Utilization factor according to Schwaiger

The Schwaiger utilization factor (also known as the degree of homogeneity ) is a measure of the homogeneity of an electric field . He then plays a role in a high-voltage system to be well utilized the available space as possible without too high field strengths occur to spark or arc discharges can cause. “Ideal” in this sense is the homogeneous field of an ideal plate capacitor .

The utilization factor is named after Anton Schwaiger . ${\displaystyle \eta }$

Definition:

${\displaystyle \eta ={\frac {E_{\mathrm {mittel} }}{E_{\mathrm {max} }}}}$

If U is the voltage and s is the mean distance between the electrodes , then is

${\displaystyle \eta ={\frac {U/s}{E_{\mathrm {max} }}}}$.

The maximum field strength in an electrode arrangement with a known value is therefore ${\displaystyle \eta }$

${\displaystyle \Leftrightarrow E_{\mathrm {max} }={\frac {U}{\eta \cdot s}}}$.

Distinctions:

• ${\displaystyle \eta =1}$: homogeneous field (e.g. plate capacitor)
• ${\displaystyle \eta <1}$: slightly inhomogeneous field (e.g. sphere-plate arrangement)
• ${\displaystyle \eta <0{,}2}$: very inhomogeneous field (e.g. tip-plate arrangement)

Schwaiger found out that from a degree of homogeneity of less than 0.2 stable partial discharges can take place, whereby this can also be viewed as a limiting degree of homogeneity .

For a coaxial cylinder arrangement, the degree of homogeneity can be determined using the geometric factor  P :

${\displaystyle \eta ={\frac {\ln P}{P-1}}=\ln P\cdot {\frac {r}{s}}}$

With

${\displaystyle P=1+{\frac {s}{r}}}$,

in which

• s represents the distance between the electrodes and
• r is defined as the radius of the more curved electrode.

P is defined between one and infinity. Once P has been calculated, the η can be read from the curves drawn up by Schwaiger . A high  P results in a small  η and vice versa.

Strongly inhomogeneous fields can arise in two cases:

• The electrodes are far apart ( s large); in this case the approximation

  ${\displaystyle \eta \approx {\frac {1}{p}}={\frac {r}{r+s}}}$

to achieve a sufficiently accurate calculation.

• The radius of the more strongly curved electrode is very small. With the same throw distance and the same radius of the electrode, a different η can still occur due to the geometric arrangements .

Individual evidence

1. ^ Anton Schwaiger: Electrical strength theory . Springer Verlag, Berlin 1925.