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Factores que afectam as classificações de corrente do condutor nu

Steady-state and transient overhead line ratings factors examined (temperature, wind speed, solar radiation etc.)

Introdução

The current rating of bare conductors is affected by the conductor temperature, weather parameters, heat losses due to convection and radiation, the solar heat gain and conductor resistance, the calculation of which is governed by a steady-state and a non-steady-state heat balance equation. Whilst these equations allow calculations of ratings to be done for any conductor temperature and any weather conditions typically a set of conservative conditions are assumed for calculating the current rating of conductors.

In this report a parametric study of the factors which affect current ratings for bare conductors is presented. All calculations are in accordance with IEEE Std. 738 [1] and have been compared with those published by conductor manufacturers.

The software used for calculating the results was ELEK LineRate Software.

For steady-state conditions the effect on the current rating of the following parameters are studied: conductor operating temperature, varying wind speed, wind incident angle, elevation above sea level and solar radiation intensity.

For transient conditions the thermal response to a step change in current and the thermal current rating over time are examined.

Further, the effects of current density on the radial temperature distribution within a bare conductor between the core and the surface temperatures are also examined.

Conductors Examined

Two common types of bare overhead conductors were examined. These were the All Aluminium Conductor (AAC) “Triton” 37/3.75 mm and Aluminium Conductor Galvanised Steel Reinforced (ACSR/GZ) “Olive” 54/7/3.5 mm conductors.

Common Parameters

Table 1 provides the common parameters which were used for modelling of the bare conductors.

Table 1. Common parameters.

Conductor:
Maximum continuous operating temperature	90 ˚C
Maximum short-time operating temperature	160 ˚C
Initial conductor temperature prior to transient	50 ˚C
Environmental conditions:
Ambient air temperature	40 ˚C
Wind velocity	1 m/s
Wind angle relative to conductor axis	90 degrees
Elevation above sea level	10 m
Solar radiation intensity	0 W/m2
Solar absorption coefficient	0.5
Surface emissivity coefficient	0.5

Note that the choice of weather conditions in this report does not constitute a recommendation of suitably conservative “worst-case” weather conditions

CIGRE Technical Brochure 299 [4] suggests both default values for weather parameters and a procedure for deriving suitably conservative weather parameters for conductor ratings.

Steady-State Conditions

Conductor operating temperature
The flow of current in a conductor causes its temperature to rise due to the effects of joule heating, the magnetic and skin effects.
Figure 1 shows as current flow in a conductor increases so does the operating temperature.

Joule heating refers to the heating of the conductor due to the electrical resistance which varies with frequency, average current density and temperature.

The magnetic effect refers to heating of the conductor due to cyclic magnetic flux caused by eddy currents, hysteresis and magnetic viscosity. In non-ferrous conductors such as All-Aluminium Conductors (AAC) at power frequencies the magnetic effect is negligible. However, for aluminium conductors where the number of layers is odd (1, 3, etc.) and with steel-reinforced cores (ACSR conductors) heating of the conductor is increased by the magnetic flux in the steel core [3].

The skin effect increases conductor resistance due to the tendency of the current to crowd toward the conductor surface. The skin effect factor is almost unity for small conductors and increases with conductor size.

The proximity effect for typical bare conductor arrangements is neglected since separation between conductors is greater than 10 times the overall conductor diameter [6].

Varying wind speed
Increasing the wind speed improves the rate of convection of heat away from the conductor which increases the current rating.
A small change of wind speed results in a relatively large change of current rating (Figure 2).

Convection heat loss is non-linearly dependent on the conductor temperature.

There are two main components to convection causing the drawing of heat away from the conductor; natural and forced convection.
The natural convection component (constant) is dominant only up until the wind speed exceeds a certain low value.
This is evident from the initial flat section of the curves shown by Figure 2 above.

Varying wind angle
Figure 3 shows that current rating increases significantly as wind incident angle relative to the conductor axis approaches 90˚ (perpendicular wind).

The angle of the wind incident on the surface of a conductor influences the heat loss due to forced convection.

The wind direction multiplying factor from [1] which is a sinusoidal function varies between 0.388 and 1 for θ = 0˚ and θ = 90˚ respectively, and is defined as:

Onde

θ is the angle between the wind direction and the conductor axis.

Elevation above sea level

Both natural and forced convection heat loss are dependent on the density of the air which is inversely proportional to elevation above sea level.

Figure 4 shows as the elevation above sea level increases the current rating slightly decreases (< 3%) due to a reduction in air density resulting in convection heat loss being not as effective.

Solar radiation intensity

Figure 5 shows that as solar radiation intensity increases conductor current rating goes down. Solar heating of a conductor is linear and independent of conductor temperature. For the same absorption coefficient (0.5 in this case) the reduction in current rating depends on the size of the exposed surface area of the conductor. For example, the rate of reduction in current rating due to increasing solar radiation intensity (refer to the slope of the equations of the linear curves in Figure 5) for the Olive ACSR/GZ conductor is greater due to its larger diameter and hence surface area compared to the Triton AAC conductor.

The heat gain rate from the sun depends on the effective surface area exposed, solar radiation intensity and the absorptivity of the conductor surface.

The intensity of solar radiation can be calculated depending upon the latitude and altitude of the conductor as well as the time of year and sky conditions.
For daytime ratings of conductors a typically conservative approach is to rate a conductor assuming that high solar radiation levels coincide with very low wind speeds.
However, this approach may not be correct since studies have shown that minimum wind speeds are three times greater due to the effects of thermals when the sun is shining [6].

Transient Conditions

Note it is assumed that the weather parameters remain constant for the duration of the transient.

