Leakage inductance
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.
Voltage drop across the leakage reactance results in often undesirable supply regulation with varying transformer load.
[3] Leakage inductance applies to any imperfectly coupled magnetic circuit device including motors.
are, in additive and subtractive series connection of the two windings, given by,[8] The coupling factor is derived from the inductance value measured across one winding with the other winding short-circuited according to the following:[11][12][13] 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.
1 depends strictly on open-circuit conditions for the respective winding inductances considered.
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.
is in practice given as where The nonideal transformer's mesh equations can be expressed by the following voltage and flux linkage equations,[20] 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,[21] The transformer inductance can be characterized in terms of the three inductance constants as follows,[25][26] where, The transformer can be expressed more conveniently as the equivalent circuit in Fig.
3 with secondary constants referred (i.e., with prime superscript notation) to the primary,[25][26] Since and we have
4 in terms of winding leakage and magnetizing inductance constants as follows,[26] The nonideal transformer in Fig.
5, with secondary constants referred to the primary and without ideal transformer isolation, where, Refined inductive leakage factor derivation a.
2.14: All equations in this article assume steady-state constant-frequency waveform conditions the
Leakage inductance has the useful effect of limiting the current flows in a transformer (and load) without itself dissipating power (excepting the usual non-ideal transformer losses).
Transformers are generally designed to have a specific value of leakage inductance such that the leakage reactance created by this inductance is a specific value at the desired frequency of operation.
Commercial and distribution transformers rated up to say 2,500 kVA are usually designed with short-circuit impedances of between about 3% and 6% and with a corresponding
Thus for purely resistive loads, such transformers' full-to-no-load voltage regulation will be between about 1% and 2%.
High leakage reactance transformers are used for some negative resistance applications, such as neon signs, where a voltage amplification (transformer action) is required as well as current limiting.
In this case the leakage reactance is usually 100% of full load impedance, so even if the transformer is shorted out it will not be damaged.
Without the leakage inductance, the negative resistance characteristic of these gas discharge lamps would cause them to conduct excessive current and be destroyed.
Transformers with variable leakage inductance are used to control the current in arc welding sets.
In these cases, the leakage inductance limits the current flow to the desired magnitude.
Transformer leakage reactance has a large role in limiting circuit fault current within the maximum allowable value in the power system.
[2] In addition, the leakage inductance of a HF-transformer can replace a series inductor in a resonant converter.
