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.

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,

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

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

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 ${\displaystyle k}$, the inductive coupling factor and ${\displaystyle \sigma }$, the inductive leakage factor. ${\displaystyle k}$ is derived according to:^{[Notes 2]}

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

where

• ${\displaystyle L_{\text{sc}}}$ is the short-circuit measurement of primary or secondary inductance
• ${\displaystyle L_{\text{oc}}}$ 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.

• Resonant inductive coupling