1. Introduction and Background
The rapid growth of the global electric vehicle market has made the performance and safety of the EV battery pack a critical research focus. According to the data released by the Chinese Ministry of Public Security, by the end of 2024, the number of new energy vehicles in China had reached 31.4 million, with pure electric vehicles accounting for 70.34% of this total. The production and sales of new energy vehicles in 2024 reached 12.888 million and 12.866 million units respectively, maintaining the world’s leading position for the tenth consecutive year.
Lithium-ion batteries have become the core power source for electric vehicles due to their high energy density, low self-discharge rate, and long cycle life. However, the inherent inconsistency in capacity, internal resistance, and other parameters among cells in an EV battery pack tends to worsen with usage, resulting in reduced energy utilization, shortened service life, and potential safety hazards. To address these challenges, battery equalization technology has become an indispensable component of the battery management system for EV battery packs.
The equalization technology can be broadly categorized into equalization topology and equalization strategy. The equalization topology provides the energy transfer path, while the equalization strategy determines how to effectively control the energy transfer based on selected equalization variables. From the perspective of circuit structure, equalization topologies are divided into passive equalization and active equalization. Passive equalization, which dissipates excess energy as heat through resistors, is simple and cost-effective but suffers from low efficiency. Active equalization, which transfers energy through capacitors, inductors, transformers, or converters, offers higher efficiency at the cost of increased complexity. From the perspective of equalization variables, the commonly used approaches are based on cell voltage, state of charge, or capacity. Among these, SOC-based equalization can accurately reflect the true state of the EV battery pack, making it particularly suitable for active equalization applications.
In my research, I conducted a comprehensive investigation into the active equalization technology for EV battery pack. I first established a second-order RC equivalent circuit model and estimated the SOC using the Extended Kalman Filter algorithm. Then, I designed a double-layer active equalization architecture based on inductors and capacitors, and proposed a fuzzy logic-based double-layer equalization control strategy. Finally, I verified the feasibility through both simulation and hardware experiments on a six-cell series-connected EV battery pack.
2. SOC Estimation Based on Extended Kalman Filter
2.1 Lithium-ion Battery Modeling
Accurate SOC estimation is fundamental to the effectiveness of any equalization strategy for an EV battery pack. Since SOC cannot be directly measured, it must be estimated through battery models and algorithms. After comparing various modeling approaches, including electrochemical models, neural network models, and equivalent circuit models, I selected the equivalent circuit model for its good balance between accuracy and computational complexity.
Among the equivalent circuit models, the Rint model is the simplest but fails to capture the polarization effect. The Thevenin model adds one RC network to simulate polarization but its accuracy degrades with aging and temperature variations. The PNGV model incorporates an additional capacitor to represent the cumulative effect of load current on open-circuit voltage, yet suffers from accumulating errors. The multi-order RC models provide increasing accuracy with higher orders but also increase computational complexity.
Considering the trade-off between accuracy and computational efficiency, I adopted the second-order RC equivalent circuit model as shown in the mathematical formulation below. This model consists of an ideal voltage source \(U_{OCV}\), an ohmic internal resistance \(R_0\), and two RC parallel networks representing the electrochemical polarization and concentration polarization effects.
Based on Kirchhoff’s laws, the mathematical expressions of this model are given by:
$$
\begin{cases}
U_0 = U_{OCV} – U_1 – U_2 – IR_0 \\
\dot{U}_1 = -\frac{U_1}{R_1C_1} + \frac{I}{C_1} \\
\dot{U}_2 = -\frac{U_2}{R_2C_2} + \frac{I}{C_2}
\end{cases}
$$
where \(I\) is the current, \(U_0\) is the terminal voltage, \(U_{OCV}\) is the open-circuit voltage, \(R_0\) is the ohmic internal resistance, \(R_1\) and \(R_2\) are the polarization and diffusion resistances, \(C_1\) and \(C_2\) are the polarization and diffusion capacitances, and \(U_1\), \(U_2\) are the voltages across \(R_1\) and \(R_2\), respectively.
