An efficient open-source implementation to compute the Jacobian matrix for the Newton-Raphson power flow algorithm

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.