**Abstract**
Traditional energy storage systems typically consist of a charge/discharge converter and an independent equalizer, resulting in redundant components and increased complexity. In this work, we propose a novel converter that integrates the voltage equalization function directly into the charge/discharge converter, thereby reducing component count and simplifying the system architecture. The proposed converter achieves automatic voltage balancing among series-connected energy storage battery cells without requiring any voltage measurement circuitry. Two topologies are introduced: Type A employs a single active switch, an n-winding inductor, and n diodes; Type B replaces the diodes with n active switches to enhance efficiency. The relationship between Type A and Type B is analogous to that between an asynchronous Buck converter and a synchronous Buck converter. This paper focuses on the analysis of Type B, and a prototype is built for experimental validation. Results demonstrate excellent voltage balancing performance, validating the effectiveness of the proposed converter for series-connected energy storage battery applications.
—
## 1. Introduction
In modern energy storage systems, rechargeable batteries such as lithium-ion cells are widely used in applications ranging from small portable devices to large-scale electric vehicles, uninterruptible power supplies, and renewable energy integration [1-5]. Due to the low nominal voltage of individual cells, multiple cells must be connected in series to meet the required voltage level. However, during repeated charge/discharge cycles, inconsistencies in capacity, internal resistance, and self-discharge rate among cells, as well as temperature gradients, lead to voltage imbalances. If not properly equalized, the weakest cell may experience overcharge or overdischarge, reducing the overall usable capacity and posing safety risks. Therefore, an equalization circuit is essential in any series-connected energy storage battery system [6].
Equalization techniques are generally classified into passive and active types. Passive equalization dissipates excess energy as heat through resistors, which is simple but inefficient and generates thermal management issues. Active equalization transfers energy between cells or between cells and the pack using capacitors, inductors, transformers, etc., offering higher efficiency but often at the cost of increased complexity and cost [7-11]. Among active topologies, multi-winding transformer-based equalizers are attractive due to their simplicity, inherent isolation, and ability to achieve automatic voltage balancing without complex control [10,24,25]. However, such equalizers typically operate independently from the main power converter.
Several studies have attempted to integrate the equalization function into the converter by sharing magnetic components [24,29-31,33-37]. For instance, references [33,24] share the inductor of a Buck or Boost converter with a multi-winding transformer for equalization, but still require an additional winding and diode. To further reduce component count and cost, we propose a new converter family that inherently equalizes series-connected energy storage battery cells using a single multi-winding coupled inductor and a minimal number of switches.
The proposed converter eliminates the need for voltage sensors, making it a cost-effective and reliable solution for energy storage battery systems.
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## 2. Topology and Operating Principle
### 2.1 Topology Description
The proposed converter is shown in Figure 1 (conceptual). Type A consists of a single active switch \(S_0\), an \(n\)-winding inductor with inductance \(L_m\) per winding, and \(n\) diodes \(D_1, D_2, \ldots, D_n\) connected to each battery cell \(B_i\) (\(i = 1,2,\ldots,n\)). Type B replaces each diode with an active switch \(S_i\). In this paper, we focus on Type B, which allows bidirectional power flow and higher efficiency, similar to the synchronous Buck converter.
The coupled inductor is designed with identical turns per winding, so each winding has the same magnetizing inductance \(L_m\) and leakage inductance \(L_{ki}\). The converter operates in continuous conduction mode (CCM) for analysis.
### 2.2 Operating Principle during Charging
Key waveforms for Type B during charging are shown in Figure 2. The switching period is \(T_s\), duty cycle \(D\) for \(S_0\), and the complementary signal drives \(S_1\)–\(S_n\). The operation can be divided into five modes, but only Modes 1 and 3 dominate energy transfer.
**Mode 1** \([t_0 \leq t < t_1]\): \(S_0\) is ON, \(S_1\)–\(S_n\) are OFF. Current flows from input \(V_{in}\) into all battery cells equally through the coupled inductor. The current through cell \(i\) is:
\[
i_{Bi}(t) = i_{Bi}(t_0) + \frac{V_{in} – \sum_{j=1}^{n} V_{Bj}}{nL_m + \sum_{j=1}^{n} L_{kj}} (t – t_0)
\]
The voltage across each winding is:
\[
V_{Lm\_1} = \frac{nL_m}{nL_m + \sum L_{kj}} \left( V_{in} – \sum_{j=1}^{n} V_{Bj} \right)
\]
**Mode 2** \([t_1 \leq t < t_2]\): After \(S_0\) is turned OFF, the inductor current freewheels, discharging the parasitic capacitors of \(S_1\)–\(S_n\). This mode is very short and can be neglected for steady-state analysis.
**Mode 3** \([t_2 \leq t < t_3]\): All \(S_1\)–\(S_n\) are turned ON (with ZVS achieved due to prior body-diode conduction). The coupled inductor forces a redistribution of currents among cells. The current in cell \(i\) becomes:
\[
i_{Bi}(t) = i_{Bi}(t_2) + \frac{V_{Lm\_3} – V_{Bi}}{L_{ki}} (t – t_2)
\]
where \(V_{Lm\_3}\) is determined by the average cell voltage:
\[
V_{Lm\_3} \approx \frac{1}{n} \sum_{j=1}^{n} V_{Bj}
\]
This mode provides automatic equalization: lower-voltage cells draw higher current, and vice versa.
