IEEE 738-2012 pdf download

IEEE 738-2012 pdf download.IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors.
4.1 Steady-state case
4.1.1 Steady-state thermal rating
For a bare stranded conductor, if the conductor’s surface temperature (Ts) and the steady state weather parameters (Va., Ta, etc.) are known, the heat losses due to convection and radiation (q and q.), the solar heat gain (qJ, and the conductor resistance R(Tavg) can be calculated by the formulas of 4.4. The corresponding conductor current (I) that produced this conductor temperature under these weather conditions can be found from the steady-state heat balance [Equation (ib) of 4.4.1]. While this calculation can be done for any conductor temperature and any weather conditions for which the heat transfer models are adequate, a maximum allowable conductor temperature (e.g., 95 °C) and “conservative” weather conditions (e.g., 0.6 mIs perpendicular wind speed, full sun, and 40 °C summer air temperature) are often used to calculate a steady-state thermal rating for the conductor.
[88] suggests both default values for weather parameters and a procedure that can be followed in order to derive suitably conservative values for wind speed, air temperature, and solar heating.
4.1.2 Steady-state conductor temperature for a given current and ambient temperature
Heat transfer terms and conductor resistance are a function of conductor temperature while solar heat input to the conductor is not. If the conductor temperature is to be calculated rather than specified (as in 4.1 . I), then the heat balance equation [Equation (I b) of 4.4. 1] must be solved for conductor temperature in terms of the current and weather variables by a process of numerical iteration (i.e., estimating a conductor temperature and solving for the current), even if the conductor is assumed to be in steady-state.
The use of a numerical solution method, as described in this standard, avoids the need to make complex and time consuming approximations necessary to linearize the radiation and convection heat loss rates. Using suitable steady-state weather conditions, the calculation process is straightforward:
a) The solar heat input to the conductor is calculated (it is independent of conductor temperature).
b) A trial conductor temperature is assumed.
c) The conductor resistance is calculated for the trial temperature.
d) In combination with the assumed weather conditions, the convection and radiation heat loss terms are calculated.
e) The conductor current is calculated by means of the heat balance in Equation (ib) of 4.4.1.
f) The calculated current is compared to the trial conductor current.
g) The trial conductor temperature is then increased or decreased until the calculated current equals the trial current within a user-specified tolerance.
The numerical method listed in Annex A to this standard utilizes a very powerful numerical tool (the “RTMI MUELLER-S ITERATION METHOD”) which consistently produces numerical convergence.
After a period of time, At, the conductor temperature has increased by a temperature change of ATarg. The increased conductor temperature yields higher heat losses due to convection and radiation and somewhat higher Joule heat generation due to the increased conductor resistance. From At to 2At, the conductor temperature continues to increase, but does so at a lower rate. After a large number of such time intervals, the conductor temperature approaches its final steady-state temperature (T1).
During each interval of time, At, the corresponding increase in conductor temperature may be calculated using the formulas given in 4.4. The computer program included in Annex A calculates the conductor temperature as a function of time after the step change in current.
As described in Annex F, the rate of change in bare overhead conductor temperature is approximately exponential, with a thermal time constant that is on the order of 5 mm to 20 mm for typical transmission conductors where the longest time constant corresponds to the largest conductors. With reference to Figure 1, this implies that the conductor temperature increases to its final value in a time period of 15 mm to 60 mm. Transient ratings are therefore typically calculated for emergency currents persisting for 5 mm and 30 mm.
Accuracy in the iterative transient calculation requires that the time interval chosen be sufficiently small with respect to the thermal time constant. It is always prudent to rerun the calculation with a smaller time interval to check whether the calculated values change. For most calculations with typical bare overhead stranded conductors, a calculation interval of 10 seconds or less is sufficient.