## 1 Introduction
### Case Introduction and Analysis of Dominant Controller Parameters  
A Drive Permanent Magnet Synchronous Generator (D-PMSG) via Voltage Source Converter-based High-Voltage Direct Current (VSC-HVDC) renewable power grid is used as the benchmark. Its topology is shown in Figure 2. The simplified model is representative of a collection of multiple renewable power plants into a base and then through the HVDC transmission system, in order to illustrate the application and value of the proposed method. In this benchmark, the operating parameters and controller parameters are set as follows. In this paper, a \"0.69 kV, 12 MW\" D-PMSG is used to represent the D-PMSG-based wind farm. The parameters of D-PMSG, VSC-HVDC and their detailed derivation process are referred to [11]. Wind speed is 12 m/s; pitch angle \(\beta\) is 0. The machine side controller (MSC) d-axis reference current id\({}_{\text{-ref}}\) is 0; the grid side controller (GSC) reactive power reference value Q\({}_{\text{s\_ref}}\) is 0; the DC voltage reference value ud\({}_{\text{c\_ref}}\) is 1.0 p.u. The reactive power reference value of sending end controller (SEC) Q\({}_{\text{s\_ref}}\) is 0.36 p.u, the DC voltage reference value ud\({}_{\text{c\_ref}}\) is 1.0 p.u., the active power reference value of receiving end controller (REC) P\({}_{\text{g\_ref}}\) is 0.85 p.u., and the reactive power reference value Q\({}_{\text{g\_ref}}\) is 0.13 p.u. The grid-connected distance of the wind farm, which means the distance between grid-side bus of D-PMSG u\({}_{\text{s}}\) and sending-side bus of VSC-HVDC u\({}_{\text{s\_1}}\), is 10 km. The initial parameters of MSC, GSC, SEC and REC are set in the following. The MSC parameters k\({}_{\text{p1}}\), k\({}_{\text{i1}}\), k\({}_{\text{p2}}\), k\({}_{\text{i2}}\), k\({}_{\text{p3}}\), k\({}_{\text{i3}}\) are 0.1, 20, 2.1, 10.2, 0.15, 100.2, respectively. The GSC parameters h\({}_{\text{p1}}\), h\({}_{\text{i1}}\), h\({}_{\text{p2}}\), h\({}_{\text{h2}}\), h\({}_{\text{p3}}\), h\({}_{\text{i3}}\) are 1.1, 100, 1.0, 1.3, 1.1, 2000, respectively. The SEC parameters b\({}_{\text{p1}}\), b\({}_{\text{i1}}\), b\({}_{\text{p2}}\), b\({}_{\text{h2}}\), b\({}_{\text{p3}}\), b\({}_{\text{h2}}\), b\({}_{\text{p4}}\), b\({}_{\text{i4}}\) are 0.2, 60, 0.6, 6.1, 51, 30, 0.6, 60 respectively. The REC parameters c\({}_{\text{p1}}\), c\({}_{\text{i1}}\), c\({}_{\text{p2}}\), c\({}_{\text{i2}}\), c\({}_{\text{p3}}\), c\({}_{\text{i3}}\), c\({}_{\text{p4}}\), c\({}_{\text{i4}}\) are 0.65, 50, 1.2, 6.1, 0.65, 30, 0.62, 6.7 respectively. The subscripts \(p\) and \(i\) of the controller parameters represent the proportional and integral coefficients, respectively. The state variables of the system are as follows. \[\left\{ \begin{array}{l}X=\left[X_{\text{PMSG}},X_{\text{PMSG-Crtl}},X_{ \text{HVDC}},X_{\text{HVDC-Crtl}}\right]^{\text{T}}\\ X_{\text{PMSG}}=\left[\Delta\omega_{1},\Delta\omega_{2},\Delta\delta_{1}, \Delta\delta_{2},\Delta\delta_{4},\Delta\delta_{4},\Delta\delta_{4},\Delta \delta_{4},\Delta\delta_{4},\Delta\delta_{4},\Delta\delta_{4}\right]\\ X_{\text{PMSG-Crtl}}=\left[\Delta\omega_{1},\Delta\omega_{2},\Delta\omega_{3}, \Delta\delta_{1},\Delta\delta_{2},\Delta\delta_{1},\Delta\delta_{2},\Delta \delta_{2}\right]\\ X_{\text{HVDC}}=\left[\Delta u_{\text{dcl}},\Delta\delta_{4},\Delta u_{ \text{dcl}},\Delta\delta_{4},\Delta\delta_{4},\Delta\delta_{4},\Delta\delta_{4 }\right]\\ X_{\text{HVDC-Crtl}}=\left[\Delta\omega_{1},\Delta\omega_{2},\Delta\omega_{3}, \Delta\delta_{4},\Delta\delta_{1},\Delta\delta_{2},\Delta\delta_{2},\Delta \delta_{3},\Delta\delta_{4}\right]\end{array} \right. \tag{11}\]  
Based on the above state variables, the 28-order state matrix is obtained, and the eigenvalues corresponding to the oscillation modes are obtained and shown in Table 1.