Step increase in current
The transient responses to a step increase in current are shown in Figure 6. Both conductors are initially carrying (different) currents maintaining a constant operating temperature of 55 ˚C. A step in current is applied causing the temperature to rise to approximately 90 ˚C (full-load).

The variation in conductor temperature with time over the first 60 minutes is approximately exponential.

The rate-of-rise of temperature of the Olive ACSR/GZ conductor is lower than the Triton AAC. This is due to the higher conductor heat capacity (thermal inertia) which is the sum of the products of the specific heat and mass per unit length of the components of the conductor.

By comparison the conductor heat capacity of Olive ACSR/GZ and Triton AAC is 1610.54 J/(m-˚C) and 1079.15 J/(m-˚C), respectively.

Transient current rating
The transient current rating of a conductor is the determination of the current which causes the conductor temperature to reach its maximum allowable value in the allotted time. Figure 7 shows that the transient current rating is highly dependent on the duration of the transient.
For example, for a 1 second duration transient the (short-circuit) current rating of the Olive ACSR/GZ conductor is 51933 A.
As the duration of the transient increases the curves for both conductors converge with their steady-state current rating values.

Radial Conductor Temperature

When a bare conductor is carrying current near to its capacity the temperature of the core wires (irrespective of whether the conductor has a steel reinforced core or is an all aluminium conductor) can be significantly higher than at the conductor surface. The problem is that if this increased core temperature is ignored then the conductor sag and loss of tensile strength due to annealing may be underestimated.

CIGRE Technical Brochure 207 [3] presents an equation which allows the calculation of the radial temperature difference if the effective radial thermal conductivity of the conductor is specified. This equation has been shown to be in reasonable agreement with laboratory measurements [5] and is ratified in the Draft 2012 edition of IEEE Std. 738 [2].

Figure 8 shows as current density within a conductor increases so too does the radial temperature difference between the core and the surface and that the radial temperature is highly dependent on the effective radial thermal conductivity factor, kr.

The thermal conductivity of solid aluminium is around 237 W/m-˚C. However, conventional overhead conductors consist of aluminium circular or trapezoidal strands and core strands with air gaps between them. These air gaps hinder the flow of heat and the contact surfaces of the strands also increases thermal resistance. This leads to an apparent or effective radial thermal conductivity which is much lower (typically in the range of 0.5 – 4 W/m-˚C [3]). Other results have shown conductors under tension have higher effective radial thermal conductivity of around 1.5 W/m-˚C than slack conductors (which in the field can be caused by plastic or thermal elongation) around 0.7 W/m-˚C [5].

For current densities above 1-2 A/mm2 the radial temperature difference, which is a function of the overall conductor diameter and also of the steel core diameter (if applicable) should not be ignored. It is recommended, if the temperature gradient within the conductor exceeds 10 ˚C then the maximum permissible operating temperature should be reduced if the higher core temperature results in conductor deterioration or inadequate sag clearance [2].

Conclusão

Accurate determination of bare conductor ratings and performance is important for providing an economical, functional and safe design.
Changing the following factors affects the current rating for bare conductors in the following ways:

Temperature – increased temperature increases electrical resistance.
Frequency – increased frequency increases the losses from the skin effect.
Wind speed and direction – higher wind speeds significantly improve the convection of heat away from the conductor. Perpendicular wind is most effective.
Elevation above sea level – conductors installed nearer to the sea level have slightly improved current ratings due to higher air density.
Solar radiation – the sun reduces the current rating of conductors.

Conductors with higher thermal capacity provide better performance during transients.
At or near to full rated current the temperature of the core can be significantly higher than the conductor surface.
In this case the effects on conductor sag and mechanical degradation should be considered.

Appendix – Conductor Data

Physical and electrical properties are required for modelling. The following conductor data was taken from the Pirelli Overhead Conductor Catalogue [8].

Physical properties	Valor
Type	AAC
Stranding and wire diameter (No./mm)	37/3.75
Nominal overall diameter (mm)	26.3
Total mass (kg/km)	1130
Electrical properties (50 Hz)	Valor
D.c. resistance at 20 ˚C (Ω/km)	0.0701
A.c. resistance at 75 ˚ (Ω/km)	0.087

Physical properties	Valor
Type	ACSR
Code name	Olive
Stranding and wire diameter (No. cond. strands/No. core strands/mm)	54/7/3.5
Nominal overall diameter (mm)	31.5
Total mass (kg/km)	1960
Electrical properties (50 Hz)	Valor
D.c. resistance at 20 ˚C (Ω/km)	0.0557
A.c. resistance at 75 ˚ (Ω/km)	0.0716

Referências

IEEE Std. 738-2006, “IEEE Standard for Calculating the Current-Temperature of Bare Overhead Conductors.”
IEEE Std. 738-2012 Draft 10, “IEEE Standard for Calculating the Current-Temperature of Bare Overhead Conductors.”
CIGRE WG 22.12, “Thermal Behaviour of Overhead Conductors”, Technical Brochure 207, agosto 2002.
CIGRE WG B2.12, “Guide for Selection of Weather Parameters for Bare Overhead Conductor Ratings”, Technical Brochure 299, agosto 2006.
CIGRE WG B2-108, “Radial and Longitudinal Temperature Gradients in Bare Stranded Conductors with High Current Densities”, 2012.
C.F. Price and R.R. Gibbon, “Statistical approach to thermal rating of overhead lines for power transmission and distribution”, IEE Proceedings, Vol. 130, Pt. C, No. 5, Sept. 1983.
Aluminium Electrical Conductor Handbook, 3rd edition 1989, The Aluminium Association.
Pirelli Overhead Conductor Catalogue.