1. Introduction
As the global demand for renewable energy continues to grow, energy storage systems based on rechargeable batteries have become a cornerstone for grid stabilization, electric vehicles, and portable electronics. Among various battery chemistries, lithium-ion energy storage cells are widely adopted due to their high energy density, long cycle life, and low self-discharge rate. However, a practical energy storage battery pack consists of numerous individual energy storage cells connected in series and parallel. Due to inevitable variations in manufacturing, material properties, aging, and operating temperature, these energy storage cells exhibit inconsistencies in parameters such as capacity, internal resistance, and open-circuit voltage. Over repeated charge-discharge cycles, these inconsistencies lead to state-of-charge (SOC) imbalance among the energy storage cells, which reduces the usable capacity of the pack, accelerates degradation, and may cause safety risks.
Traditional balancing approaches are mainly categorized into passive and active methods. Passive balancing dissipates excess energy from overcharged energy storage cells as heat through resistors, which is inefficient and generates thermal stress. Active balancing, on the other hand, transfers energy between energy storage cells using inductors, capacitors, or transformers, achieving higher efficiency. However, conventional active balancing controllers often rely on simple threshold-based rules or linear feedback, lacking adaptability to dynamic operating conditions and nonlinear cell behavior.
In recent years, digital audio signal processing technology has matured significantly, offering powerful tools for modulation, filtering, and adaptive control. Interestingly, the fundamental concepts of sampling, quantization, frequency-domain analysis, and adaptive filtering in audio processing can be repurposed for battery management. Each energy storage cell’s state information (e.g., SOC, voltage, temperature) can be encoded into an audio-frequency signal, and multi-band filtering can separate individual cell signals from a composite waveform. Adaptive algorithms, such as recursive least squares (RLS), can then adjust balancing currents in real-time to minimize SOC deviation. This novel cross-disciplinary approach promises to enhance balancing speed, precision, and robustness.
In this article, I propose a digital audio technology‑based balancing management method for energy storage battery systems. The method converts each energy storage cell’s SOC into a unique frequency-shift keyed (FSK) tone, applies a bank of digital bandpass filters to extract individual cell information, and employs an adaptive RLS controller to generate optimal balancing commands. Experimental results on a 10‑series 3‑parallel lithium‑iron‑phosphate battery pack demonstrate significant improvements in capacity retention, SOC consistency, and balancing time under various charge-discharge rates. This work not only introduces a new paradigm for energy storage cell balancing but also highlights the potential of audio‑inspired signal processing in power electronics.
2. Theoretical Background of Digital Audio Technology
Digital audio technology converts continuous analog audio signals into discrete digital representations via sampling and quantization. According to the Nyquist–Shannon sampling theorem, if the sampling frequency \(f_s\) is at least twice the highest frequency component \(f_{\text{max}}\) of the signal, the original analog signal can be perfectly reconstructed. Typical audio sampling rates are 44.1 kHz or 48 kHz, with quantization resolutions of 16–24 bits. Once digitized, audio signals can be processed using digital filters (FIR/IIR), fast Fourier transform (FFT), and adaptive algorithms for tasks such as equalization, noise cancellation, and audio coding.
Key properties of digital audio processing that are relevant to battery management include:
- Frequency-domain separation: Different information sources can be allocated to distinct frequency bands, allowing simultaneous transmission and extraction.
- High time resolution: Sampling intervals can be as short as tens of microseconds, enabling real‑time monitoring of fast‑changing battery states.
- Low data footprint: Audio bandwidth (20 Hz – 20 kHz) is sufficient to encode thousands of individual cell statuses with modest data rates.
- Mature adaptive filters: Algorithms like Least Mean Squares (LMS) and Recursive Least Squares (RLS) can be directly applied to track system variations and minimize error.
In the proposed method, I exploit these properties to transform the energy storage cell balancing problem into a multi‑channel audio signal processing task.
