# A Battery Cell Equalisation System Based on a Supercapacitors Tank and DC–DC Converters for Automotive Applications

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## Abstract

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## 1. Introduction

- The Battery Cell Equalisation System (BCES) is an indispensable part of battery pack energy storage for automotive applications. Most of the BCES are based on multiple DC–DC converters, in some cases equal to the number of the cells, which increases the number of passive elements, and, respectively, the overall volume and weight. A better structure could be a topology accommodating a central DC–DC converter with bi-directional switches, establishing the energy flow between the cells and the ES.
- The researched BCES use the energy from the battery pack to equalise the cells in it. A more efficient solution could accommodate the reverse recovery brake energy, accumulating the energy in an ES. Considering the high energy accumulated for a short time, the SCs would match the requirements for a fast charge and increased charge/discharge cycles.
- Utilising SC’s energy tank as a part of the BCES requires additional research on the charge mode, clarifying the CC and CV conditions according to the specific energy parameters of the regenerative brake and cell equalisation operations.

## 2. Battery Cell Equalisation System Analysis

- Sub-system 1: battery ES comprises cells connected in series strings that are then paralleled. In the models and design procedures that were further developed, only a cell is used as an element of charge equalisation.
- Sub-system 2: bi-directional DC–DC converter transferring the energy between the battery and main inverter (out of scope).
- Sub-system 3: traction inverter and motor (out of scope).
- Sub-system 4: battery management system (BMS) controlling the equalisation process (out of scope).
- Sub-system 5: SCES identical to the battery storage architecture. Based on analytical calculations, modelling, and simulations, the design procedure shows the recommended approach for the energy storage accommodation, giving the desired capacity and operational modes of charge and discharge.
- Sub-system 6: unidirectional DC/DC converter used for SCES fast charge from regenerative break energy. The design procedure shows the applicability of the selected topology, considering the necessary high transformation ratio and power transfer.
- Sub-system 7: bi-directional DC/DC converter for battery cell equalisation. The design procedure shows the selected transformer-less topology applicability under the necessary modes of operation: battery cell charging/discharging from the SCES and battery cell equalisation by cell-to-cell energy transfer through the SCES.

## 3. DC–DC Converters Analysis and Design

#### 3.1. SCES DC/DC Charging Converter

#### 3.2. Bi-Directional Battery Cell Equalising DC/DC Converter Analysis and Design

## 4. Battery Cell Equalisation Process Analysis

## 5. Experimental Setup

## 6. Conclusions

- The design of the SCES could be supported with models based on the presented apparatus (Table 2), which gives a reasonable estimation of the transient processes of SCs charge/discharge and power loss (Figure 5, Figure 6, Figure 7 and Figure 8). Also, the models can be used to depict the battery cell equalisation process and power transfer, as shown in Figure 11, Figure 12, Figure 13 and Figure 14. The obtained results comply with the results published in [10,24].
- To minimise the power loss in the bi-directional switches, the transistors could be oversized on current, which minimises the ${DC}_{on}$ resistance. Regarding targeted resistance, the range of ${R}_{ON}=1\text{}\mathrm{m}\mathsf{\Omega}-500\text{}\mathsf{\mu}\mathsf{\Omega}$ can be recommended.
- A buck–boost transformer-less converter (Figure 10) is a good choice for the battery cell equalisation converter as it has a simple structure and offers high power density. To accommodate this converter easily, the SCES could be selected with a nominal voltage of 2–3 times the charge voltage of the battery cells. For the SCES charge, the two-switch forward converter (Figure 9) is a good choice, as can be concluded from its experimental verification. The results comply with and complete the results published in [49,50,51,52,53,54,55].

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Electric drivetrain block diagram with an integrated system for battery cell equalisation. Red—positive DC; Blue—negative DC; Purple—communication.

**Figure 2.**Charging battery cells in automotive energy storage for voltage equalisation. Red—positive DC; Blue—negative DC.

**Figure 3.**Block diagrams of a SCES charging with a DC/DC converter—constant voltage. Red—positive DC; Blue—negative DC.

**Figure 4.**Block diagrams of a SCES charging with a DC/DC converter—constant current. Red—positive DC; Blue—negative DC.

