TheJ&P Transformer Book

AcknowledgementsThe author wishes to express grateful thanks to many friends and colleagueswho have provided assistance in this major revision of the J & PTransformer Book. In particular to my good friend W. J. (Jim) Stevenswho has read every word and provided invaluable criticism and comment;to Professor Dennis Allan, FEng, from whom much help and guidancewas received; To Dr Colin Tindall of the Department of Electrical andElectronic Engineering, the Queen’s University, Belfast, who read my firstchapter and helped me to brush up on my somewhat rusty theory; to otherfriends who have read and commented on specific sections, and to thosewho have provided written contributions; Aziz Ahmad-Marican, Universityof Wales, Cardiff, on Petersen coil earthing; Alan Darwin, GEC Alsthom,on transformer noise; Mike Newman, Whiteley Limited, on transformerinsulation; Cyril Smith, Bowthorpe EMP Limited, on surge arresters; toJeremy Price, National Grid Company, for much constructive comment andadvice on the sections relating to many specialised transformers including arcfurnace transformers, HVDC converter transformers, traction transformers andrectifier transformers. Grateful thanks are also offered to many organisationswho freely provided assistance, as well as data, diagrams and photographswhich enabled the chapters to be so generously illustrated.These include:ABB Power T & D LimitedAccurate Controls LimitedAllenwest-Brentford LimitedAssociated Tapchangers LimitedBowthorpe EMP LimitedBritish StandardsBrüel & Kjær Division of Spectris (UK) LimitedBrush Transformers LimitedCarless Refining & Marketing LimitedCIGRÉCopper Development AssociationEmform LimitedERA Technology LimitedGEA Spiro-Gills LimitedGEC Alsthom Engineering Research CentreGEC Alsthom T & D Transformers LimitedGEC Alsthom T & D Protection and Control LimitedHawker Siddeley Transformers LimitedMerlin Gerin Lindley Thompson TransformersMerlin Gerin SwitchgearPeebles TransformersSouth Wales Transformers Limited

xivAcknowledgementsStrategy and SolutionsTCM TaminiWhiteley limitedIn addition to these, special thanks must be expressed to National Power Plcfor the loan of the original artwork for over 50 illustrations which originallyappeared in my chapter on transformers in Volume D of the Third Edition ofModern Power Station Practice published by Pergamon Press.Finally, despite the extensive revision involved in the production of theTwelfth Edition, some of the work of the original authors, H. Morgan Lacey,the late S. A. Stigant, the late A. C. Franklin, and D. P. Franklin, remains;notably much of the sections on transformer testing, transformer protection,magnetising inrush, parallel operation, and third harmonic voltages andcurrents, and for this due acknowledgement must be given.

1Transformer theory1.1 INTRODUCTIONThe invention of the power transformer towards the end of the nineteenthcentury made possible the development of the modern constant voltage ACsupply system, with power stations often located many miles from centres ofelectrical load. Before that, in the early days of public electricity supplies,these were DC systems with the source of generation, of necessity, close tothe 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 outputof an electrical generator and transform this to a voltage level which wouldenable 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 efficiencywhich, by the standards of the time, was nothing less than phenomenal.Today’s transmission and distribution systems are, of course, vastly moreextensive and greatly dependent on transformers which themselves are verymuch more efficient than those of a century ago; from the enormous generator transformers such as the one illustrated in Figure 7.5, stepping up theoutput of up to 19 000 A at 23.5 kV, of a large generating unit in the UK, to400 kV, thereby reducing the current to a more manageable 1200 A or so, tothe thousands of small distribution units which operate almost continuouslyday in day out, with little or no attention, to provide supplies to industrial anddomestic consumers.The main purpose of this book is to examine the current state of transformertechnology, primarily from a UK viewpoint, but in the rapidly shrinking andever more competitive world of technology it is not possible to retain one’s1