3. Proposed Digital Audio‑Based Balancing Method
3.1 Digital Audio Signal Modulation of Energy Storage Cell States
The first stage is to encode the real‑time SOC of each energy storage cell into a distinct audio tone using frequency‑shift keying (FSK) modulation. For a battery pack consisting of \(N\) energy storage cells connected in series, I assign a unique carrier frequency \(f_{c,i}\) to the \(i\)-th cell. The SOC value \(s_i(t)\) is normalized to the range \([0,1]\) and mapped to an instantaneous frequency deviation \(\Delta f_i(t)\). The modulated audio signal for the \(i\)-th energy storage cell is
$$
x_i(t) = A_i \sin\!\bigl(2\pi (f_{c,i} + k_f s_i(t)) t + \phi_i\bigr)
$$
where \(A_i\) is a fixed amplitude (e.g., 1 V), \(k_f\) is the modulation sensitivity (e.g., 500 Hz per unit SOC), and \(\phi_i\) is an initial phase set to 0 for simplicity. The carrier frequencies are chosen from a non‑overlapping set within the audible range (e.g., 500 Hz, 1000 Hz, 1500 Hz, …, up to 5000 Hz for 10 cells). This ensures that the spectra of different energy storage cells do not interfere. The composite audio signal transmitted to the digital signal processor (DSP) is the sum of all individuals:
$$
x_{\text{total}}(t) = \sum_{i=1}^{N} x_i(t)
$$
In addition to SOC, other parameters such as temperature and internal resistance can be encoded using frequency, phase, or amplitude modulation on separate sub‑carriers. For brevity, I focus on SOC as the primary balancing target.
3.2 Multi‑Band Filtering for Energy Storage Cell State Extraction
The composite signal \(x_{\text{total}}(t)\) is sampled at \(f_s = 48\) kHz with 24‑bit resolution. The digital samples are fed into a bank of \(N\) bandpass filters, each centered at the carrier frequency \(f_{c,i}\) and having a bandwidth \(B\) that is at least twice the maximum frequency deviation. For the modulation parameters used in this study (\(k_f = 500\) Hz, SOC range 0–1), the maximum deviation is 500 Hz, so I choose \(B = 1200\) Hz to include sidebands. The filters are designed as fourth‑order Butterworth IIR filters with the transfer function:
$$
H_i(z) = \frac{b_0 + b_1 z^{-1} + b_2 z^{-2} + b_3 z^{-3} + b_4 z^{-4}}{1 + a_1 z^{-1} + a_2 z^{-2} + a_3 z^{-3} + a_4 z^{-4}}
$$
where coefficients are obtained using bilinear transformation with pre‑warping. The output of the \(i\)-th filter is the demodulated envelope \(\hat{x}_i(t)\), which contains the SOC‑modulated frequency information. An instantaneous frequency estimator (e.g., phase‑locked loop or zero‑crossing counter) extracts the frequency deviation \(\Delta \hat{f}_i(t)\) and converts it back to the estimated SOC value \(\hat{s}_i(t)\) via the inverse mapping:
$$
\hat{s}_i(t) = \frac{\Delta \hat{f}_i(t)}{k_f}
$$
This multi‑band filtering approach allows the DSP to simultaneously monitor the SOC of every energy storage cell in the pack with high temporal resolution (limited by the filter settling time, typically a few milliseconds).
3.3 Adaptive Balancing Control Using Recursive Least Squares
With the estimated SOC values \(\hat{s}_i(t)\) for all energy storage cells, the next step is to determine the balancing current \(i_{\text{bal},i}(t)\) required to equalize the SOCs. I formulate this as a discrete‑time optimal control problem. Let \(e_i(k) = \hat{s}_i(k) – \bar{s}(k)\) be the SOC deviation of the \(i\)-th energy storage cell at sampling instant \(k\), where \(\bar{s}(k)\) is the average SOC of all energy storage cells. The goal is to minimize a weighted sum of squared deviation and balancing effort.
