ON THE QUESTION OF LONG CABLE LINES

O. B. Tolpygo

1. In connection with the great Stalinist construction projects of communism, the question has arisen of the need to transmit electric power over distances on the order of 1000 km and more. In the future these distances will increase considerably with the utilization of the rich energy reserves of Siberia and the Far East.

All this makes the problem of increasing the range of electric-power transmission highly urgent. The transmission of considerable powers by alternating current over long distances is limited by the large value of the reactive impedance of the overhead line, which determines the stability of parallel operation and causes a considerable voltage drop between the beginning and the end of the line. The voltage drop between the ends of a long line can be considerably reduced if operation is carried out in the regime of transmitting natural power. The natural power characterizes the carrying capacity of the line

\[ P_n=\frac{U^2}{Z_c}, \]

where \(P_n\) is the natural power,
\(U\) is the line voltage,
\(Z_c\) is the surge impedance.

The surge impedance of overhead lines is an approximately constant quantity of \(400\text{–}380\ \Omega\) without conductor splitting, and for a line with split conductors about \(250\ \Omega\).

Thus, at the adopted voltage for the electric-power transmission of the great construction projects of \(400\ \text{kV}\) [1], the carrying capacity with split conductors will be \(640000\ \text{kW}\) per one circuit [1].

Reactive impedance is the principal factor determining the stability of parallel operation. The limit of static stability is determined by the expression

\[ P_m=\frac{EU}{X_c}, \]

where \(E\) is the e.m.f. of the generators of the transmitting station,
\(U\) is the voltage on the buses of the receiving substation,
\(X_c\) is the reactive impedance of the electric-power transmission, a significant part of which is the reactive impedance of the line.

To ensure the stability of parallel operation for overhead lines longer than 300 km, it is necessary to use devices that compensate the reactance of the overhead line. But the effectiveness of this measure for overhead power-transmission lines 1000 km long and more is already comparatively small, since the operating regime of such long overhead lines approaches the practically unstable regime—the regime of transmitting one quarter of a wave. The reduction of the magnitude of the reactive impedance of the line has led to the idea of investigating the possibility of applying…

cables for transmitting electric power over long distances, since cables have a surge impedance on the order of \(50\)—\(70\) ohms and a considerably lower inductance than overhead lines.

1. At the Department of Electrical Networks and Systems, calculations were carried out for the operating conditions of long cable lines. The calculations were made for cables with cross sections of \(700\ \text{mm}^2\), \(1000\ \text{mm}^2\), \(1500\ \text{mm}^2\) at a voltage of \(220\ \text{kV}\).

As an example, the parameters of a cable with a cross section of \(1000\ \text{mm}^2\) may be cited:

\[ r_0 = 0.0175\ \text{ohm/km}, \]

\[ x_0 = 0.125\ \text{ohm/km}, \]

\[ b_0 = 0.384 \cdot 10^{-4}\ \frac{1}{\text{ohm km}}, \]

\[ z_c = 62\ \text{ohms}, \]

\[ D = 100\ \text{mm}\ \text{(external diameter)}. \]

At the present time, cable designs for alternating current at a voltage of \(380\ \text{kV}\) have been developed. The cables are single-core. As is evident from the cable parameters, the surge impedance of such a cable is only \(62\) ohms, and therefore the transmission capacity of a cable power transmission line at a voltage of \(220\ \text{kV}\) is higher than the transmission capacity of an overhead line with bundled conductors at a voltage of \(400\ \text{kV}\).

Table 1

In addition to the increase in the transmission capacity of a cable line, it is necessary to take into account that an operating voltage of \(220\ \text{kV}\) makes it possible to use electrical equipment that has been mastered by production and for which sufficient operating experience is available.

1. Let us next consider the question of the stability of parallel operation. In this respect as well, a cable line proves to be much more advantageous than an overhead line at lengths of \(1000\ \text{km}\) and more.

The point is that the wavelength in cable lines reaches a value of up to \(2600\)—\(2800\ \text{km}\). Consequently, cable power transmissions \(1000\)—\(1700\ \text{km}\) long approach lengths equal to a half-wave. And, as is known, the half-wave transmission mode is stable without the use of any compensating devices. The half-wave transmission mode is the operating mode of a line with a length equal to zero. This means that the operation of cable lines with lengths close to a half-wave will be stable.

1. When considering long cable lines, the question naturally arises of the magnitude of the capacitive currents that occur in such lines. Since such a long line has a considerable capacitance, the capacitive currents, consequently, must reach significant values. However, as calculations have shown, the magnitude of the capacitive currents at lengths of \(1000\)—\(1700\ \text{km}\), i.e., at lengths close to a half-wave, is comparatively small, as illustrated by the curve given below (Fig. 1).

The magnitude of the no-load current at a cable-line length equal to a half-wave reaches only \(300\ \text{A}\).

1. Next, the operating conditions of a cable line were considered for various load power factors—\(1.0\), \(0.9\), \(0.8\).

The most advantageous mode is that with a power factor equal to 1.0, since in this mode the highest efficiency is obtained and, what is especially important, the voltage along the line is distributed uniformly.

The lower the power factor, the lower the efficiency and the greater the overvoltages arising on the line.

Fig. 1

At $\cos \varphi = 0.8$ and $P = P_n$, the overvoltages reach the value

\[ U = 1.4\,U_n. \]

The values of the efficiency of the cable line are as follows (Table 2).

Table 2

1. A few words on the economic side of the question. Rough economic calculations (exact data on the cost of 220 kV cables are absent from the literature) show that the cost of a 220 kV cable line (including laying), with a length of 1200–1300 km, is twice as high as the cost of a 400 kV overhead line. However, the cost of the cable line can be reduced by approximately 20% through the use of mechanization for digging trenches.

Conclusions

1. Cable lines over distances of 1000–1700 km have, in comparison with overhead lines, the advantage that at a voltage of 220 kV they have a greater transmission capacity than overhead lines with split conductors at a voltage of 400 kV.

2. Cable lines 1000–1700 km long eliminate the problem of stability in parallel operation, since their mode is close to that of a half-wave.

Overhead lines at such lengths cannot operate stably, since they are close to the quarter-wave regime, which is completely unstable.

1. It is possible to use, for cable lines, 220 kV equipment already produced by our factories and with which there is sufficient operating experience.

2. The most advantageous mode of electric-power transmission over cable lines is obtained at $\cos\varphi = 1$, when the efficiency is highest and the voltage distribution along the line is uniform.

3. A cable line is more expensive than an overhead line; its operation is more complicated.

4. A cable line requires a considerable expenditure of copper.

LITERATURE

1. A. V. Mirolyubov, S. S. Rokotyan. A 400 kV Kuibyshev–Moscow electric-power transmission line. Elektrichestvo, No. 7, 1952.