PROCEEDINGS
OF THE TOMSK POLYTECHNIC INSTITUTE
NAMED AFTER S. M. KIROV, HOLDER OF THE ORDER OF THE OCTOBER REVOLUTION AND THE ORDER OF THE RED BANNER OF LABOR

Volume 295 1976

ON THE ISSUE OF ACCOUNTING FOR CORONA LOSSES IN CALCULATIONS OF LONG-DISTANCE POWER TRANSMISSION

A. G. Miloshkin

(Presented by the scientific seminar of the Department of Electrical Systems and Networks)

Economically expedient designs and conductor cross sections adopted at present do not completely eliminate corona energy losses, which may reach a considerable magnitude. The energy losses associated with the appearance of corona on the conductors of overhead lines correspond to a certain active conductance. However, the value of the conductance \((q_o)\) depends on very many factors: for example, on weather conditions, on the condition of the conductor surface, on the magnitude of the operating voltage, and so on.

Since weather conditions, as well as the condition of the conductor surface (the presence of scratches, various kinds of damage, contamination), are random in character, the value \(q_o\), characterizing corona losses, must be determined statistically, if, of course, there is no possibility of determining the corona losses for the given transmission line experimentally.

Thus, there is a need to carry out a large number of calculations in order to determine the value of the active conductance; at the same time, accounting for corona losses by means of the per-unit-length active conductance leads to rather complex iterative computations. The solution of a certain class of problems, in particular the optimization of design solutions for long-distance alternating-current transmission lines, makes it possible to take corona losses into account approximately by means of an analytic function that is a polynomial approximating the statistical dependence of the average annual corona losses (for a certain class of transmission lines in a specific climatic region) on the voltage level. An example may be the dependence obtained as a result of calculations performed according to the method for determining the values of per-unit-length corona power losses set forth in [1], [2].

Data for calculation:

a) conductor cross section — ZASO \( \times 500\);
b) voltage class — 500 kV;
c) equivalent conductor radius — 13.42 cm;
d) radius of a single conductor — 1.51 cm;
e) distance between conductors in a phase — 40 cm;
f) distance between adjacent phases — 11.1 m;
g) average conductor suspension height — 15 m;
h) weather conditions in [1] corresponding to the region of the city of Novosibirsk;

i) annual-average current density \(0.5\ \mathrm{A/mm^2}\);

k) the voltage corresponding to the onset of general corona: \(30.9\ \mathrm{kV/cm}\).

The corona losses were calculated by the formula:

\[ \Delta P_k = n^2 r^2 \left[2\left(f'_x P_x^* + f'_{\mathrm{d}}P_{\mathrm{d}} + f'_c P_c^* + f'_{\mathrm{izm}}P_{\mathrm{izm}}^*\right) + f_x P_x^* + f_{\mathrm{d}}P_{\mathrm{d}}^* + f_c P_c^* + f_{\mathrm{izm}}P_{\mathrm{izm}}^* \right], \tag{1} \]

where \(f'_i\) is the value of the empirical function for the given \(U^*\) for the conductor bundles of the outer phases, and \(f_i\) is the analogous value for the bundle of the middle phase. The results of the calculation are summarized in Tables 1 and 2.

Table 1

Table 2

The empirical curve can be approximated by various methods; in the present case the method of least squares was used [3].

As a result of the calculation it was found that, among the adopted types of approximating functions, the best agreement with the empirical one is possessed by

a)
\[ \Delta P_{\mathrm{k}} = 27.44 U_{*}^{2} - 17.38; \]

b)
\[ \Delta P_{\mathrm{k}} = 8.86 U_{*}^{6} - 0.91. \]

The latter has better convergence, but somewhat complicates the calculation when it is used. The question of the admissibility of the value of the criterion of agreement between the empirical and theoretical functions is of independent significance and is not considered in this article.

Dependencies obtained in this way may be used in calculations of normal operating conditions of power transmission lines when the problem of the most advantageous voltage in the line is not posed, i.e., in cases where means for coordinated voltage regulation are absent.

REFERENCES

1. M. A. Babikov, N. S. Komarov, A. S. Sergeev. High-Voltage Engineering. Moscow—Leningrad, GEI, 1963.

2. A. I. Dolginov. High-Voltage Engineering in Electric Power Systems. Moscow, “Energiya,” 1968.

3. L. Z. Rumshiskii. Mathematical Processing of Experimental Results. Moscow, “Nauka,” 1971.