The computation of composite alternating-current lines

✍ Scribed by A.E. Kennelly

• Publisher: Elsevier Science
• Year: 1914
• Tongue: English
• Weight: 512 KB
• Volume: 178
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(14)90108-9

✦ Synopsis

Member of the Institute. i IT is proposed to show how conveniently and swiftly the electrical characteristics of a composite alternating-current line can be computed by means of tables and charts x of hyperbolic functions. A composite line is defined as one consisting of a plurality of successive sections, each having its own uniform electric constants. It will be evident, from an example of the process, that the tables and charts referred to can be used without any necessary familiarity with the mathematical theory of hyperbolic functions. A moderate acquaintance with the working formulas of ordinary circular trigonometry suffices.

Before analyzing the case to be considered, a few preliminary relations may be outlined.

Every uniform conducting-line circuit, carrying steadily either continuous or alternating currents, overhead or underground, may be regarded as possessing, or subtending, a certain "hyperbolic angle," which is directly proportional to the length of the line, and also depends upon the electrical constants of the line, as well as on the frequency, but is quite independent of the strength or phase of the current carried by the line. The angle subtended by the line is the same whether the line is operated alone, forms part of a transmission system, or is an element in a network of conductors. The angle subtended by a line is, therefore, a fixed property of 'the line, when the frequency, impressed on the line is fixed.

When the impressed frequency is zero,--i.e., .when the line is subjected to a continuous electromotive force,rathe * Communicated by the author. t -Tables of Complex Hyperbolic Functions," and "Chart Atlas of Complex Hyperbolic Functions," by A.