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Electrical Machines And Electrical Apparatus

1 • Construction and Principles of Power Transformer

Transformer is an indispensable component in many energy conversion systems. It makes

possible electric generation at the most economical generator voltage, power transfer at the most

economical transmission voltage, and power utilization at the most suitable voltage for the particular

utilization device. The transformer is also widely used in low-power, low-current electronic and

control circuits for performing such functions as matching the impedances of a source and its load for

maximum power transfer, isolating one circuit from another, or isolating direct current while

maintaining alternating current continuity between two circuits-

Essentially, a transformer consists of two or more windings coupled by mutual magnetic flux. If

one of these windings, the primary is connected to an alternating voltage source, an alternating flux

will be produced whose amplitude will depend on the primary voltage, the frequency of the applied

voltage, and the number of turns. The mutual flux will link the other winding, the secondary and will

induce a voltage in it whose value will depend on the number of the secondary turns as well as the

magnitude of the flux and the frequency. By properly proportioning the primary and the secondary

turns, almost any desired voltage ratio, or ratio of transformation, can be obtained.

The essence of transformer action requires only the existence of time-varying mutual flux linking

two windings. Such action can occur for two windings coupled through air, but coupling between the

windings can be made much more effectively using a core of iron or other ferromagnetic material,

because most of the flux is then confined to a definite, high-permeability path linking the windings.

Such a transformer is commonly called an iron-core transformer. Most transformers are of this type.

The following discussion is concerned almost wholly with iron-core transforme匚

In order to reduce the loss caused by eddy current in the core, the magnetic circuit usually

consists of a stack of thin laminations. Two common types of construction are shown schematically in

Fig. 1.1 • In the core type (Fig. 1.1a) the windings are wound around two legs of a rectangular

magnetic core; in the shell type() the windings are wound around the center leg of a

three-legged core. Silicon -steel laminations 0-014 mm in thick are generally used for transformer

used at frequencies below a few hundred Hz. Silicon steel has the desirable property of low cost, low

core loss, and high permeability at high flux densities (1.0 to 1.5T). The cores of small transformer

used in communication circuits at high frequencies

and low energy levels are sometimes made of compressed ferromagnetic alloys known as ferrites-

Core

—Windings

Windings

(a) (b)

In each of these configurations, most of the flux is confined to the core and therefore links both

windings. The winding also produce additional flux, known as leakage flux, which links one winding

without linking the other. Although leakage flux is small fraction of the total flux, it plays an

important role in determining the behavior of the transforme匸In practical transformers, leakage is

reduced by subdividing the windings into sections placed as close together as possible. In the

core-type construction, each winding consists of two sections, one section on each of the two legs of

the core, the primary and secondary windings being concentric coils. In the shell type construction,

variations of the concentric-winding arrangement maybe used, or the windings may consist of a

number of thin pancake coils assembled in a stack with primary and secondary coils interleaved.

2. Advantages of Balanced Three-phase Versus Single-phase Systems

In both transformers and rotating machines, a magnetic field is created by the combined action of

the currents in the windings. In an iron-core transformer, most of this flux is confined to the core and

links all the windings. This resultant mutual flux induces voltages in the windings proportional to their

number of their turns and is responsible for the voltage-changing property of a transformer. In rotating

machines, the situation is similar, although there is an air gap which separates the rotating and

stationary components of the machine. Directly analogous to the manner in which transformer core

flux links the various windings on a transformer core, the mutual flux in rotating machines crosses the

air gap, linking the windings on the rotor and stator. As in a transformer, the mutual flux induces

voltage in these winding proportional to the number of turns and time rate of change of the flux.

A significant difference between transformers and rotating machines is that in rotating machines

there is relative motion between the windings on the rotor and stator. This relative motion produces an

additional component of the time rate of change of the various winding flux linkages. The resultant

voltage component, known as the speed voltage, is characteristics of the process of electromechanical

energy conversion. In a static transformer, however, the time variation of flux linkages is caused

simply by the time variation of winding current; no mechanic motion is involved, and no

electromechanical energy conversion takes place.

The resultant core flux in a transformer induces a counter Electro-Motive Force(EMF) in the

primary which, together with the primary resistance and leakage-reactance voltage drops, must

balance the applied voltage. Since the resistance and leakage -reactance voltage drops usually are

small, the counter EMF must approximately equal to the applied voltage and the core flux adjust itself

accordingly. Exactly similar phenomena must take place in the armature windings of an AC motor.

The resultant air-flux wave must adjust itself to generate a counter EMF approximately equal to the

applied voltage. In both transformers and rotating machines, the Magneto-Motive Force (MMF) of all

the currents must accordingly adjust itself to create the resultant flux required by this voltage balance.

In any AC electromagnetic devices in which the resistance and leakage-reactance voltage drops are

small, the resultant flux is very nearly determined by the applied voltage and frequency, and the

cuiTents must adjust themselves accordingly to produce the MMF required to create this flux.

In a transformer, the secondary current is determined by the voltage reduced by the secondary

winding, the secondary leakage impedance, and the electric load. In an induction motor, the

secondary(rotor) current is determined by the voltage induced in the secondary, the secondary leakage

impedance, and mechanical load on its shaft. Essentially the same phenomena place in the primary

winding of the transformer and in the armature (stator) windings of induction and synchronous motors.

In all three, the primary, or armature, current must adjust itself so that the combined MMF of all

currents creates the flux the required by the applied voltage.

In addition to the useful mutual fluxes, in both transformers and rotating machines there are

leakage fluxes which link individual windings without linking others. Although the detailed picture of

the leakage fluxes in rotating machines is more complicated than that in transformers, their effects are

essentially the same. In both, the leakage fluxes induce voltage in AC windings which are accounted

for as leakage-reactance voltage drops. In both, the reluctances of the leakage-flux paths are

dominated by that of a path through air, and hence the leakage fluxes are

nearly linearly proportional to the current producing them・ The leakage-reactance therefore is often

assumed to be constant, independent of the degree of saturation of the main magnetic circuit.

Further examples of the basic similarities between transformer and rotating machines can be

cited. Except for friction and windage, the losses in transformer and rotating machines are essentially

the same. Tests for determining the losses and equivalent circuit parameters are similar: an open

circuit, or no-load, test gives information regarding the excitation requirements and core losses(along

with friction and windage losses in rotating machines), while a short-circuit test together with DC

resistance measurements gives information regarding leakage reactance and winding resistances.

3. Elementary Knowledge of Rotating Machines

Electromagnetic energy conversion occurs when changes in the flux linkage result from

mechanical motion. In rotating machines, voltage are generated in windings or groups of coils by

rotating these windings mechanically through a magnetic field, by mechanically rotating a magnetic

field past the winding, or by designing the circuit so that the reluctance varies with rotation of the

motor. By any of these methods, the flux linking a specific coil is changed cyclically, and a

time-varying is generated.

A set of such coils connected together is typically referred to an armature winding. In general,

the term armature winding is used to refer to a winding or a set of windings on a rotating machine

which carry AC currents. In AC machines such as synchronous or induction machines, the armature

winding is typically on the stationary portion of the motor refeiTed to as the stator, in which case

these windings may also be referred to as stator windings.

In a DC machine, the armature winding is found on the rotating member, referred to as the rotor.

The armature winding of a DC machine consists of many coils connected together to form a closed

loop. A rotating mechanical contact is used to supply current to the armature winding as the rotor

rotates.

Synchronous and DC machine typically include a second winding (or set of settings) which carry

DC current and which are used to produce the main operating flux in the machine. Such a winding is

typically refeiTed to as field winding. The field winding on a DC machine is found on the stator,

while that on a synchronous machine is found on the rotor, in which case current must be supplied to

the field winding via a rotating mechanical contact. As we have seen, permanent magnetic also

produce DC magnetic flux and are used in the place of field windings in some machines.

In most rotating machines, the stator and rotor are made of electrical steel, and the windings are

installed in slots on these structures. The use of such high-permeability material maximizes the

coupling between the coils and increase the magnetic energy density associated with the interaction.

It also enables the machine designer to shape and distribute the magnetic fields according to the

requirements of each particular machine design. The time varying flux present in the armature

structures of these machines tends to induce cuiTents, known as eddy currents, in the electrical steeL

Eddy currents can be a large source of loss in such machine and can significantly reduce machine

performance. In order to minimize the effects of eddy currents, the armature structure is typically

built from thin laminations of electrical steel with are insulated from each other.

In some machines, such as reluctance machines and stepper motors, there are no windings on the

roton Operation of these machines depends on the nonuniformity of air-gap reluctance associated

with variations in rotor position in conjunction with time-varying currents applied to their stator

windings. In such machines, both the stator and rotor structures are subjected to time-varying

magnetic flux and, as a result, both may require lamination to reduce eddy-current losses.

Rotating electric machines take many forms and are known by many names: DC, synchronous,

permanent-magnet, induction, variable reluctance, hysteresis, brushless, and so on. Although these

machines appear to be quite dissimilar, the physical principles governing their behavior are quite

similar, and it is often helpful to think of them in the same physical picture.