Transformer Book

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TRANSFORMER BOOK

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Introduction

In current transformer design, the core characteristics must be carefully selectedbecause excitation current I e essentially subtracts from the metered current andaffects the ratio and phase angle of the output current.

The higher the exciting current or core loss the larger the error

Measuring or protective current transformers?

Measuring current transformer

Permeability of the core material high and core loss low => exciting current small (Ife<<) => current error small. The exciting current determines the maximum accuracythat can be achieved with a current transformer => Study accuracy classes

Protective current transformer

Permeability of the core material is low => When remanence is reduced to a lowerlevel (increase the useful flux density, gapping), the voltage spikes produced by theleakage inductance due to the transformer saturation will be eliminated. In linearcurrent transformers there are generally air gaps in the iron core to reduce the timeconstant and remanence. Such current transformers are used only to protect objectsof major importance that require a short tripping time.

Selecting core material

A current transformer design

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When choosing a core material a reasonable value for B m (0,2 ... 0,3 T) typicallyresults in L c and R fe values large enough to reduce the current flowing in theseelements so as to satisfy the ratio and phase requirements.

Window utilization factor

The window utilization factor (K u = S 1 x S 2 x S 3 x S 4 ) is the amount of copperthat appears in the window area or transformer of inductor. The window utilizationfactor is influenced by four different factors: (1) wire insulation, (2) wire lay (fillfactor), (3) bobbin area and (4) insulation required for multilayer windings orbetween windings. In the design of high-current of low-current transformers, theratio of conductor area over total wire area can vary from 0,941 to 0,673 dependingon the wire size. The wire lay or fill factor can vary from 0,7 to 0,5, depending onthe winding technique. The amount and the type of insulation are dependent on thevoltage. [McLyman.]

A transformer intended to supply measuring instruments, meters, relays and othersimilar apparatus



Effect of Gapping

[McLyman.]

Air gap increases the effective length of the magnetic path

Air-gapped current transformers

These are auxiliary current transformers in which a small air gap is included in thecore to produce a secondary voltage output proportional in magnitude to current inthe primary winding. Sometimes termed ´transactors´ or ´quadrature currenttransformers´, this form of current transformer has been used as an auxiliarycomponent of unit protection schemes in which the outputs into multiple secondarycircuits must remain linear for and proportioned to the widest practical range ofinput currents.

[Protective Relays Application Guide.]

Anti-remanence current transformers

A variation in the overdimensioned class of current transformer has small gap(s) inthe core magnetic circuit, thus reducing the possible remanent flux fromapproximately 90% of saturation value to some 10% only. These gap(s) are quitesmall, for example 0.12mm total, and so within the core saturation limits. Errors incurrent transformation are thereby significantly reduced when compared with thosewith the gapless type of core.




Linear current transformers

The ´linear´ current transformer constitutes an even more radial departure from thenormal solid core CT in that it incorporates an appreciable air cap, for example7.5-10mm. As its name implies the magnetic behaviour tends to linearization by theinclusion of this gap in the magnetic circuit. However, the purpose of introducingmore reluctance into the magnetic circuit is to reduce the value of magnetizingreactance, this in turn reduces the secondary time-constant of the CT therebyreducing the overdimensioning factor necessary for faithful transformation.


The time constant of the circuit depends on the inductance of the coil and on theresistance in the circuit in accordance to the following simple formula:

Back to previous page Back to the main page



General

Measuring current transformer = A current transformer intended tosupply indicating instruments, integrating meters and similarapparatus.

Definitions

Composite error = Under steady-state conditions, the r.m.s value ofthe difference between:

a) the instantaneous values of the primary current

b) the instantaneous values of the actual secondary current multipliedby the rated transformation ratio.

The composite error εc is generally expressed as a percentage of the

r.m.s. values of the primary current according to the formula:

K n= rated transformation ratioI p= r.m.s. value of the primary currenti p= instantaneous value of the primary currenti s= instantaneous value of the secondary current



T= duration of one cycle

Rated instrument limit primary current = The value of the minimumprimary current at which the composite error of the measuringcurrent transformer is equal to or greater than 10%, the secondaryburden being equal to the rated burden

Instrument security factor = The ratio of rated instrument limitprimary current to the rated primary current.

