0.85 // Reactance(p.u)\n", +"x_T1 = 0.157 // Reactance(p.u)\n", +"x_T2 = 0.157 // Reactance(p.u)\n", +"x_l1 = 0.35 // Reactance(p.u)\n", +"x_l2 = 0.35 // Reactance(p.u)\n", +"E = 1.50 // Sending end voltage(p.u)\n", +"V_L = 1.0 // Load voltage(p.u)\n", +"P_0 = 1.0 // Stable power output(p.u)\n", +"\n", +"// Calculations\n", +"x = x_s+x_T1+x_T2+(x_l1/2) // Total reactance(p.u)\n", +"P_max = E*V_L/x // Maximum power limit(p.u)\n", +"M = (P_max-P_0)/P_max*100 // Steady state stability margin(%)\n", +"V_Lmin = P_0*x/E // Minimum value of V_L(p.u)\n", +"E_min = P_0*x/V_L // Minimum value of E(p.u)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.2 : SOLUTION :-')\n", +"printf('\nMinimum value of |E|, |E_min| = %.3f p.u', E_min)\n", +"printf('\nMinimum value of |V_L|, |V_Lmin| = %.3f p.u', V_Lmin)\n", +"printf('\nMaximum power limit, P_0 = %.2f p.u', P_max)\n", +"printf('\nSteady state stability margin, M = %.1f percent', M)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.30: Power_angle_and_Swing_curve_data.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.30 :\n", +"// Page number 310-311\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"f = 60.0 // Frequency(Hz)\n", +"P = 6.0 // Number of poles\n", +"H = 4.0 // Inertia constant(p.u)\n", +"P_e = 1.0 // Power supplied by generator(p.u)\n", +"E = 1.2 // Internal voltage(p.u)\n", +"V = 1.0 // Infinite bus voltage(p.u)\n", +"X = 0.3 // Line reactance(p.u)\n", +"del_t = 0.05 // Δt = Interval step size(sec)\n", +"\n", +"// Calculations\n", +"P_max = E*V/X // Maximum power(p.u)\n", +"delta_0 = asind(P_e/P_max) // δ_0(°)\n", +"G = P_e\n", +"M = G*H/(180*f) // Angular momentum(p.u)\n", +"P_a_0 = 1.0/2*(P_e-0) // (p.u)\n", +"alpha_0 = P_a_0/M // α_0(°/sec^2)\n", +"del_w_r_1 = alpha_0*del_t // Δω_r_1(°/sec)\n", +"w_r_1 = 0+del_w_r_1 // ω_r_1(°/sec)\n", +"del_delta_1 = w_r_1*del_t // Δδ_1(°)\n", +"delta_1 = delta_0+del_delta_1 // δ_1(°)\n", +"P_a_1 = 1.0*(P_e-0) // (p.u)\n", +"alpha_1 = P_a_1/M // α_1(°/sec^2)\n", +"del_w_r_2 = alpha_1*del_t // Δω_r_2(°/sec)\n", +"w_r_2 = del_w_r_1+del_w_r_2 // ω_r_2(°/sec)\n", +"del_delta_2 = w_r_2*del_t // Δδ_2(°)\n", +"delta_2 = delta_1+del_delta_2 // δ_2(°)\n", +"del_w_r_3 = del_w_r_2 // Δω_r_3(°/sec)\n", +"w_r_3 = w_r_2+del_w_r_3 // ω_r_3(°/sec)\n", +"del_delta_3 = w_r_3*del_t // Δδ_3(°)\n", +"delta_3 = delta_2+del_delta_3 // δ_3(°)\n", +"del_w_r_4 = del_w_r_2 // Δω_r_4(°/sec)\n", +"w_r_4 = w_r_3+del_w_r_4 // ω_r_4(°/sec)\n", +"del_delta_4 = w_r_4*del_t // Δδ_4(°)\n", +"delta_4 = delta_3+del_delta_4 // δ_4(°)\n", +"del_w_r_5 = del_w_r_2 // Δω_r_5(°/sec)\n", +"w_r_5 = w_r_4+del_w_r_5 // ω_r_5(°/sec)\n", +"del_delta_5 = w_r_5*del_t // Δδ_5(°)\n", +"delta_5 = delta_4+del_delta_5 // δ_5(°)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.30 : SOLUTION :-')\n", +"printf('\nPower angle, δ_0 = %.2f° ', delta_0)\n", +"printf('\nValue of δ vs t are:')\n", +"printf('\n_________________________')\n", +"printf('\n t(Sec) : δ(degree)')\n", +"printf('\n_________________________')\n", +"printf('\n %.1f : %.2f°', 0,delta_0)\n", +"printf('\n %.2f : %.2f°', (del_t),delta_1)\n", +"printf('\n %.2f : %.2f°', (del_t+del_t),delta_2)\n", +"printf('\n %.2f : %.2f°', (del_t*3),delta_3)\n", +"printf('\n %.2f : %.2f°', (del_t*4),delta_4)\n", +"printf('\n %.2f : %.2f°', (del_t*5),delta_5)\n", +"printf('\n_________________________')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.3: EX17_3.