Industrial Power Transformers--Design fundamentals (part 1)

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There are two basic types of transformers categorized by their winding/core configuration: (a) shell type and (b) core type. The difference is best under stood by reference to FIG. 1.

FIG. 1 Transformer types

In a shell-type transformer the flux-return paths of the core are external to and enclose the windings. FIG. 1(a) shows an example of a three-phase shell-type transformer.

Whilst one large power transformer manufacturer in North America was noted for his use of shell-type designs, core-type designs predominate in the throughout most of the world so that this guide will be restricted to the description of core-type transformers except where specifically identified otherwise.

FIG. 2 Typical core forms for single-phase transformers

Because of the intrinsically better magnetic shielding provided by the shell type arrangement, this is particularly suitable for supplying power at low voltage and heavy current, as for example in the case of arc furnace transformers.

Core-type transformers have their limbs surrounded concentrically by the main windings as shown in FIG. 1(b) which represents a three-phase three-limb arrangement. With this configuration, having top and bottom yokes equal in cross-section to the wound limbs, no separate flux-return path is necessary, since for a balanced three-phase system of fluxes, these will sum mate to zero at all times. In the case of a very large transformer which may be subject to height limitations, usually due to transport restrictions, it may be necessary to reduce the depth of the top and bottom yokes. These may be reduced until their cross-sectional area is only 50 percent of that of the wound limb so that the return flux is split at the top of the limb with half returning in each direction. Clearly in this case return yokes must be provided, so that the arrangement becomes as shown in FIG. 1(c). The magnetic circuits of these three-phase five-limb core-type transformers behave differently in relation to zero-sequence and third harmonic fluxes than do the more commonly used three-phase three-limb cores and this aspect will be discussed in greater depth later in this section. Of course, it is always necessary to provide a return-flux path in the case of single-phase core-type transformers and various configurations are possible according as to whether these have one or two wound limbs.

FIG. 2 shows some of the more common arrangements.

A three-phase transformer has considerable economic advantages over three single-phase units used to provide the same function, so that the great majority of power transformers are of three-phase construction. The exceptions occur at each end of the size range.

Single-phase transformers are used at the remote ends of rural distribution systems in the provision of supplies to consumers whose load is not great enough to justify a three-phase supply. These transformers almost invariably have both limbs wound. A typical core and coils assembly of this type is shown in FIG. 3.

Single-phase units are also used for the largest generator transformers.

Often the reason for this is to reduce the transport weight and dimensions, but there are other factors which influence the argument such as limiting the extent of damage in the event of faults and the economics of providing spare units as well as the ease of moving these around in the event of failures in service.

These arguments will be discussed in greater length in the section dealing with generator transformers. In the case of these very large single-phase units the high initial cost justifies a very careful study of all the economic factors affecting each individual design. Such factors include the merits of adopting a one limb wound or a two-limb wound arrangement. Because the cost of windings usually constitutes a significant proportion of the total cost of these units, it is normally more economic to adopt a single-limb wound arrangement. The core and coils of a large single-phase generator transformer are shown in FIG. 4.

The other factor descriptive of the type of transformers which constitute the great majority of power transformers is that they are double wound. That is they have two discrete windings, an LV and an HV winding. This fact is of great importance to the designers of electrical power systems in that it provides a degree of isolation between systems of different voltage level and limits the extent that faults on one system can affect another. More will be said about this in a later section.

FIG. 3 Single-phase rural-type transformer with C-type core, rated at 16 kVA 11 000/200-250 V (Allenwest Brentford)

FIG. 4 Single-phase generator transformer core and winding assembly (cruciform core) 267 MVA 432/23.5 kV bank ratio (Peebles Transformers)


Most electrical systems require an earth, in fact in the UK there is a statutory requirement that all electrical systems should have a connection with earth.

This will be discussed further in Section 6.2 which deals in greater detail with the subject of earthing of the neutral. It is convenient, therefore, if the sup ply winding of the transformer feeding the system can be star connected and thereby provide a neutral for connecting to earth, either solidly or via a fault current limiting resistor or other such device. It is also desirable that a three phase system should have a delta to provide a path for third harmonic currents in order to eliminate or reduce third harmonic voltages in the waveform, so that considering a step-down transformer, for example, it would be convenient to have the HV winding delta connected and the LV star connected with the neutral earthed.

