# Short circuit current calculation

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## I DON'T WANT THE SOLUTION

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The question is:

A three phase 50MVA, 4,160V generator with a reactance of 7.9% is connected to a three phase 4,160V/480V step down transformer rated for 1.5MVA with an impedance of 5.7%. Find the short circuit current if a fault occurs on the 4,160V side of the transformer if the transformer is fully loaded.

The instructor solution:

A fault at a location between the generator and transformer creates a new current path that places the generator and transformer in parallel with each other. Using KCL, the short-circuit current is now the sum of the generator current contribution and the transformer current contribution.

I think this is inaccurate. The fault impedance is zero and since the fault is before the transformer i.e. it’s parallel with the transformer NO fault current will flow to the transformer.

What do you think?

• OK, why are you not asking the instructor? Aug 23, 2021 at 9:53
• Consider that the fault (we're told it's a short circuit) may short one phase to neutral, or two phases together (we're not told which), leaving the remaining phase(s) unaffected. Those still power the transformer...
– user16324
Aug 23, 2021 at 14:20
• It specifically says a three-phase fault. Knowing the load current (transformer full load) you can calculate the "voltage behind the reactance" of the synchronous generator. As Charles mentions below, if there is no source on the 480V side then their will be no contribution from the transformer for this fault (if there were motor loads down there they would barf out some sub transient current but will be over fast). The teacher is correct, and so are you - IF there were a source on the 480V side then it would contribute fault current independent of the generator. Aug 23, 2021 at 18:09
• But, if not - then its contribution will be zero. Aug 23, 2021 at 18:09

Perhaps you're expected to calculate the surge current into the short as the charged transformer coils collapse. Ignore the power source for a moment and just focus on the fully "charged" inductor, it will deliver momentary power to the short as the field collapses. So then add the two currents together to get the peak spike.

• I don't know if what you're saying is even practical. I mean is it done this way? Or are you just guessing?
– OMAR
Aug 23, 2021 at 9:17
• My assumption is this question was asked of you to get to to do the math behind it. It does not sound like it's a practical question. Aug 23, 2021 at 9:21

The only contribution from the transformer would be due to energy stored in the transformer inductance. I think that would only have an effect for the first 1/2 cycle and would not be symmetrical. The impedance for the generator is presumably the symmetric reactance, so I don't think you are able to calculate anything but the symmetrical short circuit current. There could a contribution from energy stored on the load side of the transformer, but you have no information about that. Perhaps you could calculate short term effects based on L/R, but you would need to be given that or estimate it. There is data available for typical L/R for large transformers. You could possibly find typical information for synchronous generators. There may be a handbook with estimation factors that is used for this type of question.

A solution to a problem doesn't need to be fully numerical. In fact, I'd start by assigning symbols to all the constants and figuring it out symbolically. Assume that there's a certain load impedance on the secondary side, and in series with it an external current source. You don't care where that current comes from, you just give it a symbol and use it.

After you get your symbolic solution, you can assign all the symbols the values as given in the problem. And then you're forced to make assumptions. So one special case is when the external current source is set to 0. Then the solution will be fully numerical and involve no independent terms. But that is really only a special case. The general case admits e.g. the 480V load being fed from two transformers.

Another assumption you're making is that the short circuit is zero ohms. That wipes out a whole lot of information/state in the problem. Let the "short circuit" have an arbitrary impedance. As you vary it, you'll observe that the behavior of the system falls into a couple different categories, and you'll be able to say roughly at what impedance does the behavior move to another category. These categories may enable you to simplify the formulas somewhat.

So, I'd start by assuming nothing, and redrawing the circuit with explicit symbolic-valued impedances, voltage sources and current sources. All those elements would be ideal, but taken together would model the real, imperfect circuit you were given.