Capacitive Currents in DPZ Lines

V. K. Shcherbakov and K. P. Meshcheryakov

1. Three-phase electric-power transmission lines with one grounded phase, in which there are no conductors and the current of this phase flows through the earth—DPZ (Fig. 1)—have until now been built for rated voltages up to 35 kV.

Therefore, in calculations of DPZ lines there has been no need to take capacitive currents into account. This is also explained by the circumstance that the electrical networks of agricultural regions, where three-phase systems with one grounded phase have become widespread, are made exclusively as overhead lines, i.e., lines possessing low capacitance. Lines of 35 kV in agricultural regions may reach an economically expedient limiting length of 100–150 km [1]. Such a line would cause a capacitive current of 5–7 amperes, whose influence on the operating regimes of the line would be scarcely noticeable.

Fig. 1. Diagram of a three-phase electric-power transmission line “two wires—earth”.

However, the growth of electrification of agriculture in the USSR increases from year to year the power transmitted and distributed by high-voltage networks. The growth of agricultural mechanization makes it expedient to build comparatively large district power stations for the electrification of agriculture and to unite the power stations of agricultural districts into electrical systems. High-voltage electrical networks distributing electric power from district power stations and linking individual power stations into systems have become widely used, and many thousands of kilometers of electric-power transmission lines at a voltage of 35 kV have already been built and are in operation.

The electrification of remote collective farms and state farms from large interdistrict hydroelectric stations and thermal district power stations becomes expedient when using electrical networks at a voltage of 110,000 volts. Lines and networks for a rated voltage of 110 kV are already beginning to be built for the purposes of agricultural electrification, and in the near future these networks will undoubtedly become widely used in agricultural regions.

A characteristic feature of high-voltage electrical networks in agricultural regions is their great length with relatively small transmitted and distributed powers. Under these conditions, electric-power transmission lines at a voltage of 110 kV with a length of several hundred kilometers are conceivable.

A power-transmission line with a nominal voltage of 110 kV and a length of 200–300 kilometers produces a capacitive current at the beginning of the line of 40–60 amperes. As will be shown below, a capacitive current of such magnitude cannot be disregarded; moreover, in some cases this capacitive current becomes the factor determining the operating mode of the power transmission.

The successful and economical operation of DPZ 35 kV networks gives grounds to assume that networks with a nominal voltage of 110 kV in agricultural districts should likewise expediently be constructed with one grounded phase. Earlier investigations [2], as well as additional and special recent investigations on problems of the operation of power transmissions with a grounded phase, have to a considerable degree clarified the operation of the insulation of 110 kV lines and transformers in power transmissions with a grounded phase, the use of AC-70 conductors under corona conditions on the lines of these power transmissions, etc. The present article considers only the particular features of the manifestation of capacitive currents in DPZ power transmissions at a voltage of 110 kV.

1. The capacitive currents in the phases of a DPZ line may be calculated from the formulas [2]:

\[ \overline{I}_{a(c)}=-\bigl(\overline{I}_{b(c)}+\overline{I}_{c(c)}\bigr)/3.\omega =U_a\,\frac{C_{22}+C_{33}}{2}; \]

\[ \overline{I}_{b(c)}=j\omega\,\overline{U}_a(C_{22}-\alpha C_{23})(\alpha-1); \]

\[ \overline{I}_{c(c)}=j\omega\,\overline{U}_a \left(C_{33}-\frac{1}{\alpha}C_{23}\right)\cdot(\alpha^2-1), \]

where \(C_{22}\), \(C_{33}\), and \(C_{23}\) are the partial capacitances of the line to ground and between conductors.

Figure 2 gives the vector diagram of the capacitive currents of a DPZ line, it being assumed that phase \(a\) is grounded.

Fig. 2. Vector diagram of the capacitive currents of a DPZ line.

The capacitive currents in the phases form an unsymmetrical three-phase system, in the decomposition of which into symmetrical components currents of negative sequence in the phases are obtained, as is seen in Fig. 3.

The negative-sequence capacitive currents are added in the phases to the negative-sequence currents due to the flow of load currents in the line, and as a result a total asymmetry is obtained in the elements of the power transmission system—the generator, transformer, line, etc.

