An auxiliary-variable-based direct method for computing quadratic turning bifurcation points of power flow equations

Abstract

For a given one-parameter power flow equation, the quadratic turning bifurcation is the simplest and generically existent bifurcation, where the Jacobian matrix of the equation becomes singular due to rank deficiency 1. To overcome the singularity of the Jacobian matrix, usual Newton method can be applied to the so-called Moore-Spence determining system to detect the quadratic turning point. But the Moore-Spence system has very high dimensionality and causes much complexity in factorization of its Jacobian matrix. By introducing an auxiliary variable and an auxiliary equation to form an extended Moore-Spence system, this paper derives an efficient matrix reduction technique. The high dimensionality of the Jacobian matrix can thus be reduced and the complexity involved in matrix factorization can be simplified.