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. 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,


 * $$L_{\mathrm{sc1}} = (1-k^2)\cdot L_{\mathrm{1}}\,$$
 * $$L_{\mathrm{sc2}} = (1-k^2)\cdot L_{\mathrm{2}}\,$$

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:


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

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.