Accuracy requirements

For measuring current transformers the accuracy class is designatedby the highest permissible percentage current error at rated currentprescribed for the accuracy class concerned.

The standard accuracy classes for measuring current transformersare: 0,1 - 0,2 - 0,5 - 1 - 3 - 5

Accuracyclass

+/- Percentagecurrent error atpercentage of ratedcurrent shown below

+/- Phase displacement atpercentage of rated current shownbelow

Minutes Centiradians5 20 100 120 5 20 100 120 5 20 100 120

0,1 0,4 0,2 0,1 0,1 15 8 5 5 0,45 0,24 0,15 0,150,2 0,75 0,35 0,2 0,2 30 15 10 10 0,9 0,45 0,3 0,30,5 1,5 1,5 0,5 0,5 90 45 30 30 2,7 1,35 0,9 0,91 3,0 3,0 1,0 1,0 180 90 60 60 5,4 2,7 1,8 1,8

Class+/- Percentage current errorat percentage of ratedcurrent shown below50 120

3 3 3



5 5 5

[SFS 2874:E]

Marking

The rating plate shall carry the appropriate information in accordancegeneral marking.

The accuracy class and instrument security factor shall be indicatedfollowing the indication of corresponding rated output (e.g. 15 VAClass 0,5 F s 10). F s = instrument security factor

Current transformers having an extended current rating shall havethis rating indicated immediately following the class designation (e.g.15 VA Class 0,5 ext. 150%).

Back to previous page Next chapter




General●

Definitions●

Accuracy requirements●

Marking●


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General●

Definitions●

Accuracy requirements●

Marking●



General

Protective current transformer = A current transformer intended tosupply protective relays.

Definitions

Composite error = Under steady-state conditions, the r.m.s value ofthe difference between:

a) the instantaneous values of the primary current

b) the instantaneous values of the actual secondary current multipliedby the rated transformation ratio.

The composite error εc is generally expressed as a percentage of the

r.m.s. values of the primary current according to the formula:

K n= rated transformation ratioI p= r.m.s. value of the primary currenti p= instantaneous value of the primary currenti s= instantaneous value of the secondary currentT= duration of one cycle



Rated accuracy limit primary current = The value of primary currentup to which the transformer will comply with the requirements forcomposite error.

Accuracy limit factor = The ratio of the rated accuracy limit primarycurrent to the rated primary current.

Secondary limiting e.m.f = The product of the accuracy limit factor,the rated secondary current and the vectorial sum of the rated burdenand the impedance of the secondary winding.

Accuracy requirements

For protective current transformers the accuracy class is designatedby the highest permissible percentage composite error at the ratedaccuracy limit primary current prescribed for the accuracy classconcerned, followed by the letter "P" (meaning protection) atratecurrent prescribed for the accuracy class concerned.

The standard accuracy classes for protective current transformers are:5 P and 10 P

Accuracyclass

Percentagecurrent error atprimary currentin %

Phasedisplacement atrated primarycurrent

Composite error atrated accuracy limitprimary current in %

Minutes Centiradians5 P +/- 1 +/- 60 +/- 1,8 610 P +/- 3 10

Marking

The rating plate shall carry the appropriate information in accordancegeneral marking.

The rated accuracy limit factor shall be indicated following thecorresponding output and accuracy class (e.g. 30 VA Class 5 P 10). 10= Accuracy limit factor



A current transformer satisfying the requirements of severalcombinations of output and accuracy class and accuracy class limitfactor may be marked according to all of them.

15 VA Class 0,5 or 15 VA Class 0,530 VA Class 1 15 VA Class 1 ext 150%30 VA Class 5 P 10 15 VA Class 5 P 20




Rating and performance requirements

Standard values of rated currents and outputs●

Short-time current ratings●

Limits of temperature rise●

Terminal markings and rating plate markings●

Graphic symbols of current transformers●



Standard values of rated currents and outputs

The standard values of rated primary current are:

10 - 12,5 - 15 - 20 - 25 - 30 - 40 - 50 - 60 - 75 amperes

And their decimal multiples of fractions. The preferred values arethose underlined.

The standard values of rated secondary current are:

1,2 and 5 amperes, but the preferred value is 5A.

The standard values of rated output up to 30 VA are:

2,5 - 5,0 - 10 - 15 and 30 VA.

