Transformers in Power Distribution Networks

APPLICATION NOTE
TRANSFORMERS IN POWER DISTRIBUTION
NETWORKS
Stefan Fassbinder
December 2015
ECI Publication No Cu0143
Available from www.leonardo-energy.org

Publication No Cu0143
Issue Date: December 2015
Page i
Document Issue Control Sheet
Document Title: Application Note – Transformers in Power Distribution Networks
Publication No: Cu0143
Issue: 03
Release: December 2015
Author(s): Stefan Fassbinder
Reviewer(s): Roman Targosz
Document History
Issue Date Purpose
1 August
2009
Initial publication as an Application Note
2 March
2012
Reworked by the author for adoption into the Good Practice Guide
3 November
2015
Review by Roman Targosz
Disclaimer
While this publication has been prepared with care, European Copper Institute and other contributors provide
no warranty with regards to the content and shall not be liable for any direct, incidental or consequential
damages that may result from the use of the information or the data contained.
Copyright© European Copper Institute.
Reproduction is authorised providing the material is unabridged and the source is acknowledged.

Page ii
CONTENTS
Summary ........................................................................................................................................................ 1
Introduction: why do we need a transformer? ............................................................................................... 2
The design and manufacturing of conventional and of special purpose transformers..................................... 6
Transformer tank and oil........................................................................................................................................6
Core ..................................................................................................................................................................8
Windings...............................................................................................................................................................14
Special types of transformers...............................................................................................................................16
Operational behaviour.................................................................................................................................. 18
Short circuit voltage..............................................................................................................................................18
Resistive load........................................................................................................................................................19
Inductive load .......................................................................................................................................................24
Capacitive load – care required!...........................................................................................................................25
Vector groups .......................................................................................................................................................28
Protection.............................................................................................................................................................31
Operating transformers in parallel .......................................................................................................................32
Energy Efficiency........................................................................................................................................... 36
New regulation governing transformer efficiencies.............................................................................................36
Optimizing the proportion between no-load and load losses..............................................................................43
Driving up costs by buying cheap .........................................................................................................................44
An example...........................................................................................................................................................46
Amorphous steel ..................................................................................................................................................48
Transformers used in renewable energy generation systems..............................................................................50
Other countries, other customs ...........................................................................................................................51
Outlook ................................................................................................................................................................52
Special solutions for special loads................................................................................................................. 53
Evil loads...............................................................................................................................................................53
Practical measures................................................................................................................................................57
Conclusion .................................................................................................................................................... 65

Page 1
SUMMARY
In electrical engineering terminology, transformers are regarded as electrical machines, although they only
convert one form of electricity into another form of electricity. Due to this relatively simple function, among
other reasons, their losses are lower than those of any equipment converting electricity into some other form
of energy. They are probably the most efficient machines ever devised by man. Transformer efficiencies are
around 80% for very small units used in domestic appliances and nearly 99% at the level of distribution
networks. The efficiency further increases with increasing unit power rating. The largest units achieve
efficiencies of up to 99.75% at rated load and even 99.8% at half load. At first glance, it looks rather unlikely
that there is any savings potential left that would be commercially significant, but in fact there is. It is true that
the payback periods are fairly long, but a transformer has a lifetime expectancy of well over 40 years and the
majority of all transformers are operated continuously at a high degree of loading. As a result, an improved
transformer design, primarily through the use of more active material, will usually pay off several times over
the lifespan of the transformer.

Page 2
INTRODUCTION: WHY DO WE NEED A TRANSFORMER?
Why do we need a transformer? Electric power has to be transmitted at the highest feasible voltage if power
losses in the electricity line are to be kept within reasonable limits. This is true in absolute terms: the higher
the transmission voltage, the lower the current and hence the smaller the (resistive) power loss in the line. It is
also true in relative terms. While a 3 V voltage drop in a motor vehicle’s 12-volt on-board electrical system is a
significant loss, it would hardly be noticed in a 230 /400 V distribution network and certainly would not impair
the function of any load. In a high voltage network, the same 3-volt drop would be almost immeasurably small.
Consider a transformer of certain dimensions. Now double each of the three dimensions: length, width, and
height, while retaining the same transformer structure. Clearly, the area of any face of the transformer will
increase fourfold. This will also apply to those surfaces available for dissipating heat losses, to the cross-
sectional area of the conductors, and to the cross-sectional area of the iron core—each of which is an
important transformer design parameter. If the linear dimensions are doubled however, all volumes will
increase by a factor of eight and so will the corresponding mass.
Assuming that the current densities in the conductors remain unchanged, the current carrying capacity (or
ampacity) of the conductors will increase fourfold, since the cross-sectional area of the conductors is now four
times as great. The current density measured in all transformers rated from 10 VA to 1 GVA is indeed
approximately 3 A/mm² for copper conductors and about 2 A/mm² when the conductor material is aluminium.
However, doubling the dimensions of the wire not only increases the conductor’s cross-section by a factor
four, it also doubles its length. The eightfold increase in the volume of the conductor material mentioned
above corresponds to an eightfold increase in the mass of copper or aluminium used. For a given current
density and temperature (though the effect of temperature is not critical in this simple analysis), every
kilogram of a particular conductor material will generate the same amount of heat loss. Therefore, a
transformer whose length, width, and height have all been doubled will weigh eight times as much, and the
heat losses it generates will consequently also rise by a factor of eight. This eightfold increase in heat loss must
nevertheless be dissipated by cooling surfaces whose area is only four times as great—a fact that we ignored
above. In practical applications, larger transformers therefore need additional cooling. The first step is to
introduce liquid cooling of the transformer windings. Further cooling can be achieved by increasing the area of
the transformer cooling surfaces. This type of cooling system is known as ONAN cooling (oil natural circulation,
air natural circulation). Forced cooling is used in transformers with ratings above about 40 MVA. In this type of
cooling, known as ONAF cooling (oil natural circulation, air forced circulation), liquid cooling is augmented by
cool air blown in by fans. Above about 400 MVA, it becomes necessary to use pumps to help circulate the oil
coolant. This form of cooling is abbreviated OFAF and stands for oil forced, air forced circulation. In
transformers with power ratings greater than 800 MVA, simply circulating the oil is no longer sufficient and
these transformers use ODAF cooling (oil directed, air forced cooling) in which a jet of cooling oil is directed
into the oil channels of the transformer windings.
Table 1 – Power densities and efficiencies of a range of real transformers from a miniature transformer to a
generator transformer.
Example transformers
found
S [kVA] Cu [kg]
S/Cu
[kVA/kg]
S/Cu4/3
[kVA/kg4/3
]
Current
Density
[A/mm²]
Energy
Efficiency
Minimum Transformer 0.001 0.014 0.070 0.291 7.000 45.00%
Small Transformer 0.100 0.500 0.200 0.252 3.000 80.00%
Industrial Transformer 40.000 48.200 0.830 0.228 3.397 96.00%
Distribution Transformer 200.000 200.000 1.000 0.171 98.50%
Bulk Supply Point Transformer 40000.000 10000.000 4.000 0.186 3.000 99.50%
Generator Transformer 600000.000 60000.000 10.000 0.255 99.75%
Geometric Mean Value --- --- --- 0.227 --- ---

Page 3
Figure 1 – Graph showing the copper content (blue) and the efficiencies (green) of the sample transformers
listed in Table 1 as well as the theoretical copper content derived from the formula (red).
The fourfold increase in the cross-sectional area of the transformer core permits a fourfold increase in the
voltage. This multiplied by the fourfold higher current in the fourfold greater cross-sectional conductor area
means a sixteen-fold (2
4
) rise in the rated output of a transformer whose mass is eight (2
3
) times as great. The
data in Table 1 show that this theoretically derivable correlation is indeed roughly confirmed in practice. If the
nominal power of the transformer is raised by a factor of 10
4
, the size of the transformer (i.e. its volume and
mass) only increases by a factor of 10
3
(since the length, width, and height have each increased by one power
of ten). This in turn means that the material costs and the costs of manufacturing and installing the
transformer system also rise by a factor of 10
3
.
Consider a high-power transformer rated at 1,100 MVA (currently the largest size of transformer being
manufactured). From an engineering point-of-view, it is perfectly possible to build even larger units. The
problem is that the only means of transporting these devices is by rail (Figure 2, Figure 3) and even then a
specially designed 32-axle low-loader wagon is required. A transformer of this size weighs in at around 460
tonnes. Approximately 60 tonnes of this total is copper.
If a transformer with 60 tonnes of copper has a power rating of 1,100 MVA, then one might imagine that a
small transformer containing 60 g should have an output of 1,100 VA. In fact, a transformer of this size only
manages about 11 VA. Similar scaling laws apply to motors and generators. For this reason—and of course,
because of the associated labour costs—it is more economical to generate electric power in large gigawatt
power stations and subsequently distribute this power to the regions within a 100 km radius, rather than
generating smaller quantities of electrical power locally and feeding them into the low-voltage distribution
network. This is where transformers come in. It is a commonly held misconception that a fully decentralized
electricity generation system would remove the need for the interconnected pan-European grid and its
transformers. Although grid loads would fall, the presence of the grid would be more important than ever
since it would have to compensate for sporadic and strongly fluctuating local loads. It would also be needed to
take up and distribute the unpredictable supply of solar and wind-generated power.
Specific copper content
of transformers
1E-02kg
1E-01kg
1E+00kg
1E+01kg
1E+02kg
1E+03kg
1E+04kg
1E+05kg
1E-03kVA 1E-01kVA 1E+01kVA 1E+03kVA 1E+05kVA 1E+07kVA
Transformer rated throughput 
Coppercontent
20%
30%
40%
50%
60%
70%
80%
90%
100%
Efficiency
Example transformers found
Theoretical Deduction
Energy Efficiency

Page 4
Figure 2 – A 32-axle low-loader rail wagon for transporting high-power transformers.
(Source: www.lokomotive-online.de/Eingang/Sonderfahrzeuge/Uaai/uaai.html)
Figure 3 – A high-power transformer ready for transport, shown here mounted on a small 24-axle low-loader
rail wagon.(www.lokomotive-online.de/Eingang/Sonderfahrzeuge/Uaai/uaai.html)
A kilogram of copper in a large machine causes more or less the same power losses as a kilogram of copper in
a small machine. However, each kilogram of copper in the generator of a large power station is responsible for
a power output of roughly 10 kVA, whereas a kilogram of copper in a bicycle dynamo would yield only 100 VA.
It is clear then that the efficiency of larger units is greater than that of smaller units, as already seen in Table 1
and Figure 1. Although transformers actually cause power losses, they are minimal in large transformers. It
could be argued that large transformers actually help to save power.
This effect also makes it more expedient to deploy a few large generators rather than a greater number of
smaller ones. Larger generators are significantly more efficient than smaller generators. However, since
generators also have to produce excitation power and suffer from mechanical losses, their efficiencies are
substantially lower than a transformer of equivalent size. The reduction in power loss that comes from
choosing a large generator rather than several smaller ones is larger than the losses that are incurred because
of the need to use four or five voltage transformation stages (see Figure 4).

Page 5
Figure 4 – Transformers in a public power supply network:
Yellow: sub-station transformer
Red: generator transformer
Blue: grid-coupling transformer
Green: distribution transformer.
Figure 5 – Three transformer stages are also used in railway traction power systems to step the voltage down
from the generator voltage to that required to drive the motors.
0.4kV
20kV
10kV
380kV
220kV
110kV
50 Hz50 Hz
3~3~
Transmission grids
Distribution networks
Structure of Public Electricity Supply in Germany
27 kV, nuke
21 kV, e. g. coal
10 kV, e. g. hydro
0.5 kV, e. g. wind
15kV
110kV
161622
//33 HzHz
1~1~
1.5kV
21 kV, e. g. coal
10 kV, e. g. hydro
Structure of Railway Electricity Supply in Germany

Page 6
THE DESIGN AND MANUFACTURING OF CONVENTIONAL AND OF SPECIAL
PURPOSE TRANSFORMERS
There is a common conception that the refining of transformer design has been exhausted and as a result just
a bit dull. Not true. There is, in fact, a great deal more to these so-called passive devices than meets the eye.
While transformers may be simple in principle, designing and optimizing them for specific applications requires
a great deal of detailed expertise and considerable experience. Without such knowledge and experience, it
would not be possible to create the transformers we see with efficiencies of up to 99.75%. Even if you are not
responsible for designing or building a transforming, purchasing the right transformer for a specific application
still requires a solid understanding of transformer fundamentals and transformer characteristics.
TRANSFORMER TANK AND OIL
The oil-immersed transformer is the most common type of distribution transformer. There are approximately
2 million oil-immersed distribution transformers in service in the EU with power ratings up to 250 kVA. There
are a further 1.6 million rated above 250 kVA. There are also estimated to be about 400,000 cast-resin
transformers in use.
Figure 6 – Structure of a modern oil-immersed transformer.

Page 7
Figure 7 – The interior of the distribution transformer (here a museum exhibit) exposed to view. (Stadtwerke
Hannover)
Figure 8 – At one time, the yoke frames were made of wood. The winding taps and terminal leads are clearly
visible.

Page 8
Figure 9 – Manufacturing a wide copper foil winding. (Wieland Werke AG, Ulm)
The most widespread design found today is the hermetically sealed transformer with flexible corrugated walls
that deform to compensate for the thermal expansion of the oil. These transformers do not need an expansion
tank with a dehydrating breather. Nor do they require all of the maintenance procedures that need to be
performed on large transformers with attached radiators. Most of today’s distribution transformers remain
maintenance-free for the duration of their scheduled service life of 20 to 30 years. There are numerous cases
of units in service for 30 to 40 years. With service lives that span decades rather than years, many older
transformers no longer comply with current technical requirements. As a result, transformers that are
technically outdated but not actually defective (Fig. 6) tend to be left in service (Figure 7).
The oil serves both as a cooling and electrical insulating agent. Flashover distances (clearances) and creep
paths can be reduced to about one fifth of their values in air. Moreover, the active portion of the transformer
(i.e. the pre-assembled core-and-coil unit) has a relatively small area requiring cooling. Heat transfer from a
core-and-coil assembly to a liquid medium is approximately 20 times better than to air. The surface of the
corrugated tank (Figure 17), in contrast to that of the active section, can be enlarged as required to ensure an
adequate rate of heat transfer to the ambient air. Oil-immersed transformers are therefore more compact
than air-cooled designs.
CORE
In spite of the fact that the manufacture of transformers is a highly labour-intensive process, materials used in
both the core and the coils contribute significantly to the cost of a power transformer. Selecting the right sheet
steel for the laminations, accurate stacking with frequent staggering (every two sheets), and minimization of
the residual air gap are all key parameters in reducing open-circuit currents and no-load losses. Today,
practically all core laminations are made from cold-rolled, grain-oriented steel sheet despite the significantly
higher cost of this type of steel. Note that the thinner the laminations, the lower the eddy currents.

