# Exploring the Feasibility of Autonomous Lighting Systems for Pedestrian Crossings in Off-Grid Areas
## 2 Materials and Methods
### Overview of the Selected Electric Energy Storage Technologies  
A key component of autonomous lighting systems is the battery, which stores energy from the PV during the day and supplies LED luminaires after dark. Several energy storage technologies are currently available on the market, characterized by a number of features, e.g., Li-ion batteries allow fast charging and have a high capacity, while at temperatures below 0 \({}^{\circ}\)C, their charging is difficult. In addition, at negative temperatures, only part of the capacity is available due to the reduced mobility of the energy carriers in the electrolyte. This phenomenon is particularly evident in electric vehicles that operate in negative temperatures. Consequently, battery heating in winter is used in electric vehicles to improve battery efficiency. Unfortunately, heating cannot be applied to an autonomous lighting system because of the small amount of energy gained from photovoltaics. In wintertime, energy could be used entirely for heating the battery rather than powering the lighting. The selection of a suitable energy storage technology that is resistant to subzero temperatures and deep discharges is crucial for achieving the efficient operation of the entire system. Table 4 provides an overview of the currently available energy storage technologies and their selected performance characteristics. Parameters were obtained from References [39; 40; 41; 42]. Figure 14: Schematic diagram of an autonomous lighting system. According to the presented application, two battery parameters are crucial, i.e., operating temperature range and number of battery cycles. These criteria are fulfilled only by two technologies, i.e., Ni-Cd and lead-carbon batteries. When analyzing the parameters of a Ni-Cd battery, it is noticeable that it is characterized by a \"memory effect\". This is a negative feature of the battery's capacity reduction during partial discharges, which'remembers' the depth of discharge, making the remaining capacity unavailable to the user. It is extremely important that batteries of this type must be discharged to the end. Unfortunately, discharging the battery to the end is tantamount to terminating the lighting system because of lack of energy, and this type of battery cannot be used in this application. The available capacity of the battery used in the model can be calculated according to the equations given in articles [43; 44; 45]. This parameter depends on the type of construction, electrolyte temperature and load current, shown in Equation (1):  
\[C(I,T_{e})=\frac{K_{\text{C}}C_{0}\Big{(}1+\frac{T_{e}}{-I_{f}}\Big{)}^{\varepsilon }}{1+(K_{\text{C}}-1)\Big{(}\frac{I}{I_{n}}\Big{)}^{\delta}} \tag{1}\]  
where:  
\(K_{\text{C}}\), \(\varepsilon\), \(\delta\)--Constants determined on the basis of battery design data [-];  
\(C_{0}\)--Battery capacity [Ah];  
\(T_{e}\)--Electrolyte temperature [\({}^{\circ}\)C];  
\(T_{f}\)--Electrolyte freezing temperature [\({}^{\circ}\)C];  
\(I\)--Battery load current [A];  
\(I_{n}\)--Battery rated current [A]. An important issue of battery exploitation is the efficiency of the charging process, which is specified in [46]. This parameter is crucial for charging process during low charging current taken from PV, as shown in Equation (2):  
\[\eta_{charge}=1-exp\left[\frac{20.73}{\frac{I_{bat}}{I_{10}}+0.55}(SOC-1)\right] \tag{2}\]  
where:  
SOC--State of charge [-];  
\(I_{bat}\)--Battery charging current [A];