2.2 Parameter Identification
For my research, I selected the Panasonic NCR18650B ternary lithium-ion battery as the experimental object. The battery test platform comprised a host computer, a battery testing system, a constant temperature chamber, and the lithium-ion cell. The basic specifications of this battery are summarized in the following table:
| Parameter | Value |
|———–|——-|
| Rated capacity | 3.2 Ah |
| Rated voltage | 3.6 V |
| Charge cutoff voltage | 4.2 V |
| Discharge cutoff voltage | 2.5 V |
| Standard charge current | 1.6 A |
The parameter identification process involved three main experiments. First, I performed capacity tests at 25°C. The testing procedure involved discharging the battery at 1C to the cutoff voltage, resting for 30 minutes, charging at 0.5C to the upper cutoff voltage, then switching to constant-voltage charging until the current dropped to 0.2A. After resting, the battery was discharged at 1C to measure the total discharged capacity. This procedure was repeated three times, and the average value was taken as the actual capacity. The measured capacities for the six cells used in my experiments are shown below:
| Cell | Q1/Ah | Q2/Ah | Q3/Ah | Q_real/Ah |
|——|——-|——-|——-|———–|
| cell1 | 3.064 | 3.060 | 3.054 | 3.059 |
| cell2 | 3.066 | 3.062 | 3.057 | 3.063 |
| cell3 | 3.075 | 3.071 | 3.068 | 3.071 |
| cell4 | 3.088 | 3.079 | 3.074 | 3.081 |
| cell5 | 3.093 | 3.082 | 3.075 | 3.083 |
| cell6 | 3.096 | 3.088 | 3.082 | 3.089 |
For the OCV-SOC relationship, I conducted pulse discharge experiments. After fully charging the battery to 100% SOC and resting for 30 minutes, I repeatedly discharged at 1C for 6 minutes (corresponding to 10% of capacity) followed by a 30-minute rest. The terminal voltage after each rest period was taken as the OCV for that SOC level. The measured OCV-SOC relationship is tabulated below:
| SOC/% | OCV/V |
|——-|——-|
| 100 | 4.161 |
| 90 | 4.101 |
| 80 | 4.040 |
| 70 | 3.933 |
| 60 | 3.846 |
| 50 | 3.762 |
| 40 | 3.672 |
| 30 | 3.564 |
| 20 | 3.480 |
| 10 | 3.306 |
| 0 | 3.102 |
To obtain a continuous function for the OCV-SOC relationship, I used MATLAB’s curve fitting toolbox. The evaluation of polynomial fits of different orders is shown below:
| Fit order | R-squared | RMSE |
|———–|———–|——|
| 2 | 0.994 | 0.028 |
| 3 | 0.997 | 0.021 |
| 4 | 0.999 | 0.011 |
| 5 | 0.999 | 0.012 |
| 6 | 0.999 | 0.013 |
Considering the trade-off between fitting accuracy and functional complexity, I selected the fourth-order polynomial, which gave the highest R-squared value of 0.999 and the lowest RMSE of 0.011. The resulting OCV-SOC function is:
$$
U_{OCV} = 2.439SOC^4 – 5.607SOC^3 + 4.656SOC^2 + 2.546SOC + 3.101
$$
For the remaining parameters, I analyzed the voltage response during pulse discharge. The ohmic resistance \(R_0\) was calculated from the instantaneous voltage drops at the beginning and end of the discharge pulse:
$$
R_0 = \frac{(U_A – U_B) + (U_D – U_C)}{2I}
$$
During the rest period after pulse discharge (DE segment in the voltage response), the second-order RC network exhibits a zero-input response, and the terminal voltage can be expressed as:
$$
U(t) = U_{OCV} – IR_1e^{-t/(R_1C_1)} – IR_2e^{-t/(R_2C_2)} – IR_0
$$
By fitting this equation to the experimental data using MATLAB’s custom curve fitting mode, I obtained the values of \(R_1\), \(R_2\), \(C_1\), and \(C_2\) at different SOC levels. The complete parameter identification results are summarized below:
| SOC/% | R0/mΩ | R1/mΩ | C1/F | R2/mΩ | C2/F |
|——-|——–|——–|——-|——–|——|
| 100 | 0.832 | 0.126 | 5662.901 | 0.142 | 1275182.939 |
| 90 | 0.732 | 0.162 | 3234.032 | 0.021 | 232910.257 |
| 80 | 0.704 | 0.140 | 1610.615 | 0.124 | 18751.575 |
| 70 | 0.686 | 0.144 | 1919.241 | 0.095 | 57327.009 |
| 60 | 0.679 | 0.140 | 3822.481 | 0.020 | 736532.957 |
| 50 | 0.676 | 0.171 | 3566.096 | 0.038 | 136460.938 |
| 40 | 0.670 | 0.176 | 3901.914 | 0.083 | 72559.749 |
| 30 | 0.675 | 0.091 | 15550.111 | 0.029 | 766726.022 |
| 20 | 0.686 | 0.229 | 3150.989 | 0.035 | 273115.946 |
| 10 | 0.722 | 0.234 | 2267.853 | 0.093 | 95652.120 |
| 0 | 0.795 | 0.432 | 898.296 | 0.238 | 23634.828 |
2.3 SOC Estimation Using EKF
The SOC of a lithium-ion battery is defined as:
$$
SOC = \frac{Q}{Q_N} \times 100\%
$$
where \(Q\) is the remaining capacity and \(Q_N\) is the rated capacity.
