Electrochemical impedance spectroscopy (EIS) is a critical parameter for characterizing the internal state of batteries and is widely applied in diagnosing the health status and predicting failures of energy storage systems. In this paper, we propose an online EIS measurement method based on half-bridge converter switching modulation for modular multilevel energy storage systems (MESS). Our method pairs batteries with half-bridge converters to form basic submodules and cascades multiple submodules to construct multilevel systems. During stable system power operation, we leverage the low-ripple characteristics of DC bus currents and design a multi-frequency switching modulation strategy to inject wide-frequency current excitation into target battery cells, enabling online impedance spectroscopy measurement without interrupting system operation. To eliminate the impact of testing on system power stability, we introduce a coordinated control mechanism between the test module and compensation module, achieving self-cancellation of power fluctuations through complementary switching actions. Experimental results demonstrate that our proposed multi-frequency switching modulation-based electrochemical impedance spectroscopy measurement method for energy storage systems achieves an average relative error of less than 5%, validating its effectiveness and engineering applicability in practical energy storage system condition monitoring.
I. Introduction
With the high penetration of renewable energy and the rapid development of distributed energy systems, the power grid has increasingly stringent requirements for flexibility and resilience. Electrochemical energy storage systems play a crucial role in this context. Distributed energy storage, with its advantages of flexible deployment and local consumption, has become increasingly significant, driving the demand for modular and scalable storage architectures. Traditional distributed energy storage systems often use direct series-parallel connections of a large number of battery cells, which, while cost-effective, suffer from inconsistency issues in battery parameters over long-term operation, leading to reduced energy utilization and increased maintenance difficulty. To address these challenges, modular multilevel energy storage systems (MESS) have attracted growing attention. As illustrated in the concept, such systems combine battery units with storage interface circuits to form independent submodules, which are cascaded to achieve flexible energy management and fault isolation, significantly improving reliability and scalability.
However, energy management and fault isolation in energy storage systems rely on accurate identification of the state of charge (SOC) and state of health (SOH) of storage units. Battery impedance, as a key parameter reflecting the internal state of the battery, provides important basis for battery management systems (BMS) to monitor and evaluate the condition of lithium-ion batteries. By measuring the impedance response of the battery at different frequencies, its EIS can be obtained. Research has shown that battery SOC is closely related to low-frequency impedance changes, and battery aging-induced SOH degradation also causes significant changes in EIS, which provides a basis for battery life prediction based on impedance.
Traditional offline EIS measurement methods typically require additional hardware support, incur high costs, and are difficult to meet the real-time operation and condition maintenance needs of energy storage systems. In contrast, online EIS measurement techniques based on the interface converters of energy storage systems can inject excitation signals into the battery during normal system operation and obtain impedance information, making them more promising for engineering applications. Existing online EIS methods often struggle to ensure strict stability of system power interaction while rapidly and broadband obtaining electrochemical impedance spectra of storage modules. This severely limits the application of electrochemical impedance spectroscopy online measurement in large-scale energy storage systems.
In this work, we propose a multi-frequency impedance online measurement method for submodule battery cells based on current modulation in the modular multilevel energy storage system architecture. By introducing a coordinated control mechanism between the test module and the compensation module, we effectively eliminate power fluctuations caused by the switching actions of the test module, realizing EIS online measurement for energy storage systems in uninterrupted operation.
II. Current Modulation Based Multi-Frequency Impedance Measurement Method
2.1 Current Modulation Principle
We adopt the half-bridge circuit as the submodule converter in the cascaded system. When the energy storage system is in charging mode, the battery cell is connected to the cascaded system via the half-bridge circuit. Its operating state is controlled by the switches: when the upper switch Q11 is on and the lower switch Q12 is off, the bus current flows into the battery cell, allowing the cell to participate in system power exchange; when Q11 is off and Q12 is on, the battery cell is bypassed and does not interact with the external system.
