Improved Reduced-Order Model for PLL Instability Investigations

There is a rapid increase in the installed capacity of offshore wind power plants (WPPs) worldwide, and this trend will continue in the context of the recent EU energy crisis and the Ukraine war. As the share of the capacity of wind power plants increases in power systems, it is essential that WPPs can stay connected to the grid during different operational events and provide ancillary services. Recent research has identified the Phase Locked Loop (PLL) converter control as a contributing factor to instabilities driven by large-signal disturbances (i.e. severe grid faults). This type of instability is referred to as grid-synchronisation stability (GSS). In light of this, grid codes are being revised to secure the connection of WPPs and specify the services that need to be provided. To study GSS, it is essential to accurately model the wind turbine (WT) system and grid conditions. However, the actual WT models are often unavailable, black-boxed, or computationally too heavy to model in detail. Thus, simplified reduced-order models (ROM) resembling the actual system behaviour are the need of the hour. This paper presents an improved reduced-order model that considers a systematic approach to modelling the misalignment of the PLL angle in the converter states. Moreover, it considers the time-varying parameters and the step changes of initial states after fault triggering, which otherwise are neglected in the present literature. Our focus in this paper is to propose a novel WT ROM and demonstrate its effectiveness for offline studies. Based on transient stability studies, the improved reduced-order model accurately tracks the grid-angle post-grid disturbances, and its trajectory is a good match compared to a detailed simulation model in the time domain.