This paper presents a novel converter that integrates a voltage equalizer into a charge/discharge converter for series-connected energy storage cells. The proposed topology automatically balances the voltages of individual energy storage cells without requiring any voltage measurement circuits. Two types are introduced: Type A uses one active switch, one n-winding inductor, and n diodes; Type B replaces the diodes with active switches for higher efficiency. Detailed steady-state analysis, experimental validation, and a comprehensive comparison with existing techniques are provided.
1. Introduction
Energy storage cells, such as lithium-ion batteries, are widely used in applications ranging from low-power portable electronics to high-power systems like electric vehicles and renewable energy storage. These cells have low nominal voltages; thus, multiple cells must be connected in series to meet system voltage requirements. However, due to manufacturing tolerances, temperature gradients, and aging effects, the voltages of series-connected energy storage cells tend to diverge during repeated charge/discharge cycles. Without an equalization circuit, some cells may become overcharged or overdischarged, leading to reduced capacity, accelerated degradation, and even safety hazards.
Equalization techniques are broadly classified into passive and active types. Passive equalizers dissipate excess energy as heat, which is simple but wasteful. Active equalizers transfer energy among cells using capacitors, inductors, or transformers, achieving higher efficiency. Among active methods, multi-winding transformer topologies offer simplicity and automatic balancing without complex control. However, they typically require separate charge/discharge converters, increasing component count and system complexity.
In this work, we propose a converter that inherently integrates the equalization function into the power conversion stage. The converter uses a single multi-winding inductor (or transformer) and either diodes (Type A) or active switches (Type B) to automatically balance the voltages of series-connected energy storage cells. The control is straightforward—only one complementary PWM pair is needed for Type B. The converter operates in a buck-like manner during charging and can be extended to bidirectional operation. This paper focuses on the analysis, design, and experimental verification of the proposed converter.
2. Proposed Converter Topology and Operating Principle
2.1 Topology Description
The proposed converter for a string of n series-connected energy storage cells (B1 to Bn) is shown in Figure (a) for Type A and Figure (b) for Type B. The magnetic component is an n-winding inductor with all windings having the same number of turns, giving each winding identical inductance Lm (magnetizing inductance referred to one winding). Each winding Li is connected in series with an energy storage cell Bi. In Type A, a diode Di is placed in series with each cell; in Type B, an active switch Si replaces the diode. A main switch S0 controls the input power flow. The input voltage Vin is applied across the series combination of all cells during the on‑time of S0.
| Feature | Type A | Type B |
|---|---|---|
| Active switches | 1 (S0) | n+1 (S0, S1…Sn) |
| Diodes | n (D1…Dn) | 0 |
| Magnetic core | 1 with n windings | 1 with n windings |
| Control signals | Single PWM for S0 | Complementary PWM for S0 and Si |
| Direction | Unidirectional (charging) | Bidirectional (charging/discharging) |
| Efficiency | Lower (diode drop) | Higher (synch. rectification) |
| Reliability against short circuit | Higher | Lower (cross conduction risk) |
| Cost (n=3) | ~2.15 $ | ~2.3 $ |
2.2 Operating Modes of Type B During Charging
The key waveforms are given in Figure. The switching period is Ts, S0 has duty cycle D, and Si are turned on during the complementary interval (Si is off when S0 is on, and vice versa, with a small dead time). Five modes can be identified. For clarity, we neglect the dead‑time intervals and assume continuous conduction mode (CCM).
- Mode 1 [t0–t1]: S0 on, Si off. Input voltage Vin is applied across the magnetizing inductance in series with all cells. The currents iBi increase linearly and are identical because all windings are coupled.
- Mode 2 [t1–t2]: S0 turned off. The magnetizing current charges the parasitic capacitors of Si until their body diodes conduct, allowing ZVS turn‑on of Si after a short dead time.
- Mode 3 [t2–t3]: Si all turned on (synchronous rectification). The stored energy in the magnetizing inductance is delivered to the cells. Due to coupling, the current distribution among cells depends on their individual voltages: cells with lower voltage receive higher current, thereby achieving equalization.
- Mode 4 [t3–t4]: Si turned off; dead time before next cycle.
- Mode 5 [t4–t0]: S0 turned on. The currents redistribute and become equal again.
