A3 ϕ, 11 kv, 60 hz, 25 mva, y-connected cylindrical-rotor synchronous machine generator has ra =0: 45 ω per phase and xs =4: 5 ω per phase. the generator delivers the rated load at 11 kv and 0.85 lagging power factor. determine the excitation voltage, ef , for this operating condition.

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

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