Based on the selection behavior of the submodule, the current flowing through the submodule battery cell, \( i_{\text{bat}}(t) \), can be expressed as:
\[
i_{\text{bat}}(t) = S(t) \cdot i_{\text{dc}}(t)
\]
where \( i_{\text{dc}}(t) \) is the cascaded system bus current, and \( S(t) \) is the switching function representing the submodule’s access/bypass state. The definition of \( S(t) \) is given in Table 1.
| Upper switch Q11 state | Lower switch Q12 state | Switching function \( S(t) \) | Submodule state |
|---|---|---|---|
| On | Off | 1 | Access |
| Off | On | 0 | Bypass |
When the energy storage system power remains constant within a certain range, despite possible small fluctuations in DC-side voltage, the bus current \( i_{\text{dc}}(t) \) can be approximated as a constant value \( I_{\text{dc}} \) due to the presence of the bus inductor \( L_{\text{dc}} \). Therefore, equation (1) simplifies to:
\[
i_{\text{bat}}(t) \approx I_{\text{dc}} \cdot S(t)
\]
From equation (2), the amplitude of the current flowing through the battery cell of the submodule is determined by the system operating condition (i.e., \( I_{\text{dc}} \)), while its spectral characteristics are entirely determined by the switching function \( S(t) \). Thus, by appropriately designing the switching function \( S(t) \) (i.e., controlling the operating mode of the half-bridge circuit), we can effectively inject a disturbance current of a specific frequency into the battery. By collecting the battery terminal voltage response \( v_{\text{bat}}(t) \) under this disturbance current, we can compute the battery electrochemical impedance spectrum.
2.2 Multi-Frequency Excitation Signal Design
To measure impedance at target frequency points \( [f_1^*, f_2^*, f_3^*, \dots, f_N^*] \), we construct a multi-frequency sinusoidal signal \( f_{\text{MFS}}(t) \) containing these frequency components:
\[
f_{\text{MFS}}(t) = \sum_{n=1}^{N} \sin(2\pi f_n^* t)
\]
Taking a subset of frequency components as an example, the multi-frequency sinusoidal signal is the superposition of multiple component signals, and we use it to design the half-bridge modulation signal. As shown in the conceptual illustration, we convert the multi-frequency signal \( f_{\text{MFS}}(t) \) into the switching function \( S(t) \) of the half-bridge circuit using the sign function:
\[
S(t) = \begin{cases}
1, & \text{if } f_{\text{MFS}}(t) > 0 \\
0, & \text{if } f_{\text{MFS}}(t) < 0
\end{cases}
\]
When \( f_{\text{MFS}}(t) > 0 \), \( S(t) = 1 \) (Q11 on, Q12 off), and the bus current \( I_{\text{dc}} \) flows into the battery cell; when \( f_{\text{MFS}}(t) < 0 \), \( S(t) = 0 \) (Q11 off, Q12 on), the battery cell is bypassed, and the bus current \( I_{\text{dc}} \) flows through the freewheeling path formed by Q12, not through the battery.
Through this current modulation method, a current with harmonics at the target frequencies is injected into the battery cell, generating a voltage response at specific frequencies. By real-time acquisition of battery terminal voltage \( v_{\text{bat}}(t) \) and current \( i_{\text{bat}}(t) \), and performing Fourier analysis to extract the voltage component \( \hat{V}_{\text{bat}}(f_k^*) \) and current component \( \hat{I}_{\text{bat}}(f_k^*) \) at each target frequency \( f_k^* \), the complex impedance \( \hat{Z}_{\text{bat}}(f_k^*) \) at frequency \( f_k \) can be calculated as:
\[
\hat{Z}_{\text{bat}}(f_k^*) = \frac{\hat{V}_{\text{bat}}(f_k^*)}{\hat{I}_{\text{bat}}(f_k^*)}
\]
III. Coordinated Control of Modular Multilevel Energy Storage Systems
As described in Section II, the excitation current of the energy storage submodule battery cell originates from the switching action of the interface converter. However, the periodic switching of the battery cell’s access and bypass states to inject perturbation current essentially modulates the power path of the test module, causing its charging power \( p_1(t) = V_{\text{bat}} \cdot I_{\text{dc}} \cdot S_1(t) \) to exhibit intermittent fluctuations, directly affecting the overall system power stability. To address this issue, we propose a real-time power compensation strategy based on complementary switching actions. In the cascaded energy storage system architecture, thanks to the independent decoupled control of each submodule, we can specifically configure a compensation module (e.g., Module 2) for the target module undergoing online impedance testing (called the test module, e.g., Module 1). By precisely coordinating the switching states of the two modules, the power fluctuation of the compensation module instantaneously cancels the power deviation caused by the perturbation injection of the test module.
