Help finding typical inductance of large transformer 1

[eeprom]

Hello,
I am trying to determine the inductance value (as measured from the secondary) of a 37MVA transformer 120kv/13.8kv, rated impedance is 6.17%. I have calculated a value of approximately 1 mH, and it seems too small. The calculation is fairly simple, but I don't have any kind of baseline to determine whether or not this value is reasonable. Does someone out there know whether or not this number is within a typical range for large transformers?

thanks

 

[dpc]

If you have the test data on the no-load losses and exciting current, you should be able to back into it from that. Winding resistance is generally also available. With this data you can compute the effective impedance, back out the resistance to get reactance and then compute the inductance from that.

I assume you are just interested in the inductance of a transformer with the other winding open circuit.

 

[eeprom]

DPC,
I don't have any test data. All I have is manufacturer provided data, which is what I listed earlier. I am trying to model the transformer as it is connected to the grid so that I can roughly estimate how much a current surge would affect the bus voltage. Based on the percent impedance given, and the other ratings, I found that the impedance measured from the high voltage side was about 41 ohms. Measured from the secondary it was about 0.55 ohms. I assumed that this was mostly inductive and so I can up with 377*L=0.50, which got me in the area of 1mH. As I said, the calculation is pretty simple; I just want to know how realistic this value is.

 

[dpc]

How did you measure that? Sounds like you measured the dc resistance, not the impedance.

If you are trying to determine the current inrush and voltage dip, that is more complicated than simply knowing the inductance. The transformer impedance is going to be very non-linear, due to the ferro-magnetic core. It is also a function of the phase angle of the voltage when the transformer is initially energized as well as the residual flux in the core.

You can get a very rough idea from assuming 10 times the full load current for about 0.1 seconds. It could be 100 times for 0.01 seconds. If you are energizing from the low side, it could be double that.

Hope that helps.

 

[magoo2]

What you calculated looks correct. 1 mH is what I get based on the 13.8 kV side and 50 hertz. It's about 0.8 mH at 60 hertz.

 

[dpc]

The impedance given on the nameplate is the leakage reactance, not the excitation reactance.

Take a look at the equivalent circuit of a transformer - the leakage reactance corresponds to the series reactance. You need the shunt reactance.

.

 

[Runsor]

The secondary inductance will be more near 10 H than 1 mH. If the name plate contains S₀, the idle apparent power, that can be used to calculate the winding inductances.

Anyway, I think dpc hit the nail on the head in his second comment:

If you are trying to determine the current inrush and voltage dip, that is more complicated than simply knowing the inductance. The transformer impedance is going to be very non-linear, due to the ferro-magnetic core. It is also a function of the phase angle of the voltage when the transformer is initially energized as well as the residual flux in the core.

 

[eeprom]

Guys,
I was trying to figure out what the transformer looks like in the circuit as it is running - NOT inrush current. Please read the question. The percent impedance rating, along with the other name plate data, is sufficient to determine the impedance of the transformer.

 

[dpc]

Your question wasn't very clear. Your term "current surge" was interpreted as referring to the transformer inrush. If you just want the voltage drop across the transformer during normal operation, you can just convert the %impedance to ohms. No need to convert to inductance unless you are looking at something other than normal power frequency.

Transformer Z in ohms = Base kV^^2/Base MVA * Zpu

In your case (from low side) = 0.317 ohms

You can assume an X/R of about 25 for a transformer of this size and voltage.

 

[eeprom]

dpc,
You are correct. My question could have been clearer. I was referring to a current surge. But not at start-up.

 

[waross]

