Application of the Power Division Theorem for Network Loss Formula Correction, Back Power Flow Tracking, and Validating Superposition Theorem Applicability in Automated EMS Grid Optimization

Accurate determination of individual component sharing of system loads and grid losses has been a long-standing challenge in power systems engineering. Traditional loss formulations based on net branch currents introduce cross-product errors that obscure physical accountability during bidirectional power flows. This paper utilizes the Power Division Theorem (PDT) to establish a rigorous, flow-aware framework that corrects the element loss formula. By converting quadratic power dependencies into a linearized inner-product format, this approach provides definitive mathematical validation for the applicability of the Superposition Theorem in active power loss calculations. The theorem defines an exact mathematical approach to trace back power flows and apportion discrete generator contributions to specific loads and network losses. Furthermore, this paper provides mathematical proof that operating a grid under Equal Source Node Voltage conditions yields absolute minimum network losses without iterative numerical optimization. Designed with low computational overhead, this framework can be easily integrated into modern real-time SCADA/EMS systems utilizing industry-standard protocols.