Value above 30 VA may be selected to suit the application.(Recommended values: 45,60 VA)

Short-time current ratings

Current transformer supplied with a fixed primary winding ofconductor shall comply with the requirements of rating below.

Thermal rating = A rated short-time thermal current shall be assignedto the transformer.

Dynamic rating = The values of the rated dynamic current shallnormally be 2,5 times the rated short-time thermal current and it shallbe indicated on the rating plate when it is different from this value.

Limits of temperature rise

The temperature rise of a current transformer when carrying aprimary current equal to the rated continuous thermal current, with aunity power-factor burden corresponding to the rated output, shall notexceed the appropriate value given in the table below.

Class of insulation (in accordance withIEC Publication 85)

Maximum temperaturerise0 C



All classes immersed in oil 60All classes immersed in oil andhermetically sealed 65

All classes immersed in bituminouscompound 50

Classes not immersed in oil or bituminouscompoundY 45A 60E 75B 85F 110H 135

Terminal markings - general rules

The terminal markings shall identify: the primary and secondarywindings; the winding sections, if any; the relative polarities ofwindings and winding sections; the intermediate tapings, if any.



[SFS 2874:E]

Graphic symbols of current transformers

current transformer:one output at thesecondarytwo alternativesymbols

two coils with the samecore

double core currenttransformer



Types of current transformers

Pictures of current transformers:

1. Current transformers for indoor use 2. Indoor type cable current transformers 3. Indoor bushing type current transformers



http://leeh.ee.tut.fi/transformer/curtrans.htm [01/03/2003 01:30:38 a.m.]

KOFA Current transformers for indoor use

[ABB Catalogue. KOFA Sisälle asennettavat virtamuuntajat.]

Use the back button of the browser for viewing the previous page

Current transformers

http://leeh.ee.tut.fi/transformer/kofa.htm [01/03/2003 01:30:40 a.m.]

KOLMA and IHDA Indoor type cable current transformers

[ABB Catalogue. KOLMA and IHDA Indoor Type Cable Current Transformers.]



http://leeh.ee.tut.fi/transformer/kolma.htm [01/03/2003 01:31:39 a.m.]

KOMA Indoor bushing type current transformers

[ABB Catalogue. KOMA Indoor Bushing Type Current Transformers.]



http://leeh.ee.tut.fi/transformer/koma.htm [01/03/2003 01:31:41 a.m.]


Definitions●

Measuring current transformer●

Protective current transformer●

Rating and performance requirements●

Types of current transformers●

A current transformer design●

Current transformer


Definitions (SFS 2874:E)

Introduction●

Current error●

Phase displacement and accuracy class●

Burden●

Rated thermal and dynamic currents●

Definitions


Introduction

Current transformer is an instrument transformer in which thesecondary current, in normal conditions of use, is substantiallyproportional to the primary current and differs in phase from it by anangle which is approximately zero for an appropriate direction of theconnections.

Current error

The error which a transformer introduces into the measurement of acurrent arises from the fact that the actual transformation ratio is notequal to the rated transformation ratio. The higher the excitingcurrent or core loss the larger the error.

The current error expressed in percent is given by the formula:

Definitions


Phase displacement and accuracy class

Phase displacement = The difference in phase between the primaryand secondary current vectors, the direction of the vectors being sochosen that the angle is zero for a perfect transformer.

Accuracy class = A designation assigned to a current transformer theerror of which (Current error, phase displacement, composite error)remain with specified limits under prescribed conditions of use.

Burden

Burden = The impedance of the secondary circuit in ohms and powerfactor. The burden is usually expressed as the apparent power (S) involt-amperes absorbed at a specified power-factor at the ratedsecondary current.

Secondarywindingimpedance(internalburden) Z s

SecondaryloadimpedanceZ 0

Definitions


The secondary load S = V 0 Is (cos φ = 0.8 ind for

example)

As a matter of safety, the secondary circuits of a current transformershould never be opened under load, because these would then be nosecondary mmf to oppose the primary mmf, and all the primarycurrent would become exciting current and thus might induce a veryhigh voltage in the secondary.

Rated thermal and dynamic currents

Rated short-time thermal current = The r.m.s. value of the primarycurrent which a transformer will withstand for one second withoutsuffering harmful effects, the secondary winding beingshort-circuited.