If a two-winding three-phase transformer has one-winding delta connected and the other in star, there will be a phase shift produced by the transformer as can be seen by reference to FIG. 5. In the example shown in the diagram, this phase shift is 30º after 12 o'clock (assuming clockwise rotation) which is referred to as the 1 o'clock position. The primary delta could also have been made by connecting A1B2, B1C2 and C1A2 which would result in a phase displacement of 30º anticlockwise to the '11 o'clock' position. It has also been assumed that the primary and secondary windings of the transformer have been wound in the same sense, so that the induced voltages appear in the same sense. This produces a transformer with subtractive polarity, since, if the line terminals of a primary and secondary phase are connected together, the volt ages will subtract, as can be seen in FIG. 5(c). If the secondary winding is wound in the opposite sense to the primary, additive polarity will result. The full range of phase relationships available by varying primary and secondary connections can be found in EN 60076, Part 1. There are many circumstances in which it is most important to consider transformer phase relationships, particularly if transformers are to be paralleled or if systems are to be interconnected. This subject will therefore be considered in some detail in Section 6.4 which deals with the requirements for paralleling transformers.

Star/star-connected transformers

One such situation which creates a need for special consideration of transformer connections occurs in the electrical auxiliary system of a power station. When the generator is synchronized to the system and producing power, a small part of its output is generally tapped off the generator terminals to pro vide a supply for the electrical auxiliaries and this is usually stepped down to a voltage which is less than the generator voltage by means of the unit transformer. Such an arrangement is shown in FIG. 6, with a 660 MW generator generating at 23.5 kV stepped up to 400 kV via its generator transformer and with a unit transformer providing a supply to the 11 kV unit switchboard.

Whilst the unit is being started up, the 11 kV unit board will normally be sup plied via the station transformer which will take its supply from the 400 kV system, either directly or via an intermediate 132 kV system. At some stage during the loading of the generator, supplies will need to be changed from station to unit source which will involve briefly paralleling these and so, clearly, both supplies must be in phase.

FIG. 5 Winding connections, phasor and polarity diagram

FIG. 6 Power station auxiliary system

The generator transformer will probably be connected star/delta, with the 23.5 kV phasor at 1 o'clock, that is YNd1. The 23.5/11 kV unit transformer will be connected delta/star, with its 11 kV phasor at the 11 o'clock position, that is Dyn11. This means that the 11 kV system has zero-phase shift com pared with the 400 kV system; 400 and 132 kV systems are always in phase with each other so that regardless of whether the station transformer is connected directly to the 400 or 132 kV, it must produce zero-phase displacement and the simplest way of doing this is to utilize a star/star transformer. Such an arrangement ensures that both 400 and 11 kV systems are provided with a neutral for connection to earth, but fails to meet the requirement that the transformer should have one winding connected in delta in order to eliminate third harmonic voltages. It is possible, and it may indeed be necessary, to provide a delta-connected tertiary winding in order to meet this requirement as will be explained later.

The interconnected star connection

The interconnected star connection is obtained by subdividing the transformer windings into halves and then interconnecting these between phases. One possible arrangement is shown in FIG. 7(a), producing a phasor diagram of FIG. 7(b). There is a phase displacement of 30º and, by varying the interconnections and sense of the windings, a number of alternatives can be produced.

The interconnected star arrangement is used to provide a neutral for connection to earth on a system which would not otherwise have one, for example when the LV winding of a step-down transformer is delta connected as shown in FIG. 8. It has the special feature that it has a high impedance to normal balanced three-phase voltages, but a low impedance to the flow of single-phase currents. More will be said about interconnected star transformers in Section 7.7 and about their use in providing a neutral for connection to earth in Section 6.2.

FIG. 7 Interconnected-star winding arrangement


It is possible and in some circumstances economically advantageous for a section of the HV winding to be common with the LV winding. Such transformers are known as autotransformers and these are almost exclusively used to interconnect very high voltage systems, for example in the UK the 400 kV and 132 kV networks are interconnected in this way. Three-phase autotransformers are invariably star/star connected and their use requires that the systems which they interconnect are able to share a common earthing arrangement, usually solid earthing of the common star-point. For very expensive very high voltage transformers the economic savings resulting from having one winding in common can offset the disadvantages of not isolating the interconnected systems from each other. This will be discussed further in the later section dealing specifically with autotransformers.

