Modelling of an autonomous power system at variable speed for transient simulation using Lagrange´s laws

The dynamical equations of a power system are usually obtained by applying the laws of electrotechnics and Newton´s second law. The authors extend the use of Lagrange´s laws, classically used to model mechanical systems, to the derivation of the dynamical model of an autonomous power system. One of the major advantages of the proposed approach is its simplicity, which directly derives from the unified aspect of the modelling procedure. The obtained dynamical model is transformed into a generalized state-space model, and is used to simulate the transient behaviour of the autonomous power system to the presence of variable speed.