Temperature rise of stationary electrical: Apparatus as influenced by radiation, convection and altitude

Abstract

Part I of the paper takes up first the division of losses by radiation and convection from tall vertical planes. It is shown that the loss by convection from tall planes can be expressed by the formula <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W_{c} = 0.0014\ A \theta^{5/4}$</tex> in which W <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> is the watts, A the square inches of surface and θ the temperature rise in degrees centigrade. It is then shown that the division of losses from a black plane is, for temperature rises up to 100 deg. cent., approximately 45 per cent convection and 55 per cent radiation. Based upon this division, a simple formula is given for determining the ratio of losses for an irregular surface where the greater part of the loss is by convection. The effect of various colors on the temperature rise of transformers having both plain and corrugated tanks is discussed. In Part II it is shown that altitude does not affect radiation. The general average of the results obtained by various investigators shows that convection varies as the square root of the air density. Based on this, it is shown that for a constant loss by convection the temperature rise increases about 4.6 per cent for each 1000 meters increase in altitude. For transformers where a part of the loss is by radiation (unaffected by air density) the effect is reduced by the ratio of the convection loss to the total loss. Also the effect on the winding rise over the ambient is further reduced by the fact that the winding rise over the oil is not affected by altitude. The effect of the copper loss, however, is to increase the effect of altitude because the resistance is increased by temperature. Based upon the above facts it is shown that the temperature rise and rating of the two main classes of oil-immersed self-cooled transformers are affected by altitude as follows: Per cent increase in Copper Rise per 1000 Meters Increase in Altitude Per cent decrease in Kv-a. per 1000 Meters Increase in Altitude Self-cooled transformers (a) with plain tanks 1.75 1.35 (b) with corrugated, tubular and radiator tanks 3.0 2.3