FIG. 8 Transformer with delta secondary and interconnected star earthing transformer with neutral connected to earth


As explained in Section 1, for a given supply frequency the relationship between volts per turn and total flux within the core remains constant. And since for a given core the cross-sectional area of the limb is a constant, this means that the relationship between volts per turn and flux density also remains constant at a given supply frequency. The number of turns in a particular winding will also remain constant. (Except where that winding is pro vided with tappings, a case which will be considered shortly.) The nominal voltage and frequency of the system to which the transformer is connected and the number of turns in the winding connected to that system thus determines the nominal flux density at which the transformer operates.

The designer of the transformer will wish to ensure that the flux density is as high as possible consistent with avoiding saturation within the core. System frequency is normally controlled within close limits so that if the voltage of the system to which the transformer is connected also stays within close limits of the nominal voltage then the designer can allow the nominal flux density to approach much closer to saturation than if the applied voltage is expected to vary widely.

It is common in the UK for the voltage of a system to be allowed to rise up to 10 percent above its nominal level, for example at times of light system load.

The nominal flux density of the transformers connected to these systems must be such as to ensure a safe margin exists below saturation under these conditions.


Transformers also provide the option of compensating for system regulation, as well as the regulation which they themselves introduce, by the use of tap pings which may be varied either on-load, in the case of larger more important transformers, or off-circuit in the case of smaller distribution or auxiliary transformers.

Consider, for example, a transformer used to step down the 132 kV grid system voltage to 33 kV. At times of light system load when the 132 kV system might be operating at 132 kV plus 10 percent, to provide the nominal voltage of 33 kV on the low voltage side would require the HV winding to have a tap ping for plus 10 percent volts. At times of high system load when the 132 kV system voltage has fallen to nominal it might be desirable to provide a voltage higher than 33 kV on the low voltage side to allow for the regulation which will take place on the 33 kV system as well as the regulation internal to the transformer. In order to provide the facility to output a voltage of up to 10 percent above nominal with nominal voltage applied to the HV winding and allow for up to 5 percent regulation occurring within the transformer would require that a tapping be provided on the HV winding at about 13 percent. Thus, the volts per turn within the transformer will be:

100/87 = 1.15 approximately

so that the 33 kV system voltage will be boosted overall by the required 15 percent.

It is important to recognize the difference between the two operations described above. In the former the transformer HV tapping has been varied to keep the volts per turn constant as the voltage applied to the transformer varies. In the latter, the HV tapping has been varied to increase the volts per turn in order to boost the output voltage with nominal voltage applied to the transformer. In the former case, the transformer is described as having HV tappings for HV voltage variation; in the latter, it could be described as having HV tappings for LV voltage variation. The essential difference is that the former implies operation at constant flux density whereas the latter implies variable flux density.

Except in very exceptional circumstances transformers are always designed as if they were intended for operation at constant flux density. In fixing this value of nominal flux density some allowance is made for the variations which may occur in practice. The magnitude of this allowance depends on the application and more will be said on this subject in Section 7 when specific types of transformers are described.


In Section 1, it was explained that the leakage reactance of a transformer arises from the fact that all the flux produced by one winding does not link the other winding. As would be expected, then, the magnitude of this leakage flux is a function of the geometry and construction of the transformer. FIG. 9 shows a part section of a core-type transformer taken axially through the center of the wound limb and cutting the primary and secondary windings. The principal dimensions are marked in the figure, as follows:

l is axial length of windings (assumed the same for primary and secondary)

a is the radial spacing between windings

b is the radial depth of the winding next to the core

c is the radial depth of the outer winding

FIG. 9 Arrangement of windings on single-phase and three phase cores

If mlt is then the mean length of turn of the winding indicated by the appropriate subscript, mltb for the inner winding, mltc for the outer winding and mlta for a hypothetical winding occupying the space between inner and outer windings, then the leakage reactance in percent is given by the expression:

%X _ KF(3amlta _ bmltb _ cmltc)/Fml (eqn. 1)

where K is a constant of value dependent on the system of units used

F is equal to the ampere-turns of primary or secondary winding, that is m.m.f. per limb

Fm is the maximum value of the total flux in the core

The above equation assumes that both LV and HV windings are the same length, which is rarely the case in practice. It is also possible that a tapped winding may have an axial gap when some of the tappings are not in circuit.

