Bucephalus
Member
Engineering student:
I'm doing a question from a text book and I'm having trouble understanding a part of the solution.
the question goes:
A 100 MVA, 13.8 KV, Y-connected, three-phase, 60 Hz synchronous generator is operating at the rated voltage and no load when a three-phase fault develops at its terminals. Its reactances in per unit to the machines own base are:
Xs = 1.00, X' = 0.25, X'' = 0.12
and its time constants are
T' = 1.10s, T'' = 0.04s
The initial DC component in this machine averages 50 percent of the initial AC component.
a) What is the AC component of current in this generator the instant ofter the fault?
Anyway, this is a worked example, and I still can't understand the preliminary working out. IN the lead up to the answer to this question a) it says this
"The base current of this generator is given by the equation:
IL,base = Sbase/(((3)^1/2)*13.8) = 4184
The subtransient, transient, and steady-state currents in per-unit and in amperes are:
I'' = Ea/X'' = 1.0/0.12 = 8.3333
= (8.3333)(4184) = 34 900 A
I' = Ea/X' = 1.0/0.25 = 4.0
= (4.00)(4184) = 16 700 A
Iss etc, etc.
Given that this book defines subtransient reactance X'' = Ea/I'', as,
"the ratio of the fundamental component of the internal generated voltage Ea to the subtransient component of the current at the beginning of the fault", how did they get a value of Ea = 1.0 for the above calculations?
Has this something to do with per-units?
Thanks
I'm doing a question from a text book and I'm having trouble understanding a part of the solution.
the question goes:
A 100 MVA, 13.8 KV, Y-connected, three-phase, 60 Hz synchronous generator is operating at the rated voltage and no load when a three-phase fault develops at its terminals. Its reactances in per unit to the machines own base are:
Xs = 1.00, X' = 0.25, X'' = 0.12
and its time constants are
T' = 1.10s, T'' = 0.04s
The initial DC component in this machine averages 50 percent of the initial AC component.
a) What is the AC component of current in this generator the instant ofter the fault?
Anyway, this is a worked example, and I still can't understand the preliminary working out. IN the lead up to the answer to this question a) it says this
"The base current of this generator is given by the equation:
IL,base = Sbase/(((3)^1/2)*13.8) = 4184
The subtransient, transient, and steady-state currents in per-unit and in amperes are:
I'' = Ea/X'' = 1.0/0.12 = 8.3333
= (8.3333)(4184) = 34 900 A
I' = Ea/X' = 1.0/0.25 = 4.0
= (4.00)(4184) = 16 700 A
Iss etc, etc.
Given that this book defines subtransient reactance X'' = Ea/I'', as,
"the ratio of the fundamental component of the internal generated voltage Ea to the subtransient component of the current at the beginning of the fault", how did they get a value of Ea = 1.0 for the above calculations?
Has this something to do with per-units?
Thanks