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.3 :\n", +"// Page number 270-271\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"E_1 = 1.25 // Sending end voltage(p.u)\n", +"x_d = 1.0 // Reactance(p.u)\n", +"x_T1 = 0.2 // Reactance(p.u)\n", +"x_l1 = 1.0 // Reactance(p.u)\n", +"x_l2 = 1.0 // Reactance(p.u)\n", +"x_T2 = 0.2 // Reactance(p.u)\n", +"E_2 = 1.0 // Receiving end voltage(p.u)\n", +"x_L = 1.0 // Shunt inductor reactance(p.u)\n", +"x_C = 1.0 // Shunt capacitor reactance(p.u)\n", +"\n", +"// Calculations\n", +"// Case(a)\n", +"Z_1_a = x_d+x_T1+(x_l1/2.0) // Reactance(p.u)\n", +"Z_2_a = x_T2+x_d // Reactance(p.u)\n", +"Z_3_a = x_L // Reactance(p.u)\n", +"Z_a = Z_1_a+Z_2_a+(Z_1_a*Z_2_a/Z_3_a) // Transfer reactance(p.u)\n", +"P_max_1 = E_1*E_2/Z_a // Maximum power transfer if shunt inductor is connected at bus 2(p.u)\n", +"// Case(b)\n", +"Z_1_b = x_d+x_T1+(x_l1/2.0) // Reactance(p.u)\n", +"Z_2_b = x_T2+x_d // Reactance(p.u)\n", +"Z_3_b = -x_C // Reactance(p.u)\n", +"Z_b = Z_1_b+Z_2_b+(Z_1_b*Z_2_b/Z_3_b) // Transfer reactance(p.u)\n", +"P_max_2 = E_1*E_2/Z_b // Maximum power transfer if shunt capacitor is connected at bus 2(p.u)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.3 : SOLUTION :-')\n", +"printf('\nCase(a): Maximum power transfer if shunt inductor is connected at bus 2, P_max1 = %.3f p.u', P_max_1)\n", +"printf('\nCase(b): Maximum power transfer if shunt capacitor is connected at bus 2, P_max2 = %.2f p.u', P_max_2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.4: Maximum_power_transfer_and_Stability_margin.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.4 :\n", +"// Page number 271\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"V = 400.0 // Voltage(kV)\n", +"L = 220.0 // Line length(km)\n", +"P = 0.58 // Initial real power transfer(p.u)\n", +"PF = 0.85 // Lagging power factor\n", +"V_L = 1.00 // Load bus voltage(p.u)\n", +"x_d = 0.460 // Reactance(p.u)\n", +"x_T1 = 0.200 // Reactance(p.u)\n", +"x_T2 = 0.15 // Reactance(p.u)\n", +"x_line = 0.7 // Reactance(p.u)\n", +"\n", +"// Calculations\n", +"x = x_d+x_T1+x_T2+(x_line/2) // Net reactance(p.u)\n", +"phi = acosd(PF) // Φ(°)\n", +"Q = P*tand(phi) // Reactive power(p.u)\n", +"E = ((V_L+(Q*x/V_L))**2+(P*x/V_L)**2)**0.5 // Excitation voltage of generator(p.u)\n", +"P_max = E*V_L/x // Maximum power transfer(p.u)\n", +"M = (P_max-P)/P_max*100 // Steady state stability margin(%)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.4 : SOLUTION :-')\n", +"printf('\nMaximum power transfer, P_max = %.2f p.u', P_max)\n", +"printf('\nStability margin, M = %.f percent', M)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.5: QgB_Phase_angle_of_VB_and_What_happens_if_QgB_is_made_zero.