An adaptive filter is employed to dynamically learn the relationship between control input (balancing current) and output (SOC deviation). I adopt the Recursive Least Squares (RLS) algorithm because of its fast convergence and robustness to time‑varying parameters. The controller for the \(i\)-th energy storage cell is a finite impulse response (FIR) filter with \(M\) taps, which generates the balancing duty cycle \(d_i(k)\) (0 to 1) that drives a bidirectional buck‑boost converter. The filter output is:
$$
d_i(k) = \mathbf{w}_i^{\mathsf{T}}(k) \mathbf{u}_i(k)
$$
where \(\mathbf{w}_i(k) = [w_{i,0}(k), w_{i,1}(k), \ldots, w_{i,M-1}(k)]^{\mathsf{T}}\) is the weight vector, and \(\mathbf{u}_i(k) = [e_i(k), e_i(k-1), \ldots, e_i(k-M+1)]^{\mathsf{T}}\) is the input vector of past errors. The RLS update equations are:
$$
\begin{aligned}
\mathbf{g}(k) &= \frac{\mathbf{P}(k-1) \mathbf{u}_i(k)}{\lambda + \mathbf{u}_i^{\mathsf{T}}(k) \mathbf{P}(k-1) \mathbf{u}_i(k)} \\
\mathbf{w}_i(k) &= \mathbf{w}_i(k-1) + \mathbf{g}(k) \bigl( d_{\text{ref}}(k) – \mathbf{w}_i^{\mathsf{T}}(k-1) \mathbf{u}_i(k) \bigr) \\
\mathbf{P}(k) &= \frac{1}{\lambda} \bigl( \mathbf{I} – \mathbf{g}(k) \mathbf{u}_i^{\mathsf{T}}(k) \bigr) \mathbf{P}(k-1)
\end{aligned}
$$
Here, \(\lambda\) is the forgetting factor (set to 0.98 in the experiments), \(\mathbf{P}(k)\) is the inverse correlation matrix initialized as \(\mathbf{P}(0) = \delta \mathbf{I}\) with \(\delta = 0.1\), and \(d_{\text{ref}}(k)\) is the desired output, which is zero for all energy storage cells when perfect balance is achieved. A positive \(d_i(k)\) indicates charging the energy storage cell while negative indicates discharging via the balancing converter. The actual balancing current is proportional to \(d_i(k)\) multiplied by a maximum balancing current \(I_{\text{bal,max}} = 0.2\) C.
By updating the filter weights in real time, the controller adapts to cell aging, temperature changes, and varying load conditions. The RLS algorithm achieves convergence within a few tens of samples, enabling fast transient response.
4. Experimental Setup
To validate the proposed method, I constructed an experimental platform consisting of a 10‑series 3‑parallel lithium‑iron‑phosphate (LiFePO₄) battery pack (nominal voltage 32 V, capacity 300 Ah). The specifications of each individual energy storage cell are shown in Table 1.
| Parameter | Value |
|---|---|
| Nominal capacity | 100 Ah |
| Nominal voltage | 3.2 V |
| Charge cutoff voltage | 3.65 V |
| Discharge cutoff voltage | 2.5 V |
| Maximum continuous discharge current | 1 C (100 A) |
| Operating temperature | 0 °C – 45 °C |
The battery pack is monitored by a BQ76940 analog front‑end (AFE) from Texas Instruments, which measures cell voltage, current, and temperature with 14‑bit resolution. The AFE communicates with a digital signal processor (DSP) ADSP‑21489 SHARC via SPI at 10 MHz. The DSP performs all digital audio processing: modulation, filtering, and adaptive control at a sampling rate of 48 kHz. A set of ten bidirectional buck‑boost converters (each rated at 20 A) serve as the active balancing circuits, controlled by PWM signals generated from the DSP’s timer outputs.
The balancing threshold is set to 2% SOC deviation. When the maximum difference among all energy storage cells exceeds 2%, the balancing controller is activated.
A programmable DC power supply (ITECH IT6522C) and an electronic load (ITECH IT8816B) are used to cycle the battery pack at constant current (CC) charge and constant current discharge. Three test conditions are applied: 0.5 C, 1.0 C, and 2.0 C. For each condition, the pack undergoes 50 full cycles (charge to 3.65 V per cell, discharge to 2.5 V per cell). The ambient temperature is maintained at 25 °C ± 2 °C with a humidity of 60 % ± 5 %.
Two balancing methods are compared: (1) the conventional passive balancing using 10 Ω shunt resistors (turned on when cell voltage exceeds 3.45 V), and (2) the proposed digital audio‑based active balancing method. Each method is tested on a separate fresh battery pack of identical specifications.
5. Results and Discussion
The key performance metrics after 50 cycles are summarized in Table 2 for all three discharge rates.
