Voltage Stability Index (VSI) Calculation Guide per CIGRE TB 756
The Voltage Stability Index (VSI) per CIGRE Technical Brochure 756 is a dimensionless, real-time computable metric that quantifies proximity to voltage collapse by evaluating the reactive power裕度 and loadability margin at a given bus or system node. It integrates local voltage magnitude, active and reactive power flows, and line impedance parameters to provide an early warning indicator of static voltage instability. VSI values range from 0 (stable, ample margin) to 1 (critical point—voltage collapse imminent), with thresholds typically set between 0.7–0.9 for actionable alerts.
📖 Overview
📑 Key Components
🎯 Applications
- ✓ Real-time voltage stability monitoring in control centers
- ✓ Pre-contingency screening for N-1 security assessment
- ✓ Reactive power reserve allocation and optimization for grid-forming inverters
📐 Key Formulas
VSI at bus i (two-bus approximation)
VSI_i = \frac{4 \cdot X_{ij} \cdot Q_j + (V_i^2 - V_j^2)^2}{4 \cdot X_{ij} \cdot (Q_j + Q_{\text{max},j})}
Estimates voltage stability margin at bus i relative to adjacent bus j; derived from solving for the maximum Q_j before V_i reaches zero discriminant in the quadratic voltage equation.
Generalized VSI (multi-bus extension)
VSI_i = \frac{\sum_{k \in \mathcal{N}_i} \left[ 4 X_{ik} Q_k + (V_i^2 - V_k^2)^2 \right]}{\sum_{k \in \mathcal{N}_i} 4 X_{ik} Q_{\text{max},k}}
Aggregates contributions from all neighboring buses k in set 𝒩_i to assess composite stability margin at bus i.
Critical VSI threshold condition
VSI_i \geq 1 \iff \text{Voltage collapse singularity reached at bus } i
Defines the theoretical boundary of static voltage stability; VSI = 1 corresponds to zero eigenvalue of the reduced Jacobian (reactive power-voltage sensitivity).