A Multiport Converter for Flexible Active Balancing in Li-Ion Batteries

Active balancing techniques have become increasingly popular for mitigating voltage mismatches in series-connected lithium-ion (Li-ion) batteries. These techniques outperform passive balancing in enhancing battery capacity as the battery ages, leading to an increased lifetime, especially in the electric transportation sector, where residual capacitance plays a crucial role in determining battery lifespan. This study proposes a circuit configuration that utilizes a multiport active half-bridge converter for active cell balancing. The proposed method offers a high degree of flexibility owing to multiple operating modes and a relatively straightforward circuit configuration. Based on the state of charge of each cell, bidirectional power flow can be controlled between two or more arbitrary cells or between the entire battery string and a group of batteries. The proposed approach has been experimentally validated in a battery pack of seven Li-ion cells.

Abstract-Active balancing techniques have become increasingly popular for mitigating voltage mismatches in series-connected lithium-ion (Li-ion) batteries.These techniques outperform passive balancing in enhancing battery capacity as the battery ages, leading to an increased lifetime, especially in the electric transportation sector, where residual capacitance plays a crucial role in determining battery lifespan.This study proposes a circuit configuration that utilizes a multiport active half-bridge converter for active cell balancing.The proposed method offers a high degree of flexibility owing to multiple operating modes and a relatively straightforward circuit configuration.Based on the state of charge of each cell, bidirectional power flow can be controlled between two or more arbitrary cells or between the entire battery string and a group of batteries.The proposed approach has been experimentally validated in a battery pack of seven Li-ion cells.

I. INTRODUCTION
T HE widespread use of electric vehicles (EVs) is an impor- tant contribution to contrast climate change and to reduce the CO 2 emissions [1].However, several challenges need to be overcome to allow the diffusion of EVs, such as the implementation of effective charging infrastructures, improvements in battery technologies, and efficiency of the powertrain.Despite impressive advances in battery technologies, some relevant improvements are still needed to optimize the battery pack [2].
Lithium-ion (Li-ion) batteries usually have a nominal voltage of about 3.6 V and a wide variation in nominal capacity depending on the technology [3].As a higher voltage is required in EV applications, battery packs are realized with hundreds of cells connected in series [4].To ensure the optimal performance and longevity of the battery, a battery management system (BMS) is imperative to safeguard against harmful conditions such as overvoltage and excessive temperature.The BMS plays a key role in protecting Li-ion battery packs by continuously monitoring the voltage levels of individual cells within the pack, preventing them from operating outside the safe voltage range [5].
Moreover, the principal function of a BMS for a multicell battery pack is the charge equalization.Due to manufacturing variability, cell architecture, and usage-related degradation, individual cells typically present variations in terms of capacity and impedance [6].These differences are limited in brand-new cells but increase over the pack life due to slightly different initial and operating conditions [7].Thus, even if they are charged with the same current, the cell voltages in the string could be different and can worryingly reach the limits of their safe operating area.Thus, a balancing circuit is needed to ensure uniform cell voltages.
According to the literature, the main balancing techniques are based on passive and active approaches [8], [9].In the passive solution, excess energy is dissipated during charging, whereas in the active one, it is shared between other cells, even during discharging [10].The main drawback of the passive solution is the capacity degradation of the battery string is driven by the most degraded cell.Instead, with active balancing, the battery capacity is determined by the average cell capacity.Accordingly, the active balancing circuit enables a much longer battery life when this is determined by the residual capacity, as in EV applications.
The main shortcoming of active balancing techniques is related to the higher cost compared to the passive solution due to the higher number of components required.However, when the voltage differences between cells become significant, especially in second-life applications, the active balancing techniques allow the extension of battery pack run-time as they allow the extraction of all the energy stored in it [11].
The battery equalizers are often classified based on the energy transferring paths [12], [13].The adjacent-based topologies allow us to exchange energy only between adjacent cells [14], [15], [16] or modules [17].The nonadjacent-based ones employ active equalizers connected to each cell or module and the whole battery pack to transfer energy between them [18], [19].Finally, the mixed topology allows energy exchange between cells that may or may not be adjacent and the entire string or module [20], [21].
A widely used active balancing circuit is based on the switched capacitor network [15], [16].This technique is easily implementable but not very efficient [12].In [14], an active balancing circuit is proposed, where an LC series resonant circuit is used as the energy carrier, reaching higher efficiency and allowing the balancing only between adjacent cells.
In the literature, several active equalizers based on dc-dc converters have been discussed [20], [22], [23], [24].In [24], the dc-dc converter is connected to the cells through a matrix of switches providing modularity and high efficiency but allowing the balancing of only one cell at a time.Furthermore, because of the high number of switches, protection against short circuits must be guaranteed.In [23], the series-connected battery string is divided into modules, and a transformer is used to transfer energy between modules but not within the cells of the same module.In [20], a two-layer modular configuration is proposed: The low-level layer transfers energy between adjacent cells using a buck-boost converter while the high-level layer groups the cells into modules interconnected with a multiport converter.
This article presents a novel mixed-topology equalizer that offers a high degree of flexibility in the active balancing of series-connected Li-ion batteries, building upon the prior work presented in [21].The proposed circuit employs a multiport active half-bridge converter (MAHB) converter in parallel with the battery cells, along with a multiwinding transformer (MWT), enabling the operation in both cell-to-cell (c2c) and pack-to-cell (p2c) modes.The key contribution of this research is the introduction of a circuit configuration that, in contrast to similar techniques utilizing dc-dc converters, offers a wide range of options for balancing modes while simultaneously maintaining low circuit complexity and requiring only a limited number of components.
The rest of the article is organized as follows.The proposed equalizer is analyzed with its operating modes in Section II.The design is sketched in Section III focusing mainly on the MWT.In Section IV, a prototype with seven series-connected Li-ion cells is used to validate the effectiveness of the proposed solution.Section V reports a comparison with other active equalizers.Finally, Section VI concludes this article.

