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

: A battery cell equalisation system for automotive applications based on a supercapacitors energy storage SCES tank is proposed. The main advantages of the developed system are the utilisation of the regenerative brake energy for battery cell equalisation, reduction in the number of DC–DC converters, the ﬂexible operation expressed by the possibility to address each battery cell with bi-directional switches, and acceptable efﬁciency in all modes of operation. The energy transfer between the SCES and battery cells is precisely analysed with modelling and simulations in steady-state and transient conditions. Power loss is estimated per sub-system, systemising the loss reduction techniques and achieving the maximum efﬁciency. The required DC–DC converters are described and designed according to the speciﬁc modes of operation in the developed application. Finally, the experimental veriﬁcation is provided using a small physical model.


Introduction
The battery pack is an electric vehicle's (EV) most expensive and sensitive part. Usually, it consists of hundreds or thousands of battery cells connected as a pack in series in parallel. As the cells are complex electrochemical elements, they have differences in their parameters which progress further due to temperature, charge-discharge cycles, environmental differences, etc. This leads to different cell capacitances, voltage, and selfdischarge rates, eventually leading to battery pack performance and lifetime expectancy degradation. Because of this, the proposed Battery Cell Equalisation System (BCES) is a vital part of battery storage (BS).
The battery cell equalisation techniques have been an object of research in numerous studies in recent years [1][2][3][4][5][6]. The review of the primary equalisation circuits in [1] presents and compares capacitive and inductive energy storage, single and multi-tube flyback, and different DC-DC converter topologies. As the study concludes, further improvements to the battery cell equalisation system must be focused on circuit design, giving a reliable system; flexibility improvement, leading to easy expansion on a large scale; and overall efficiency increase. A widely used circuit for equalisation is inductor-based, presented in better detail in [2,3], which usually requires a significant number of inductors and completes the energy transfer between adjacent cells only. A review and comparison study [2] of the inductor-based topologies suggests universal control equalisation algorithms. Some studies present the operation of an inductor equalisation circuit developed further to a dual interleaved inductor equalisation circuit [3]. As a primary benefit, the study reports an equalisation efficiency improvement of 4.89% and a time reduction of 37.4% based on an adaptive fuzzy neural network equalisation algorithm. Further efficiency and equalisation time improvements are found using zero voltage switching quasi-resonant converters [4], giving an efficiency improvement of 6%. 4 of 28 demonstrated that this topology can easily be used in constant current (CC) and constant voltage (CV) close loop control. Also, the two-switch converter could operate with reduced oscillations and mitigated reverse recovery [57,58], offering the ability of digital control with digital signal processors (DSPs) [59].
Based on the conducted literature review, the following conclusions could be summarised: • 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.
The summary points above suggest that achieving a flexible BCES utilising the reverse recovery break energy in a SCs tank still requires substantial research. This includes identifying the topology of the bi-directional DC-DC converter for cell equalisation and its integration with the battery pack with bi-directional switches, estimating the installed SC capacity and SC-to-cell energy transfer and proposing a unidirectional DC-DC converter for an SC storage charge. Based on these considerations, the main aim of this paper is to offer a novel, complete BCES for automotive battery packs, utilising regenerative braking energy in a redundant SC storage for cell equalisation. The system must be capable of addressing each of the battery cells, equalising their state-of-charge in both charge and discharge mode and using only one bi-directional converter for this purpose.
The rest of the paper is structured as follows: Part Two presents the suggested BCES with the necessary topology, mathematical apparatus, and modes of operation supported with models and simulations in MATLAB; Part Three presents the design procedures of the implemented bi-directional DC-DC converter for cell equalisation and the unidirectional DC-DC converter for SCs regenerative brake charging; Part Four is focused on the equalisation operation mode utilising the designed sub-systems-SCs energy tank, DC-DC converters, and battery pack with bi-directional switches; Part Five shows the experimental verification conducted with a physical model of the designed BCES.

