SELECTION OF CONDUCTORS OF IDENTICAL CROSS SECTION BY ECONOMIC CURRENT DENSITY FOR POWER-TRANSMISSION LINES WITH DISTRIBUTED LOAD

R. I. BORISOV

(Presented by Prof. I. D. Kutyavin, Doctor of Technical Sciences)

The creation of intersystem electrical connections for the exchange of capacities between systems will apparently, in a number of cases, take place simultaneously with the electrification of railways from these same lines. Under these conditions, transmission lines will be able to play a dual role, which will to a considerable degree increase the effectiveness of their use in the national economy of the country.

The operating regimes of such transmissions will be characterized by a large number of hours of utilization of maximum power and by substantial loads; consequently, the selection of conductor cross sections for such lines should be made according to economic current density. The load regimes of consumers at the intermediate points of such lines are approximately the same; therefore, the number of hours of utilization of the maximum will be one and the same value, and the selection of conductor cross section should be carried out according to a constant current density. A line calculated according to constant current density will have cross sections that differ by section, and will ensure the lowest operating costs, taking into account the values of the calculated loads and market considerations for nonferrous metals.

This method of selecting conductors is also applied to main-network lines that supply a distributed industrial and domestic load. However, considerations arising from the conditions of the structural design of the network and the convenience of operation make it desirable to construct lines with a conductor of one cross section. In this case, the conditions for installation and operation of the networks are significantly facilitated, and these works become less expensive.

For determining one conductor cross section along a line with a distributed load, let us consider the diagram in Fig. 1.

Fig. 1.

In general form, the total annual costs for the line, depending on the conductor cross section, are expressed by the equation...

\[ \sum U = a_* \sum_{1}^{n} K_k + \beta \sum_{1}^{n} \Delta A_k, \]

where \(K_k\) is the cost of the individual sections of the network;

\(a_*\) is the relative value of deductions for depreciation and current network expenses;

\(\beta\) is the cost of 1 kWh of lost energy;

\(\Delta A_k\) is the energy loss by sections.

When the line is made with a conductor of one cross-section, the annual expenditures will be:

\[ U = a_* K_\ell + 3r_0 \tau \beta \sum_{1}^{n} I_k^2 l_k, \]

where \(K_\ell\) is the cost of the entire line made with a conductor of the required cross-section;

\(I_k\) are the currents by sections;

\(l_k\) are the lengths of the sections.

Since the network calculated on the basis of constant current density, and the network with one conductor cross-section along its entire length, must have identical annual expenditures, we equate the right-hand sides of these equations:

\[ a_* \sum_{1}^{n} K_k + \beta \sum_{1}^{n} \Delta A_k = a_* K_\ell + 3r_0 \tau \beta \sum_{1}^{n} I_k^2 l_k. \]

It is proposed to solve this equation by trial selection. The final choice of variants of the network with one cross-section is made by means of techno-economic calculations according to the payback period of the lump-sum expenditures.

Example

Select conductors of one cross-section for the line in Fig. 1. The voltage at the supply point \(A\) is 110 kV. The calculated load powers in MW and the section lengths in km are given in the diagram. The number of hours of utilization of the maximum for all loads is taken as 4500 h. The number of loss hours is \(\tau = 2700\) h. The cost of lost energy is \(\beta = 0.1\) rub/kWh.

The calculation of cross-sections, carried out for a constant current density \(j = 1.0\ \mathrm{A/mm^2}\), at the average nominal voltage of the network made it possible to select conductors of the following grades.

On section \(A\)—2 AS—300 mm\(^2\), \(r_0 = 0.105\ \Omega/\mathrm{km}\). Cost: 160 thousand rub/km.

On section \(ab\)—2 AS—240 mm\(^2\), \(r_0 = 0.131\ \Omega/\mathrm{km}\). Cost: 135 thousand rub/km.

On section \(bv\)—AS—300 mm\(^2\), \(r_0 = 0.105\ \Omega/\mathrm{km}\). Cost: 85 thousand rub/km.

On section \(vd\)—AS—120 mm\(^2\), \(r_0 = 0.27\ \Omega/\mathrm{km}\). Cost: 60 thousand rub/km.

Annual depreciation and current expenses:

\[ a_* \sum_{1}^{4} K_k = 0.04(160 \times 60 + 135 \times 50 + 85 \times 50 + 60 \times 40) = 0.92 \times 10^3\ \text{thousand rub}. \]

Annual cost of energy losses by sections:

\[ \beta \sum_{1}^{4} \Delta A = 3\left(I_1^2 R_1 + I_2^2 R_2 + I_3^2 R_3 + I_4^2 R_4\right)\tau \beta = \]

\[ --3(0.63^2 \times 3.15 + 0.45^2 \times 3.27 + 0.3^2 \times 5.25 + 0.116^2 \times \]

\[ \times 10.8)\times 2700 \times 0.1 \times 10^3 = 2.05 \times 10^3 \ \text{thousand rubles}. \]

The total annual expenditures are

\[ \sum U = (0.92 + 2.05)\,10^3 = 2.97 \times 10^3 \ \text{thousand rubles}. \]

The results of the calculations when the entire line is made with wires 2AC-300, 2AC-240, and 2AC-185 are given in the table.

Table

Comparing the variants 2 AC-300 and 2 AC-240 in terms of the payback period, which proves to be 12.5 years for the first variant, we come to the conclusion that the line should be made as a double-circuit line with AC-240 mm\(^2\) wires.