II. PROPOSED EQUALIZER
Fig. 1 displays the design of the proposed equalizer that utilizes a MAHB converter, which involves a primary half-bridge (HB) that is positioned parallel to the battery string and connected to each cell via an MWT and an additional HB.The transformer's turn ratio is equivalent to the number of cells in the string.
The main properties of the proposed equalizer are summarized as follows: 1) flexible power flow, two operating modes can be implemented, the c2c and the p2c modes.The first transfers energy between any two cells (e.g., from the highest charged cell to the lowest one), and the second between any cell and the full string.In both modes, two or more cells can be balanced simultaneously; 2) single magnetic element, the proposed topology uses a single high-frequency MWT boosting the power density; 3) high efficiency, with the proper design of the transformer, zero-voltage switching (ZVS) operation can be ensured for a wide range of balancing currents; 4) simple control, the control strategy is based on well-known phase-shift modulation.The  control signal is applied only to the cells exchanging energy while all other switches are kept OFF, improving efficiency and simplifying the control.Furthermore, the modulation scheme could be improved to increase the efficiency as shown in [25].
The possible operating modes featured by the proposed equalizer are set out in more detail ahead.The analyses are carried out using the well-known operation of the dual active HB (DAHB) converter.The MWT is modeled, as shown in Fig. 2. The magnetic inductance L μ is considered at the primary side (i.e., at the battery string side), and the leakage inductances and resistances of the string and cells windings are marked as L 1 -L 2,h and R 1 -R 2,h , respectively.The MWT model is connected with two voltage sources emulating the 2-level waveforms provided by the HBs at each side.Supposing constant the voltages at the capacitive voltage dividers (i.e., C 1 -C 2 and C 3,h -C 4,h ), v 1 can vary between ±V S /2 while v 2,h between ±V C,h /2.The model of Fig. 1 can be extended for c2c mode by considering connecting another cell to the 1-port.
Assuming negligible magnetizing current and winding resistances, the power transferred from the 1-port to the 2-port of the MWT follows the relationship of a conventional phase-shift modulated dual active bridge (DAB) converter as where V 1 and V 2,h are the dc voltage amplitudes at 1-port and 2-port, respectively, f s is the switching frequency, n is the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.transformer turns ratio at the considered ports, L is equal to the sum of leakage inductances at the primary side (i.e., ), and ϕ is the phase shift between the voltage waveforms [26], [27].The main waveforms at two ports of the MWT are reported in Fig. 3.
In the c2c mode, a symmetrical structure of secondary windings minimizes the mismatch among the control parameters of the energy transfer law between cells, making it independent of the positioning of cells along the battery string.As the number of cells increases, the design complexity escalates drastically and maintaining symmetrical operation becomes progressively more challenging.The maximum number of secondary windings is then limited to ensure symmetry for all secondary windings and maintain a compact transformer design (e.g., not far exceeding 10 units).
The proposed architecture can be extended to accommodate more series cells by subdividing the battery string into smaller modules.This approach enables the system to retain the desired symmetrical operating condition while effectively managing a higher number of cells and, thus, a higher rating power.

