IEC TR 61597-2021 Overhead electrical conductors – Calculation methods for stranded bare conductors.
5.9 Determination of the maximum permissible aluminium temperature
The maximum permissible aluminium temperature is determined either from the economical optimization of losses or from the maximum admissible loss of tensile strength in aluminium.
In all cases, appropriate clearances under maximum temperature have to be checked and maintained.
If needed, the equation of core temperature versus surface temperature can be found in [4].
5.10 Calculated values of current carrying capacity
Equation (8) enables the current carrying capacity (CCC) of any conductor at any condition to be calculated. Table B.1 gives indicative conditions in some countries and regions for CCC calculation. .
6 Alternating current resistance, Inductive and capacitive reactances
6.1 General
The electrical resistance of a conductor is a function of the conductor material, length, cross- sectional area and effect of the conductor lay. In more accurate calculations, it also depends on current and frequency.
The nominal values of DC resistance are defined in IEC 61089 at 20 °C temperature for a range of resistance exceeding 0,02 Q/km.
In order to evaluate the electrical resistance at other temperatures, a correction factor has to be applied to the resistance at 20。C.
The alternating current (AC) resistance at a given temperature T is calculated from the DC resistance, corrected to the temperature T and considering the skin effect increment on the conductor that reflects the increased apparent resistance caused by the inequality of current density.
The other important effects due to the alternating current are the inductive and capacitive reactances. They can be divided into two terms: the first one due to flux within a radius of 0,30 m and the second which represents the reactance between 0,30 m radius and the equivalent return conductor.
The methods of calculation adopted in this clause refer to [1] and [5].
6.2 Alternating current (AC) resistance
The DC resistance of a conductor increases linearly with the temperature, according to the following equation:
Rr2= Rr:[1 +a(Tz-T)]   (9)
Based on these values at 20°C, the DC resistances have been calculated for temperatures of 50°C, 80 °C and 100 °C. The AC resistance is calculated from the DC resistance at the same temperature. Calculation methods are in [1],[2],[3],[4]. Clause A.2 gives an example based on [1]. .
The AC resistance of the conductor is higher than the DC resistance at the same temperature. The cause of this phenomenon can be explained by the fact that the inner portion of the conductor has a higher inductance than the outer portion because the inner portion experiences more flux linkages. Since the voltage drop along any length of the conductor must be necessarily the same over the whole cross-section, there will be a current concentration in the outer portion of the conductor, increasing the effective resistance. Various methods are available for computing the ratio between AC and DC resistances ([1], [2], [3], [4]). For conductors having steel wires in the core (Ax/Sxy or Ax/xySA conductors), the magnetic flux in the core varies with the current, thus the AC/DC ratio also varies with it, especially when the number of aluminium layers is odd, because there is an unbalance of magnetomotive force due to opposite spiraling directions of adjacent layers. Although this magnetic effect may be significant in some single layer Ax/Sxy conductors and moderate in 3-layer conductors, the values of AC resistances for these types of conductors have been calculated without this influence. Further information and a more complete comparison and evaluation of magnetic flux and unbalance of magnetomotive force may be found in chapter 3 of [1].IEC TR 61597 pdf dwonload.