## 2 Materials and Methods  
### Preliminaries  
This section describes a hybrid AC/DC microgrid system that utilizes renewable energy sources such as wind and PV as the primary power source. The AC/DC power generated by the system is rectified to produce a stable DC voltage, which is then transmitted to the DC bus as the power source. The system consists of three main parts: the power generation system, which includes the AC/DC power generation equipment and rectifier; the control and regulation system, which includes energy storage devices such as batteries, electrolyzers, fuel cells, and hydrogen storage tanks, as well as an MPC system; and the load demand side, which consists of the power demand of various loads. Together, these three parts form the hybrid AC/DC microgrid system. The AC/DC hybrid power generation equipment on the power supply side provides stable electrical energy \(P_{RES}\), while the control system is responsible for regulating energy storage or supply in cases of energy surplus or shortage. The loads on the demand side consume electrical energy \(P_{Load}\). The control structure principle is illustrated in Figure 1.  
In the aforementioned power distribution system, the energy consumed by the loads is influenced by external factors and electricity usage patterns. For example, the electricity demand of the loads varies across different seasons and time periods. As a result, it becomes challenging to maintain a balance between the power supply and demand, leading to issues of energy surplus or shortage. To address the energy supply-demand imbalance in this power distribution system, this paper presents the following mathematical problem formulation to tackle the aforementioned challenges:  
\[P_{Load}(\tau)=P_{RES}(\tau)-P_{Bat}(\tau)+P_{F_{c}}(\tau)-P_{E_{z}}(\tau), \tag{1}\]  
where \(P_{Load}(\tau)\) represents the electrical energy required by the load at time \(\tau\), \(P_{RES}(\tau)\) represents the electrical energy generated by the power generation equipment, \(P_{Bat}(\tau)\) represents the energy stored in the battery, \(P_{F_{c}}(\tau)\) represents the energy generated by the fuel cell through hydrogen combustion, and \(P_{E_{z}}(\tau)\) represents the energy consumed by the electrolyzer in electrolyzing water. Therefore, by utilizing the control system composed of energy conversion and storage devices such as batteries, electrolyzers, fuel cells, and hydrogen storage tanks, the control section adjusts these components to achieve a balance between energy supply and demand. Taking into account the constraints of the lifespan of energy conversion and storage devices, it is necessary to reconstruct a state model that satisfies the supply-demand  
Figure 1: AC/DC hybrid microgrid electric-to-hydrogen conversion control schematic. relationship. In order to prolong the lifespan of the energy conversion and storage devices consisting of batteries, electrolyzers, fuel cells, and hydrogen storage tanks, the following constraints were applied to the battery capacity and hydrogen storage tank capacity:  
\[\left\{ \begin{array}{l}\min\chi_{soc}\leq\chi_{soc}\leq\max\chi_{soc},\\ \min\chi_{loth}\leq\chi_{loth}\leq\max\chi_{loth},\end{array} \right. \tag{2}\]  
where \(\chi_{soc}\) represents the capacity of the battery at time \(\tau\), while \(\min\chi_{soc}\) and \(\max\chi_{soc}\) represent the lower and upper limits of the battery capacity, respectively. \(\chi_{loth}\) represents the capacity of the hydrogen storage tank at time \(\tau\), while \(\min\chi_{loth}\) and \(\max\chi_{loth}\) represent the lower and upper limits of the hydrogen storage tank capacity, respectively. To constrain the capacity of the battery and hydrogen storage devices within a certain range, this paper establishes the following models for battery and hydrogen storage capacity:  
\[\left\{ \begin{array}{l}\chi_{soc}(\tau+1)=\chi_{soc}(\tau)+\frac{\eta_{ Bat}T}{C_{max}}P_{Bat}(\tau),\\ \chi_{loth}(\tau+1)=\chi_{loth}(\tau)+\frac{\eta_{Bat}T}{\overline{\
u_{max}}}P _{H}(\tau),\end{array} \right.