Battery Cell Equalisation System Analysis
The suggested BCES is integrated into the electric drivetrain system, as shown in Figure 1. The overall system is divided into seven sub-systems to be able to present the analysis of the sub-systems 1, 5, 6, and 7 in more detail. The accepted designations are as follows: • 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 recom- • 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. The connection between the DC-DC converters, SCES tank, and the battery is shown in Figure 2. The structure is based on bi-directional MOSFET switches, the combination of each ensures a flexible system with connections between the SC tank and each battery cell through the converter DC-DC 2 (sub-system 7, Figure 1). Each battery string is connected to two DC Grids (DCgr1 and DCgr2) with two switches on the positive and negative side, which requires four input switches per each string (Qs1.1-Qs1.4, String 1). Two switches The connection between the DC-DC converters, SCES tank, and the battery is shown in Figure 2. The structure is based on bi-directional MOSFET switches, the combination of each ensures a flexible system with connections between the SC tank and each battery cell through the converter DC-DC 2 (sub-system 7, Figure 1). Each battery string is connected to two DC Grids (DCgr1 and DCgr2) with two switches on the positive and negative side, which requires four input switches per each string (Qs1.1-Qs1.4, String 1). Two switches connect each battery cell to the positive and negative sides. The bi-directional energy transfer charging or discharging the battery cell is transferred respectively from or to the SCES. Energy cell-to-cell equalisation is possible between every two different strings, connecting DC-DC 2 between DCgr1 and DCgr2 with switches Qb1-Qb4. The same operation mode is unsupported between two cells in the same string. This mode must be achieved through the SCs, connecting the DC-DC 2 with the SC tank with two switches, Qa3 and Qa4. The SCs charging is given from DC-DC 1 (sub-system 6, Figure 1), taking energy from the regenerative braking (sub-system 3, Figure 1). This converter is connected to the SC tank with unidirectional switches Qa1, Qa2. connect each battery cell to the positive and negative sides. The bi-directional energy transfer charging or discharging the battery cell is transferred respectively from or to the SCES. Energy cell-to-cell equalisation is possible between every two different strings, connecting DC-DC 2 between DCgr1 and DCgr2 with switches Qb1-Qb4. The same operation mode is unsupported between two cells in the same string. This mode must be achieved through the SCs, connecting the DC-DC 2 with the SC tank with two switches, Qa3 and Qa4. The SCs charging is given from DC-DC 1 (sub-system 6, Figure 1), taking energy from the regenerative braking (sub-system 3, Figure 1). This converter is connected to the SC tank with unidirectional switches Qa1, Qa2. is calculated from the number of cells per each string V and the constant number of the input switches = 4: The total number of switches at the bi-directional DC-DC 2 converter ( − ) is 4, as well as the total number of the SC tank ( − ). The total number of switches for the entire system can be calculated from the number of the paralleled strings : The switches' ON/OFF operation is shown in Table 1, according to the systems' modes of operation. To clarify the switching pattern, every operational mode is given for String 1 and String N, according to Figure 2. The number of switches of the string Q n.str is calculated from the number of cells per each string V cell−str and the constant number of the input switches Q SN = 4: The total number of switches at the bi-directional DC-DC 2 converter (Q b1 − Q b4 ) is 4, as well as the total number of the SC tank (Q a1 − Q a4 ). The total number of switches for the entire system can be calculated from the number of the paralleled strings N str : The switches' ON/OFF operation is shown in Table 1, according to the systems' modes of operation. To clarify the switching pattern, every operational mode is given for String 1 and String N, according to Figure 2. The SCES design mainly focuses on estimating the stored energy necessary for the battery cell charging and the capacitors' power loss estimation. This requires an analysis of the selected converter architecture, focused on the specific CC/CV charging modes of operation. The design procedure must define the necessary number of capacitors in series, strings in parallel (sub-system 4, Figure 1), and the total capacitance. The required energy for the battery cell charge is estimated as the constant power delivered over time, which must be delivered from the SC tank with no external source available. The energy stored in the SCES must be more than what is required for the charging process to be completed, compensating for the residual energy after each cycle. The precise amount, respectively, the integrated tank capacity and structure, is to be estimated analytically and depicted using simulation procedures. Considering the non-isolated bi-directional DC-DC converter, the maximum SCES voltage could be recommended in a range between 2 and 2.5 times the battery cells' voltage. A value of 10 V is accepted, based on the nominal 3.7 V Li-ion battery cells voltage. The relatively small voltage difference allows a transformer-less bi-directional buck-boot DC-DC converter to be utilised, giving a simple structure and high efficiency.
The required capacitors' energy W C is given with the integral of the power P C over the time t [3,4,6,7,12,19,20,29,30]: The energy accumulated in a capacitor is given by the equation: The transfer of the entire energy accumulated in the SCES physically requires the tank voltage to be discharged to 0 V. Such an operation would not sustain the charging process for several reasons: (a) the DC-DC converter cannot operate under its specific minimum voltage; therefore, the discharge to 0 V cannot maintain the power transfer; (b) the power discharge and energy curves follow the voltage curve proportionally, decreasing exponentially, which makes the power transfer ineffective; (c) with the voltage decrease, the discharge current must increase causing increased losses. Therefore, the SC tank discharge will cause a residual voltage V res . The ratio between the residual voltage and maximum tank voltage V max can be defined as the discharge radio D, expressed in percentages as follows [29,30]: The maximum energy W max can be calculated for the entire pack using the maximum voltage V max : The useable energy W use can be defined as a fraction of W max depending on the discharge coefficient ξ, specified over the discharge ratio as follows: The SCES charge and discharge basic equations [3,4,6,7,12,19,20,29,30] necessary for the simulation models are given in Table 2      The simulations are conducted with a SCES with a structure sugge the above-presented considerations: SCs capacitance = 100 F; capac 35 mΩ ; capacitors nominal voltage = 2.5 V ; maximum energy = 10 V ; total energy storage capacitance = 175 F , tota ESR = 20 mΩ; capacitors connected in series 5; capacitors' stri parallel 7. Figure 5 shows the results for CV charging as follows: (A) the transi cess continues for 17.5 s, e.g., five times the time constant = 3.5 s wi voltage = 10 V ; (B) the peak current at the beginning of the tra 499.86 A, and the average current is 100.72 A, which are considered una selected battery cells; (C) the peak capacitor loss is 44.64 W, and the a loss is 17.61 W; (D) the peak power delivered to the energy storage is 12 average power is 493.13 W; (E) the peak energy is 8629.12 J, and the lated energy is 6124 J.  Table 2. SCES charge and discharge mathematical models.

