path: root/Electric_Machines_by_C_I_Hubert/8-Synchronous_Motors.ipynb

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	   "source": [
       "# Chapter 8: Synchronous Motors"
	   ]
	},
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		   "metadata": {},
		   "source": [
			"## Example 8.1: EX8_1.sce"
		   ]
		  },
  {
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"// Example 8.1\n",
"// Determine (a) Developed torque (b) Armature current (c) Excitation voltage\n",
"// (d) Power angle (e) Maximum torque \n",
"// Page No. 317\n",
"\n",
"clc;\n",
"clear;\n",
"close;\n",
"\n",
"// Given data\n",
"f=60;                       // Operating frequency\n",
"P=4;                        // Number of poles\n",
"Pmech=100;                  // Mechanical power\n",
"eta=0.96;                   // Efficiency\n",
"FP=0.80;                    // Power factor leading\n",
"V=460;                      // Motor voltage\n",
"Xs_Mag=2.72;                // Synchronous reactnace magnitude\n",
"Xs_Ang=90;                  // Synchronous reactnace magnitude\n",
"deltaPull=-90;               // Pullout power angle\n",
"// (a) Developed torque\n",
"ns=120*f/P;                 // Synchronous speed\n",
"Td=5252*Pmech/(ns*eta); \n",
"\n",
"\n",
"// (b) Armature current\n",
"S=Pmech*746/(eta*FP);\n",
"Theta=-acosd(FP);          // Power factor angle (negative as FP is leading)\n",
"V1phi=V/sqrt(3);           // Single line voltage\n",
"S1phi_Mag=S/3;             // Magnitude \n",
"S1phi_Ang=Theta;           // Angle\n",
"VT_Mag=V1phi;\n",
"VT_Ang=0;\n",
"Ia_Mag=S1phi_Mag/VT_Mag;   // Armature current magnitude\n",
"Ia_Ang=S1phi_Ang-VT_Ang;   // Armature current angle\n",
"Ia_Ang=-Ia_Ang;            // Complex conjugate of Ia\n",
"\n",
"// (c) Excitation voltage\n",
"Var1_Mag=Ia_Mag*Xs_Mag;\n",
"Var1_Ang=Ia_Ang+Xs_Ang;\n",
"\n",
"/////////\n",
"N01=VT_Mag+%i*VT_Ang;\n",
"N02=Var1_Mag+%i*Var1_Ang;\n",
"// Polar to Complex form\n",
"\n",
"N01_R=VT_Mag*cos(-VT_Ang*%pi/180); // Real part of complex number 1\n",
"N01_I=VT_Mag*sin(VT_Ang*%pi/180); //Imaginary part of complex number 1\n",
"\n",
"N02_R=Var1_Mag*cos(-Var1_Ang*%pi/180); // Real part of complex number 2\n",
"N02_I=Var1_Mag*sin(Var1_Ang*%pi/180); //Imaginary part of complex number 2\n",
"\n",
"FinalNo_R=N01_R-N02_R;\n",
"FinalNo_I=N01_I-N02_I;\n",
"FinNum=FinalNo_R+%i*FinalNo_I;\n",
"// Complex to Polar form...\n",
"\n",
"FN_M=sqrt(real(FinNum)^2+imag(FinNum)^2); // Magnitude part\n",
"FN_A = atan(imag(FinNum),real(FinNum))*180/%pi;// Angle part
\n",
"//////\n",
"Ef_Mag=FN_M;\n",
"Ef_Ang=FN_A;\n",
"// (d) Power angle\n",
"delta=Ef_Ang;\n",
"\n",
"// (e) Maximum torque \n",
"Pin=3*(-VT_Mag*Ef_Mag/Xs_Mag)*sind(deltaPull);   // Active power input\n",
"Tpull=5252*Pin/(746*ns);\n",
"\n",
"\n",
"\n",
"// Display result on command window\n",
"printf('\n Developed torque = %0.0f lb-ft ',Td);\n",
"printf('\n Armature current magnitude= %0.2f A ',Ia_Mag);\n",
"printf('\n Armature current angle= %0.2f deg ',Ia_Ang);\n",
"printf('\n Excitation voltage magnitude = %0.0f V ',Ef_Mag);\n",
"printf('\n Excitation voltage angle = %0.1f deg ',Ef_Ang);\n",