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.5 :\n", +"// Page number 271-272\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"V_A = 1.0 // Voltage at bus A(p.u)\n", +"Z_AB = %i*0.5 // Impedance(p.u)\n", +"S_DA = 1.0 // p.u\n", +"S_DB = 1.0 // p.u\n", +"V_B = 1.0 // Voltage at bus B(p.u)\n", +"\n", +"// Calculations\n", +"// Case(i) & (ii)\n", +"X = abs(Z_AB) // Reactance(p.u)\n", +"sin_delta = 1.0*X/(V_A*V_B) // Sin δ\n", +"delta = asind(sin_delta) // δ(°)\n", +"V_2 = V_B\n", +"V_1 = V_A\n", +"Q_gB = (V_2**2/X)-(V_2*V_1*cosd(delta)/X)\n", +"// Case(iii)\n", +"V_2_3 = 1/2.0**0.5 // Solving quadratic equation from textbook\n", +"delta_3 = acosd(V_2_3) // δ(°)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.5 : SOLUTION :-')\n", +"printf('\nCase(i) : Q_gB = %.3f', Q_gB)\n", +"printf('\nCase(ii) : Phase angle of V_B, δ = %.f° ', delta)\n", +"printf('\nCase(iii): If Q_gB is equal to zero then amount of power transmitted is, V_2 = %.3f∠%.f° ', V_2_3,delta_3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.6: EX17_6.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.6 :\n", +"// Page number 272\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"funcprot(0)\n", +"\n", +"// Given data\n", +"A = 0.98*exp(%i*0.3*%pi/180) // Constant\n", +"B = 82.5*exp(%i*76.0*%pi/180) // Constant(ohm)\n", +"C = 0.0005*exp(%i*90.0*%pi/180) // Constant(mho)\n", +"D = A // Constant\n", +"V_S = 110.0 // Sending end voltage(kV)\n", +"V_R = 110.0 // Receiving end voltage(kV)\n", +"\n", +"// Calculations\n", +"alpha = phasemag(A) // α(°)\n", +"beta = phasemag(B) // β(°)\n", +"P_max = (V_S*V_R/abs(B))-(abs(A)*V_R**2/abs(B)*cosd((beta-alpha))) // Maximum power transfer(MW)\n", +"B_new = abs(B)*sind(beta) // Constant(ohm)\n", +"beta_new = 90.0 // β(°)\n", +"P_max_new = (V_S*V_R/B_new)-(V_R**2/B_new*cosd(beta_new)) // Maximum power transfer(MW)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.6 : SOLUTION :-')\n", +"printf('\nSteady state stability limit, P_max = %.2f MW', P_max)\n", +"printf('\nSteady state stability limit if shunt admittance is zero & series resistance neglected, P_max = %.2f MW \n', P_max_new)\n", +"printf('\nNOTE: Changes in the obtained answer from that of textbook is due to precision')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.8: EX17_8.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.8 :\n", +"// Page number 273-275\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"funcprot(0)\n", +"\n", +"// Given data\n", +"V = 33.0*10**3 // Line voltage(V)\n", +"R = 6.0 // Resistance per phase(ohm)\n", +"X = 15.0 // Reactance per phase(ohm)\n", +"\n", +"// Calculations\n", +"V_S = V/3**0.5 // Sending end phase voltage(V)\n", +"V_R = V/3**0.5 // Receiving end phase voltage(V)\n", +"beta = atand(X/R) // β(°)\n", +"Z = (R**2+X**2)**0.5 // Impedance(ohm)\n", +"delta_0 = 0.0 // δ(°)\n", +"P_0 = (V_R/Z**2)*(V_S*Z*cosd((delta_0-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"delta_1 = 30.0 // δ(°)\n", +"P_1 = (V_R/Z**2)*(V_S*Z*cosd((delta_1-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"delta_2 = 60.0 // δ(°)\n", +"P_2 = (V_R/Z**2)*(V_S*Z*cosd((delta_2-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"delta_3 = beta // δ(°)\n", +"P_3 = (V_R/Z**2)*(V_S*Z*cosd((delta_3-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"delta_4 = 90.0 // δ(°)\n", +"P_4 = (V_R/Z**2)*(V_S*Z*cosd((delta_4-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"delta_5 = 120.0 // δ(°)\n", +"P_5 = (V_R/Z**2)*(V_S*Z*cosd((delta_5-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"delta_6 = (acosd(R/Z))+beta // δ(°)\n", +"P_6 = (V_R/Z**2)*(V_S*Z*cosd((delta_6-beta))-V_R*R)/10**6 // Power received(MW/phase)\n", +"\n", +"\n", +"delta = [delta_0,delta_1,delta_2,delta_3,delta_4,delta_5,delta_6]\n", +"P = [P_0,P_1,P_2,P_3,P_4,P_5,P_6]\n", +"a = gca() ;\n", +"a.thickness = 2 // sets thickness of plot\n", +"plot(delta,P,'ro-')\n", +"a.x_label.text = 'Electrical degree' // labels x-axis\n", +"a.y_label.text = 'Power in MW/phase' // labels y-axis\n", +"xtitle('Fig E10.7 . Power angle diagram') \n", +"xset('thickness',2) // sets thickness of axes\n", +"xstring(70,14.12,'P_max = 14.12 MW/phase(approximately)')\n", +"P_max = V_R/Z**2*(V_S*Z-V_R*R)/10**6 // Maximum power transmitted(MW/phase)\n", +"delta_equal = 0.0 // δ With no phase shift(°)\n", +"P_no_shift = (V_R/Z**2)*(V_S*Z*cosd((delta_equal-beta))-V_R*R)/10**6 // Power transmitted with no phase shift(MW/phase)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.8 : SOLUTION :-')\n", +"printf('\nPower angle diagram is plotted and is shown in the Figure 1')\n", +"printf('\nMaximum power the line is capable of transmitting, P_max = %.2f MW/phase', P_max)\n", +"printf('\nWith equal voltage at both ends power transmitted = %.f MW/phase', abs(P_no_shift))" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17.9: Maximum_steady_state_power_that_can_be_transmitted_over_the_line.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// A Texbook on POWER SYSTEM ENGINEERING\n", +"// A.Chakrabarti, M.L.Soni, P.V.Gupta, U.S.Bhatnagar\n", +"// DHANPAT RAI & Co.\n", +"// SECOND EDITION \n", +"\n", +"// PART II : TRANSMISSION AND DISTRIBUTION\n", +"// CHAPTER 10: POWER SYSTEM STABILITY\n", +"\n", +"// EXAMPLE : 10.9 :\n", +"// Page number 275\n", +"clear ; clc ; close ; // Clear the work space and console\n", +"\n", +"// Given data\n", +"V = 132.0*10**3 // Sending end voltage(V)\n", +"Z_line = complex(4,6) // Line impedance per phase(ohm)\n", +"\n", +"// Calculations\n", +"V_S = V/3**0.5 // Sending end phase voltage(V)\n", +"V_R = V/3**0.5 // Receiving end phase voltage(V)\n", +"Z = abs(Z_line) // Impedance(ohm)\n", +"R = real(Z_line) // Resistance per phase(ohm)\n", +"P_max_phase = ((V_S*V_R/Z)-(R*V_R**2/Z**2))/10**6 // Maximum steady state power that can be transmitted over the line(MW/phase)\n", +"P_max_total = 3.0*P_max_phase // Maximum steady state power that can be transmitted over the line(MW)\n", +"\n", +"// Results\n", +"disp('PART II - EXAMPLE : 10.9 : SOLUTION :-')\n", +"printf('\nMaximum steady state power that can be transmitted over the line, P_max = %.f MW (total 3-phase)', P_max_total)" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |