Answer:
Excitation Voltage = Ef = 11.012 kV / phase
Power Angle = δ = + 25.29
Explanation:
Given Data:
Line Voltage: VL = 11 kV
Power Factor: Pf = 0.85 lagging
Synchronous Reactance: Xs = 4.5 ohm / phase
Armature Resistance: Ra = 0.45 ohm / phase
Required:
Excitation Voltage: Ef to be determined
Solution:
The excitation voltage for cylindrical/round rotor synchronous generator can be calculated using formula:
EF = Vp + Ia Ra + j Xs Ia
In phasor form, the equation can be written as:
Ef ∠δ = Vp ∠0° + (Ia∠-θ)(Ra) + j( Xs)( Ia∠-θ)-------------------- (1)
Where:
Ef ∠δ = Excitation voltage (δ is the angle between EF and Vp)
Vp = Phase Voltage (Vp is taken as reference phase that’s why angle is 0°)
Ia∠-θ = Armature Current (θ is angle between Vp and Ia, minus sign is taken because the pf is lagging)
Calculating Vp:
Since, for Y-Connection,
Vp = VL / Sqrt (3)
Vp = 11000 / Sqrt (3)
Vp = 6350.85 V / phase
Calculating Ia :
Since, Power output from the generator is given as:
P = Sqrt (3) x VL x IL x Cos θ
Since, phase current is equal to line current in Y-Connection, therefore, IL = Ip = Ia. Therefore, rearranging the above equation to find Ia:
Ia = P / Sqrt (3) x VL x Cos θ
Since, Apparent Power (S) = Active Power (P) / Power Factor (Cos @) = 25 MVA,
Therefore,
Ia = S / Sqrt (3) x VL
Ia = 25 MVA / Sqrt (3) x (11 kV)
Ia = 1312.16 A
Since, Cos @ = 0.85
@ = Cos-1 (0.85)
@ = 31.79 degrees
Therefore, Ia = 1312.16 ∠- 31.79 (minus sign is taken because the power factor is lagging)
Calculating Excitation Voltage (Ef):
Substituting all values in equation (1), we get,
Ef ∠δ = 6350.85 <0 + (1312.16 ∠-31.79)(0.45) + j(4.5)( 1312.16∠-31.79)
Ef ∠δ = 9963.4 + j4707.86
Ef ∠δ = 11019.7 ∠25.29
Excitation Voltage = Ef = 11.012 kV / phase
Power Angle = δ = + 25.29
