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Small-Signal Modelling and Stability Assessment of Phase-Locked Loops in Weak Grids


Claudio Burgos-Mellado

Alessandro Costabeber

Professor of Electrical Energy Systems




This paper proposes a low-complexity small signal model for a 3-leg converter connected to a balanced three-phase, three-wire weak grid and synchronised to this grid using a PLL implemented in a synchronous rotating d-q axis. A thorough analysis of the system stability as a function of the PLL bandwidth and the short circuit ratio (SCR) of the grid is performed based on a linearised model. By using the proposed model, an improved design process is proposed for the commonly used dq-PLL that accounts for the potential stability issues which may occur in weak grids. Using the proposed approach, it is possible to optimise the PLL design to find the fastest PLL that can operate stably considering the SCR of the grid. In addition, the proposed model is very simple, resulting in a straightforward design tool that could also be used for online stability monitoring. The method is validated through simulations and experimental results from a 5kW laboratory system.


Burgos-Mellado, C., Costabeber, A., Sumner, M., Cárdenas-Dobson, R., & Sáez, D. (2019). Small-Signal Modelling and Stability Assessment of Phase-Locked Loops in Weak Grids. Energies, 12(7), 1227.

Journal Article Type Article
Acceptance Date Mar 20, 2019
Online Publication Date Mar 30, 2019
Publication Date Apr 1, 2019
Deposit Date Apr 3, 2019
Publicly Available Date Apr 3, 2019
Journal Energies
Electronic ISSN 1996-1073
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 12
Issue 7
Pages 1227
Keywords General Computer Science
Public URL
Publisher URL


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