During Mode 3, the equivalent circuit can be represented by a network where the magnetizing inductance Lm is effectively in parallel with the series‑connected cells through their leakage inductances Lki. The voltage across the magnetizing inductance, VLm_3, is approximately the average of the cell voltages when the cells are balanced, but deviates proportionally to voltage imbalances to force equalizing currents.
3. Steady‑State Analysis
3.1 Input‑Output Voltage Relationship
By applying the volt‑second balance to the magnetizing inductance (neglecting the short dead‑time intervals), we obtain:
$$(V_{in} – \sum_{j=1}^{n} V_{Bj}) D T_s = \sum_{j=1}^{n} V_{Bj} (1-D) T_s$$
Simplifying yields:
$$\sum_{j=1}^{n} V_{Bj} = V_{in} D$$
Thus, the total output voltage (sum of all cell voltages) equals D times the input voltage, identical to a standard buck converter. This relationship holds for both Type A and Type B because the dead‑time intervals have negligible effect.
3.2 Equalization Current
During Mode 3, the instantaneous equalization current ΔiBi for cell Bi is the difference between its actual current and the average current entering all cells:
$$\Delta i_{Bi}(t) = i_{Bi}(t) – \frac{i_{Le}(t)}{n}$$
Using the equivalent circuit and assuming Lm >> Lki, the average equalization current over one switching period can be approximated as:
$$\Delta I_{Bi} = \frac{V_{Lm\_3} – V_{Bi}}{L_{ki}} \cdot \frac{(1-D)T_s}{2}$$
where VLm_3 is given by:
$$V_{Lm\_3} = \frac{\sum_{j=1}^{n} \left( \frac{L_m}{L_{kj}} V_{Bj} \right)}{1 + \sum_{j=1}^{n} \frac{L_m}{L_{kj}}}$$
When all leakage inductances are equal (Lki = Lk), this simplifies to:
$$V_{Lm\_3} \approx \frac{1}{n}\sum_{j=1}^{n} V_{Bj}$$
and the equalization current becomes:
$$\Delta I_{Bi} = \frac{\left( \frac{1}{n}\sum_{j=1}^{n} V_{Bj} – V_{Bi} \right)}{L_{k}} \cdot \frac{(1-D)T_s}{2}$$
Equation shows that the equalization current is proportional to the voltage difference between a cell and the average voltage. Cells with below‑average voltage receive positive ΔI (extra current), while those above average receive negative ΔI (less current). The magnitude can be adjusted by the duty cycle D (larger D reduces equalization) and the switching frequency (through Ts). Mismatch in leakage inductances will disturb the ideal equalizing behavior, but automatic balancing still occurs as long as voltages are unequal.
3.3 Influence of Leakage Inductance Mismatch
Simulations were performed with parameters: Vin=15 V, Lm=13 μH, T=20 μs, D=0.75, VB1=3.8 V, VB2=VB3=3.9 V. Table 2 summarizes the peak equalizing current for various leakage values.
| Case | Lk1 (μH) | Lk2 (μH) | Lk3 (μH) | Peak ΔiB1 (mA) | Peak ΔiB2 (mA) | Peak ΔiB3 (mA) |
|---|---|---|---|---|---|---|
| 1 | 0.7 | 0.7 | 0.7 | ~350 | ~350 | ~-700 |
| 2 | 1.0 | 1.0 | 1.0 | ~240 | ~240 | ~-480 |
| 3 | 1.3 | 1.3 | 1.3 | ~180 | ~180 | ~-360 |
| 4 | 1.0 | 1.0 | 0.7 | ~200 | ~200 | ~-400 |
| 5 | 1.0 | 1.0 | 1.3 | ~260 | ~260 | ~-520 |
Results confirm that equalization current decreases with larger leakage, and mismatch causes unequal sharing, but the automatic balancing mechanism remains effective.
4. Experimental Verification
4.1 Prototype and Setup
A Type B prototype was built for three series‑connected lithium‑ion energy storage cells (NCR21700T). Key components are listed in Table 3. The control was implemented using an STM32 microcontroller generating a complementary PWM pair with adjustable dead time. No cell‑voltage measurement was used for the equalization function; only the total stack voltage was monitored for charge control.
| Component | Parameter |
|---|---|
| Main switch S0 | STP220N6F7, Ron=2.40 mΩ |
| Switches S1–S3 | STP220N6F7 |
| Output capacitor C0 | MLCC 22 μF ×3 |
| Magnetizing inductance Lm | 12.2 μH |
| Switching frequency fs | 100 kHz (adjustable 50–250 kHz) |
| Input voltage Vin | 15 V (adaptive) |
4.2 Waveforms and Equalization Current
Figure shows the charging current waveforms for three cells under different imbalance conditions (Table 4). In Case 1 (VB1=VB2 > VB3), the lower‑voltage cell B3 receives a higher average current during the freewheeling interval, confirming automatic equalization. In Case 3 (all cells balanced), the currents are identical.
| Case | VB1 (V) | VB2 (V) | VB3 (V) | Iave1 (A) | Iave2 (A) | Iave3 (A) | ΔIB1 (mA) | ΔIB2 (mA) | ΔIB3 (mA) |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 3.82 | 3.82 | 3.78 | 1.56 | 1.56 | 1.67 | -22 | -22 | +44 |
| 2 | 3.76 | 3.76 | 3.80 | 1.46 | 1.46 | 1.42 | +8 | +8 | -16 |
| 3 | 3.78 | 3.78 | 3.78 | 1.43 | 1.43 | 1.43 | 0 | 0 | 0 |
4.3 Input‑Output Characteristic
The voltage transfer ratio was tested using three capacitors instead of cells to avoid battery dynamics. Figure 11 shows that the measured output voltage (sum of three capacitor voltages) matches Vin·D, confirming buck‑mode operation.
4.4 Equalization Performance
Two charging experiments were performed:
- Experiment I (mild imbalance): Initial voltages: 3.220 V, 3.250 V, 3.282 V. CC‑CV charging at 1 A / 12.3 V. After 7200 s, voltages became 4.105 V, 4.109 V, 4.114 V, with standard deviation reducing from 25.3 mV to 3.6 mV.
- Experiment II (severe imbalance): Initial voltages: 3.234 V, 3.121 V, 2.735 V. CC‑CV charging at 4.8 A / 1.6 A final current. After 5200 s, voltages reached 4.109 V, 4.092 V, 4.083 V, standard deviation from 213.6 mV to 10.6 mV.
4.5 Efficiency and Comparison
The measured efficiency of the Type B prototype peaked at 94.7% at 13.5 W output power. Table 5 compares the proposed converter with several existing integrated topologies for n=3 series‑connected energy storage cells. The proposed Type A offers the lowest component cost among single‑switch topologies, while Type B provides high efficiency with a moderate cost increase.
| Topology | Active switches | Magnetic cores (windings) | Diodes | Capacitors | Estimated cost ($) |
|---|---|---|---|---|---|
| Boost + voltage multiplier [40] | 1 | 1 (1,1) | 6 | 3 | 2.8 |
| Forward‑flyback resonant [41] | 1 | 1 (1,2) | 6 | 4 | 3.2 |
| Multi‑stacked Buck‑Boost [42] | 1 | 4 (4,4) | 3 | 3 | 5.65 |
| Multi‑winding Buck [33] | 1 | 1 (1,4) | 4 | 0 | 2.5 |
| Multi‑winding Boost [24] | 1 | 1 (1,4) | 4 | 0 | 2.5 |
| Proposed Type A | 1 | 1 (1,3) | 3 | 0 | 2.15 |
| Proposed Type B | 4 | 1 (1,3) | 0 | 0 | 2.3 |
5. Conclusion
This paper has proposed a converter that integrates a voltage equalizer into a charge/discharge converter for series-connected energy storage cells. The topology eliminates the need for additional voltage measurement circuits by automatically steering higher charging current toward lower‑voltage cells during the freewheeling interval. Two variants are available: Type A (diode‑based) for low‑cost, unidirectional applications, and Type B (synchronous) for high‑efficiency, bidirectional operation. The input‑output characteristic follows a simple buck‑converter relation, while the equalization current is proportional to the voltage deviation from the average. Experimental tests on three lithium‑ion cells demonstrate effective voltage balancing, with standard deviations reducing to a few millivolts after charging. The comparison with existing integrated topologies indicates that the proposed design achieves a favorable trade‑off among cost, component count, and performance. The converter can be extended to larger strings through modularity, making it a promising solution for future energy storage systems.