Selection and Rating of Transformers

A). Introduction

The number of non-linear loads – which draw non-sinusoidal currents even if fed with sinusoidal voltage -
connected to the power supply system is large and is continuing to grow rapidly. These currents can be
defined in terms of a fundamental component and harmonic components of higher order.
In power transformers the main consequence of harmonic currents is an increase in losses, mainly in
windings, because of the deformation of the leakage fields. Higher losses mean that more heat is generated
in the transformer so that the operating temperature increases, leading to deterioration of the insulation
and a potential reduction in lifetime.

As a result, it is necessary to reduce the maximum power load on the transformer, a practice referred to as
de-rating, or to take extra care in the design of the transformer to reduce these losses.
To estimate the de-rating of the transformer, the load’s K-factor may be used. This factor is calculated
according to the harmonic spectrum of the load current and is an indication of the additional eddy current
load losses. It reflects the excess losses experienced in a traditional wire wound transformer.
Modern transformers use alternative winding designs such as foil windings or mixed wire/foil windings.

B). Transformer losses

Transformer losses consists of no-load (or core loss) and load losses. This can be expressed by the equation
below.

?
where:
PC = core or no-load loss,
PLL = load loss
PT = total loss.
Core or no-load loss is due to the voltage excitation of the core. Although the magnetizing current does
include harmonics, these are extremely small compared with the load current and their effect on the losses
is minimal. Load losses are made up of I2 R loss, eddy current loss and stray loss, or in equation form:

?
Where:
I2R = loss due to load current and DC resistance of the windings
PEC = winding eddy current loss
PSL = stray losses in clamps, tanks, etc.

The I2R loss is due to the current flowing in the resistance of the windings. It is also called ohmic loss or
dc ohmic loss. The ohmic loss is proportional to the square of the magnitude of the load current,
including the harmonic components, but is independent of the frequency. It is determined by measuring
the dc resistance and calculating the resulting loss using the winding currents at full load.
There are no test methods available to determine individual winding eddy current loss or to separate
transformer stray loss from eddy current loss. Instead, the total stray and eddy current loss is determined
by determining the total load loss and subtracting the calculated ohmic losses, i.e.,

The eddy current loss is assumed to vary with the square of the rms current and the square of the frequency
(harmonic order h), i.e.,