Impedance is an important battery parameter during the development, manufacture and use of an automotive battery. During production, checking impedance of individual cells is a common quality control technique. These checks may be done again with assembled module and/or packs to ensure the final product is within specification and therefore less like to have problems whilst in use. In the design and development stage, impedance characteristics can be used to parameterize battery models used for development. In battery management systems, impedance is important in predicting expected lifetime as well as provide updates of battery health throughout the usage period.
Internal resistance is the most commonly known form of battery impedance, which is the ohmic resistance of a battery in response to a DC current. However, battery impedance isn’t limited to pure resistance. Capacitance within electrochemical cells causes a phase shift between voltage and current resulting in capacitive (referred to as imaginary) impedance. These capacitive processes have different time constants associated with them, causing impedance to be frequency dependant. Electrochemical impedance spectroscopy (EIS) can be used to give insight into ion-transfer behaviour and may highlight issues involving electrochemical processes such as solid electrolyte interphase (SEI) formation.
Direct Current Internal Resistance (DCIR)
Direct current internal resistance (DCIR) tests provide a method of calculating internal resistance from a short current pulse. The change in voltage of the battery in response to the pulse is indicative of the internal resistance. According to Ohms law:
Where R=Resistance, V=Voltage and I=Current. However, due to the open circuit voltage of a battery, it can be more helpful to write it as in Equation 2. Where dI = magnitude of the current step and dV = change in voltage of the battery.
Ideally, the current step and voltage measurement would be instantaneous to avoid the voltage changing due to other effects. Whilst current is flowing the state of charge will change, changing the open circuit voltage of the battery. Polarization will also have an effect, which occurs due to the relatively slow diffusion of ions through the electrode causing a build-up of ions at its surface. When the current flow stops, the built-up ions dissipate causing the voltage to drop down to open circuit levels.
Figure 1 shows the response of an automotive battery module to a 100 A current step, taken at 50% SOC and 23°C. The step is completed in both positive and negative directions and an average of the two is taken, showing overall resistance of 2.885 mΩ. DCIR tests may be completed at a range of temperatures and SoC levels as internal resistance can change significantly depending on operating condition.
Figure 1: DCIR Test
Equipment limitations can create non-ideal measurements, usually due to response times of power supplies and sensing equipment. Figure 2 shows example DCIR data logged at 1 kHz. Inductance in the power supply electronics creates ringing on the output which takes time to stabilise, an accurate voltage measurement cannot be taken until the ringing has decayed.
With the voltage data and knowledge of Ohms law, it is relatively easy to gain an idea of the shape of the current profile. However, for an accurate resistance calculation the current must be measured and checked to ensure the setpoint is being achieved. The current sensor used in this example has a response time of ~150 ms, obscuring the true current profile. The voltage changes by ~0.03 V between power supply and current sensor stabilisation. This corresponds to a 0.3 mΩ (or 10.4%) change in estimated internal resistance.
Figure 2: Time response of equipment
Electrochemical Impedance Spectroscopy (EIS)
Whilst DCIR is a useful tool to evaluate internal resistance, EIS allows more detail analysis of the electrochemical properties of the cell.
The premise of EIS is to measure the phase shift between voltage and current in response to a sinusoidal excitation. The excitation can be voltage (potentiostatic) or current (galvanostatic).
Figure 3: Galvanostatic EIS Excitation
Figure 4 shows a Nyquist plot of data gathered through EIS (0.1 Hz to 250 Hz) in comparison to DCIR. The point at which the Nyquist plot has zero imaginary impedance (crosses the x-axis) is considered to show the ohmic internal resistance. The estimate of internal resistance from EIS is 2.91 mΩ, in comparison 2.885 mΩ gathered from DCIR. The similarity of internal resistance measurement shows good equivalency for both methods.
The benefit of EIS is the extra data gathered at lower frequencies, showing how the relationship between capacitive and resistive properties changes according to the frequency of excitation. Each semi-circular figure in the Nyquist plot is an indication of a process with an associated time-constant. Whilst there is only one semi-circle evident in Figure 4, its slight elongation suggests there are at least two process present. Several process can merge into one semi-circle if time constants are similar. Knowledge of these time constants can be used to assess aspects such as charge transfer efficiency and polarization, leading the way to improved charging rates and better battery management via accurate parametrisation of battery models.
Like DCIR, EIS can be performed at differing states of charge and temperature to track the performance of electrochemical properties across the operating window of the battery. A frequency sweep like the one seen in Figure 4 takes a few minutes to complete, but EIS can take much longer depending on the number of points in the sweep and the frequency range tested.
Figure 4: EIS vs DCIR Impedance Data
Summary
Choosing which impedance measurement technique is most appropriate for your application is dependent the objectives of the project. DCIR is a relatively quick and simple test which provides accurate internal resistance measurements as long as equipment limitations do not negatively impact the results. EIS is a more powerful tool in understanding battery behaviour, but does have downsides in terms of test duration and equipment requirements.
CamMotive has expert knowledge of electric vehicle and battery testing as well as decades of experience in the automotive testing industry. To discuss your testing requirements, or for more information, contact CamMotive to connect to an expert: