Teoriya Transformerê da Li Daxwazda û Da Neda Xebitkirina

Taybetîna Transformer

Transformer dike nav bêk têkînî elektrîkî ye ku dixwaze nergyên elektrîkî di du veyan an zêdetir de bi rêbaza endamîya elektromagnetîkê.

Teoriya Transformer da Nabe Qebûl

Bê Resistança Veyan û Bê Reaktansa Lêkêje

Pêşniyaz bike transformerek ji bilan core losses tenê, ya'ni ne heye copper loss an reaktansa lêkêje. Heke çavkanî jorî yên alternating current li ser veyanê yekem bibêje, ew hêza bibêje barê magnetizekirina core ya transformer.

Lê ew hêz ne hêza magnetizing rastî ne; ew qicik pir e ji magnetizing hêza rastî. Hêza girtî yên ji sereka herî divê di du parçeyan de be, yekan hêza magnetizing e ku tenê bikar îne barê magnetizekirina core, û parçeya din li ser hêza sereka hatine pêşand kirin barê core losses.

Bi rêbaza parçeya core loss, hêza nabe qebûl li ser sereka ne bi 90° lagîn dikare, lê bi angle θ, ku qicik e ji 90°. Hêza girtî Io parçeya Iw di phase-a bi voltage-a sereka V1, ku parçeya core loss represent dike.

Parçeya ji bo source voltage hatine pêşand kirin çünki ew li ser active an working losses di transformers de. Parçeya din li ser hêza sereka bi Iμ hatine namendin.

Parçeya din alternating magnetic flux di core de dide, dema ku ew watt-less e; ya'ni ew part reaktif a hêza sereka ya transformer. Dema ku Iμ bi quadrature bi V1 û bi phase bi alternating flux Φ. Di dema ku, hêza girtî yên yekem a transformer da nabe qebûl condition da wate:

Niha tiştî xwe şopandin ku teoriya transformer da nabe qebûl piştgiri bike.

Teoriya Transformer da Qebûl

Bê Resistança Veyan û Reaktansa Lêkêje

Niha tiştî xwe şopandin behavior-a transformer da qebûl, ya'ni qebûl li ser terminals a secondary bêtir. Pêşniyaz bike, transformer ek ji bilan core loss, lê bê copper loss û reaktansa lêkêje. Heke qebûl li ser secondary winding bêtir, hêza qebûl dibêje flow bikin di qebûl û secondary winding de.

Hêza qebûl tenê di cihazên qebûl û di voltage-a secondary a transformer de depend dibêje. Hêza din bi I2 hatine namendin. Ji ber ku I2 di secondary de flow bikin, self MMF di secondary winding de dibe. Li vir, N2I2, ku N2 heye number of turns a secondary winding a transformer.

MMF an magnetomotive force di secondary winding de flux φ2 dide. φ2 main magnetizing flux oppose dikare û momentane main flux weak dikare û tries to reduce primary self-induced emf E1. Ji ber ku E1 falls below primary source voltage V1, there will be an extra current flowing from source to primary winding.

This extra primary current I2′ produces extra flux φ′ in the core which will neutralize the secondary counter flux φ2. Hence the main magnetizing flux of core, Φ remains unchanged irrespective of load. So total current, this transformer draws from the source can be divided into two components.

The first one is utilized for magnetizing the core and compensating the core loss, i.e., Io. It is the no-load component of the primary current. The second one is utilized for compensating the counter flux of the secondary winding. 

It is known as the load component of the primary current. Hence total no-load primary current I1 of an electrical power transformer having no winding resistance and leakage reactance can be represented as follows

Where θ2 is the angle between the Secondary Voltage and Secondary Current of the transformer.Now we will proceed one further step toward a more practical aspect of a transformer.

Theory of Transformer On Load, with Resistive Winding, but No Leakage Reactance

Now, consider the winding resistance of the transformer but no leakage reactance. So far we have discussed the transformer which has ideal windings, means winding with no resistance and leakage reactance, but now we will consider one transformer which has internal resistance in the winding but no leakage reactance. As the windings are resistive, there would be a voltage drop in the windings.

We have proved earlier that, total primary current from the source on load is I1. The voltage drop in the primary winding with resistance, R1 is R1I1. Obviously, induced emf across primary winding E1, is not exactly equal to source voltage V1. E1 is less than V1 by voltage drop I1R1.

Again in the case of secondary, the voltage induced across the secondary winding, E2 does not totally appear across the load since it also drops by an amount I2R2, where R2 is the secondary winding resistance and I2 is secondary current or load current.

Similarly, the voltage equation of the secondary side of the transformer will be:

Theory of Transformer On Load, with Resistance as well as Leakage Reactance

Now we will consider the condition when there is leakage reactance of the transformer as well as winding resistance of the transformer.

Let leakage reactances of primary and secondary windings of the transformer are X1 and X2 respectively. Hence total impedance of primary and secondary winding of transformer with resistance R1 and R2 respectively can be represented as,

We have already established the voltage equation of a transformer on load, with only resistances in the windings, where voltage drops in the windings occur only due to resistive voltage drop.

But when we consider leakage reactance of transformer windings, the voltage drop occurs in the winding not only due to resistance but also due to the impedance of transformer windings. Hence, the actual voltage equation of a transformer can easily be determined by replacing resistances R1 & R2 in the previously established voltage equations with Z1 and Z2.

Therefore, the voltage equations are,

Resistance drops are in the direction of the current vector. But a reactive drop will be perpendicular to the current vector as shown in the above vector diagram of the transformer.