Page 9
Table 2 – Historical development of core sheet steels.
It is worthwhile mentioning the revolutionary technology of amorphous steel here, which further reduces the
no-load losses (more on this technology at the end of this publication). Minimizing noise levels requires
application of the right amount of pressure to the yoke frame that holds the yoke laminations in place (Figure
10, Figure 22). Applying the greatest possible pressure is not necessarily the best approach. One of the key
aspects in core construction is ensuring the absence of eddy current loops. Even in small transformers with
ratings above about 1 kVA (depending on the manufacturer), the clamping bolts are electrically insulated on
one side (see Figure 10 and Figure 11) for this reason. These benefits would also be apparent in transformers
with power ratings below 100 VA. Given the advantages that insulated fastening bolts can yield in relatively
small transformers, the benefits gained in much larger distribution and high-power transformers is obvious.
An interesting real-life case in which a transformer was earthed twice via its yoke clamping bolts illustrates just
how important it is to take these apparently innocuous elements into consideration. The transformer was
fitted with an earth conductor on the high voltage side that ran from one of the yoke clamping bolts to the
earthing system; a similar earth conductor was installed on the low-voltage side. However, the technical
expert examining the transformer discovered a current of 8 A in each of the earth conductors. The two
conductors formed a current loop that was short-circuiting the insulation of the bolt. It was only because the
engineer had a detector for magnetic leakage fields that he was able to discover the current in the loop.
Figure 10 – A small three-phase transformer has a very similar structure to a distribution transformer. While
these small transformers do not generally need to be equipped with round coils...
Year Material
Thick-
ness
Loss
(50Hz)
at flux
density
1895 Iron wire 6.00W/kg 1.0T
1910 Warm rolled FeSi sheet 0.35mm 2.00W/kg 1.5T
1950 Cold rolled, grain oriented 0.35mm 1.00W/kg 1.5T
1970 Cold rolled HiB sheet 0.30mm 0.80W/kg 1.5T
1975 Amorphous iron 0.03mm 0.20W/kg 1.3T
1980 Cold rolled HiB sheet 0.23mm 0.70W/kg 1.5T
1983 Laser treated HiB sheet 0.23mm 0.60W/kg 1.5T
1987 Plasma treated HiB sheet 0.23mm 0.60W/kg 1.5T
1991 Chemically etched HiB sheet 0.23mm 0.60W/kg 1.5T

Page 10
Figure 11 – …the yoke frames are similar in shape to those used in distribution transformers and the single-side
insulation for the yoke clamping bolts is essential.
This would not have been a problem when yoke frames were still being manufactured from wood (Figure 8),
were it not for the fact that the frame (whether made of wood, or steel as is the case today) and the yoke
laminations are frequently drilled (or punched) to accept the clamping bolts. These holes have to be large
enough so that an insulating bushing can be pushed over the shaft of the bolt to ensure that the bolt does not
come into contact with the burred edges of the yoke plates and only touches one side of the yoke frame. If
multiple contact points occur, it essentially short-circuits the relevant section of the yoke. In addition, cutting
bolt holes effectively reduces the cross-sectional area of the core, and eddy currents are also induced in the
bolt, which, for obvious reasons, cannot be manufactured from laminated sheet. Clamping bolts made of
stainless steel are sometimes chosen. This is because, perhaps surprisingly, stainless steel is not in fact
ferromagnetic although it consists predominantly of iron and nickel—both ferromagnetic elements. The
magnitude of the magnetic field in these stainless steel bolts is therefore lower, thus reducing eddy current
losses. In addition, stainless steel is much better at suppressing eddy currents because its electrical
conductivity is only about one seventh of that of conventional steels. However, stainless steel bolts can in no
way replace the sheet iron that was removed when punching the bolt holes, which is to some extent possible
when conventional steel bolts are used. These two effects can be illustrated in the following experiment
performed on a small transformer (Figure 12 and Figure 13).
Transformers of this size are typically not fitted with insulating flanged bushings. Inserting the bolts results in a
reduction in the magnetizing reactive power of up to 7%. This is because the bolts are to some extent able to
replace the sheet iron lost through the creation of the bolt holes. However, no-load losses increase by 20%
partly as a result of eddy currents in the bolts, but, primarily, because of the earth loops created when the
bolts are inserted.
A better means of clamping the yoke laminations, though more costly than employing stainless steel bolts, is
to use a clamping frame that wraps around the yoke (Figure 22). However, it is essential to ensure that the
clamping ring does not form a closed electrical circuit that could short-circuit the yoke. An experimental set-up
using a small single-phase transformer demonstrates the potential consequences of an electrically closed
clamping ring (Figure 14 and Figure 15).

Page 11
Figure 12 – Unfortunately, a less stringent approach is taken in the case of single-phase transformers.
Figure 13 – The sheet metal casing and fixing screws slightly reduce the magnetizing reactive power, but the
no-load active power is significantly greater.
Figure 14 – Not the most intelligent fastenings for a small transformer—the no-load power increases to more
than six times that measured without the fastening clamps in place. (Figure 15)

Page 12
Figure 15 – The no-load active power measured for the same transformer without the fastening clamps.
Figure 16 – A Swiss tubular tank transformer (photo: Rauscher & Stoecklin) 1958. This type of transformer is
still being widely built in newly industrialized countries where labour costs are not an issue.

Page 13
Figure 17 – The oil-immersed transformer has been the standard since about 1930. The typical corrugated tank
design was introduced around 1965. (Photo: Pauwels)
Figure 18 – A typical, commercially available cast-resin transformer.
Eddy currents can also be induced in electrically conducting parts that are not actually located within the
transformer core but simply situated in its immediate vicinity. This is particularly relevant in the case of
ferromagnetic materials that attract stray magnetic fields. In larger transformers, the insides of the tank are
sometimes fitted with so-called flux traps made from core sheet steel that attract stray magnetic fields and
through which the field flux lines will preferentially flow rather than through solid, non-laminated, structural
steel parts. In some dry-type transformers, the clamping bolts (Figure 20 and Figure 22) and other screws are
made from glass-cloth laminate. In oil-immersed transformers, one occasionally finds nuts and bolts made
from a moulded synthetic resin/compressed wood compound, but this material is of insufficient strength to be
used for coil clamping bolts.

Page 14
WINDINGS
In distribution transformers, the low-voltage coil is usually foil-wound because of the low number of windings
and the high cross-sectional area of the conductor. The length of the finished coil is approximately equal to the
width of the foil (Figure 9).
Several strip-wound coils arranged adjacently in the axial direction can be used for smaller sized transformers
or when higher voltages are involved. The high voltage coil is also usually constructed in this way. Round wire
windings are used in smaller transformers; shaped wire windings are used in larger devices.
Figure 19 – In small transformers, such as the 40 kVA device shown here, the coil windings can be
approximately rectangular in section reflecting the rectangular geometry of the core. (Photo: Riedel)
Figure 20 – The upper yoke frame and the coils clamped tightly in the axial direction. (Photo: Rauscher &
Stoecklin)
Figure 21 – In larger transformers, the rectangular core is adapted to more or less match the circular
geometrical form of the coil.

Page 15
The coils in small transformers are rectangular in section (Figure 10 and Figure 11). The same type of coil
geometry is sometimes found in special types of low-rating distribution transformers. Elliptical coils are used in
larger transformers and circular-section coils are used in transformers with the highest power ratings
(generally 1 MVA and higher). In addition, if the coils were not circular before, they certainly are if they ever
suffer a short circuit. Such a change in coil geometry is the result of the magnetic forces acting between the
conductors. These forces play no role at the transformer’s nominal current density, but increase
proportionately with the product of the currents in the low-voltage and high voltage windings.
Since the currents in the LV and HV coils flow in opposite directions (Figure 21), the coils repel each other. If a
short circuit does occur and the winding current is correspondingly large, the outer coil will try to expand
outward and, since the circle is the geometrical form that encloses the greatest possible area for a given
circumference, the coil will seek to adopt a circular shape. Such a shape offers the maximum average distance
from the inner coil.
The inner coil, which is usually the low-voltage winding, will be pressed against the core. Since the low-voltage
coil is typically a copper foil winding, a short circuit will often result in a core that looks as if it has been copper
clad. This is the reason why the coils are very tightly clamped in the axial direction (Figure 20). It is also why
any taps in the high voltage winding, which allow for any variation in the input voltage (typically two steps of
+2.5% above the nominal voltage, and two steps of -2.5% below), are located in the central section of the
winding (Figure 22) and not at its upper or lower ends. This ensures that the effective axial height of that
portion of the high voltage coil that carries current is essentially constant as is the relative height of the HV and
LV coils.
Without the tight clamping, a number of windings at the upper or lower end of the coil will be lost if a short
circuit causes a significant force in the axial direction between the coils. In transformers that have been in
service for a long time, the coils may no longer be as rigidly clamped as they were at the time of manufacture
and the insulating materials may be showing signs of age. A short circuit in such a transformer or a breakdown
of the insulation material because of a lightning strike often causes the device to fail completely. At
installations where short circuits or lightning strikes only occur every few decades, a transformer can remain
operational for as long as 60 years before finally having to be replaced for economic reasons.
The rectangular core is altered to approximately match the geometry of the circular coils as shown in Figure
21. The yokes have exactly the same cross-sectional area. Five-leg cores are normally only used in high-power
transformers since this allows the cross-sectional area of the yoke to be halved. This slightly reduces the total
height of the transformer, making transport somewhat easier. Looked at mathematically, the five-leg core has
only four legs (three + two half-legs), because the two outermost return legs only need to carry half of the flux
in this type of core. We will take a look at the special case of a five-leg core in a distribution transformer later
on.
The structure of the transformer’s active part can be seen in Figure 22 and Figure 23, though in these diagrams
the active portion is not depicted large enough to illustrate the staggering of the core laminations. This detail
has therefore been shown in the magnified image on the right in Figure 23. Normally every two, sometimes
every four, laminations are staggered by, for example, 15 mm relative to the previous two or four core
laminations. The yoke laminations are staggered to the left and to the right, while in the legs, the laminations
are displaced upward and downward. In addition, the upper and lower asymmetrical tips of the central leg
differ in that one tip is located more to the left and the other more to the right. Offsetting the joints in this way
improves magnetic contact between the abutting surfaces.

Page 16
Figure 22 – The structure of a transformer’s core-and-coil assembly (active part). The design shown here is the
more elegant solution with unperforated yokes.
Figure 23 – The yoke frame and coil clamping bolts have been removed and the upper yoke lifted off to expose
the inner structure.
SPECIAL TYPES OF TRANSFORMERS
The quality and performance specifications that transformer oil has to fulfil are extremely high. The oil in a
hermetically sealed transformer tank has to provide forty or more years of service and it generally cannot be
subjected to tests during that time. Irrespective of its quality however, the mineral oils used in transformers
are of course combustible. It was for this reason that several decades ago oil-immersed transformers were
forbidden for use in interior locations and sites subject to high risk in the event of a fire. Mineral cooling oil
was replaced in such locations by polychlorinated biphenyls (PCBs), a group of substances that are classified as
non-combustible or nearly non-combustible. Unfortunately it was subsequently realized, especially in the wake
of the Seveso disaster, that these substances form highly toxic dioxins when partially oxidized.
The search for alternatives led to the use of low-flammability, non-toxic, synthetic silicone oils. However, those
silicone oils never really became established, at least not for the size of transformer being discussed here. As a
result, dry-type transformers enjoyed a revival. The new models no longer used paper and varnish for
Yoke frames
Coil clamping
bolts
Yoke
lamination
retaining strap
Wooden coil-
clamping
blocks
HV coil
Yoke
lamination
clamping bolts
LV coil
Tapping points

Page 17
insulation, but were manufactured as cast-resin transformers. Depending on the required degree of
protection, these cast-resin transformers can be used unenclosed or with the appropriate protective
enclosure.
As with other types of transformers, the conductor materials used in distribution transformers can be either
copper or aluminium. Though more expensive, copper is usually chosen because it enables more compact (as
well as more robust) designs. Because the volume of conductor material is less if copper is used, the volume of
the winding space is correspondingly smaller. This results in a somewhat heavier but slightly smaller device.
Aluminium, however, is the preferred material in cast-resin transformers because its greater thermal
expansion coefficient is closer to the generally very high expansion coefficient exhibited by organic materials,
and this helps to reduce the thermal stresses within the rigid winding assembly.
One very special type of transformer was developed in 1987: gas-cooled transformers. They had in fact already
been the subject of research some 25 years earlier. When gas cooling is involved, physicists tend to think
immediately of hydrogen as it has a very high heat capacity. However, heat capacity is generally expressed
relative to mass, and the density (i.e. the mass per unit volume) of hydrogen is almost one tenth of that of air.
If on the other hand, the key parameter is the speed of circulation in a cooling circuit, then heat capacity per
volume is more relevant since the resistance to flow is proportional to the square of the volume flow in any
given system. The gaseous material finally selected was sulphur hexafluoride (SF6), a well-known substance
that was already in use as an insulating material in switchgear and that has a density five times that of air and
with considerably better dielectric strength.
Although the heat capacity of a kilogram of SF6 is only half that of a kilogram of air, its heat capacity per litre is
2.5 times greater. That means that if SF6 is used as the coolant, it only needs to circulate at 40% of the speed
used in air-cooled devices in order to produce the same cooling effect. As a result, the fan power can be
reduced to about 32% of that needed in an equivalent forced-air cooling system. Two prototype transformers
each with a power rating of 2 MVA, a corrugated tank, and internal forced cooling (i.e. cooling Class GFAN—
gas-forced, air natural) were built and successfully operated in an explosion hazard area within a chemical
manufacturing plant.
The dielectric strength and the cooling capacity of SF6 can be increased by raising the pressure and
compressing the gas. A hand-welded tubular tank transformer, similar to the one shown in Figure 16, was built
to test this effect. This type of transformer design used to be common but its construction is far too labour-
intensive for it to be economical today. Nevertheless, the test device allowed the test engineers to
demonstrate that the observed temperature rise agreed approximately with that expected from
computational analysis. The transformer with GNAN cooling handled 630 kVA at an overpressure of 3 bar and
was of an acceptable size. Having completed these trails, the project team set about developing a more
economical method of production. Apparently, these transformers sell well in the Far East, or at least sold well
for a time, where they were used in high-rise buildings. Widespread use in the domestic market failed because
of the very stringent regulations governing the construction and use of pressure vessels. The principle behind
the technology had, however, been shown to work.

Page 18
OPERATIONAL BEHAVIOUR
Transformers inevitably affect the power networks to which they are connected. However, to a certain extent
some of the operating parameters of a transformer can have a beneficial—and in some cases even essential—
influence on the operation of the supply network. In what follows, we will be investigating how to
manufacture and select transformers to optimize these parameters.
In a distribution transformer with a short circuit voltage of 6% that is operating at its rated current, there will
be a drop of 6% in the voltage across the device’s internal impedances. That means that when the transformer
is operating at its rated load, the voltage is 6% lower than the open-circuit voltage. There are additional
voltage drops along the wires and cables that lead away from the transformer as well as in the upstream
power supply network. In total, it is reasonable to expect voltage losses totalling approximately 10%. While
10% may sound excessive, the situation is not as bad as it appears. To see why requires a precise definition of
the term short circuit voltage.
SHORT CIRCUIT VOLTAGE
The characterization of the operating behaviour of a transformer relies on its rated voltage and its rated power
output. The next most important parameter is the short circuit voltage. To anyone training to become an
electrical technician, the expression short circuit voltage might initially appear to be a misnomer. After all,
when a short circuit occurs, the voltage is generally defined as being zero. However, this is not the case when
the short circuit is on the output side and the voltage is on the input side of a transformer. The short circuit
voltage (Usc) is the voltage applied to the primary winding in the event that:
1) The secondary winding of the transformer is short-circuited
2) The voltage applied to the primary winding is large enough to generate the rated current in the
secondary winding
The short circuit voltage is usually not expressed in volts but rather as a percentage of the rated voltage (usc).
In large transformers, the short circuit voltage can reach values of 18-22%. In contrast, the rated short circuit
voltages in distribution transformers are typically between 4% and 6%. The actual value is measured during the
final testing of the device and is printed on the transformer's rating plate (Figure 24). However, deviations
from the typical values of 4% to 6% usually have little practical relevance.
Figure 24 – Whether it is called Tension court circuit, Kortsluitspanning or Short circuit voltage, the actual value
is measured during final testing and is printed on the transformer’s rating plate.

Page 19
The short circuit voltage thus characterizes the voltage drop within the transformer. If the short circuit voltage
is known, the short circuit current Isc can be readily calculated. For example, if all upstream impedances are
ignored, the short circuit current in a transformer with usc = 6% is:
𝐼𝑆𝐶 =
𝐼 𝑁
𝑢 𝑠𝑐
=
𝐼 𝑁
6%
≈ 16.7 𝐼 𝑁
For a transformer with usc = 6%, six percent of the rated input voltage is therefore needed to generate the
rated (nominal) current IN in the short-circuited secondary winding. However, only a small part (uR) of the
voltage drop in a medium-sized distribution transformer is due to the ohmic resistances in the windings. The
largest factor contributing to the voltage drop is by far the reactive/inductive voltage drop uX. This stems from
the leakage inductance caused by the portion of the magnetic flux that bypasses the core (leakage flux) and
permeates only a single winding. This leakage flux does not flow in the primary and secondary windings
simultaneously. Rather it flows in the main leakage channel between the high voltage winding, which is
generally located on the outside, and the low-voltage winding on the inside [c.f. Section 2 Design]. The leakage
flux is therefore part of the magnetic flux of the outer but not the inner winding. This also has the incidental
effect that the short circuit voltage cannot be influenced by the non-linearity of the iron core. uX is also
referred to as the leakage reactance voltage. The principal function of the main leakage channel is cooling; its
secondary function is insulation. In addition, it also serves to maintain the so-called leakage reactance, which is
in effect a defined short circuit voltage.
As shown in Figure 28, the sum of the squares of the inductive voltage drop uX and the ohmic voltage drop uR
equals the square of the overall voltage drop usc (c.f. Pythagoras’ theorem concerning the sides of a right-
angled triangle). Fortunately, the ohmic voltage drop uR is, as already mentioned, the smaller portion. The
larger the transformer, the smaller this is. A simple calculation proves this point: If a transformer in the 630
kVA range has an efficiency of 98.5% when operating at its rated load, then the total ohmic voltage drop across
the two windings can be no more than 1.5% of the rated voltage. In practice however, the value is lower, for
example 1%, because the 1.5% includes losses other than the ohmic losses in the coils. Our usc of 6% is
therefore made up of uR = 1% and uX = 5.91% of the rated voltage (6² =1² + 5.91²).
RESISTIVE LOAD
A transformer’s power rating is always specified relative to its resistive load. The ohmic resistance of the
winding contributes linearly to the (rated) load, while the inductive resistance (reactance) of the leakage
inductance contributes quadratically. Therefore the resistance of the winding contributes only 1% to the load
resistance, with the remaining 5.91% having only a negligible effect on the total voltage drop across the
transformer and the load. We now want to determine precisely how small this effect actually is.
The non-ideal behaviour of a transformer can be illustrated by an equivalent circuit model (Figure 25). The
model assumes that the input and output windings have the same number of turns. As this is obviously not
usually the case, the values associated with one side of the transformer are moved (i.e. referred) to the other
side by multiplying them by the ratio of the number of turns on the two windings. The behaviour of the
transformer can then be calculated for the relevant reference side. In Figure 25, all elements have been
referenced to the load (i.e. secondary) side.

