A detailed formulation of sensitivity matrices for probabilistic load flow assessment considering electro-thermal coupling effect

In recent times, use of an analytical method (AM) is prevalent in solving probabilistic load flow (PLF) problem for better computational efficiency. AMs are employed to power system models that endure linear relations between the result variables and input random variables via sensitivity matrices. The accuracy of a sensitivity matrix-based PLF model can be improved by considering the effects of environmental conditions on line parameters. Looking out for an opportunity to upgrade existing PLF model to foresee the strength of thermal resistance model, a temperature-augmented model is presented. A detailed mathematical formulation of the aforesaid model is deliberated. The influence of temperature-augmentation on distributions of resistances, temperatures, power flows, and power losses of the temperature dependent branches is studied in detail. Finally, a note on applicability of the proposed model in the assessment of various power system studies is discussed.