# Multi-Mode Lithium-Ion Battery Balancing Circuit Based on Forward Converter with Resonant Reset

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Balancing Circuit

#### 2.1. Circuit Structure

_{11}~S

_{1n}and S

_{21}~S

_{2n}, respectively. The right side of the balancing main circuit is set as the access port of the low-energy cells; this also is called the energy-receiving side. The positive and the negative terminals of the low-energy cells and ports are connected by S

_{41}~S

_{4n}and S

_{31}~S

_{3n}, respectively. Considering the design of the drive circuit and the voltage stress of the components, SPST relays are selected for the switching matrix, while the 74HC595 is used as its main drive component.

#### 2.2. Operation Principle

_{4,}B

_{5}, B

_{6}are high-energy cells and B

_{1}, B

_{2}, B

_{3}are low-energy cells, as shown in Figure 2, currently, the balancing process is as follows: S

_{16}and S

_{24}are closed to connect the energy-sending side. S

_{31}and S

_{43}are closed to connect the energy-receiving side. Currently, a voltage difference is produced on the energy transmission line of the balancing main circuit by voltage mapping of two primary side inductors of the forward converters. The transferred current will transmit energy from high-energy cells to low-energy cells.

_{4}, B

_{5}, and B

_{6}are high-energy cells and B

_{1}and B

_{2}are low-energy cells, as shown in Figure 3. The balancing process currently is as follows: S

_{16}and S

_{24}are closed to connect the energy-sending side. S

_{31}and S

_{42}are closed to connect the energy-receiving side. For now, a voltage difference is produced on the energy transmission line of the balancing main circuit by voltage mapping of two primary side inductors of the forward converters. The transferred current will transmit energy from high-energy cells to low-energy cells.

#### 2.3. Circuit Analysis

_{T1a}, R

_{T2a}, R

_{T1b}, and R

_{T2b}. The output resistors of the forward converters are represented by R

_{o1}and R

_{o2}; U

_{H}and U

_{L}denote the voltage of the high-energy cell and the voltage of the low-energy cell, respectively. The excitation inductors of the primary side of the forward converter are reflected by L

_{m1}and L

_{m2}. C

_{r1}and C

_{r2}denote the resonant capacitors.

_{B}, and the current of the primary side circuit of the forward converter is reflected by i

_{a}. The balancing process in one switching cycle is divided into five steps as follows.

_{Ta}, R

_{Tb}, and R

_{o}.

_{0}~t

_{1}]: At t

_{0}, the MOSFETs are turned on. The transformer’s secondary side maps out N times the primary side voltage, and the transmission current is produced on the energy transmission line. N times transmission currents are generated in the primary side coil of the forward converters, and the currents of the excitation inductors L

_{m}

_{1}and L

_{m}

_{2}increase at the slopes of $\frac{{di}_{Lm1}}{dt}$ and $\frac{{di}_{Lm2}}{dt}$. At t

_{0}~t

_{1}, the voltages mapped out on the secondary side of the two forward converters are presented as follows:

_{AVG}can be expressed as:

_{T}

_{1}

_{a}, i

_{T}

_{2}

_{a}of the forward converter are presented as:

_{T}

_{1}

_{b}, i

_{T}

_{2}

_{b}are expressed as:

_{0}, the excitation currents i

_{Lm}

_{1}and i

_{Lm}

_{2}of the forward converters can be calculated by (8):

_{0}, i

_{1}and i

_{2}in the two primary circuits can be deduced, respectively, as:

_{1}, the excitation currents i

_{Lm1}and i

_{Lm2}of the forward converters can be calculated by (10):

_{1}, i

_{1}and i

_{2}in the two primary circuits can be deduced, respectively, as:

_{1}~t

_{2}]: At t

_{1}, MOSFETs are turned off, L

_{m}and C

_{r}begin to resonate, and the circuit enters the resonant state. Because the voltage added to the excitation inductor is still positive at this time, the excitation currents i

_{Lm}

_{1}and i

_{Lm}

_{2}will continue to increase. Charges are accumulated on the resonant capacitors C

_{r1}and C

_{r2}, respectively, and the resonant capacitors are charged. At t

_{2}, the resonant capacitors C

_{r1}and C

_{r2}are charged to the voltage of cells U

_{H}and U

_{L}, differently, and the voltage drops across the excitation inductors are zero. i

_{Lm}

_{1}and i

_{Lm}

_{2}reach the maximum values of i

_{Lm1 (max)}and i

_{Lm2 (max)}, respectively.

