Developments in the Newton Raphson power flow formulation based on current injections

This paper describes a sparse Newton Raphson formulation for the solution of the power flow problem, comprising 2n current injection equations written in rectangular coordinates. The Jacobian matrix has the same structure as the (2n x 2n) nodal admittance matrix, in which each network branch is represented by a (2 x 2) block. Except for PV buses, the off-diagonal (2 x 2) blocks of the proposed Jacobian equations are equal to those of the nodal admittance matrix. The results presented show the proposed method leads to a substantially faster power flow solution, when compared to the conventional Newton Raphson formulation, expressed in terms of power mismatches and written in polar coordinates.