A. c2c Mode
The c2c mode aims to balance two different cells exchanging power between them.The PWM controller drives only the two HBs connected to the cells concerned while all other unnecessary switches are OFF.Starting from (1) and considering that the voltage across the transformer in an MAHB is half that of a DAB, the transferred power P c2c C between the hth and the yth cell is with V C,h and V C,y are the voltages at the active cells and n = 1.
As can be noted in (2), the direction of power transfer between the hth cell and the yth cell depends on the sign of the phase shift ϕ.The power is transferred from hth cell to yth cell if ϕ > 0 and vice versa.This bidirectional power transfer capability allows energy to be transferred between two cells regardless of the cell voltages.This feature overcomes a significant limitation of techniques that rely on energy tanks, such as switched-capacitor and LC-tank methods, where energy transfer is accomplished through switches connected in parallel with the cells [15].These tank-based approaches face challenges when implemented in systems with low voltage differences between cells.For instance, Li-ion battery cells typically cannot have a voltage difference exceeding 0.1 V [28].Consequently, the narrow voltage gap between cells makes it difficult for the equalizer's switches to conduct properly, leading to residual voltage imbalances among the cells.Fig. 4 depicts an example of the c2c mode, wherein the energy transfer occurs from cell V C,h to cell V C,y .

B. p2c Mode
The p2c mode purposes transferring energy from the battery string into a single or more cells and vice versa.This highflexibility feature allows choosing the most appropriate power flow direction according to the state of charge (SOC) of each cell.
In the p2c operating mode, the PWM signals are used to drive the HB placed on the primary winding (i.e., string side) and those corresponding to the cells to be charged or discharged.All the other switches are OFF, reducing the converter losses.
Assume, for the sake of simplicity, to charge the cell with the lower SOC in the string.The power equation is slightly different concerning the c2c mode (2), as power is provided by the entire battery pack, and different windings are involved.
The power injected into the cell is C is a fraction of the processed power by MAHB, namely P MAHB = V S I S as where V S is the voltage of the entire battery string.Analogously to ( 2) and (3) can be expanded as The sign of the phase-shift ϕ depends on the direction of the power flow, with ϕ > 0, the power is given from the string, and L = L 1 + n 2 L 2,h .When multiple cells are charged or discharged simultaneously, the energy-transfer inductance L changes as a function of the total number of activated cell-side converters.Fig. 5 reports the power flows in the case of packto-multicell with two cells activated.In this scenario, the entire battery pack is used to charge V C,1 and V C,y cells.

C. Additional Relevant Operating Modes
The particular structure of the equalizer can be exploited for additional operating modes that are not strictly related to active Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.balancing.Smart diagnostic techniques, such as electrochemical impedance spectroscopy (EIS), can be implemented by the proposed structure by controlling the current injected into the cell (e.g., injecting a sinusoidal current perturbation).Usually, the measure of Li-ion battery impedance requires an external current source to provide the perturbation signal [29], [30].The proposed solution can perform the EIS without external sources or dc biases thanks to the bidirectional capability of each HB module.
The basic concept of impedance measurement methods is to inject limited sinusoidal currents i S (jω) into the battery at different frequencies and collect its voltage response v S (jω).The amplitude of the signal should be large enough to ensure a sufficient signal-to-noise ratio of the response without exceeding the linear range of the amplifier and/or current generator.The impedance Z S (jω) can be calculated as The real and imaginary parts of the impedance Z S are usually reported in the Nyquist plot allowing for some qualitative and quantitative considerations.

