Swing equation in power systems: Approximate analytical solution and bifurcation curve estimate

Area of Science:

• Power Systems Engineering
• Nonlinear Dynamics
• Applied Mathematics

Background:

• The swing equation is fundamental to power system dynamics, influencing small-signal and transient stability.
• Its mathematical form is shared across disciplines like mechanics, physics, and electronics, highlighting its broad relevance.
• Analyzing limit cycle behavior and homoclinic bifurcations is critical for understanding system stability.

Purpose of the Study:

• To obtain an approximate solution for the limit cycle of the swing equation using the incremental harmonic balance (IHB) method.
• To address challenges with distorted limit cycles near homoclinic bifurcation curves.
• To extend the IHB method for analyzing generalized swing equations with excitation voltage dynamics.

Main Methods:

• Application of the incremental harmonic balance (IHB) method.
• Incorporation of higher-order harmonics into the IHB method to improve accuracy.
• Extension of the IHB method to a generalized swing equation model.

Main Results:

• The IHB method successfully obtained approximate solutions for the swing equation's limit cycle.
• Including higher-order harmonics effectively resolved issues with distorted limit cycles near homoclinic bifurcations.
• The method accurately predicted the homoclinic bifurcation curve.
• The IHB method was successfully extended to analyze generalized swing equations.

Conclusions:

• The incremental harmonic balance method, especially with higher-order harmonics, provides an accurate and effective tool for analyzing power system dynamics and predicting bifurcations.
• This enhanced method offers a robust approach for studying complex power system behaviors, including those involving excitation voltage dynamics.