Leakage inductance derives from the electrical property of an imperfectly coupled transformer whereby each winding behaves as a self-inductance in series with the winding's respective ohmic resistance constant. These four winding constants also interact with the transformer's mutual inductance. The winding leakage inductance is due to leakage flux not linking with all turns of each imperfectly coupled winding.
Leakage reactance is usually the most important element of a power system transformer due to power factor, voltage drop, reactive power consumption and fault current considerations.
Leakage inductance depends on the geometry of the core and the windings. Voltage drop across the leakage reactance results in often undesirable supply regulation with varying transformer load. But it can also be useful for harmonic isolation (attenuating higher frequencies) of some loads.
Leakage inductance applies to any imperfectly coupled magnetic circuit device including motors.
Leakage inductance and inductive coupling factor
The magnetic circuit's flux that does not interlink both windings is the leakage flux corresponding to primary leakage inductance LPσ and secondary leakage inductance LSσ. Referring to Fig. 1, these leakage inductances are defined in terms of transformer winding open-circuit inductances and associated coupling coefficient or coupling factor .
The primary open-circuit self-inductance is given by
------ (Eq. 1.1a)
where
------ (Eq. 1.1b) ------ (Eq. 1.1c)
and
is primary self-inductance
is primary leakage inductance
is magnetizing inductance
is inductive coupling coefficient
Measuring basic transformer inductances & coupling factor
Transformer self-inductances & and mutual inductance are, in additive and subtractive series connection of the two windings, given by,
in additive connection, , and,
in subtractive connection,
such that these transformer inductances can be determined from the following three equations:Harris 1952, p. 723, fig. 43
.
The coupling factor is derived from the inductance value measured across one winding with the other winding short-circuited according to the following:
Per Eq. 2.7, and Such that
The Campbell bridge circuit can also be used to determine transformer self-inductances and mutual inductance using a variable standard mutual inductor pair for one of the bridge sides.Khurana 2015, p. 254, fig. 7.33 It therefore follows that the open-circuit self-inductance and inductive coupling factor are given by ------ (Eq. 1.2), and, , with 0 < < 1 ------ (Eq. 1.3)
where
and
is mutual inductance
is secondary self-inductance
is secondary leakage inductance
is magnetizing inductance referred to the secondary
is inductive coupling coefficient
is the approximate turns ratio
The electric validity of the transformer diagram in Fig. 1 depends strictly on open-circuit conditions for the respective winding inductances considered. More generalized circuit conditions are as developed in the next two sections.
Inductive leakage factor and inductance
A nonideal linear two-winding transformer can be represented by two mutual inductance-coupled circuit loops linking the transformer's five impedance constants as shown in Fig. 2.
where
M is mutual inductance
& are primary and secondary winding resistances
Constants , , , & are measurable at the transformer's terminals
Coupling factor is defined as
, where 0 < < 1 ------ (Eq. 2.1)
The winding turns ratio is in practice given as
------ (Eq. 2.2).
where
NP & NS are primary and secondary winding turns
vP & vS and iP & iS are primary & secondary winding voltages & currents.
The nonideal transformer's mesh equations can be expressed by the following voltage and flux linkage equations,
------ (Eq. 2.3) ------ (Eq. 2.4) ------ (Eq. 2.5) ------ (Eq. 2.6),
where
is flux linkage
is derivative of flux linkage with respect to time.
These equations can be developed to show that, neglecting associated winding resistances, the ratio of a winding circuit's inductances and currents with the other winding short-circuited and at open-circuit test is as follows,
------ (Eq. 2.7),
where,
ioc & isc are open-circuit and short-circuit currents
Loc & Lsc are open-circuit and short-circuit inductances. is the inductive leakage factor or Heyland factor & are primary and secondary short-circuited leakage inductances.