Sensitivity analysis and continuation methods are powerful tools for assessing power system stability. They help engineers identify critical parameters and determine voltage stability limits, guiding system improvements and control strategies.

These techniques provide valuable insights into system behavior under varying conditions. By analyzing sensitivity indices and PV curves, operators can make informed decisions to enhance stability margins and prevent potential blackouts.

Sensitivity Analysis for Power System Stability

Principles and Techniques

• Sensitivity analysis determines how changes in system parameters affect power system stability
• Involves computing partial derivatives of state variables or eigenvalues with respect to system parameters
• Sensitivity indices, such as participation factors and modal sensitivity, quantify the relative importance of different parameters on specific modes of oscillation or stability margins

Applications and Benefits

• Assesses the impact of parameter variations on small-signal stability, transient stability, and voltage stability
• Identifies critical parameters that significantly influence system stability (generator excitation controls, power system stabilizers, transmission line reactances)
• Guides the selection of remedial actions, such as parameter tuning or control system design, to enhance system stability

Continuation Methods for Voltage Stability

Continuation Power Flow (CPF) Method

• Numerical technique used to trace the equilibrium points of a nonlinear system (power system) as a parameter varies
• Computes PV (power-voltage) curves or QV (reactive power-voltage) curves of a power system
• Incrementally increases the loading factor until the maximum loadability point (critical point) is reached
• Involves predictor and corrector steps to trace the PV curve and identify the nose point (point of voltage collapse) accurately

Bifurcation Analysis and Stability Limits

• Handles the singularity of the Jacobian matrix at the critical point, enabling the computation of unstable equilibrium points beyond the nose point
• Performs bifurcation analysis, such as saddle-node bifurcation detection, to determine the margin to voltage instability
• Provides insights into voltage stability limits, reactive power margins, and critical loading conditions of a power system

Interpreting Stability Margins

Sensitivity Analysis Results

• Sensitivity indices and participation factors indicate the relative influence of different parameters on system stability
• High sensitivity values suggest small changes in corresponding parameters can significantly impact system stability
• Modal sensitivity analysis identifies critical modes of oscillation and associated generator or control parameters contributing to those modes

Continuation Method Results

• PV and QV curves provide a visual representation of the system's voltage stability characteristics
• Nose point of the PV curve represents the maximum loadability point, beyond which the system becomes unstable
• Distance between the current operating point and the nose point indicates the voltage stability margin, quantifying the system's proximity to voltage collapse
• Reactive power margin from the QV curve represents the additional reactive power support needed to maintain voltage stability at a given loading condition
• Results should be analyzed with other stability indices (eigenvalues, damping ratios) to comprehensively assess system stability margins

Strategies for Stability Improvement

Control Parameter Optimization

• Adjust or optimize parameters with high sensitivity to improve stability margins
• Tune generator excitation controls, power system stabilizers, and other control parameters based on sensitivity analysis to dampen critical oscillatory modes

Reactive Power Compensation and Load Shedding

• Install shunt capacitors or static var compensators (SVCs) at critical buses identified by continuation methods to improve voltage stability margins
• Design load shedding schemes based on the proximity to the nose point, allowing controlled disconnection of loads to prevent voltage collapse

Transmission System Reinforcement and Control Coordination

• Add new transmission lines or upgrade existing ones to alleviate congestion and improve voltage stability
• Coordinate control actions (generator redispatch, transformer tap adjustments, reactive power support) based on sensitivity and continuation method findings
• Employ stability-constrained optimal power flow (SCOPF) techniques to determine optimal control settings while maintaining system stability