In the realm of modern energy systems, electrochemical energy storage has emerged as a pivotal technology due to its high energy density, rapid response, low maintenance costs, and flexibility. Among these systems, energy storage batteries, particularly lithium-ion batteries, play a critical role in applications ranging from electric vehicles to grid-scale storage. However, the safe and efficient operation of energy storage batteries is often compromised by issues such as aging, thermal runaway, and misuse. Therefore, accurate and timely assessment of their health state is paramount. Electrochemical impedance spectroscopy (EIS) has long been recognized as a powerful tool for probing the internal state of energy storage batteries, offering insights into parameters like state of charge (SOC), state of health (SOH), and remaining useful life (RUL). Traditionally, EIS measurements rely on voltage excitation via electrochemical workstations, which involve slow frequency sweeps, especially in the low-frequency range, leading to prolonged testing times and limited suitability for in-situ monitoring. In this article, I present a novel fast detection method based on current excitation, leveraging multi-frequency superimposed signals to rapidly reconstruct EIS curves for energy storage batteries. This approach not only enhances detection efficiency but also enables safer in-situ applications due to its high input impedance characteristics.
The core principle of EIS hinges on the linear time-invariant (LTI) behavior of electrochemical systems. For energy storage batteries, the relationship between current and voltage at the electrode-electrolyte interface can be described by the Butler-Volmer equation. Under small-signal conditions, where perturbations are minimal, the system approximates linearity, allowing impedance analysis. The impedance \( Z(j\omega) \) at an angular frequency \( \omega \) is defined as the ratio of voltage response \( E(j\omega) \) to current excitation \( I(j\omega) \):
$$ Z(j\omega) = \frac{E(j\omega)}{I(j\omega)} $$
By sweeping \( \omega \) across a broad range, typically from 0.01 Hz to 1 kHz, one obtains the EIS curve, often plotted as a Nyquist diagram with real part \( Z’ \) against negative imaginary part \( -Z” \). Conventional voltage-excitation methods, while accurate, suffer from two major drawbacks: they require extensive time for low-frequency points due to long signal periods, and their low input impedance poses risks during in-situ testing, such as current diversion or short circuits in charging circuits. In contrast, current excitation offers a high input impedance, making it compatible with ongoing charging processes without disrupting the energy storage battery operation. This aligns with the need for real-time monitoring and early warning systems for thermal runaway in energy storage batteries.
To address the inefficiency in low-frequency EIS acquisition, I propose using a multi-frequency superimposed current signal as the excitation. Instead of sequential sine waves, a composite signal containing multiple frequency components is applied simultaneously. This time-domain signal \( e(n) \) can be expressed as a sum of sinusoids:
$$ e(n) = \sum_{k=1}^{p} A_k \sin\left(2\pi k f_0 n T_s + \phi_k\right) $$
where \( A_k \) and \( \phi_k \) are the amplitude and phase of the \( k \)-th frequency component, \( f_0 \) is the fundamental frequency, \( T_s \) is the sampling interval, and \( p \) is the number of frequencies. The key advantage lies in the dramatic reduction of testing time. For instance, covering 0.02 Hz to 0.2 Hz with a fundamental frequency of 0.02 Hz and one period yields a signal duration of only 50 seconds, whereas traditional sweep methods might take over 20 minutes. The response voltage signal \( r(n) \) is then captured and processed using discrete Fourier transform (DFT) to extract amplitude and phase information at each frequency component. The impedance magnitude and phase are calculated as:
$$ |Z(f)| = \frac{|E_f|}{|I_f|}, \quad \phi_Z = \phi_e – \phi_i $$
where \( |E_f| \) and \( |I_f| \) are the voltage and current amplitudes at frequency \( f \), and \( \phi_e \) and \( \phi_i \) are their respective phases. This method ensures that all frequencies are measured concurrently, preserving the LTI assumption as long as the excitation amplitude is kept small (e.g., below 20 mV in voltage response to maintain linearity).