**Figure 5.**SC tank charging with CV. (

**A**) Constant charging voltage (1 Black), and capacitor’s tank voltage (2 Blue); (

**B**) charging current (Red); (

**C**) capacitor’s power loss (Red); (

**D**) input source power (Green); (

**E**) accumulated energy (Red).

**Figure 6.**SCES charging with CC. (

**A**) Constant charging current (Red); (

**B**) capacitors tank voltage (Black); (

**C**) capacitor’s power loss (Red); (

**D**) input source power (Green); (

**E**) accumulated energy (Red).

**Figure 7.**CC and CV charging from a battery cell (sub-system 7, Figure 1). (

**A**) A block diagram for CC/CV charger (Red—positive DC; Blue—negative DC); (

**B**) charging current (1 Red) and charging voltage (2 Black); (

**C**) capacitor’s power loss (Red); (

**D**) power delivered from the source (Green); (

**E**) accumulated energy (Red).

**Figure 8.**CC and CV charging from regenerative breaking (sub-system 6, Figure 1). (

**A**) Charging current (Red); (

**B**) Charging voltage (1 Black) and capacitor’s tank voltage (2 Blue); (

**C**) capacitor’s power loss (Red); (

**D**) power delivered from the source (Green); (

**E**) accumulated energy (Red).

**Figure 9.**Two-switch DC–DC converter accommodated in the designed system for SCES charge from regenerative braking.

**Figure 10.**Buck–boost bi-directional converter, accommodated in the designed system for battery cell equalisation.

**Figure 11.**SCES discharge. (

**A**) Discharge current (Red); (

**B**) tank voltage (Blue); (

**C**) energy transferred from the tank (Red).

**Figure 12.**SCs discharge process supplying the battery cell charge. (

**A**) A block diagram of battery cell charging from the SCES (Red—positive DC; Blue—negative DC); (

**B**) SCES voltage (Blue); (

**C**) SCES current (Red); (

**D**) delivered constant power to the battery cell (Green); (

**E**) SCs tank energy discharge (Red); (

**F**) SCs power loss (Red).

**Figure 13.**SCES charge from a battery cell (

**A**–

**D**) and regenerative braking (

**E**–

**H**) with initial voltage. (

**A**) Constant current (1 Red) and voltage (2 Black) from a battery cell (Sub-system 7, Figure 1); (

**B**) SCs power loss (Red); (

**C**) power from Sub-system 7 (Green); (

**D**) accumulated energy (Red); (

**E**) constant current (1 Red) and voltage (2 Black) from regenerative braking (Sub-system 6, Figure 1), SCs voltage (3 Blue); (

**F**) SCs power loss (Red); (

**J**) power from Sub-system 6 (Green); (

**H**) accumulated energy (Red).

**Figure 14.**A battery cell charging for voltage equalisation. (

**A**) Constant charging current of 2 A (1 Red), converter voltage (2 Black), battery cell voltage equalisation from 2.5 V to 3 V (3 Blue); (

**B**) power on the primary converter side (1 Red) and secondary side (2 Green). (

**C**) Energy accumulated in the battery cell (Red).

**Figure 15.**SC tank charging with constant voltage. Probe 1—current (Red), probe 2—voltage over the SC tank (Blue).

**Figure 17.**Converter DC–DC 2 (Figure 2) buck mode of operation. Probe 1—current (Blue), probe 2—drain-to-source over the transistor voltage (Red), and probe 3—PWM (Green).

**Figure 18.**The output of the buck–boost converter. Probe 1—voltage (Red) and probe 2—current (Blue) to the battery cell under charge for equalisation. Probe 3 (Green) and probe 4 (Red)—PWM and Q1 drain–source voltage, respectively.

**Figure 19.**Battery cell equalisation with SC discharge (T1) and charge (T2) periods. Probe 1 SC voltage (Red), and probe 2 SC current (Blue).

Converters’ Mode of Operation | ON Switches | OFF Switches |
---|---|---|

SCES charging from regenerative breaking | ||

DC–DC 1 (ON) DC–DC 2 (OFF) | Qa1, Qa2 | Qa3, Qa4; Qb1–Qb4 Qs1.1–QsN.4; Q1.1–QN.M |

Battery cell equalisation—battery charging from the SCES (String 1, Cell V1.1 undercharge) | ||

DC–DC 1 (OFF) DC–DC 2 (ON, Buck mode) | Qa3, Qa4; Qb3, Qb4; Qs1.3,Qs1.4; Q1.1, Q1.2 | Qa1, Qa2; Qb1, Qb2; Qs1.1, Qs1.2; QsN.1–QsN.4; QN.1–QN.M |

Battery cell equalisation—battery charging from the SCES (String N, Cell VN1.1 undercharge) | ||

