The sub-synchronous interactions (SSIs) observed in wind power plants have gained attention in recent years. These oscillations are characterised by the diversity of wind power generation types, power grids and power electronic devices. Two pure electrical oscillations, namely induction generator effect (IGE) and sub-synchronous control interaction in wind farms, are firstly discussed on their different characteristics. Particularly, IGE normally falls into the category of sub-synchronous resonance. Then two major types of wind turbines: doubly fed induction generator and permanent magnet synchronous generator with respect to their participations in SSI are reviewed according to the current research status. Several typical analysis and mitigation techniques in existing literature are also expounded in regard to their advantages and disadvantages. Additionally, the research on a grid-connected voltage-source converter in combination with the phase-locked loop, which has caused instability issues including SSI, is briefly introduced. Conclusions are drawn and several perspectives on the future work are presented at the end of this study.

Fractional Frequency Transmission is a competitive technology for offshore wind power transmission. Modular Multilevel Matrix Converter (M 3 C) plays a key role in a Fractional Frequency Transmission System (FFTS) as the frequency changer. M 3 C is broadly considered as the AC-AC converter for the future with its attractive advantages in high voltage and high power applications. Due to the lack of a DC link, electrical quantities at different frequencies from two AC systems couple in M 3 C, resulting in a complex harmonic condition. Harmonics can lead to stability issues and its analysis is of great importance. This paper focuses on the harmonic analysis of M 3 C. The arm capacitor voltage ripples and the harmonic currents are analyzed at various frequencies. Major factors influencing the harmonics magnitude are discussed. Analysis is conducted on sub-module capacitance and arm inductance selection. A zero-sequence current mitigation controller for M 3 C is implemented and tested. It is found that for a FFTS, some current harmonics flow into AC systems even though the system is balanced, while the others circulate within the converter. The theoretical harmonic analysis is verified by simulations in Real Time Digital Simulator (RTDS) of a M 3 C system where each arm consists of forty sub-modules. Index Terms-Fractional frequency transmission system, harmonic analysis, modular multilevel matrix converter (M 3 C), offshore wind power, energy storage. I. INTRODUCTION U NDER the pressure of fossil energy depletion and environmental pollution, renewable energy development has drawn worldwide attention. Offshore wind power is favored with merits of not taking up land in cities, rich and stable resource and suitability for large-scale development. Three main offshore Manuscript

The wind turbine is usually integrated into the power grid via back to back converter, and the inertia is decreased. Virtual synchronous machine (VSM) control was proposed to improve inertia of the wind farm. While for the doubly-fed induction generator (DFIG)-based wind farm with traditional control strategy, sub-synchronous resonance (SSR) has become a significant problem when it is connected to series compensation transmission lines. Therefore, the impacts of VSM control strategy for DFIG on SSR need to be investigated. In this paper, a detailed small-signal stability analysis model of the VSM control strategy is first established and eigenvalue analysis is then carried out. SSR in the wind farm with the VSM control under different series compensation levels, controller parameters and wind speeds is analyzed, and it is also compared to that in the wind farm with the conventional vector control strategy (VC). Simulations are performed in PSCAD/EMTDC to verify the result of SSR analysis.

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