how one can determine a power transformer capacity in kVA when it is without nameplate and no sign of its capacity?
In order to conduct the full range of tests you would need to do to make and approximation of what the kVA rating might be, you need to know what voltage the transformer primary is rated for. If there is no nameplate to tell you what that rating is, I wouldn't bother going any further. There may be some clues inside the transformer case, but you are putting yourself and the transformer at risk by going through the testing, which now has become an experiment.
Reynaldo and Derek are correct. It is a science fair project.
And the open ended question is too broad to answer definitively.
Is this a school project?
Or maybe a derelict transformer out in the boneyard?
Is it something you want to reuse?
What do you have for test equipment?
How much time and money do you have?
If school project, and all you asked about was the KVA, here are some questions for you to start with: (These are questions for you - nothing I can help you with)
Oil filled or dry?
How big?
Deck of playing cards
bread box?
Volkswagen?
Semi-truck?
freight train locomotive?
Look up transformer data matching the criteria and select a close match.
Now if it is a real transformer (derelict out back), then I would start with asking the old timers -
Where did this thing come from?
Was it dead when it came out?
You can do this with out endangering yourself or the transformer - requires time. money , test equipment, and some basic physics knowledge.
carl
Seth, I usually don't answer questions I was not invited for (suggested by the Author). However for the sake of knowledge of all Z4E Members, and to improve safety, I am attending to a Reynaldo suggestion to reply here. Thanks, Reynaldo.
Identify Terminals: terminal marking of Power Transformers is determined by ANSI standards, if manufactured in US (or Japan, or even in other country for US-export). Two-winding transformers have terminals designated by H and X (e.g. H1, H2, X1, X2, etc.) where H is the High-voltage-rated winding and X is the Low-voltage winding. As viewed from the High-voltage side, H1 bushing terminal will be located on the RIGHT. While 3-or-more-winding Transformers will have winding designation H, X, Y and Z, where H is the High-voltage winding or, the HIGHEST kVA-RATED winding if windings have the same voltage rating and X, Y, and Z are for other winding voltage ratings, in decreasing order.
ESTIMATE Turns (Voltage) Ratio and Impedance Ratio: with a high precision Ohmmeter measure both sides resistances. The High-voltage side has more turns than Low-voltage side, consequently has higher resistance (Rh). Calculate both estimated ratios as this:
R-ratio = Rh / Rl and V-ratio = sqrt(R-ratio)
Example: if R-ratio is 100:1, then V-ratio is 10:1 - meaning if Vh = 100V then Vl = 10V;
Please keep in mind these are ESTIMATE values, since the Transformers have also high inductive impedances (Zi), that can be measured with an Inductance Meter if you have one. There are also capacitive impedances (Zc) mainly on big transformers, that can be measured with a Capacitance Meter. In this way you can have such impedances calculated in this way:
Zi = 2 x pi x f x L where L is measured inductance;
Zc = 1 /(2 x pi x f x C) where C is measured capacitance, and f = 50Hz or 60Hz depending where the transformer is used in both formulas;
Since such impedances can be paralleled to resistance previous measured, this could reduce the total impedances of Transformer sides excessively for the next step (Zt = R // Zi // Zc), so we use only resistances Rh and Rl to estimate a relatively safe Average Power Rating.
ESTIMATE Average Power Rating in KVA (using voltages): with the data above and if you know (any of) the voltages of the system where the Transformer is (was) used, apply on the formula:
Ph[KVA] = (Vh^2 /Rh)/1000
Pl[KVA] = (Vl^2 /Rl)/1000
Compare both values Ph and Pl, if they are close to each other consider to use the mean of them, but proceed the further tests with lowest value for safety.
If you don't know any voltage the Transformer could work with, then try the following...
ESTIMATE Ampacity of windings: through wiring identification, check the AWG (or mm2) and material (Copper, Aluminum, or even both on same Transformer, different material on each side) of wiring in both sides of transformer. Usually, the Low-voltage side has a larger wire size. If you can't visually identify the wiring sizes, with a pachymeter (or caliper) measure the diameters (D) of wires. The actual section of a wire can be calculated:
S = pi x (D/2)^2 where pi= 3.14
Since this an actual section, check the equivalence to the nearest AWG (or mm2) in a table, usually available in Internet. The equivalence shall be related to 60oC (140oF) Temperature Rating of Conductor ONLY, no higher temperature rating conductors are used in common Transformers. If you can't identify the wiring material(s) consider safer Aluminum ampacities, however if the final calculations indicates less than 5kVA Transformer, consider Copper ampacities and re-calculate - Aluminum transformers with such lower power rating are very rare.
Common ampacities of conductors can be found in tables in the Internet, just as an example these are AWG x Ampacity that can be found in NEC/NFPA:
Copper:
AWG8 40A - AWG6 55A - AWG4 70A - AWG3 85A - AWG2 95A - AWG1 110A
AWG1/0 125A - AWG2/0 145A - AWG3/0 165A - AWG4/0 195A
Aluminum:
AWG8 35A - AWG6 40A - AWG4 55A - AWG3 65A - AWG2 75A - AWG1 85A
AWG1/0 100A - AWG2/0 115A - AWG3/0 130A - AWG4/0 150A
ESTIMATE Average Power Rating in KVA (using estimated currents): with found ampacities, consider that Manufacturers 15% to 25% safety rate apply, since the wiring do not have a common insulation as a commercially available conductor this safety rate can reach 30% or even higher depending on the Manufacturer and Transformer application. In your case we can use a relatively common 25% safety rate for High-voltage (Low-current) side and 30% for Low-voltage (High-current) side. Estimate current first:
Ih = Amp_h/125 x 100 where Amp_h is ampacity of wiring at High-voltage side;
Il = Amp_l/130 x 100 where Amp_l is ampacity of wiring at Low-voltage side;
Ph[KVA] = (Ih^2 x Rh)/1000
Pl[KVA] = (Il^2 x Rl)/1000
Again compare both values Ph and Pl, if they are close to each other consider to use the mean of them, but proceed the further tests, if any, with lowest value for safety.
For single-phase Transformer (1 coil each side), the calculations above would be enough. For three-phase Transformer, let's say 3 coils each side, you must do this procedure for every single winding (coil). For STAR (Wye) or (closed) DELTA, you need to sum up all three power ratings of each side to find Ph and Pl respectively. However for an OPEN Delta Transformer you must also divide this power sums by sqrt(3).
Rounding the calculated Power Rating to commercial Power Rating:
Up to 1kVA: round to the nearest 1/10 of kVA;
1 to 9kVA: round to the nearest units of kVA;
10 to 99kVA: round to the nearest 5 units of kVA;
100 to 1000kVA: round to the nearest 10 units of kVA;
1MVA to 9MVA: round to the nearest 100 units of kVA (or 0.1MVA);
and so on...
If the Transformer is not requested to order by a Customer for a specific project or application, and it is mass-produced for a commercially available model, a common power rating sequence used by Manufacturers is 1-2-5, such as: 100VA, 200VA, 500VA, 1kVA, 2kVA, 5kVA, 10kVA, and so on. However such sequence is not mandatory, and other sequences can be chosen by a Manufacturer according the relation between its manufacturing resources and market demanding.
Further tests can be applied to get more data about the transformer, but I will post here only under your request. Good luck.
I hope this helps. Regards.