DC–DC 1 (OFF) DC–DC 2 (ON, Buck mode) | Qa3, Qa4; Qb3, Qb4; QsN.3, QsN.4; QN.1, QN.2 | Qa1, Qa2; Qb1, Qb2; Qs1.1–Qs1.4; Q1.1–Q1.N; QsN.1, QsN.2; QN.3–QN.M |

Battery cell equalisation—energy cell-to-cell distribution (String 1, Cell V1.1 overcharged, String N Cell VN1.1. undercharge) | ||

DC–DC 1 (OFF) DC–DC 2 (ON, Buck mode) | Qb1-Qb4; Qs1.1, Qs1.2; QsN.3, QsN.4; Q1.1, Q1.2; QN.1, QN.2 | Qa1-Qa4; Qs1.3, Qs1.4; QsN.1, QsN.2; Q1.3–Q1.N; QN.3–QN.M |

Battery cell equalisation—energy cell-to-cell distribution (String 1, Cell V1.1 undercharged, String N Cell VN1.1. overcharge) | ||

DC–DC 1 (OFF) DC–DC 2 (ON, Buck mode) | Qb1-Qb4; Qs1.3, Qs1.4; QsN.1, QsN.2; Q1.1, Q1.2; QN.1, QN.2 | Qa1-Qa4; Qs1.1, Qs1.2; QsN.3, QsN.4; Q1.3–Q1.N; QN.3–QN.M |

Battery cell discharge—energy transfer to the SCES (String 1, Cell V1.1 overcharged, no cell undercharge) | ||

DC–DC 1 (OFF) DC–DC 2 (ON, Boost mode) | Qa3, Qa4; Qb3, Qb4; Qs1.3, Qs1.4; Q1.1, Q1.2 | Qa1, Qa2; Qb1, Qb2; Qs1.1, Qs1.2; QsN.1–QsN.4; Q1.3–Q1.N; QN.1–QN.M |

Battery cell discharge—energy transfer to the SCES (String N, Cell VN.1 overcharged, no cell undercharge) | ||

DC–DC 1 (OFF) DC–DC 2 (ON, Boost mode) | Qa3, Qa4; Qb3, Qb4; QsN.3, QsN.4; QN.1, QN.2 | Qa1, Qa2; Qb1, Qb2; Qs1.1–Qs1.4; QsN.1, QsN.2; Q1.1–Q1.N; QN.3–QN.M |

Charge | Discharge | ||
---|---|---|---|

Transient capacitor’s voltage ${\mathrm{V}}_{\mathrm{C}}\text{}\mathrm{and}\text{}\mathrm{current}\text{}{\mathrm{I}}_{\mathrm{C}}$ | |||

${V}_{C}={V}_{in}\left(1-{e}^{-\frac{t}{RC}}\right)$ | (9) | ${V}_{C}={V}_{o}{e}^{-\frac{t}{RC}}$ | (10) |

${I}_{C}=\frac{{V}_{in}}{R}\times \left({e}^{-\frac{t}{RC}}\right)$ | (11) | ${I}_{C}=-\left(\frac{{V}_{o}}{R}\right)\times \left({e}^{-\frac{t}{RC}}\right)$ | (12) |

${V}_{Cini}={V}_{in}+\left({V}_{ini}-{V}_{in}\right){e}^{-\frac{t}{RC}}$ | (13) | - | |

${I}_{Cini}=\frac{{V}_{in}-{V}_{ini}}{R}\times \left({e}^{-\frac{t}{RC}}\right)$ | (14) | - | |

Where C is the equivalent tank capacitance (F), R is the equivalent circuit resistance ($\mathsf{\Omega}$), ${\mathrm{V}}_{\mathrm{i}\mathrm{n}}$ and ${\mathrm{V}}_{\mathrm{o}}$, respectively, the tank input and initial discharge voltages (V), t is the time (s), ${\mathrm{V}}_{\mathrm{C}\mathrm{i}\mathrm{n}\mathrm{i}}$ is the initial voltage capacitor charge, and ${\mathrm{I}}_{\mathrm{C}\mathrm{i}\mathrm{n}\mathrm{i}}$ is the initial current capacitor charge | |||

$\mathrm{SCES}\text{}\mathrm{voltage}\text{}{V}_{cap}$ $\mathrm{under}\text{}\mathrm{constant}\text{}\mathrm{charge}\text{}\left({I}_{CCh}\right)$ $\mathrm{and}\text{}\mathrm{discharge}\text{}({I}_{CDh}$) currents | |||