"printf('\n Power angle = %0.1f deg ',delta);\n",
"printf('\n Maximum torque = %0.0f lb-ft ',Tpull);\n",
"\n",
""
   ]
   }
,
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		   "source": [
			"## Example 8.2: EX8_2.sce"
		   ]
		  },
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"// Example 8.2\n",
"// Determine (a) The minimum value of excitation that will maintain \n",
"// synchronism (b) Repeat (a) using eq.(8.16) (c) Repeat (a) using eq.(8.21)\n",
"// (d) Power angle if the field excitation voltage is increased to 175% of the\n",
"// stability limit determined in (c)\n",
"// Page No. 322\n",
"\n",
"clc;\n",
"clear;\n",
"close;\n",
"\n",
"// Given data\n",
"Pin=40;                     // Input power\n",
"Pin1phase=40/3;             // Single phase power\n",
"Xs=1.27;                    // Synchronous reactnace \n",
"VT=220/sqrt(3);             // Voltage\n",
"delta=-90;                  // Power angle\n",
"\n",
"f=60;                       // Operating frequency\n",
"P=4;                        // Number of poles\n",
"Pmech=100;                  // Mechanical power\n",
"eta=0.96;                   // Efficiency\n",
"FP=0.80;                    // Power factor leading\n",
"V=460;                      // Motor voltage\n",
"Xs_Mag=2.72;                // Synchronous reactnace magnitude\n",
"Xs_Ang=90;                  // Synchronous reactnace magnitude\n",
"deltaPull=-90;               // Pullout power angle\n",
"\n",
"// (a) The minimum value of excitation that will maintain synchronism\n",
"Ef=98;                      // From the graph (Figure 8.13)\n",
"\n",
"// (b) The minimum value of excitation using eq.(8.16)\n",
"Ef816=-Pin*Xs*746/(3*VT*sind(delta));\n",
"\n",
"\n",
"// (c) The minimum value of excitation using eq.(8.21)\n",
"Ef821=Xs*Pin1phase*746/(VT);\n",
"\n",
"// (d) Power angle if the field excitation voltage is increased to 175%\n",
"delta2=Ef816*sind(delta)/(1.75*Ef816);\n",
"delta2=asind(delta2);\n",
"\n",
"// Display result on command window\n",
"printf('\n The minimum value of excitation = %0.0f V ',Ef);\n",
"printf('\n The minimum value of excitation using eq.(8.16) = %0.0f V ',Ef816);\n",
"printf('\n The minimum value of excitation using eq.(8.21) = %0.0f V ',Ef821);\n",
"printf('\n Power angle = %0.0f deg ',delta2);"
   ]
   }
,
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		   "metadata": {},
		   "source": [
			"## Example 8.3: EX8_3.sce"
		   ]
		  },
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"// Example 8.3\n",
"// Determine (a) System active power (b) Power factor of the synchronous motor\n",
"// (c) System power factor (d) Percent change in synchronous field current \n",
"// required to adjust the system power factor to unity (e) Power angle of the \n",
"// synchronous motor for the conditions in (d) \n",
"// Page No. 324\n",
"\n",
"clc; \n",
"clear;\n",
"close;\n",
"\n",
"// Given data\n",
"\n",
"Php=400;                    // Power in hp\n",
"eta=0.958;                  // Efficiency\n",
"Pheater=50000;              // Resistance heater power \n",
"Vs=300;                     // Synchronous motor voltage\n",
"eta2=0.96;                  // Synchronous motor efficiency\n",
