Power geometry of general transmission systems

IN its present known form^1–6 the power-circle diagram of a transmission system applies to operating conditions where constant voltages are maintained at both the sender and the receiver. While this is by far the most frequent type of operation, instances are numerous where the designer or analyst is confronted with conditions requiring only one of these two voltages to be constant. This is true particularly when the concept of a transmission system is taken in a broader sense as applied to a generator, motor, transmission line, or generally speaking, to any part of a composite transmission system. To mention but one example, the induction motor may be considered a transmission system which supplies power in varying amounts to an equivalent electric load of unity power factor, and its circle diagram accordingly is of a different character. From a viewpoint which looks at all equipment having input and output terminals as general transmission systems, it seemed desirable to formulate on a broader basis the relations between sender and receiver power as exemplified by the constant-voltage circles of the conventional sender and receiver charts. Moreover, a more general relation will permit the translation from one chart to the other, not only of actual power loci of operation, but also of efficiency contours, contours of loss, power factor, receiver wattage and amperage, and other concepts of interest. As it happens, all these cases fall into the wider class where (a). The voltage is maintained constant at one terminal point of the system. (b). The operating locus or contour is a circle for this terminal point.