// ELECTRICAL MACHINES // R.K.Srivastava // First Impression 2011 // CENGAGE LEARNING INDIA PVT. LTD // CHAPTER : 6 : SYNCHRONOUS MACHINES // EXAMPLE : 6.5a clear ; clc ; close ; // Clear the work space and console // GIVEN DATA printf("\n EXAMPLE : 6.5a( Data is same as Example 6.4): \n\n Given Data \n"); printf("\n Voc(v) 215 284 320 380 400 422 452 472 488 508 520 532 540 552 560 \n"); printf("\n If(A) 6.5 8 9 10 11 12 14 15 16 17 18 19 20 22 24 \n\n"); m = 3; // Total Number of phase in Induction Motor p = 6; // Total number of Poles of Induction Motor V = 400; // Operating voltage of the Induction motor in Volts I = 13.5; // Operating current of the Induction motor in Amphere N = 1000; // speed of the Induction motor in RPM Ia_scc = 13.5; // SCC test Armature current in Amphere at If = 9.5 A If_scc = 9.5; // SCC test field Rated current in Amphere Ia_zpf = 13.5; // ZPF test Armature current in Amphere at If = 24 A If_zpf = 24; // ZPF test field Rated current in Amphere // CALCULATIONS // Some of the data obtained from OCC and SCC test Graph or Pottier triangle in Figure6.15 & Page no:-386 Ra = 1.0; // Armature resistance in Ohms v = V/sqrt(3); // Rated phase Voltage in Volts // For case (a) EMF_a1 = 345; // From OCC and SCC test Graph or Pottier triangle in Figure6.15 & Page no:-386 open-circuit line-line voltage per phase is 345vVfor If = 9.50A in Volts Zs_a1 = EMF_a1/(Ia_zpf*sqrt(3)); // Unsaturated synchronous impedance at If=9.50A in Ohms Xs_a1 = sqrt((Zs_a1^2)-(Ra^2)); // Synchronous reactance at If =9.50A in Ohms Ia_a2 = 15.75; // Current from SCC in Figure6.15 & Page no:-386 is 15.75A for correspounding to the rated Voltage in Volts Zs_a2 = V/(Ia_a2*sqrt(3)); // Unsaturated synchronous impedance at If=9.50A in Ohms Xs_a2 = sqrt((Zs_a2^2)-(Ra^2)); // Synchronous reactance at If =9.50A in Ohms // For Case (b.1) 0.8 pf Lagging pfa_b1 = acosd(0.8); // Power factor angle in degree real_b1 = (v+Ia_zpf*Ra*cosd(pfa_b1)+Ia_zpf*Xs_a1*sind(pfa_b1)); imag_b1 = (Ia_zpf*Xs_a1*cosd(pfa_b1)-Ia_zpf*Ra*sind(pfa_b1)); E_b1 = sqrt(real_b1^2+imag_b1^2); // Induced Voltage pr phase in Volts from Figure6.19 (a) & Page no:-394 shows the phasor diagram for lagging pf del_b1 = atand(imag_b1/real_b1); // Power angle in degree r_b1 = 100*(E_b1-v)/v; // Percantage regulation // For Case (b.2) 0.8 pf Leading pfa_b2 = acosd(0.8); // Power factor angle in degree real_b2 = (v+Ia_zpf*Ra*cosd(pfa_b2)-Ia_zpf*Xs_a1*sind(pfa_b2)); imag_b2 = (Ia_zpf*Xs_a1*cosd(pfa_b2)+Ia_zpf*Ra*sind(pfa_b2)); E_b2 = sqrt(real_b2^2+imag_b2^2); // Induced Voltage pr phase in Volts from Figure6.19 (b) & Page no:-394 shows the phasor diagram for leading pf del_b2 = atand(imag_b2/real_b2); // Power angle in degree r_b2 = 