For SOC estimation, I evaluated several methods including ampere-hour integration, open-circuit voltage method, neural networks, and Kalman filter-based approaches. The ampere-hour integration method is simple but suffers from accumulated errors and sensitivity to initial SOC. The open-circuit voltage method requires long rest periods and is unsuitable for dynamic conditions. Neural networks require extensive training data. Considering the nonlinear nature of lithium-ion batteries, I chose the Extended Kalman Filter algorithm as it linearizes the nonlinear system through first-order Taylor expansion while maintaining good estimation accuracy.
The nonlinear state and observation equations of the battery system are:
$$
\begin{cases}
x_{k+1} = f(x_k, u_k) + w_k \\
y_k = h(x_k, u_k) + v_k
\end{cases}
$$
For the second-order RC model, I selected the state vector as \(x = [SOC, U_1, U_2]^T\), the input as the current \(I\), and the output as the terminal voltage \(U_0\). The discretized state equation is:
$$
\begin{bmatrix}
SOC_{k+1} \\
U_{1,k+1} \\
U_{2,k+1}
\end{bmatrix}
=
\begin{bmatrix}
1 & 0 & 0 \\
0 & e^{-t/(R_1C_1)} & 0 \\
0 & 0 & e^{-t/(R_2C_2)}
\end{bmatrix}
\begin{bmatrix}
SOC_k \\
U_{1,k} \\
U_{2,k}
\end{bmatrix}
+
\begin{bmatrix}
-\frac{\eta t}{Q_{real}} \\
R_1(1-e^{-t/(R_1C_1)}) \\
R_2(1-e^{-t/(R_2C_2)})
\end{bmatrix}
I_k + w_k
$$
The observation equation is:
$$
U_{0,k} = U_{OCV}(SOC_k) – U_{1,k} – U_{2,k} – R_0I_k + v_k
$$
Since the state equation is linear but the observation equation is nonlinear (due to the OCV-SOC relationship), the observation matrix is obtained by linearizing the observation equation:
$$
C_k = \left[ \frac{\partial U_{OCV}}{\partial SOC} \bigg|_{SOC=\widehat{SOC}_k}, -1, -1 \right]
$$
The EKF algorithm proceeds through the following steps:
**(1) State prediction:**
$$
\hat{x}_{k+1|k} = f(\hat{x}_{k|k}, u_k)
$$
**(2) Error covariance prediction:**
$$
P_{k+1|k} = A_k P_{k|k} A_k^T + Q_k
$$
**(3) Kalman gain computation:**
$$
K_{k+1} = P_{k+1|k} C_{k+1}^T (C_{k+1} P_{k+1|k} C_{k+1}^T + R_k)^{-1}
$$
**(4) State update:**
$$
\hat{x}_{k+1|k+1} = \hat{x}_{k+1|k} + K_{k+1}(y_{k+1} – h(\hat{x}_{k+1|k}, u_{k+1}))
$$
**(5) Error covariance update:**
$$
P_{k+1|k+1} = (I – K_{k+1}C_{k+1})P_{k+1|k}
$$
I implemented this algorithm in MATLAB/Simulink and validated it under a 1C constant-current discharge condition. The simulation results showed that the maximum SOC estimation error during the entire discharge process remained below 3%, confirming the high accuracy of the EKF-based estimation and the validity of the battery model.
3. Design of Double-Layer Equalization Circuit
3.1 Overview of the Double-Layer Equalization Structure
To address the limitations of existing equalization circuits—such as low efficiency and long equalization time—I designed a double-layer active equalization architecture based on inductors and capacitors. The structure divides the entire EV battery pack into \(2n\) battery modules \(M_i\) (i=1,2,…,2n), with each module consisting of 3 series-connected cells. Each battery module is connected to its corresponding bottom-layer equalizer. The top-layer equalizer connects to each battery module through a module selection matrix and relay switches.
The bottom-layer equalization handles energy transfer within each battery module, enabling cell-to-cell or cell-to-module energy transfer. The top-layer equalization manages energy transfer between battery modules. This double-layer topology provides multiple equalization paths, which can improve equalization speed and reduce the losses associated with long energy transfer paths.
3.2 Bottom-Layer Equalization Circuit
For the bottom layer, I adopted an improved single-inductor equalization topology based on the traditional Buck-Boost converter. The topology consists of lithium-ion cells, a switch array, relay switches, and an inductor. Each cell’s positive and negative terminals are connected to two bridge arms of the switch array, each composed of an N-channel MOSFET and a diode connected in anti-parallel.
When equalization is needed within a battery module \(M_i\), the relay switch \(Q_i\) is closed, connecting the switch array to the inductor \(L_i\). Based on the imbalance scenario, the switch array controls energy transfer between any cell pair or between a cell and an adjacent cell module.
