Short circuit inductance

Measurement of the short circuit inductance

In electrical engineering, the short-circuit inductance is the inductance of a transformer as measured from one side, the primary side or the secondary side of the transformer, with the other side being short-circuited . This value is often confused with the transformer's leakage inductance .

General

similar circuit

Assuming that the transmission ratio or the coupling factor between the primary and secondary sides is k , the self-inductance of the primary winding is L ₁ and the self-inductance of the secondary winding is L ₂ . The short-circuit inductances L _{k1,2 of} the primary side and the secondary side are then as follows:

${\displaystyle L_{k1}=(1-k^{2})\cdot L_{1}}$

${\displaystyle L_{k2}=(1-k^{2})\cdot L_{2}}$

This short-circuit inductance value is a parameter which determines the resonance frequency in a resonance transformer and in wireless resonant-inductive coupling .

Coupling factor and leakage inductance

→ Main article : Coupling factor in the real transformer

The coupling factor k can then be expressed _briefly by the two inductance values L _open and L obtained by measurement as:

${\displaystyle k={\sqrt {1-{\frac {L_{\text{kurz}}}{L_{\text{offen}}}}}}}$

The coupling factor has the same value if it is measured from the primary side or from the secondary side. The relationship with the main inductance L _h1 and the two leakage inductances L _σ1 and L _σ2 is:

${\displaystyle L_{h1}=k\cdot L_{\text{offen1}}=k\cdot L_{1}}$

${\displaystyle L_{\sigma 1}=(1-k)\cdot L_{\text{offen1}}=(1-k)\cdot L_{1}}$

${\displaystyle L_{\sigma 2}=(1-k)\cdot L_{\text{offen2}}=(1-k)\cdot L_{2}}$

${\displaystyle L_{\sigma 2}=(1-k)\cdot {\frac {L_{1}}{\gamma ^{2}}}}$

Since the distribution of the leakage inductance on the primary and secondary side is often irrelevant for the loss estimation, transformer manufacturers often only specify the total leakage inductance as short-circuit inductance L _k , which corresponds to inductance L _short .

Individual evidence

1. ^ Dieter Gerling: Lecture Electrical Machines and Drives . University of Munich, 2016, p. 169 .