_{1}can be expressed by (12) and (13):

_{2}~t

_{3}]: At t

_{2}, C

_{r1}and C

_{r2}continue to charge by L

_{m1}and L

_{m2}. At the same time, U

_{Cr}

_{1}and U

_{Cr}

_{2}reach their maximum values U

_{Cr1 (max)}and U

_{Cr2 (max)}at t

_{3}, while i

_{Lm}

_{1}and i

_{Lm}

_{2}decrease to zero to achieve a magnetic reset.

_{2}can be expressed as:

_{3}~t

_{4}]: At t

_{3}, the resonant capacitors C

_{r1}and C

_{r2}are discharged, the excitation inductors L

_{m1}and L

_{m2}are stored, and the excitation currents i

_{Lm}

_{1}and i

_{Lm}

_{2}are increased in the reverse direction.

_{4}~t

_{5}]: At t

_{4}, the resonant capacitors C

_{r1}and C

_{r2}discharge again to U

_{H}and U

_{L}, and the excitation currents i

_{Lm}

_{1}and i

_{Lm}

_{2}reach the reverse maximum i

_{Lm1 (max)}and i

_{Lm2 (max)}. At t

_{5}, the resonant capacitor discharges to zero, at which point MOSFETs are opened again with ZVS and the balancing circuit enters the next stage of balancing.

#### 2.4. ZVS Analysis

_{m}

_{1}= L

_{m}

_{2}and C

_{r}

_{1}= C

_{r}

_{2}are replaced by L

_{m}and C

_{r}, respectively.

_{Lm}(t) replaces i

_{Lm}

_{1}(t) and i

_{Lm}

_{2}(t), and U

_{B}replaces U

_{H}and U

_{L}.

_{2}− t

_{1}and t

_{5}− t

_{4}satisfy (25), ZVS can be realized normally in T

_{off}:

_{1}and α

_{2}satisfy the following equation, (25) is true:

_{c}can be calculated by:

_{S}can be calculated by (30).

## 3. Analysis and Verification

#### 3.1. Verification

#### 3.1.1. Verification of Balancing Circuit

#### 3.1.2. Verification of ZVS

#### 3.2. Analysis of Balancing Performance

_{1}, the power of the primary circuit at the energy-sending side is set to P

_{in}and the power of the primary circuit at the energy-receiving side is set to P

_{out}. According to expressions (11), P

_{in}and P

_{out}are obtained:

#### 3.3. Influencing Factors of Balancing Performance

#### 3.3.1. Effect of Converter Turn Ratios

_{S}= 40 μs to develop the circuit simulation. The relationships between different converter turn ratios and balancing performances are shown in Figure 7.

_{in}and output power P

_{out}of the balancing main circuit are increased, and the balancing time is shortened. However, the balancing efficiency is not affected. In principle, the turn ratio of the forward converter should be set larger to achieve higher power energy transmission. However, when the turn ratio of the forward converters iare enlarged, the voltage error of the cells is increased. Therefore, with high-power balancing, more moderate turn ratios are set. Based on the data in Figure 7, the turn ratio of the forward converters is chosen to be 1:2 in this paper.

#### 3.3.2. Effect of Switching Cycles

_{in}and P

_{out}are increased. Figure 8c shows that for any balancing model, balancing efficiency is less influenced by the change in the switching period. From Figure 8d, balancing time and switching period are inversely related in any balancing mode. In summary, increasing the switching period has less effect on the balancing efficiency, but P

_{in}and P

_{out}are enlarged by this increase. Then, the balancing time is shortened, helping to improve the balancing speed.

#### 3.3.3. Effect of Output Resistances

_{o1}= R

_{o2}= 1 Ω and R

_{o1}= R

_{o2}= 5 Ω is selected for simulation to study the relationships between output resistors and balance performances. The results are shown in Figure 9.

_{in}and P

_{out}corresponding to the balancing circuit are decreased by the increase in the output resistances. Figure 9c shows that changing the output resistors leads to a smaller effect on the balancing efficiency for the same switching period. Figure 9d, for the same switching cycle, the longer balancing time results from larger output resistances. In summary, smaller output resistances help to increase P

_{in}and P

_{out}, and a shorter balancing time and faster balancing speed will be obtained.

#### 3.3.4. Effect of Balancing Modes

_{S}= 40 μs is chosen to simulate the relevant balancing models. The relationship between various voltage differences and balancing performances is shown in Figure 10.

