page_title: Leakage inductance
section_title: Inductive leakage factor and inductance
hierarchical_section_title: Leakage inductance / Inductive leakage factor and inductance
caption_attribution_description: English: Transformer equivalent circuit with Heyland factor constants expressed in terms of coupling coefficient k.
context_page_description: 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 of some loads.
  Leakage inductance applies to any imperfectly-coupled magnetic circuit device including motors.
context_section_description: 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.
  The transformer inductance can be characterized in terms of the three inductance constants as follows,
   ------ (Eq. 2.8)
   ------ (Eq. 2.9)
   ------ (Eq. 2.10) ,
  where,
  c is magnetizing inductance, corresponding to magnetizing reactance XM
  LPσ & LSσ are primary & secondary leakage inductances, corresponding to primary & secondary leakage reactances XPσ & XSσ.
  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,
  .
  Since 
   ------ (Eq. 2.11)
  and
   ------ (Eq. 2.12),
  we have
   ------ (Eq. 2.13),
  	
  which allows expression of the equivalent circuit in Fig. 4 in terms of winding leakage and magnetizing inductance constants as follows,
   ------ (Eq. 2.14  Eq. 1.1b)
   ------ (Eq. 2.15  Eq. 1.1c).
  The nonideal transformer in Fig. 4 can be shown as the simplified equivalent circuit in Fig. 5, with secondary constants referred to the primary and without ideal transformer isolation, where,
   ------ (Eq. 2.16)
   is magnetizing current excited by flux ΦM that links both primary and secondary windings
   is the primary current
   is the secondary current referred to the primary side of the transformer.
caption: Fig. 4 Nonideal transformer equivalent circuit in terms of coupling coefficient k[27]
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