"Xs=0.667;                   // Synchronous reactnace\n",
"VT=460;                     // 3-Phase supply voltage\n",
"delta=-16.4;                // Power angle\n",
"\n",
"// (a) System active power \n",
"Pindmot=Php*0.75*746/(eta);   // Motor operating at three quarter rated load\n",
"Psynmot=Vs*0.5*746/(eta2);    // Synchronous motor power  \n",
"Psys=Pindmot+Pheater+Psynmot;\n",
"Psysk=Psys/1000;\n",
"\n",
"// (b) Power factor of the synchronous motor\n",
"Pin=Psynmot;                 // Power input\n",
"Vtph=VT/sqrt(3);             // Voltage per phase\n",
"Ef=-(Pin*Xs)/(3*Vtph*sind(delta));\n",
"// Complex to Polar form...\n",
"\n",
"Ef_Mag=Ef;          // Magnitude part \n",
"Ef_Ang=delta;       // Angle part
\n",
"Vtph_Mag=Vtph;      \n",
"Vtph_Ang=0;\n",
"////////////\n",
"N01=Ef_Mag+%i*Ef_Ang;      // Ef in polar form \n",
"N02=Vtph_Mag+%i*Vtph_Ang;  // Vt in polar for\n",
"\n",
"N01_R=Ef_Mag*cos(-Ef_Ang*%pi/180); // Real part of complex number Ef\n",
"N01_I=Ef_Mag*sin(Ef_Ang*%pi/180); //Imaginary part of complex number Ef\n",
"\n",
"N02_R=Vtph_Mag*cos(-Vtph_Ang*%pi/180); // Real part of complex number Vt\n",
"N02_I=Vtph_Mag*sin(Vtph_Ang*%pi/180); //Imaginary part of complex number Vt\n",
"\n",
"FinalNo_R=N01_R-N02_R;\n",
"FinalNo_I=N01_I-N02_I;\n",
"FinNum=FinalNo_R+%i*FinalNo_I;\n",
"// Complex to Polar form...\n",
"\n",
"FN_M=sqrt(real(FinNum)^2+imag(FinNum)^2); // Magnitude part\n",
"FN_A = atan(imag(FinNum),real(FinNum))*180/%pi;// Angle part
\n",
"\n",
"Ia_Mag=FN_M/Xs;          // Magnitude of Ia\n",
"Ia_Ang=FN_A-(-90);       // Angle of Ia\n",
"Theta=0-Ia_Ang;\n",
"FP=cosd(Theta);          // Power factor\n",
"\n",
"\n",
"// (c) System power factor\n",
"ThetaIndMot=acosd(0.891);    // Induction motor power factor\n",
"Thetaheat=acosd(1);          // Heater power factor\n",
"ThetaSyncMot=-34.06;         // Synchronous motor power factor\n",
"Qindmot=tand(27)*Pindmot; \n",
"Qsynmot=tand(ThetaSyncMot)*Psynmot;\n",
"Qsys=Qindmot+Qsynmot;\n",
"Ssys=Psys+%i*Qsys;         // System variable in complex form\n",
"\n",
"// Complex to Polar form...\n",
"\n",
"Ssys_Mag=sqrt(real(Ssys)^2+imag(Ssys)^2);         // Magnitude part\n",
"Ssys_Ang = atan(imag(Ssys),real(Ssys))*180/%pi;   // Angle part
\n",
"\n",
"FPsys=cosd(Ssys_Ang);                             // System power factor \n",
"\n",
"// (d) Percent change in synchronous field current required to adjust the \n",
"// system power factor to unity\n",
"\n",
"Ssynmot=Psynmot-(%i*(-Qsynmot+Qsys));   // Synchronous motor system\n",
"\n",
"// Complex to Polar form...\n",
"\n",
"Ssynmot_Mag=sqrt(real(Ssynmot)^2+imag(Ssynmot)^2);     // Magnitude part\n",
"Ssynmot_Ang=atan(imag(Ssynmot),real(Ssynmot))*180/%pi; // Angle part
\n",
"\n",
"Ssynmot1ph_Mag=Ssynmot_Mag/3;            // For single phase magnitude\n",
"Ssynmot1ph_Ang=Ssynmot_Ang;              // For single phase angle\n",
"\n",
"Iastar_Mag=Ssynmot1ph_Mag/Vtph;          // Current magnitude\n",
"Iastar_Ang=Ssynmot1ph_Ang-0;             // Current angle\n",
"\n",
"IaNew_Mag=Iastar_Mag;\n",
"IaNew_Ang=-Iastar_Ang;\n",
"\n",
"IaXs_Mag=IaNew_Mag*Xs;\n",
"IaXs_Ang=IaNew_Ang-90;\n",