**Mode 4** and **Mode 5** are transition intervals similar to Mode 2 and are negligible.
The converter behaves essentially like a Buck converter with integrated equalization. The voltage gain is derived from volt-second balance across the inductor:
\[
(V_{in} – \sum V_{Bj}) D T_s = \sum V_{Bj} (1-D) T_s
\]
which simplifies to:
\[
\sum_{j=1}^{n} V_{Bj} = D V_{in}
\]
This equation confirms that the total output voltage equals the input multiplied by duty cycle, identical to a Buck converter.
—
## 3. Steady-State Analysis
### 3.1 Input-Output Characteristics
From the volt-second balance, Equation (10) in the original derivation yields:
\[
D V_{in} = \sum_{j=1}^{n} V_{Bj}
\]
Thus, the total battery pack voltage is regulated by duty cycle \(D\) and input voltage \(V_{in}\). This characteristic holds for both Type A and Type B.
### 3.2 Equalization Current Analysis
The equalization mechanism is driven by the imbalance in cell voltages. In Mode 3, the difference between the average voltage \(V_{Lm\_3}\) and individual cell voltage \(V_{Bi}\) produces a balancing current \(\Delta i_{Bi}\). From the equivalent circuit, neglecting leakage inductance mismatch, we obtain:
\[
\Delta i_{Bi}(t) = \frac{V_{Lm\_3} – V_{Bi}}{L_{ki}} (t – t_2)
\]
The average equalization current over a switching cycle is:
\[
\overline{\Delta I}_{Bi} = \frac{V_{Lm\_3} – V_{Bi}}{L_{ki}} \cdot \frac{(1-D)T_s}{2}
\]
Since \(V_{Lm\_3} \approx \frac{1}{n} \sum V_{Bj}\), the equalization current is proportional to the voltage deviation. When all cells are balanced, the net equalization current is zero. This demonstrates the automatic balancing property without requiring any voltage measurement.
### 3.3 Impact of Leakage Inductance
Leakage inductance \(L_{ki}\) affects the balancing current amplitude. Simulations were performed with parameters: \(V_{in}=15\)V, \(L_m=13\mu\)H, \(T=20\mu\)s, \(D=0.75\), \(V_{B1}=3.8\)V, \(V_{B2}=V_{B3}=3.9\)V. Results in Table I show that larger leakage inductance reduces balancing current, while asymmetry in leakage inductances causes uneven balancing currents.
**Table I: Influence of Leakage Inductance on Balancing Currents**
| Case | \(L_{k1}\) | \(L_{k2}\) | \(L_{k3}\) | Peak \(i_{B1}\) (mA) | Peak \(i_{B2}\) (mA) | Peak \(i_{B3}\) (mA) |
|——|———-|———-|———-|——————–|——————–|——————–|
| (a) | 0.7 μH | 0.7 μH | 0.7 μH | 420 | 420 | 420 |
| (b) | 1.0 μH | 1.0 μH | 1.0 μH | 300 | 300 | 300 |
| (c) | 1.3 μH | 1.3 μH | 1.3 μH | 230 | 230 | 230 |
| (d) | 1.0 μH | 1.0 μH | 0.7 μH | 300 | 300 | 420 |
| (e) | 1.0 μH | 1.0 μH | 1.3 μH | 300 | 300 | 230 |
The results confirm that balancing current is inversely proportional to leakage inductance, and that even with asymmetric leakage, the converter still performs equalization, though at different rates for different cells.
—
## 4. Experimental Verification
### 4.1 Prototype Setup
A prototype of Type B was built using three NCR21700T lithium-ion cells. Components are listed in Table II. The control diagram is shown in Figure 3: only a pair of complementary PWM signals is required; no voltage sensing per cell is needed. The pack voltage is monitored for charging control.
**Table II: Prototype Components**
| Component | Part/Value | Parameters |
|—————–|——————————–|——————————-|
| MOSFETs (\(S_0\)–\(S_3\)) | STP220N6F7 | \(R_{on}=2.40\) mΩ |
| Output Capacitor \(C_o\) | MLCC, 22 μF × 3 | |
| Magnetizing Inductance \(L_m\) | 12.2 μH | Winding ratio 1:1:1 |
| Switching Frequency \(f_s\) | 50–250 kHz | |
### 4.2 Charging Current and Balancing Current Waveforms
Three experiments were conducted with different initial cell voltages (see Table III). The switching frequency was 100 kHz, duty cycle \(D=0.75\), input voltage \(V_{in}=15\)V.