100*(E_b2-v)/v; // Percantage regulation // For Case (b.3) Unity pf pfa_b3 = acosd(1.0); // Power factor angle in degree real_b3 = (v+Ia_zpf*Ra); imag_b3 = (Ia_zpf*Xs_a1); E_b3 = sqrt(real_b3^2+imag_b3^2); // Induced Voltage pr phase in Volts from Figure6.19 (a) & Page no:-394 shows the phasor diagram for unity pf del_b3 = atand(imag_b3/real_b3); // Power angle in degree r_b3 = 100*(E_b3-v)/v; // Percantage regulation // For Case (b.4) ZPF pf Lagging pfa_b4 = acosd(0); // Power factor angle in degree real_b4 = (v+Ia_zpf*Xs_a1); imag_b4 = (-Ia_zpf*Ra); E_b4 = sqrt(real_b4^2+imag_b4^2); // Induced Voltage pr phase in Volts ZPF for lagging pf del_b4 = atand(imag_b4/real_b4); // Power angle in degree r_b4 = 100*(E_b4-v)/v; // Percantage regulation // For Case (b.5) ZPF pf Leading pfa_b5 = acosd(0); // Power factor angle in degree real_b5 = (v-Ia_zpf*Xs_a1); imag_b5 = (Ia_zpf*Ra); E_b5 = sqrt(real_b5^2+imag_b5^2); // Induced Voltage pr phase in Volts ZPF for lagging pf del_b5 = atand(imag_b5/real_b5); // Power angle in degree r_b5 = 100*(E_b5-v)/v; // Percantage regulation // DISPLAY RESULTS disp(" SOLUTION :-"); printf("\n (a.1) Synchronous reactance for rated current at If = %.2f, Xs = %.2f Ohms \n",If_scc,Xs_a1) printf("\n (a.2) Synchronous reactance for rated per phase Voltage at v = %.f, Xs = %.2f Ohms \n",v,Xs_a2) printf("\n For Case (b.1) 0.8 pf Lagging \n Induced EMF per phase , EMF = %.2f V \n",E_b1) printf("\n Percenatge Regulation, R = %.2f Percenatge \n",r_b1) printf("\n Power angle = %.2f degree \n",del_b1) printf("\n For Case (b.2) 0.8 pf Leading \n Induced EMF per phase, EMF = %.2f V \n",E_b2) printf("\n Percenatge Regulation, R = %.2f Percenatge \n",r_b2) printf("\n Power angle = %.2f degree \n",del_b2) printf("\n For Case (b.3) Unity pf Lagging \n Induced EMF per phase, EMF = %.2f V \n",E_b3) printf("\n Percenatge Regulation, R = %.2f Percenatge \n",r_b3) printf("\n Power angle = %.2f degree \n",del_b3) printf("\n For Case (b.4) ZPF Lagging \n Induced EMF per phase, EMF = %.2f V\n",E_b4) printf("\n Percenatge Regulation, R = %.2f Percenatge \n",r_b4) printf("\n Power angle = %.1f degree \n",del_b4) printf("\n For Case (b.5) ZPF Leading \n Induced EMF per phase, EMF = %.2f V \n",E_b5) printf("\n Percenatge Regulation, R = %.2f Percenatge \n",r_b5) printf("\n Power angle = %.2f degree \n\n",del_b5) disp(" Calculated Answer in Tabular Column") printf("\n Power Factor 0.8 Lag 0.8 Lead 1.0 ZPF Lag ZPF Lead \n") printf("\n Open circuit EMF (V) %.2f %.2f %.2f %.2f %.2f \n",E_b1,E_b2,E_b3,E_b4,E_b5) printf("\n Percenatge Regulation %.2f %.2f %.2f. %.2f %.2f \n",r_b1,r_b2,r_b3,r_b4,r_b5) printf("\n Power angle %.2f %.2f %.2f. %.1f %.2f \n",del_b1,del_b2,del_b3,del_b4,del_b5)