P–V Curve Tracing and CPF Validation for Static Voltage Stability Assessment Under Constant Power Factor Loading

Abstract

This paper presents an implementation-oriented methodology for static voltage stability assessment using P–V curve tracing, continuation power flow (CPF) validation, near-collapse voltage sensitivity analysis, and reactive capability diagnostics. Using the IEEE 30-bus benchmark system, the load at selected PQ buses is increased one bus at a time under a constant power factor (pf) growth model, and the resulting voltage magnitudes are recorded to form P–V curves. A two-stage step refinement strategy (coarse scan followed by fine steps near collapse) efficiently approximates the maximum solvable loading level and the corresponding critical voltage. To quantify vulnerability beyond loadability margin alone, a local slope-based sensitivity index, dV/dP, is computed from the tail of each curve. System-wide reactive power reserves and reactive limit hit/violation indicators are also extracted to characterize reactive support sufficiency and identify conditions where generator Q saturation would likely reduce practical margins. CPF is then applied to a subset of buses to benchmark the conventional tracing estimates and report PF-versus-CPF error statistics. The complete analysis is repeated for pf ∈ {0.8, 0.9, 1.0} to quantify the impact of reactive demand coupling on voltage stability margins, curve steepness, and weak-bus ranking. A formal monotonicity theorem is established, proving that the loadability margin is nondecreasing in the load power factor under standard regularity conditions. The results demonstrate consistent identification of vulnerable buses, strong agreement between two-stage tracing and CPF nose points, and substantial margin improvement as pf approaches unity.