###### Abstract
\begin{array}{l}P_{WF}=-\frac{3}{2}\left(\varepsilon_{gd}i_{gd}+ \varepsilon_{gq}i_{gq}\right)=-\frac{3}{2}E_{g}i_{gd}\\ \\ Q_{WF}=-\frac{3}{2}\left(\varepsilon_{gq}i_{gd}+\varepsilon_{gd}i_{gq}\right)= -\frac{3}{2}E_{g}i_{gq}\end{array} \right. \tag{3}\]  
where \(P_{WF}\) and \(Q_{WF}\) are the output active power and reactive power of the grid-side converter. From Equation (3), it can be seen that by adopting grid voltage orientation, the decoupling of active and reactive currents can be achieved. The active power of the converter can be controlled by controlling the \(d\)-axis, and the reactive power of the converter can be controlled by controlling the \(q\)-axis. Considering that the DC voltage is directly related to the active power output on the grid side, the d-axis current reference of the grid-side converter \(i_{gdref}\) can be obtained by the PI controller from the difference between the DC bus voltage command value \(v_{dcref}\) and the DC bus voltage \(v_{dc}\). Unit power factor control is used in this paper. The output of the wind turbines to the grid is all active power. So, \(i_{gqref}\) is set to 0. The grid-side converter control strategy is designed as shown in Figure 2.  
The machine-side converter employs a rotor-flux-oriented control (RFOC) strategy to regulate the electromagnetic torque [21]. By aligning the rotor flux vector with the d-axis of the synchronous rotating reference frame, the stator current components are decoupled, where the \(d\)-axis current (\(i_{sd}\)) controls the amplitude of the stator flux. The \(q\)-axis current governs the electromagnetic torque \(T_{e}\). Under the maximum torque per ampere condition (\(i_{sd}=0\)), the electromagnetic torque is proportional to \(i_{gq}\). The electromagnetic  
Figure 2: Control strategy of the PMSG grid-side converter. torque is positively correlated with the q-axis current of the machine-side converter. The electromagnetic torque is expressed as:  
\[T_{e}=\frac{3}{2}n_{p}\psi_{f}i_{sq} \tag{4}\]  
where \(n_{p}\) is the number of pole pairs, and \(\psi_{f}\) is the permanent magnet flux linkage. Considering that the electromagnetic power \(P_{e}\) is also positively correlated with the electromagnetic torque \(T_{e}\), the PI controller is introduced. Through the difference between the reference value of the active power \(P_{mrf}\) and the active power \(P_{m}\), the reference value of the q-axis current of the converter on the machine side \(i_{sprf}\) can be obtained. Finally, the control strategy of the machine-side converter is given, as shown in Figure 3.  
The common control strategies of wind farms and MMC-HVDC systems both adopt grid-following control. Offshore wind farms are passive systems. To ensure that the wind farm energy has stable access, the MMC-HVDC needs to provide a stable voltage and frequency. Therefore, the WFMMC should adopt fixed AC voltage/frequency control (V/f control). The GSMMC undertakes the task of maintaining DC voltage stability by adopting fixed DC voltage control. This is similar to that of a PMSG grid-side converter. The GSMMC's outer-loop controller is configured with \(d\)-axis oriented DC-link voltage regulation and \(q\)-axis based reactive power tracking. Because the control method is relatively common, it will not be repeated in this article.