The inductor can operate in either continuous conduction mode or discontinuous conduction mode. To avoid magnetic saturation and ensure safe operation, I designed the bottom-layer circuit to operate in discontinuous conduction mode.
Taking battery module \(M_1\) as an example, when cells \(B_{1-1}\) and \(B_{1-2}\) have higher SOC than the module average while cell \(B_{1-3}\) has lower SOC, the equalization process proceeds as follows:
**Mode 1:** Cells \(B_{1-1}\) and \(B_{1-2}\) charge the inductor. MOSFETs \(S_{1-1}\) and \(S_{1-6}\) are turned on, and energy flows from the high-SOC cells to the inductor. The inductor current rises linearly from zero to its peak value.
**Mode 2:** The inductor discharges to cell \(B_{1-3}\). MOSFETs \(S_{1-6}\) and \(S_{1-7}\) are turned on, and the stored energy transfers to the low-SOC cell. The inductor current decreases from its peak to zero.
To ensure safe and stable operation, I performed a detailed parameter analysis. The equivalent circuit model and the theoretical inductor current waveform are shown in the previous analysis. Based on Kirchhoff’s laws, the inductor current over one switching cycle can be expressed as:
$$
I_L = \begin{cases}
\frac{V_1 – V_D}{L}t, & 0 \leq t \leq DT \\
\frac{V_1 – V_2 – 2V_D}{L} – \frac{V_1 – V_D}{L}DT, & DT \leq t \leq DT + t_1 \\
0, & DT + t_1 \leq t \leq T
\end{cases}
$$
To ensure the inductor operates in discontinuous conduction mode, the following condition must be satisfied at t=T:
$$
\frac{V_1 – V_2 – 2V_D}{L}T – \frac{V_1 – V_D}{L}DT < 0
$$
This leads to the duty cycle constraint:
$$
D < \frac{2(V_2 – V_D)}{V_1 + V_2 – 2V_D}
$$
The peak inductor current is given by:
$$
I_{Li-max} = \frac{V_1 – V_D}{L}DT
$$
And the switching frequency can be calculated as:
$$
f_i = \frac{V_1 – V_D}{L I_{Li-max}}D
$$
From this analysis, I determined that when the cell voltages are fixed, the bottom-layer equalization current mainly depends on the switching frequency, duty cycle, and inductance value. Smaller inductance or switching frequency results in larger equalization current, while larger duty cycles produce larger currents.
3.3 Top-Layer Equalization Circuit
The top-layer equalization topology consists of battery modules, a module selection matrix, relay switches, and a full-bridge LC resonant circuit. The full-bridge structure periodically reverses the capacitor polarity, which solves the problem of insufficient resonance recovery caused by non-negligible equivalent resistance in the equalization loop.
When equalization is needed between battery modules, the relay switches \(Q_{i-1}\) and \(Q_{i-2}\) of the participating modules are closed. Through the module selection matrix and the full-bridge LC resonant circuit, energy is transferred between modules. One complete switching cycle consists of four operating modes:
**Mode 1:** Under positive capacitor polarity, the high-energy module \(M_1\) charges the LC resonant circuit. MOSFETs \(S_{1-1}\), \(S_1\), \(S_2\), \(S_3\), \(S_4\), and \(S_{1-8}\) are turned on. The resonant inductor current rises sinusoidally while the capacitor voltage increases.
**Mode 2:** Under positive capacitor polarity, the LC resonant circuit discharges to the low-energy module \(M_2\). MOSFETs \(S_{2-2}\), \(S_1\), \(S_2\), \(S_3\), \(S_4\), and \(S_{2-7}\) are turned on. The inductor current becomes negative, and the capacitor voltage decreases.
**Mode 3:** Under negative capacitor polarity, the high-energy module \(M_1\) again charges the LC resonant circuit. MOSFETs \(S_{1-1}\), \(S_5\), \(S_6\), \(S_7\), \(S_8\), and \(S_{1-8}\) are turned on. The inductor current is negative and sinusoidal.
**Mode 4:** Under negative capacitor polarity, the LC resonant circuit discharges to the low-energy module \(M_2\). MOSFETs \(S_{2-2}\), \(S_5\), \(S_6\), \(S_7\), \(S_8\), and \(S_{2-7}\) are turned on.