Rated continuous thermal current = The value of the current whichcan be permitted to flow continuously in the primary winding, thesecondary winding being connected to the rated burden, without thetemperature rise exceeding the values specified.

Rated dynamic current = The peak value of the primary currentwhich a transformer will withstand without damaged electrically ormechanically by the resulting electromagnetic forces, the secondarywinding being short-circuited.


Definitions


Definitions



Introduction●

Measuring or protective current transformers?●

Selecting core material●

Window utilization factor●



conductor area = copper area

wire area = copper area + insulation area

S 1 is dependent upon wire size.

Back



wound area = number of turns x wire area of one turn

usable window area = available window area minus residual areawhich results from the particular winding technique used

S 2 is the fill factor for usable window area. It can be shown that forcircular cross-section wire wound on a flat form the ratio of wire areato the area required for the turns can never be greater than 0,91. InPractise, the actual maximum value is dependent upon the tightnessof winding, variations in insulation thickness, and wire lay.Consequently, the fill factor is always less than the theoreticalmaximum. A typical working value for copper wire is 0,6.

Back




window area = available window area

S 3 defines how much of the available window space may actually beused for the winding. The winding area available to the designerdepends on the bobbin configuration. A single bobbin design offersan effective area Wa between 0,835 to 0,929 while a two bobbinconfiguration offers an effective area Wa between 0,687 to 0,872. Agood value to use for both configurations is 0,75.

Back




insulation area = area usable for winding insulation

S 4 defines how much of the usable window space is actually beingused for insulation. If the transformer has multiple secondary havingsignificant amont of S 4 should be reduced by 10% for eachadditional secondary winding because of the added space occupiedby insulation and partly due to poorer space factor.

Back



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TRANSFORMER BOOK

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Kinds of core alloys

There are five main groups of magnetically soft alloys classified primarily bythe chief constituents of the metal.

low-carbon steelsilicon steelnickel-ironcobalt-nickel-ironcobalt-iron

Also look at:

Hysteresis curve of a hard and soft alloy

Look at trade names

Core types

The configuration of a three-phase transformer depends on the coretype of the transformer. There are three choices:

The "shell" type

The "core" type

3x single-phase

Core configuration

Configuration of a distribution transformer


Core type shape is mostly used in three-phase distributiontransformers. The window height H a depends on a coil height andthe core area A r depends on the rated power S n.

The cross section of the core

The bulk factorof the leg canbe definedwhen the crosssectional areaof the leg isknown:



k = acoefficient thatdepends on thenumber of steps

Core sheet



Coil material

The coil material can be copper or aluminum. The term copper loss isstill used to indicate resistance losses of winding materials whethercopper or aluminum is used.

Copper ρ k = 8.93 kg/dm3

Aluminum ρ k = 2.69 kg/dm3

ρ k = The weight by volume

Coil configuration

Foil coil

Show the primary!!



Tank

The tank and the cover are manufactured of hot-rolled, unalloyedsteel sheet and profile balks. Fine granular steel is used intransformers for low ambient temperatures.

Areas where strong eddy currents can be generated due to highcurrents, and where ordinary hot-rolled steel can become too warm,are made of non-magnetic (austenite) steel. Such areas are forexample the surroundings if high current bushings and bushbars. Thetanks are welded and manufactured in accordance with modernwelding methods.



The tank has lifting lugs for lifting the transformer (fully-equippedtransformer including oil) and at least four jacking points an thelower part if the tank for lifting by hydraulic jacks. For transportwheels there are fixing points at the bottom of the tank. The tank isprovided with at least two earthing lugs made of stainless steel.

The connecting flanges of the coolers and the flanges for filling,draining, filtering and sampling valves are welded to the tank. Alsothe fixing brackets of cooler fans are welded to the tank. Usually thesupport of the oil conservator is fastened to the tank too. Thetransformer cover is fixed to the tank usually by means of a bolt jointusing oil resistant rubber cork as the gasket. A gasket made of specialrubber can also be used. The cover can also be fixed to the tank bywelding. The welded seams are tighter and more reliable than boltedones. They can be quite easily opened and rewelded.