Charge Discharge
Transient capacitor's voltage V C and current I C - Where C is the equivalent tank capacitance (F), R is the equivalent circuit resistance (Ω), V in and V o , respectively, the tank input and initial discharge voltages (V), t is the time (s), V Cini is the initial voltage capacitor charge, and I Cini is the initial current capacitor charge SCES voltage V cap under constant charge (I CCh ) and discharge (I CDh ) currents Where D ini and D max are the initial and maximum discharge ratios, T CH and T DH are charge and discharge times (s), and V max is the maximum voltage (V) Energy loss during the charge (W lossCH ) and discharge (W lossDH ) process Where ∆W cap is the stored/recovered energy, R ESR is the equivalent series resistance of the tank (Ω) Charge (η CH ) and discharge (η DH ) efficiency

Charge Discharge
The simulations are conducted with a SCES with a structure suggested according to the above-presented considerations: SCs capacitance C sc = 100 F; capacitors ESR R ESR = 35 mΩ; capacitors nominal voltage V max caps = 2.5 V; maximum energy storage voltage V max = 10 V; total energy storage capacitance C = 175 F, total storage tank ESR R ESR total = 20 mΩ; capacitors connected in series 5; capacitors' strings connected in parallel 7.
Where ∆W is the stored/recovered energy, R is the equivalent series resistance of the tank (Ω) Charge ( ) and discharge ( ) efficiency The results from the CV and CC simulations in Figures 5 and 6 show that CV SCs charge applies high energy stress over the charging power supply and the capacitors, caused by a high initial current and leading to a high capacitor loss. The CC charging The results from the CV and CC simulations in Figures 5 and 6 show that CV SCs charge applies high energy stress over the charging power supply and the capacitors, caused by a high initial current and leading to a high capacitor loss. The CC charging mode shows superior energy parameters, giving lower capacitor loss and potentially lower stress over the charging DC-DC converter. As given in Figure 6, the energy transfer process and cell charge equalisation cannot be completed only in the CC operation. Therefore, CC/CV charging can be recommended in order to use the maximum energy storage capacity [29]. The results are depicted in Figure 7 fore, CC/CV charging can be recommended in order to use the maximum energy storage capacity [29]. The results are depicted in Figure 7: (A) A block diagram showing the necessary current and voltage feedback, giving the CC/CV mode of operation; (B) the constant current of 1 A and the voltage reaching the constant voltage of 10 V; (C) peak and average capacitor loss, respectively, of 0.36 W and 0.04 W ; (D) the maximum power reaches 10.12 W with an average power of 1.1 W; (E) the average accumulated energy is 5961.75 J.