For the parameter design of the top-layer circuit, I analyzed the LC resonant circuit with circuit equations:
$$
\begin{cases}
V_{in} = V_{LC} + L\frac{dI_{LC}}{dt} + I_{LC}R \\
I_{LC} = C\frac{dV_{LC}}{dt}
\end{cases}
$$
Combining these equations yields a second-order differential equation:
$$
LC\frac{d^2V_{LC}}{dt^2} + RC\frac{dV_{LC}}{dt} + V_{LC} = V_{in}
$$
The solution to this equation is:
$$
V_{LC} = c_1e^{\alpha t}\cos(\beta t) + c_2e^{\alpha t}\sin(\beta t) + V_{in}
$$
where:
$$
\begin{cases}
\alpha = -\frac{R}{2L} \\
\beta = \frac{\sqrt{4L – R^2C}}{2L\sqrt{C}}
\end{cases}
$$
By applying the boundary conditions for each operating mode, I obtained the expressions for the inductor current and capacitor voltage in each mode. The peak inductor currents in the four modes are:
$$
\begin{cases}
I_{1-max} = I_{3-max} = \frac{(1+k)V_H + (1+k)V_L}{1-k^2}e^{\alpha T/2}\sin(\beta T/2) \cdot \frac{1}{\beta L} \\
I_{2-max} = I_{4-max} = \frac{(1+k)V_L + (1+k)V_H}{1-k^2}e^{\alpha T/2}\sin(\beta T/2) \cdot \frac{1}{\beta L}
\end{cases}
$$
From this analysis, I determined that when the module voltages are fixed, the top-layer equalization current primarily depends on the L/C ratio and the equivalent resistance \(R\). Larger L/C ratios or larger resistances produce smaller equalization currents. Therefore, I prioritized components with smaller resistance values to achieve better equalization performance.
3.4 Simulation Analysis of Circuit Parameters
Using MATLAB/Simulink, I analyzed the effects of circuit parameters on equalization speed and efficiency through controlled variable experiments.
For the bottom-layer circuit, I considered two series-connected cells with initial SOC values of 65% and 60%. The simulation results for different inductance values and switching frequencies are summarized below:
| Inductance/μH | Frequency/kHz | Peak Current/A | Time/s | Efficiency/% |
|—————|—————|—————-|——–|————-|
| 200 | 1 | 5.26 | 203.11 | 98.18 |
| 200 | 2 | 2.97 | 348.30 | 98.54 |
| 250 | 1 | 4.41 | 235.56 | 98.32 |
| 250 | 2 | 2.43 | 418.31 | 98.65 |
| 300 | 1 | 3.80 | 275.45 | 98.37 |
| 300 | 2 | 2.06 | 493.50 | 98.70 |
| 400 | 1 | 2.97 | 346.78 | 98.55 |
| 400 | 2 | 1.58 | 639.53 | 98.65 |
The simulation results showed that for a fixed switching frequency, increasing the inductance reduces the peak current and slows down the equalization speed. The equalization efficiency first increases and then decreases because excessive current increases circuit losses, while insufficient current results in longer equalization times that offset the efficiency gains. Based on these findings, I selected an inductance of 300 μH and a switching frequency of 2 kHz for cell-to-cell equalization. For module-to-cell and cell-to-module cases, I calculated the appropriate frequencies as 3.7 kHz and 3 kHz, respectively, to maintain safe current levels.
For the top-layer circuit, I analyzed two battery modules with average SOC values of 65% and 60%. The effect of the L/C ratio on equalization efficiency is shown below:
| L/C Ratio | Efficiency/% |
|———–|————-|
| 1 | 94.33 |
| 4 | 95.08 |
| 9 | 95.30 |
I selected an inductance of 90 μH and a capacitance of 10 μF (L/C ratio of 9) to achieve high efficiency while limiting the maximum current. For the switching frequency, I found that when the module selection matrix switching period equals \(4\pi\sqrt{LC}\), the equalization efficiency is 95.31%, and the inductor current safely returns to zero before the next cycle begins.
4. Fuzzy Logic-Based Double-Layer Equalization Control Strategy
4.1 Equalization Algorithm Analysis
The equalization strategy determines the effectiveness of the equalization topology. I evaluated several common equalization algorithms:
**Extreme value method:** This approach selects the cells with the highest and lowest SOC for pairwise equalization. It is simple to implement but can cause logic confusion, repeated equalization, and over-equalization as the number of cells increases.
**Mean-difference method:** This method calculates the difference between each cell’s SOC and the pack average. It provides good consistency control but involves significant computation and can cause repeated equalization.
**Fuzzy control method:** This intelligent control approach mimics human reasoning and does not require a precise mathematical model. It dynamically adjusts the equalization current based on fuzzy rules, offering strong robustness, good real-time performance, and tolerance to noise. The main disadvantage is that different battery types require different fuzzy rules.
Given the nonlinear characteristics of lithium-ion batteries and the varying battery states during equalization, I chose fuzzy control for the bottom layer to dynamically regulate the duty cycle. For the top layer, where the equalization current is relatively fixed, I used the mean-difference method to achieve module-level equalization.
