Improved geometric parameterisation techniques for continuation power flow

This study presents efficient geometric parameterisation techniques for the continuation power flow. The Jacobian matrix singularity is eliminated by the addition of the line equations which pass through the points in the plane determined by the variables loading factor and the sum of nodal voltage magnitudes, or angles, of all system buses. These techniques enable the complete tracing of P-V curves and the computation of the maximum loading point for any power system, including those with voltage instability problems that have the strong local characteristics, for which the global parameterisation techniques are considered inadequate. An efficient criterion to change the set of lines, based on the analysis of the total power mismatch evolution, is also defined. The obtained results show that the characteristics of Newton's conventional method are preserved and the convergence region around the Jacobian matrix singularity is enhanced. The computational time required to trace the P-V curve can also be reduced, without losing robustness, when the Jacobian matrix is updated only after the system undergoes a significant change.