DC-DC Converters Analysis and Design
According to the above analysis, the two DC-DC converters (Figure 2) have different energy parameters, thus applying an individual set of requirements to their design. Converter DC-DC 1 converts high power, estimated at 1 kW. The high voltage input, estimated at 300-500 V to a low output voltage of 10 V, requires the topology to be trans-

DC-DC Converters Analysis and Design
According to the above analysis, the two DC-DC converters ( Figure 2) have different energy parameters, thus applying an individual set of requirements to their design. Converter DC-DC 1 converts high power, estimated at 1 kW. The high voltage input, estimated at 300-500 V to a low output voltage of 10 V, requires the topology to be transformer-based. Converter DC-DC 2 is bi-directional with power estimated at 10 W, converting the SCES voltage of 10 V to the battery cell voltage of 3.5 V and vice versa.

SCES DC/DC Charging Converter
The selected topology for the DC/DC charger is a two-switch forward converter which offers significant advantages in the designed battery cell charging sub-system: primary-to-secondary side transformer isolation; two switches in series on the primary side, giving additional potential for functional safety implementation in this topology; a simple structure and control system, providing a possibility for a budget-friendly solution; and relatively good, over 90%, expected efficiency for a hard-switching converter. Along with this, taking into account the specific energy requirements in the developed system, the inherent topology drawbacks can be mitigated: the secondary side inductor volume can be minimised; due to the relatively narrow secondary side voltage range and the significant primary to secondary side voltage difference, the duty cycle 50% limitation does not apply substantial design difficulties.
The converter is shown in Figure 9, where C1 is the input filter capacitor, Q1 and Q2 are primary side MOSFET switches, D1 and D2 are primary side demagnetisation diodes, TX1 is the high-frequency pulse transformer, diodes D3 and D4 form the secondary side rectifier and freewheeling diode, and the output filter is formed from the inductor L2 and capacitor C2. Following the suggested system architecture (Figure 1), the voltage source V1 represents sub-system 3, supplying the regenerative break energy, and the secondary side load is sub-system 5, e.g., the SCES under charge. V1 represents sub-system 3, supplying the regenerative break energy, and the secondary side load is sub-system 5, e.g., the SCES under charge. The transformer turns ratio can be calculated from the converter's maximum output voltage [60,61]: where is the nominal output voltage; is the estimated efficiency; is the minimum operating input voltage; is the maximum duty cycle; is the turns ratio of the transformer.
The minimum voltage must be matched with the SC minimum voltage, and, respectively, the residual pack voltage , giving the required discharge ratio, Equation (3). The converter output voltage must take into consideration the battery cell charging voltage, assumed as 4.2 V for Li-ion batteries, plus the expected voltage drops from the The transformer turns ratio can be calculated from the converter's maximum output voltage [60,61]: where V out is the nominal output voltage; η is the estimated efficiency; V in min is the minimum operating input voltage; DC max is the maximum duty cycle; N is the turns ratio of the transformer.
The minimum voltage V in min must be matched with the SC minimum voltage, and, respectively, the residual pack voltage V res , giving the required discharge ratio, Equation (3). The converter output voltage must take into consideration the battery cell charging voltage, assumed as 4.2 V for Li-ion batteries, plus the expected voltage drops from the cell's switches (Figure 2).
From the previous equation, the turns radio N and the duty cycle DC can be written as follows [60,61]: The primary transformer inductance L mag can be calculated assuming that the magnetising current is 10% of the primary side current.
The output capacitor C out and the required equivalent series resistance R ESR can be calculated using the following equation: where ∆I out and ∆V out are the output current and voltage ripples, and f c is the crossover frequency.
The estimated R ESR from the last equation must be minimised when the output capacitor is selected. The peak-to-peak output current ripple is calculated using the following equation [60,61]: Having the output current ripple ∆I L , the inductor value could be calculated using the following: The secondary side peak current can be calculated using the equation The primary side current I pr pk is calculated from the secondary side current I sec pk , and the transformer turns ratio: The valley current will reach The primary side RMS current can be calculated using Transistors' conductive losses are given by the equation The switching ON P sw on and OFF P sw o f f losses are calculated from where the time ∆T is calculated from the gate drive charge Q GD and drive peak current I DRV pk : Primary side freewheeling diodes selection requires the primary side peak magnetisation current I mag pk and the rest time t rest to be calculated using The average current will be I mag average = F SW I mag pk × (t on + t rest ) 2 The secondary side diodes (D3 and D4) reverse voltage peak depends on the transformer turns ratio N ratio and maximum input voltage V in max : where k D is the diode derating factor. Considering the low-voltage secondary side, battery cell charge, it can be recommended that the range is k D = 0.6 − 0.7. The power dissipated from the rectifier D3 is calculated from the forward voltage drop V f : From the previous equation, the freewheeling diode D4 dissipates: The converter parameters, calculated according to the presented methodology, are shown in Table 3. Table 3. Two-switch converter design parameters (Figure 9).