III. CONVERTER DESIGN
The converter design presented in this study adheres to the established design of the multiport active bridge described in [27].The maximum string voltage is 29.4 V and 4.2 V for the cells.Additionally, the maximum output current is determined by considering the batteries' parameters in Table I, ensuring that the converter operates within the specified current limits.To limit the current ripple within the cells, the output inductor L o is carefully selected.However, in the presented solution, the main design bottleneck is the MWT.A design is proposed herein starting from the most demanding condition of MAHB.
During the p2c operation, a subset K (whose cardinality is k < n) of the cells composing the pack are mainly involved in the energy transfer process, meaning the corresponding HB at the secondary side of the MWT is working.Assuming to charge k cells in the p2c mode, the power processed by MAHB, namely P MAHB , is given by the power provided by the string, which will be equal to the total power transferred to the active cells in the secondary branches such that From ( 6), P MAHB can be expressed as a function of the required power from each active cell P C,h , as Assuming the battery string voltage is close to its maximum voltage V S n VC and charges the cells with the same current I C , (7) becomes The maximum allowed current ÎC must guarantee a string current lower than the maximum discharge current of the cells I dis , such that At the same time, ÎC must be lower than the allowed one provided by the manufacturer I ch , so the limit of charging current will be dependent on the number of active cells.The limit condition of (10) defines a maximum number of cells k charging at I ch (i.e., maximum current) as The condition of (11) defines the operating point with higher transferred power.Substituting (10) into (8), the maximum processed power by MAHB saturates at PMAHB = n VC I dis in case the battery stack is composed by n > 1 + I dis /I ch .In this condition, the string current is equal to I dis , which is the target current for the primary winding design.Remarkably, secondary windings are designed to provide the corresponding current at the cell port (i.e., I s,i = I S + I ch ).The rms current of the primary winding I rms 1 is a function of the pack voltage V S , the phase-shift ϕ n = ϕ/π and the cell voltage V C [31], as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
Supposing to transfer the maximum power at ϕ n = 0.5 (ϕ = π/2), (12) can be simplified using ( 7) and ( 4) as Since the primary current is shared among k active cells, the rms value of each secondary winding Îrms 2 is given by To design of MWT, ( 13) and ( 14) constraints the needed wiring cross-section A w selecting a reasonable current density J rms , as with N p and N s are the number of turns of primary and secondary windings, respectively.Considering to reach the maximum value of the flux density B pk in the core at the minimum switching frequency f s,min , the maximum flux is given by where A e is the cross section of the magnetic core.Combining ( 15) and ( 16), the cross-section product A e A w can be used for the choice of a proper core with k w the filling factor of the winding area.Chosen a feasible core satisfying (17), the other design parameters of the MWT are calculated going consecutively backward through the found relations.

IV. EXPERIMENTAL RESULTS
To validate the effectiveness and functionality of the proposed architecture, an experimental prototype has been designed, as shown in Fig. 7.The design phases are thoroughly supported by simulations and tests conducted on LTSpice.By employing LTSpice, various performance parameters and characteristics are analyzed and optimized to ensure the prototype's reliability.The results reported in this section are obtained using the experimental prototype.

A. Experimental Setup
The prototype aims to demonstrate the feasibility of active balancing on a small-scale setup using a battery pack with seven Samsung IRF18650 cells connected in series (see Table I).
The MAHB BMS prototype features eight HB converters operating at a frequency of 100 kHz, one for the primary side and one for each cell.Each HB has two Nichicon RR5 FPCAP aluminum electrolytic capacitors and a Texas Instrument CSD87333 NexFET PowerBlock driven by a Skyworks SI8232AC dual isolated gate driver.

TABLE II PARAMETERS OF THE MWT
at the primary and 2 turns for the secondary.The secondary windings are twisted together, entailing similar transformer parameters concerning the primary winding and the other secondary.The twisted structure guarantees good symmetry improving the control of the BMS also.The transformer parameters are shown in Table II.
The BMS additional features, such as intermediate voltage monitoring and temperature readings, are provided by a Linear Technology LTC6810 multicell battery stack monitor.It is interfaced with a Texas Instrument LAUNCHXL-F28379D microcontroller board, which also generates the PWM signals for the HBs.In addition, the output current of the battery string is sensed through a TMCS1108 (Hall-effect sensor) implementing overcurrent and short-circuit protections.
The prototype board is reported in Fig. 7, highlighting the main parts of the BMS.The microcontroller is not visible in the picture as it is located on the bottom side of the board.
The key parameter of active-type BMS design is the balancing current.The selected value depends on the quality of the cells (e.g., high-quality cells have lower unbalances and therefore less  current is required), the used components, and the application.The dataset in [32] is used to find a reasonable value of balancing current.A Monte Carlo analysis is performed to achieve the same performance as a passive BMS with a balancing current of 150 mA.The proposed converter is designed with 2.25 A of the maximum cell current in the p2c mode and 1.5 A in the c2c mode.
Fig. 8 shows the current value in the p2c mode as a function of the phase shift ϕ at V S = 26.87V and V C = 4.15 V of the battery string and cell voltage, respectively.