The transformer cover is constructed so that no water pockets orother water collector points are formed. An air pipe is connected tothe gas relay from all the turrets, flanges etc. where it is possible forgas pockets to develop.

[ABB Catalogue. Power Transformers Construction.]

Coolers

Transformers are usually provided with radiators for cooling (coolingmethod ONAN or ONAN/ONAF). The radiators are manufactured ofwelded elements and they are vacuum-proof.

The radiators are connected to the transformer tank by means ofshut-valves. This method allows individual radiators to be removedwithout draining oil from the transformer. The shut-off valve isprovided with a position indicating handle and with a locking spring.The lower part of the radiators has a plug for oil outlet and the upperpart a plug for air release.

In the transformers which have ONAN/ONAF cooling, the fansforcing the air circulation are under or at a low noise level and theyare equipped with steel sheet guard and the necessary protectivemesh. The fan motors can normally be connected to the 380/220 Vsupply, but if required, motors with other voltage ratings can also be



used.

The transformer can also be provided with water cooling, coolingmethod OFWF or oil-air cooler, cooling method OFAF. In each case,the oil circulation through coolers is handled by means of an oilpump. The coolers can be installed so as to rest upon the transformertank or on a frame separated from the transformer. The pipe work isprovided with the necessary valves for removing the cooler and thepump for inspection and maintenance.


Heating of the windings

The heating of the windings depend on the current density anddimensions of coil wires. The smaller the selected current density isthe more copper or aluminum is needed for the coil. As the heating issmaller, the load losses become lower. The heating is squarelyproportional to the current density. Standards set some restrictions tothe heating of the windings. Therefore, the designer should alwayscalculate the heating when designing the coils. An average heating ofthe windings compared to the outer air according to the IEC 76standards can be:

V < 65 0 C




The hysteresis curve of soft alloys

The hysteresis curve of soft alloys is thin and therefore the coercive force issmall. These alloys are mostly used in electromechanical machines andtransformers.

The hysteresis curve of hard alloys

The hysteresis curve

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The hysteresis curve of hard alloys is wide and therefore the coercive force ishigh. These alloys are mostly used in permanent magnets.

Back

The hysteresis curve

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Tradenames

Composition Saturatedfluxdensity, a(tesla)

CD coerciveforce,amp-turn/cm3

Squarenessratio

Materialdensity,g/cm3

Lossfactorat 3kHzand 0.5T,W/kg

Magnesil 3% Si 1.5-1.8 0.5-0.75 0.85-1.00 7.63 33.1Silectron 97% FeMicrosilSupersilDeltamax 50% Ni 1.4-1.6 0.125-025 0.94-1.00 8.24 17.66Orthonol 50% Fe49 Sq. MuAllegheny4750

48%Ni 1.15-1.4 0.062-0.187 0.80-0.92 8.19 11.03

48 Alloy 58%Fe

Carpenter 494-79 Permalloy 79% Ni 0.66-0.82 0.025-0.05 0.80-1.0 8.73 5.51Sq. Permalloy 17% Fe80 Sq. Mu 79 4% Mo

Supermalloy 78%Ni 0.65-0.82 0.0037-0.01 0.40-0.70 8.76 3.75

17%Fe5%Mo

1 1 T = 10 4

Gause2 1 g / cm 3 =

0.036 1b / in 3

[McLyman.]

Magnetic core material characteristics


BackMagnetic core material characteristics


Coil configuration

Foil coil configuration isnowadays widely used in thesecondary winding. Folio sheetis wound around the iron core.The sheet is covered withinsulation layer.

Cylinder coilShow the primary!

Coil configuration

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Coil configuration

The conduct wire has a round shape at the primary winding.

Layer coil

Coil configuration

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Collar coil

Show the secondary!

Coil configuration

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kinds of core alloys●

core types●

core configuration●

core sheet●

coil material●

coil configuration●

Tank●

Coolers●

Heating of the windings●



Losses of a transformer

Load loss No-load loss


Losses


No-load loss

No-load losses are mainly iron losses. The iron loss become important incases where a lighting load is being supplied and in which thetransformer itself remains excited, even though not actually supplyingany load. It is also important in cases where a transformer is working ona low load factor.

Apparent loss

The loss that is due to the magnetizing current in the primary winding iscalled the apparent loss.