Bi-Directional Battery Cell Equalising DC/DC Converter Analysis and Design
The selected topology for the DC-DC 2 ( Figure 2) is a transformer-less bi-directional buck-boost converter, shown in Figure 10. The converter comprises two MOSFET Q1 and Q2, inductor L1 and output capacitor C1. The SCES is connected on the primary side, and the battery cell (R1, V2) on the secondary side. The converter operates in buck mode charging the battery cell, or boost mode discharging the cell with overcharge.

Bi-Directional Battery Cell Equalising DC/DC Converter Analysis and Design
The selected topology for the DC-DC 2 ( Figure 2) is a transformer-less bi-directional buck-boost converter, shown in Figure 10. The converter comprises two MOSFET Q1 and Q2, inductor L1 and output capacitor C1. The SCES is connected on the primary side, and the battery cell (R1, V2) on the secondary side. The converter operates in buck mode charging the battery cell, or boost mode discharging the cell with overcharge. High side Q1 and low side Q2 transistors loss (Figure 10), respectively, and are calculated using [62,63] where is the peak ripple current value; is the minimum valley ripple current High side Q1 and low side Q2 transistors loss (Figure 10), respectively, P on−Q1 and P on−Q2 are calculated using [62,63] where I pk is the peak ripple current value; I valley is the minimum valley ripple current value; I out is the average output current; V out and V in are the output and input voltages; R on−Q1 and R on−Q2 are Q1 and Q2 ON resistances. The inductor L1 value ( Figure 10) can be determined from the above variables and the switching frequency F sw as follows: where the current ripple ∆I L on the inductor is calculated using The switching losses of both transistors P SW−Q1 and P SW−Q2 can be calculated based on the transistors' datasheet data for the rise t rise and fall t f all times and the switching frequency F SW as follows [62,63]: where V D−Q2 is the Q2 body diode forward voltage drop. The Q2 body diode reverse-recovery loss P D−Q2 is calculated using where I RR is the peak value of the body diode reverse recovery current; t rr is the body diode reverse recovery time; Q rr is the body diode reverse recovery charge. The dead-time loss depends on the rise t rise−DT and fall t f all−DT dead-times.
The gate loss can be calculated using the equation where Q gate−Q1 and Q gate−Q2 are the gate charges of the transistors Q1 and Q2; V GS is the gate voltage. The inductor loss P L−DCR depends on the inductor resistance R DCR : The output capacitor loss is The total converter loss is a sum of the above equations: P total = P on−Q1 + P on−Q2 + P SW−Q1 + P SW−Q1 +P D−Q2 + P DT + P Gate + P L−DCR + P C1 Output capacitor C1 ( Figure 10) is calculated using the equation where the DC is the duty cycle, and the V p−p is the peak-to-peak voltage ripple. The converter efficiency is estimated from the equation The designed converter parameters are given in Table 4. Table 4. Buck-boost bi-directional converter output design parameters ( Figure 10).

