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The above formula is valid for a single phase transformer





Usually the LV winding has less turn of coils but bigger cross sectional area because it carries a lot of current and installed close to laminated steel core. The HV winding has more turn of coils but smaller cross sectional area because it carries less current and installed outside the LV windings. For sample calculation go to problem #6 below.


For a three phase transformer, the single phase voltage ratio is not always equal to the three phase voltage ratio, you need to know what is the primary winding and secondary winding configuration. For delta - wye winding configuration, the multiplying factor for single phase voltage ratio is 1.732 [67/13.75*1.732 = 8.439 ] to get the equivalent calculated three phase voltage ratio as shown by the above circuit model. Modern Transformer Turn Ratio (TTR) test instrument are using software lookup table to find the correct multiplying factor depending on specified winding configuration entered during Transformer Turn Ratio (TTR) testing session.

It is a good practice to review the TTR test instrument winding configuration setting and make sure it is the same with the transformer winding configuration shown on the transformer nameplate. Factory test report calculated value for three phase transformer voltage ratio can be evaluated using single phase voltage ratio multiplied by a factor based on winding configuration. Shown below are the single phase multiplying factor based on transformer winding connection to convert line to phase voltage or current.


HOW TO USE: Enter new number on any white input boxes. Answer is automatic.

The De-Energized Tap Changer (DETC) of a 3 phase power transformer was set at primary voltage of 67 kV and the OnLoad Tap Changer (OLTC) at secondary winding is set at 13.75 kV as the rated voltage also called the secondary voltage. If you look at transformer nameplate, the neutral voltage is indicated by letter "N"; Calculate the Voltage Ratio at the given DETC & OLTC tap settings. This voltage ratio or turn ratio is your baseline value for a healthy transformer with respect to normal winding turn to turn ratio. If there is no turn to turn short circuit on your primary windings or secondary windings the voltage ratio value or turn ratio value should remained very close to your voltage ratio baseline value. Assuming that the instrument was properly calibrated.

Problem #1, Valid for 3 Φ , Δ - Y only

3 phase voltage Ratio,"a" , single phase voltage ratio * 1.732 =
=
kV Primary Voltage * 1.732

kV Secondary Voltage

Click white input box to enter new number


If your primary winding is shorted, you will expect to have a lower turn ratio (a) in your TTR measurement compare to factory test report. It is also indicated by lower primary voltage reading. Use the calculator below to do simulation. What will happen to your primary voltage if your TTR reading goes down to 7.125?

Problem #2, Valid for 3 Φ , Δ - Y only

Given three phase turn ratio 8.4396 and Secondary voltage 13.75 kV; Calculate the expected primary voltage

three phase turn ratio, a
=
kV Primary Voltage * 1.732

kV Secondary Voltage

Click white input box to enter new number


If your secondary winding is shorted, you will expect to have a higher turn ratio (a) in your TTR measurement compare to factory test report. It is also indicated by lower secondary voltage reading. Use the calculator below to do simulation. What will happen to your secondary voltage if your TTR reading goes up to 9.521?

Problem #3, Valid for 3 Φ , Δ - Y only

Given a three phase turn ratio 8.4396 and Primary voltage 67 kV; Calculate the expected secondary voltage

three phase turn ratio, a
=
* 1.732 Primary Voltage

Secondary Voltage

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Knowing the factory report of voltage ratio (TTR) of the above 3 phase transformer as 8.4396 your baseline for a healthy condition, what do you think happen to the same transformer if the voltage ratio (TTR) from the latest test report is 7.3163 ? Can you estimate the coil location of the Turn to Turn winding short? Can you tell which side of the winding (HV or LV) the Turn to Turn winding short happen? Can you make a generalization about the location of the turn to turn winding short if the TTR test report value is less than the baseline TTR value?

Knowing the factory report of voltage ratio (TTR) of the above 3 phase transformer as 8.4396 your baseline for a healthy condition, what do you think happen to the same transformer if the turn to turn ratio (TTR) from the latest test report is 9.1247? Can you estimate the coil location of the Turn to Turn winding short? Can you tell which side of the winding (HV or LV) the Turn to Turn winding short happen? Can you make a generalization about the location of the turn to turn winding short if the TTR test report value is greater than the baseline TTR value?


Problem #4, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given single phase voltage ratio of 4.8727 and Secondary voltage 13.75 kV; Calculate the expected primary voltage

Voltage Ratio, a , single phase
=
Primary Voltage

Secondary Voltage

Click white input box to enter new number


Problem #5, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given Turn Ratio, a , single phase 5.333 and Primary voltage 69 kV; Calculate the expected secondary voltage

Turn Ratio, a
=
Primary Voltage

Secondary Voltage

Click white input box to enter new number


Assuming from your transformer design review you learned that the primary coil winding turns is 484 for 67 kV tap setting on your DETC and the secondary coil winding turns is 90 to get 12.47 kV and set at Neutral tap setting on your OLTC. Calculate your transformer turn to turn ratio using the given number of turns as your baseline for a healthy condition.