The flow of the magnetizing current through the resistance of thewinding does create a real I 2 R loss and voltage drop, although both aregenerally quite small.

No-load loss


Core loss (iron loss)

Time-varying fluxes produce losses in ferromagnetic materials, knownas core losses. These iron losses are divided into hysteresis losses andeddy-current losses.

Hysteresis losses are proportional to the area of the hysteresis loop,volume of the iron core and the frequency of the flux in hertz.

Hysteresis losses

The hysteresis loss per cycle in a core of volume V that has a uniformflux density B throughout its volume is

where the line integral represents the area of the loop.

A cyclic variation of the flux at f hertz results in f hysteresis loops persecond and the power is

The hysteresis loss is expressed empirically using a relationship fromCharles P. Steinmetz that

[Matsch L. W. , Morgan J. D.]

Eddy-current losses

No-load loss


The AC flux induces emfs in the core that produce eddy currents thatcirculate in the iron. Eddy-current losses are proportional to thefrequency, the maximum flux density, the thickness of the core sheet andthe resistivity of the iron (inversely).



No-load loss


Excited = ?

= running idle

= running without load

Back

Selitykset


k = the load factor

The load factor is the ratioof a load and the rated load.

Back

Load factor

http://leeh.ee.tut.fi/transformer/loadf.htm [01/03/2003 01:32:46 a.m.]

Load loss

The sum of copper losses and the stray losses is called the loadlosses, being I 2 R eg , as determined from the short-circuit test. Whilethe equivalent circuits, including the approximate equivalent circuit,may be used to calculate the losses for a given output, it is usuallymore convenient to use data of the short-circuit test directly.

The term copper loss is still used to indicate resistance losses ofwinding materials whether copper of aluminum is used.

●

The term copper losses is still sometimes used instead of loadlosses and when so used is meant to include the stray losses.

●


Copper loss

The load currents through the resistance's of the primary andsecondary windings create I 2 R losses that heat up the copper wiresand cause voltage drops. There load losses are called copper losses(winding material can be copper or aluminum).

Stray loss

Two factors that contribute to losses (and other undesirablephenomena) are stray capacitance and leakage inductance. Straycapacitance inevitably exists between turns, between one windingand another, and between windings and the core.

Load loss


[Lowdon E.]

Back to previous page Next page

Load loss


What is a transformer?

A transformer is a device that transfers energy from one AC system to another.A transformer can accept energy at one voltage and deliver it at anothervoltage. This permits electrical energy to be generated at relatively lowvoltages and transmitted at high voltages and low currents, thus reducing linelosses, and to be used at safe voltages.

[McPherson G. , Laramore R. D.]

Transformer in electric network

Three-phase transformer

Three-phase power may be transformed by using either two or threesingle-phase transformers, or by a single three-phase transformer. When a setof single-phase transformers is employed to transform three phases, it is calleda three-phase bank of transformers.

Symmetrical three-phase transformer

Basics of a transformer


[Sähkötekniikan käsikirja]

Figure below presents a three-phase core transformer and a three-phaseshell transformer. Every phase of the core transformer has its own bar withtwo windings belonging to phase. In the shell transformer the one-phasemagnetic flux has a return path, independent from the other phases.


Types of distribution transformers

A two-winding transformer

The transformer may be defined as a device in which two or more stationaryelectric circuits are coupled magnetically, the windings linked by a commontimevarying magnetic flux. One of these windings, known as the primary,receives power at a given voltage and frequency from the source; and the other



winding known as the secondary, delivers power, usually at a different voltagebut at the same frequency, to the load.


Figure below presents a one-phase core transformer and a one-phase shelltransformer. To the iron core in a one-phase core transformer belong two barswith cylindrical windings around them. Bars are connected to each others withyokes. Bars and yokes build together a closed magnetic circuit. There are twowindings. They are called high-voltage- and low-voltage windings or,according to the power direction, primary or secondary windings. As materialare used copper or aluminum. A one-phase shell transformer´s iron core isconstructed of three bars and two yokes. The windings are placed on themiddle bar.


Three-phase transformer connections




Yy0, Dy11, Yd11 and Yz11 connections are used in Finland.In the case of one three-phase transformer or of three single-phasetransformers, several three-phase arrangements can be used. The following arequite common: the delta-delta, the wye-wye, wye-zigzag and the wye-delta ordelta-wye connections.