Fig. 3. Vector diagram of the capacitive currents of a DPZ-110 kV line and their symmetrical components.

In Fig. 4 (curve 2) the degree of asymmetry in the generator feeding a line of various lengths according to the scheme of Fig. 5 is shown. The line is made with AS-185 conductors; the power transmitted over the line is limited by losses—

Fig. 4. Dependence of the degree of asymmetry in the generator on the length of a DPZ-110 kV line.

—of positive-sequence voltage in the line of 10%; \(\cos \varphi_{\text{load}} = 0.85\). Curve 2 indicates a very high degree of current asymmetry for line lengths of the order of 300 km (20–25%). The role of the capacitive current in creating current asymmetry in the generator is shown by curve 3, Fig. 4. In the left—

in lines up to 150 km long, the capacitance of the line has a favorable effect on the ratio of negative- and positive-sequence currents in the generator and, obviously, in other elements of the power transmission system. For these line lengths, the current unbalance in the generator, calculated without taking account of the capacitive current—curve 1 (Fig. 4)—is higher than the total (actual) value calculated with allowance for the capacitive current—curve 2.

However, in lines whose length exceeds 150 km, the capacitance of the line already has an adverse effect on the ratio of negative- and positive-sequence currents in the generator and is decisive in this sense. Power transmission without load gives the greatest degree of unbalance—curve 3, Fig. 4.

Fig. 5. Simplest diagram of a DPZ—110 kV transmission line.

In a branched 110 kV network of agricultural districts, constructed, as a rule, with conductors of cross-section smaller than 185 mm² and, consequently, designed to transmit comparatively small powers over sections of the network, the “capacitive effect” in creating current unbalance in the generator and other elements of the power transmission system will manifest itself still more strongly. In this case it will not be a great exaggeration to take as the limiting unbalance, i.e., the unbalance of the network at no load.

Fig. 6. Dependence of the load current and the capacitive current in the grounded phase on the length of the DPZ line.

1. The capacitive current in a DPZ line at a voltage of 110 kV has a strong effect on the magnitude of the line current in the ground. The ratio, by magnitude, of the capacitive and load currents in the grounded phase of the line is shown in Fig. 6. As can be seen, for large line lengths the magnitude of the capacitive current is equal to or greater than the magnitude of the load current in the grounded phase. These two currents, being added geometrically, form the current in the line ground.

The power factor of the load current has a great influence on the magnitude of the total current in the ground. The vector diagram of the currents in the grou—

grounded phase, Fig. 7, and the graph in Fig. 8 clearly show within what broad limits the magnitude of the total current in the ground can vary, depending on the power factor of the line load, for the particular, but most probable, ratio of capacitive and load currents.

Fig. 7. Vector diagram of currents in the ground at \(I_c = 0.75 I_n\).

If it is assumed that most often lines in agricultural districts will carry a load with a power factor of about 0.85, then in this particular case the total current in the ground of the line \((\dot I_{\text{load}} + \dot I_{c3})\) will differ comparatively little in magnitude from the line load current, Fig. 9.

Fig. 8. Dependence of the current in the ground on the value of \(\cos \varphi\) for

\[ \frac{I_c}{I_n} = 0.75. \]

It is important to note that the greatest value of the total current in the ground of the line does not coincide with the greatest line load. On the contrary, the greatest value of the total current in the ground of the line may occur when the line is running idle, for certain values of the load power factor.

1. 1) In extended 110 kV DPZ lines serving the power supply of agricultural districts, capacitive currents may reach-

may reach a value equal to, or even greater than, the current caused by the line load;

2) the asymmetry of the currents in the line and at the load, as well as in the generators feeding the DPZ lines, is to a considerable degree, and often exclusively, determined by the capacitive current of the line;

Fig. 9. Graph of the influence of capacitive current on the ground current for various lengths of a DPZ line.

3) when determining the greatest value of the total ground current of a line, it is necessary to investigate the variation of this current as a function of fluctuations in the line load, taking into account the variability of the load power factor.

REFERENCES

1. Shcherbakov V. K. Power supply of agricultural regions from high-voltage networks. Proceedings of the Tomsk Polytechnic Institute, vol. 72, 1952.

2. Shcherbakov V. K. Asymmetrical electric-power transmission. Electrical calculation. Tomsk, 1946.