## 1 Introduction  
The use of electro-chemical impedance spectroscopy (EIS) for the diagnostics of batteries is a great topic in the literature [1; 2; 3; 4; 5; 6]. The advantage of impedance spectroscopy is the possibility to determine electro-chemical processes and the short measurement duration. In case of lead-acid batteries (LAB) EIS is affected not only by current rate, temperature and SoC, but also by pre-history and stratification of the electrolyte [7]. In particular, flooded LAB suffer from stratification. However, stratification is also present in valve-regulated LAB, when the porous structure of the separator is not small enough [8]. Stratification has not been considered yet, when diagnostic technics using EIS were developed for LAB [2,4,5]. In the lead-acid battery the electrolyte is part of the charging-discharging reactions. The density of the acid decreases during discharging and increases during charging. Electrolyte with high density sinks to the bottom of the battery and increases the concentration while the concentration is decreased in the top [9]. [PERSON] et al. used radioelement detection with tracers in the electrolyte to characterize degradation of lead-acid test cells due to cycling with stratified acid. They observed that in case of stratification the top part of the cells is preferably charged while the lower part is discharged. They could detect sulfation in the lower part of positive electrode after cycling in stratified conditions. Because of the deficient charge of the bottom part of electrodes, both electrodes suffer from sulfation [10,11]. Stratification is an issue for LAB. In automotive applications, the high-rate charging and discharging promotes stratification and together with the partial State-of-Charge operating mode sulfation is abetted and degrades the battery capacity [12]. Based on simulations [PERSON] et al. found out, that LAB in PV-systems suffer from sulfation in the bottom part, because of stratification and small discharge currents [13]. In general large LAB in stationary applications, which are charged and discharged with high current rates suffer from stratification followed by sulfation [8]. So that improvements of LAB have also the focus to either prevent the resulting sulfation due to stratification [14,15] or to directly reduce stratification [8]. For the diagnostic of LAB using EIS the knowledge is missing to what extent stratification affects the measured impedance. For the online parameterization of battery models from frequently recorded spectra, as it is proposed by [PERSON] [5], this information is essential. [PERSON] had already shown based on simulations with spatially-resolved equivalent electrical circuits that height dependent equilibrium voltage, which is an effect of stratification, generates significant errors of the identified model parameters [16]. Based on the sulfation analysis performed by [PERSON] et al. [10] and own experiments with EIS on sulfated LAB [17] it is expected that the cell impedance not only change due to the stratification of the acid, but also from the inhomogeneous usage of active mass over the height of the electrodes. First investigations were done to analyze the influence of stratification on the impedance spectra [7]. However, the grade of stratification was not quantified and no characteristic changes of the spectrum were described. In the work presented here EIS measurements were performed on a lead-acid test cell with homogeneous and adjusted stratification acid. In the test cell the State-of-Charge (SoC) was set independently to the acid stratification, so that the initial SoC distribution was known. Furthermore, the acid concentrations were measured frequently to track changes in the stratification. These changes were small, as the duration of EIS measurements were below 15 h before conditions were changed again. Long-term diffusion processes in the electrolyte had no effect on the measurements.