Exciting current

The exciting current I e, is considered as having two components, the core-losscurrent I fe and the magnetizing current I m. The core-loss current is areal-power component and is due to the core losses. The magnetizing currentis, in effect, the component of current that furnishes the mmf to overcome themagnetic reluctance of the core.



The waveform of the exciting current is not sinusoidal. However, it issymmetrical, the exciting current can therefore be represented by a series ofodd harmonics.

Current inrush of a transformer

Frequently upon energizing a power transformer, there is an inrush of excitingcurrent which may initially be as high as eight times the rated current of theexcited winding even with all other windings open. The inrush is most severewhen the transformer is energized at the instant the voltage goes through zeroimmediately following which the polarity of the voltage is such that the fluxincreases in the direction of the residual flux.

Figure. Inrush current for a transformer energized at zero instantaneous voltage

Voltage Regulation

The voltage regulation is an important measure of transformer performanceand is expressed by the formula:



The percent regulation is of 100 times the per-unit regulation. In the aboveexpression, V 2 Io is the secondary voltage under load, and V 2 nI is thesecondary no-load voltage (I 2 = 0), with primary voltage held constant at thevalue it had under load. The quantities used in the formula are magnitudes, notphasors.


Losses and efficiency

The losses in a transformer are the core losses, which for a given voltage andfrequency are practically independent of the load; the copper losses due to theresistance of the windings; and the stray losses, largely due to eddy currentsinduced by the leakage fluxes in the tank and other parts of the structure. Thesum of copper losses and the stray losses is called the load losses. Theefficiency of a transformer at rated load is quite high. A value of 90 percent isnot uncommon for transformers as small as 1 kVA, with greater values ofefficiency as the rating increase. The efficiency is expressed by





Clickable imagemap





Power transformer

[ABB Catalogue. Kotimaan vakiomuuntajesarja.]


Power transformer

http://leeh.ee.tut.fi/transformer/pwrtrans.htm [01/03/2003 01:34:13 a.m.]

Power transformer



Power transformer

http://leeh.ee.tut.fi/transformer/powtrans.htm [01/03/2003 01:34:45 a.m.]

Distribution transformer (3-phase distribution line)

[ABB Catalogue. Jakelumuuntajat.]


Distribution transformer

http://leeh.ee.tut.fi/transformer/pylvas.htm [01/03/2003 01:35:13 a.m.]

Types of Distribution Transformers

Dry type Distribution Transformer Oil insulated Distribution Transformer

[ABB Catalogue. RESIBLOC-hartsimuuntajat] , [ABB Catalogue. Jakelumuuntajat]


Types of Distribution Transformers

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What is a transformer?●

Three-phase transformer●

A two-winding transformer●

Connections●

Exciting current●

Current inrush●

Voltage Regulation●

Losses and efficiency●



Magnetic materials

Each magnetic material belongs to one of the three groups.

Diamagnetic materials have a very low value of relative

permeability µ. These materials can even decrease the magneticfield.

1.

Magnetic materials include certain forms of iron and its alloys incombination with cobalt, nickel, aluminum and tungsten. Theseare known ferromagnetic materials and are easy to magnetize

since they have a high value of relative permeability µ.

2.

Electromagnetism


The permeability µ of paramagnetic materials is very close tothat permeability what is in the vacuum. Their magneticproperties are almost neutral.

3.

Permeability

Permeability is the ability to conduct flux. Mathematically, it is theratio of the flux density (B) to the magnetizing force (H) that causesB. In Symbols

When B is plotted against H, a curve is obtained variously called themagnetization curve. [Lowdon E.]

Electromagnetism


Magnetic permeance and reluctance

Generally the steady or slowly varying flux φ in magnetic circuits ofhomogeneous material with a uniform cross-sectional area can beapproximately expressed by

F m = The magnetomotoric force

ρ = The permeance of the circuitR m = The reluctance of the circuit

Saturation

Electromagnetism


The B-H curve shows the meaning of saturation. It can be seen thatbeyond a certain value of H (point C). There is a little increase in B;the iron is approaching the saturation.

Different materials saturate at different values of flux density. At thesaturation point the permeability is very small or zero. These meansthat the inductance is very small.

