A Sufficient Condition for Power Flow Insolvability With Applications to Voltage Stability Margins

• Published in: IEEE transactions on power systems Vol. 28; no. 3; pp. 2592 - 2601
• Main Authors: Molzahn, D. K., Lesieutre, B. C., DeMarco, C. L.
• Format: Journal Article
• Language: English
• Published: IEEE 01-08-2013
• Subjects: Equations; Generators; Mathematical model; Maximum loadability; Optimization; power flow; power flow solution existence; Power system stability; Reactive power; solution space boundary; Voltage control
• ISSN: 0885-8950; 1558-0679
• DOI: 10.1109/TPWRS.2012.2233765

For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient condition is constructed in a framework of an associated feasible, convex optimization problem. The objective employed in this optimization problem yields a measure of distance (in a parameter set) to the power flow solution boundary. In practical terms, this distance is closely related to quantities that previous authors have proposed as voltage stability margins. A typical margin is expressed in terms of the parameters of system loading (injected powers); here we additionally introduce a new margin in terms of the parameters of regulated bus voltages.