4.2 Design of the Double-Layer Equalization Control Strategy
The proposed control strategy operates in a bottom-layer-first, top-layer-next sequence. The specific steps are as follows:
**Step 1:** Collect the voltage and current of each cell, estimate the SOC using the EKF algorithm, and calculate the average SOC of each battery module (\(SOC_{avg-i}\)) and the entire EV battery pack.
**Step 2:** Calculate the SOC difference between each cell and its module average:
$$
\Delta SOC_{i-j} = SOC_{i-j} – SOC_{avg-i}
$$
**Step 3:** If any \(\Delta SOC_{i-j}\) exceeds the bottom-layer threshold \(\alpha_1\), activate the bottom-layer equalizer:
– Cells with \(\Delta SOC_{i-j} > \alpha_1\) are marked as high-energy cells.
– Cells with \(\Delta SOC_{i-j} < -\alpha_1\) are marked as low-energy cells.
– If adjacent high-energy cells exist, group them as a discharging module; otherwise, select the cell with the highest SOC.
– Similarly, if adjacent low-energy cells exist, group them as a charging module; otherwise, select the cell with the lowest SOC.
– Use fuzzy control to dynamically adjust the PWM duty cycle.
**Step 4:** Calculate the SOC difference between each module average and the pack average:
$$
\Delta SOC_i = SOC_{avg-i} – SOC_{avg-pack}
$$
**Step 5:** If any \(\Delta SOC_i\) exceeds the top-layer threshold \(\alpha_2\), activate the top-layer equalizer to transfer energy from the highest-SOC module to the lowest-SOC module until all module averages are within the threshold.
The complete control flowchart was illustrated in the detailed design section.
4.3 Fuzzy Controller Design
The fuzzy controller has two input variables and one output variable. The inputs are the module average SOC (\(SOC_{avg-i}\)) and the maximum SOC difference among cells participating in equalization (\(\Delta SOC\)). The output is the PWM duty cycle for the MOSFETs.
The input variables are defined as:
$$
SOC_{avg-i} = \frac{1}{N}\sum_{j=1}^{N} SOC_{i-j}
$$
$$
\Delta SOC = SOC_{max-i} – SOC_{min-i}
$$
The fuzzy subsets for all variables are {VS, S, M, L, VL}, representing very small, small, medium, large, and very large, respectively. I used triangular membership functions for their good control performance and computational simplicity.
The universes of discourse depend on the equalization scenario:
– For cell-to-cell equalization: duty cycle D1 ∈ [0, 0.6], \(SOC_{avg-i}\) ∈ [0, 1], \(\Delta SOC\) ∈ [0, 0.2]
– For module-to-cell equalization: duty cycle D2 ∈ [0, 0.4]
– For cell-to-module equalization: duty cycle D3 ∈ [0, 0.8]
The fuzzy rule base consists of 25 rules based on the following principles:
1. When \(SOC_{avg-i}\) is very high or very low and \(\Delta SOC\) is small, use a small duty cycle to prevent overcharge or overdischarge.
2. When \(SOC_{avg-i}\) is very high or very low and \(\Delta SOC\) is large, use a medium duty cycle to balance speed and safety.
3. When \(SOC_{avg-i}\) is moderate and \(\Delta SOC\) is small, use a medium duty cycle to prevent over-equalization.
4. When \(SOC_{avg-i}\) is moderate and \(\Delta SOC\) is large, use a large duty cycle to improve speed.
The complete fuzzy rule table for output D is shown below:
| SOC_avg-i \ ΔSOC | VS | S | M | L | VL |
|——————|—-|—-|—-|—-|—–|
| VS | VS | VS | S | M | M |
| S | S | M | L | L | VL |
| M | M | L | L | VL | VL |
| L | L | L | VL | VL | VL |
| VL | VS | S | S | M | L |
For defuzzification, I selected the centroid method because it encompasses all information of the fuzzy subsets and provides smooth control:
$$
D = \frac{\int z\mu(z)\,dz}{\int \mu(z)\,dz}
$$
4.4 Simulation Results and Analysis
To validate the proposed equalization strategy, I built a MATLAB/Simulink simulation model of a six-cell series-connected EV battery pack. The initial SOC values were set to 72%, 65%, 61%, 56%, 50%, and 44%. The bottom-layer circuit used 300 μH inductors with frequencies of 2 kHz, 3.7 kHz, and 3 kHz for different scenarios. The top-layer circuit used 90 μH and 10 μF. The bottom-layer threshold was 0.03% and the top-layer threshold was 0.1%.
