## 3 Modelling and Simulation of Solid-State Hydrogen Storage Device
The change in the mass of hydrogen and MH inside the MHT is expressed as follows:  
\[\dot{\mathrm{m}}_{\mathrm{a,d}}^{\mathrm{H_{2}}}=\dot{\mathrm{m}}_{\mathrm{a,d}}^ {\mathrm{MH}}\frac{M_{\mathrm{H_{2}}}SC}{M_{\mathrm{MH}}} \tag{8}\]  
where \(M_{\mathrm{H_{2}}}\) and \(M_{\mathrm{MH}}\) represent the molar masses of hydrogen and MH, respectively; \(SC\) is the stoichiometric coefficient, which denotes the molar amount of hydrogen contained per molar of MH and is taken here as 2.76. (2) Reaction dynamics  
The parameters affecting the reaction rate of the hydrogen storage material with hydrogen include the pressure, temperature, and SOC value inside the device [21; 22; 23]. For the reaction dynamics of LaNi5, the following model is fitted experimentally [24]:  
\[ \begin{cases}\dot{\mathrm{m}}_{a}^{\mathrm{MH}}=C_{a}\cdot e^{-\frac{E_{a}}{RT} }\cdot\ln\left(\frac{P_{\mathrm{g}}}{P_{\mathrm{eq},d}}\right)\cdot(m_{ \mathrm{s}}^{\mathrm{sat}}-m_{\mathrm{MH}})&,\ P_{\mathrm{g}}>P_{\mathrm{eq},d} \\ \dot{\mathrm{m}}_{\mathrm{d}}^{\mathrm{MH}}=C_{\mathrm{d}}\cdot e^{-\frac{E_{a}}{RT} }\cdot\frac{P_{\mathrm{g}}-P_{\mathrm{eq},d}}{P_{\mathrm{eq},d}}\cdot m_{ \mathrm{MH}}&,\ P_{\mathrm{g}}<P_{\mathrm{eq},d}\\ \dot{\mathrm{m}}_{a,\mathrm{d}}^{\mathrm{MH}}=0&,\ P_{\mathrm{eq},d}<P_{ \mathrm{g}}<P_{\mathrm{eq},d}\end{cases}  \tag{9}\]  
where \(C_{a}\) and \(C_{\mathrm{d}}\) denote hydrogen absorption and release reaction constants, respectively; \(P_{\mathrm{g}}\) denotes the pressure in the device; and \(P_{\mathrm{eq},d}\) and \(P_{\mathrm{eq},d}\) represent the balance pressure during hydrogen absorption and hydrogen release, respectively. (3) Thermodynamic balance  
In this paper, a constant slope term is added to approximate the real material behaviour based on the Van 't Hoff equation to describe the balance pressure in the hydrogenation reaction [25]:  
\[\left\{ \begin{array}{l}P_{\mathrm{eq},d}=P_{0}\exp\left[\frac{\Delta H_{d}} {RT}-\frac{\Delta S_{a}}{R}+sl\left(\frac{m_{\mathrm{MH}}}{m_{\mathrm{g}}^{ \mathrm{sat}}}-0.5\right)\right]\\ P_{\mathrm{eq},d}=P_{0}\exp\left[-\frac{\Delta H_{d}}{RT}+\frac{\Delta S_{d}}{R }+sl\left(\frac{m_{\mathrm{MH}}}{m_{\mathrm{g}}^{\mathrm{sat}}}-0.5\right) \right]\end{array} \right. \tag{10}\]  
where \(P_{0}\) denotes the reference pressure, 0.1 Mpa; \(\Delta H_{a}\) and \(\Delta H_{\mathrm{d}}\) represent the enthalpy variations for the hydrogen absorption and release reactions, respectively; \(\Delta S_{a}\) and \(\Delta S_{\mathrm{d}}\) represent the entropy variations for the hydrogen absorption and release reactions, respectively; and \(sl\) denotes the slope of the platform. (4) Conservation of energy  
The energy variations can be obtained based on the heat balance analysis of the MHT:  
\[\left\{ \begin{array}{l}\dot{\mathrm{Q}}_{\mathrm{MHT},a}=\dot{\mathrm{Q}} _{\mathrm{H_{2},in}}+\dot{\mathrm{Q}}_{\mathrm{react,a}}+\dot{\mathrm{Q}}_{ \mathrm{cool,in}}-\dot{\mathrm{Q}}_{\mathrm{cool,out}}-\dot{\mathrm{Q}}_{ \mathrm{exc}}\\ \dot{\mathrm{Q}}_{\mathrm{MHT},d}=-\dot{\mathrm{Q}}_{\mathrm{H_{2}out}}+\dot{ \mathrm{Q}}_{\mathrm{react,d}}+\dot{\mathrm{Q}}_{\mathrm{cool,in}}-\dot{ \mathrm{Q}}_{\mathrm{cool,out}}-\dot{\mathrm{Q}}_{\mathrm{exc}}\end{array} \right. \tag{11}\]  
where \(\dot{\mathrm{Q}}_{\mathrm{MHT},a}\) and \(\dot{\mathrm{Q}}_{\mathrm{MHT},d}\) represent the energy variations during hydrogen absorption and release, respectively; \(\dot{\mathrm{Q}}_{\mathrm{react,a}}\) and \(\dot{\mathrm{Q}}_{\mathrm{react,d}}\) represent energy variations for the hydrogen absorption and release reactions, respectively; \(\dot{\mathrm{Q}}_{\mathrm{cool,in}}\) and \(\dot{\mathrm{Q}}_{\mathrm{cool,out}}\) represent the energy variations into and out of the MHT, respectively; and \(\dot{\mathrm{Q}}_{\mathrm{exc}}\) represents the heat exchange between the MHT and the outside.