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 are considered. The QCPF provides a basis for the PCPF. From the characteristic of the second order expression, the estimation of an 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 probabilistic voltage stability analysis. The presented approaches are illustrated on an IEEE test system.