The design of the multi-frequency signal involves careful consideration of amplitude and phase modulation to ensure uniform excitation across frequencies and avoid signal distortion. In my implementation, I focused on phase modulation to improve signal distribution while keeping amplitudes constant. For the low-frequency band (0.02–0.2 Hz), I used \( A_k = 0.75 \) and \( \phi_k = 0 \), resulting in a periodic signal that effectively excites the energy storage battery without exceeding linear limits. Higher frequency bands (above 0.2 Hz) are still addressed via sweep methods due to their shorter periods, but the overall testing time is drastically reduced.
The hardware system for this fast EIS detection was built around a V/I converter using an OPA549 power amplifier, driven by a programmable signal generator (NI6356 card). The current excitation is applied to the energy storage battery, and the voltage response is measured through a precision resistor (1 Ω) for current sensing. Data acquisition is performed with a high-resolution card (Smaqc 5711) at a sampling rate of 5 kHz, ensuring accurate capture of both signals. The system is powered by dual switchable supplies (±24 V) to handle the power demands of the energy storage battery under test. Key components are summarized in the table below:
| Component | Specification | Role |
|---|---|---|
| Signal Generator | NI6356, 16-bit, 100 kHz output | Generates multi-frequency voltage signal |
| V/I Converter | OPA549 power amplifier, 170 W max | Converts voltage to current excitation |
| Current Sensor | 1 Ω precision resistor | Measures loop current via voltage drop |
| Voltage Acquisition | Smaqc 5711, 16-bit, ±5 V range | Captures battery voltage response |
| Power Supply | Dual 24 V, 150 W each | Provides ±24 V to amplifier |
Signal processing involves filtering to mitigate noise, particularly in low-frequency regions where environmental interference can be significant. A low-pass digital filter with a cutoff frequency of 10 Hz is applied to both excitation and response signals to enhance signal-to-noise ratio while compensating for phase shifts. The DFT analysis then yields the impedance spectra, which are fitted to equivalent circuit models to extract parameters like ohmic resistance \( R_s \), charge transfer resistance \( R_{ct} \), and double-layer capacitance \( C_{dl} \). These parameters are crucial for assessing the health of energy storage batteries, as they correlate with internal degradation mechanisms.
To validate the method, I conducted experiments on a commercial lithium iron phosphate (LFP) energy storage battery with a capacity of 27 Ah. The battery was tested at various open-circuit voltages (OCVs) from 2.9 V to 3.33 V, simulating different SOC states. The repeatability of the system was evaluated through five consecutive EIS measurements at an OCV of 3.3 V. The results, as shown in the Nyquist plots, demonstrated high consistency with a maximum standard deviation of 0.03167 mΩ in the real part at 0.3 Hz. This confirms the robustness of the current-excitation approach for energy storage batteries.
Comparative analysis with a commercial electrochemical workstation (Zahner) revealed close agreement in EIS curves across frequencies from 0.02 Hz to 1 kHz. However, the testing time was reduced from over 20 minutes to merely 120 seconds—a 90% improvement—while maintaining comparable accuracy. This efficiency gain is pivotal for in-situ applications where energy storage battery states may change rapidly during operation.
The sensitivity of the method was further assessed by measuring EIS at different OCVs. As the OCV increased, the Nyquist curves shifted leftward, indicating decreases in \( R_{ct} \) due to enhanced charge transfer kinetics. The high-frequency intercept, representing \( R_s \), remained relatively constant, aligning with the notion that ohmic resistance is less dependent on SOC. The low-frequency Warburg region, associated with diffusion processes, showed varying slopes, which can be modeled to estimate diffusion coefficients. These observations underscore the capability of fast EIS to capture dynamic changes in energy storage battery states.