## 4. Balancing Strategy

_{ref1}and U

_{ref2}are two key parameters in the process and are set in the balancing strategy according to the circuit operation requirements. The execution flow of the balancing strategy is shown in Figure 11. The balancing strategy is divided into five main steps:

- (1)
- The voltage of each cell in the battery pack is measured. U
_{max}and U_{min}are found by the measured voltages. Then the numbers of cells of U_{max}and U_{min}are recorded. - (2)
- (U
_{max}− U_{min}) is calculated and compared with U_{ref1}. If (U_{max}− U_{min}) > U_{ref1}, the balancing circuit is activated. If (U_{max}− U_{min}) ≤ U_{ref1}, the system is stopped to enter the balancing operation. - (3)
- When the balancing system is controlled to enter the balancing state, U
_{avg}is calculated, and (U_{i}− U_{avg}) is calculated with U_{i}. Then (U_{i}− U_{avg}) is compared with U_{ref2}. If (U_{i}− U_{avg}) ≥ U_{ref2}, the cell is identified as a high-energy cell. If (U_{i}− U_{avg}) ≤ −U_{ref2}, the cell is identified as a low-energy cell. - (4)
- The numbers of high-energy cells and low-energy cells involved in balancing are counted, and their numbers are noted as a and b. The balancing mode is selected according to the result of the comparison of a and b.
- (5)
- After completing the above operations, the balancing system enters a waiting state, and the next cycle is entered by the balancing system.

_{ref1}and U

_{ref2}are set to 0.05 V and 0.01 V, respectively.

## 5. Experiments and Analysis

#### 5.1. Experimental Parameters

#### 5.2. Prototype Verification

#### 5.3. Experimental Results

_{S}= 50 μs is chosen as the switching period of the MOSFETs in the experiment since different switching periods of MOSFETs have a small effect on the balancing efficiency, but a large effect on the balancing speed.

_{B1}= 2.951 V, U

_{B2}= 2.898 V, U

_{B3}= 2.841 V, U

_{B4}= 2.865 V, U

_{B5}= 2.921 V, U

_{B6}= 3.678 V, U

_{B7}= 3.663 V, and U

_{B8}= 3.435 V, and the balancing result is shown in Figure 14. The comparison of the balancing result with the balancing circuit in [35] is shown in Table 4.

## 6. Discussion

## 7. Conclusions

- The proposed balancing circuit utilizes a forward converter to achieve high-power balancing.
- A switching matrix consisting of an SPST relay realizes the MC2MC (Multi-Cell-to-Multi-Cell)) balancing method, simplifies the structure of the balancing circuit, makes the circuit easier to drive and control, and reduces the cost of the balancing circuit.
- The proposed balancing strategy allows the balancing circuit to have both n-cell-to-n-cell and n-cell-to-(n-1)-cell balancing modes and provides a flexible transmission path for energy.
- An experiment with an eight-cell lithium-ion battery pack was performed. The experiment result at 1260 s shows that the proposed method has a fast balancing speed, and the comparison with [31] shows that the balancing time in the proposed method is reduced by about 82.5%. Moreover, the maximum balancing efficiency of the proposed method is about 83.31%. Consequently, the proposed method has a good balancing performance.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Equivalent circuit and current-flow paths: (

**a**) equivalent circuit, (

**b**) Stage 1, (

**c**) Stage 2, (

**d**) Stage 3, (

**e**) Stage 4, (

**f**) Stage 5.

**Figure 5.**Operational waveforms of the balancing main circuit voltage and current: (

**a**) n-cell-to-n-cell balancing mode, (

**b**) n-cell-to-(n-1)-cell balancing mode.

**Figure 6.**Simulation waveforms of balancing circuit: (

**a**,

**b**) one-cell-to-one-cell balancing mode, Ts = 40 μs, Ts = 50 μs, (

**c**,

**d**) two-cell-to-one-cell balancing mode, Ts = 40 μs, Ts = 50 μs.

**Figure 7.**Effect of converter turns ratios on balancing performances: (

**a**) input powers and output powers, (

**b**) balancing efficiencies and balancing times.

**Figure 8.**Effect of switching cycles on performances in different balancing mode: (

**a**) input powers, (

**b**) output powers, (

**c**) balancing efficiencies, (

**d**) balancing times.

**Figure 9.**Effect of output resistances on balancing performances: (

**a**) input powers, (

**b**) output powers, (

**c**) balancing efficiencies, (

**d**) balancing times.

**Figure 12.**Experiment prototype and experiment platform: (

**a**) prototype front side, (

**b**) prototype back side, (

**c**) experiment platform.

**Figure 13.**Verification waveforms of balancing circuit: (

**a**,

**b**) one-cell-to-one-cell balancing mode T

_{S}= 40 μs, T

_{S}= 50 μs, (

**c**,

**d**) two-cell-to-one-cell balancing mode T

_{S}= 40 μs, T

_{S}= 50 μs.

