# UKF-Based State Estimation for Electrolytic Oxygen Generation System of Space Station
## 2 Operation Analysis and Working Principle of EOGS
### The Working Principle of EOGS  
The basic process of oxygen generation by water electrolysis is that direct current is applied to the electrolyzer body, and water molecules react electrochemically on the electrode to decompose into hydrogen and oxygen. Figure 2: The block diagram of EOGS. Cathode reaction:  
\[2H_{2}O+2\mathbf{e}\to H_{2}\uparrow+2 OH^{-} \tag{1}\]  
Anode reaction  
\[2 OH^{-}-2\mathbf{e}\rightarrow\frac{1}{2}O_{2}\uparrow+2H_{2}O \tag{2}\]  
Total reaction equation:  
\[H_{2}O\to H_{2}\uparrow+\frac{1}{2}O_{2}\uparrow \tag{3}\]  
The electrolysis of water follows [PERSON]'s law of electrolysis. The gas output is proportional to the current, and the working current depends on the working voltage, working temperature and electrolyte concentration. The principle of water electrolysis is also used in the oxygen production system of the space station. However, the solid polymer electrolyte (SPE) is used as the membrane. The SPE is a perfluorosulfonate polymer ion exchange membrane with a thickness of only 0.3 mm and many physical properties of polytetrafluoroethylene. When the SPE is immersed in water, it is a good ionic conductor with good conductivity. It is the only electrolyte required for water electrolysis. Take a schematic diagram of an electrolytic cell, as shown in Figure 3. Two electrodes are connected on both sides of the solid polymer electrolytic membrane to form an anode and a cathode. The conductivity of ions is provided by hydrous ions. Ions are transferred from anode to cathode by solid polymer and ion exchange membrane. Water is fed into the electrolytic cell from the cathode (hydrogen electrode), which simplifies the requirements of water supply system and water gas separation under weightlessness. In order to dissipate heat, the circulating water flow should be greater than the water supply required by electrolysis. Enough water is transported from the hydrogen electrode to the oxygen electrode through the solid-state electrolytic membrane, and the oxygen, hydrogen ions and electrons are discharged by electrochemical decomposition at the oxygen electrode. Hydrogen ions in the cathode are electrochemically reacted to release hydrogen, hydrogen and water are discharged together, and the oxygen produced does not contain free water. Figure 3: Schematic of electrolytic cell. Based on the analysis of the basic principle of EOGS and the working principle of electrolytic cell, it can be assumed that:  
1. The oxygen, hydrogen and water vapor in the core are all ideal gases, and the working pressure in the cell will not exceed 150 kPa;
2. Water vapor and water can quickly saturate with oxygen and hydrogen in the mixed gas flow;
3. Hydrogen and oxygen are insoluble in water;  
The mass conservation equation of the electrolytic oxygen system is as follows:  
\[q_{s}=q_{\rm O_{2}}+q_{\rm H_{2}}+q_{mix} \tag{4}\]  
where \(q_{s}\) is the amount of water supplied to the system, kg; \(q_{mix}\) is the flow rate of water vapor in the mixed flow of hydrogen and water, kg; \(q_{\rm O_{2}}\) is the oxygen production, kg; \(q_{\rm H_{2}}\) is the hydrogen production, kg. According to the basic thermodynamic conservation law, the energy conservation equation of the electrolysis oxygen system is as follows:  
\[N=Q_{\rm O_{2}}+Q_{\rm H_{2}}+Q_{E}+Q_{O_{2}}^{ex}+Q_{H_{2}}^{ex}+Q_{H_{2}}^{ Sep}+Q^{mix}_{H_{2}}+Q_{cold}+Q_{\rm H_{2}O}\cdot q_{\rm H_{2}O} \tag{5}\]  
where \(Q_{H_{2}O}=P_{H_{2}O}\cdot q_{H_{2}O}\); \(P_{H_{2}O}=1.588\times 10^{7}\)J/kg.