## 1 Introduction
Thus, these measurement devices will show deviating absolute values and relative increases. Additionally, the impedance reading is influenced by the overlaying direct current (DC) and is dependent on SoC and temperature. Therefore, a clear understanding of the measurement and its conditions is necessary to get to the right implications for maintenance decisions. While the relative increase of one specific impedance reading at one frequency can be a good indicator for early failure detection [2], a reliable absolute correlation between available capacity and the gained impedance at only one frequency over the lifetime of a lead-acid battery is hard to find [3; 4; 5; 6; 11]. This is because singular impedance readings regardless of the measured frequency cannot derive all parameters that affect the available capacity. In addition, [PERSON] et al. [10] have shown that the frequency range of one specific process (e.g., charge transfer of the negative electrode) changes with SoH. Consequently, the choice of single-frequency measurements must be made with care. A more descriptive evaluation of one battery's electrical behavior can be derived via the simulation of a representative equivalent electrical circuit (EEC). The parameters of such an EEC are gainedthrough the fitting of impedance spectra measured with EIS. Consequently, faster and slower processes can be parameterized. Diverse EEC-based models have been described in literature (for an overview see [12]). The main components are typically the inductive element (L), the inner resistance (\(R_{\rm i}\)) as sum of the half-cell resistances, and two RC-elements with \(R_{\rm ct,NAM}\), \(C_{\rm ct,NAM}\) and \(R_{\rm ct,PAM}\), \(C_{\rm ct,PAM}\) representing each one charge transfer (ct) at the negative active mass (NAM) and positive active mass (PAM). It is expected that the different processes and thus the parameters of the underlying EEC do change differently not only with SoC (e.g., [13; 14]), current rate (e.g., [14]) and temperature but with SoH of the battery (e.g., [5; 10; 11; 15]). In addition, different aging mechanisms are expected to vary the EEC elements distinguishable. The common aging mechanisms of a lead-acid battery can be summarized as sulfation, corrosion, water loss and shedding of active mass (for further description see [16]). For the conducted experiment under UPS conditions with commonly used valve-regulated lead-acid (VRLA) batteries corrosion and water loss or dry out in combination with contact loss between electrodes and separator are often detected degradation mechanisms ([17; 18], see also tear down analysis in [2]). Nevertheless, the operation in large strings under float charge conditions can cause voltage deviations between the batteries. This can lead to batteries at high voltages while other batteries stay below the necessary charging voltage. Consequently, in strings with high voltage deviations, sulfation due to undercharge conditions can also be investigated [18; 19]. In VRLA such an undercharge can also occur in each cell due to an imbalance between the two electrodes [20]. Several authors have investigated the influence of the aforementioned aging processes on the EEC elements. For resistance measurements, [PERSON] and [PERSON] [5] describe that water loss and corrosion in VRLA batteries can be distinguished through the comparison of voltage drops after 500 \(\upmu\)s (2 kHz) and 5 s (0.2 Hz) within a discharge pulse (the rated current was 0.15 C\({}_{\rm n}\)). Before the test the battery was in open circuit voltage (OCV) state at 100% SoC. According to the authors, the short-term drop describes the internal resistance and thus, the change due to corrosive attack of the positive electrode. The second voltage deviation is caused by diffusion processes and gives an indication for the change due to water loss. Subsequent to this time domain evaluation, [PERSON] measured in [11] the change of electrical parameters for the full battery as well as the single electrodes in the frequency domain.