Parameters | Values |
---|---|

L_{m1} L_{m2} | 80 μH |

C_{r1} C_{r2} | 100 nF |

R_{o1} R_{o2} | 1 Ω |

R_{T1a} R_{T2a}/R_{T1b} R_{T2b} | 0.36 Ω/3 Ω |

T_{S} | 25 μs 30 μs 35 μs 40 μs 45 μs 50 μs |

T_{S}/μs | Theory/% | Simulation/% |
---|---|---|

25 | 44 | 55 |

30 | 53 | 64 |

35 | 60 | 70 |

40 | 65 | 75 |

45 | 69 | 78 |

50 | 72 | 80 |

Component | Parameter |
---|---|

Rated capacity | 3.2 Ah |

MOSFET | SPN2054 |

MOSFET driver | UCC27524 |

Relay driver | 74HC595 |

MCU controller | STM32 |

Transformer inductance/turn ratio | 80 μH/1:2 |

Resonant capacitor | 100 nF |

Output resistance | 1 Ω |

Switch period/duty cycle | 50 μs/73% |

Balancing Circuit | Balancing Time/s | Balancing Voltage/V |
---|---|---|

Balancing Circuit in ref. [35] | 7250 | 3.533–3.58 |

Proposed Balancing Circuit | 1260 | 3.151–3.193 |

Balancing Circuit | Type | Component | ||||||
---|---|---|---|---|---|---|---|---|

M | D | L | C | RE | T | DR | ||

SC circuit [24] | AC2C | 2n | 0 | n-1 | n-1 | 0 | 0 | 2n |

LCSR circuit [26] | DC2C | 2n + 10 | 4 | 1 | 1 | 0 | 0 | n + 5 |

Flyback circuit [30] | C2P | n + 2 | n + 2 | 0 | 0 | 0 | 1 | n + 2 |

Forward circuit [35] | AC2AC | n | n | 0 | n | 0 | n | n |

BRLC circuit [37] | MC2MC | 4(n + 1) | 4 | 1 | 1 | 0 | 0 | 2(n + 1) |

Proposed circuit | MC2MC | 2 | 2 | 0 | 4 | 4n | 2 | n/2 + 1 |

Balancing Circuit | Type | Size | Cost (USD) | Speed | Drive | |
---|---|---|---|---|---|---|

SC circuit [24] | AC2C | Large | 21.6 | Very High | Poor | Good |

LCSR circuit [26] | DC2C | Small | 17 | High | Normal | Poor |

Flyback circuit [30] | C2P | Small | 9.3 | Very Low | Normal | Good |

Forward circuit [35] | AC2AC | Medium | 18.8 | High | Normal | Good |

BRLC circuit [37] | MC2MC | Small | 23 | Very High | Good | Poor |

Proposed circuit | MC2MC | Large | 13.9 | Low | Excellent | Excellent |

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## Share and Cite

**MDPI and ACS Style**

Zong, Y.; Li, K.; Wang, Q.; Meng, J.
Multi-Mode Lithium-Ion Battery Balancing Circuit Based on Forward Converter with Resonant Reset. *Appl. Sci.* **2023**, *13*, 10430.
https://doi.org/10.3390/app131810430

**AMA Style**

Zong Y, Li K, Wang Q, Meng J.
Multi-Mode Lithium-Ion Battery Balancing Circuit Based on Forward Converter with Resonant Reset. *Applied Sciences*. 2023; 13(18):10430.
https://doi.org/10.3390/app131810430

**Chicago/Turabian Style**

Zong, Yanliang, Kun Li, Qing Wang, and Jiaheng Meng.
2023. "Multi-Mode Lithium-Ion Battery Balancing Circuit Based on Forward Converter with Resonant Reset" *Applied Sciences* 13, no. 18: 10430.
https://doi.org/10.3390/app131810430