Battery Cell Equalisation Process Analysis
The battery cell equalisation is conducted in three operational modes: an undercharged cell is charged from the SC tank; an overcharged cell is discharged to the SC tank; cell-to-cell energy is transferred, respectively, from an overcharged to an undercharged cell in two different strings. As the first mode requires the SCES discharge, the impact of the same process on the tank energy parameters requires a more profound study. Figure 11 shows the SCES discharge process from a model based on Equations (1)- (27). The negative current (A) is determined according to its direction from the tank to the battery cell. The tank voltage reaches the accepted minimum voltage for 178 s (B), which determines an area of operation (ON) and an area with residual voltage (OFF) in each DC-DC converter that does not operate. The exact process determines the residual energy after the process is completed. Selected inductor (L1, Figure 10); Inductance/Rdc 150 μH, 50 mΩ (53), (54) Selected capacitor (C1, Figure 10)

Battery Cell Equalisation Process Analysis
The battery cell equalisation is conducted in three operational modes: an undercharged cell is charged from the SC tank; an overcharged cell is discharged to the SC tank; cell-to-cell energy is transferred, respectively, from an overcharged to an undercharged cell in two different strings. As the first mode requires the SCES discharge, the impact of the same process on the tank energy parameters requires a more profound study. Figure 11 shows the SCES discharge process from a model based on Equations (1)- (27). The negative current (A) is determined according to its direction from the tank to the battery cell. The tank voltage reaches the accepted minimum voltage for 178 s (B), which determines an area of operation (ON) and an area with residual voltage (OFF) in each DC-DC converter that does not operate. The exact process determines the residual energy after the process is completed.     Figure 13A-D shows the SCES charge from a battery cell. This mode of operation supports the battery cell discharge due to overcharge. Considering the parameters of the cell equalisation buck-boost converter (DC-DC 2, Figure 2), it could be suggested that during normal operation, the SCES is always charged to an initial voltage. In this design, the minimum input voltage in the buck mode of operation is accepted at 6 V. Therefore, the result of the charging process between the minimum and maximum voltage is as follows: (A) constant charging current 1 A determines the maximum battery cell discharge current of 2 A (1) and maximum voltage over the SCES of 10 V (2); (B) capacitor's peak power loss of 0.36 W giving an average power loss of 0.16 W; (C) peak (10 W) and average (4.57 W) power from the converter operating in boost mode; (D) peak (8829.89 J) and average energy (6250.70 J) transferred from the battery cell.   Figure 2), it could be suggested that during normal operation, the SCES is always charged to an initial voltage. In this design, the minimum input voltage in the buck mode of operation is accepted at 6 V. Therefore, the result of the charging process between the minimum and maximum voltage is as follows: (A) constant charging current 1 A determines the maximum battery cell discharge current of 2 A (1) and maximum voltage over the SCES of 10 V (2); (B) capacitor's peak power loss of 0.36 W giving an average power loss of 0.16 W; (C) peak (10 W) and average (4.57 W) power from the converter operating in boost mode; (D) peak (8829.89 J) and average energy (6250.70 J) transferred from the battery cell.
The same model is used to investigate the SCES charging process from the regenerative brake from the two-switch forward unidirectional converter (DC-DC 1, Figure 2). The results are depicted in Figure 13E The same model is used to investigate the SCES charging process from the regenerative brake from the two-switch forward unidirectional converter (DC-DC 1, Figure 2). The results are depicted in Figure 13E  The overall system's power loss depends on the converter's loss, capacitor's and battery cell's loss, depicted with models and simulations, and the switch's conductive loss. As a relatively high number of switches is required (Equations (1) and (2)), the number of active switches at each mode of operation and the conductive loss must be determined. As Table 5 shows, the SCES charge from the two-switch converter requires two unidirec- The overall system's power loss depends on the converter's loss, capacitor's and battery cell's loss, depicted with models and simulations, and the switch's conductive loss. As a relatively high number of switches is required (Equations (1) and (2)), the number of active switches at each mode of operation and the conductive loss must be determined. As Table 5 shows, the SCES charge from the two-switch converter requires two unidirectional switches, the battery cell equalisation of eight bi-directional switches, the battery cell equalisation with energy distribution between two cells requires twelve bi-directional switches, and the battery cell discharge requires eight bi-directional switches. Considering all switches are connected in series, and only the conductive loss applies, the MOSFET transistors could be selected for a relatively low voltage but high current, giving a low drain-to-source resistance. Therefore, for Qa1 and Qa2, a transistor SiJA22DP is used with an ON resistance R ON = 0.0005 Ω. For all other switches, a pair of transistors IPD50P04P4-13 is used, each having an ON resistance of R ON = 0.009 Ω. According to the maximum expected currents in the designed system, the total power loss in the switches can be assumed as acceptable, taking into account that they are covered by the power coming from the regenerative braking.

