Electrochemical impedance spectroscopy can be used to obtain simulation models for the non-linear, non-stationary dynamic behavior of electrochemical power sources. Some extensions of porous-electrode theory are necessary for this purpose, which are not provided by standard EIS data evaluation software. This paper presents experimental data and consistent equivalent-circuit models for different dc conditions, regarding three electrochemical systems: supercapacitors as almost ideally blocking porous electrodes, lead/acid batteries under overcharge (water electrolysis) operation, and the same battery type under discharge/charge operation. The series inductance which masks the electrochemical behavior for frequencies as low as 100 Hz for a 100 Ah cell can be attributed mainly to the macroscopic cell geometry. The dependence of impedance parameters on direct current (non-linearity), temperature, state-of-charge, and previous discharge/charge regime is investigated. It is shown that model parameters extracted from the impedance spectra are closely linked with the charge-transfer kinetics, double-layer capacitance, transport limitation, and porous structure of the electrodes. Consequences for impedance-based determination of the battery's state-of-charge or state-of-health are discussed.