B. Efficiency Analysis
Several tests are carried out to measure the efficiency of the proposed equalizer in both operating modes for different cell voltages and switching frequencies.
In Fig. 9, the efficiency of active BMS is shown in the c2c mode for different switching frequencies f sw as a function of the transferred power P c2c C between two cells at 4.2 V and 4.1 V, respectively.Fig. 9 shows the peak efficiency reached at f sw = 50 kHz.As outlined by (2), for a given transferred power, as the switching frequency f sw decreases, the phase-shift ϕ decreases also (e.g., ϕ = 9 • at f sw = 50 kHz compared to ϕ = 27 • at f sw = 200 kHz.This behavior may cause control issues, asking for a tradeoff between efficiency and controllability.In the current design, the switching frequency of 100 kHz is chosen.
The efficiency also depends on the mismatch and the absolute values of the cell voltages.In Fig. 10, the efficiency curves for different cell voltages are reported as a function of the required power.The maximum efficiency of 91.7% is reached with 4.2 V and 4.1 V cell voltages with a phase shift of 6 • corresponding to 1.68 W of transferred power.
The efficiency curves in the p2c mode are shown in Fig. 11.As in the previous case, the efficiency is analyzed as a function  of string and cell voltage.Unlike in the c2c mode, the maximum efficiency is constant across the three considered test conditions (around 96.3%).

C. c2c Mode
Recalling Section II-A, this operating mode is used to transfer energy between two cells through HBs connected to the secondary windings.Main voltage and current waveforms are shown in Fig. 12 with two cells at the same voltages V C = 3.95 V, ϕ = 20 • , I C = 910 mA, and P c2c C = 3.6 W. The results are consistent with the theoretical analysis and the simulations.
The not perfectly trapezoidal shape of the current in Fig. 12(b) is due to the small leakage inductance of the secondary and the nonnegligible resistance of the current path, mainly in the transformer windings.

D. p2c Operating Mode
As reported in Section II-B, the proposed equalizer is also aimed to transfer power from the entire battery string to a single cell.Main voltage and current waveforms are depicted in Fig. 13 with V C = 3.85 V, V S = 25.9V, ϕ = 20 • , I C = 1.65 A, I S = 300 mA, and P C = 6.35W.
From the observation of the currents in Fig. 13(b), it is clear the efficiency in c2c is lower than in the p2c mode because of the lower rms current on the power-feeder HB.

E. Balancing Test
To verify the effectiveness of the proposed solution for achieving balance among Li-ion cells, a balancing test is conducted.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Initially, the c2c operating mode is examined by employing a test case composed of two batteries with distinct SOC levels.The SOC is estimated by employing a well-established relationship between the open-circuit voltage (OCV) and the remaining capacity.
An experimental test is carried out to determine the SOC as a function of the OCV of the cell.As the SOC-OCV relationship is derived under no-load conditions, the SOC estimation during normal operating conditions must be corrected.Considering  the voltage drop caused by the cumulative internal resistance, the OCV can be resolved for a given current flowing through the cell.The EIS test capability of the proposed equalizer is used to estimate the total internal resistance as described in the following.
The two batteries employed in the c2c test initially have a voltage of 4.02 V and 3.60 V, respectively, with a SOC of 38% and 85%.Consequently, the more charged cell transfers energy to the more discharged one by activating only the HBs of the two cells with a positive phase, in accordance with (3).
The balancing process is considered complete when the voltage difference among the two cells is below 15 mV in magnitude.The threshold is chosen considering the maximum error in SOC estimation (below 3%) and the tradeoff between quantization, accuracy, and noise in the voltage measurement system.The balancing process lasts 70 min with both cells at 3.67 V with a final SOC = 53%, as shown in Fig. 14.The operating efficiency, computed as the ratio between the initial SOC and the final one is 80.2%.
The architecture of the proposed solution allows for the packto-multicell operation in which energy is transferred between the battery pack and more than one cell simultaneously.A string of seven Li-ion batteries with voltages between 3.6 V and 4.2 V is used for testing this balancing operation.The balancing algorithm shown in Fig. 15 is used.The initial step involves the measurement of all cell voltages within the system and their subsequent arrangement in ascending order, ranging from 1 to 7. Cells exhibiting a voltage difference of less than 10 mV are categorized as balanced and assigned with the same index.If the voltage difference ΔV between the most and least charged cells is below 40 mV, the string is considered fully equalized,

TABLE III INITIAL FINAL STATES OF THE P2C BALANCING TEST
and the balancing process is concluded.Alternatively, the p2c mode is employed to transfer energy from the string to the least charged cell(s) identified by index 1.This procedure is repeated, following the representation in Fig. 15, until the state of a balanced string is achieved.The test lasts 126 min as shown in Fig. 16.The battery string voltage reaches a final value of 26.61 V with a voltage mismatch between the cells of 24 mV.
During the balancing phase in the p2c mode, the assessment of operating efficiency can be conducted by examining the initial and final states of the balancing test.The recorded data presented in Table III reveals that the average initial SOC is 73.2%.Following the completion of the balancing operation, an average SOC of 66.5% is observed.Based on these measurements, an overall efficiency of 90.9% is recorded.

