Accelerated time domain solutions of a VFT using the Poincaré map method with an embedded implicit integration algorithm

This paper presents a powerful analysis tool based on the Poincareacute map method and an implicit integration algorithm to compute periodic steady-state solutions of a variable frequency transformer, suitable for harmonic-oriented studies. Whilst the computation of the periodic steady-state solution is achieved with an acceleration procedure based on the Poincareacute map and a _{Newton method}, an implicit integration algorithm based on a Numerical Differentiation formulation is implemented to solve power networks with stiff problems. The incorporation of implicit integration algorithms into the Poincareacute map method paves the way to efficiently solve complex and realistic networks. This time domain approach is particularly useful for the fast determination of the periodic steady-state of the variable frequency transformer because of the inherently large inertia of its rotary machine, which may cause a prolonged transient response after a system disturbance. The time domain modelling of the variable frequency transformer includes a wound rotor induction machine, a DC motor, reactive compensation and conventional transformers. Transient and steady-state analyses are carried-out for a synchronous interconnection of two power networks, where the variable frequency transformer allows power exchange between the grids considering different power transfer scenarios. Furthermore, results are reported in terms of convergence to the steady-state, harmonics and waveform of the state variables.