Machine Computation of Power Network Performance

The planning of modern power system expansion demands that voltages, phase angles, power flow, and reactive power flow throughout the network be determined in advance of actual system changes. Determination by calculation of these quantities increases in difficulty to such an extent, as the system increases in size, that, for large interconnected systems, it heretofore has been considered necessary to use a network analyzer for this work. Since the first a-c network analyzer was put in service at the Massachusetts Institute of Technology in 1929 the scale model method of handling complex power system problems has grown in popularity, and the number and size of analyzers in the United States has been increasing steadily. To date, 14 network analyzers have been constructed, and more are on order, all at a total cost approaching two million dollars. A widespread, but misguided, belief prevails among power system engineers that the foregoing problems are not solvable practically except with the aid of an analyzer. It is the purpose of this paper to set forth certain principles and methods which so facilitate the handling of problems of power flow in networks that the mathematical solution appears more feasible than the analyzer solution. The methods and equations presented in this paper have been tested by recomputing an actual network analyzer study by mathematical means for comparison. Data and answers from this study are tabulated in this paper. The mathematical solution was first made with a key calculating machine.