Voltage-Current Characteristics and Critical Corona Voltage on Conductors Exposed to Rain

N. B. Bogdanova

Introduction

The study of changes in the critical corona voltage, current, and losses during bad weather, i.e., in connection with changes in air humidity and the presence of precipitation on corona-producing conductors, is of considerable interest. It should be expected that the critical corona voltage \(U_{cr}\) will be lower on conductors covered with precipitation, owing to the appearance on the surface of the conductors of additional sharp points in the form of water drops, ice particles, etc.^1 Air humidity can also influence the magnitude of \(U_{cr}\). Investigation of this question [7], [8] has shown that the initial voltage in an atmosphere of water vapor differs from that in air and, for example, for symmetrical electrodes proved to be 16% higher. According to investigators of alternating-current corona [1], [9], and others, air humidity by itself, provided the conductor surface is dry, has no effect on the magnitude of the critical corona voltage.

The current and power losses due to corona on conductors exposed to rain, in an atmosphere of fog, and under icing conditions must change in comparison with the current and losses measured under normal conditions: first, as a result of the above-mentioned change in the critical corona voltage \(U_{cr}\), and second, as a result of a change in the mobility of air ions.

From Zhebrovsky’s investigations [2] with a tubular electrofilter (with direct current) it may be concluded that an increase in air humidity causes a decrease in the corona current. This is also to be expected, since an increase in air humidity leads to a decrease in the mobility of air ions and, consequently, to a decrease in the current. On the other hand, in the opinion of Peek et al. [1, 9], air humidity, while having no effect on \(U_{cr}\), likewise does not change the magnitude of the alternating-current corona power losses \(P\).

According to these same authors, the losses \(P\) increase considerably when precipitation is present on the conductors, as a result of the decrease in the critical voltage to the value

\[ U''_{cr} = m_{weather} U_{cr}, \]

where \(m_{weather} \le 1\) is the weather coefficient.

It should be noted that in technical calculations of corona losses on high-voltage transmission lines, carried out by Peek’s empirical formula,

\[ P = C(U - m_{weather} U_{cr})^2, \]

^1 Under icing conditions the critical corona voltage may even be higher than under normal conditions, owing to the increase in conductor diameter.

the weather coefficient is considered equal to unity only in sunny weather. Thus it is tacitly assumed, contrary to Peek’s statement, that in cloudy weather, but in the absence of precipitation, the critical voltage decreases and the losses increase. An increase in the corona current on conductors covered with precipitation was also noted in Schriegel’s work [10]. On the other hand, Kuhn [11], in experiments with a dc corona, found that the magnitude of the corona current is independent of whether the conductors are covered with precipitation or not.

The purpose of the present work is to investigate the influence of air humidity and precipitation on conductors on the technical characteristics of a dc corona—the critical voltage and current, i.e., to clarify the following questions: 1) whether the critical corona voltage changes on conductors located in humid air if the conductor surface remains dry; 2) how the critical voltage changes when there is precipitation on the conductors; 3) what is the course of the voltage-current characteristics of the corona in the case when the conductors corona in a humid atmosphere and their surface remains dry; 4) when drops are deposited on the surface of the conductors.

The measurements were carried out during corona of a conductor placed inside a coaxial cylinder, of a conductor placed opposite a plane, and on two parallel conductors. For more details on the experimental arrangements, see the preceding communication [3]. In all experiments measures were taken to shield the insulators from moisture falling on them. The leakage currents measured during rain proved to be negligible and in general equal to the leakage currents under normal conditions. The absence of an edge effect was checked for all arrangements. A spray atomizer filled with distilled water was connected to an air blower through a tee, which made it possible, within certain limits, to vary the intensity of the rain; in all experiments it did not exceed \(1\ \mathrm{mm/min}\).

It was shown earlier [3,4] that as the voltage above the critical corona voltage increases, moisture is deposited on the conductors in ever smaller amounts, and at certain voltages \(U_c\) the conductors remain dry while under rain. This makes it possible, at \(U > U_c\), to study the corona of conductors in a humid atmosphere but in the absence of precipitation on them; at \(U < U_c\), the precipitation falling on the conductors and the air humidity jointly affect the magnitude of the current and the critical corona voltage. In this case the air humidity remains the same in both cases.

Voltage-current characteristics of the corona discharge

To determine the influence of precipitation on the magnitude of the corona current, the following experiments were performed. The conductors were kept under rain for some time. Then the rain was stopped, a dc voltage \(U\), somewhat exceeding \(U_{\mathrm{cr}}\), was switched on. The conductors gradually dried. At the same time the number of drops in the field of view of a sighting tube directed at the conductor, and the corona current \(I\), were recorded. Fig. 1 gives the results of such an experiment for parallel conductors; as the conductors dried, with the decrease in the number of drops \(n\), the corona current \(I\) decreased, and at \(n = 0\), \(I = I_0\)—the current measured previously in the absence of rain.