"\n",
"// Convert these number into complex and then perform addition\n",
"// Polar to Complex form\n",
"\n",
"// Y=29.416<-62.3043 //Polar form number\n",
"IaXs_R=IaXs_Mag*cos(-IaXs_Ang*%pi/180);  // Real part of complex number\n",
"IaXs_I=IaXs_Mag*sin(IaXs_Ang*%pi/180);   // Imaginary part of complex number\n",
"Efnew=Vtph+IaXs_R+%i*IaXs_I;\n",
"// Complex to Polar form...\n",
"\n",
"Efnew_Mag=sqrt(real(Efnew)^2+imag(Efnew)^2);     // Magnitude part\n",
"Efnew_Ang=atan(imag(Efnew),real(Efnew))*180/%pi; // Angle part
\n",
"\n",
"DeltaEf=(Efnew_Mag-Ef)/Ef; \n",
"\n",
"// (e) Power angle of the synchronous motor\n",
"deltasynmot=Efnew_Ang;\n",
"\n",
"// Display result on command window\n",
"printf('\n System active power  = %0.1f kW ',Psysk);\n",
"printf('\n Power factor of the synchronous motor = %0.3f leading ',FP);\n",
"printf('\n System power factor = %0.3f lagging ',FPsys);\n",
"printf('\n Percent change in synchronous field current = %0.2f Percent ',DeltaEf*100);\n",
"printf('\n Power angle of the synchronous motor = %0.2f deg ',deltasynmot);"
   ]
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		   "source": [
			"## Example 8.4: Determine_Developed_torque_and_Developed_torque_in_percent_of_rated_torque.sce"
		   ]
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"// Example 8.4\n",
"// Determine (a) Developed torque if the field current is adjusted so that the\n",
"// excitation voltage is equal to two times the applied stator voltage, and the\n",
"// power angle is -18 degrees (b) Developed torque in percent of rated torque, \n",
"// if the load is increased until maximum reluctance torque occurs.\n",
"// Page No. 328\n",
"\n",
"clc; \n",
"clear;\n",
"close;\n",
"\n",
"// Given data\n",
"Vt1ph=2300/sqrt(3);         // Applied voltage/phase\n",
"Ef1ph=2300/sqrt(3);         // Excitation voltage/phase\n",
"Xd=36.66;                   // Direct axis reactance/phase\n",
"delta=-18;                  // Power angle\n",
"Xq=23.33;                   // Quadrature-axis reactance/phase\n",
"n=900;                      // Speed of motor\n",
"deltanew=-45;\n",
"RatTor=200;                 // Rated torque of motor\n",
"// (a)  Developed torque\n",
"Pmag1ph=-((Vt1ph*2*Ef1ph)/Xd)*sind(delta);  // Power \n",
"Prel1ph=-Vt1ph^2*( (Xd-Xq) / (2*Xd*Xq)) *sind(2*delta); // Reluctance power\n",
"Psal3ph=3*(Pmag1ph+Prel1ph);  // Salient power of motor\n",
"Psal3phHP=Psal3ph/746;\n",
"T=(5252*Psal3phHP)/n;         // Developed torque\n",
"\n",
"// (b) Developed torque in percent of rated torque\n",
"// The reluctance torque has its maximum value at delta= -45 degrees\n",
"Pmag1phnew=-((Vt1ph*2*Ef1ph)/Xd)*sind(deltanew); // Power\n",
"Prel1phnew=-Vt1ph^2*( (Xd-Xq) / (2*Xd*Xq)) *sind(2*deltanew); // Reluctance power\n",
"Psal3phnew=3*(Pmag1phnew+Prel1phnew);  // Salient power of motor\n",
"Psal3phHPnew=Psal3phnew/746;\n",
"PerRatTorq=Psal3phHPnew*100/RatTor;\n",
"\n",
"// Display result on command window\n",
"printf('\n Developed torque  = %0.0f lb-ft ',T);\n",
"printf('\n Developed torque in percent of rated torque = %0.0f Percent ',PerRatTorq);"
   ]
   }
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