I compared three approaches:
1. Traditional Buck-Boost multi-inductor equalization with mean-difference control
2. The proposed double-layer equalization with mean-difference control
3. The proposed double-layer equalization with fuzzy control
4.4.1 Resting State Equalization
The simulation results under resting condition are summarized below:
| Method | Equalization Time/s | Final Average SOC/% |
|——–|——————–|——————-|
| Traditional Buck-Boost | 2702 | 56.87 |
| Double-layer (mean-difference) | 2311 | 54.63 |
| Double-layer (fuzzy) | 1843 | 54.49 |
The double-layer circuit improved the equalization speed by 14.5% compared to the traditional Buck-Boost method. The fuzzy-based strategy further improved the speed by 20.3% compared to the mean-difference double-layer method. Although the double-layer circuit slightly reduced the final average SOC due to increased switch losses, the significant improvement in speed validates the effectiveness of the approach.
4.4.2 Charging State Equalization
Under charging conditions with a current of 1A, the results were:
| Method | Equalization Time/s |
|——–|——————-|
| Traditional Buck-Boost | 2674 |
| Double-layer (mean-difference) | 2268 |
| Double-layer (fuzzy) | 1806 |
The double-layer circuit improved the speed by 15.2% over the traditional method. The fuzzy strategy further improved the speed by 20.4% over the mean-difference method.
4.4.3 Discharging State Equalization
Under discharging conditions with a current of 1A, the results were:
| Method | Equalization Time/s |
|——–|——————-|
| Traditional Buck-Boost | 2730 |
| Double-layer (mean-difference) | 2371 |
| Double-layer (fuzzy) | 1874 |
The double-layer circuit improved the speed by 13.2% over the traditional method. The fuzzy strategy further improved the speed by 21% over the mean-difference method.
These simulation results consistently demonstrate that the proposed double-layer equalization circuit combined with the fuzzy control strategy provides faster equalization across all operating conditions, confirming its effectiveness for EV battery pack equalization.
5. System Design and Experimental Verification
5.1 Overall System Architecture
The equalization system architecture consists of four main modules: the battery pack module, the main control module, the data acquisition module, and the equalization module. The battery pack module comprises six series-connected ternary lithium-ion cells. The data acquisition board collects voltage, current, and temperature information from the EV battery pack and sends it to the main control module. The main control module processes the received data, determines the control strategy, and generates control signals for the equalization module. The equalization module executes the switching operations to transfer energy according to the control signals.
5.2 Hardware Design
5.2.1 Main Control Module
I selected the STM32F103ZET6 microcontroller from STMicroelectronics as the main controller. This chip features:
– ARM Cortex-M3 core with a maximum frequency of 72 MHz
– 512 KB of Flash and 64 KB of SRAM
– 112 I/O ports and 8 16-bit timers
– 3 ADC units with 16 channels each
– Support for USART, TWI, and SPI communication interfaces
The ADC interfaces with the INA282 chip for current measurement, the TWI bus controls the SH367309 chip for voltage and temperature acquisition, and the USART enables communication with the host computer.
5.2.2 Data Acquisition Module
For voltage and temperature acquisition, I designed a circuit based on the SH367309 chip from SINO WEALTH Electronic. The chip provides 16 voltage acquisition channels with a detection range of 0-5V and 3 temperature channels with external thermistor connections. Each cell voltage is filtered through an RC network (1 kΩ resistor and 100 nF capacitor) before entering the chip’s input pins.
For current acquisition, I used the INA282 chip from Texas Instruments. The chip has a built-in 6 kΩ differential input resistance and amplifies the voltage across a shunt resistor by 50 times. Each cell is connected in series with a 10 mΩ shunt resistor, and the output voltage is proportional to the current flowing through the cell.
5.2.3 Equalization Module
The equalization module consists of the equalization circuit and driver circuits. The equalization circuit matches the double-layer topology designed in Chapter 3, using:
– IRF630NPBF MOSFETs (200V drain-source voltage, 9.3A continuous current, 0.3Ω on-resistance)
– HFKW-012-1ZW relay switches (12V coil, 20A maximum continuous current)
– SS54 Schottky diodes (40V reverse voltage, 5A rated current, 0.55V forward drop)
– 300 μH inductors for the bottom layer and 90 μH for the top layer
– 10 μF resonant capacitor for the top layer
The driver circuit uses the 1ED120N12AF single-channel isolated gate driver from Infineon, which provides peak output currents of 4A sourcing and 3.5A sinking to ensure reliable MOSFET switching.
5.3 Software Design
The software was developed in the Keil uVersion5 environment using C language, running on the STM32F103ZET6 platform. The main program performs system initialization (clock, GPIO, ADC, interrupts, and peripherals), then sequentially calls the data acquisition, SOC estimation, and equalization control subroutines.
