Transformator Measurements

You may want to determine the various parameters of a transformer without having any manufacturer's information available. In the early stages of experimentation, you may be working with equipment and components that have been "acquired" from other projects as surplus. Or, you may be at a surplus yard, and want to determine if that transformer you can pick up cheap is going to work for your needs. I own a lot of very heavy scrap now, having bought a number of transformers on spec, hoping they would work for my needs.
You'll need a variable voltage AC source (like a variac), a voltmeter, an ammeter, and for some measurements either a watt meter or an oscilloscope. A couple of big power resistors in low resistances (100 ohms, 100 W) will also be useful.
Often, the nameplate or markings on the transformer don't tell you everything you would like to know, particularly in the case of surplus.
Per Unit system of ratings - commercial power distribution transformers have fairly complete data on their nameplates, but it is often stated in terms "per unit". Per Unit measurements are essentially percentages of the rated capacity. For instance, a power transformer might be rated at 10 kVA, and have a rated loss of .03 per unit. 10 kVA multiplied by the .03 gives a rated loss of 300 Watts. Impedances are also usually stated in per unit values
First, you need to identify the windings. An ohmmeter can help you determine which wires are connected to which windings, by looking for continuity. Sometimes, you can determine the order of taps by the resistances. However, the resistance is affected by the size of the wire, as well as the number of turns, so you can't use the ohmmeter to determine voltages or currents. In general, the heavy wires or terminals are for the low voltage windings. A notable exception is some power supply transformers that have some medium voltage windings to provide isolated bias supplies at low currents.
Almost all the parameters of the transformer can be determined by making a series of measurements with the secondary open circuited and then shorted. The choice of which winding is primary and secondary is arbitrary for measurement purposes. For commercial distribution transformers, these measurements are often made at 115 Volts, as measurement equipment is readily available for that voltage. In the case of a transformer with a HV winding and a LV winding, the 115 Volts is applied to the HV winding for safety reasons. In the lab, lower voltages are convenient: using 1.15 Volts or 11.5 Volts allows simple scaling of the results.
Real transformer model

 Transformer Model

First, identify windings and approximate no load turns ratios. Apply a low voltage (say 10 volts) to what you think a high voltage winding might be. Measure the voltages on the other windings. You use the high voltage side here for safety: Say you had a 110V:15kV transformer with a 6.3V filament winding. If you applied 10 volts to the 6.3V winding, you'll get 20 kV+ out of the high voltage winding which might cause a few surprises. So, until you've identified all the windings, work with low voltages.

Potential Transformer

Hook up a voltmeter to the secondary. Apply power to the primary, measuring the current, voltage, and active power drawn. Note the power meter shown in the above diagram. If a true watt meter is not available, you can measure the active power consumption by putting a resistor in series, and making a set of RMS measurements.
The turns ratio can be calculated by:
Turns ratio = Esec/Epri
which, of course, should be an integer. Be aware that the output voltage written on the spec sheet or the transformer itself may be at rated load, and somewhat less than the no load voltage. The active power drawn is due to the core losses, and will typically be a few percent of the rated capacity.
The magnetizing power is:

Now, disconnect the primary voltage. Short the secondary through an ammeter.

Current Transformer

Starting with a low primary voltage, bring the primary voltage up until the current is a reasonable value, say half the rated primary current. Measure the secondary current (which should be the primary current divided by the turns ratio), the primary voltage, current, and active power.

Circular Mils

The area of conductors is often specified in Circular Mils, defined as the diameter in thousandths of an inch (mils) squared. This is different from the actual cross sectional area in square mils, which would be PI/4 * diam^2. That is, square mils = .7854 * circular mils.

Estimating the power handling

1) Look at the size of the wires. No right thinking transformer manufacturer is going to run hundreds of amps down 20 gauge wires, nor are they going to use 4/0 wire for a winding that will carry 30 mA. Very low current windings may use heavier wire than required to carry the current to make fabrication easier. However, copper costs money, as does a larger core to accommodate bigger windings, so particularly for mass production transformers, the wire is probably the smallest that will carry the current. Typical design guidelines are 700 circular mils/amp or 1000 cmil/amp. The following table relates common wire gauges to rated current.

Wire Gauge	Diameter	Area	Design Current
30	mils mm 10 0.254	Circular   Mils   mm^2 100 0.0507	@ 700  cmil/A    @ 1000 cmil/A 0.146 0.10

2) Look at the core cross section:
Here are some approximate transformer design equations that will get you into the right area:

• Core cross section area (sq inch) = .16 * sqrt( VA)
• Turns/Volt = 5 / Core cross section

This last equation is a special case of:
Voltage = 4 * F * f * a * B * N * 1E-8
where
F = Form factor, typically around 1.11
f = frequency in Hz
a = core cross sectional area in sq inch
B = flux per square inch (typ 75,000)
N = number of turns