Power circle diagrams drawn for either sending or receiving ends of a transmission line do not have a common centre for the voltage circles, nor are the power axes within the same semicircle. There is also a possibility of confusion over the sign of reactive power when conditions at both ends of the line are estimated by means of separate diagrams. A quadrant diagram with current taken as reference, which complies with the convention of the American Institute of Electrical Engineers for reactive power, is shown to be a satisfactory base on which a combined send-receive power circle diagram may be constructed. If such a diagram is built as a calculating board, all sending-and receiving-end quantities may be simply read with sufficient accuracy for the estimation of system load conditions. Examples of the use of the calculating board are given.

Transmission-line estimations by combined power circle diagrams

Throughout the history of electrical engineering education, vector and phasor diagrams have been used as a fundamental learning tool. Currently, computational power has replaced these with long data lists, the result of solving equation systems with numerical methods. In this sense, diagrams have been relegated to an academic background topic that, although theoretically explained, is not used in practice. This fact may work against the understanding of the complex behavior of electrical power systems by students. This paper proposes a modification of the classic Perrine-Baum diagram construction to allow both a more practical representation and a better understanding of the behavior of a high-voltage transmission line under different load levels. A tool capable of evaluating the moment in time when demand exceeds the line's carrying capacity is also introduced. In addition, the impact of this tool on the learning process is evaluated.

Modification of the Perrine–Baum Diagram to Improve the Calculation of High-Voltage Transmission Lines

Through the history of Electrical Engineering education, vectorial and phasorial diagrams have been used as a fundamental learning tool. At present, computational power has replaced them by long data lists, the result of solving equation systems by means of numerical methods. In this sense, diagrams have been shifted to an academic background and although theoretically explained, they are not used in a practical way within specific examples. This fact may be against the understanding of the complex behavior of the electrical power systems by students. This article proposes a modification of the classical Perrine-Baum diagram construction to allowing both a more practical representation and a better understanding of the behavior of a high-voltage electric line under different levels of load. This modification allows, at the same time, the forecast of the obsolescence of this behavior and line’s loading capacity. Complementary, we evaluate the impact of this tool in the learning process showing comparative undergraduate results during three academic years

Modification of the Perrine-Baum diagram to improve the calculation of high voltage electric lines

There seems to be a popular superstition among engineers that the voltage and current relations at different points in a transmission line are peculiar and are not governed by Ohms law. This idea is not true. A transmission line is governed by Ohms law just as is any other alternating-current circuit containing resistance inductance and capacity. The only difference from an ordinary circuit is that in a transmission line we must make a correction for the effect of distributed constants. If we change the current flowing through a line by an amount I, there will be a voltage change eq-ual to I Z between the two ends of the line. The Z in this case, however, is corrected for the distributed constants of the line. The hyperbolic formula which are so widely coming into use, since Doctor Kennelly has given us tables of complex hyperbolic functions, are merely short methods of determining this Z as well as certain other constants which we must use. If we start wth a certain voltage Eg at the generator; on open circuit, we will have a slightly higher voltage at the receiver, due to the line capacity drawing a leading current through the inductance. As we load the line with a lagging current this voltage rise is counteracted by the impedance drop. In a similar manner the generator current is equal to the vector sum of the charging current, and the load current which has been multiplied by a constant.

Collis H. Holladay

Papers

A Graphic Method for the Exact Solution of Transmission Lines