2Transformer theoryplace in it without a knowledge of all that is going on on the other side of theglobe, so the viewpoint will, hopefully, not be an entirely parochial one.For a reasonable understanding of the subject it is necessary to make abrief review of transformer theory together with the basic formulae and simplephasor diagrams.1.2 THE IDEAL TRANSFORMERVOLTAGE RATIOA power transformer normally consists of a pair of windings, primary andsecondary, linked by a magnetic circuit or core. When an alternating voltageis applied to one of these windings, generally by definition the primary, acurrent will flow which sets up an alternating m.m.f. and hence an alternatingflux in the core. This alternating flux in linking both windings induces ane.m.f. in each of them. In the primary winding this is the ‘back-e.m.f.’ and, ifthe transformer were perfect, it would oppose the primary applied voltage tothe extent that no current would flow. In reality, the current which flows is thetransformer magnetising current. In the secondary winding the induced e.m.f.is the secondary open-circuit voltage. If a load is connected to the secondarywinding which permits the flow of secondary current, then this current createsa demagnetising m.m.f. thus destroying the balance between primary appliedvoltage and back-e.m.f. To restore the balance an increased primary currentmust be drawn from the supply to provide an exactly equivalent m.m.f. sothat equilibrium is once more established when this additional primary currentcreates ampere-turns balance with those of the secondary. Since there is nodifference between the voltage induced in a single turn whether it is part ofeither the primary or the secondary winding, then the total voltage induced ineach of the windings by the common flux must be proportional to the numberof turns. Thus the well-known relationship is established that:E1 /E2 D N1 /N2 1.1 and, in view of the need for ampere-turns balance:I1 N1 D I2 N2 1.2 where E, I and N are the induced voltages, the currents and number of turnsrespectively in the windings identified by the appropriate subscripts. Hence,the voltage is transformed in proportion to the number of turns in the respectivewindings and the currents are in inverse proportion (and the relationship holdstrue 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 therate of change of flux linkage, and Lenz’s law which states that its polarityis such as to oppose that flux linkage change if current were allowed to flow.This is normally expressed in the forme D N d /dt

Transformer theory3but, for the practical transformer, it can be shown that the voltage induced perturn isE/N D K8m f 1.3 where K is a constant, 8m is the maximum value of total flux in Weberslinking that turn and f is the supply frequency in hertz.The above expression holds good for the voltage induced in either primaryor secondary windings, and it is only a matter of inserting the correct value ofN for the winding under consideration. Figure 1.1 shows the simple phasordiagram corresponding to a transformer on no-load (neglecting for the momentthe fact that the transformer has reactance) and the symbols have the significance shown on the diagram. Usually in the practical design of a transformer,the small drop in voltage due to the flow of the no-load current in the primarywinding is neglected.Figure 1.1 Phasor diagram for a single-phase transformer on opencircuit. Assumed turns ratio 1:1If the voltage is sinusoidal, which, of course, is always assumed, K is 4.44and equation (1.3) becomesE D 4.44f8N

4Transformer theoryFor design calculations the designer is more interested in volts per turn andflux density in the core rather than total flux, so the expression can be rewrittenin terms of these quantities thus:E/N D 4.44Bm Af ð 10 6where E/NBmAfDDDD 1.4 volts per turn, which is the same in both windingsmaximum value of flux density in the core, teslanett cross-sectional area of the core, mm2frequency of supply, HzFor practical designs Bm will be set by the core material which the designerselects and the operating conditions for the transformer, A will be selectedfrom a range of cross-sections relating to the standard range of core sizesproduced 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 todetermine the number of turns in each winding from the specified voltage ofthe winding.1.3 LEAKAGE REACTANCETRANSFORMER IMPEDANCEMention has already been made in the introduction of the fact that the transformation between primary and secondary is not perfect. Firstly, not all of theflux produced by the primary winding links the secondary so the transformercan be said to possess leakage reactance. Early transformer designers sawleakage reactance as a shortcoming of their transformers to be minimised to asgreat an extent as possible subject to the normal economic constraints. Withthe growth in size and complexity of power stations and transmission anddistribution systems, leakage reactance or, in practical terms, impedance,since transformer windings also have resistance gradually came to be recognised as a valuable aid in the limitation of fault currents. The normal methodof expressing transformer impedance is as a percentage voltage drop in thetransformer at full-load current and this reflects the way in which it is seen bysystem designers. For example, an impedance of 10% means that the voltagedrop at full-load current is 10% of the open-circuit voltage, or, alternatively,neglecting any other impedance in the system, at 10 times full-load current, thevoltage drop in the transformer is equal to the total system voltage. Expressedin symbols this is:Vz D %Z DIFL Zð 100E where Z is R2 C X2 , R and X being the transformer resistance and leakagereactance respectively and IFL and E are the full-load current and open-circuitvoltage of either primary or secondary windings. Of course, R and X maythemselves be expressed as percentage voltage drops, as explained below.The ‘natural’ value for percentage impedance tends to increase as the rating