Figs. 2, 3, and 4 give typical voltage-current characteristics of the corona discharge (solid curves—measured under normal conditions, dashed curves—during rain). Fig. 2 relates to the case of corona of a conductor inside a coaxial cylinder (a conductor of diameter \(2r_0 = 2.3\ \mathrm{mm}\) is at negative polarity with respect to the cylinder). The corona current \(I\), measured during rain at low voltages, is greater than the current \(I_0\), measured under normal conditions. As the increas—

Fig. 1. Dependence of the magnitude of the corona current on the number of drops on the surface of the conductors.

Visible labels in the figure: \(I\ \mu\mathrm{A}/\mathrm{cm}\); “Parallel conductors”; \(2r_0 = 2.3\ \mathrm{mm}\); \(h = 10\ \mathrm{cm}\); “Number of drops per unit length of the wire.”

Fig. 2. Volt-ampere characteristics of a corona discharge. The conductor is placed inside a cylinder coaxial with it.

Visible labels in the figure: \(I\ \mu\mathrm{A}/\mathrm{cm}\); “Coaxial cylinders”; \(2r_0 = 2.3\ \mathrm{mm}\); \(I_{\mathrm{ok}}\); \(U\ \mathrm{kV}\); “Voltage”; curves \(a\), \(b\).

Fig. 3. Volt-ampere characteristics of a corona discharge. The conductor is placed opposite a plane.

Visible labels in the figure: \(I\ \mu\mathrm{A}/\mathrm{cm}\); “\((-)\) conductor–plane”; \(2r_0 = 0.2\ \mathrm{mm}\); \(h = 10\ \mathrm{cm}\); \(I_{\mathrm{ok}}\); \(U\ \mathrm{kV}\); “Voltage”; curves \(I\), \(I_0\), \(I - I_0\).

Fig. 4. Volt-ampere characteristics of a corona discharge. Parallel conductors.

Visible labels in the figure: \(I\ \mu\mathrm{A}/\mathrm{cm}\); “Parallel conductors”; \(2r_0 = 0.8\ \mathrm{mm}\); \(h = 20\ \mathrm{cm}\); \(2r_0 = 2.3\ \mathrm{mm}\); \(h = 10\ \mathrm{cm}\); \(I_{\mathrm{ok}}\); \(U\ \mathrm{kV}\); curves \(I\), \(I_0\), \(I - I_0\).

...of voltage, \(I\) tends to \(I_0\) and then becomes less than \(I_0\) (beginning at certain voltages the ratio \(\dfrac{I}{I_0}\) becomes constant, equal to approximately 0.7–0.8).

The volt–ampere characteristics of the discharge have a somewhat different course in the case of corona of a wire opposite a plane (Fig. 3) and in the case of parallel wires (Fig. 4). As the voltage is increased, the current \(I\) approaches in magnitude the current \(I_0\), and in some cases becomes equal to it (Fig. 3 and the upper curve of Fig. 4), but does not become less than \(I_0\). Numerous experiments have shown that, at the voltage at which: 1) in coaxial cylinders the ratio \(\dfrac{I}{I_0}\) becomes equal to a constant fractional number (0.7–0.8); 2) in the two other cases \(I \simeq I_0\), visual, photographic, and other observations revealed no precipitation on the wires. We have defined this voltage as the voltage \(U_c\), at which the corona wires remain dry while under rain.

Fig. 5. Dependence of the relative change in corona current on voltage for the case of a wire placed inside a cylinder.

At voltages \(U\) lying in the range between \(U_{\mathrm{cr}}\) and \(U_c\), moisture is deposited on the wires. In this case the current must be greater than when measured in the absence of rain (Fig. 1), which is indeed observed—see the volt–ampere curves in Figs. 2, 3, and 4. As the voltage is increased, droplets are deposited in ever smaller quantities—the current \(I\) approaches the values of the current \(I_0\). It should be noted that even a small amount of precipitation on the wires is sufficient for \(I\) not to equal \(I_0\) (wire–plane and parallel wires). Thus it may be stated that precipitation on the wires undoubtedly leads to an increase in the corona current in all the cases considered.

For \(U > U_c\), the current \(I\) can differ from \(I_0\) only because of the influence of air humidity on the current or a change in \(U_{\mathrm{cr}}\). If it is assumed that \(U_{\mathrm{cr}}\) does not change (and we shall see below that this is correct), then one may expect a decrease in the corona current owing to a reduction in the mobility of the ions. Such an effect was observed by us only in the case of corona of a wire inside a coaxial cylinder (Fig. 5, for \(U > U_c\), \(\dfrac{I}{I_0} = 0.8\)). In the two other cases the influence of air humidity is evidently small; at any rate, we never once recorded currents smaller than \(I_0\); for \(U > U_c\), \(I = I_0\).

