On the compatibility of electric equivalent circuit models for enhanced flooded lead acid batteries based on electrochemical impedance spectroscopy

Vehicle emission regulations have been forcing the automotive industry worldwide to reduce its carbon footprint. Environmentally friendly, full electric and plug-in hybrid vehicles are gaining popularity and their sales numbers increase each year but due to limited sales volumes, their effect on total fleet emission reduction is limited. The trend in the mass market is also progressing in the same direction and as a result, fuel-efficient micro-hybrid vehicle sales are also gaining popularity. According to market research, total micro-hybrid vehicle sales will increase from 8.8 million in 2013 to 55.3 million in 2022. Lead-acid batteries are still unrivaled for micro-hybrid vehicles as well as conventional vehicles due to their robust and safe design, low-cost raw materials, mature and cost optimized manufacturing process, and already established efficient recycling processes. A lead acid car battery designed for a micro-hybrid vehicle should have additional duties over a standard battery designed only for starting, lighting, and ignition (SLI) applications. A micro-hybrid vehicle battery should be able to supply energy during idle engine stop periods. It can be charged at high current rates during regenerative braking or even it may help the engine to boost acceleration via alternator/generator. To achieve these new duties, some breakthrough improvements have been adapted to lead acid batteries. Newly developed carbon additives have been applied to negative electrodes to increase the cyclic ability and dynamic charge acceptance. Electrode grids have been designed with computer-aided optimization techniques to minimize voltage loss at high current rates without increasing the grid weight. High porous and low tortuous separators with low electric resistances are now commercially available and they have been utilized in lead acid batteries to improve their electrical performance such as increased cyclic endurance and higher dynamic charge acceptance. These new type lead acid batteries are called enhanced flooded batteries (EFB). EFB can last much longer than that of regular flooded lead acid batteries under the high electrical stress of micro-hybrid vehicles. Unlike conventional vehicles, micro-hybrid vehicles utilize lead-acid batteries in a partial state of charge (SOC) to capture energy during the regenerative braking. The electronic control unit of the micro-hybrid vehicle should know the battery SOC to decide to stop the engine or not and to decide the charging current during deceleration. Therefore, in recent studies rival lead acid battery technologies have been focusing to understand the SOC of the battery inside the micro-hybrid vehicles. There are several conventional SOC prediction techniques which are used for SLI batteries such as open circuit voltage measurement, electrolyte density measurement, and internal resistance measurement. In the lifetime of a lead acid battery, various electrochemical degradation processes like sulphation, acid stratification, grid corrosion, etc. could occur. These degradation processes can result in changes in the crystallographic structure of battery materials, influencing electrode potentials. Thus, it usually misleads the end user or car electronic control unit to get an idea about exact SOC from open circuit voltages. Similar to SOC prediction based on open circuit voltage, SOC prediction based on electrolyte density has some shortcomings as well. As the battery gets older acid density may increase because of active material affusion from plates. Stratification of electrolyte decreases the density on the top while it increases at the bottom of the cell and finally as all other substances density of electrolyte is a function of temperature which varies in a broad range inside the car hood. Beside these fast but not accurate methods, there are numerous theoretical studies that explain electrochemical degradation processes of a lead acid battery to understand their SOC and state of health (SOH) levels in the literature. Most of these works are based on highly non-linear and complex equations based on the underlying physics of an electrochemical cell. Usually, these models need more time to simulate. If there is a need of SOC or SOH information in a real-time simulation faster method with high prediction accuracy become a necessity. Electrochemical impedance spectroscopy (EIS) is a technique that has a potential to identify the SOC and SOH of a lead acid battery if data sets have been interpreted with a convenient electric equivalent circuit (EEC) model. Besides SOC and SOH predictions, another reason to use an EEC for energy storage unit of an automobile has emerged in recent years. Batteries are increasingly incorporated into the complex electronic system of a car as hybrid powertrain systems are getting more complicated. The resulting electronic and electrochemical combined systems need to be analyzed as a whole. EEC is an easier and efficient way of representing a battery which is in interaction with other electronic components of a hybrid powertrain in a simulation environment. EEC models have been widely used to interpret the inner dynamics of all type of batteries. In addition to material researches, they also have been used to estimate SOC and SOH values of batteries in combination with different methods. In this thesis, four EEC models are considered for EFB which three of these are widely used for lead acid batteries in the literature. Impedance and phase prediction capabilities of models throughout a frequency spectrum from 1 mHz to 10 kHz are compared with those of experimental results to investigate their consistency with the data. The battery is charged, discharged, and aged according to CENELEC standards for lead-acid batteries designed for micro hybrid vehicles. These standards imitate a lifetime of a micro hybrid vehicle battery under high current partial cycling. Impedance tests are repeated between different charge and health states until the end of the battery's lifetime. Before interpreting the impedance analysis results, pure real internal resistances have been obtained in the high-frequency region of the spectrum where the capacitive and inductive related imaginary part is zero at the exact transition frequency. It is seen that the battery internal resistance increase wrt. SOC is very limited at higher SOH though the relation between SOC and internal resistance become stronger as the battery ages. It is seen that adding transmission line elements to mimic the high porous electrode-electrolyte interface to a double parallel constant phase element resistance model (ZARC) can increase the model data representing capability by 100%. The mean average percentage error (MAPE) of the conventional model with respect to data is 3.2% while the same value of the transmission line added model found as 1.6%. The results can be helpful to represent an EFB in complex simulation environments, which are used in automobile industry. In the second part of the thesis, Lissajous graphs have been recorded during the EIS experiments. 128 voltage and current points have been logged for each frequency point thorough a broad SOH and SOC range for an EFB battery. Following the data logging procedure, applied current and observed voltage data have been transformed to Fourier domain to understand whether the signal contains only a single frequency which is the applied one or is there any sub-harmonic frequencies inside the applied signal. It is seen that 99.75% of the applied current consist of the frequency that is applied. On the other hand, voltage response Fourier transforms shows that subharmonic signals inside the voltage readings can be as high as 18% depending on the SOC and SOH values of the battery. Subharmonic signals are making a local peak around 80 mHz for all the SOC and SOH values and the level of this peak is changing with respect to SOC and SOH values. Batteries that are fully charged shows much higher subharmonic responses due to overcharging at low frequency region. In addition to those finding, as the frequency decreases sub harmonic signals are gaining strength and this behavior is becoming dominant as the SOH decreases. The method of subharmonic analysis for the batteries is presented and applied for the first time in this thesis. It is seen that; sub harmonic signals contain valuable information that is not accessible by standard EIS analysis. Most of the informative data is obtained between 60mHz to 100mHz makes subharmonic analysis a faster method with respect to EIS which gives informative results in lower frequency for the lead acid batteries.