On the Determination of the Weather Coefficient

N. B. Bogdanova

The presence of precipitation on the surface of corona-producing conductors causes a lowering of the critical corona voltage to the value

\[ U_{kp}^{\prime\prime}=m_{pog}U_{kp}, \tag{1} \]

where \(U_{kp}\) is the critical corona voltage under normal conditions, and \(m_{pog}\) is the weather coefficient, a quantity less than unity.

For direct current, the equation of the reduced corona characteristic on conductors not under rain is represented in the form

\[ \frac{I_0}{U}=A(U-U_{kp}). \tag{2} \]

Here \(U\) is the applied voltage,
\(A\) is a coefficient depending on geometrical factors, ion mobility, and air density.

The validity of this equation is beyond doubt for the case of a unipolar corona. In the corona of two parallel conductors (bipolar-current corona), Kaptsov [1] proposes using a formula of the type of formula (2). Popkov [2], as a result of extensive theoretical and experimental investigation carried out by him, arrives at a more complex dependence of the corona current on the voltage. In our reasoning we shall proceed from the validity of formula (2) also for parallel conductors.

In the case of corona of conductors under rain,

\[ \frac{I}{U}=A_1(U-U_{kp}^{\prime\prime}). \tag{3} \]

The coefficient \(A\) in formula (2) has changed, since it depends on ion mobility, and the latter changes when the humidity of the air changes. In the preceding communication [3] it was noted that air humidity by itself, provided the surface of the conductors is dry, changes the values of the current \(I\) only in the case of corona of a conductor inside a cylinder. In the corona of a conductor located opposite a plane and of parallel conductors, the influence of humidity on the current is insignificant; thus for these configurations one may assume

\[ A=A_1 \]

and write equation (3) in the following form:

\[ \frac{I}{U}=A(U-m_{pog}U_{kp}). \tag{4} \]

With a constant value of the weather coefficient, the straight line (4) is parallel to the straight line (3), and the value \(U_{kp}^{\prime\prime}=m_{pog}U_{kp}\) could be found by extending the straight line (4) to its intersection with the \(U\)-axis. But, first, the weather coefficient \(m_{pog}\) is not a constant quantity; when the voltage changes, the co-

the amount of precipitation on the corona wires changes [4], \(m_{\mathrm{pog}}\) also changes, and it is essentially impossible to realize dependence (4) with a constant value of \(m_{\mathrm{pog}}\). Secondly, this is not necessary. It is sufficient to know, at some voltage \(U_1\), the current \(I_1\) when the surface of the wires is covered with precipitation. Through this point \(\left(\dfrac{I_1}{U_1}, U_1\right)\) one can draw a straight line parallel to the straight line of the reduced discharge characteristic under normal conditions (2), and, extending it to its intersection with the \(U\)-axis, determine \(U''_{\mathrm{cr}} = m_{\mathrm{pog}} U_{\mathrm{cr}}\). An example of such a construction for corona on a wire opposite a plane is shown in Fig. 1. The straight line \(a\) represents the reduced characteristic of the corona discharge on a wire with a dry surface; the dashed straight line \(b\) is drawn through the point

\[ C\left(\frac{I_1}{U_1}=3.4\cdot 10^{-3}\ \frac{\mu\mathrm{A}}{\mathrm{cm}\,\mathrm{kV}},\ U_1=37\ \mathrm{kV}\right) \]

parallel to the straight line \(a\). The weather coefficient \(m_{\mathrm{pog}}\) determined from this construction proved to be equal to 0.83. If \(A\) and \(U_{\mathrm{cr}}\) are found from the equation of the reduced corona characteristic on wires with a dry surface, then the coefficient \(m_{\mathrm{pog}}\) can also be determined from the following calculation:

\[ m_{\mathrm{pog}}=\frac{1}{U_{\mathrm{cr}}}\left[U_1-\frac{I_1}{U_1 A}\right]. \tag{5} \]

Fig. 1. Determination of the weather coefficient from the construction of straight lines of reduced corona characteristics.

The proposed method for determining the weather coefficient has an advantage over determining this quantity from the inception of the corona current-voltage characteristic: \(U''_{\mathrm{cr}}\), determined from the inception of the current-voltage characteristic, is not the quantity that determines the current (local corona!), and consequently \(m_{\mathrm{pog}}\) will then be determined incorrectly. This method makes it possible, on the basis of only one measurement of current and voltage, to determine the weather coefficient and its change under the influence of any causes. Using this method, we were able [4] to trace the change in the weather coefficient with increasing applied voltage \(U\). Since, as the voltage increased, the amount of precipitation on the wires decreased, the weather coefficient increased, tending, as the wires “dried,” toward unity.

References Cited

1. N. A. Kaptsov — Electrical Phenomena in Vacuum and Gases, ONTI, 1947.
2. V. I. Popkov — Reports of the Academy of Sciences, vol. LVIII, no. 5, 1947.
3. N. B. Bogdanova — Proceedings of TPI, 1948.
4. A. A. Vorob'ev and N. B. Bogdanova — Proceedings of TPI, ZhTF, 1948.