Specifically, the switching function \( S_1(t) \) of test module 1 is designed according to the method in Section 2.2 to generate the disturbance current containing target frequencies. The switching function of compensation module 2 is designed as the logical complement of \( S_1(t) \):
\[
S_2(t) = \overline{S_1(t)}
\]
This means: when \( S_1(t)=1 \), test module 1 is connected to the system, its input power \( p_1(t) = V_{\text{bat}} \cdot I_{\text{dc}} \); at this time \( S_2(t)=0 \), compensation module is bypassed, \( p_2(t)=0 \). Conversely, when \( S_1(t)=0 \), test module 1 is bypassed, \( p_1(t)=0 \); at this time \( S_2(t)=1 \), compensation module 2 is connected, \( p_2(t) = V_{\text{bat}} \cdot I_{\text{dc}} \). Therefore, the combined unit consisting of the test module and compensation module has a constant total instantaneous input power:
\[
p_{\text{test+comp}}(t) = p_1(t) + p_2(t) = i_{\text{dc}}(t)S_1(t)V_{\text{bat}} + i_{\text{dc}}(t)S_2(t)V_{\text{bat}} = I_{\text{dc}}V_{\text{bat}}[S_1(t) + (1-S_1(t))] = V_{\text{bat}} I_{\text{dc}}
\]
That is:
\[
p_{\text{test+comp}}(t) = P_{\text{module\_rated}}
\]
where \( P_{\text{module\_rated}} = V_{\text{bat}} I_{\text{dc}} \) is the rated power of a single submodule. This equation shows that regardless of how \( S_1(t) \) switches, this combined unit always draws a constant rated power \( P_{\text{module\_rated}} \) from the external system, completely eliminating the specific frequency power fluctuation components introduced by the \( S_1(t) \) switching action. It is equivalent to a continuously stable “virtual module.”
It is worth noting that the power compensation for the test module can also be achieved through multi-module coordinated control. By scheduling two or more modules to work together, the power fluctuation caused by Module 1 during impedance testing can be jointly compensated. It is only necessary to ensure that the switching functions of the test module and coordinated compensation modules satisfy the following relationship:
\[
S_1(t) + S_2(t) + \cdots + S_k(t) = 1
\]
where \( k \) is the number of modules participating in measurement and compensation. More compensation modules provide higher flexibility in system power compensation, but also impose higher demands on the computational capability and real-time performance of the controller. Additionally, as more modules are used for power compensation, the number of modules available for maintaining DC bus voltage stability decreases accordingly, which may affect the system’s voltage regulation ability. Therefore, although multi-module coordinated compensation is feasible in theory, the trade-off between the number of compensation modules and system stability needs to be considered based on real-time power requirements and controller performance in practical applications.
Based on the above characteristics, the test-compensation combined unit can be regarded as a constantly engaged module with rated power \( P_{\text{module\_rated}} \) in terms of power interaction. In this case, if the total system power demand is \( M \cdot P_{\text{module\_rated}} \), we only need to ensure that among the remaining \( N-k \) modules, \( M-1 \) are engaged to achieve power balance. The power balance relationship is:
\[
P_{\text{total}} = P_{\text{module\_rated}} + (M-1) \cdot P_{\text{module\_rated}} = M \cdot P_{\text{module\_rated}}
\]
In summary, by configuring one or more compensation modules and coordinating their switching functions according to equation (9), we achieve self-cancellation of power fluctuations within the test-compensation unit. The system only needs to routinely adjust the number of engaged remaining modules (targeted at \( M-1 \)) to maintain the precise stability of the total input power \( P_{\text{total}} \) of the entire energy storage system without disturbing the online impedance identification of the test module, thereby minimizing the impact on normal system operation.