Transformer theory5of the transformer increases with a typical value for a medium-sized powertransformer being about 9 or 10%. Occasionally some transformers are deliberately designed to have impedances as high as 22.5%. More will be saidabout transformer impedance in the following chapter.1.4 LOSSES IN CORE AND WINDINGSThe transformer also experiences losses. The magnetising current is requiredto take the core through the alternating cycles of flux at a rate determined bysystem frequency. In doing so energy is dissipated. This is known variouslyas the core loss, no-load loss or iron loss. The core loss is present wheneverthe transformer is energised. On open-circuit the transformer acts as a singlewinding of high self-inductance, and the open-circuit power factor averagesabout 0.15 lagging. The flow of load current in the secondary of the transformerand the m.m.f. which this produces are balanced by an equivalent primaryload current and its m.m.f., which explains why the iron loss is independentof the load.The flow of a current in any electrical system, however, also generates lossdependent upon the magnitude of that current and the resistance of the system.Figure 1.2 Phasor diagram for a single-phase transformersupplying a unity power factor load. Assumed turns ratio 1:1

6Transformer theoryTransformer windings are no exception and these give rise to the load loss orcopper loss of the transformer. Load loss is present only when the transformeris loaded, since the magnitude of the no-load current is so small as to producenegligible resistive loss in the windings. Load loss is proportional to the squareof the load current.Reactive and resistive voltage drops and phasor diagramsThe total current in the primary circuit is the phasor sum of the primaryload current and the no-load current. Ignoring for the moment the questionof resistance and leakage reactance voltage drops, the condition for a transformer supplying a non-inductive load is shown in phasor form in Figure 1.2.Considering now the voltage drops due to resistance and leakage reactanceof the transformer windings it should first be pointed out that, however theindividual voltage drops are allocated, the sum total effect is apparent at thesecondary terminals. The resistance drops in the primary and secondary windings are easily separated and determinable for the respective windings. TheFigure 1.3 Phasor diagram for a single-phase transformersupplying an inductive load of lagging power factor cos 2 .Assumed turns ratio 1:1. Voltage drops divided between primaryand secondary sides

Transformer theory7reactive voltage drop, which is due to the total flux leakage between the twowindings, is strictly not separable into two components, as the line of demarcation between the primary and secondary leakage fluxes cannot be defined.It has therefore become a convention to allocate half the leakage flux to eachwinding, and similarly to dispose of the reactive voltage drops. Figure 1.3shows the phasor relationship in a single-phase transformer supplying aninductive load having a lagging power factor of cos 2 , the resistance andleakage reactance drops being allocated to their respective windings. In factthe sum total effect is a reduction in the secondary terminal voltage. The resistance and reactance voltage drops allocated to the primary winding appear onthe diagram as additions to the e.m.f. induced in the primary windings.Figure 1.4 shows phasor conditions identical to those in Figure 1.3, exceptthat the resistance and reactance drops are all shown as occurring on thesecondary side.Figure 1.4 Phasor diagram for a single-phase transformersupplying an inductive load of lagging power factor cos 2 .Assumed turns ratio 1:1. Voltage drops transferred to secondarysideOf course, the drops due to primary resistance and leakage reactance areconverted to terms of the secondary voltage, that is, the primary voltage dropsare divided by the ratio of transformation n, in the case of both step-up and

