Technical terms used in the lab assignment material.

Newton-Raphson method

(also known as Newton’s method) is an algorithm to find the root of a function (i.e. find \(x\) such that \(f(x)=0\)). In particular, it is a popular method to solve the AC power flow equations (default method in MATPOWER, see §4.1 of the manual [MATPOWER-man]).

It proceeds in an iterative manner, starting from an initial guess \(x_0\) (provided by the user). This guess is refined with a linear approximation of the function, using the knowledge of the gradient \(f'(x)\))

\[x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}\]

see e.g. Wikipedia for a graphical animation of the method in 1D’s_method