A primary current surge is not a cause, it is an effect.
It is an effect caused by a fault or heavy load applied to the secondary or a voltage surge on the primary.
Your question may be a little more complex than you realize. I am thinking possibly three or more chapters in my transformer book.
But let's see it we can shorten the story a little.
First, lets start with a single phase example.
Yes the transformer has impedance, but the impedance is a combination of resistance and inductive reactance.
The impedance, resistance and inductive reactance are a combination of both primary windings, which are separated by (among other things), the transformer ratio.
This is one of the reasons that per-unit or percent values are used.
The impedance determines the current under short circuit conditions. Voltage drop at normal load levels or regulation depends more on the resistance of the transformer.
Now the voltage drop due to resistance and the voltage drop due to inductive reactance act a right angles to each other.
With a ratio of 25 to one (it varies with different transformers), the reactance prodominates and the current is almost purely reactive.
With 100% resistive load, the inductive voltage drop is still much greater than the resistive voltage drop, but the load voltage is over 12 times as much as both of them combined. The smaller resistive voltage drop, being in phase with the load current often has a greater effect on the terminal voltage than the inductive voltage drop working at right angles.
A rigourous solution requires both the load impedance and the transformer impedance to be resolved into resistance and inductive reactance.
The next question is the nature of the surge. If it is a secondary surge, it will have been caused either by a fault or the application or removal of a heavy load.
If it is a primary surge that has been caused by a voltage surge, just the question of whether it will push the transformer into saturation depends on several factors.
The magnitude of the surge, the point in the cycle that the surge hits, the design of the transformer, and the actual line voltage as opposed to rated line voltage all have an influence on possible saturation.
Surges associated with saturation depend more on the impedance of the primary than the impedance of the whole transformer.
I you care to describe the effect that you are trying to model, you will probably get excellent help, but just asking about voltage dips and surges without describing the circumstances is not very productive.
What do you see as causing the current surge and what will be the power factor of the surge?
Did I forget to mention, the phase angle of the current surge will have a significant influence on the voltage drop at the bus. Current surges of identical value will NOT result in the same voltage drop unless the phase angle is also identical.



Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[eeprom]

Waross,
Thanks for your in-depth analysis of my situation. I have considered most of those things you mentioned. But since you appear so motivated, let me give you the actual situation. I believe I have it figured out, but I welcome your opinion.
A steam power plant generator (synchronous, 13.8kv) is operating at 30MW, with 5MW being for station service, and the remaining 25MW going to the grid through the main transformer. The main transformer is rated as follows: 37MVA, 120kv/13.8kv, 6.2% impedance. There is a fault which occurs on the 4160V station service bus, and it trips all of the station service off line. The 52G (generator breaker) and the 52T (breaker to the grid) have not tripped. And so, at least for a few moments, the generator is on line with no station service, and it is pushing 30MW into the grid. The main transformer sees an increase in current of around 220A per phase. The generator eventually tripped, but it could have tripped for various reasons. The over-voltage relay flag had been set, but it is not clear if that occurred before or after the generator breaker tripped. So what I want to determine is approximately how high the bus voltage got when the current surge went through the main. There is a lot of information not included here, such as the states of various lockout relays and other relay flags, etc. All I was trying to determine is how high the bus voltage got during the surge. And according to my calculations, it didn't get high enough to trip the over-voltage relay.

 

[slavag]

Hi.
What is a setting of 59(overvoltage) protection, Un and time too.
Regards.
Slava

 

[slavag]

BTW, maybe overflux Vhz operated

 

[eeprom]

The 59 relay was set for something like 2 seconds at 16.6kv and 1.1 seconds at 17.5kv. Those numbers are approximate, but they are close.

 

[slavag]

OK, Eeprom.
1. 16.6kV for 2sec its seems OK, its about 1.2Un
2. Second setting 17.5kV for the 1.1sec isnt seems, you need something about 1.4Un for 0.1-0.5sec.
3. I assume you have some problem with tripping matrix and with trip of CB, you dont send trip to AVR and turbine in additional to some maybe not correct control of AVR,
Im not believe in some problem with surge.
Regards.
Slava

 

[waross]

Just a guess, does this fit with your trip times?
When the fault hit, the heavy current would have taken the generator voltage down. The Automatic Voltage Regulator may have have gone full out, (I believe the technical term in the UK is "Balls to the Walls").
When the fault was cleared there would probably have been a voltage surge for a few seconds at least until the AVR cut back and the field magnetism decayed.
Your faults and the current surge would have dropped the voltage, not increased it.
I think the answer to your problem may lie in the dynamics of a generator recovering from a fault rather than with the transformer characteristics.
The connection to the grid will buffer the generator response.
The impedance of the transformer will be a significant factor in the amount of buffering.
The impedance of the line connecting you to the backbone of the grid may also be a non trivial factor.
Let's hope some of the power plant experts get involved here.

Bill
--------------------
"Why not the best?"
Jimmy Carter