Experimental Setup
To verify the suggested system for battery cell equalisation based on SCES, a simple model has been prototyped and tested. The model consists of the designed DC-DC converters in Part 2, and the designed SCES with 100 F SCs. Five SCs are connected in series in string and seven strings in parallel, giving a total storage capacitance of 175 F. The battery pack has been presented with a fraction of a real automotive battery, consisting of four Li-ion battery strings in parallel with seven cells each. With this, the installed resources were enough to emulate all operation modes in actual conditions.
The experimental results depict the system's primary functions, presented with the experimentally recorded oscillograms in Figures 15-18 as follows. Figure 15 shows the SCES charging current and voltage from the DC-DC 1 converter (Figure 2). Probe 1 shows the current with the initial value of 100 A, and probe 2 shows the SCES voltage charge between 0 V and 10 V. The experiment supports the CV operation of charge. The experiment supports the simulations shown in Figure 5. The current is limited according to the converter parameters. The process continues for 12 s, simulating a charge from the regenerative brake of an electric vehicle. As shown, the peak current could be supported by the designed DC-DC converter, but the installed resource will not be fully used. Hence, the charging time exceeds the expected regenerative brake time, compromising the system's efficiency. of charge. The experiment supports the simulations shown in Figure 5. The current is limited according to the converter parameters. The process continues for 12 s, simulating a charge from the regenerative brake of an electric vehicle. As shown, the peak current could be supported by the designed DC-DC converter, but the installed resource will not be fully used. Hence, the charging time exceeds the expected regenerative brake time, compromising the system's efficiency.  Figure 16 shows the SCES charging with CC operation. The experiment supports the simulation results shown in Figure 6. The constant current is fixed at 100 A, which continues for 4.6 s. For this time, the voltage rises from 0 to the maximum of 10 V, after which the system operates with CV. The installed converter's maximum power is better used, and the charging time complies with the expected regenerative brake time. Both experiments support the validity of the designed two-switch converter (point 3.1, Figure 9) for SCES charge from the regenerative brake. Figure 17 shows the DC-DC 2 converter (Figure 2) in the buck mode of operation during a battery cell equalisation. Probe 1 is the current over the inductor L1, probe 2 is the voltage over the MOSFET Q1 (Figure 10), and probe 3 is the PWM signal to the Q1 gate. The voltage peaks over the transistor's drain-to-source are acceptable but could be limited with snubber capacitors. The calculated inductor of 150 µH is selected with a saturation current of 2 A, i.e., double the nominal current. This inductor could be further increased in order for the current ripples to be reduced.  Figure 16 shows the SCES charging with CC operation. The experiment supports the simulation results shown in Figure 6. The constant current is fixed at 100 A, which continues for 4.6 s. For this time, the voltage rises from 0 to the maximum of 10 V, after which the system operates with CV. The installed converter's maximum power is better used, and the charging time complies with the expected regenerative brake time.
Both experiments support the validity of the designed two-switch converter (point 3.1, Figure 9) for SCES charge from the regenerative brake. during a battery cell equalisation. Probe 1 is the current over the inductor L1, probe 2 is the voltage over the MOSFET Q1 (Figure 10), and probe 3 is the PWM signal to the Q1 gate. The voltage peaks over the transistor's drain-to-source are acceptable but could be limited with snubber capacitors. The calculated inductor of 150 µH is selected with a saturation current of 2 A, i.e., double the nominal current. This inductor could be further increased in order for the current ripples to be reduced.   Both experiments show the validity of the designed buck-boost converter in point 3.2, Figure 10. Figure 19 shows the SC discharge process (time T1) and SC charge process (time T2) due to battery equalisation. This experiment depicts the energy transferred to a battery cell for T1 = 50 s when the same is undercharged and the energy transferred from the battery to the SC tank for T2 = 10 s when the battery cell is overcharged. Probe 1 depicts the SCs tank voltage between the maximum 10 V and minimum 6 V, and probe 2 the current through the converter DC-DC 2 with a peak value of 1 A.  Figure 17 shows the DC-DC 2 converter (Figure 2) in the buck mode of operation during a battery cell equalisation. Probe 1 is the current over the inductor L1, probe 2 is the voltage over the MOSFET Q1 (Figure 10), and probe 3 is the PWM signal to the Q1 gate. The voltage peaks over the transistor's drain-to-source are acceptable but could be limited with snubber capacitors. The calculated inductor of 150 µH is selected with a saturation current of 2 A, i.e., double the nominal current. This inductor could be further increased in order for the current ripples to be reduced. Figure 18 shows the output DC-DC 2 voltage (probe 1) and current (probe 2) to the battery cell during the charging process. Probes 3 and 4 are the controlled PWM impulses to both Q1 and Q2 transistors at a switching frequency of 100 kHz.
Both experiments show the validity of the designed buck-boost converter in point 3.2, Figure 10. Figure 19 shows the SC discharge process (time T1) and SC charge process (time T2) due to battery equalisation. This experiment depicts the energy transferred to a battery cell for T1 = 50 s when the same is undercharged and the energy transferred from the battery to the SC tank for T2 = 10 s when the battery cell is overcharged. Probe 1 depicts the SCs tank voltage between the maximum 10 V and minimum 6 V, and probe 2 the current through the converter DC-DC 2 with a peak value of 1 A. Both experiments show the validity of the designed buck-boost converter in point 3.2, Figure 10. Figure 19 shows the SC discharge process (time T1) and SC charge process (time T2) due to battery equalisation. This experiment depicts the energy transferred to a battery cell for T1 = 50 s when the same is undercharged and the energy transferred from the battery to the SC tank for T2 = 10 s when the battery cell is overcharged. Probe 1 depicts the SCs tank voltage between the maximum 10 V and minimum 6 V, and probe 2 the current through the converter DC-DC 2 with a peak value of 1 A. Figure 19. Battery cell equalisation with SC discharge (T1) and charge (T2) periods. Probe 1 SC voltage (Red), and probe 2 SC current (Blue). Figure 19. Battery cell equalisation with SC discharge (T1) and charge (T2) periods. Probe 1 SC voltage (Red), and probe 2 SC current (Blue).
The final experiment depicts the functionality of the entire system. The obtained results comply with and complete the results obtained in [34,36,37].
The conducted experimental verification confirms the working capacity of the designed system, the possibility of completing all modes of operation, the stable operation of the designed converters and SCES, and the lack of oscillations and thermal losses in the converters and bi-directional switches.