8Transformer theorystep-down transformers. In other words the percentage voltage drops considered as occurring in either winding remain the same.To transfer primary resistance values R1 or leakage reactance values X1to the secondary side, R1 and X1 are divided by the square of the ratio oftransformation n in the case of both step-up and step-down transformers.The transference of impedance from one side to another is made as follows:LetZs D total impedance of the secondary circuitincluding leakage and load characteristicsZ0s D equivalent value of Zs when referred tothe primary windingThensoN2N2 E2N2I2 Dand E2 DE1N1N1 ZsN1 N2 2 E10I2 DN1ZsI02 DAlso,V1 D E1 C I02 Z1whereE1 D I02 Z0sThereforeI02 D E1 /Z0s 1.5 1.6 Comparing equations (1.5) and (1.6) it will be seen that Z0s D Zs N1 /N2 2 .Figure 1.5 Phasor diagram for a single-phase transformersupplying a capacitive load of leading power factor cos 2 .Assumed turns ratio 1:1. Voltage drops transferred to secondaryside

Transformer theory9The equivalent impedance is thus obtained by multiplying the actualimpedance of the secondary winding by the square of the ratio oftransformation n, i.e. N1 /N2 2 . This, of course, holds good for secondarywinding leakage reactance and secondary winding resistance in addition tothe reactance and resistance of the external load.Figure 1.5 is included as a matter of interest to show that when the loadhas a sufficient leading power factor, the secondary terminal voltage increasesinstead of decreasing. This happens when a leading current passes through aninductive reactance.Preceding diagrams have been drawn for single-phase transformers, but theyare strictly applicable to polyphase transformers, so long as the conditions forFigure 1.6 Phasor diagram for a three-phase transformer supplyingan inductive load of lagging power factor cos 2 . Assumed turnsratio 1:1. Voltage drops transferred to secondary side. Symbolshave the same significance as in Figure 1.4 with the addition of A,B and C subscripts to indicate primary phase phasors, and a, band c subscripts to indicate secondary phase phasors

10Transformer theoryall the phases are shown. For instance Figure 1.6 shows the complete phasordiagram for a three-phase star/star-connected transformer, and it will be seenthat this diagram is only a threefold repetition of Figure 1.4, in which primaryand secondary phasors correspond exactly to those in Figure 1.4, but the threesets representing the three different phases are spaced 120 apart.1.5 RATED QUANTITIESThe output of a power transformer is generally expressed in megavoltamperes (MVA), although for distribution transformers kilovolt-amperes (kVA)is generally more appropriate, and the fundamental expressions for determiningthese, assuming sine wave functions, are as follows:Single-phase transformersOutput D 4.44f8m NI with the multiplier 10 3 for kVAand 10 6 for MVAThree-phase transformerspOutput D 4.44f8m NI ð 3 with the multiplier 10 3 for kVAand 10 6 for MVAIn the expression for single-phase transformers, I is the full-load current in thetransformer windings and also in the line; for three-phase transformers, I isthe full-load current in each line connected to the transformer. That part of theexpression representing the voltageprefers to the voltage between line terminalsof the transformer. The constant 3 is a multiplier for the phase voltage inthe case of star-connected windings, and for the phase current in the case ofdelta-connected windings, and takes account of the angular displacement ofthe phases.Alternatively expressed, the rated output is the product of the ratedsecondary (no-load) voltage E2 and the rated full-load output current I2although these do not, in fact, occur simultaneously and, in the case ofpolyphase transformers, by multiplying by the appropriate phase factor andthe appropriate constant depending on the magnitude of the units employed.It should be noted that rated primary and secondary voltages do occursimultaneously at no-load.Single-phase transformersOutput D E2 I2 with the multiplier 10 3 for kVAand 10 6 for MVA

Transformer theory11Three-phase transformerspOutput D E2 I2 ð 3 with the multiplier 10 3 for kVAand 10 6 for MVAThe relationships between phase and line currents and voltages for star- andfor delta-connected three-phase windings are as follows:Three-phase star connectionphase current D line current I D VA/ E ðpphase voltage D E/ 3p3 Three-phase delta conn

7.8 Distribution transformers 707 7.9 Scott and Le Blanc connected transformers 729 7.10 Rectifier transformers 736 7.11 AC arc furnace transformers 739 7.12 Traction transformers 745 7.13 Generator neutral earthing transformers 750 7.14 Transformers for electrostatic precipitators 756 7.15 Series reactors 758 8 Transformer enquiries and .