To quantify the extracted parameters, I fitted the EIS data to a common equivalent circuit model comprising series resistance \( R_s \), a parallel \( R_{ct}-C_{dl} \) element, and a Warburg impedance \( W \). The trends in \( R_s \) and \( R_{ct} \) with OCV are summarized below:
| Open-Circuit Voltage (V) | \( R_s \) (mΩ) | \( R_{ct} \) (mΩ) |
|---|---|---|
| 2.9 | 1.05 | 12.3 |
| 3.0 | 1.02 | 10.8 |
| 3.15 | 1.01 | 8.5 |
| 3.25 | 1.00 | 6.9 |
| 3.3 | 0.99 | 5.2 |
| 3.33 | 0.98 | 4.7 |
The decrease in \( R_{ct} \) with rising OCV reflects improved electrode reactivity, whereas \( R_s \) shows minimal variation, consistent with the intrinsic ohmic losses in energy storage batteries. Additionally, the low-frequency slope \( K \) in the Nyquist plot, related to diffusion, varied with SOC, highlighting the richness of information in this region. The fast detection method enables precise tracking of these features, which is essential for accurate state estimation and prognostics in energy storage batteries.
From a theoretical perspective, the linearity of the energy storage battery system under small-signal excitation is justified by the Taylor expansion of the Butler-Volmer equation. For a perturbation \( \Delta E \), the current response \( \Delta I \) can be approximated as:
$$ \Delta I = f^{(1)} \Delta E + \frac{f^{(2)}}{2} \Delta E^2 + \cdots $$
where \( f^{(1)} \) is the first derivative at the operating point. When \( \Delta E \) is sufficiently small (e.g., corresponding to a current excitation yielding less than 20 mV voltage response), the higher-order terms become negligible, ensuring LTI behavior. This foundation allows the application of frequency-domain analysis via impedance spectroscopy.
The multi-frequency signal design also benefits from spectral efficiency. By packing multiple frequencies into one time record, the frequency resolution \( \Delta f \) is determined by the record length \( L \):
$$ \Delta f = \frac{1}{L} $$
Choosing a fundamental frequency \( f_0 = M \Delta f \) with integer \( M \) ensures that all harmonics fall within the DFT bins, minimizing spectral leakage. For my setup, \( f_0 = 0.02 \) Hz and \( L = 50 \) s give \( \Delta f = 0.02 \) Hz, perfectly aligning with the desired frequency points. This design principle enhances the accuracy of amplitude and phase retrieval for each component.
In terms of hardware considerations, the high input impedance of the current-excitation system (on the order of kilohms) prevents loading effects on the energy storage battery during in-situ tests. This is particularly advantageous when monitoring batteries under charge or discharge, as the excitation current adds minimally to the main circuit current. The topology essentially places the detection system in series with the battery, avoiding the shunt risks associated with voltage excitation. This makes it feasible for continuous monitoring in real-world energy storage battery packs, contributing to safety and longevity.
Looking ahead, the fast EIS method opens avenues for advanced battery management systems (BMS) that integrate impedance-based diagnostics. By periodically injecting multi-frequency current pulses and analyzing the responses, BMS can estimate SOC, SOH, and even predict thermal runaway precursors in energy storage batteries. The reduced testing time allows for higher sampling rates, enabling dynamic tracking of internal states during operation. Furthermore, the method can be extended to other types of energy storage batteries, such as sodium-ion or solid-state batteries, by adapting the excitation profiles and equivalent models.
In conclusion, the current-excitation fast EIS detection method represents a significant step forward in the characterization of energy storage batteries. It combines speed, accuracy, and safety, addressing the limitations of traditional voltage-based approaches. The use of multi-frequency signals efficiently captures low-frequency impedance details, while the high-input-impedance design facilitates in-situ applications. Experimental results on lithium-ion energy storage batteries validate the method’s repeatability and sensitivity, with testing times cut by 90%. As energy storage systems continue to expand, such innovative diagnostic tools will be crucial for ensuring reliability and performance. Future work may focus on miniaturizing the hardware for embedded use and developing machine learning algorithms to interpret EIS data in real-time for predictive maintenance of energy storage batteries.
The implications of this research extend beyond laboratory settings. In grid-scale energy storage, where thousands of energy storage batteries operate in tandem, fast and non-invasive monitoring can prevent cascading failures and optimize utilization. Similarly, in electric vehicles, onboard EIS could enhance battery lifespan and safety. By harnessing current excitation and multi-frequency techniques, we pave the way for smarter, more resilient energy storage battery systems that meet the demands of a sustainable energy future.