Page 20
Figure 25 – General single-phase equivalent circuits for a two-winding transformer.
If we are only interested in the modulus (absolute magnitude) of the voltage drop at the rated load, which by
definition is an ohmic load, then we can adopt the simplified expression:
𝑈2 = 𝑈1
′
− 𝐼𝑙𝑎𝑠𝑡 (𝑅 𝐶𝑢1
′
+ 𝑅 𝐶𝑢2 +
(𝑋1𝜎
′
+ 𝑋2𝜎)2
𝑅 𝐿𝑎𝑠𝑡
)
where:
U2 = secondary voltage,
𝑈1
′
=
𝑛2
𝑛1
𝑈1 = primary voltage referred to the secondary side,
𝑅 𝐶𝑢1
′
= (
𝑛2
𝑛1
)
2
𝑅 𝐶𝑢1 = resistance of primary winding referred to the secondary side,
RCu2 = resistance of secondary winding,
𝑋𝑙𝜎
′
= (
𝑛2
𝑛1
)
2
𝑋𝑙𝜎 = leakage reactance of primary winding referred to the secondary side,
X2 = leakage reactance of secondary winding,
n1 = number of turns in primary winding,
n2 = number of turns in secondary winding.
ILoad and RLoad are related to one another in accordance with Ohm’s law:
𝑅𝑙𝑜𝑎𝑑 =
𝑈2
𝐼𝑙𝑜𝑎𝑑
and cannot therefore be changed independently of one another.
Load
X1‘ X2
RFe
Xm
RCu1‘ RCu2
Load
X1‘ X2
RFe
Xm
RCu1‘ RCu2
Load
X1‘ X2
RFe
Xm
RCu1‘ RCu2

Page 21
Figure 26 – No-load currents in a high-quality Swiss distribution transformer with a power rating of 630 kVA to
which a voltage of 400 V has been applied to the low-voltage side. The currents are relative to the rated output
current of 909 A.
The parameters
RFe = core resistance
XH = magnetizing reactance
have not been taken into account in this simplified model. With the exception of small transformers, the
magnitudes of these quantities are usually so large that the currents flowing through these elements are
insignificant, at least as far as the effect of the transformer on connected loads is concerned. (Their relevance
for the transformer’s internal losses is far greater, as will be shown in Section 4). XM is the magnetizing
reactance under open-circuit conditions (in this case, XM is referred to the secondary voltage, as if the
excitation voltage was being applied to the output side of the transformer, which is perfectly possible, and was
indeed the case when making the measurements for Figure 26.) The no-load current in a good-quality
distribution transformer is only around 0.5% of the rated current (Figure 26) and more than half of the no-load
current is attributable to the magnetization current. Consequently, as the magnetizing reactance XM is the
main cause of the open-circuit current, its magnitude must be at least 200 times that of the load impedance.
RFe is a fictitious resistance that represents the iron (or core) losses and whose magnitude, if good-quality iron
is used, is generally substantially greater than XM. The shunt impedance of these two elements that determine
the open-circuit behaviour of the transformer is therefore significantly more than 100 times greater than the
load impedance. In contrast, for a transformer with a short circuit current of 6%, the short circuit impedance
(i.e. the effective sum of X1σ’, X2σ, RCu1’ and RCu2), which are all in series with the load, is only 0.06 times as large
as the load impedance. The short circuit impedance is therefore more than 100/0.06 (i.e. almost 2,000) times
smaller than the shunt impedance comprising RFe and XM. As a result, the currents flowing through RFe and XM
can be ignored when describing the transformer’s behaviour with respect to its connected load. This is even
more the case when the transformer is under short circuit conditions. The expression for the leakage
reactance can therefore be simplified to:
𝑋 𝜎 = 𝑋1𝜎
′
+ 𝑋2𝜎 = 2𝑋2𝜎

Page 22
A similar expression applies for the resistive components of the short circuit impedance.
𝑅 𝐾 = 𝑅1
′
+ 𝑅2 ≈ 2𝑅2
Figure 27 – Phasor diagram showing the voltage drops in a transformer and its rated (ohmic) load.
Figure 28 – Diagram showing the voltage drops in the transformer itself, shown here at a magnification of
about ten times that in Figure 27, Figure 29, and Figure 30.
InputvoltageU1referredtothesecondaryside(100%)
Inductive drop uX in the transformer
Ohmic drop
uR in the
transformer
Total voltage
drop usc in the
transformer
(e.g. 6%)
InductivedropuXinthetransformer
Ohmic drop uR in the transformer

Page 23
This approach provides a simple means of describing the operation of a non-ideal transformer and enables
quantities of interest to be calculated with sufficient accuracy. Although Figure 25 does not model the
substantial non-linearity of the iron core and the resulting strong distortion of the magnetizing current
waveform, the fact that the magnetizing current is so small means that this equivalent circuit model is
applicable in practice. In fact, the magnetizing current can usually be ignored when compared to the rated
current, as was assumed above. In that case, the voltage drops found in a transformer driving a load are as
shown in Figure 27. The phasor diagram can be thought of as an instantaneous snapshot. The individual
voltages are represented as vectors that precess around the fixed origin (below), in a manner analogous to the
generation of an AC voltage in rotating machines. The input voltage (green) serves as the reference and is
always shown as its peak positive value, i.e. as a vertically aligned voltage vector. The vector sum of all the
voltage drops must equal the applied voltage. Graphically, this means that if the voltage drop vectors are
placed in sequence starting at the origin (base of the green vector), they must arrive at the same point as the
tip of the green vector representing the applied voltage. It then becomes apparent that in this transformer
with a short circuit voltage drop (usc) of 6% and an ohmic voltage drop (uR) of 1%, the modulus of the output
voltage at rated load is almost 99% (and not approximately 94%) of the open circuit voltage. The only
difference is the phase shift on the output side relative to that of the input voltage, but that has no effect on
the load.
The voltage drops within the transformer are barely discernible in the diagram. The resistive (ohmic)
component in particular is almost inconspicuous. This is good, since this component represents the ohmic
losses. If one wants to visualize these voltage drops, they need to be magnified and shown without the input
and output voltage vectors (see Figure 28).
Figure 29 – Inductive load.
Voltagedropacrossload(99%)
Inductive drop uX in the transformer
Ohmic drop
uR in the
transformer
Total voltage
drop usc in the
transformer
(e.g. 6%)

Page 24
Figure 30 – Capacitive load.
INDUCTIVE LOAD
The situation changes, however, if we are dealing with an inductive load. This adds linearly (i.e. completely) to
the inductive voltage drop within the transformer and quadratically to the much smaller ohmic component. In
this case, the output voltage is calculated by means of the following equation:
𝑈2 = 𝑈1
′
− 𝐼𝑙𝑜𝑎𝑑 (𝑋1𝜎
′
+ 𝑋2𝜎 +
(𝑅 𝐶𝑢1
′
+ 𝑅 𝐶𝑢2)2
𝑅𝑙𝑜𝑎𝑑
)
This can be rewritten using the simplifications introduced earlier:
𝑈2 = 𝑈20 − 𝐼𝑙𝑎𝑜𝑑 (𝑋 𝜎 +
𝑅 𝐶𝑢
2
𝑅𝑙𝑜𝑎𝑑
)
where U20 is the no-load voltage on the low-voltage side. When the rated current is flowing, the output voltage
does indeed drop by almost 6%, at least as far as the absolute value (magnitude) of the voltage is concerned.
This is because the rated load is defined as an ohmic load (see Figure 25). By introducing power-factor
compensation in parallel with the load, we can reduce the overall load being driven by the transformer. This
not only reduces the copper loss, it also reduces the size of the voltage drop, since this is predominantly
inductive in nature. If we are dealing with an alternating inductive load, the compensation circuit must be
controllable. The more rapidly the load changes, the faster the controller must be able to respond. These
control systems can be used to avoid the flicker that is caused by rapidly changing, strongly inductive loads
such as spot welding machines or three-phase induction motors (without a power converter). Anyone who has
Voltagedropacrossload(99%)
Inductive
drop uX in
the
transformer
Ohmic drop
uR in the
transformer
Total voltage drop usc in the
transformer (e.g. 6%)

Page 25
lived for a time next to a building site where a tower crane has been operating (without power-factor
correction) will know exactly what this refers to
1
. Luckily, mobile units are now available that can be used to
counteract such flicker sources
2
.
The same approach can be used to determine whether the primary cause of the voltage drop at a domestic
power socket is the leakage inductance of the distribution transformer or the ohmic resistance of the power
cables. For instance, when a fan heater with a current input of 9 A is operating, the voltage at a particular
power socket is found to decrease from 230.7 V to 226.3 V. If a large inductive load that draws over four times
as much current (see Figure 27) is connected, we see that there is no discernible increase in the voltage drop.
With reference to the phasor diagrams shown in Section 3.2, it can be concluded that the ohmic resistance is
by far the larger component—at least in the case of this particular cable and transformer. However, this test
must be performed with great caution. Since this test involves a substantial overload, the duration of the test
must be kept short. Failure to do this will trigger the 16-ampere circuit breaker, which is normally rated for a
power factor range from 1 to 0.6. A circuit breaker is not really the best means of switching off what is
essentially a purely inductive load.
Figure 31 – Large inductive load on a domestic power socket.
CAPACITIVE LOAD – CARE REQUIRED!
Things get really exciting when dealing with capacitive loads. In principle, this is the situation described earlier
in which the transformer is excited from the output side, i.e. compensation of the inductive magnetizing
reactive power by the capacitive load. If the load is so small that it is just sufficient to provide compensation,
then only the transformer will be excited—a perfectly normal situation, irrespective of the winding. The
picture changes however, as the capacitive load increases. The passage of the load current through the
leakage reactance results in a voltage drop with a phase lead of 90°. Its passage through the capacitive load is
accompanied by a voltage drop lagging by 90°. In other words, these two voltage drops have opposite signs
and therefore subtract from one another rather than add. At 100% of the rated input voltage, we have a
1
Fassbinder, Stefan: Netzstörungen durch passive und aktive Bauelemente, VDE Verlag, Berlin / Offenbach
2002, p. 188
2
Bolliger, R.: Wenn die Lichter flackern [‘When the lights flicker’]. ET Schweizer Zeitschrift für angewandte
Elektrotechnik 11/2003, p. 26

Page 26
voltage drop of almost 6% across the leakage reactance and therefore almost 106% of the open circuit voltage
across the load. The result is an overvoltage on the output side at full load current, despite applying only the
rated voltage on the input side (Figure 30). As the load—or more precisely its impedance—must be assumed
to be constant, the current rises in accordance with the increased voltage, creating an even greater voltage
drop within the transformer and hence an even greater voltage at the output. Ultimately, the voltage stabilizes
at a level slightly above rather than just below 106%. This was exactly what was observed when a medium-
voltage customer of an electric utility company wanted to have a power factor correction system of 1,400 kVAr
connected on the MV side, because that was the side where active and reactive power were metered. It
turned out, however, to be cheaper to buy a low-voltage power factor correction unit in combination with a
1,600 kVA transformer. Note that although this solution was cheaper, it was not more cost-effective, as the
method saves only the additional price that the electric utility company would have charged for the reactive
power, but not the costs generated by letting this reactive current circulate around the installation and
through the transformer.
A test run on the customer’s system mentioned above resulted in the phase voltage increasing from 230 to
255 V. This was because the transformer was driving a capacitive load only and was working more or less at
full load. In this particular case, the problem was solved by reconnecting the input side of the transformer at
an input voltage of 22 kV, even though only 20 kV were actually being applied. This enabled the output voltage
to be lowered to near its rated value. Since the excitation current was coming from the output side, this
proved to be the only way to prevent over-excitation of the transformer. This is one of the rare cases in which
the output side is the reference side.
If overloading is severe, the situation will eventually escalate. Current overload creates a voltage overload in
both the load and in the transformer. Overvoltage across the load then generates further current overloading,
which will drive the overvoltage even higher. Taken together, the leakage reactance and the capacitive load
form an LC oscillator circuit, whose resonance frequency f0 can be calculated as follows:
𝑓0 =
1
2𝜋√𝐿𝐶
At this frequency, the inductive leakage reactance and the capacitive reactance of the load are of equal
magnitude but opposite sign and thus cancel each other out. This is not, however, the case when the
transformer is passing its rated current. In the example transformer discussed earlier (for which usc = 6%), the
reactance of the load was about 16 times greater than that of the internal reactance of the transformer. The
resonance frequency is then:
𝑓0 = 50 𝐻𝑧 ∗ √16 = 200 𝐻𝑧

Page 27
Figure 32 – The output current of a transformer with uR = 1% and usc = 6% (for which Isc ≈ 16.7 * IN) can in
theory climb to 100 * IN at a capacitive overload of 16.7 times the rated load, rather than just the 16.7 * IN that
would arise in a short circuit.
Figure 33 – Detail from Figure 32 (see box bottom left) with the current values typically found in practice.
However, if a ripple-control signal of similar frequency is present, the ripple-control signals through the series
resonant circuit comprising the transformer’s leakage reactance and the capacitive load, will be shorted and
lost, and therefore fail to reach the low-voltage level. In a transformer with a short circuit voltage usc = 4%, the
critical point is shifted to 224 Hz. If we were dealing with capacitive loads that could be varied (e.g. by means
of a VAr controller), the critical point would also vary in a potentially uncontrollable manner.
If the transformer is subjected to a capacitive overload of 16 times the transformers rated load, which can be
achieved, say, by connecting a 1,600 kVAr power-factor correction unit to a 100 kVA transformer, we find that
the resonant frequency drops to 50 Hz. In this case, the inductive leakage reactance would be compensated
for by the capacitive reactance of the load. Since the current would be limited only by the resistance of the
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
RelativeloadcurrentI/IN
Relative load admittance Y/YN 
Current with resistive load
Current with inductive load
Current with capacitive load

Rated load
Short-circuit current
ISC=16.7*IN

16.7*rated load (ZSC=ZLoad or YSC=YLoad, resp.) 

Page 28
winding, it would rise to almost six times the short circuit current or 100 times the rated current (see Figure
32). In Figure 32, the actual current is plotted against the ratio of the magnitude of the conductance G to the
rated conductance GN:
𝐺 𝑁 =
𝐼 𝑁
𝑈 𝑁
depending on the phase angle of the ohmic, inductive, or capacitive load. For
𝐺 =
𝐺 𝑁
6%
≈ 16.7 𝐺 𝑁
the impedance of the load is equal to the internal impedance of the transformer. However, that should not be
interpreted to mean that the output voltage always corresponds to half the open-circuit voltage. If that were
the case, one would not need to include the phase angle in the calculations. The curves for the ohmic,
inductive and capacitive loads will only converge at infinite conductance (which corresponds to short circuit
conditions).
Fortunately, capacitive loads of that magnitude do not occur in practice. Nevertheless, this thought
experiment shows just how rapidly things change when the capacitive load starts to increase. A more detailed
look at the part of Figure 32 that covers realistic operating currents (see Figure 33) confirms remarks made
earlier: the transformer’s output voltage is 99% of the open-circuit voltage for the ohmic rated load. If the
transformer drives an inductive load of equal size, the output voltage drops to 94%. If the load is capacitive in
nature (and of equal magnitude), the voltage is about 107%. Care is therefore paramount when dealing with
capacitive loads.
Note however, that the transient overloading of a transformer with a capacitive load does occur and is in fact
purposely used on occasions to eliminate voltage dips and the resulting flicker in ohmic and ohmic-inductive
impulse loads. For this to occur, the required correction capacitance has to be connected to the transformer at
the same time as the critical load. The resulting voltage rise compensates for the voltage dip that would have
been caused by the critical load alone.
Considerable care has to be taken when dimensioning such systems. Although temporarily connecting the
capacitive load to an ohmic load (e.g. a spot welding machine) causes the voltage dip to disappear, the total
load current increases and places the transformer under greater stress than would have been the case with
the critical ohmic load on its own. It is only when the flicker is generated by an inductive load, such as the
tower crane referred to in a previous example, that this type of compensation actually reduces the load on the
transformer. In both cases, it is recommended that the load and the compensation unit be connected jointly to
the transformer so that compensation is immediate and proactive rather than delayed and reactive.
VECTOR GROUPS
Distribution transformers are normally designed with the Dyn5 vector group. That means that the transformer
has a delta-connected HV winding, a star-connected LV winding, and with the star point brought out as a
neutral terminal. The input and output voltages have a relative phase-shift of 150° (5 x30°). Phase shifts are
restricted to steps of 30°, hence the index 5 to signify 150°. At least that is the case if one limits oneself to
zigzag connections in which the delta-connected and the star-connected parts of the relevant winding have
the same voltage. This transformer classification scheme simply reflects the fact that in the past the use of
other ratios would have made little sense. Today, special-purpose transformers are available that offer a 1:3
voltage ratio and therefore phase-shift steps of 15°. However, understandably, no one has attempted to
market them as, say, transformers with vector group Dyn4½. This type of transformer is used to generate

Page 29
greater than 12-pulse rectifiers such as those used to reduce harmonic emissions in electrolysis plants and in
very large converter drives.
A transformer that is star-connected on both sides, whether with neutral points (YNyn) or without (Yy), can
only have the vector group Y(N)y(n)0 or Y(N)y(n)6 as the sole variation possible in star-star transformers. Either
the three start of winding points are joined to form a neutral point and the end of windings are brought out as
phase conductor connections, or vice versa (i.e. reversing the polarity of each of the coils).
Is this in fact the sole possible variation? Strictly speaking, no. It is possible to re-label the phase conductors
and define, say, conductor L1 on the input side as L2 or L3 on the output side. This would lead to something
that could be designated as a Y(N)y(n)4 or a Y(N)y(n)8 vector group—or one could simply call it a mistake. The
mistake would become apparent only if the output sides of a correctly wired and an incorrectly wired
transformer were to be connected in parallel. In all probability such a connection would destroy the
installation. This is hardly the sort of failure detection method that one would use intentionally!
Some in the electrical industry refer to the brought-out neutral point as a PEN connection. This is incorrect. In
spite of what is sometimes assumed, the carefully insulated neutral point brought out from an oil-immersed
transformer is never actually connected to the inside of the tank. While conceivable in theory, it is unlikely that
a customer would ever want a transformer configured in such a manner. If a transformer was customized in
this way, it would no longer be possible to operate it in the modern, standardized
3
multi-feed power
distribution networks in use today.
In principle, transformers with other vector groups could conceivably be used to feed into public low-voltage
networks. However, these transformers cost more and have no advantage over the standard vector group
(Dyn5). At least that has been the case up until now. Recent developments have begun to reshape the power
engineering landscape and we will be looking at these later on.
Since medium-voltage networks do not generally have a neutral conductor, only a delta winding is feasible on
the HV side of the transformer. If the windings were star-connected, this would reduce the voltage across a
coil by a factor of 3 making it easier to control. This is precisely why all grid coupling transformers (i.e.
transformers that interconnect EHV and HV power networks) are configured with the YNyn0 vector group.
However these networks always have a neutral conductor, even if this only means that the neutral points on
each side of the transformer have been earthed. As a rule, a medium-voltage power network does not have a
neutral conductor. If a loadable neutral is needed on the output side in order to be able to tap two different
AC output voltages, then current will flow in only one LV coil generating magnetic flux and only in that one
limb under single-phase supply conditions.
The operating principle of a transformer dictates that this flux must be compensated by a corresponding
counter flux generated by the HV coil in that same limb. This can only occur however if the input voltage is
directly applied to both ends of the input winding. This is only possible in the case of a delta winding or a
connected neutral point.
The delta connection could be approximated using a parallel circuit. Likewise, the star connection without a
neutral terminal could be modelled by an equivalent series circuit (as shown in the modified equivalent circuit
diagram in Figure 34). In the case of an open neutral point on the input side and the single-phase load on the
output side, the result would be like a loaded coil in series with an unloaded coil (the unloaded coil
3
Cf. amendment of EN 50174-2 (VDE 0800 Part 174-2) from January 2002 für the September 2001 edition

Page 30
representing a reactor with a very high magnetizing reactance XM that reduces the load current). As a result,
almost all of the voltage across the quasi-series circuit drops across this unloaded coil, which excites the core
and drives the core into magnetic saturation. The consequence of this is a dramatic increase of the iron losses
and of the magnetic leakage losses.
Although the magnetizing reactance falls, it does not fall far enough for it not to cause a substantial shift in the
voltages. The voltage across the load collapses to a fraction of the rated voltage while a substantial
overvoltage is present on the unloaded output winding. If the winding is in fact not completely unloaded, but
actually feeds a relatively small load, then this load will have to cope with a continuous 3-fold overvoltage.
This is a situation that brings with it a genuine risk of damaging or destroying the load and of fire damage. This
is why Yyn0 and Yyn6 vector groups are generally not used if the only brought-out neutral point (i.e. the one
on the output side) is loaded. The input windings of distribution transformers are usually delta-connected for
this reason.
Figure 34 – Equivalent circuit representing single-phase loading of a Yyn transformer. Since the load impedance
is considerably less than XM and RFe, the total impedance of the upper circuit is much smaller than that of the
lower circuit.
This is the case, unless you happen to be dealing with a TT system of a type still frequently found in Belgium.
These TT systems are fed by a transformer with the usual Dyn5 vector group but for which the output voltage
is only 133/230 V. In this case, we could have used Yyn0 or the Yyn6 vector groups equally well, since the
neutral point on the low-voltage side is brought out, but is not connected and therefore not loaded. Its only
use is for measurement and testing procedures such as monitoring earth faults. The voltage at the AC power
socket is between the two phase conductors. Therefore the current from the power socket (which for example
in Germany would be a single-phase current) flows as a two-phase current through two low-voltage windings
and expects a corresponding current through the two high voltage coils on the relevant limbs. If the high
voltage side is star-connected without a neutral terminal, there is nothing to prevent this current from flowing.
But a single-phase load on the output side would mean that the current in the HV winding would have to first
flow through a loaded coil and then through an unloaded one, the latter acting, as already described, as a
reactor that attenuates the current. This sort of behaviour needs to be taken into account if the LV neutral
point is earthed with the intent of reducing the earth-fault loop impedance. This impedance is in any case
much higher in TT systems than in TN systems because of the resistance of the earth path in the impedance
loop. Clearly the high load-imbalance impedance of the transformer will prevent any noticeable reduction in
the impedance of the earth fault loop.
RLoad
RFe
X1‘ X2
Xm
RCu1‘ RCu2
RFe
X1‘ X2
Xm
RCu1‘ RCu2
L1
N
L2

Page 31
A voltage tester will light up whenever it touches any active conductor in an AC power socket, though only
weakly, because the voltage on each active conductor is only about 133 V relative to earth. In an IT earthing
system, the circuit for the voltage tester is closed via the stray coupling capacitances. An ordinary tungsten-
filament lamp would no longer be able to light up. However in a TT system, this current—although sufficient to
illuminate the lamp and to cause a dangerous electric shock—would not be enough to trigger an overcurrent
protection device. This is the well-known problem of the TT system and one that is exacerbated by this type of
(Belgian) supply. Dangerous shock currents can also arise in IT earthing systems, making RCD protection
necessary in both TT and IT systems. This however depends upon the extent and the age of the supply network
and the possible capacitive leakage currents, especially those in modern loads.
In addition, neither variant allows for the possibility of driving single-phase and three-phase AC loads designed
for a 400 V supply. For example, the popular German flow heater requiring a three-phase 400 VAC connection
would not function in parts of Belgium (unless of course the user was prepared to accept only a third of the
device’s rated output). In contrast, an electric cooker designed for a three-phase supply works without
difficulty. Cookers are usually designed to be able to cope with these supply networks by having a means of
reconnecting the terminals on the terminal board so that 230 V is always supplied to each of the three load
groups. The cooker does not actually need 400 V to operate. However, this approach will not work in the case
of the flow heater, since the individual heating elements are usually dimensioned for 400 V, i.e. for a delta
connection. While it would be possible in principle to design a flow heater to run on a 230 V/400 V delta/star
supply, there is a big difference between providing 7.5 kW for an electric cooker or 27 kW for a flow heater.
Providing the latter level of power becomes complicated if no 400 V supply is available.
PROTECTION
The distribution transformers used in public power supply networks are generally not protected on the output
side. The input side, in contrast, is equipped with HV HRC (high voltage high-rupturing capacity) fuse links.
However, if such a fuse is subjected to an overcurrent in the range between one and three-times the fuse’s
current rating, it will tend to overheat but will not interrupt the fault current.
But before a cynic turns round and says that HRC is obviously an abbreviation of Hopelessly Redundant
Component, we need to set the record straight. This type of fuse provides protection against a short circuit
fault, but not against overloading. This kind of protection is usually perfectly adequate, because by properly
planning the network based on parameters gained from years of experience, and by designing-in sufficient
levels of reserve power, it is possible to prevent overloading in, say, Germany. It simply does not occur.
However, overloading is the normal state in other regions of the world. Transformers are pretty tough devices
that can put up with a lot. The question of whether this makes economic sense is something that we will be
examining a little later. The crucial areas in which protection is needed are short-circuiting or arcing on the
output side and the rare occurrence of an internal fault within the transformer. Turn-to-turn faults in the LV
foil windings in particular can result in some spectacular damage. Arcing can cause some of the oil to vaporize
or can cause it to decompose into gaseous components. The resulting pressure wave swells the sides of the
transformer tank. The tank tries to attain a spherical form that offers greater volume per surface area in much
the same way coils react when a short circuit occurs. If such a damaged transformer is subsequently
disassembled, the conductor material found in the base of the tank has the form of egg-sized, egg-shaped
globules of red copper or pale silver aluminium speckled with soot. The coils, and in many cases the tank as
well, are now simply scrap, with only the core and transformer accessories still usable.
If the fault had persisted for even a few seconds, the tank would have burst, leaking copious amounts of oil
that would have ignited and acted as a fire accelerant. It is therefore quite clear, that short circuit protection is
essential, but overload protection is not. The development of electronic control systems means that it is now
common to have remote monitoring of the oil temperature. This not only helps to prevent hazardous

Page 32
situations from arising, but it also helps to optimize the operation of the supply network, since the difference
between the temperature of the oil and the ambient temperature provides an indication of the degree of
transformer loading.
The issue of short circuit protection again underscores the problems described earlier concerning the use of
inappropriate vector groups. If, for instance, there is a single-pole-to-earth fault on the output side and an
unconnected neutral point on the input side, and the magnetizing reactance of a limb not involved in the short
circuit is in the way of the short circuit, then the short circuit current that flows will be too small to trigger the
fuse. The extreme shift in the voltage system of almost a factor of √3 causes the limb in question to become
overexcited and magnetically saturated. As a result, that portion of the voltage that exceeds the rated voltage
is more or less only affected by the leakage reactance of the corresponding limb of the core. The amount of
current flowing can therefore be well above the rated current for the transformer itself and for the fuse, yet
still too small to trigger the fuse. The question then is which of the two blows first. It is worth repeating our
call to spend time carefully choosing the right vector group so that if a short circuit does occur, it is definitely
big enough to be identified as such by the fuse system, which can then react as it should and interrupt the
fault current. If that is not possible, then other protective and monitoring systems need to be put in place.
OPERATING TRANSFORMERS IN PARALLEL
Connecting transformers in parallel is of course possible in principle. This obviously means that the voltage
ratings of the two coils to be operated in parallel must be identical. Any off-load tap changers or strap panels
must also have the same settings. As an example, we will assume that we want to operate two transformers,
which have the same output power rating, with their primary windings in parallel and the secondary windings
also connected in parallel. Each transformer has a voltage changer with a range of ±5% of the rated voltage,
but one is set to +5%, while the other is set to -5%. One transformer has a short circuit voltage of usc = 4%; for
the other usc = 6%. In this case, the two short circuit impedances are in series and both transformers are
coupled via an impedance of 4% + 6% = 10% of the load impedance relative to the rated load of one of the
transformers.
Similarly, the difference between the parallel voltages is also 10% (of the rated voltage). As a result, the
transformer that exhibited the 10% higher open-circuit voltage will drive the rated current through the other
transformer, which will in turn transform this current back onto the input side. All windings on both
transformers would therefore be carrying the rated current, one forward and the other backwards, and
without supplying any electrical power. If a load was then connected, the voltage across the parallel output
terminals would decrease slightly. This would reduce the load on the backward-feeding transformer, but the
forward-feeding transformer would be overloaded.
Even if the asymmetric input voltage settings were to be corrected, the assumption made above should never
have been made. Even when all the voltages are identical, one should never operate transformers that have
different short circuit voltages with their output sides connected in parallel, since the load will still be
distributed unequally. Now assume the following: our two example transformers are both connected to the
same voltage source and have the same tap changer positions or that some other measures have been taken
to ensure that the open-circuit terminal voltages on the LV sides of both transformers are of the same
magnitude and have the same phase relationship. The two secondary windings are now connected in parallel
and drive a load that corresponds to the sum rated output of the two transformers. In this situation, each
device would be working at full capacity (but no more), if, that is, each played its part. But they do not. The
one with a short circuit voltage of 6% will only be loaded to
4
/5 of its rated load, the one with usc = 4% has to
deal with
6
/5 of its rated load, i.e. with a 20% overload.
Once again however, that’s not quite the whole truth. The size of the transformers (i.e. the ratio of their rated
outputs) also plays a role. Experts generally state that transformers that differ in size by more than a factor of

Page 33
three should not have their secondary windings connected in parallel. In fact, since 1997, the recommendation
is that the size difference should not exceed a factor of two
4
. As was already briefly mentioned, the ohmic
voltage drop across the winding decreases as the size of the transformer increases. In a small transformer, the
short circuit voltage usc contains substantially more uR and slightly less uX (Figure 35).
As the size of the transformer increases, uR gradually becomes increasingly negligible, at least in terms of what
we are considering here. But as Figure 27, Figure 29, and Figure 30 show, the size of the voltage drop in the
transformer depends on whether the device is driving an ohmic or an inductive load. If the voltage drop in the
transformer has only a small ohmic component, it will be reduced more if the transformer is attached to an
inductive load than when it is attached to an ohmic load, and vice versa. As a result, transformers with
different uR/uX ratios may well have exactly the same open-circuit voltage, but when operating under load,
there will be a slight difference in their voltages. Depending on the phase angle of the load, either the reactive
voltage or the ohmic voltage will drop more strongly. Consequently, if the transformer is operating under load
(i.e. not under open-circuit conditions), connecting the secondary windings in parallel will generate a
circulating current. The magnitude and direction of the circulating current will depend on the phase angle of
the load—something that is hard to predict.
As a consequence, connecting a large and a small transformer in parallel requires the introduction of a safety
factor, though this in turn makes the whole argument somewhat circular as the following example illustrates.
There is little point in providing a large 630 kVA transformer with a small assistant transformer with a rated
power of say 63 kVA or 100 kVA. The large transformer should have been dimensioned so that it offers at least
that amount of reserve capacity. If an assistant is required, the safety factor mentioned above means that the
actual capacity required is more like 250 kVA. But that would satisfy the 3:1 ratio rule, making the safety factor
superfluous to requirements—and we are back to where we started.
Figure 35 – Differing ratios of the active to the reactive voltage drop in a large transformer with a 630 kVA
Class C rating according to HD 428 (left) and a smaller transformer with a 50 kVA Class B rating (right).
In contrast to an electric motor, the most economical operating point for a transformer is well below its rated
load, so it makes sense to design in plenty of reserve capacity during the planning phase. In the example
discussed above, it is worth budgeting for a transformer with a rating of 1,000 or even 1,250 kVA—or better
4
www.a-eberle.de/pdf/info_12.pdf
uX=3.91%
uR = 0.9%
uX=2.95%
uR = 2.7%

Page 34
still—introducing system redundancy by including a pair of 630 kVA transformers, each of which is capable in
an emergency of handling the load on its own. Having reserve capacity also helps to settle the nerves. First,
conversion or retrofitting costs are far lower if there is a need to handle greater loads at some later date.
Secondly, power losses are reduced and, thirdly, the voltage drop in the transformer is lower as a result of
using either two 630 kVA devices in parallel or from using a single large device. Indeed this can be the
optimum solution for flicker problems since it gets things right at the start rather than attempting to deal with
the problem by grafting on a solution later
5
. Of course, the price for this improved resistance to flicker in the
supply system is a higher short circuit power. The short circuit power rises linearly with the size of the
transformer (provided the rated short circuit voltage is constant) and is the sum of the short circuit powers of
the individual transformers if they are connected in parallel. This needs to be considered when configuring the
downstream distribution network.
The term short circuit power needs to be used with care. According to the definition, the short circuit power is
calculated by multiplying the open-circuit (i.e. no-load) voltage by the short circuit current. The operating
states no-load and short circuit are however mutually exclusive. Short circuit power is a purely fictional
computational parameter, but never-the-less one that is useful in estimating what could happen in the event
of a short circuit.
There is one further and very obvious condition for operating transformers in parallel: the vector group codes
of the units to be connected in parallel must be the same. The important aspect here is that the digits
following the letter codes are identical. If they were not the same, one would end up connecting windings with
different phase relationships—a situation that is obviously unacceptable. For instance, two transformers with
the vector group codes Dd0 and YNyn0 can certainly be operated in parallel. But if the neutral point is loaded,
the single-phase or non-linear load will be borne by only one of the transformers, since the other does not
have a neutral point. This needs to be taken into consideration. Additionally, the short circuit voltages on the
rating plates refer to symmetric, linear, three-phase loads. If another type of load is connected, quite different
values will apply. The size of the deviation will then depend strongly on the vector groups involved
6
. By this
point, things can have begun to get quite confusing. Connecting transformers with different vector groups in
parallel is certainly not to be recommended, and should only really be seen as an emergency measure.
When we discuss operating transformers in parallel, we normally mean that the output sides are connected in
parallel, as the input sides are usually connected either directly or indirectly in parallel. It is possible, however,
that a distribution transformer is fed from different MV systems, which in turn are fed from the same HV
system but via HV transformers with differing vector group codes (and therefore having different phase
relationships). In this case, the sum of the vector group code digits for the HV transformer and the
downstream distribution transformer must be the same for each HV transformer so that the voltages at the
secondary windings have the same phase.
But as is so often the case, that’s not quite the whole truth. Vector group codes are not the only significant
elements. We also need to take the power transmission networks into account. The case capacitance (i.e. the
5
See [1], p. 51
6
Fender, Manfred: Vergleichende Untersuchungen der Netzrückwirkungen von Umrichtern mit Zwischenkreis
bei Beachtung realer industrieller Anschlußstrukturen [‘Comparative studies of the effects of converters with
intermediate circuits on power quality in real industrial installations], Ph.D. thesis, Wiesbaden 1997

Page 35
capacitance per unit length)
7
of underground cable is very large, while its series inductance (i.e. inductance per
unit length) is rather small. In overhead power lines, on the other hand, the capacitance is smaller and the
inductance is greater. Phase relationships will therefore vary depending on the specific load conditions.
Let us assume that we have two distribution transformers that are connected in parallel on their output sides.
They have the same rated outputs, the same vector groups, the same short circuit voltages, the same output
voltages, and even approximately the same copper losses. In other words, they are ideally suited to be
operated in parallel. One of the transformers is fed via a relatively long underground MV cable, the other via a
relatively long overhead MV line. As we assume that the voltages supplied at the start of the two cables have
the same phase and the modulus of the impedance is similar for the two cables, it is reasonable to expect that
there will not be any appreciable imbalance in the distribution of the common load. However, the phases of
the voltages arriving at the input sides of the two parallel distribution transformers (i.e. at the ends of the MV
supply cables) can indeed be different. The phase relationships measured at the LV bushings are therefore also
different and if the bushings are connected in parallel, a circulating current will begin to flow and the two
transformers will appear to heat up even under open circuit (no-load) conditions. However this is not actually
the case since the transformers are not really under no-load conditions. In fact, they drive the circulating
current. The power losses are almost purely reactive in nature. The only exception is the ohmic losses in the
two transformers as well as in their connection cables on the high voltage and low-voltage sides as far as the
coupling points.
The underground cable also represents a substantial capacitive load for the HV feeder transformer and, as
already described, this can cause an increase in the output voltage (Figure 33). In contrast, the capacitance of
the overhead line is probably small enough to be compensated (at least at full load) by the leakage inductance
of the distribution transformer that is being fed. The voltages can therefore differ not only in terms of their
absolute magnitudes but also with respect to phase. The question of whether this difference could become
critical is something that has to be calculated for a wide range of load cases during the planning phase. That is
not as simple as it sounds, given the large number of transformer and supply system parameters that need to
be taken into account.
Summary: Conditions for operating transformers in parallel
 Same voltage across the windings to be connected in parallel
 Same rated short circuit voltages
 Same vector group codes
 Ensure supply networks have the same phase relations
 If the transformers are not connected in parallel on the input side, ensure that the supply networks
have approximately the same short circuit power levels
 Maximum size ratio of transformers operated in parallel: 3:1
7
Fassbinder, Stefan: ‘Erdkabel kontra Freileitung’ [‘Underground vs overhead power transmission cables’], in
de, vol. 9/2001, p. gig9, appears in DKI reprint s180 ‘Drehstrom, Gleichstrom, Supraleitung – Energie-
Übertragung heute und morgen’ [‘Three-phase AC, DC and superconducting systems – Power transmission now
and in the future’] from the German Copper Institute (DKI), Düsseldorf

Page 36
ENERGY EFFICIENCY
In 1999, the Swiss journal Bulletin SEV/VSE
8
carried a cover story entitled Replacing old transformers pays off
9
.
The article showed that as a result of the significant improvements in the efficiency of modern transformers,
there are now sound economic reasons (in addition to important environmental arguments) why older
transformers should be decommissioned even when they are still functioning properly. In this section, we
explain how these efficiency improvements have been achieved and their current and future significance for
those responsible for purchasing and deploying transformers.
NEW REGULATION GOVERNING TRANSFORMER EFFICIENCIES
On July 1st 2015 the new European Regulation N 548/14
10
on power transformers entered into force. This was
a world premier of a regulation stipulating a minimum energy performance for large power transformers.
The regulation establishes eco-design requirements for power transformers with a minimum power rating of 1
kVA used in 50 Hz electricity transmission and distribution networks or for industrial applications. The
regulation indicates that transformers are strategic assets in the electrical networks, playing an important role
in achieving the ambitious energy efficiency targets set by most industrialized countries. Considering Europe
only, 16.7 TWh (corresponding to 3.7 megatons of CO2) will be saved in 2025 through the reduction of no-load
and load losses of transformers falling under this regulation.
The requirements for distribution transformers are formulated in the form of maximum load and no-load
losses (in W).
Requirements for three-phase liquid-immersed medium power transformers with one winding are listed
below, for respectively Um (maximum voltage) ≤ 24 kV and for Um ≤ 1.1 kV:
8
SEV/Electrosuisse: Swiss Association for Electrical Engineering, Power and Information Technologies
VSE: Association of Swiss Electricity Utility Companies
9
Borer Edi: ‘Ersatz von Transformatoren-Veteranen macht sich bezahlt’ [‘Replacing old transformers does
pay’], in Bulletin SEV/VSE, vol. 4/1999, p. 31
10
http://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=OJ:L:2014:152:FULL&from=EN

Page 37
Tier 1 (from 1 July
2015)
Tier 2 (from 1 July
2021)
Rated
Power
(kVA)
Maximum
load
losses Pk
(W) (*)
Maximum
no-load
losses Po
(W) (*)
Maximum
load
losses Pk
(W) (*)
Maximum
no-load
losses Po
(W) (*)
≤ 25
Ck (900) Ao (70) Ak (600) Ao – 10 %
(63)
50
Ck (1 100) Ao (90) Ak (750) Ao – 10 %
(81)
100
Ck (1 750) Ao (145) Ak (1 250) Ao – 10 %
(130)
160
Ck (2 350) Ao (210) Ak (1 750) Ao – 10 %
(189)
250
Ck (3 250) Ao (300) Ak (2 350) Ao – 10 %
(270)
315
Ck (3 900) Ao (360) Ak (2 800) Ao – 10 %
(324)
400
Ck (4 600) Ao (430) Ak (3 250) Ao – 10 %
(387)
500
Ck (5 500) Ao (510) Ak (3 900) Ao – 10 %
(459)
630
Ck (6 500) Ao (600) Ak (4 600) Ao – 10 %
(540)
800
Ck (8 400) Ao (650) Ak (6 000) Ao – 10 %
(585)
1 000
Ck (10
500)
Ao (770) Ak (7 600) Ao – 10 %
(693)
1 250
Bk (11
000)
Ao (950) Ak (9 500) Ao – 10 %
(855)
1 600
Bk (14
000)
Ao (1 200) Ak (12
000)
Ao – 10 %
(1080)
2 000
Bk (18
000)
Ao (1 450) Ak (15
000)
Ao – 10 %
(1 305)
2 500
Bk (22
000)
Ao (1 750) Ak (18
500)
Ao – 10 %
(1 575)
3 150
Bk (27
500)
Ao (2 200) Ak (23
000)
Ao – 10 %
(1 980)
Table 3 – Eco-design regulation for three-phase liquid-immersed medium power transformers.
Most of DSO owned transformers are of the liquid immersed type, but the category “Distribution
transformers” also covers the dry type. The requirements for three-phase dry-type medium power
transformers with one winding and a maximum voltage Um ≤ 24 kV and Um ≤ 1,1 kV respectively, are listed
below:

Page 38
Tier 1 (1 July 2015) Tier 2 (1 July 2021)
Rated
Power
(kVA)
Maximum
load
losses Pk
(W) (*)
Maximum
no-load
losses Po
(W) (*)
Maximum
load
losses Pk
(W) (*)
Maximum
no-load
losses Po
(W) (*)
≤ 50
Bk (1 700) Ao (200) Ak (1 500) Ao – 10 %
(180)
100
Bk (2 050) Ao (280) Ak (1 800) Ao – 10 %
(252)
160
Bk (2 900) Ao (400) Ak (2 600) Ao – 10 %
(360)
250
Bk (3 800) Ao (520) Ak (3 400) Ao – 10 %
(468)
400
Bk (5
500)
Ao (750) Ak (4
500)
Ao – 10
% (675)
630
Bk (7
600)
Ao (1
100)
Ak (7
100)
Ao – 10
% (990)
800
Ak (8
000)
Ao (1
300)
Ak (8
000)
Ao – 10
% (1 170)
1 000
Ak (9
000)
Ao (1
550)
Ak (9
000)
Ao – 10
% (1 395)
1 250
Ak (11
000)
Ao (1
800)
Ak (11
000)
Ao – 10
% (1 620)
1 600
Ak (13
000)
Ao (2
200)
Ak (13
000)
Ao – 10
% (1 980)
2 000
Ak (16
000)
Ao (2
600)
Ak (16
000)
Ao – 10
% (2 340)
2 500
Ak (19
000)
Ao (3
100)
Ak (19
000)
Ao – 10
% (2 790)
3 150
Ak (22
000)
Ao (3
800)
Ak (22
000)
Ao – 10
% (3 420)
Table 4 – Eco-design regulation for three-phase dry type medium power transformers.
To harmonize the requirements of the EU regulation on power transformer efficiency with European
standards, Cenelec Technical Committee No. 14 for Power Transformers adopted 3 new standards:
• EN 60076-19: Rules for the determination of uncertainties in the loss measurements on power
transformers and reactors. These rules are important for market surveillance verification.
 EN 50588-1: Medium power transformers, 50 Hz, with the maximum rated voltage not exceeding 36
kV - Part 1: General requirements. This standard introduces efficiency classes for medium power
transformers.
 EN 50629: Energy performance of large power transformers (Um > 36 kV or Sr ≥ 40 MVA). This
standard introduces efficiency requirements for large power transformers.
Transformers are now far more efficient than in the past. The EN50588-1 standard reflects this transformer
technology development by setting new loss classes. The following tables are defined for step-down or step-up
transformers with one winding and a maximum voltage Um ≤ 24 kV or Um ≤ 1.1 kV respectively.

Page 39
Rated
power
AAAo AAo LWA Ao LWA
kVA W W dB(A) W dB(A)
≤ 25 35 63 36 70 37
50 45 81 38 90 39
100 75 130 40 145 41
160 105 189 43 210 44
250 150 270 46 300 47
315 180 324 48 360 49
400 220 387 49 430 50
500 260 459 50 510 51
630 300 540 51 600 52
800 330 585 52 650 53
1000 390 693 54 770 55
1250 480 855 55 950 56
1600 600 1080 57 1200 58
2000 730 1305 59 1450 60
2500 880 1575 62 1750 63
3150 1100 1980 63 2200 64
Table 5 – No load loss (P0) and sound power level for liquid immersed transformers.
The sound power level LWA for transformers AAA0 has to be agreed between the manufacturer and the
purchaser.

Page 40
Rated power Ak Bk Ck Short-circuit Impedance
kVA W W W %
≤ 25 600 725 900 4
50 750 875 1100 4
100 1250 1475 1750 4
160 1750 2000 2350 4
250 2350 2750 3250 4
315 2800 3250 3900 4
400 3250 3850 4600 4
500 3900 4600 5500 4
630 4600 5400 6500 4 or 6
800 6000 7000 8400 6
1000 7600 9000 10500 6
1250 9500 11000 6
1600 12000 14000 6
2000 15000 18000 6
2500 18500 22000 6
3150 23000 27500 6
Table 6 – Load loss (Pk) and short circuit impedance for liquid immersed transformers.

Page 41
Rated power Pk P0 P0 LWA Short-circuit
Impedance
Ak Bk AAA0 AA0 A0
kVA W W W W dB (A) W dB (A) %
≤ 50 1500 1700 115 180 48 200 49 6
100 1800 2050 160 252 50 280 51 6
160 2600 2900 230 360 53 400 54 6
250 3400 3800 300 468 56 520 57 6
400 4500 5500 430 675 59 750 60 6
630 7100 7600 630 990 61 1100 62 6
800 8000 750 1170 63 1300 64 6
1000 9000 890 1395 64 1550 65 6
1250 11000 1035 1620 66 1800 67 6
1600 13000 1265 1980 67 2200 68 6
2000 16000 1495 2340 69 2600 70 6
2500 19000 1780 2790 70 3100 71 6
3150 22000 2185 3420 73 3800 74 6
Table 7 – Losses, short circuit impedance and sound power levels for dry-type transformers.
Transformers can be requested and offered with a sound power level LWA other than the listed values. The
sound power level LWA for transformers AAA0 has to be agreed between the manufacturer and the purchaser.
Medium power pole mounted transformers with a rated power of up to 315 kVA suitable for outdoor service
and designed to be mounted on the support structures of overhead power lines have separate less demanding
efficiency requirements. The reason is weight limitation.
Rated power
(kVA)
A0
(W)
25 70
50 90
100 145
Table 8 – Maximum values of no load loss for pole mounted transformer with weight limitations and sr < 160
kva.

Page 42
Rated power
(kVA)
B0
(W)
C0
(W)
160 270 (C0 -10%)
a)
300
200 310 356
250 360 425
315 440 520
a)
This value is a deviation from the value reported in
EN 50464-1.
Table 9 – Maximum values of no load loss (p0) for pole mounted transformer with weight limitations and sr ≥
160 kva.
Rated power
(kVA)
Bk
(W)
Ck
(W)
25 725 900
50 875 1100
100 1475 1750
160 3102 (Ck +32%)
a)
3102 (Ck +32%)
a)
200 2333 2750
250 2750 3250
315 3250 3900
a)
This value is a deviation from the value reported in EN 50464-1.
Table 10 – Maximum values of load loss (pk) for pole mounted transformer with weight limitations.

Page 43
OPTIMIZING THE PROPORTION BETWEEN NO-LOAD AND LOAD LOSSES
Figure 36 – Reduced noise levels and improved efficiency go hand in hand.
Figure 37 – The operational characteristics of the transformer depend on whether one minimizes the no-load
(iron, Fe) losses or the load (copper, Cu) losses, as shown here in a comparison of the A0DK and E0AK classes for
a 1,000 kVA transformer using data from Table 3 and Table 4.

Page 44
The relative weight given to load losses and no-load losses in the design of a transformer can determine
whether the transformer has more conductor material in the coil windings and less core material or vice versa.
The design choices made will also affect the transformer’s operational behaviour, particularly its losses. For
instance, optimum efficiency can be achieved at a load factor of 24% or at 47%, depending upon the design
(see Figure 37). When compared at constant current density, a transformer with more conductor material will
exhibit greater load or copper losses since they are also known. Strictly speaking, a more accurate trivial name
for these losses would be aluminium losses, since the losses in an aluminium conductor are 35% greater than
those in a copper conductor of identical cross-section. But the term copper losses is unlikely to change, since it
reflects the fact that copper is historically the standard conductor material used in transformers.
If the magnetic flux density, frequency, and iron quality are held constant, the no-load losses in a transformer
(also known as core losses or iron losses) depend only on the amount of iron used in the core. Similarly, if the
current density is held constant, then, roughly speaking, the copper losses will depend only on the amount of
copper used. On the other hand, iron losses can be reduced by increasing the number of windings on the core
and thus reducing the magnetic flux density (induction). In contrast, copper losses can be reduced by operating
at a higher flux density and using fewer windings on the core. However, this can only be realized within strict
limits, since high-quality magnetic materials have quite sharp magnetic saturation points and most
conventionally designed transformers operate close to this limit. The primary means of reducing copper losses
is to lower the current density, while maintaining the number of turns and the core cross-section and
modifying the core in such a way that the winding window is larger and thicker wire can then be used for the
windings.
A transformer that spends most its life operating under no load or minimal load conditions should therefore be
designed to minimize the no-load losses, i.e. less iron and more copper. It would however be wrong to
conclude from this that any transformer designed for permanent full-load operation (something that only
really occurs in generator transformers in power stations and in certain industrial applications) should contain
as little copper as possible. In this case, the preferred approach is to maximize the cross-section of the iron
core in order to minimize the number of turns. The cross-section of the conducting wires should also be as
large as possible in transformers running under continuous full load.
Unfortunately, splitting a 1,250 kVA transformer into two units each with a power rating of 630 kVA, as
suggested earlier in the section on operational characteristics, results in a slight rise in all losses irrespective of
the size of the load. Nevertheless, the beneficial redundancy achieved means that this sort of splitting is
frequently utilized in practice. With two smaller transformers there is also the option of switching off one of
the transformers during light-load periods and thus reducing the losses during these periods to below the level
that would be incurred if a single larger transformer were used. Of course, both sides of the transformer have
to be disconnected from the power supply. If only one side is disconnected, the transformer remains excited
and no-load losses continue to be incurred.
DRIVING UP COSTS BY BUYING CHEAP
If the power required from a conventional small transformer is a slightly below what is in principle physically
obtainable from a transformer of that size, one often finds that the coil formers are not fully wound. It is
almost as if achieving a minimum temperature rise is an essential part of the design. In fact, this problem is not
restricted to conventional small transformers; it is also common in the type and size of transformers
considered in this paper. This is completely consistent with the view, widely held by both transformer
manufacturers and users alike, that a transformer belonging to a higher thermal insulation class is better than
one in a lower insulation class. Transformers in a higher thermal insulation class are by definition able to get
hotter and they generally do heat up more than those with a lower thermal insulation rating. Because they get
hotter, the manufacturers employ (expensive) insulation materials. The temperature is higher, the losses are

Page 45
higher, and the transformer generates correspondingly more heat in the electrical system to which it is
connected.
The best that can be said about this practice is that the transformer is a little smaller in size. But that is its sole
advantage and even that benefit can be lost because the higher temperatures generated mean that other
components have to be kept further away from it. Furthermore, the higher losses often require more effort
and expense to be spent on managing heat dissipation. The voltage drop is also larger. It is essential that
transformer professionals rid themselves of the ludicrous notion, which, when expressed provocatively, might
be phrased: ‘my transformer is better than yours, because it’s hotter.’ If progress means stepping up from
class H (with a continuous duty temperature rating of 180º C) to class C (220º C) then the heat really will be on.
How did this mind-set arise? Price pressure is the usual reason cited, with price meaning only the purchase
price and all follow-up costs conveniently ignored. But that would imply that market forces should have
eliminated any manufacturer offering more expensive devices. There are however a number of transformer
manufacturers who have decided to put quality first, and who are thriving as a result, despite the fact that the
first thing the customer is usually interested in is the price. The key here is to carefully explain to the customer
why the coil former is always fully wound, why these transformers are usually somewhat more expensive, and
occasionally significantly more expensive than apparently equivalent competitor products, and why using the
cheapest transformer usually leads to the most expensive system overall. The commercial success of these
companies
11
is clear proof that they are indeed managing to convince their clients that the purchase price of a
transformer is not its most important feature.
One manufacturer uses only grain-oriented sheet steel in the cores of all its transformers with a power rating
above about 1 kVA. This may well be due to the fact that the company uses some of these (auto)transformers
in one of its other business units to manufacture energy management units
12
as well as special DC link
converters. And an article on the latter reiterates what was said above about the danger of focusing only on
the price: ‘Over the last few years, cost and space considerations have led to an expansion of the thermal
insulation classes up to class H (180ºC)—a development that has brought with it numerous disadvantages…
13
’.
Apart from the fact that—strictly speaking—it should have read ‘…price and space considerations…’ (since
price and cost are not the same), the article underscores the company’s praiseworthy attitude regarding the
question of transformer efficiency.
11
www.riedel-trafobau.de, www.buerkle-schoeck.de
12
Decker, Christiane: ‘Energie sparen mit EMU’ [‘Saving energy with EMUs’], in de, vol. 15-16/2000, p. 34
13
Bürkle, Thomas: ‘Wassergekühlte Zweipunkt-Zwischenkreisdrosseln’ [‘Water-cooled two-point DC link
reactors’], in etz, vol. 22/2000, p. 18

Page 46
AN EXAMPLE
Figure 38 – The coil of a single-phase transformer, both the primary and secondary sides have been configured
as multilayer winding…
Figure 39 – …similar to the one considered in the analysis below.
In the following example, we study a 40 kVA single-phase dry-type industrial transformer in order to
demonstrate just how strongly transformer losses depend on the specific transformer design, and just how
quickly the extra investment in a higher-quality device can be recovered. The reason we focus on an industrial
application is because there is a greater need for action in the industrial sector than in the public electricity
supply network. Eight different transformer variants were computed and quoted to the customer (Table 11).
Version 0 was the cheapest and most basic variant. Note that we have avoided the use of such popular but
often misleading euphemisms like most economical or most cost-effective to describe this basic version of the
transformer. It is neither; it is simply the version with the lowest purchase price. The rectangular windings
were designed in such a way that cooling ducts were required between all layers and on all sides.
Starting from this basic version, loss-reduction measures were then progressively designed into the following
seven variants, of which the first six simply involved using conductor wire of successively larger cross-section.
One might think that this would result in a larger sized transformer, but in fact the opposite is true. Although
the transformer gets heavier on moving from Version 0 to 7, it also gets smaller rather than larger. The thicker
wire obviously takes up some of the space occupied by the air cooling ducts. However since the wire becomes
thicker, the need for a cooling duct disappears.
The first ducts that can be dispensed with are those between the layers of a winding on the long sides of the
transformer (similar to the coil shown in Figure 38 and Figure 39). Then, as the diameter of the wire used
increases, it becomes possible to do so without the cooling ducts located on the long sides between the two
coils and finally to eliminate the ducts on the end faces. In Version 7, the winding data (wire diameters and
number of turns) are identical to those in Version 6, but the core uses grain-oriented rather than hot-rolled

Page 47
sheet steel. Although moving from Version 6 to 7 involves only a change in the core material, the copper losses
also decrease due to the higher magnetizability of the grain oriented steel. The stack height of the core in
Version 7 is lower and the average length of a turn is therefore shorter.
Table 11 – Improving a cheap transformer (Version 0) in seven steps.
The effects of the stepwise introduction of loss-reducing measures are not immediately apparent in the data in
Table 11 and for this reason have been presented graphically in Figure 40. Two results stand out straight away:
 Viewed across the series of improvements, the losses decrease significantly faster than the price rises.
 The payback period is nearly always under 1.5 years, only the version with the higher quality sheet
steel core requires longer. The calculations assumed an electricity price of 10 cents per kWh, 242
working days per year, and a single eight-hour shift per day. If there are two shifts a day, the payback
periods are halved.
There is one other beneficial technical side effect from the loss reduction measures: The voltage drop in the
transformer decreases as one moves from Version 0 to 7. This is not always advantageous, especially in
transformers larger than the one considered here where a defined voltage drop is highly desirable. In large
transformers, cooling and electrical insulation requirements mean that it is not possible to eliminate the
cooling ducts. But the example transformer is relatively small, and both the input and output sides are in the
low-voltage range. Furthermore, a small voltage drop (both ohmic and inductive) was advantageous given the
particular industrial process under consideration.
When asked one year later about which of the eight variants the customer finally chose, the manufacturer
became a little embarrassed: ‘I really ought not to say. The customer went for the cheapest product. But not
only that, he also got the loads wrong. So one by one, the transformers are now burning out.’ Any one of the
improved transformer variants 5, 6, or 7 would have had sufficient reserve capacity to cope with the erroneous
load specifications and to prevent transformer failure.
Channels / Design Measures & Weights Calculated Electrical Values Pay-
Ver-
sion
betw. core &
LV winding
in LV winding
betw. LV &
HV winding
in HV winding
stack
height
width length mFe mCu mtot Pv Fe Pv Cu Pvtot U
Price back
time
front
[mm]
long
[mm]
front
[mm]
long
[mm]
front
[mm]
long
[mm]
front
[mm]
long
[mm]
[mm] [mm] [mm] [kg] [kg] [kg] [W] [W] [W] [V] [%] [€] [a]
0 10 10 10 10 10 10 10 10 100 450 360 202 30.7 232.7 417 1634 2051 13 95.1% 877 ---
1 10 10 10 0 10 10 10 0 100 415 365 196 42.4 238.4 406 1343 1749 11 95.8% 932 0.944
2 10 10 0 0 10 10 10 0 100 417 342 196 46.6 242.6 406 1217 1623 10 96.1% 946 0.839
3 10 10 0 0 10 0 10 0 100 400 342 196 48.2 244.2 406 1090 1496 9 96.4% 955 0.723
4 10 10 0 0 10 10 0 0 100 406 340 196 59.9 255.9 406 874 1280 6 96.9% 1027 1.004
5 10 10 0 0 0 0 0 0 100 408 335 196 65.9 261.9 406 753 1159 5 97.2% 1062 1.072
6 As in 5, but with even thicker wire 100 412 341 196 71.3 267.3 406 626 1032 4 97.5% 1100 1.133
7 As in 5, but with grain-oriented steel, lower stack height 80 412 311 155 64.7 219.7 223 580 803 4 98.0% 1249 1.541

Page 48
Figure 40 – Graphical presentation of the data in Table 6
But there is light at the end of the tunnel. A number of manufacturers of resin-encapsulated distributor
transformers still aim to save their customers a few euros by doing without a couple of extra kilograms of
copper (in the high voltage winding) and aluminium (in the lower-voltage winding) and by employing forced
ventilation to cool the windings. Other manufacturers, however, are wary of the risk of failure associated with
these mechanical ventilation systems and have consciously decided to avoid this approach wherever possible.
Naturally air-cooled cast-resin transformers are now available with power ratings of up to 6.3 MVA. At these
sorts of powers, highly efficient insulating materials are essential. (This is not the case in smaller transformers,
as discussed earlier, where they serve to mask avoidable energy wastage.) Other manufacturers use fans when
the transformer has a power rating of around 1 MVA, though they are only activated in emergencies and when
the transformer is overloaded. The fans are not needed when the transformer operates at its rated load and at
normal ambient temperatures. This is a sensible approach, since deploying a large transformer in order to
cope with a few hours of emergency loading makes neither economic nor environmental sense. In fact,
averaged over the year, losses can be higher if an oversized transformer is running for long periods under
capacity (see Figure 37).
AMORPHOUS STEEL
In terms of energy conservation, any transformer operating at low loads for long periods of its service life
should ideally have minimal iron losses. Whereas load losses depend on the square of the current and will
drop to a quarter of their nominal value when the transformer operates at half load, the no-load (i.e. core or
iron) losses depend on the voltage and the frequency. Since both the voltage and the frequency normally
remain constant, the iron losses also remain at their maximum value for as long as the transformer is
operating, irrespective of whether it is connected to a large load, a small load, or no load. Hence, the term no-
0W
500W
1000W
1500W
2000W
2500W
0 1 2 3 4 5 6 7
94.5%
95.0%
95.5%
96.0%
96.5%
97.0%
97.5%
98.0%
98.5%
Pvtot
Efficiency
Voltage drop no load / rated load
0V
2V
4V
6V
8V
10V
12V
14V
0 1 2 3 4 5 6 7
0 €
200 €
400 €
600 €
800 €
1,000 €
1,200 €
1,400 €
0 1 2 3 4 5 6 7
0.0a
0.2a
0.4a
0.6a
0.8a
1.0a
1.2a
1.4a
1.6a
1.8a
Price
Payback
Weights and measures
0mm
100mm
200mm
300mm
400mm
500mm
0 1 2 3 4 5 6 7
0kg
50kg
100kg
150kg
200kg
250kg
300kg
width length
mtot mCu

Page 49
load losses. Despite the fact that no-load losses are almost an order of magnitude smaller than the load losses,
the former are far more important as a practical matter.
We should even perhaps revise our earlier statement that no-load losses are particularly significant at low
loads, since they remain (almost) unchanged and certainly do not disappear when the load and therefore the
associated load losses increase. Once a transformer has been installed, the load—and thus the load losses—
can be controlled by demand side management methods. However there is no way to influence the no-load
losses. Nevertheless, if a new transformer is to be chosen or configured for a particular application, it makes
good sense to look at the potential loss ratios (Figure 37).
Figure 41 – An amorphous steel core (photo: Pauwels), shown here in a five-legged design normally only seen in
high-power transformers.
Figure 42 – Coil assembly with amorphous core (photo: Pauwels).
No-load losses can be reduced by lowering the magnetic flux density and by using special core steels. The
thinner the sheet steel, the smaller the extent of eddy current formation. Eddy currents are completely absent
in core materials that do not conduct electricity (so-called ferrites), but these are reserved for radio-frequency
applications since their magnetizability is too low for transformers operating at grid frequencies. Amorphous
steel is a new type of core material that offers a compromise between sufficiently high magnetizability and

Page 50
significantly reduced core losses. Amorphous steel is made by atomizing the liquid metal and spraying it onto a
rotating roller where it is quenched extremely quickly. It is quenched so rapidly in fact that it cannot crystallize
and remains in a disordered amorphous state, hence the name. While the resulting core material has a
saturation magnetization of at most 1.3 T compared to the 1.75 T exhibited by modern cold-rolled grain-
oriented steels, the no-load losses in a transformer with an amorphous steel core are around 60% lower (see
Figure 41 and Figure 42).
Since the saturation flux density of the core material is lower, these transformers tend to be larger and heavier
and correspondingly more expensive. The transformer with an amorphous steel core is also about 12 dB
louder. Despite these disadvantages, there are factors in favour of amorphous core transformers. Studies in
Belgium, Great Britain, and Ireland have shown that the expected payback periods can be as short as three to
five years. With an expected service life of 30 years, these transformers would therefore pay for themselves six
to ten times over.
The market does not however appear fully ready for amorphous core transformers. One company in Germany
tried its luck
14
. Extensive studies were also conducted in Belgium and Ireland and a number of amorphous core
transformers were sold
15
. But then came the liberalization of the European electricity markets and electricity
prices began to fall. In spite of what economic logic dictates, it seems that once again only prices and not costs
play an unfortunate but defining role in the free market.
TRANSFORMERS USED IN RENEWABLE ENERGY GENERATION SYSTEMS
Every wind turbine contains a transformer that steps-up the generator voltage (typically from 690 V) so that
the power generated can be fed into the medium-voltage collection grid. When transformers are
manufactured or purchased for a specific application it is usual that a so-called loss evaluation is carried out in
accordance with established formulae used by both transformer manufacturers and electricity companies. This
loss evaluation analysis determines the specific level of capital investment that is economically justified in
yielding a unit reduction in the transformer’s no-load or load losses.
In the case of large transformers, the loss evaluation formulae are sometimes used to compute either
contractual penalties, in which the purchase price is reduced if the contractually agreed loss levels are
exceeded in practice, or contractual bonuses, in which an additional payment is made if the losses turn out to
be lower than contractually agreed. In our example, a transformer used in a wind turbine, the no-load loss
evaluation factor was calculated to have the relatively (but justifiably) high value of 9.28 €/W. The load loss
evaluation factor was computed using standard methods to be 0.79 €/W. That value would be low even for a
conventional transformer and in the present case it led to the conclusion that the current transformer (C0BK
class) would still be economical.
However, a recently developed probabilistic method
16
that computes the expected losses for around 4,000
different operational states of the transformer yielded a load loss factor of 1.43 €/W. At that level, the Swiss
transformer discussed earlier (to which we gave the hypothetical DD' rating and that will in future belong to
Class B0AK) or even an A0AK transformer would be the device of choice. This raises the question of how this
discrepancy in the load loss factors did arise.
14
www.marxtrafo.de
15
www.power-technology.com/contractors/switchgear/pauwels
16
www.efficient-transformers.org

Page 51
The usual method of calculation assumes an average load level, and this is low as windless conditions are not
uncommon, and when the wind does blow it is rarely so strong that the turbine operates at full load. However,
using the average load introduces errors into the calculation since load losses vary quadratically and not
linearly with the load. For instance, if the rated copper losses are 8 kW, they are only 2 kW if the transformer is
running at half load. One hour at full load and one hour at standstill result in load losses of 8 kWh; two hours
running at half load generate load losses of only 4 kWh. The difference is analogous to that between the real
root-mean-square value and the rectified mean value of alternating currents. The difference is greater the
more discontinuous the load profile is. Renewable sources of energy are typically significantly more
discontinuous than conventional sources.
In the case of a wind turbine, the blades are frequently motionless or rotating at slow speed without
generating electrical power. Theoretically, the turbine is then generating negative power, as it needs to
consume power to keep the control and monitoring systems active. Although the energy required by these
systems is minimal compared the situation in a coal-fired power station, where about 7% of the gross
generator output is consumed for the power station’s own use, it still needs to be drawn from the grid. This
means that the transformer has to stay operational even though it is essentially under no-load conditions. No-
load losses thus remain relevant for 8,760 hours per year, irrespective of how long the wind turbine is
operating at full, partial, or no load.
In Germany, a further issue has to be taken into consideration. The German Renewable Energy Sources Act
(EEG) specifies that owners of sources of renewable energy shall receive payments for power fed into the grid
and that these payments are above the average market price. If no-load losses and load losses were to be
economically reassessed in the light of this, wind farms would need very different types of transformers than
those typically used in the public electricity supply network. This in fact, would be an ideal application for an
amorphous core transformer.
OTHER COUNTRIES, OTHER CUSTOMS
The reason why Ireland became the test bed for amorphous core transformers was not simply because the
manufacturer had a production facility there. It was also because grid losses in 1980 were almost 12%—an
embarrassingly high level of loss by European standards. Although the reason losses were so high had more to
do with Ireland’s sparse population (and lower grid density) than with poor grid management, the perceived
need to act was perhaps greater than elsewhere. Today losses are below 10%, although this improvement
cannot be ascribed purely to a couple of pilot projects involving amorphous core transformers.
Most European countries have losses of between 6 and 10% in their electricity distribution networks. In
Germany, grid losses are a very creditable 4.6%. The transformers used in the German grid are selected,
irrespective of the voltage level, so that they operate at between 30 and 60% of capacity during a typical daily
load profile. That is the optimal range in which to operate in (Figure 36). However even this still leaves a
theoretical energy saving potential of 4.6%. The only country with lower grid losses is Luxembourg with 2%,
but in such a small, densely populated country, in which no transmission line is longer than 20 km, achieving
low losses is perhaps not as much of a challenge as it is elsewhere. Generally speaking, half of the energy
saving potential is to be found in the transformers, predominantly in the distribution transformers.
The situation in other more distant countries is considerably worse. Reports from India claim that distribution
transformers are regularly operating at 50 to 100% overload levels. As a result, the failure rate is an incredible
25% a year. Quoting the February 2002 issue of the Bulletin on Energy Efficiency, the official journal of the
Indian Renewable Energy Developmental Agency (IREDA), the Indian Copper Development Centre (ICDC)
reports that less than 50% of the electricity consumed in India is actually billed. The rest is lost through
transmission and distribution losses (about 18%), illegal use, or poor management because the electricity
companies simply do not install meters.

Page 52
In Europe, some believe that the introduction of higher voltage levels would also help to reduce the amount of
electrical energy consumed illegally—referred to euphemistically as non-technical losses’. Transformers as
anti-theft devices? It has even been suggested that the introduction of the lower frequency of 16.7 Hz for the
railway traction power grids used in Germany, Switzerland, Austria, and a number of Scandinavian countries
also served the same purpose. The truth, however, is that the lower frequency helps to reduce commutation
problems affecting the ac commutating series motors (universal motors) that power the traction units.
OUTLOOK
While switched-mode power supplies have replaced small transformers in numerous applications, there is
presently no sign that conventional grid transformers will be replaced by any other technology in the near
future. There are suggestions that the extra high voltage level 220 kV will disappear over the long term and
that at some even later date the 380 kV level will be replaced by a DC network
17
. Such developments would
dispense with the need for at least some of the transformers presently required. Regarding energy loss
however, these changes would be essentially neutral, since the inverters and the requisite interference
suppression filters would also generate losses of a similar magnitude.
Attempts have also been made to develop low-loss transformers with superconducting coils
18
. Unfortunately,
these conductors are only really loss-free when conducting direct current. The iron losses can even rise if the
core is also cooled. A further problem is that cooling power has to be supplied continuously at its maximum
required level, thus increasing the no-load losses, despite the fact that in practice, the transformer hardly ever
runs at full load, or if it does, then only for a short time. When all these factors are taken into account, overall
loss reductions turn out to be minimal. The one place where superconducting transformers can be used
effectively is in railway vehicles. Once these transformers go into industrial production they will save not only
weight (and therefore extra energy), but also space. Weight and space limitations in railway vehicles also mean
that the transformers currently in use in railway vehicles are working at their design limits and are thus
significantly less efficient than comparable grid transformers.
17
Fassbinder, Stefan: ‘Hochspannungs-Gleichstrom-Übertragung (HGÜ)’ [‘High-voltage DC power
transmission’], in de, vol. 11/2001, p. gig9, appears in DKI reprint s180 ‘Drehstrom, Gleichstrom, Supraleitung –
Energie-Übertragung heute und morgen’ [‘Three-phase AC, DC and superconducting systems – Power
transmission now and in the future’] from the German Copper Institute (DKI), Düsseldorf.
18
Fassbinder, Stefan: ‘Supraleitung – ein Teil zukünftiger Energieversorgung?’ [‘Superconductivity – What part
will it play in energy supplies of the future?], in de, vol. 9/2001, p. 38, appears in DKI reprint s180 ‘Drehstrom,
Gleichstrom, Supraleitung – Energie-Übertragung heute und morgen’ [‘Three-phase AC, DC and
superconducting systems – Power transmission now and in the future’] from the German Copper Institute
(DKI), Düsseldorf.

Page 53
SPECIAL SOLUTIONS FOR SPECIAL LOADS
Transformer losses, specifically no-load and load losses, have already been mentioned on several occasions. In
what follows, we will be focusing particularly on those load losses that arise when a transformer is subjected
to loads other than those for which it was designed—a situation that is not uncommon in today’s networks.
Such loads require careful analysis.
EVIL LOADS
While overloading a transformer can obviously be problematic, evil loads can be worse. But what do we mean
by evil load? If a transformer is fed—as ideally envisaged—with a sinusoidal voltage and subjected to a
sinusoidal current, it is relatively straightforward to analyse the losses that occur. The primary-side voltage
generates a slight magnetization or no-load current and thus a certain degree of no-load loss (iron loss) due to
the eddy currents that cannot be completely suppressed in the transformer’s core. The load current causes
ohmic loss (copper loss) in each winding. The Joule heating due to the no-load current in the primary winding
is negligible. Since the voltage and frequency are constant, so too is the iron loss. Additional power is lost
when stray magnetic fields induce eddy currents in electrically conducting structural components; this is
particularly the case with ferromagnetic materials that attract the stray magnetic fields. This loss is also
constant under no-load conditions and is in fact treated as part of the transformer’s no-load loss. The
capacitive load, which we looked at earlier, is the only traditional type of evil load since it generates a negative
voltage drop in the transformer and reinforces the no-load loss and the load voltage.
Under no-load conditions these stray magnetic fields are not particularly strong. A second type of stray
magnetic field appears when the transformer operates under load. This field stems from the main leakage
channel, i.e. the gap between the coils, and permeates the outermost coil. As described in Section 3.1, the gap
between the coils is needed in distribution and larger transformers for:
1) Insulation
2) Cooling
3) Limiting the short circuit current
The intensity of the leakage field is directly proportional to the magnitude of the load current and induces (in
proportion to its strength) what one could call an eddy voltage in those conducting components permeated by
the field. It is this voltage that drives the eddy currents in such components.
In the conductors, whose conductivity is almost an order of magnitude higher than that of the structural steel
components, an additional circulating current flows in a plane vertical to the direction of the main current and
whose magnitude increases with the thickening of the conductor. Assuming that the temperature is constant,
Ohm’s law applies and this transverse current is directly proportional to the eddy voltage. This part of the eddy
current loss therefore also varies as the square of the load current and is normally treated as a 5-10%
supplement that is added to the load loss calculated from the currents and winding resistances. Normally
meaning here ‘at the nominal frequency stated on the transformer’s rating plate’. An induced voltage is
proportional to the rate of change of the magnetic flux density, i.e. to the peak value and the frequency of the
excitation field. The eddy current loss therefore grows as the square of the current and the square of the
frequency.
If several currents of different frequencies (including direct currents) share a common conductor, the total
root mean-square (rms) current in the conductor is calculated by summing the squares of the individual values
and then taking the square root of the result. Let us first take a look at the following simplified example:

Page 54
A transformer with an eddy-current loss of 10% of its copper loss is subjected to the following load (and no
other): 70.7% of its rated current at the 50 Hz fundamental and 70.7% of its rated current at the 150 Hz third
harmonic. The total current is then:
𝐼 = √(0.707 𝐼 𝑁)2 + (0.70 𝐼 𝑁)2 = 𝐼 𝑁
The transformer is therefore operating with its rated current. The contribution of the fundamental frequency
to the eddy-current losses (also known as supplementary load losses PSupp) is given by:
𝑃𝑆𝑢𝑝𝑝 = 0.7072
𝑃𝑆𝑢𝑝𝑝𝑁 = 0.5 𝑃𝑆𝑢𝑝𝑝𝑁
The fundamental with an amplitude of 70.7% of the rated current therefore creates eddy-current losses that
are 50% of the eddy-current power when the device is operating at its rated load, that is, 5% of the nominal
copper losses. The third harmonic current (150 Hz) appearing on the output side, which is fed in as a third-
harmonic on the input side, causes an eddy current power loss of
𝑃𝑆𝑢𝑝𝑝 = 0.7072
𝑃𝑆𝑢𝑝𝑝𝑁 (
150 𝐻𝑧
50 𝐻𝑍
)
2
= 4.5 𝑃𝑆𝑢𝑝𝑝𝑁
To recap: The total rms current is exactly equal to the rated current. One might conclude from this that the
transformer will not become overloaded. However, the eddy-current losses generated jointly by both these
components of the total current are some five times greater than the corresponding losses the transformer
would generate at its rated load (50 Hz sinusoidal)—losses that would normally be regarded simply as a minor
contribution to the transformer’s copper losses. This effect has in the past led to overheating whose cause was
not immediately apparent.
Converter transformers have been around for a long time and these additional supplementary load losses
resulting from harmonic distortion effects are taken into account when dimensioning the device. The devices
are also designed to reduce the size of these losses. The size of the eddy currents can, where necessary, be
reduced by:
1) Splitting up the thick conductors into numerous mutually insulated individual wires (similar to the
method used in high-frequency coils wound with litz wire) or
2) By increasing the distances between certain mechanical components and the magnetic leakage field
or
3) By using components made of magnetically or electrically non-conducting materials. One such
material is, perhaps surprisingly, stainless steel which is not ferromagnetic—in contrast to
conventional structural steel. Furthermore, the conductivity of stainless steel, and therefore its ability
to conduct eddy currents, is about half that of conventional steel.
The sole use of this type of converter transformer is to feed a single power converter whose harmonic
spectrum is known beforehand; an example being the need to avoid overheating in a commercially available
transformer operating in the presence of harmonics such as those found in a high-rise office block. There are a
number of factors that can be used to calculate the loading capacity of the transformer relative to its rated
load. The so-called K-factor was introduced for this purpose in North America. As just explained, the K-factor
expresses the magnitude of the eddy current loss relative to the losses associated with a purely sinusoidal
load:
𝐾 = ∑ 𝐼 𝑛
2
𝑛2
𝑛
1

Page 55
where n is the harmonic order and In is the associated current expressed as a fraction of the rated current, as
in the numerical example discussed above. But this number is only of use if the terms of reference are known,
i.e. if we know what fraction of the transformer’s losses are made up by the eddy-current losses PSupp.
Normally, though, the only losses (if any) stated on the rating plate are the iron losses P0 and the copper losses
PCu.
In Europe, it is not the K factor, but factor K that is computed, in accordance with harmonization document HD
538.3.S1:
𝐾 = [1 +
𝑒
1 + 𝑒
(
𝐼ℎ
𝐼
)
2
∑ (𝑛 𝑞
(
𝐼 𝑛
𝐼1
)
2
)
𝑛=𝑁
𝑛+2
]
0.5
Where
𝐼 = (∑(𝐼 𝑛)2
𝑛=𝑁
𝑛=1
)
0.5
= 𝐼1 [∑ (
𝐼 𝑛
𝐼1
)
2𝑛=𝑁
𝑛=1
]
0.5
Figure 43 – Current and harmonic spectrum of an 11 watt compact fluorescent lamp (CFL). Top: CFL connected
to a transformer driving an average load in a residential area. Bottom: Simulation of a transformer operating
at its rated current and driving only CFLs.
That is probably enough to frighten most people off. If an electrical engineer or technician working on real
practical problems puts in the hard work and succeeds in correctly applying these exact formulae, he or she is
still left with the question of just what these results are actually saying and how exact they really are. Since the
transformer system being planned does not actually exist, the output values fed into the equations above can
only be based on assumptions, guesswork, or experience. Clearly neither prior measurement on the system
nor prior questioning of the subsequent user is possible. Many buildings today are planned and built and only
then does the owner seek tenants or buyers. Consequently, the harmonic profile of the power supply system is
unknown at the time of planning. We should no doubt adopt a more practical approach to this problem.

Page 56
If a conventional transformer is to be used, a conservative estimate would put the supplementary load losses
at 10% of the load loss specified for 50 Hz operation. Having made this assumption, let us now conduct a
thought experiment in which we fully load a transformer with a load made up purely of energy saver lamps
(Figure 43).
The rms values of the individual harmonic components (from 1st to 51st order) of the supply voltage and the
lamp current were read off the display of the measurement instrument (Table 12). The bottom row shows the
total rms values, which were computed as the square root of the sum of the squares of the individual values.
For this 11 watt CFL, the apparent power input is
230.7 𝑉 ∗ 64.8 𝑚𝐴 = 15.0 𝑉𝐴
For the sake of simplicity, let us now assume that the three-phase supply transformer has a rated power of 15
kVA and is driving a load made up solely of 1,000 of these 11 watt CFLs, distributed symmetrically across the
three phase conductors. Strictly, of course, if we want to meet this requirement, we would have to assume a
load of 999 lamps and a rated transformer power of 14.985 kVA—but this is only an illustrative example and
we can tolerate this minor inaccuracy. Since it is not so easy to actually find a transformer of the right type and
load it with 1,000 energy saver lamps, we chose to load it with a single lamp and then connect the short circuit
resistance Rsc and the short circuit impedance Xsc 1,000 times, as shown in Figure 43. It would seem that with
this load the transformer is operating at its maximum capacity, without being overloaded. But that is only how
things seem, if you ignore the eddy-current losses, which as already stated grow with the square of the current
and the square of the frequency. The third harmonic, for instance, generates an eddy-current loss that is
29.5% of the copper loss quoted for the transformer at its rated load. The fundamental, in contrast, generates
an eddy-current loss that is only 5.6% of PCu. The fundamental is significantly smaller than the total rms value
(itself equal to the rated current) and is the reason for our earlier assumption that the eddy-current loss is
about 10% of PCu.

Page 57
Table 12 – Values measured for a typical compact fluorescent lamp and the effect on the power supply
transformer, on the assumption that the transformer is operating at its rated current and these CFLs are its
only load.
If one now adds all the contributions from the fundamental to the 51st order, it is apparent that in such cases
of high harmonic distortion, the eddy-current losses in the transformer are not the 10% of the copper loss
assumed on the basis of a sinusoidal rated current, but are a massive 81.4%.
PRACTICAL MEASURES
So what should a technician or engineer facing a practical problem do, if, as is likely, the formulae discussed
above were of no real value? Start by memorizing, writing down, or copying the following values and make
sure they are available when you need them.
Leakage loss makes up no more than 10% at most of a transformer’s load losses. The figure for modern
transformers—and converter transformers in particular—is more likely to be 5% or less. This reduces the
additional supplementary load losses caused by harmonic distortion to about half, i.e. approximately 40% or
more of the copper loss. Rarely will a transformer have to drive a load made up only of compact fluorescent
lamps or similar devices such as switched-mode power supplies, though such a situation is conceivable for the
power supply system of a computer centre. But let’s stay with this extreme case in which the supplementary
Analysis of harmonics in an 11-W
Osram Dulux CFL with serial
impedance R =29.1W & X L=113W
U U² I L I L² Pad /PCu
n V V² mA mA²
1 230.2 52992.0 48.5 2352.3 5.6%
3 8.3 68.9 37.1 1376.4 29.5%
5 10.7 114.5 20.3 412.1 24.5%
7 4.3 18.5 5.3 28.1 3.3%
9 1.1 1.2 3.0 9.0 1.7%
11 2.3 5.3 3.8 14.4 4.2%
13 1.0 1.0 1.5 2.3 0.9%
15 0.6 0.4 1.5 2.3 1.2%
17 1.1 1.2 1.5 2.3 1.5%
19 0.5 0.3 0.9 0.8 0.7%
21 0.5 0.3 1.3 1.7 1.8%
23 0.6 0.4 0.8 0.6 0.8%
25 0.4 0.2 0.6 0.4 0.5%
27 0.6 0.4 0.8 0.6 1.1%
29 0.4 0.2 0.5 0.3 0.5%
31 0.3 0.1 0.5 0.3 0.6%
33 0.3 0.1 0.5 0.3 0.6%
35 0.3 0.1 0.4 0.2 0.5%
37 0.3 0.1 0.4 0.2 0.5%
39 0.3 0.1 0.3 0.1 0.3%
41 0.1 0.0 0.3 0.1 0.4%
43 0.2 0.0 0.2 0.0 0.2%
45 0.1 0.0 0.2 0.0 0.2%
47 0.1 0.0 0.2 0.0 0.2%
49 0.1 0.0 0.1 0.0 0.1%
51 0.1 0.0 0.1 0.0 0.1%
Supplementary losss: PSupp/PCu = 81.4%

Page 58
load losses make up at least 80% rather than the 10% of copper losses typically assumed. That is, at the rated
operating point we have 70% more load losses than originally calculated. In order to reduce the copper losses
(including the eddy-current and supplementary load losses) and thus the associated joule heating effect back
to a level that corresponds to 100% at 50 Hz, the rms load current used to select the transformer must be
multiplied by the following factor in order to take account of the quadratic dependence between the current
and the heat generated:
𝐾 = √
170%
100%
≈ 1.3
This means that the power of the transformer should be approximately 30% greater than that calculated on
the basis of the apparent power requirement Urms * Irms, as the remainder of the power loss, the no-load loss,
is essentially unaffected by the presence of harmonic currents. The no-load loss only increases when the
excitation voltage is non-sinusoidal. However in most cases, the voltage harmonics are far smaller than the
current harmonics. We will take a look at a counter example later.
Safety factors are not affected by any of this and they must remain part of the planning process. If the planning
process has taken into account all relevant factors except harmonics (redundancy, reserve capacity to
accommodate future load growth, etc.) and if it identifies a requirement of 1,000 kVA, then the planner should
(based on our arguments above) choose a transformer with a rated capacity of 1,250 kVA. Over the long-term
this also provides benefits for the customer, since a distribution transformer is at its most economical when
operating in the range of 24-47% of its rated power depending on the exact configuration of the transformer.
In addition, the neutral point must also be capable of handling 173% of the phase conductor current. In most
cases, this condition represents the most stringent criterion to be fulfilled. In distribution transformers we
normally assume that the neutral loading capacity is 100% and only then, if we have a single or double-phase
load (i.e. one of the limbs remains unloaded). If we actually do have a full, three-phase load, it is assumed that
the return currents in the neutral conductor will mutually annihilate each other. This, however, is actually only
true for harmonics in the order of 3n (so-called triple-n harmonics) and for the fundamental. Because they all
have the same phase, triple-n harmonics sum linearly in the neutral conductor. The squares of their
amplitudes add to the squares of the amplitudes of the other frequencies flowing in the neutral conductor to
generate the total rms return current, as shown in Table 7.
Under certain conditions, power supply faults can mutually cancel each other out. It is characteristic of the sort
of single-phase loads shown in Figure 43 that they only draw current from the power supply when the voltage
is close to its peak value, with the result that the current flows in short bursts of large magnitude. It should be
mentioned that in a three-phase system, it is the phase-to-neutral voltage being referred to. The voltage
between L2 and L3, for example, is 90º out-of-phase with the voltage between L1 and N. As a result the
voltage between L2 and L3 passes through zero when the voltage between L1 and N is reaching its peak value
(which is higher as a result of the evil load). While the voltage that drives this current collapses near its peak
value as a result of the network impedances, the distortion of the voltage between the phase conductors
shows the opposite picture (Figure 44). By selecting the transformer vector group, a phase-to-neutral voltage
(coil voltage) on the output side can be generated either by a phase-to-neutral voltage or a phase-to-phase
voltage on the input side, depending on the particular vector group chosen. That is, in principle, the same as if
one were to use a single-phase transformer to transform the voltage shown in the lower part of Figure 44 from
400 V down to 230 V and then use this voltage for part (ideally half) of those loads that originally caused the
voltage distortion evident in the upper part of Figure 44. Such an arrangement would almost completely
eliminate the voltage distortion. In other words: transformers with different vector groups could make a
substantial contribution to clearing up distortion in power supply networks, provided they were deployed in
the right mixture.

Page 59
Figure 44 – Measured and simulated phase-to-neutral voltage and phase-to-phase voltage in a residential area
during the final of the Football World Cup.
Such a method was in fact suggested by Professor Fender and others (Figure 45) and was realized in the early
years of electrical engineering at the Catholic University of Leuven (Louvain) in Belgium. In addition to the
advantage mentioned earlier in the section on vector groups, we can in the case of non-liner loads being
considered here, add the following benefit: If every second one of the usual Dyn5 transformers were to be
replaced by a corresponding transformer with a Dzn6 or Yzn6 vector group, then half of the single-phase
rectifier loads would (from the perspective of the MV supply) draw their current hump with a 30º phase lag
relative to the other half. Or put another way: some of the harmonics released into the power supply network
by single-phase loads would arrive at the MV network with a phase difference of 180º (relative to their higher
frequencies) and would cancel each other out. The simulation shown on the right in Figure 44 makes this point
clear. The middle section of Figure 44 also shows the phase angle of the fifth harmonic and one can see that
the fifth harmonic is responsible for most of the distortion in both the upper and the lower cases illustrated.
But since these two fifth-order harmonics have opposite polarity, if one can put it that way, they would cancel
each other out if half of each voltage were to arise in the same circuit (Figure 45).
So why doesn’t anyone make use of this method? Once again, it is because people confuse costs with price. A
transformer with a zigzag winding has a purchase price that is about 5% or even 10% higher. However, the
costs that arise do not appear explicitly on any one sheet of paper and are in fact paid by another cost centre,
making it someone else’s problem. Cynically perhaps, that is the real reason. The reason usually put forward is
that it would not be possible to connect the transformers in parallel. Doing so, however, would be impossible
anyhow in the sort of installations where this type of configuration makes sense, namely in high-rise office
buildings with their own LV supply network. The one vector group in one building, the other vector group in
the next or next-but-one building; that is all that would be needed. No one is suggesting that transformers
with different vector group codes should be installed side-by-side in the same building.

Page 60
Figure 45 – Using transformers with different vector groups leads to a phase shift in the current hump on the
MV leve.l (Source: Prof. Fender, Wiesbaden University of Applied Science).
The usual Dyn5 transformers also play their part in cleaning up the power supply system, by splitting the one
current hump per half-cycle and per phase conductor as generated by the single-phase rectifier loads into two
humps on two phase conductors on the input side (one leading by 60º, the other lagging by 60º) and located
either side of the peak voltage (see Figure 45b). A further effect is due to the triple-n harmonics, which are
practically short circuited in Dyn5 transformers. These harmonics flow in-phase from the consumer side
towards the transformer, returning via the neutral point as if all three phase conductors were connected in
parallel. These three currents demand an in-phase reverse flow of charge in the high voltage winding, which
they get by inducing a circulating current in the delta-connected HV winding. The only impedances they will
come across are the leakage reactance and the rather small winding resistances. But this only works if the
current on the low-voltage side really does arrive from all three phase conductors at the same time. The
reason is essentially the same as that given in Section 3.5 in the discussion of neutral loading capacity. It is for
this reason alone that the usual power supply voltages contain only small fractions of the third-order
harmonic, even though this is the predominant order in the current. Should it ever proved possible to gather
all of the distorting loads on one phase conductor and all of the linear loads on the other two, then the effect
would disappear. To demonstrate the effect (Figure 46) one can connect a two-kilowatt electric heater via a
rectifier and a smoothing capacitor to a conventional domestic power outlet (caution: the power drawn
increases to over 3 kW).
By combining this intrinsic ability of the Dyn5 transformer to clean up the power supply with the 30º phase
shift from the transformer with another vector group, we can almost restore the beauty of the original
sinusoidal curve (sinus: lat. bosom). However, effectively eliminating the voltage harmonics from the supply
network comes at a price. Restoring the quality of the voltage waveform results in a stronger flow of current
harmonics within and through the transformers. The circulating current induced in the delta winding in
particular generates additional heat loss. Such losses also contribute to the additional supplementary load
losses. An experiment carried out with a small transformer (Figure 47) illustrates just how quickly this
additional loss channel can attain a significant size. The series resistance of the delta-connected secondary
winding is 0.1 ohm. A THD of only 3.2% in the primary voltage results in a circulating current of 2.3 A (Figure
48). The resulting I² * R loss is therefore about 0.5 W. Half a watt is about 1% of the total copper losses and
doesn’t actually sound that bad. If the voltage THD rises to 6.4%, which can occur in practice, the joule heating
loss will increase to 4% of the total copper losses or 4.6 A. In this case that would correspond to 28% of the

Page 61
rated current. The transformer load would therefore have to be reduced by 28% solely in order to prevent
overheating of the secondary winding by the 150-Hz circulating current. The 30% over-dimensioning
introduced earlier to cope with the supplementary load losses caused by eddy currents would still need to be
taken into account separately.
Figure 46 – The asymmetric distribution of rectifier loads—in this case 2.5 kW on a single phase conductor—
results in a third harmonic of the voltage waveform that is larger than the fifth harmonic (see lower middle
panel).
The zero-sequence system, that is, the homopolar components of the input currents in the three-phase
transformer, can be identified by means of the three no-load currents (Figure 49). All three currents
simultaneously show a pronounced peak of the same polarity and this occurs six times per cycle, despite the
fact that the voltages driving these currents are each phase shifted by 120º relative to each other. If one
disconnects the delta-connected high voltage winding and thus interrupts the current in Figure 48, the
phenomenon described above disappears and the three currents become essentially independent of one
another.
One final remark on operating transformers in parallel. If you run two transformers with differing short circuit
voltages in parallel, you will find that the harmonic currents are distributed quite asymmetrically, in fact more
asymmetrically than the current’s fundamental component. The reason is that the leakage reactance is greater
for higher frequencies. This is another good reason not to connect transformers in parallel. A transformer with
a rated short circuit voltage of 4% has a short circuit voltage of almost 12% at 150 Hz. At 250 Hz it will have
increased further to nearly 20% because the inner voltage drop is predominantly inductive. Obviously, if the
rated short circuit voltage is 6%, these figures will be correspondingly higher. The only case where this does
not apply is for Dyn-type transformers and triple-n harmonics due to the formation of circulating currents.
But let’s take one more look at the voltage. There are certain situations in which the voltage can be so
distorted that it has a detrimental effect on the performance of the transformer that it is driving. For example,
it is an inherent characteristic of small UPS systems that when power loss occurs, they generate square-wave
rather than a sinusoidal voltage. However, a non-stepped square-wave will have a form factor that is 11%
smaller than that of a sinusoidal waveform. This 11% is the factor linking the mean value and the rms value.
The quoted value is always the rms value or at least it should be. But the degree of magnetization depends on
the mean value. The right rms value at the output side of a small UPS can cause significant over-excitation of
the transformer to which it is connected. In addition, the harmonic distortion of a square wave is so high that
very substantial no-load losses must be expected.

Page 62
Figure 47 – Experimental set-up for Figure 46.
Figure 48 – A THD of only 3.2% in the primary voltage drives a circulating current in the delta-connected
secondary winding whose size is about 14% of the rated current.

Page 63
Figure 49 – No-load currents in a small three-phase transformer with a YNd11 vector group.
As we have seen, transformers don’t just sit around humming all day long. They can be very beneficial in
helping to clean up low-quality power supply networks. That is not to say that they are not sometimes the
source of interference themselves. Computer monitors in a ground-floor office may well flicker because of
noise emissions or alternating magnetic fields from a transformer installed in the basement immediately
below. But the transformer is often not the guilty party. The stray fields generated by transformers are
typically not as large as they are often assumed to be. In many cases, the faults stem from cable runs in an ill-
conceived network configuration that permits currents originally planned for the neutral conductor to escape
to all other conducting structural components.
If this problem has been rectified, the only approach left is to increase the distance between the source of the
disturbance and any potentially susceptible equipment and to minimize the distance between the outward
and return current paths. It may also prove helpful in such situations to deploy a special transformer design in
which the bushings are arranged in a rectangular pattern near the base of the unit rather than in a row on the
lid as is the case in conventional designs (Figure 50 and Figure 51). This sort of engineering solution will not be
found described in any industrial standard. Indeed the manufacturer claims in an advert that: ‘When we build
transformers, the first thing we focus on is complying with our customers’ requirements and only then on
complying with standards. Why? Because it is customer needs and not standards that offer real scope for
product innovation.’ This is something that we have already seen in connection with transformer efficiency—
an area in which standardization is hardly outstanding. It has to be said, however, that much has been done in
the meantime to improve the standards, but the processes involved still take far too long as the standards are
increasingly subjected to international harmonization. Until the standards have finally caught up, industrial
companies will need to focus on technical creativity and on communication with their customers.

Page 64
Figure 50 – EMC transformer (Source: Rauscher & Stoecklin).
Figure 51 – Magnetic flux density as a function of the horizontal distance from the centre of the transformer
measured two metres above the transformer’s lid. (Source: Rauscher & Stoecklin).

Page 65
CONCLUSION
It was shown that—perhaps unexpectedly—there is an economically viable energy savings potential in
efficiency improvement of transformers, although transformer efficiencies are, by their nature, already very
high. This is true across the entire range of transformer power ratings, due to two anti-parallel trends:
 The efficiencies of bigger units (i.e. greater apparent power ratings) are better than those of smaller
units. This enables a wider margin of improvement among small transformers.
 The power densities are higher in bigger units, i.e. each kilogram of mass stands for a greater power
throughput in a bigger unit. As the principal measures of improvement are the use of more active
material (magnetic steel + copper or aluminium), improvements are more easily and quickly paid back
in bigger units.
Hence, the payback periods of efficiency improvement measures, relative to the average transformer lifetime,
are about the same from the smallest to the largest units.
Care has to be taken, however, because the load profile has a crucial impact upon the payback time. About
20% to 25% of the losses occur among the no-load or iron losses and are constant, even while the transformer
is kept active without any load connected. The other 75% to 80% of the losses are the so called load losses and
depend on the square of the load current. Technically there is a range of freedom to design a transformer with
more no-load losses and lower load losses or vice versa. As a result, knowing the type of load is crucial to
optimize the transformer design for minimal life cycle cost.
Moreover, consideration needs to be given to special types of load where the currents are not sinusoidal, even
if the feeding voltage is. Such non-sinusoidal currents will create additional losses and hence additional heat in
a transformer. If not taken into adequate consideration during transformer selection or design, this can not
only shift the optimal point of operation but will also substantially jeopardize the transformer’s life expectancy
due to overheating.

Transformers in Power Distribution Networks

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