Inductance can be described as the property of coil that causes it tooppose a change in the current through it. A coil is said to have aninductance of 1,0 henry if it induces an opposing or "back" emf of 1.0V when the current through it changes at the rate of 1.0 ampere persecond

L = The inductanceR m = The reluctance of circuitA = The core areaI = The length of the magnetic circuit

Electromagnetism


µ = The permeability of the core

Hysteresis

The nonlinear properties of magnetic materials are characterized bythe hysteresis loop.

[Matsch L. W., Morgan J. D.]

In increasing current through a range of values such that the magneticfield intensity or magnetizing force reaches a value of +Hmax asshown in figure, the flux density in the core reaches a maximum valuealong the curve 0ab. If the current is decreased to zero, the fluxdensity will have the value of. The application of a current in thereverse direction so as to produce the magnetizing force -Hmaxreverses the direction of the flux density, as indicated by e´b´ infigure. Now if the current is again reversed and adjusted to producethe initial value +Hmax for the magnetizing force, the flux density willbe ec, which is lower than the initial value eb. Cycling the material anumber of times produces equal values of +Bmax and -Bmax andresults in a symmetrical hysteresis loop. [Matsch L. W., Morgan J. D.]

Electromagnetism


Magnetic Leakage and Fringing

Leakage

The portion of flux that does not link the two magnetic circuits beingcoupled is called leakage flux or simply leakage.


Fringing

The phenomenon of flux spreading to a larger cross section when itleaves a high-permeability material entering a relativelylow-permeability material such as air in an air gap.

Electromagnetism



Faraday's induction law

If the magnetic flux alternates inside the coil. This induces anelectromagnetic force in the winding. The magnitude of this force isproportional to the number of turns and the speed of the alternatingflux. The mathematical model of faraday's induction law is

Electromagnetism


Kirchhoff's laws for magnetic circuits

Electromagnetism



Electromagnetism


Electromagnetics

Magnetic materials●

Permeability●

Magnetic permeance and reluctance●

Saturation●

Hysteresis●

Magnetic Leakage and Fringing●

Faraday's induction law●

Kirchoff´s laws●

Electromagnetics


Distribution transformers

Basics of a transformer●

Configuration of a distribution transformer●

Losses of a transformer●

Distribution transformer


DIRECTORY

in alphabetic order

Air-gapped current transformers

Anti-remanence current transformers

Burden

coil configuration

coil material


connections Three-phase transformer

Coolers

core alloys Kinds of core alloys

core configuration

core sheet

core types

Current error

Current inrush

Current transformer

Exciting current

Faraday´s induction law

Graphic symbols of current transformers

Heating of the windings

Hysteresis

Hysteresis curve of a soft and hard alloy

Inductance

Kirchhoff´s laws

Linear current transformers

Losses and efficiency

Losses of a transformer

Magnetic Leakage and Fringing

Magnetic materials

Magnetic permeance and reluctance


Permeability


Saturation

Tank

Three-phase transformer



Types of distribution transformers

A two-winding transformer

Voltage Regulation

Directory

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REFERENCES

ABB Catalogue. Jakelumuuntajat.ABB Catalogue. KOFA Sisälle asennettavat virtamuuntajat.ABB Catalogue. KOLMA and IHDA Indoor Type Cable Current Transformers.ABB Catalogue. KOMA Indoor Bushing Type Current Transformers.ABB Catalogue. Kotimaan vakiomuuntajasarja.ABB Catalogue. Power Transformers Construction.ABB Catalogue. RESIBLOC - hartsimuuntajat.Lowdon E. Practical Transformer Design Handbook - 2nd ed., 1989.Matsch L. W., Morgan J. D. Electromagnetic and Electromechanical Machines, 1987.McLyman. Transformer and Inductor Design Handbook, 1978.McPherson G., Laramore R. D. An introduction to Electrical Machines and Transformers, 1990.Protective Relays Application Guide. GEC Alsthom T&D Protection & Control Limited, 1987 .Standard SFS 2874:E, 1983.Sähkötekniikan käsikirja osa 1, Tammi 1975.

References

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MAIN PAGE

Working group

Main page

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Ilpo HavunenLeena KorpinenKimmo KähäräErja ToivonenThomas Hager

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Working group

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