IV. Simulation Verification
To verify the effectiveness of the proposed multi-frequency perturbation active injection and multi-module coordinated control strategy, we built a simulation model containing five submodules. The key parameters are listed in Table 2. Each submodule consists of 104 LFP cells in series, with a rated voltage of approximately 332.8 V. Three modules work together using the strategy illustrated in the coordinated compensation concept, forming a power-stable virtual module, which connects to the system together with two constantly-on modules to establish a 1000 V DC bus. In this configuration, the system has two modules in standby mode, which can be used for subsequent inspections or module balancing replacements.
| Parameter | Value |
|---|---|
| Bus voltage | 1000 V |
| Number of modules | 5 |
| Single module voltage | 332.8 V (104 LFP cells × 3.2 V) |
| Number of rated working modules | 3 |
| Test frequencies | [1, 2, 4, 10, 16, 25, 40] Hz |
The simulation waveforms demonstrate the coordinated operation of multiple modules. At t=0 s, battery cell 1 starts impedance measurement; modules 4 and 5 are constantly on, and no compensation module is used. The system voltage fluctuates synchronously with the port voltage fluctuation of module 1. At t=0.5 s, module 3 enters compensation mode, executing a switching modulation strategy complementary to module 1, thereby compensating for the voltage fluctuation caused by module 1, and the bus voltage recovers stability. At t=1 s, module 3 switches to bypass mode and module 2 enters compensation mode; the bus voltage remains stable. At t=1.5 s, module 1 exits impedance test mode and enters bypass mode awaiting next instruction, while module 2 switches to constantly-on state; the system voltage remains stable. Throughout this coordination, module 1 maintains stable testing, modulating the DC bus current through the switching function and measuring the battery cell voltage response to obtain multi-frequency impedance data. Since batteries are typical nonlinear elements, we only illustrate the mechanism and compensation effect of multi-module coordinated operation here, leaving the specific impedance analysis for the experimental section.
V. Experimental Verification
To validate the effectiveness of the proposed method, we built a small-scale experimental platform as shown in Figure 1. The platform uses a DC source (50 V) and a resistive load (5 Ω) to simulate the DC bus of a modular multilevel energy storage system in steady-state operation, and a single lithium-ion battery cell (EVE 32 Ah LFP) serves as the test battery cell. To effectively extract key low-to-mid-frequency impedance information, we set the test frequencies to [1, 2, 4, 10, 16, 25, 40] Hz. By programming the drive signals of the half-bridge converter switches (Q11/Q12), we dynamically adjust the submodule switching function \( S_1(t) \) to inject the target excitation current into the battery. Key parameters of the platform are listed in Table 3.
| Parameter | Value |
|---|---|
| DC source voltage | 50 V |
| Resistive load | 5 Ω |
| Inductance | 3.2 μH |
| Battery parameters | EVE 32 Ah LFP battery |
| Test frequencies | [1, 2, 4, 10, 16, 25, 40] Hz |
| Controller | TI TMS320F28377D |
| Voltage ripple amplification factor | ×105 |
Using this experimental platform, we performed impedance measurements on the battery cell. The key waveforms are shown in the captured time-domain plots. The blue waveform is the DC bus current \( i_{\text{bat}}(t) \) (amplitude \( I_{\text{dc}} = 10 \text{ A} \)), the green waveform is the Q11 drive signal (i.e., the switching function \( S_1(t) \)), the dark red waveform is the modulated battery current, and the magenta waveform is the battery voltage response \( v_{\text{bat\_ac}}(t) \) after removing the DC component and amplifying by a factor of 105. The experimental results indicate that the proposed current switching modulation method based on the half-bridge circuit can accurately generate current excitation signals containing the target frequency components. By real-time acquisition of \( i_{\text{bat}}(t) \) and \( v_{\text{bat}}(t) \) and performing Fourier analysis, we observe from the frequency spectrum that, besides the DC component, the amplitudes at the specified frequency points (1 Hz, 2 Hz, 4 Hz, 10 Hz, 16 Hz, 25 Hz, 40 Hz) dominate in both current and voltage spectra, validating the effectiveness of the excitation signal design.