Critical corona voltage

The critical corona voltage \(U_{\mathrm{cr}}\) in the absence of rain was determined from straight, reduced characteristics

\[ \frac{I}{U} = A(U - U_{\mathrm{cr}}).^{1)} \]

\(^{1)}\) In light of recent work, such a construction for bipolar corona (two parallel wires) is not entirely legitimate, and the dependence of current on voltage has a more complicated form [5].

Taking advantage of the circumstance that at \(U>U_c\) the conductor remains dry while under rain, we can determine the critical corona voltage in a humid atmosphere, \(U'_{\mathrm{cr}}\), under the condition of a dry conductor surface. To do this, we construct the reduced characteristic of such a conductor “dried” by the corona; in the coordinates \(\frac{I}{U}, U\) we plot the points corresponding to \(U>U_c\) and, extending the resulting straight line to its intersection with the \(U\)-axis, determine \(U'_{\mathrm{cr}}\) in a humid atmosphere as the intercept cut off on the \(U\)-axis. Such constructions are carried out in Fig. 6 for a conductor coronating inside a cylinder (conductor diameter \(0.38\) mm)—straight line \(b\); straight line \(a\) represents the reduced corona characteristic under normal conditions. It follows from the figure that \(U'_{\mathrm{cr}}=U_{\mathrm{cr}}\). Having carried out the same constructions for a large number of other cases, we invariably arrive at the same conclusion. For the case of a conductor placed opposite a plane and of parallel conductors, such constructions are superfluous, for at \(U>U_c\), \(I=I_o\), and the straight lines of the reduced characteristics coincide, \(U'_{\mathrm{cr}}=U_{\mathrm{cr}}\).

To confirm this same proposition, we constructed the reduced characteristics of a corona discharge in a tubular electrofilter at various air humidities, using Zhebrovsky’s data [2] (Fig. 7). On

Fig. 6. Straight lines of the reduced corona characteristics for the case of a conductor placed inside a cylinder.

Fig. 7. Straight lines of the reduced characteristics of a corona discharge in a tubular electrofilter at different air humidities (according to Zhebrovsky’s data).

the basis of these data, one may likewise conclude that the magnitude of the critical corona voltage remains unchanged when the air humidity varies over a fairly wide range. Let us note that in our experiments, in the atmosphere surrounding the conductor, there was not only an increased amount of water vapor, but the entire space was filled with water droplets (the rain continued!). Consequently, rain itself, provided the surface of the conductors is dry, does not change the magnitude of the critical corona voltage.

Let us now turn to experiments in which, in contrast to those just considered, moisture was deposited on the conductors. The critical corona voltage under these conditions is

\[ U'_{\mathrm{cr}} = m_{\mathrm{pog}} U_{\mathrm{cr}}. \]

We also found the value of the weather coefficient from the reduced characteristics [6]. The weather coefficient under the same “meteorological conditions” (rain intensity) proved to depend very strongly on the conductor diameter and on the magnitude of the—

the magnitude of the applied voltage. In the case of conductors of large cross section (2.5 mm), the values of the weather coefficient \(m_{\text{wea}}\) fell to 0.5.

As the voltage increased, the weather coefficient approached unity in its values, at those voltages at which the conductor remained dry while under rain \((U > U_c)\), \(m_{\text{wea}} = 1\).

In experiments with alternating voltage, we observed a change in the sign of corona rectification in those cases when drops settled on the conductor; as the voltage increased, as the amount of moisture on the surface of the conductors decreased, the current again changed its direction to the initial one—the direction it had in the absence of rain.

Conclusion

It has been shown that the corona current when precipitation is present on the conductors is greater than the current measured under normal conditions; an increase in the amount of moisture on the conductors leads to an increase in the current, and vice versa. The corona current in a humid atmosphere, but in the absence of precipitation on the conductors, is either smaller (our experiments with coaxial cylinders and Zhebrovsky’s experiments), or close (our experiments with parallel conductors and with a conductor placed opposite a plane) to the values of the current measured under normal conditions. If moisture is not deposited on the conductors, the corona current may change as a result of a decrease in the mobility of ions in humid air. There is nothing surprising in the fact that this change is substantial for the closed space of coaxial cylinders and imperceptible for the open space of the other two arrangements.

The critical corona voltage depends only on the condition of the surface of the conductors and does not depend on the humidity of the air. This provides grounds for taking the weather coefficient as equal to unity not only in sunny weather; in cloudy weather, when the surface of the conductors nevertheless remains dry, the weather coefficient should also be taken as equal to unity. This will make it possible, in technical calculation, to proceed not from the number of average annual sunny days, but from the number of average annual days without precipitation.

In conclusion, I express my deep gratitude to Professor Doctor A. A. Vorobiev for valuable advice and guidance.

References Cited

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