It is usual therefore to apply various correction factors to l to take account of these practical aspects. However, these corrections do not change the basic form of the equation.

Equation (eqn. 1) together with (eqn. 1) and (eqn. 2) given in the previous section determine the basic parameters which fix the design of the transformer. The m.m.f. is related to the MVA or kVA rating of the transformer and the maximum total flux, Fm, is the product of the maximum flux density and core cross-sectional area. Flux density is determined by consideration of the factors identified in the previous section and the choice of core material. The transformer designer can thus select a combination of Fm and I to provide the value of reactance required. In practice, of course, as identified in the previous section, the transformer winding has resistance as well as reactance so the parameter which can be measured is impedance. In reality for most large power transformers the resistance is so small that there is very little difference between reactance and impedance.

For many years the reactance or impedance of a transformer was considered to be simply an imperfection creating regulation and arising from the unavoidable existence of leakage flux. It is now recognized, however, that transformer impedance is an invaluable tool for the system designer enabling him to determine system fault levels to meet the economic limitations of the switch gear and other connected plant. The transformer designer is now, therefore, no longer seeking to obtain the lowest transformer impedance possible but to meet the limits of minimum and maximum values on impedance specified by the system designer to suit the economics of his system design. (It may, of course, be the case that he would like to see manufacturing tolerances abolished and no variation in impedance with tap position, but generally an accept able compromise can be reached on these aspects and they will be discussed at greater length later.) It is worthwhile looking a little more closely at the factors determining impedance and how these affect the economics of the transformer. The relationship must basically be a simple one. Since reactance is a result of leakage

flux, low reactance must be obtained by minimizing leakage flux and doing this requires as large a core as possible. Conversely, if high reactance can be tolerated a smaller core can be provided. It is easy to see that the overall size of the transformer must be dependent on the size of the core, so that a large core means large and expensive transformer, a small core means a less expensive transformer. Hence, providing a low reactance is expensive, a high reactance is less expensive. Nevertheless within the above extremes there is a band of reactances for a particular size of transformer over which the cost variation is fairly modest.

Looking more closely at Eq. (eqn. 1) gives an indication of the factors involved in variation within that band. A larger core cross-section, usually referred to as the frame size, and a longer l will reduce reactance and, alternatively, reducing frame size and winding length will increase reactance. Unfortunately, the designer's task is not quite as simple as that since variation of any of the principal parameters affects the others which will then also affect the reactance.

For example, increasing Fm not only reduces reactance, because of its appearance in the denominator of Eq. (1), but it also reduces the number of turns, as can be seen by referring to Eq. (eqn. 1), which will thus reduce reactance still further. The value of I can be used to adjust the reactance since it mainly affects the denominator of Eq. (1). Nevertheless, if l is reduced, say, to increase reactance, this shortening of the winding length results in an increase in the radial depth (b and c) of each winding, in order that the same number of turns can be accommodated in the shorter axial length of the winding. This tends to increase the reactance further. Another means of fine tuning of the reactance is by variation of the winding radial separation, the value 'a' in Eq. (1). This is more sensitive than changes in b and c since it is multiplied by the factor 3, and the designer has more scope to effect changes since the dimension 'a' is purely the dimension of a 'space.' Changes in the value of 'a' also have less knock-on effect although they will, of course, affect 'mltc.' For a given trans former 'a' will have a minimum value determined by the voltage class of the windings and the insulation necessary between them. In addition, the designer will not wish to artificially increase 'a' by more than a small amount since this is wasteful of space within the core window.

It should be noted that since the kVA or MVA factor appears in the numerator of the expression for percent reactance, the value of reactance tends to increase as the transformer rating increases. This is of little consequence in most transformers, as almost any required reactance can normally be obtained by appropriate adjustment of the physical dimensions, but it does become very significant for large generator transformers, as permissible transport limits of dimensions and weight are reached. It is at this stage that the use of single phase units may need to be considered.

Table 1 lists typical impedance values for a range of transformer ratings which may be found in transmission and distribution systems. It should be recognized that these are typical only and not necessarily optimum values for any rating. Impedances varying considerably from those given may well be encountered in any particular system.

Table 1 Typical percentage impedances of 50 Hz three-phase transformers


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