According to equation (5), we calculated the electrochemical impedance spectra of the battery under different conditions. The results, compared with those from a commercial electrochemical impedance tester (Hioki BT4560), show that the impedance spectra obtained by our method agree well with the reference in both magnitude and phase. To quantitatively evaluate the measurement accuracy, we use the Absolute Percentage Error (APE) and Mean Absolute Percentage Error (MAPE) as metrics, defined as:
\[
\text{APE}(f_k) = \frac{|Z_{\text{measured}}(f_k) – Z_{\text{actual}}(f_k)|}{|Z_{\text{actual}}(f_k)|}
\]
\[
\text{MAPE} = \frac{1}{N} \sum_{k=1}^{N} \frac{|Z_{\text{measured}}(f_k) – Z_{\text{actual}}(f_k)|}{|Z_{\text{actual}}(f_k)|} \times 100\%
\]
Analysis of the results shows that under different test conditions, the APE of impedance measurements at each frequency point is below 7%, and the MAPE across the full frequency range is less than 5% (see error distribution plots). This confirms that the proposed method meets the accuracy requirements for online impedance monitoring.
To further illustrate the advantages of our method, we compare it with several existing online EIS measurement techniques in Table 4. The comparison considers the excitation circuit, excitation waveform, impact on system operation, and measurement time for obtaining impedance at [1,2,4,10,16,25,40] Hz.
| Method | Excitation circuit | Excitation waveform | Impact on system operation | Measurement time |
|---|---|---|---|---|
| DC/DC [10] | DC/DC converter | Square wave perturbation | Directly affects output power | >1 s |
| DC/AC [11] | Inverter | Sweep sine | Directly affects output power | 1.95 s |
| Reconfigurable circuit [12,13] | Reconfigurable switches | Pseudo-random binary sequence | Directly affects output power | 1 s |
| Balancing circuit [14] | Balancing inductor | Near-triangular wave | Minor impact | >1 s |
| Our method | Interface selection circuit | Multi-frequency current modulation | Almost no impact | 1 s |
Through comparative analysis, our proposed method based on interface circuit selection and test-compensation coordination strategy can achieve multi-frequency online EIS measurement of target battery cells with almost no impact on the system’s interactive power, offering superior performance and easy scalability to large-capacity energy storage systems.
VI. Conclusion
In this paper, we have proposed a multi-frequency online identification method for electrochemical impedance spectroscopy of submodule battery cells in modular multilevel energy storage systems. The method is based on the half-bridge interface converter and achieves precise injection of excitation current at target frequencies (1-40 Hz) into the battery cell by designing a switching function containing multiple frequency components. This approach directly uses the battery cell’s inherent interface power converter to generate the excitation, without requiring additional hardware costs. To eliminate the impact of the testing process on system power stability, we innovatively introduced a coordinated control mechanism between the test module and compensation module. Through complementary switching actions, the combination of two or more modules maintains constant power, ensuring that the EIS online measurement is completed while the system total power remains constant. Simulation results verified that the proposed multi-module coordinated operation mechanism can fully suppress system power fluctuations caused by impedance measurement. Experimental results showed that the proposed EIS online measurement method can quickly obtain the battery EIS; compared with professional equipment, the multi-frequency average relative error is less than 5%, validating the effectiveness of the method and providing a reliable online monitoring indicator for real-time state estimation and health management of energy storage systems.