Question

A 480 V, 60 Hz, 470 kVA, 0.85 PF lagging, 2-pole, Y-connected synchronous generator has a synchronous reactance of XS=0.016 Ω and an armature resistance of RA=0.016 Ω. At rated
conditions the core losses are 7 kW. Friction losses and field winding losses are 8 kW. Suppose the machine is connected to an infinite bus (hence the terminal voltage is fixed) and it is running at the rated conditions.

a) What is the rotor speed in rpm?

b) Calculate the phase current (IA) and line current (IL) magnitudes.

c) Calculate the magnitude and phase of the internal voltage (back emf) ?̅?. What is the power angle?

d) Draw the phasor diagram including phase voltage, phase current and BEMF phasors. On the diagram, specify the numerical values of the angle between phase voltage and BEMF, and angle between phase voltage and phase current.

e) Calculate the output power of the generator, total losses, input mechanical power to the generator, and the efficiency.

f) Suppose the field current remains constant and mechanical power from turbine is increased until steady state stability limit of the generator is reached. Under these conditions, calculate the BEMF phasor, phase current phasor, and output power of the generator.

g) Under conditions of part (f), if the generator’s load were suddenly disconnected from the line, what would be the terminal voltage immediately after that?

Note:
kindly provide detailed step by step solution of each part in clear handwriting. My professor wants full solution so please don't use any shortcut or direct procedures. Also see the attached question picture for more clarification.

3. A 480 V, 60 Hz, 470 kVA, 0.85 PF lagging, 2-pole, Y-connected synchronous generator has a synchronous reactance of Xs=0.016 12 and an armature resistance of RA=0.0.16 1. At rated conditions the core losses are 7 kW. Friction losses and field winding losses are 8 kW. Suppose the machine is connected to an infinite bus (hence the terminal voltage is fixed) and it is running at the rated conditions. a) What is the rotor speed in rpm? b) Calculate the phase current (IA) and line current (IL) magnitudes. c) Calculate the magnitude and phase of the internal voltage (back emf) Ēg. What is the power angle? d) Draw the phasor diagram including phase voltage, phase current and BEMF phasors. On the diagram, specify the numerical values of the angle between phase voltage and BEMF, and angle between phase voltage and phase current. e) Calculate the output power of the generator, total losses, input mechanical power to the generator, and the efficiency. f) Suppose the field current remains constant and mechanical power from turbine is increased until steady state stability limit of the generator is reached. Under these conditions, calculate the BEMF phasor, phase current phasor, and output power of the generator. g) Under conditions of part (f), if the generator's load were suddenly disconnected from the line, what would be the terminal voltage immediately after that?

3. A 480 V, 60 Hz, 470 kVA, 0.85 PF lagging, 2-pole, Y-connected synchronous generator has a synchronous reactance of Xs=0.016 12 and an armature resistance of RA=0.0.16 1. At rated conditions the core losses are 7 kW. Friction losses and field winding losses are 8 kW. Suppose the machine is connected to an infinite bus (hence the terminal voltage is fixed) and it is running at the rated conditions. a) What is the rotor speed in rpm? b) Calculate the phase current (IA) and line current (IL) magnitudes. c) Calculate the magnitude and phase of the internal voltage (back emf) Ēg. What is the power angle? d) Draw the phasor diagram including phase voltage, phase current and BEMF phasors. On the diagram, specify the numerical values of the angle between phase voltage and BEMF, and angle between phase voltage and phase current. e) Calculate the output power of the generator, total losses, input mechanical power to the generator, and the efficiency. f) Suppose the field current remains constant and mechanical power from turbine is increased until steady state stability limit of the generator is reached. Under these conditions, calculate the BEMF phasor, phase current phasor, and output power of the generator. g) Under conditions of part (f), if the generator's load were suddenly disconnected from the line, what would be the terminal voltage immediately after that?

This is actual question picture with only one changes. Ra value is 0.016 ohms. So provide me detailed step by step solution.

Answer 1

Soin est 480v m nius 25 Y bees Vio ay Rolor speed: (Ns) 120 x 60 3600 rpm Ms a. 120f. Р. 2 by since the Generalor is operations at rated Condition lo sa BV I S = B e Ie 4 T0 = 13 (480) IL

3 > ម, 4 TO 10 565. 32 . W3 x 480 line urrent 56.5.32 e phase current line current a = 565.324 CY.connect') CY E + łažs E 450 Lot d3 + (565.32 (-630.85)(0.016* 0.016 480 Lot 12.8113.21 BB

1 289.59 10.578 I EI (magnitede of inlernal voulage) cper phas e) TEL 289.59 Volt = A3 (289.59) volt (line vollase 501.58 volt s = power angle phase angle = .sa 0.578 Phasor Diag. dy Ef lazs Laxs 2 IaRa Ia

and angle blon phase vollage BEMF is called the power angle.(5) 0.578 S. angle bon phase vollage and Phase urrent is called Power factor angle Lost 0.85 31.78 Ø - ex outpeet power PM V IC 650 Х a 3 x 480 x 565.32 x 0.85 PE 399.49 kw

Tolal losses core loss + field loss ☆ copper loss 7.+ 8 + 3(I'Ra) 15 * 3 * (565-32) * 0.016 17 100 15 * 15.34 Total loss 30.34 input mechanical porrer Ploi Pdev 3 Ej la cosa 소 Se o y internal Pt angle = 32.36 Pale = 3 x 289.59 x 565.32 x 60532.36 414.86 kw Pder

Prictrón losses Pior = Pdert 41८.86 +8 Pior Getty g५२२.४८ porel- Efticeny 3११.५१ ५२२.86 Pior 17- १८.५77. n