Introducing a Concise Formulation of the Jacobian Matrix for Newton-Raphson Power Flow Solution in the Engineering Curriculum

Abstract

The power flow computer program is fundamentally important for power system analysis and design. Many textbooks teach the Newton-Raphson method of power flow solution. The typical formulation of the Jacobian matrix in the NR method is cumbersome, inelegant, and laborious to program. Recent papers have introduced a method for calculating the Jacobian matrix that is concise, elegant, and simple to program.The concise formulation of the Jacobian matrix makes writing a power flow program more accessible to students. However, its derivation in the research literature involves advanced manipulations using higher dimensional derivatives, which are challenging for dual level students. This paper presents alternative derivations of the concise formulation that are suitable for undergraduate students, where some cases can be presented in lecture while other cases are assigned as exercises. These derivations have been successfully taught in a dual level course on computational methods for power systems for about ten years.

A Method for Directly Extracting the Jacobian Matrix of the Power Flow Equations of a Power System in Polar Coordinates

“…In Varwandkar (2019), the realification of PF is studied, and the disadvantages of the conventional PF method that needs to estimate the Jacobian matrix are investigated. The Jacobian matrix for Newton-Raphson power flow solutions is given in a concise form (Conlin et al, 2021). Moreover, a variety of Jacobian matrix calculating methods is also explored (Conlin et al, 2021).…”

“…The Jacobian matrix for Newton-Raphson power flow solutions is given in a concise form (Conlin et al, 2021). Moreover, a variety of Jacobian matrix calculating methods is also explored (Conlin et al, 2021).…”