This version is available at https://strathprints.strath.ac.uk/62289/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.This paper is a post-print of a paper submitted to and accepted for publication in IEEE Transactions on Power Delivery and is subject to Institution of Electrical and Electronic Engineering Copyright. The copy of record is available at IEEE Xplore Digital Library.Abstract-A distributed PLL-based frequency control is proposed in this paper for offshore wind turbine converters connected with diode-rectifier based high-voltage-direct-current (HVDC) systems. The proposed control enables a large number of wind turbines to work autonomously to contribute to the offshore AC frequency and voltage regulation. The proposed control also provides automatic synchronization of the offline wind turbines to the offshore AC grid. Stability of the proposed frequency control is analyzed using root locus method. Moreover, an active dc voltage control of the onshore modular multilevel converter (MMC) is proposed to ride-through onshore AC fault, where the onshore MMC converter quickly increases the dc voltage by adding additional submodules in each phase, in order to rapidly reduce wind farm active power generation so as to achieve quick active power re-balance between the offshore and onshore sides. Thus the overvoltage of the submodule capacitor is alleviated during the onshore fault, reducing the possibility of system disconnection. Simulation results in PSCAD verify the proposed control strategy during start-up, synchronization and under onshore and offshore fault conditions. Index Terms-diode-rectifier based HVDC, distributed PLLbased frequency control, offshore wind power integration, onshore AC fault, synchronization of wind turbine converters I. INTRODUCTION N Europe, onshore wind farms have already been well developed, and more attention has been drawn to offshore sites. Many large offshore wind farms will be developed in the ...