Tensorial Analysis of Integrated Transmission Systems; Part III. The "Primitive" Division [includes discussion]

Part III of the series lays down the foundations for the co-ordinated technical and economic study of several interconnected transmission systems. In particular, it establishes the basic equations of one isolated "primitive" division before it is interconnected with several others. The study merely introduces additional reference frames number 3.1 (between frames numbers 3 and 4) or frame number 6.1 (after frame number 6) that replace the several tie lines, extending between two neighboring divisions, by one "hypothetical" tie line carrying the resultant interchange power (the "sum" power) between the two divisions. All measurements and all numerical calculations, previously performed for each individual division, are taken over unaltered. The only change consists of the introduction of C3.13 (or C6.16). The concept of "tensor" equivalent circuits also is introduced to simplify the eventual representation of the large variety of power flow that may exist between the component divisions of an interconnected system. Numerical calculations of I2R losses in the component divisions of a large interconnected power system are given in a companion paper1 for various power-interchange conditions.