**Appendix A**

#### *Appendix A.1. LCC Station Modeling*

Figure A1 shows the connection diagram and equivalent circuit of the LCC station. *Uac*1 and *Xac*1 are the equivalent voltage and reactance of the AC grid coupled to the LCC station, respectively; *XT*1 is the transformer leakage reactance; *ILCC* and *Udcr* indicate the equivalent AC current and DC voltage sources of the LCC station.

The switching functions of the AC current and the DC voltage are *SLCC-abci* (*SLCC-ai*, *SLCC-bi, SLCC-ci*) and *SLCC-abcu* (*SLCC-au*, *SLCC-bu, SLCC-cu*), respectively. The mathematical equations are obtained as follows:

$$
\begin{bmatrix} i\_{LCC-a} \\ i\_{LCC-b} \\ i\_{LCC-c} \end{bmatrix} = \begin{bmatrix} S\_{LCC-al} \\ S\_{LCC-bl} \\ S\_{LCC-cl} \end{bmatrix} I\_{dcr} \tag{A1}
$$

$$
\begin{bmatrix}
\mathbf{U}\_{L,\mathbf{C}\mathbf{C}-\mathbf{a}} \\
\mathbf{U}\_{L,\mathbf{C}\mathbf{C}-\mathbf{b}} \\
\mathbf{U}\_{L,\mathbf{C}\mathbf{C}-\mathbf{c}}
\end{bmatrix} = \begin{bmatrix}
\ \mathbf{S}\_{L,\mathbf{C}\mathbf{C}-\mathbf{a}\mathbf{u}} & \ \mathbf{S}\_{L,\mathbf{C}\mathbf{C}-\mathbf{b}\mathbf{u}} & \ \mathbf{S}\_{L,\mathbf{C}\mathbf{C}-\mathbf{c}\mathbf{u}}
\end{bmatrix}^{-1} \mathbf{U}\_{\mathrm{dcr}} \tag{A2}
$$

where *Idcr* is the DC current of the LCC station; *ULCC* is the voltage over the equivalent AC current source.

**Figure A1.** LCC station. (**a**) Connection diagram, (**b**) equivalent circuit.

#### *Appendix A.2. VSC Station Modeling*

Figure A2 shows the connection diagram and equivalent circuit of the VSC station. *Uac*2 and *Xac2* are the equivalent voltage and reactance of the AC grid coupled to the VSC station, respectively; *XT2* is the leakage reactance of the converter transformer; *XVSC* is the series reactance of the VSC; *UVSC* and *Idci* are the equivalent AC voltage and DC current sources of the VSC station.

**Figure A2.** VSC station. (**a**) Connection diagram, (**b**) equivalent circuit.

The equations of voltage and current can be modeled as:

$$
\begin{bmatrix}
\mathcal{U}\_{VSC-a} \\
\mathcal{U}\_{VSC-b} \\
\mathcal{U}\_{VSC-c}
\end{bmatrix} = \begin{bmatrix}
\mathcal{S}\_{VSC-au} \\
\mathcal{S}\_{VSC-bu} \\
\mathcal{S}\_{VSC-cu}
\end{bmatrix} \mathcal{U}\_{dcl} \tag{A3}
$$

$$
\begin{bmatrix} I\_{VSC-a} \\ I\_{VSC-b} \\ I\_{VSC-c} \end{bmatrix} = \begin{bmatrix} S\_{VSC-al} & S\_{VSC-bl} & S\_{VSC-cl} \ \end{bmatrix}^{-1} I\_{dcl} \tag{A4}
$$

#### *Appendix A.3. Control Modeling*

Figure A3 shows the basic control curves of the hybrid HVDC system. For the LCC station (rectifier side), it configures a constant dc current controller and a voltage-dependent current order limiter (VDCOL). For the VSC station (inverter side), it adopts a direct current control mode, including an outer-loop voltage/reactive power controller and an inner-loop current controller.

**Figure A3.** Basic control curves of the hybrid HVDC system.

*Appendix A.4. The solution of the DC Fault Current in the VSC Station*

To seek a solution of the DC fault current in the VSC station, two assumptions are applied:

(i) Once the firing angle controller of the LCC station is activated, the DC fault current of the LCC station can be down to zero in a relatively short period after the fault;

(ii) The fault resistance is very little.

Supposing that the initial DC voltage and current are respectively marked as *U*0 and *I*0, the following equations are obtained:

$$
\Delta L\_{d\varepsilon l} = A\_1 e^{\lambda\_1 l} + A\_2 e^{\lambda\_2 l} \tag{A5}
$$

$$I\_{dci-f} = C\_{VSC}(A\_1\lambda\_1e^{\lambda\_1t} + A\_2\lambda\_2e^{\lambda\_2t})\tag{A6}$$

where *λ*1, *λ*2, *A*1, *A*2 are expressed as:

$$\begin{array}{ll} \lambda\_{1,2} = \quad -\frac{\frac{R\_{\text{SFCLI}} + R\_{\text{d4}} + R\_{\text{f}}}{2\left(L\_{\text{sur}} + L\_{\text{d4}}\right)}}{\pm\sqrt{\left(\frac{R\_{\text{SFCLI}} + R\_{\text{d4}} + R\_{\text{f}}}{2\left(L\_{\text{sur}} + L\_{\text{d4}}\right)}\right)^{2} - \frac{1}{\left(L\_{\text{sur}} + L\_{\text{d4}}\right)\widehat{C}\sqrt{\kappa}}} \\ \end{array} \tag{A7}$$

$$\begin{cases} \begin{array}{c} A\_1 = \frac{\lambda\_2 \|L\_0 + I\_0/C\_{VSC}}{\lambda\_2 - \lambda\_1} \\ A\_2 = \frac{\lambda\_1 \|L\_0^\* + I\_0/C\_{VSC}}{\lambda\_1 - \lambda\_2} \end{array} \end{cases} \tag{A8}$$
