Power Division Theorem Proves Sharing Principle at a Node Disproves for Networks

Dr. P. S. Kannan

Abstract: Traditionally, Power System Engineers / Scientists apply Power Sharing Principle (PSP) for electrical tracing, determining the transmission cost and all other analysis needed in Deregulated Power Environment (DPE). This paper clearly demonstrates the innovated Power Division Theorem (PDT) proves the PSP applied at a Node in power system network and disproves for the network loads. It establishes a new Complex Power Sharing Principle (CPSP). However; the principle is not applicable for system network and valid for a Node only. The fundamental concept is the flow of current through a node or network creates power. The PDT is established by applying this concept along with the KCL The Complex Power Distribution Matrix (CPDM) generated by PDT at a node is the same created by CPSP, but invalid in the case of network. As an example, a node in a power system network with complex power flow at a particular operating point is considered in this paper for validation. In many IEEE research papers PSP is still now applied for the analysis in DPE. However, the innovated fundamental PDT which is the basis for PSP must be applied to perform any analysis and to solve all the problems related with the DPE. The PDT must be included in the curriculum of all the Universities as one of the Fundamental Circuit Theorem.

Keywords: Deregulated Power Environment, Power Sharing principle, Power Division Theorem, complex power distribution matrix, complex power sharing, Kirchhoff's Current Law, power system network, power tracing, transmission cost

How to Cite?: Dr. P. S. Kannan, "Power Division Theorem Proves Sharing Principle at a Node Disproves for Networks", Volume 14 Issue 10, October 2025, International Journal of Science and Research (IJSR), Pages: 1401-1403, https://www.ijsr.net/getabstract.php?paperid=SR251025124021, DOI: https://dx.doi.org/10.21275/SR251025124021