## 1 Introduction  
The share of lead-acid batteries in installed batteries is still the highest of all battery technologies [1]. However, the attention paid to lead-acid batteries will abate in mobile applications with the replacement of the combustion engine by electric motors. Stationary installations lead-acid batteries will remain attractive if the costs stay competitive with respect to the costs of lithium-ion batteries. Typical stationary applications are uninterruptible power supply (_UPS_) systems, in which the batteries are float-charged until their stored energy is required. New business models for UPS systems plan an additional utilization for grid stabilizations, where the battery is charged or discharged to equilibrate peaks in the grid [2]. With such a new task, UPS systems become more attractive. Thereby, the utilization will change from mostly fully charged to partially discharged and frequently cycled. Accurate predictions of the state of health (_SoH_) become more crucial for an unobstructed operation of storage systems with lead-acid batteries. The direct measurement of capacity for _SoH_ determination together with the required full-charge for at least 24 h is time-consuming, and the storage system is unavailable for its actual task. Moreover, the test itself ages the battery. Many methods for _SoH_ estimation are based on impedance measurements at only one frequency. [PERSON] et al. summarized these methods and rated them as inaccurate and contradictory, basically because impedance information at only one measurement frequency are not sufficient [3]. Contradictory statements were found about the correlation between impedance and capacity loss [4; 5]. Dependencies of the impedance on state of charge (_SoC_), temperature, and current rate [3] further impede the _SoH_ estimation. The benefit of a spectrum is an accurate determination of the ohmic resistance and the characterization of electro-chemical processes, which is not possible with an impedance measured only at one frequency. It seems likely that changes in these electro-chemical processes due to aging are superiorly detectable within the spectrum. For the testing of lead-acid batteries, it is common to use electro-chemical impedance spectroscopy (_EIS_) [6; 7; 8; 9]. However, for _SoH_ estimation _EIS_ was intensively applied on other battery technologies such as lithium-ion batteries [10; 11; 12], but not yet on lead-acid batteries. During _EIS_, the battery is stimulated with a sinusoidal current (galvanostatic method) or voltage (potentiostatic method) of a defined amplitude and different frequencies. [PERSON] et al. recommend charge or discharging the lead-acid battery with a constant current and a limited _SoC_ change of not more than 5% during _EIS_ to obtain reproducable spectra [13]. This limits the possibly measured frequencies. However, the superimposed DC-current ensures the measurement of only the charge or discharge process and not both. In lead-acid batteries, the main gradual aging processes can be classified as sulfation, corrosion, or shedding [14]. Sulfation describes the accumulation of sulfate crystals on the surface of the electrodes. The low conductivity of the crystals provokes local inactivity with consequently inaccessible parts of capacity [15]. Sulfate crystals are the product of the discharge reaction on both electrodes and are dissolved during the recharge process. In applications, in which the battery is in partial SoC, these crystals grow with diminishing solubility over time until the crystals cannot be further dissolved during the usual charging strategy. Due to the smaller surface area in comparison to the positive electrode, the negative electrode suffers more from sulfation [16]. Corrosion of the positive grid dominates the aging processes if the potential of the positive electrode and the temperature are permanently increased. With the corrosion, the cross-section area of the grid and the connection between the grid and the active mass, decrease [14]. This aging process reduces the efficiency of the battery.