New York Paper - Electric Furnace Problems (with Discussion)

There are two general classes of problems in connection with electric furnaces. First, those relating to the best utilization of the electrical power inside the furnace; second, those connected with the bringing of the electrical power to the point where it is to be utilized. Referring particularly to the latter class of problems, many calculations have been made, covering a wide variety of furnaces, to check the electrical capacity and power factor found from test. The following analysis, made for the purpose of determining the maximum capacity and approximate performance of a new furnace, to operate at 160 volts on a 60-cycle circuit, may be of interest. The first characteristic necessary to determine is the inductance, since this is the factor that limits the amount of power which can be put into the furnace. Inductance is calculated from the dimensions of the furnace, according to formulas of the U. S. Bureau of Standardsll as follows. Formula 99, for mutual inductance, is: M = 2l [log 2l/d-1 +d/l] Formula 103, for self-inductance, is: Both of these formulas are approximations which are nearly correct when 1 is great compared to d or R. 1 = length of circuit, in centimeters, d = separation between the conductors, in centimeters, R = geometric mean radius of conductors. For a circular tube, R = the radius of the circle. For a solid circular conductor, R = 0.7788 X the radius of the conductor. For a rectangular conductor, R = 0.2235 X (a + b), a being the length, and b being the width of the rectangle. To calculate the inductance of a three-phase circuit, it is customary to figure the inductance of one leg. In circuits where the three conductors