Rating of bare overhead conductors for intermittent and cyclic currents

Abstract

Equations are derived and solutions given for determining the variation with time of the temperature of bare overhead conductors carrying intermittent and cyclic currents. The temperature variation depends on the rate of heat input, the heat capacity of the conductor and the rate of total heat transfer. The latter is proportional to (temperature rise) 9 . If the heat transfer by radiation can be neglected, q = 1 for forced convection and approximately 1 • 25 for natural convection. If radiation is not negligible, q is greater than 1, the actual value being obtained from calculations or steady-state measurements. Thermal time constants can only be used when q = 1, and they are then only approximations. Measured heating-and cooling-time constants agree reasonably well with calculated values. The significance of the difference between heating-and cooling-time constants is discussed. f The importance of the heat source or sink formed by the core in steel-cored conductors is shown, and calculated values of the radial thermal conductivity are similar to those found from previous steady-state measurements. Calculated temperature/time characteristics for conductors in still air are in good agreement with measured characteristics. List of symbolsa = thermal diffusivity, m 2 /s c = specific heat capacity at constant pressure, J/kgdegC C = heat capacity per unit length, J/mdegC D = diameter of the circle circumscribing the conductor, m e = base of natural logarithm h = total heat-transfer coefficient, W/m 2 degC H = specific total heat-transfer coefficient, W/mdegC / = current, A J = current density, A/m 2 k = factor to allow for the increase of resistance due to skin effect, proximity, hysteresis and eddy currents / = length, m m = mass per unit length, kg/m n = integer p s = solar irradiance at conductor surface, W/m 2 P = power gain per unit length by Joule heating, W/m p s = power gain per unit length by solar irradiation, W/m P T = total power gain per unit length, W/m q = heat-transfer exponent r = radius, m R = d.c. resistance per unit length, Q/m / = time, s V = potential difference, V a = temperature coefficient of resistance, degC" 1 /3 = temperature coefficient of specific heat capacity, degC" 1 y = specific mass, kg/m 3 A = effective radial thermal conductivity, W/mdegC 6 = temperature rise, degC p = resistivity, Qm T = thermal time constant, s

Study of different mathematical approaches in determining the dynamic rating of overhead power lines and a comparison with real time monitoring data

“…Finally, an analytical approach obtained by V.T. Morgan from the general heat equation for a homogeneous and isotropic solid can be utilized [4,9]. This leads to a time response function for each variable which depends on the thermal time constant of the conductor (Fig.…”

Forecasting for dynamic line rating

“…In 1958, House and Tuttle at Alcoa Research Laboratories (USA) suggested the steady state ampacity model [11], which is basically the one currently used. About ten years later, Morgan [12] at the National Standards Laboratory of Sydney (AU) proposed a similar steadystate rating model, while [13,14] at Jersey Central Power (USA) proposed dynamic models for describing the thermal behaviour of conductors. These models are the basis of the International Council for Large Electric Systems (CIGRE) [1] and Institute of Electrical and Electronics Engineers (IEEE) [15] models still broadly used today.…”

Numerical Algorithms for Calculating Temperature, Layered Stress, and Critical Current of Overhead Conductors

“…Many experimental studies [4][5][6][7][8][9][10][11][12] have shown that the radial temperature of conductors is not evenly distributed. IEEE specifications [13] proposed that there is radial temperature gradient among each layer.…”