Abstract: Various embodiments are provided for conducting a power flow analysis using a set of line-wise power balance equations. In at least some embodiment, the set of line-wise power balance equations is solved using a Newton-Raphson technique. In various cases, the Jacobian matrix generated by the Newton-Raphson technique may directly indicate the transmission lines, or sets of transmission lines, which are most susceptible to voltage collapse. In at least one example application, the set of line-wise power balance equations may be used as equality constraints in an optimal power flow (OPF) formulation for solving an optimal power flow (OPF) problem.

Abstract: Various embodiments are provided for conducting a power flow analysis using a set of line-wise power balance equations. In at least some embodiment, the set of line-wise power balance equations is solved using a Newton-Raphson technique. In various cases, the Jacobian matrix generated by the Newton-Raphson technique may directly indicate the transmission lines, or sets of transmission lines, which are most susceptible to voltage collapse. In at least one example application, the set of line-wise power balance equations may be used as equality constraints in an optimal power flow (OPF) formulation for solving an optimal power flow (OPF) problem.