1.1 INTRODUCTION

The invention of the power transformer towards the end of the nineteenth century made possible the development of the modern constant voltage AC supply system, with power stations often located many miles from centres of electrical load. Before that, in the early days of public electricity supplies, these were DC systems with the source of generation, of necessity, close to the point of loading.

Pioneers of the electricity supply industry were quick to recognise the benefits of a device which could take the high current relatively low voltage output of an electrical generator and transform this to a voltage level which would enable it to be transmitted in a cable of practical dimensions to consumers who, at that time, might be a mile or more away and could do this with an efficiency which, by the standards of the time, was nothing less than phenomenal.

Todays transmission and distribution systems are, of course, vastly more extensive and greatly dependent on transformers which themselves are very much more efficient than those of a century ago; from the enormous generator transformers such as the one illustrated in Fig. 7.5, stepping up the output of up to 19 000 A at 23.5 kV, of a large generating unit in the UK, to 400 kV, thereby reducing the current to a more manageable 1200 A or so, to the thousands of small distribution units which operate almost continuously day in day out, with little or no attention, to provide supplies to industrial and domestic consumers.

The main purpose of this book is to examine the current state of transformer technology, inevitably from a UK viewpoint, but in the rapidly shrinking and ever more competitive world of technology it is not possible to retain one’s place in it without a knowledge of all that is going on the other side of the globe, so the viewpoint will, hopefully, not be an entirely parochial one.

For a reasonable understanding of the subject it is necessary to make a brief review of transformer theory together with the basic formulae and simple phasor diagrams.

1.2 THE IDEAL TRANSFORMER: VOLTAGE RATIO

A power transformer normally consists of a pair of windings, primary and secondary, linked by a magnetic circuit or core. When an alternating voltage is applied to one of these windings, generally by definition the primary, a current will flow which sets up an alternating m.m.f. and hence an alternating flux in the core. This alternating flux in linking both windings induces an e.m.f. in each of them. In the primary winding this is the ‘back-e.m.f’ and, if the transformer were perfect, it would oppose the primary applied voltage to the extent that no current would flow. In reality, the current which flows is the transformer magnetising current. In the secondary winding the induced e.m.f. is the secondary open-circuit voltage. If a load is connected to the secondary winding which permits the flow of secondary current, then this current creates a demagnetising m.m.f. thus destroying the balance between primary applied voltage and back-e.m.f. To restore the balance an increased primary current must be drawn from the supply to provide an exactly equivalent m.m.f. so that equilibrium is once more established when this additional primary current creates ampere-turns balance with those of the secondary. Since there is no difference between the voltage induced in a single turn whether it is part of either the primary or the secondary winding, then the total voltage induced in each of the windings by the common flux must be proportional to the number of turns. Thus the well-known relationship is established that:

and, in view of the need for ampere-turns balance:

where E, I and N are the induced voltages, the currents and number of turns respectively in the windings identified by the appropriate subscripts. Hence, the voltage is transformed in proportion to the number of turns in the respective windings and the currents are in inverse proportion (and the relationship holds true for both instantaneous and r.m.s. quantities).

The relationship between the induced voltage and the flux is given by reference to Faraday’s law which states that its magnitude is proportional to the rate of change of flux linkage and Lenz’s law which states that its polarity such as to oppose that flux linkage change if current were allowed to flow. This is normally expressed in the form

but, for the practical transformer, it can be shown that the voltage induced per turn is

where K is a constant, Φm is the maximum value of total flux in Webers linking that turn and f is the supply frequency in Hertz.

The above expression holds good for the voltage induced in either primary or secondary windings, and it is only a matter of inserting the correct value of N for the winding under consideration. Figure 1.1 shows the simple phasor diagram corresponding to a transformer on no-load (neglecting for the moment the fact that the transformer has reactance) and the symbols have the significance shown on the diagram. Usually in the practical design of transformer, the small drop in voltage due to the flow of the no-load current in the primary winding is neglected.

If the voltage is sinusoidal, which, of course, is always assumed, K is 4.44 and Eq. (1.3) becomes

For design calculations the designer is more interested in volts per turn and flux density in the core rather than total flux, so the expression can be rewritten in terms of these quantities thus:

where E/N = volts per turn, which is the same in both windings

Bm = maximum value of flux density in the core, Tesla

A = net cross-sectional area of the core, mm2

f = frequency of supply, Hz.

For practical designs Bm will be set by the core material which the designer selects and the operating conditions for the transformer, A will be selected from a range of cross-sections relating to the standard range of core sizes produced by the manufacturer, whilst f is dictated by the customer’s system, so that the volts per turn are simply derived. It is then an easy matter to determine the number of turns in each winding from the specified voltage of the winding.