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leakage reactance

Leakage inductance derives from the electrical property of an imperfectly-coupled

transformer whereby each winding behaves as a self-inductance constant in series

with the winding's respective ohmic resistance constant, these four winding

constants also interacting with the transformer's mutual inductance constant. Thewinding self-inductance constant and associated leakage inductance is due to

leakage ux not linking with all turns of each imperfectly-coupled winding.

The leakage ux alternately stores and discharges magnetic energy with each

electrical cycle acting as an inductor in series with each of the primary and

secondary circuits. Leakage inductance depends on the geometry of the core and

the windings. oltage drop across the leakage reactance results in often undesirable

supply regulation with varying transformer load. !ut it can also be useful for

harmonic isolation "attenuating higher fre#uencies$ of some loads. %lthough

discussed exclusively in relation to transformers in this article, leakage inductance

applies to any imperfectly-coupled magnetic circuit device including especiallymotors

Leakage &lux in Transformer

n ideal transformer, all the ux will link with both primary and secondary windings

but in reality, it is impossible to link all the ux in transformer with both primary and

secondary windings. %lthough maximum ux will link with both windings through

the core of transformer but still there will be a small amount of ux which will link

either winding but not both. This ux is called leakage ux which will pass through

the winding insulation and transformer insulating oil instead of passing through

core. (ue to this leakage ux in transformer, both primary and secondary windings

have leakage reactance. The reactance of transformer is nothing but leakage

reactance of transformer. This phenomenon in transformer is known as )agnetic

leakage.

Leakage reactance in *ynchronous machine

t is the reactance due to ux setup by armature windings, but not crossing the air

gap. t can be divided into end-winding leakage and slot leakage. % convenient way

of picturing the reactance is to view these in terms of permeances of various

magnetic paths in the machine, which are functions of dimensions of iron and

copper circuits and independent of the ux density or the current loading. The

permeances thus calculated can be multipliedby a factor to consider the ux

density and current. &or example, the leakage reactance is mainly given by the slot

permeance and the end-coil permeance

Leakage reactance in *ynchronous machine

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+ext, we consider the reactance pertaining to the armature winding. &irst, the

leakage reactance is caused by the leakage uxes linking the armature conductors

only because of the currents in the conductors. These uxes do not link with the

eld winding and are therefore not mutual uxes. %s in an induction motor, for

convenience in calculation, the leakage reactance is divided into "$ end-connection

leakage reactance, "$ slot-Leakage reactance, "/$ tooth- top and 0ig0ag leakagereactance, and "1$ belt-leakage reactance. %ll of these components are not

signicant in every synchronous machine. n most large machines the last two

reactance are a small portion of the total leakage reactance.