## 2 Problem  
In order to be able to use zinc-air batteries, however, adapted battery management systems are required. Battery management systems are electronic circuits that ensure the safe state of the battery systems and monitor and control the charging and discharging processes of the batteries. Their protective functions include, for example, deep discharge protection, overcharge protection and overcurrent protection. For these essential functions to work safely, the state of charge (SoC) of the respective cell must be known or determinable. In current cell technologies, the cell voltage is usually used for this purpose, as typically the cell voltage of an empty cell is lower than that of a full cell. Deep discharge protection is also necessary for lead-acid and lithium-ion batteries, as this can disable the battery. In lithium-ion batteries, even a slight deep discharge leads to irreversible damage and loss of capacity. In the case of a significant deep discharge, it is even likely that copper bridges will form, leading to a short circuit. In this condition, the cell becomes unstable and heats up very strongly, creating a fire hazard [23]. Deep discharge should also be avoided for zinc-air batteries. Although there is no fire hazard here, a loss of capacity, performance, and lifetime is to be expected. In the charged state, the zinc anode consists mainly of metallic zinc and is therefore mechanically stable. During deep states of discharge, the zinc oxidizes to zincate, which mixes within the electrolyte to form a viscous paste. Due to gravity, the anode mass now slowly sinks towards the bottom of the cell and the anode surface area decreases along with a loss of capacity and power. If the cell remains in a SoC that is too low for a longer period of time, more and more anode mass accumulates at the bottom of the cell and flows towards the counter electrode. Once this is reached, a short circuit occurs, preventing further battery operation. Therefore, zinc-air batteries must also be protected against deep discharge to ensure a long cycle life. Overcharging can also damage batteries. When various lithium-ion batteries are overcharged, metallic lithium can be reduced and accumulated at the cathode; this can also result in the release of oxygen at the anode. In an ideal case, the produced oxygen will outgas through a safety valve. Otherwise, it reacts with the electrolyte or the anode. As a result, the accumulator heats up and can even catch fire [24; 25]. Less critical is the electrolysis that occurs when a zinc-air battery is overcharged. The water component of the electrolyte outgasses during this process, and the electrolyte level drops so that some of the anodes can no longer be used for battery operation. In addition to the loss of liquid and capacity, the electrolyte concentration also increases. Typically, the initial concentration is selected to achieve maximum conductivity. The change in concentration therefore additionally leads to reduced cell performance by increasing losses. Although it is possible for zinc-air batteries to compensate for the loss with distilled water, overcharging the cells should generally be avoided for the reasons mentioned. In order for these essential protective functions can work, the SoC of the respective cell must be known or determinable. In current cell technologies, the cell voltage is usually used for this purpose, as typically the cell voltage of an empty cell is lower than that of a full cell [26]. The Nernst equation can be used to estimate the resulting change of the open circuit voltage. The Nernst equation describes the dependence of the electrode potential of a redox couple on temperature and concentration [27; 28]:  
\[E_{red}=E_{red}^{\Theta}-\frac{RT}{zF}\ln\frac{a_{Rel}}{a_{Ox}} \tag{2}\]  
where \(E_{red}^{\Theta}\) corresponds to the standard electrode potential at normal conditions, \(R\) is the universal gas constant, \(T\) specifies the absolute temperature, and \(z\) defines the number of electrons transferred in the reaction.