Question

A 3 -phase, \(60-\mathrm{H} 2\), synchronous generator has the following data:

Rated MVA \(=22.8 \mathrm{MVA}\)

Rated voltage \(=13.8 \mathrm{kV}\)

\(X_{d}=1.8\) pu on rated MVA and rated voltage base \(X_{d}^{\prime}=0.3\) pu on rated MVA and rated voltage base CT ratio \(=1200 \mathrm{~A}: 5 \mathrm{~A}\)

PT ratio \(=14.4 \mathrm{kV}: 120 \mathrm{~V}\)

a) Explain why it is important to have synchronous generator under-exciation or loss of excitation protection. [5 marks]

b) Design a loss of excitation relay for this generator based on the standard single mho circle design, and plot the characteristics of relay on an apparent impedance diagram in secondary ohms. [10 marks]

c) At one instant the generator produces \(10 \mathrm{MW}\) and absorbs \(20 \mathrm{MVar}\) due to the opening of the field winding, would the generator apparent impedance enter the protection zone of the loss of excitation protective relay as determined in part (b)? Justify your answer. Assume that the generator terminal voltage drops to \(10 \mathrm{kV}\) line to line during the disturbance. [10 marks]