Frequency and sequence couplings can compromise the trustworthiness of multi-frequency models for converter-based systems. There have been effective attempts to address the couplings mainly by linearized averaged models. Only a few studies have been conducted on practical optimization of such models with enormous matrices and experimental results. This paper provides a generic theory for coupling patterns and proposes a multi-frequency modelling method to detect and address only the main couplings in the sequence domain for converter-connected renewable energy generators. The proposed generic model is based on empirical tests using small-signal perturbations and adopting Fourier transform on the switching converter response. The proposed theory and modelling methodology are verified using a 7MVA grid emulator for voltage perturbation tests on a 2MVA photo-voltaic converter. Accordingly, the couplings can exist in more generic forms, including multiples of perturbation and fundamental frequencies. To the best of our knowledge, the patterns with the multiples of the perturbation frequency have been overlooked in the literature. Furthermore, the mirror frequency concept is valid for all coupling patterns and is included in the proposed model. Besides, the proposed patterns and the environment noise levels have been practical criteria for selecting the main couplings.
- Generic multi-frequency modelling
- Frequency and sequence couplings
- Perturbation test
- Impedance modelling