The data acquisition program sends commands through the TWI bus to the SH367309 chip and reads back temperature and voltage data. Current data is obtained through the ADC channels from the INA282 output.
The SOC estimation program implements the EKF algorithm based on the second-order RC model established in Chapter 2, using the collected voltage and current data as inputs.
The equalization control program first evaluates the SOC consistency of the EV battery pack. If the equalization condition is satisfied, it sends the appropriate control signals to the equalization module according to the double-layer fuzzy control strategy designed in Chapter 4. After each switching cycle, the program re-evaluates the battery consistency until the termination condition is met.
5.4 Experimental Verification
The experimental platform consisted of a host computer, an IT6302 programmable DC power supply, a Fluke 289C digital multimeter, six Panasonic NCR18650 cells, and the equalization system (main control board, data acquisition board, and equalization circuit board). The three boards were connected via dupont wires, the DC power supply provided the operating voltage, and the compiled code was downloaded to the main control board. The host computer received experimental data through serial communication.
5.4.1 Voltage Acquisition Accuracy Test
I first verified the voltage acquisition accuracy by comparing the measured values from the data acquisition board with the Fluke 289C multimeter readings. The results are shown below:
| Cell | Actual Voltage/V | Measured Voltage/V | Error/V |
|——|—————–|——————-|———|
| cell1 | 4.1077 | 4.095 | 0.0127 |
| cell2 | 3.6089 | 3.594 | 0.0149 |
| cell3 | 3.6356 | 3.623 | 0.0126 |
| cell4 | 3.5351 | 3.522 | 0.0131 |
| cell5 | 3.6046 | 3.591 | 0.0136 |
| cell6 | 4.0591 | 4.043 | 0.0161 |
The maximum acquisition error was less than 0.02V, confirming that the data acquisition system provides reliable data for the equalization experiments.
5.4.2 Static Equalization Experiment
For the equalization experiment, I used the battery testing system to discharge the cells to the desired initial SOC values of 72%, 65%, 61%, 56%, 50%, and 44%. The equalization system was then activated under resting conditions. The bottom-layer equalization threshold was set to 0.3% and the top-layer threshold to 0.5%.
The experimental results showed that the SOC differences among cells gradually decreased over time. The equalization system stopped after 73.1 minutes, at which point the cell SOC values were essentially consistent. Before equalization, the average SOC of the EV battery pack was 58%, and after equalization, it was 51.47%, corresponding to an equalization efficiency of 88.74%.
The six-cell equalization experiment demonstrated that the designed equalization system can effectively achieve battery pack equalization, verifying the feasibility of the proposed equalization circuit and control strategy.
6. Conclusions and Future Work
6.1 Conclusions
In this research, I conducted a systematic investigation into the active equalization technology for EV battery pack based on fuzzy algorithms. The main conclusions are as follows:
(1) I established a second-order RC equivalent circuit model for the lithium-ion battery and performed parameter identification through capacity tests, pulse discharge experiments, and exponential function fitting. Using the EKF algorithm for SOC estimation, the maximum estimation error remained below 3% under 1C constant-current discharge, confirming the accuracy of the battery model.
(2) I designed a double-layer active equalization architecture based on inductors and capacitors. The bottom layer uses an improved Buck-Boost topology with a single inductor for cell-to-cell and cell-to-module energy transfer. The top layer uses a full-bridge LC resonant circuit for module-to-module equalization. This architecture provides multiple energy transfer paths, improving equalization speed while reducing the losses associated with long transfer paths.
(3) I proposed a fuzzy logic-based double-layer equalization control strategy. The bottom layer uses fuzzy control to dynamically adjust the PWM duty cycle of the MOSFETs, achieving dynamic equalization current regulation. The top layer uses the mean-difference method for module-level equalization. Simulation results under resting, charging, and discharging conditions showed that the proposed strategy improves equalization speed by 20.3%, 20.4%, and 21% respectively, compared to the mean-difference-based control strategy.
(4) I designed the hardware circuits and software programs for the equalization system and built an experimental platform with six series-connected cells. The voltage acquisition error was below 0.02V, and the static equalization experiment successfully reduced the SOC differences among cells, verifying the feasibility of the proposed equalization method.
6.2 Future Work
Due to limitations in research time and experimental equipment, several aspects require further improvement:
(1) The battery model did not fully consider the influence of environmental temperature on battery parameters. Future research should incorporate temperature effects to improve model accuracy and SOC estimation precision.
(2) The double-layer equalization circuit improved speed but introduced additional switching devices, increasing energy losses. Future work should focus on reducing the number of switches to improve equalization efficiency.
(3) The equalization experiments were only performed under resting conditions. Given the complex operating environments of EV battery packs in real-world applications, future studies should validate the equalization system under various current profiles to confirm its practical applicability.