A $1500-\mathrm{MVA} 20-\mathrm{kV}, 60-\mathrm{Hz}$ Three-Phase Generator Is Connected Through A $1500-\mathrm{MVA}$ $20-\mathrm{kV} \Delta / 500-\mathrm{kV}$

Essay

A $1500-\mathrm{MVA} 20-\mathrm{kV}, 60-\mathrm{Hz}$ three-phase generator is connected through a $1500-\mathrm{MVA}$ $20-\mathrm{kV} \Delta / 500-\mathrm{kV}$ Y transformer to a $500-\mathrm{kV}$ circuit breaker and a $500-\mathrm{kV}$ transmission line. The generator reactances are $\mathrm{X}_{d}^{\prime \prime}=0.17, \mathrm{X}_{d}^{\prime}=0.30$ , and $\mathrm{X}_{d}=1.5$ per unit, and its time constants are $\mathrm{T}_{d}^{\prime \prime}=0.05, \mathrm{~T}_{d}^{\prime}=1.0$ , and $\mathrm{T}_{\mathrm{A}}=0.10 \mathrm{~s}$ . The transformer series reactance is 0.10 per unit; transformer losses and exciting current are neglected. A three-phase short-circuit occurs on the line side of the circuit breaker when the generator is operated at rated terminal voltage and at no-load. The breaker interrupts the fault 3 cycles after fault inception. Determine (a) the subtransient current through the breaker in per-unit and in kA rms; and (b) the rms asymmetrical fault current the breaker interrupts, assuming maximum dc offset. Neglect the effect of the transformer on the time constants.