The power system is a nonlinear complicated system. For power system analysis problems, they are mainly based on nonlinear equations. In practical systems, the calculation speed of a specific problem is very important. For most classical power system analysis methods, their one-time calculation speed with enough accuracy is difficult to be further improved after decades of research. However, if we see many-time calculations of different analysis functions as a whole, the new breakout may be made. This paper aims to present a novel foundational technique to improve the many-time calculation performance of power system problems. With the technique in this paper, the analysis of grid topology, bus types and line parameters can be separated, and the speed of online calculation of some problems can be improved by more than 10 times faster without any sacrifice of accuracy. This paper points out why the holistic speed of many-time calculations has the potential to be largely improved. The concept of a linear relationship based nonlinear problem (LRBNP) is proposed, which is critical to this technique. The detailed theory derivations are carefully performed. The proposed technique also shows a new way to understand the power systems. Finally, the verification of the derived formulas is performed.
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