Problem #6, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given primary coils number of turns = 484 and secondary number of turns = 90

Given primary voltage 525 kV and secondary voltage 230 kV ; 3 Φ Y-Y

Calculate the expected Turn to Turn Ratio (TTR).

Turn Ratio, a , single phase
=
Primary coils or voltage

Secondary coils or voltage

Click white input box to enter new number


Problem #7, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given Turn ratio = 5.3778 and Secondary number of turns = 90; Calculate the expected primary number of turns of coil. Now assuming your TTR value a = 5.00, what is the expected number of turns now in primary winding? How many coil turns have been bypass or short circuited from original 484 turns? Is it possible to locate where they are in your primary winding? Possibly with acoustic triangulation methods of diagnostic.

Turn Ratio, a , single phase
=
Primary coils or voltage

Secondary coils or voltage

Click white input box to enter new number


Problem #8, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given Turn Ratio, a , single phase = 5.3778 and Primary number of turns = 484; Calculate the expected secondary number of turns of coil. How can you tell if the turn to turn short circuit happen in primary winding? Answer, usually if the turn ratio value goes down from the baseline value. For example the baseline value of a = 5.3778 then it goes down to 5.00 what will happen when you enter new value by changing the value of 5.3778 to 5.00? The secondary coil number of turns goes up to 96.8 from original coil turn number of 90. At this point, you know immediately the short circuit happens in the primary winding. How? Because you can't add additional turn in your existing secondary transformer coil. It's number will always stay at 90 turns of coil if nothing is shorted on the secondary winding. Now you know the fault happens in primary winding, try changing the number of turns of your primary coil winding until the value of your secondary coil turns is 90. Try 450, you should get 90 on your secondary coil turns. At this time you do the math and you know there were 34 turns in your primary winding that was compromised. It's location could be anywhere in the primary winding side.

Turn Ratio, a , single phase
=
Primary coils or voltage

Secondary coils or voltage

Click white input box to enter new number


Problem #9, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given Secondary FLA = 1296.41 and Primary FLA = 241.28;

Given Primary voltage = 525 kV and Secondary = 230 kV ; 3Φ Y - Y

Calculate the expected turn ratio

Turn Ratio, a , single phase
=
Secondary current or voltage

Primary current or voltage

Click white input box to enter new number


Problem #10, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given Turn Ratio, a , single phase = 5.3778 and Primary FLA = 241.28; Calculate the expected secondary full load ampere (FLA)

Turn Ratio, a
=
Secondary current or voltage

Primary current or voltage

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Problem #11, Valid for 1 Φ only or 3 Φ Y-Y or 3 Φ Δ - Δ

Given Turn Ratio, a , single phase = 5.5334 and Secondary FLA = 1296.41; Calculate the expected primary full load ampere (FLA)

Turn Ratio, a
=
Secondary current or voltage

Primary current or voltage

Click white input box to enter new number


Problem #12, Valid for 3 Φ only

Given 3 Phase MVA rating = 28 and Secondary voltage = 69 kV; Calculate the expected primary full load ampere (FLA)

3 Phase MVA RATED POWER TRANSFORMER

Primary, Amp
=
3 Phase MVA Rating

Primary kV * 1.732

Click white input box to enter new number


Problem #13, Valid for 3 Φ only

Given Secondary FLA = 1296.41 and Secondary voltage = 12.47 kV; Calculate the expected 3 Φ MVA rating of transformer

Secondary, Amp
=
3 Phase MVA Rating

Secondary kV * 1.732

Click white input box to enter new number


Problem #14, Valid for 3 Φ only

Given 3 phase kVA = 1000 and Primary voltage = 480; Calculate the expected primary full load ampere (FLA)

3 Phase KVA RATED POWER TRANSFORMER

Primary, Amp
=
3 Phase kVA Rating

Primary V * 1.732

Click white input box to enter new number


Problem #15, Valid for 3 Φ only

Given Secondary FLA = 2405.70 and Secondary voltage = 240; Calculate the 3 Φ kVA rating of transformer

Secondary, Amp
=
3 Phase kVA Rating

Secondary V * 1.732

Click white input box to enter new number


Problem #16, Valid for 3 Φ only

Given Primary FLA = 1202.85 and 3 phase kVA = 1000; Calculate the expected primary voltage

Primary, Amp
=
3 Phase kVA Rating

Primary V * 1.732

Click white input box to enter new number

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