Line-Wise Power Flow and Voltage Collapse

Voltage collapse is a phenomenon where voltage collapses at one or more busses due to lack of reactive power characterized by a decrease in voltage with increase in reactive power injection and voltage drop in connected lines due to large power flows. Bus-wise power balance equations, solved using the Newton-Raphson (NR) technique, are widely used to analyze power systems for VC. While bus-wise power balance equations succinctly model a power system, it and its Jacobian do not readily point out the most critical set of lines without additional analysis. In this paper, first, a line-wise set of equations for modeling a power system and its solution method using the NR technique for power flow analysis are proposed. Study results on 6-, 14-, 57-, and 118-bus IEEE systems, a 582-bus real system, 2383-bus Polish power system, and 9241-bus PEGASE system show that the proposed method is accurate, provides monotonic convergence, scales well of large systems, and is consistently faster up to twice the speed of the bus-wise NR method, while using sparse matrices. Second, a line-wise VC index is derived and shown to be directly present in the Jacobian of the line-wise NR method, identifying the susceptible set of lines without additional computation. Usefulness of VC index as an online VC assessment tool is demonstrated for a critical loading condition on test systems.