${V}_{cap}=\left({V}_{max}\times \frac{{D}_{ini}}{100}\right)+\left(\frac{{I}_{CCh}\times t}{C}\right)$ | (15) | ${V}_{cap}=\left({V}_{max}\times \frac{{D}_{ini}}{100}\right)+\left(\frac{{I}_{CDh}\times t}{C}\right)$ | (16) |

${T}_{CH}=C\times \frac{{V}_{max}\times \left({D}_{max}-{D}_{ini}\right)}{100{I}_{CCh}}$ | (17) | ${T}_{DH}=C\times \frac{{V}_{max}\times \left({D}_{max}-{D}_{ini}\right)}{100{I}_{CDh}}$ | (18) |

Where ${\mathrm{D}}_{\mathrm{i}\mathrm{n}\mathrm{i}}$ and ${\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ are the initial and maximum discharge ratios, ${\mathrm{T}}_{\mathrm{C}\mathrm{H}}$ and ${\mathrm{T}}_{\mathrm{D}\mathrm{H}}$ are charge and discharge times (s), and ${\mathrm{V}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum voltage (V) | |||

Energy loss during the charge $\left({W}_{lossCH}\right)$ and discharge $({W}_{lossDH}$) process | |||

${W}_{lossCH}={R}_{ESR}\times C\times {I}_{CCh}\times $ $\frac{{V}_{max}\times \left({D}_{max}-{D}_{ini}\right)}{100}$ | (19) | ${W}_{lossDH}={R}_{ESR}\times C\times {I}_{CDh}\times $ $\frac{{V}_{max}\times \left({D}_{max}-{D}_{ini}\right)}{100}$ | (20) |

$\u2206{W}_{cap}=\left(\frac{C\times {V}_{max}^{2}}{2}\right)\times \left[{\left(\frac{{D}_{max}}{100}\right)}^{2}-{\left(\frac{{D}_{ini}}{100}\right)}^{2}\right]$ | (21) | ||

Where $\u2206{\mathrm{W}}_{\mathrm{c}\mathrm{a}\mathrm{p}}$ is the stored/recovered energy, ${\mathrm{R}}_{\mathrm{E}\mathrm{S}\mathrm{R}}$ is the equivalent series resistance of the tank ($\mathsf{\Omega}$) | |||

$\mathrm{Charge}\text{}\left({\eta}_{CH}\right)\text{}\mathrm{and}\text{}\mathrm{discharge}\text{}({\eta}_{DH}$) efficiency | |||

${\eta}_{CH}=\frac{\mathsf{\Delta}{W}_{cap}}{\mathsf{\Delta}{W}_{cap}+{W}_{r}}$ | (22) | ${\eta}_{DH}=\frac{\mathsf{\Delta}{W}_{cap}+{W}_{r}}{\mathsf{\Delta}{W}_{cap}}$ | (23) |

${\eta}_{CH}=\frac{1}{\left[\begin{array}{c}1+2{R}_{ESR}\times \\ \left(\frac{100{I}_{CCh}}{{V}_{max}\times \left({D}_{max}+{D}_{ini}\right)}\right)\end{array}\right]}$ | (24) | ${\eta}_{DH}=1+2{R}_{ESR}\times $ $\left(\frac{100{I}_{DCh}}{{V}_{max}\times \left({D}_{max}+{D}_{ini}\right)}\right)$ | (25) |

${\eta}_{CH}=\frac{{T}_{CH}}{\left[\begin{array}{c}{T}_{CH}+2{R}_{ESR}C\times \\ \left(\frac{{D}_{max}-{D}_{ini}}{{D}_{max}+{D}_{ini}}\right)\end{array}\right]}$ | (26) | ${\eta}_{DH}=1+2{R}_{ESR}C\times \left(\frac{{D}_{max}-{D}_{ini}}{{T}_{CH}\times \left({D}_{max}+{D}_{ini}\right)}\right)$ | (27) |

**Table 3.**Two-switch converter design parameters (Figure 9).

Design Parameter | Value | Equation |
---|---|---|

Input design parameters | ||

Input/output voltage ranges | 300–500 V/0–12 V | - |

Nominal/maximum output current | 100 A/120 A | - |

Switching frequency/targeted efficiency | 100 kHz/90% | - |

Output design parameters | ||

Transformation turns ratio and minimum duty cycle | 0.1; 0.27 | (29), (30) |

Selected output capacitor (C2, Figure 9) | $6800\text{}\mathsf{\mu}\mathrm{F},\text{}10\text{}\mathrm{m}\mathsf{\Omega}$ | (32), (33) |

