Results of discrete frequency immittance spectroscopy (DFIS) measurements of lead acid batteries

Electrochemical Impedance Spectroscopy (EIS) has become a common research tool in laboratory studies of many electrochemical processes. The EIS methodology begins with an assumed equivalent-circuit model of the system under investigation. It then utilizes either a graphical analysis procedure or a nonlinear complex least-squares curve-fitting procedure to make the assumed model conform to measurements of the system's complex impedance acquired over a wide range of frequencies. (See, e.g., Macdonald (1), Robinson (2).) Although a few EIS investigations of lead-acid battery systems have been reported, very little work has been reported on real batteries - batteries actually found in the field (Karen et al (3), Huet (4)). In addition, most EIS battery investigations have focused on the millihertz and microhertz frequency range. At such low frequencies, a single impedance measurement can take hours. The battery's properties may change in the meantime. The combination of the graphical or least-squares curve-fitting procedure, the many measurements required, and the low frequencies employed, means that conventional EIS takes a very long time. Such a time-consuming procedure is probably not very practical for testing real batteries in the field. Discrete Frequency Immittance Spectroscopy (DFIS) also begins with a circuit model of the battery and uses small-signal measurements of complex immittance (i.e., either impedance or its reciprocal, admittance). However, instead of measuring the complete immittance spectrum, measurements are made at only a few, judiciously chosen, discrete frequencies. A direct calculation then yields element values of the circuit model exactly in terms of the measurements. Although there is no reason why DFIS could not be employed at millihertz or microhertz frequencies, we have found very significant information in the spectrum above one hertz. The combination of using f > 1, making few measurements, and doing the analysis with a direct calculation, means that DFIS can be performed very quickly - generally in less than one minute.