Contributions of individual generators to complex power losses and flows. I. Fundamental theory

The contributions of individual complex power sources to branch complex losses and flows cannot be found using existing circuit theory. However, the contributions are the basis for supplement charge allocation in a competitive environment. To determine the contributions accurately and unequivocally, active and reactive currents flowing into a branch from a generator are defined. Based on the definitions and concepts of total differential and definite integral, a new method is derived theoretically to determine contributions of individual complex power generations to branch active and reactive losses, and contributions of individual active or reactive generations to branch complex losses. The nonlinear relationship between the complex power components flowing into and out of a branch from a power source is established. The interaction between active and reactive power flows is considered accurately throughout the study. The theory for determining branch complex loss and flow components incurred by individual generators is founded. It lays theoretical foundations for complex power tracing in lossy power networks