  Power flow calculations for systems with a large number of buses, e.g. grids
with multiple voltage levels, or time series based calculations result in a
high computational effort. A common power flow solver for the efficient
analysis of power systems is the Newton-Raphson algorithm. The main
computational effort of this method results from the linearization of the
nonlinear power flow problem and solving the resulting linear equation. This
paper presents an algorithm for the fast linearization of the power flow
problem by creating the Jacobian matrix directly in CRS format. The increase in
speed is achieved by reducing the number of iterations over the nonzero
elements of the sparse Jacobian matrix. This allows to efficiently create the
Jacobian matrix without having to approximate the problem. A comparison of the
calculation time of three power grids shows that comparable open-source
implementations need 3-14x the time to create the Jacobian matrix.
