Supermodal Decomposition of the Linear Swing Equation for Multilayer Networks

Area of Science:

• Electrical Engineering
• Network Dynamics
• Power Systems Analysis

Background:

• The swing equation is crucial for power system stability analysis.
• Existing models often assume simplified dynamics and equal damping coefficients.
• Multilayer networks require more sophisticated modeling approaches.

Purpose of the Study:

• To analyze the swing equation in multilayer networks with heterogeneous generator (second-order) and motor (first-order) dynamics.
• To remove the assumption of equal damping coefficients in generator models.
• To develop a simplified network model and quantify errors in perturbation propagation.

Main Methods:

• Decomposition of the linear swing equation into independent modes.
• Identification of network symmetries to derive a quotient network.
• Comparison of full network dynamics with the quotient network model.
• Modal decomposition of error dynamics and quantification of steady-state and overshoot errors.

Main Results:

• A modal decomposition of the linear swing equation was achieved under general conditions.
• A novel quotient network model was derived by identifying network symmetries.
• Methods for quantifying steady-state and maximum overshoot errors were established.
• The dynamics of the full and quotient networks were compared, revealing error dynamics.

Conclusions:

• The developed method provides a generalized approach to analyzing power system stability in multilayer networks.
• The quotient network offers a simplified yet accurate representation for studying perturbation propagation.
• The quantification of errors is essential for assessing the reliability of simplified models in power system dynamics.