Conclusions
In this paper, a battery cell equalisation system for automotive applications based on SCES has been analysed, designed, prototyped, and experimentally tested. The suggested system, presented in Figures 1 and 2, shows stable work, equalising the battery cells SoC with the ability to allocate each cell from the battery pack in order for the charge or discharge processes to be completed with only one DC-DC converter (DC-DC 2, Figure 2). For this purpose, bi-directional switches were implemented, operating with acceptable power loss (Table 5). A buck-boost topology with 1 A 12 V/5 V parameters was used for the battery cells' equalisation.
The system benefits from an additional SC tank used as ES to accumulate energy from the regenerative brake. For this design, the SC tank consists of a total capacitance of 175 F, a maximum voltage of 10 V, and an accumulated energy of 8750 J. The installed resource is enough for battery cell equalisation, according to the suggested topology in Figures 1 and 2.
The charging process is supported by a unidirectional DC-DC converter (DC-DC 1, Figure 2), converting the regenerative brake energy to the SC tank charge. It has been revealed that the converter's main parameters of 100 A nominal current, 300-500 V input voltage, and low 12 V output vulgate can be recommended for various automotive applications.
For the future development, design, and integration of the suggested system in automotive applications, the following recommendations could be systemised:

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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 (Figures 5-8). Also, the models can be used to depict the battery cell equalisation process and power transfer, as shown in Figures 11-14. The obtained results comply with the results published in [10,24].

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The charging of the SCES could be based on CC operation as presented in Figures 6-8. Charging the SCs with CV in this application should be avoided. The result complies with and completes the results in [29,30].

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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 mΩ − 500 µΩ can be recommended.

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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].

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The two-switch converter topology is a good choice for the SCES charge from the regenerative brake, operating stably in the entire input voltage range. The results comply with and complete the results published in [59][60][61].