Two extended approaches for voltage stability studies of quadratic and probabilistic continuation load flow

Two extended approaches are presented in this paper, i.e. the quadratic CPF (QCPF) with second-order terms retained, and the probabilistic CPF (PCPF) with load variation and load dependency considered. The QCPF provides a basis for the PCPF. From the characteristic of the second order expression, the estimation of a initial point is directly merged into the exact solution process at each load level in the QCPF. Based on the QCPF and the accepted range limits of random variables of +/-3 *(standard deviation), the variation of one PV-curve will distribute in a certain range to provide a probablistic voltage stability analysis. The presented approaches are illustrated on a IEEE testing system.