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# About transformer turns ratio

is it possible the turns ratio of a transformer can verify with its percentage impedance value?

#1

09-01-2014 02:21 PM

Top #2

The main inductance of the transformer can be found as a function of number of turns. The percentage impedance should change for any change in inductance. When you have shorted secondary side to determine the percentage impedance of transformer, the current could be determined by the reactance offered by the leakage and main inductance for applied constant voltage. I hope this helps.

Please correct me if I am wrong or misunderstood your question. On a larger picture, The percent impedance values depend on various factors including the number of windings, particular phase, transformer kVA rating etc.

Please correct me if I am wrong or misunderstood your question. On a larger picture, The percent impedance values depend on various factors including the number of windings, particular phase, transformer kVA rating etc.

09-01-2014 05:17 PM

Top #3

In a transformer having for example, two windings W1 and W2 with N1 and N2 turns you can measure in OPEN circuit two magnetizing inductances L1 and L2 which are good estimated as: L1 = KxN1xN1 and L2 = KxN2xN2; therefore N1/N2 = Squareroot(L1/L2).

K is a constant of the whole equivalent magnetic circuit.

Or if you measure the impedances X1 and X2 which are proportional to the measurements frequency you can rewrite N1/N2 = squareroot(X1/X2).

The calculation is well very approximated if the leakage inductances are quite smaller than the magnetizing inductances and this happens in most cases.

If you want more precision you have to estimate als the two leakage inductances Lµ1 and Lµ2 because the inductance L1 and L2 that you measure through the windings are in reality L1 = L1t + Lµ1 and L2 = L2t + Lµ2 where L1t and L2t are the true magnetizing inductances.

And so N1/N2 = Squareroot((L1-Lµ1)/(L2-Lµ2)) = Squareroot((X1-Xµ1)/(X2-Xµ2))

(I assume you use always the same measurements frequency!)

X1 and X2 are measured with all windings in open circuit while Xµ1 is the impedance measured with W2 in SHORT circuit and Xµ2 with W1 in SHORT circuit.

The measurements frequency should stay from 1kHz to 10 Khz otherwise you may have the effects of the parassitic capacitive components of the transformer.

The calculation does not take in account the influence of the resistive part of the winding but normally you get a good approximation also ignoring the leakage inductances

Hope this can help you

K is a constant of the whole equivalent magnetic circuit.

Or if you measure the impedances X1 and X2 which are proportional to the measurements frequency you can rewrite N1/N2 = squareroot(X1/X2).

The calculation is well very approximated if the leakage inductances are quite smaller than the magnetizing inductances and this happens in most cases.

If you want more precision you have to estimate als the two leakage inductances Lµ1 and Lµ2 because the inductance L1 and L2 that you measure through the windings are in reality L1 = L1t + Lµ1 and L2 = L2t + Lµ2 where L1t and L2t are the true magnetizing inductances.

And so N1/N2 = Squareroot((L1-Lµ1)/(L2-Lµ2)) = Squareroot((X1-Xµ1)/(X2-Xµ2))

(I assume you use always the same measurements frequency!)

X1 and X2 are measured with all windings in open circuit while Xµ1 is the impedance measured with W2 in SHORT circuit and Xµ2 with W1 in SHORT circuit.

The measurements frequency should stay from 1kHz to 10 Khz otherwise you may have the effects of the parassitic capacitive components of the transformer.

The calculation does not take in account the influence of the resistive part of the winding but normally you get a good approximation also ignoring the leakage inductances

Hope this can help you

09-01-2014 07:40 PM

Top #4

Are you asking will the transformer impedance change when you apply different taps? Yes, the transformer resistance and leakage reactance will change slightly at different taps. This change is typically neglected in power system studies. The bigger challenge would be in modeling the transformer's per unit impedance in a multibus network. If you select a base voltage that agrees with the tap value, you can use the transformer impedance as modified by only the kVA base as needed. But if you are using a nomminal voltage rating as the voltage base, and it disagrees with the tap, then the transformer impedance needs to be modified for the difference in voltage bases, where the multiplying factor is the ratio of the old voltage base squared over the new voltage base squared (V1^2/V2^2). This is discussed in both IEEE Std 551 ("The Violet Book" Short Circuit Calculations) and IEEE Std 399 ("The Brown Book" Power System Analysis).

09-01-2014 10:16 PM

Top #5

Balaji,

The way I understand your question is, if you know the turns ratio of the transformer, you can determine its percent impedance. My answer is no, because aside from the turns ratio, there are other factors that will affect the leakage or percent impedance of a transformer like the material of its windings and the construction of its core. The best way to measure the percent impedance of a transformer is to short its LV or secondary winding, use a Variac to gradually apply a voltage to its HV or primary side and measure the current on the shorted secondary side until it reaches its rated current, then measure the applied voltage on the primary.

Then you can determine the percent impedance based on the measured voltage.

The way I understand your question is, if you know the turns ratio of the transformer, you can determine its percent impedance. My answer is no, because aside from the turns ratio, there are other factors that will affect the leakage or percent impedance of a transformer like the material of its windings and the construction of its core. The best way to measure the percent impedance of a transformer is to short its LV or secondary winding, use a Variac to gradually apply a voltage to its HV or primary side and measure the current on the shorted secondary side until it reaches its rated current, then measure the applied voltage on the primary.

Then you can determine the percent impedance based on the measured voltage.

09-02-2014 12:23 AM

Top #6

With transformer ratio test, you will have the turns ratio.

By supplying the source on the HV side, and shorting the LV side you can get the measures to calculate somehow accurately the transformer impedance. Even if you have a basic AC voltage source, and be careful the current could be quite high, then if you do it I would strongly recommend you to get a manual switch to apply the voltage not that long for the impedance/short-circuit test.

Not the most classic method, but it could help for failure investigation, if performed by a skilled electrician.

Hope it helps.

By supplying the source on the HV side, and shorting the LV side you can get the measures to calculate somehow accurately the transformer impedance. Even if you have a basic AC voltage source, and be careful the current could be quite high, then if you do it I would strongly recommend you to get a manual switch to apply the voltage not that long for the impedance/short-circuit test.

Not the most classic method, but it could help for failure investigation, if performed by a skilled electrician.

Hope it helps.