## IEEE STANDARD 738-1993 TEMPERATURE CALCULATION METHOD OF OVERHEAD CONDUCTORS FOR TRANSMISSION LINES

Calculation of temperature of overhead conductors as defined in IEEE Standard Std 738-1993 can be found below. These methods are being used by the Working Group on the Calculation of Bare Overhead Conductor Temperatures. It is applied in calculating heat transfer and ampacities of transmission line conductors.

Methods that were studied included the following:
a) House and Tuttle
b) House and Tuttle, as modeled by East Central Area Reliability (ECAR)
c) ALCAN
d) Pennsylvania-New Jersey-Maryland Interconnection
e) Schurig and Frick
f) Hilpert
g) Davis
h) Morgan
i) Black and Byrd
j) Foss, Lin, and Fernandez

The mathematical models of this standard are based upon the House and Tuttle method as modeled by
ECAR . The House and Tuttle formulas consider all of the essential factors without the simplifications that made in some of the other formulas. To differentiate between laminar and turbulent air ßow, the House and Tuttle method uses two different formulas for forced convection; the transition from one to the other is made at a Reynolds number of 1000.

Because turbulence begins at some wind velocity and reaches its peak at some higher velocity, the transition from one curve to another is a curved line, not a discontinuity. The single transition value was selected as a convenience in calculating conductor ampacities.

The single transition value results in a discontinuity in current magnitude when this value is reached. Therefore, to avoid this discontinuity that occurs using the House and Tuttle method, ECAR elected to make the change from laminar to turbulent air flow at the point where the curves developed from the two formulas. The formulas for forced convection heat loss have an upper limit of application validity of a Reynolds number of 50 000.

Since the primary purpose of this standard is the calculation of thermal ratings for constant weather conditions, the slower but simpler iterative approach is taken. Alternate noniterative methods may be used to calculate the conductor temperature given the current and weather conditions. The heat balance equation is expressed as a biquadratic equation that can be solved to give the conductor temperature directly.

The radiation term is linearized and the resulting approximate linearized heat balance equation is solved using standard methods of linear differential equations. A somewhat more precise linearized radiation term is used to reduce the number of iterations required.

These methods are computationally faster than the iterative method described in this standard; however, the algebraic expressions are more complex. While one expects to get the same answer from any valid calculation method, the noniterative methods are used normally in real-time thermal rating algorithms where calculation speed is essential.