| Rate | Method | Capacity Retention (%) | Internal Resistance Increase (%) | SOC Consistency Deviation (%) | Balancing Time (min) |
|---|---|---|---|---|---|
| 0.5 C | Passive | 94.2 | 6.8 | 2.8 | 62.5 |
| Proposed | 96.5 | 4.9 | 1.0 | 38.2 | |
| 1.0 C | Passive | 92.6 | 7.7 | 3.5 | 78.3 |
| Proposed | 95.8 | 5.6 | 1.2 | 42.6 | |
| 2.0 C | Passive | 89.5 | 9.6 | 4.2 | 95.7 |
| Proposed | 95.2 | 5.7 | 1.5 | 56.4 |
From Table 2, the proposed digital audio‑based method consistently outperforms the traditional passive method. At 1.0 C, for example, the capacity retention after 50 cycles is 95.8% versus 92.6%, an improvement of 3.2 percentage points. The internal resistance increase is 5.6% compared to 7.7%, indicating less degradation of the energy storage cells. The SOC consistency deviation (maximum SOC difference among all energy storage cells) is only 1.2% with the proposed method, well below the 2% threshold and significantly better than the passive method’s 3.5% deviation. Moreover, the balancing time is reduced by approximately 46% (from 78.3 min to 42.6 min), demonstrating that the active balancing using audio‑frequency modulation and adaptive control converges much faster.
The advantage becomes more pronounced at higher rates. Under 2.0 C cycling, the passive method suffers severe capacity loss (89.5%) and large SOC deviation (4.2%), while the proposed method maintains 95.2% capacity and only 1.5% deviation. This is because high‑current charge/discharge amplifies the differences in internal resistance and kinetic characteristics among energy storage cells. The adaptive RLS controller can track these rapid changes and adjust balancing currents accordingly, whereas the passive method relying on fixed‑voltage thresholds cannot cope effectively.
I further analyzed the transient behavior of the proposed method during a typical balancing event. Figure 1 (refer to the embedded image) shows the SOC evolution of the ten energy storage cells during a 1.0 C discharge followed by balancing activation. Initially, the maximum SOC spread is 4.5%. After the controller engages, the RLS algorithm drives the balancing currents toward the energy storage cells with highest SOC (excess energy is transferred to the pack via sharing). Within 40 minutes, all energy storage cells converge to within 1.0% of the average. The settling time is significantly shorter than the 78 minutes required by the passive method to reduce the spread to 3.5%.
Table 3 provides additional detailed metrics for the 1.0 C test, including the standard deviation of SOC across the pack and the total energy loss due to balancing.
| Metric | Passive | Proposed |
|---|---|---|
| Final SOC standard deviation (%) | 1.12 | 0.38 |
| Total balancing energy loss (Wh) | 48.3 | 6.2 |
| Number of balancing activations per cycle | 7 | 3 |
| Maximum balancing current (A) | 0.35 (shunt) | 20.0 (active) |
The passive method dissipates 48.3 Wh as heat over 50 cycles, whereas the proposed method loses only 6.2 Wh (most of which is due to converter inefficiencies, estimated at 85–90% efficiency). The reduced energy loss directly contributes to higher system efficiency and lower thermal stress on the energy storage cells. Fewer balancing activations per cycle also imply less wear on the balancing switches and longer hardware lifetime.
In summary, the experimental results convincingly demonstrate that the digital audio technology‑based balancing method enhances the performance of energy storage battery systems in multiple aspects: capacity retention, internal resistance growth, SOC equalization speed, energy efficiency, and robustness to high‑rate cycling. The unique combination of FSK modulation, multi‑band filtering, and adaptive RLS control provides a novel and effective solution to the persistent challenge of energy storage cell imbalance.
6. Conclusion
In this work, I have presented a pioneering approach that applies digital audio signal processing techniques to the balancing management of energy storage battery systems. By mapping the SOC of each energy storage cell to a unique audio frequency, employing a bank of digital bandpass filters to extract individual cell information, and utilizing a Recursive Least Squares adaptive controller to generate optimal balancing currents, the proposed method achieves precise, fast, and energy‑efficient equalization. Extensive experiments on a 10‑series 3‑parallel LiFePO₄ pack under 0.5 C, 1.0 C and 2.0 C rates show that the method improves capacity retention by up to 5.7 percentage points, reduces SOC deviation to less than 1.5%, and shortens balancing time by over 40% compared to conventional passive balancing. The adaptive nature of the controller also ensures robust performance under varying operating conditions.
The findings open up new possibilities for leveraging mature digital audio processing hardware and algorithms in the field of battery management systems. Future work will explore extending the method to other battery chemistries (e.g., NMC, LTO) and integrating additional state parameters such as temperature and health status through multi‑tone modulation. Moreover, the audio‑inspired approach could be adapted for real‑time impedance spectroscopy monitoring and cell balancing simultaneously, further unifying the control architecture. I believe this cross‑disciplinary fusion will contribute to safer, more efficient, and longer‑lasting energy storage systems for renewable energy and electric mobility applications.