**Appendix A**

$$\begin{cases} \begin{aligned} \text{G}\_{\text{PVVB}} &= \frac{\Delta \text{u}\_{\text{Bus}}}{\Delta \text{i}\_{\text{Bus}}} = \frac{s^2 \text{L}\_{\text{PV}} \text{C}\_{\text{PV}} + s \text{S}\_{\text{PV}} \text{C}\_{\text{PV}} + 1}{s^3 \text{L}\_{\text{PV}} \text{C}\_{\text{PV}} \text{C}\_{\text{Bus}} + s^2 \text{R}\_{\text{PV}} \text{C}\_{\text{P}} \text{C}\_{\text{Bus}} + s \left( \text{G}\_{\text{Bus}} + \text{C}\_{\text{PV}} \text{D}\_{\text{PV}}^2 \right)} \end{aligned} \\\\ \begin{aligned} \text{G}\_{\text{PVJB}} &= \frac{\Delta \text{u}\_{\text{Bus}}}{\Delta \text{i}\_{\text{PV}}} = \frac{s^2 \text{R}\_{\text{PV}} \text{C}\_{\text{P}} \text{C}\_{\text{Bus}} + s \left( \text{C}\_{\text{V}} \text{D}\_{\text{V}}^{\text{V}} \text{L}\_{\text{Bus}} - \text{R}\_{\text{PV}} \text{L}\_{\text{PV}} \text{C}\_{\text{V}} \right) - \text{l}\_{\text{L} \text{PV}} \text{L}\_{\text{S}}}{\text{s}^3 \text{L}\_{\text{L} \text{V}} \text{C}\_{\text{Bus}} + s^2 \text{R}\_{\text{PV}} \text{C}\_{\text{Bus}} + s \left( \text{C}\_{\text{Bus}} + \text{C}\_{\text{V}} \text{D}\_{\text{V}}^2 \right)} \end{aligned} \\\\ \begin{aligned} \text{G}\_{\text{PVLB}} &= \frac{\Delta \text{i}\_{\text{PV}}}{\Delta \text{i}\_$$

$$\begin{cases} \begin{aligned} \text{G\_{\text{BIB}}} &= \frac{\Delta u\_{\text{Basis}}}{\Delta t\_{\text{Basis}}} = \frac{sL\_{\text{Basis}} + R\_{\text{Bast}}}{s^2 L\_{\text{Basis}}c\_{\text{Basis}} + sR\_{\text{Bist}}C\_{\text{Basis}} + D\_{\text{Bist}}^2} \\ \text{G\_{\text{BdB}}} &= \frac{\Delta u\_{\text{Btu}}}{\Delta t\_{\text{Bst}}} = \frac{(sL\_{\text{Bnt}} + R\_{\text{Bnt}})I\_{\text{Bnt}} - D\_{\text{Bnt}}I\_{\text{Bans}}}{s^2 L\_{\text{Bnt}}C\_{\text{Bans}} + sR\_{\text{Bnt}}C\_{\text{Bans}} + D\_{\text{Bnt}}^2} \\ \text{G\_{\text{Bi}}} &= \frac{\Delta i\_{\text{Bkt}}}{\Delta t\_{\text{Bus}}} = \frac{D\_{\text{Btu}}}{s^2 L\_{\text{Bust}}C\_{\text{Bust}} + sR\_{\text{Bnt}}C\_{\text{Bns}} + D\_{\text{Bnt}}^2} \\ \text{G\_{\text{Bd}}} &= \frac{\Delta i\_{\text{Bnt}}}{\Delta t\_{\text{Bnt}}} = \frac{sL l\_{\text{Bnt}}C\_{\text{Bns}} + D\_{\text{Bnt}}L\_{\text{Bnt}}}{s^2 L\_{\text{Bnt}}C\_{\text{Bns}} + sR\_{\text{Bnt}}C\_{\text{Bnt}} + D\_{\text{Bst}}^2} \\ \text{G\_{\text{Bu}}} &= k\_{\text{Bup}} + \frac{k\_{\text{Btu}}}{s} \end{aligned} \tag{A2}$$
  $G\_{\text{Bi}} = k\_{\text{Bip}} + \frac{k\_{\text{Btu}}}{s}$ 

#### **Appendix B**

The passive criterion is additionally proven from the perspective of the dissipative system: Based on the DC bus, the equivalent impedance circuit of "PV-Battery-locomotive network" is obtained by using Thevenin's and Norton theorems, as shown in Figure A1, where *u*(*t*) = *U*dc.

**Figure A1.** "PV-Battery-locomotive network" equivalent impedance circuit.

The energy function is listed using the output current and voltage, as shown in the following equation.

$$\rho(t) = \int\_{-\infty}^{+\infty} u(t)i(t)dt\tag{A3}$$

When the above equation is always greater than zero, the system is a dissipative system and remains stable at all times. According to Passerval's theorem, the conversion to the frequency domain yields:

$$\begin{split} \int\_{-\infty}^{+\infty} u(t)i(t)dt &= \frac{1}{2\pi} \int\_{0}^{+\infty} (u^\*(\omega)i(\omega) + u(\omega)i^\*(\omega))d\omega \\ &= \frac{1}{2\pi} \int\_{0}^{+\infty} (u(\omega))^2 (\mathcal{Y}\_{\text{tot}}(\omega) + \mathcal{Y}\_{\text{tot}}"(\omega))d\omega \end{split} \tag{A4}$$

Among them, \* represents conjugation, *Y*tot represents the sum of the admittance realities of the optical storage network, and ensuring that the above equation is greater than 0 is ensuring that the admittance *Y*tot real part is greater than 0.

#### **References**


**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