**Table III: Cell Voltages for Experiments**
| Experiment | \(V_{B1}\) (V) | \(V_{B2}\) (V) | \(V_{B3}\) (V) |
|————|—————|—————|—————|
| 1 | 3.80 | 3.80 | 3.85 |
| 2 | 3.80 | 3.80 | 3.75 |
| 3 | 3.80 | 3.80 | 3.80 |
The measured average charging currents during the freewheeling interval (Mode 3) are given in Table IV. The equalization current \(\Delta I_{Bi}\) is computed as \([I_{avei} – (I_{ave1}+I_{ave2}+I_{ave3})/3] \times D\).
**Table IV: Measured Balancing Currents**
| Experiment | \(I_{ave1}\) (A) | \(I_{ave2}\) (A) | \(I_{ave3}\) (A) | \(\Delta I_{B1}\) (mA) | \(\Delta I_{B2}\) (mA) | \(\Delta I_{B3}\) (mA) |
|————|—————–|—————–|—————–|———————-|———————-|———————-|
| 1 | 1.56 | 1.56 | 1.67 | -22 | -22 | 44 |
| 2 | 1.46 | 1.46 | 1.42 | 8 | 8 | -16 |
| 3 | 1.43 | 1.43 | 1.43 | 0 | 0 | 0 |
These results confirm that cells with lower voltage receive higher charging current in the freewheeling phase, achieving automatic balancing. When all cells are balanced, the net balancing current is zero.
### 4.3 Input-Output Characteristics
To validate the voltage gain, three capacitors (4.7 μF each) replaced the battery cells. With fixed \(D=0.7\), input voltage varied from 11 V to 29 V, and total output voltage was measured. Figure 4 plots measured values against theoretical \(V_{out}=D V_{in}\). Excellent agreement is observed.
### 4.4 Long-Term Balancing Tests
**Test 1 (CC-CV):** Initial voltages: \(V_{B1}=3.220\)V, \(V_{B2}=3.250\)V, \(V_{B3}=3.282\)V. Charged at 1 A constant current until 12.3 V, then constant voltage. After 7200 s, the standard deviation dropped from 25.3 mV to 3.6 mV.
**Test 2 (CC-CC):** Initial voltages: \(V_{B1}=3.234\)V, \(V_{B2}=3.1214\)V, \(V_{B3}=2.735\)V. Charged at 4.8 A then 1.6 A constant current. After 5200 s, the standard deviation reduced from 213.6 mV to 10.6 mV. Figures 5 and 6 illustrate the voltage evolution, demonstrating effective balancing even under large initial imbalance.
### 4.5 Efficiency Measurement
Efficiency was measured for Type B at various output power levels (Figure 7). Peak efficiency reached 94.7% at 13.5 W output, which is competitive with dedicated chargers while providing integrated equalization.
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## 5. Comparison with Related Works
Table V compares the proposed converter with several similar integrated equalization topologies in terms of component count and estimated cost (based on unit prices from Digi-Key [43]). The number of series cells is \(n=3\) for cost estimation.
**Table V: Comparison of Integrated Topologies (n=3)**
| Topology | Active Switches | Magnetic Cores | Windings | Diodes | Capacitors | Estimated Cost (USD) |
|———————————————|—————-|—————-|———-|——–|————|———————-|
| Multiplier + Boost [40] | 1 | 1 | 1 | 6 | 3 | 2.8 |
| Forward–Flyback Resonant [41] | 1 | 1 | 2 | 6 | 4 | 3.2 |
| Multi-stacked Buck-Boost Sepic [42] | 1 | 4 | 4 | 3 | 3 | 5.65 |
| Multi-winding Buck [33] | 1 | 1 | 4 | 4 | 0 | 2.5 |
| Multi-winding Boost [24] | 1 | 1 | 4 | 4 | 0 | 2.5 |
| **Proposed Type A** | **1** | **1** | **3** | **3** | **0** | **2.15** |
| **Proposed Type B** | **4** | **1** | **3** | **0** | **0** | **2.3** |
The proposed Type A uses the fewest components and lowest cost among all compared topologies while maintaining automatic balancing. Type B offers higher efficiency and bidirectional capability at slightly higher cost. Both eliminate the need for voltage sensors, simplifying control and improving reliability.
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## 6. Conclusion
We have presented a novel converter family that integrates voltage equalization directly into the charge/discharge converter for series-connected energy storage battery strings. The converter achieves automatic voltage balancing without any voltage measurement, using only a single multi-winding coupled inductor and a minimal number of switches. Two variants are provided: Type A (low cost, unidirectional) and Type B (higher efficiency, bidirectional). Theoretical analysis, simulation, and experimental results confirm the voltage gain identical to a Buck converter and the automatic balancing capability. A prototype with three lithium-ion cells demonstrates that the standard deviation of cell voltages reduces dramatically during charging, from tens to a few millivolts. The converter offers a compact, low-cost, and reliable solution for energy storage battery systems, especially suitable for applications where simplicity and cost are critical.
Future work will focus on modular extension to accommodate larger numbers of series-connected energy storage battery cells, as well as further optimization of the multi-winding inductor design to minimize leakage inductance mismatch.