Lagrangian Modelling and Motion Stability of Synchronous Generator Power Systems

TL;DR

This paper introduces a Lagrangian model for analyzing the motion stability of synchronous generator power systems, offering a unified approach to study electromagnetic transients and stability using Lyapunov theory.

Contribution

It develops a novel Lagrangian modeling framework for synchronous generators that unifies electrical and mechanical dynamics and enables stability analysis beyond traditional methods.

Findings

Lagrangian model accurately describes electromagnetic transients

Model validated against PSCAD simulations

Enables stability analysis of power angle, voltages, and frequency

Abstract

This paper proposes to analyze the motion stability of synchro-nous generator power systems using a Lagrangian model derived in the configuration space of generalized position and speed. In the first place, a Lagrangian model of synchronous generators is derived based on Lagrangian mechanics. The generalized potential energy of inductors and generalized kinetic energy of capacitors are defined. The mechanical and electrical dynamics can be modelled in a unified manner through constructing a Lagrangian function. Taking the first benchmark model of subsynchronous oscillation as an example, a Lagragian model is construct-ed and numerical solution of the model is obtained to validate the accuracy and effectiveness of the model. Compared with the traditional EMTP model in PSCAD, the obtained Lagrangian model is able to accurately describe the electromagnetic transient process of the system. Moreover, the Lagrangian model is analytical, which enables to analyze the motion stability of the system using Lyapunov motion stability theory. The Lagrangian model can not only be used to discuss the power angle stability, but also used for analyzing the stability of node voltages and frequency. It provides the feasibility for studying the unified stability of power systems.