Question

A 100MVA synchronous generator is connected to a 25kV infinite bus through two parallel transmission lines. The synchronous reactance of the generator is 2.5Ω. Each transmission line has inductive reactance of 2Ω and 0.2Ω resistance. The generator delivers 90MVA to the infinite bus at 0.8 power factor lagging.    For the above conditions, calculate:

a. The terminal voltage of the generator     

b. The equivalent field voltage and power angle     

c. The real power output at the generator terminals   

d. The reactive power consumed by the transmission lines   

e. Draw the system phasor diagram

Answer 1

Ans)

Assuming synchronous generator is star connected

given line voltage at infinite bus is

The phase voltage is

take it as reference voltage

Given impedance of transmission line

equivalent impedance of two transmission lines in parallel is

Given load

The phase current same as line current in star connection is given as

negative sign for angle as load PF is lagging

a)

Now using per phase equivalent circuit terminal voltage of generator per phase is

line voltage at generator terminals will be

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b) given synchronous reactance of generator i s

equivalent field voltage per phase is

power angle is angle of field voltage i.e

equivalent field voltage per line is

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c)

The real power output at generator terminals is

Re means real part

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d)

The reactive power consumed by transmission lines is

Img means imaginary part

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e)