Engineering: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,
- [math]\displaystyle{ L_{\mathrm{sc1}} = (1-k^2)\cdot L_{\mathrm{1}}\, }[/math]
- [math]\displaystyle{ L_{\mathrm{sc2}} = (1-k^2)\cdot L_{\mathrm{2}}\, }[/math]
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 [math]\displaystyle{ k }[/math], the inductive coupling factor and [math]\displaystyle{ \sigma }[/math], the inductive leakage factor. [math]\displaystyle{ k }[/math] is derived according to:[Notes 2]
- [math]\displaystyle{ k = \sqrt{1 - \frac{L_\text{sc}}{L_\text{oc}}} }[/math]
where
- [math]\displaystyle{ L_\text{sc} }[/math] is the short-circuit measurement of primary or secondary inductance
- [math]\displaystyle{ L_\text{oc} }[/math] 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.
See also
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
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