Selection of Conductors of Equal Cross-Section by Economic Current Density for Power Transmission Lines with Distributed Load
Abstract Generated abstract
This paper addresses the choice of a single conductor cross-section for power transmission lines serving distributed loads, a problem arising when intersystem ties also supply railway, industrial, or domestic consumers. It formulates annual costs as the sum of capital-related charges and the cost of energy losses, then compares a line designed by constant economic current density, with varying section sizes, to alternatives using one conductor size throughout. The proposed procedure uses trial selection and subsequent techno-economic comparison by payback period. A worked 110 kV example shows that although a larger conductor option has slightly lower annual costs, the payback comparison leads to selection of a double-circuit line using 240 square millimeter conductors.
Full Text
Selection of Conductors of Identical Cross-Section by Economic Current Density for Power Transmission Lines with Distributed Load
R. I. Borisov
(Presented by Prof., Doctor of Technical Sciences I. D. Kutyavin)
The creation of intersystem electrical ties for the exchange of capacities between systems will evidently, 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 perform a dual role, which will substantially increase the effectiveness of their use in the national economy of the country.
The operating conditions of such transmissions will be characterized by a high number of hours of utilization of maximum power and by considerable loads; consequently, the selection of conductor cross-sections for such lines should be carried out according to economic current density. The load conditions of consumers at intermediate points of such lines are approximately identical; therefore the number of hours of utilization of the maximum will be one and the same value, and the selection of conductor cross-section must be conducted according to a constant current density. A line calculated according to a constant current density will have cross-sections that differ by section and will ensure the least operating costs, taking into account the values of the calculated loads and market considerations regarding nonferrous metals.
This method of selecting conductors is also applied for lines of the main network that feed a distributed industrial and domestic load. However, considerations arising from the conditions of the structural design of the network and the convenience of operation compel one to strive to construct the lines with a conductor of one cross-section. In this case the conditions for installation and operation of networks are substantially simplified, and these works become cheaper.
For determining a single conductor cross-section for a line with distributed load, let us consider the scheme in Fig. 1.
Fig. 1.
In general form, the total annual costs for a line that depend 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 amount of deductions for amortization and current network expenses;
\(\beta\) is the cost of 1 kWh of lost energy;
\(\Delta A_k\) are the energy losses by sections.
When the line is constructed with a conductor of one cross-section, the annual expenses will be:
\[ U=a_*K_l+3r_0\tau\beta\sum_{1}^{n}I_k^2l_k, \]
where \(K_l\) is the cost of the entire line constructed 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 according to constant current density and the network with one conductor cross-section along its entire length must have identical annual expenses, we equate the right-hand sides of these equations:
\[ a_*\sum_{1}^{n}K_k+\beta\sum_{1}^{n}\Delta A_k = a_*K_l+3r_0\tau\beta\sum_{1}^{n}I_k^2l_k. \]
It is proposed to solve this equation by trial selection. The final selection of network variants with one cross-section is made by means of techno-economic calculations based on the payback period of one-time 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 maximum utilization for all loads is taken as 4500 h. The number of hours of losses 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 network voltage, made it possible to select conductors of the following grades.
On section \(A—2\): AC—300 mm\(^2\), \(r_0=0.105\ \Omega/\mathrm{km}\). Cost: 160 thousand rub/km.
On section \(ab\): 2 AC—240 mm\(^2\), \(r_0=0.131\ \Omega/\mathrm{km}\). Cost: 135 thousand rub/km.
On section \(bv\): AC—300 mm\(^2\), \(r_0=0.105\ \Omega/\mathrm{km}\). Cost: 85 thousand rub/km.
On section \(vd\): AC—120 mm\(^2\), \(r_0=0.27\ \Omega/\mathrm{km}\). Cost: 60 thousand rub/km.
Annual amortization and current expenses:
\[ a_*\sum_{1}^{4}K_k = 0.04(160\times60+135\times50+85\times50+60\times40) = 0.92\times10^3\ \text{thousand rub}. \]
Annual cost of energy losses by sections:
\[ \beta\sum_{1}^{4}\Delta A = 3\left(I_1^2R_1+I_2^2R_2+I_3^2R_3+I_4^2R_4\right)\tau\beta = \]
\[ =3(0.63^2 \times 3.15+0.45^2 \times 3.27+0.3^2 \times 5.25+0.116^2 \times \]
\[ \times 10.8)\times 2700 \times 0.1 \times 10^3 = 2.05 \times 10^3 \text{ thousand rubles.} \]
Total annual expenditures
\[ \sum U=(0.92+2.05)10^3=2.97 \times 10^3 \text{ thousand rubles.} \]
The results of the calculations when the entire line is made with conductors \(2AC\text{—}300\), \(2AC\text{—}240\), and \(2AC\text{—}185\) are summarized in the table.
Table
| Conductor type | \(a_\phi K_\ell\), million rubles | \(3\tau\beta r_0 \displaystyle\sum_1^4 I_i^2 l_i\), million rubles | \(U\), million rubles |
|---|---|---|---|
| \(2\,AC\text{—}300\) | 1.28 | 1.66 | 2.94 |
| \(2\,AC\text{—}240\) | 1.08 | 2.06 | 3.14 |
| \(2\,AC\text{—}185\) | 0.96 | 3.64 | 3.64 |
Comparing the \(2AC\text{—}300\) and \(2AC\text{—}240\) alternatives in terms of the payback period, which proves to be 12.5 years for the first alternative, we conclude that the line should be built as a double-circuit line with conductors of type \(AC\text{—}240\ \mathrm{mm}^2\).