Direct, Accelerated, and Accurate  PDT-Superposition Approach for Sharing of Branch Power Losses and Loads  in the IEEE 9-Bus System

Kannan Perumal Subbiah

Direct, Accelerated, and Accurate PDT-Superposition Approach for Sharing of Branch Power Losses and Loads in the IEEE 9-Bus System

Author(s)	Kannan Perumal Subbiah
Country	India
Abstract	Accurate allocation of individual generator contributions to specific loads and branch power losses is essential for transparent electricity pricing in deregulated power markets. Conventional allocation methodologies such as flow-tracing algorithms, Bialek’s method, and Kirschen’s method suffer from heavy computational burdens due to complex matrix iterations and non-invertible flow matrices. To overcome these limitations, this paper presents an innovative Power Division Theorem (PDT)-Superposition framework that eliminates iterative computations by linearizing quadratic, non-linear power dependencies into a structural current framework. Grounded in network circuit theory, the proposed framework establishes explicit nodal equations for the IEEE 9-bus system, embedding operational constraints directly into a back-solvable Mathcad solve block for direct verification and independent auditing. Experimental validation proves that while the PDT-Superposition framework provides an exact complex power benchmark, the standalone PDT formula resolves load-sharing profiles within a tight <5% error margin. This allows grid operators to strategically bypass the superposition principle entirely to minimize execution overhead. Ultimately, this approach provides a faster, direct, and highly transparent methodology for real-time power and loss tracking in modern energy management systems.
Keywords	Power Division Theorem (PDT), Superposition theorem, Branch power losses, Power allocation, Deregulated electricity markets, computational complexity.
Field	Engineering
Published In	Volume 8, Issue 5, September-October 2026
Published On	2026-09-20

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Direct, Accelerated, and Accurate PDT-Superposition Approach for Sharing of Branch Power Losses and Loads in the IEEE 9-Bus System

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