# Improved Control Strategy of MMC-HVDC to Improve Frequency Support of AC System
## 3 Control Method of MMC-HVDC System  
As shown in Figure 1, the entire system consists of three parts: offshore wind power farm, onshore AC system, and MMC-HVDC system. In addition, the system has an HVDC cable and an AC cable in the modeling. In the MMC converter on the side of the offshore wind power farm, the P-Q control strategy is adopted, and on the side of the MMC converter connected to the onshore AC system, the Vdc-Q control strategy is adopted. The Vdc control strategy is used to quickly adjust the output active power from the MMC converter side. The reactive power control strategy aids the AC system in quickly adjusting the voltage level by using a set-point value. First, the detailed modeling of the controller of the MMC-HVDC is described in this section. The MMC-HVDC model contains three-phase legs, and each phase contains an upper and lower arm. Each item's upper and lower arms have an equal number of submodules in series. There is a capacitor inside each submodule for storing energy. Therefore, a DC-link capacitor is not required for MMC-HVDC [20; 22]. For detailed information on MMC-HVDC modeling, please refer to [20; 22]. Figure 2 shows a detailed model of the half-bridge submodule, which contains two insulated-gate bipolar transistor (IGBT) switches and a capacitor for energy storage. Figure 2 presents the equivalent circuit of the submodule, which simplifies the mathematical formula. \[R_{eq}=R_{T1}\bigg{[}1-\frac{R_{T1}}{R_{T1}+R_{T2}+R_{C}}\bigg{]} \tag{1}\]  
\[V_{\alpha q}=\frac{V_{c}R_{T1}}{R_{T1}+R_{T2}+R_{c}} \tag{2}\]  
\(R_{T1}\) and \(R_{T2}\) are the corresponding resistances of the IGBT switches, \(R_{C}\) is the voltage of the capacitors, and \(V_{C}\) is the resistance of the capacitor. The changes in these values depend on changes in the time and state of the IGBT switch. Therefore, the time-varying formula can be expressed as follows:  
\[V_{arm}=V_{\alpha q}(t-\Delta t)+R_{eq}(t)I_{arm} \tag{3}\]  
where \(V_{arm}\) is the time-varying voltage value of the upper/lower arm of the MMC-HVDC. Figure 1 shows the basic control strategy logic for the MMC-HVDC control. Figure 1 presents a d-axis control strategy that provides two control strategies--active power control and DC voltage control--for calculating the d-axis current reference. Figure 1 also presents a q-axis control strategy that provides two control strategies--reactive power control and AC voltage control--for calculating the q-axis current reference. The proportional-integral (PI) controller is used primarily in the control strategy loop of this study. Figure 1: System outline and conventional control loop of modular multilevel-converter high-voltage direct-current (MMC-HVDC). Figure 2: Thevenin equivalent circuit of submodules. To ensure that the voltage components of the HVDC and the point of common coupling (PCC) are the same, we use a phase-locked loop (PLL) to realize control. When the voltage of the PCC is maintained at a constant value and balanced (\(u_{d_{ac}}=V_{ab_{ac}},\ u_{q_{ac}}=0\)), the MMC dynamic formula is as follows:  
\[u_{d_{dc}}=u_{d_{ac}}-Ri_{d}-L\frac{di_{d}}{dt}-Xi_{q} \tag{4}\]  
\[u_{q_{dc}}=-Ri_{q}-L\frac{di_{q}}{dt}+Xi_{d} \tag{5}\]  
where \(u_{d_{dc}}\) is the d-component voltage of the DC side, \(u_{d_{ac}}\) is the d-component voltage of the AC side, and R, L, and X are the equivalent resistance, inductance, and impedance of the three-phase reactor and transformer, respectively. The current component required for control by the proportional-integral (PI) controller is calculated, and the MMC voltage reference component is then calculated. Using these calculated values, the active power and reactive power output of the MMC-HVDC injected into the AC system through the dq-to-abc transformer is then calculated.