Output inductor and DC resistance (L1, Figure 9) | $20\text{}\mathsf{\mu}\mathrm{H},\text{}300\text{}\mathrm{m}\mathsf{\Omega}$ | (35) |

Primary/secondary RMS current | 100.5 A/7.3 A | (36), (37), (38), (39) |

Selected MOSFETS (Q1, Q2, Figure 9) | NTHL040N65 | |

Conductive/switching/total power loss | 2.12 W/4.1 W/6.2 W | (40), (41), (42), (43) |

Primary side demagnetisation peak/average current | 1 A/0.4 A | (45), (47) |

Selected primary side diodes (D1, D2, Figure 9) | STTH812 | |

Selected secondary side diodes (D3, D4, Figure 9) | VS-150EBU02 | |

Rectifier (D3)/freewheeling (D4) diodes power loss | 37.8 W/46.2 W | (49), (50) |

**Table 4.**Buck–boost bi-directional converter output design parameters (Figure 10).

Design Parameter | Value | Equation |
---|---|---|

Input design parameters | ||

Input/output voltages | 12 V/5 V | - |

Nominal/maximum current | 2 A/2.5 A | - |

Switching frequency | 100 kHz | - |

Output design parameters | ||

Selected MOSFETS (Q1, Q2, Figure 10) | FDP8896 | |

Transistors Q1/Q2 total power loss | 0.39 W/0.17 W | (51), (52), (55), (56)(57), (58), (59) |

Selected inductor (L1, Figure 10); Inductance/Rdc | $150\text{}\mathsf{\mu}\mathrm{H},\text{}50\text{}\mathrm{m}\mathsf{\Omega}$ | (53), (54) |

Selected capacitor (C1, Figure 10); capacitance/ESR | $100\text{}\mathsf{\mu}\mathrm{F},\text{}35\text{}\mathrm{m}\mathsf{\Omega}$ | (63) |

Inductor/capacitor power loss | 0.17 W/0.034 W | (60), (61) |

Converter total loss/estimated efficiency | 1.07 W/90.4% | (62), (64) |

**Table 5.**Power loss in the switches connected, according to Figure 2, during different modes of operation.

Mode of Operation | ON Switches Secondary Side DC–DC1 | ON Switches Primary Side DC–DC2 | ON Switches Secondary Side DC–DC2 | Total Conductive Loss (W) | Switches Estimated Efficiency |
---|---|---|---|---|---|

Estimated maximum DC current/voltage/power | 100 A/10 V 1000 W | 1 A/10 V 10 W | 2 A/5 V 10 W | - | - |

SCES charging (regenerative breaking) | Qa1, Qa2 | - | - | 10 | 99% |

Battery cell equalisation | - | Qa3, Qa4 | Qb3, Qb4, Qs1.3, Qs1.4, Q1.1, Q1.2 | 0.468 | 95.3% |

Battery cell equalisation—energy distribution | - | Qb1, Qb2, Qs1.1, Qs1.2, Q1.1, Q1.2 | Qb1, Qb4, QsN.3, QsN.4, QN.1, QN.2 | 0.54 | 94.6% |

Battery cell discharge | - | Qa3, Qa4 | Qb3, Qb4, Qs1.3, Qs1.4, Q1.1, Q1.2 | 0.468 | 95.3% |

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## Share and Cite

**MDPI and ACS Style**

Dimitrov, B.; Konaklieva, S.
A Battery Cell Equalisation System Based on a Supercapacitors Tank and DC–DC Converters for Automotive Applications. *World Electr. Veh. J.* **2023**, *14*, 185.
https://doi.org/10.3390/wevj14070185

**AMA Style**

Dimitrov B, Konaklieva S.
A Battery Cell Equalisation System Based on a Supercapacitors Tank and DC–DC Converters for Automotive Applications. *World Electric Vehicle Journal*. 2023; 14(7):185.
https://doi.org/10.3390/wevj14070185

**Chicago/Turabian Style**

Dimitrov, Borislav, and Sylvia Konaklieva.
2023. "A Battery Cell Equalisation System Based on a Supercapacitors Tank and DC–DC Converters for Automotive Applications" *World Electric Vehicle Journal* 14, no. 7: 185.
https://doi.org/10.3390/wevj14070185