Short-circuit inductance

Measurement of short-circuit inductance

Short-circuit inductance of a real linear two-winding transformer is inductance measured across the primary or secondary winding when the other winding is short-circuited.^[1]^{[Notes 1]}　 The method of measuring the short circuit inductance is described in industrial standard. The industrial standard also stipulates a method for obtaining the coupling factor by combining it with the open circuit inductance value.

Equivalent circuit

Measured primary and secondary short-circuit inductances may be considered as constituent parts of primary and secondary self-inductances. They are derived by using Ho-Thevenin's theorem from the equivalent inductance of the three-terminal equivalent circuit as follows. Then they are related according to the coupling factor as,

L_{\mathrm {sc1} }=(1-k^{2})\cdot L_{\mathrm {1} }\,

L_{\mathrm {sc2} }=(1-k^{2})\cdot L_{\mathrm {2} }\,

Where

k is coupling coefficient
L₁ is primary self-inductance
L₂ is secondary self-inductance

Short-circuit inductance measurement is used in conjunction with open-circuit inductance measurements to obtain various derived quantities like $k$ , the inductive coupling factor and $\sigma$ , the inductive leakage factor. $k$ is derived according to:^{[Notes 2]}

k={\sqrt {1-{\frac {L_{\text{sc}}}{L_{\text{oc}}}}}}

where

$L_{\text{sc}}$ is the short-circuit measurement of primary or secondary inductance
$L_{\text{oc}}$ is the corresponding open-circuit measurement of primary or secondary inductance

Other transformer parameters like leakage inductance and mutual inductance which cannot be directly measured may be defined in terms of k.

Short-circuit inductance is one of the parameters that determines the resonance frequency of the magnetic phase synchronous coupling in a resonant transformer and wireless power transfer. Short-circuit inductance is the main component of the current-limiting parameter in leakage transformer applications.

References[]

^ Japan Industrial Standard C 5602-1986, pp 34, 4305

Notes[]

^ This value is sometimes imprecisely referred to as leakage inductance
^ the same k value can be obtained measured from the primary side or from the secondary side

[1] Japan Industrial Standard C 5602-1986, pp 34, 4305

[2] This value is sometimes imprecisely referred to as leakage inductance

[3] the same k value can be obtained measured from the primary side or from the secondary side

[1]

[Notes 1]

[Notes 2]

Short-circuit inductance

See also[]

References[]

Notes[]