Abstract
This chapter presents synchronisation algorithms aimed to provide an estimation of the angular frequency and the fundamental component of a reference signal (grid voltage). Schemes for both single-phase and three-phase cases are presented. The proposed schemes do not require transformation of variables into the synchronous frame coordinates as conventional phase-locked loop (PLL) schemes. Therefore, they are not based on the phase angle detection. Instead, the angular frequency is detected and used for synchronisation purposes. The design of the proposed schemes is based on a complete model description in terms of stationary frame coordinates of a reference signal subject to a considerable amount of harmonic distortion. The proposed schemes include explicit harmonic compensation mechanisms to alleviate the effect of such harmonic distortion. Therefore, they are intended to perform properly under considerable distortion caused by low order harmonics, and are robust against angular frequency variations in the reference signal. Moreover, in the three-phase case, the model description involves both positive and negative sequences in stationary coordinates of the fundamental and harmonic components. Therefore, this scheme is able to perform well under severe unbalanced conditions, providing clean estimates for both the positive and negative sequences of the fundamental component of an unbalanced and distorted three-phase reference signal.
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Notes
- 1.
Also referred as square phase signal, that is, a signal with a phase shift of 90 degrees with respect to the reference signal.
- 2.
Notice that auxiliary variable φ αβ is strictly necessary to allow a complete model description in the unbalanced case.
- 3.
This expression is used later to recuperate the positive and negative sequences.
- 4.
The stability analysis can be completed using properties of the involved signals. It is omitted here for the sake of space limitations.
- 5.
Notice that the estimate \(\hat{\omega}_{0}\) is obtained for display purposes only, and is not used as a feedback variable.
- 6.
Ï– 0 is used for scaling purposes only. This avoids numerical errors, and facilitates the tuning process.
- 7.
This coincides with definition (4.30) in the single-phase case.
- 8.
The stability and convergence analysis of the proposed scheme can be completed using the signals properties. It has been omitted here for the sake of space limitations.
- 9.
Notice that the estimate \(\hat{\omega}_{0}\) is calculated for display purposes only, and is not used as a feedback variable.
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Escobar, G., Ho, NM., Pettersson, S. (2012). Grid Synchronisation Based on Frequency-Locked Loop Schemes. In: Vasca, F., Iannelli, L. (eds) Dynamics and Control of Switched Electronic Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2885-4_4
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