F. EIS Analysis
The measure of the impedance in Li-ion cells with the proposed solution is demonstrated herein.
The impedance measurement is performed using two converters placed on the secondary side (i.e., as in the c2c mode).The current signal injected into the tested cell is a sinusoidal perturbation at a frequency between 5 Hz and 1.2 kHz.The measured string voltage is then analyzed with the software tool frequency response analyzer (SFRA) provided by Texas Instrument.Measurements are carried out in 21 points requiring an overall time of about 42 s.
Fig. 17 shows the waveform of the current signal injected into the cell.One of the advantages of using the proposed solution to perform impedance measurement lies in using a zero-mean perturbation signal.In addition, the energy balance of the measurement is virtually zero since, during the measurements, two cells exchange energy symmetrically.
In the literature, there is no absolute indication of the minimum excitation current to make an accurate measurement of the battery impedance [33].Several tests are performed using different current amplitudes from 10 mA to 600 mA (i.e., a fraction of 1 C rate by the rule of thumb).The EIS test is reported in Fig. 18.The current magnitude is selected to guarantee a good  ratio between the battery voltage response and the superimposed switching noise.For example, the voltage response is almost comparable to the switching noise with an amplitude of 10 mA, providing inaccurate measurements, as shown in Fig. 18.

V. COMPARISON WITH CONVENTIONAL EQUALIZERS
Table IV presents a comprehensive assessment of the proposed equalizer, comparing it to conventional bidirectional balancers.The evaluation focuses on three key criteria: 1) components; 2) functionality; and 3) performance.The components index provides an estimation of the cost for each equalizer by specifying the number of components involved.The functionality index offers insights into the working principle, including the operating mode and potential auxiliary functions.Finally, the performance index quantifies the performance of the equalizers based on information regarding peak efficiency for each operating mode.(Note: "-" in the efficiency tab indicates that only efficiency for a specific operating mode is provided.) To facilitate a numerical comparison of circuit performance in terms of control simplicity, modularity, and equalization speed, the fuzzy comparison method can be employed as in [17].In this method, each parameter can be converted into fuzzy scales, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE IV COMPARISON OF THE PROPOSED EQUALIZER WITH CONVENTIONAL BIDIRECTIONAL EQUALIZERS
where "1," "3," and "4" represent poor, satisfactory, good, and excellent performances, respectively.The evaluation of equalization speed is computed by considering the ratio between the balancing time and the difference between the most charged cell and the most discharged cell.
The proposed solution exhibits a comparable number of components compared to existing solutions found in the literature, as indicated in [19], [22], and [34] or slightly lower [15], [35].However, it possesses a significant advantage in terms of flexibility.Unlike conventional equalizers, the proposed MAHB enables cell-to-any-cell operation as well as pack-to-multicell operation.Notably, the latter functionality is absent in any of the previously proposed solutions.Additionally, similar to the capability described in [35], the MAHB allows for EIS analysis to be performed on any individual cell.
In terms of performance, the proposed solution outperforms other equalizers, achieving higher efficiency levels across all operating modes.Specifically, it allows the same efficiency level as the solution presented in [17] during c2c operation.Furthermore, the control algorithm of the proposed solution, based on well-established phase-shift modulation, is straightforward to implement, similar to the approach described in [22].

VI. CONCLUSION
This article proposed an architecture for an equalizer that provides several advantages, including power flow flexibility, reduced component count, and the possibility of ZVS operation.Experimental testing through a prototype confirmed the effectiveness of the proposed architecture in terms of flexible balancing while also exhibiting good efficiency results under various operating modes and voltage conditions.Furthermore, this article highlighted the efficacy of the impedance spectroscopy analysis feature without negatively impacting the SOC of the battery pack.The MWT represented the bottleneck of the proposed solution, as its symmetrical characteristics need to be maintained even with an increasing number of cells connected to the secondary.Consequently, the complexity of the design escalated, rendering the task of ensuring symmetrical operation progressively more arduous.Overall, this study provided a promising solution for managing battery imbalances in EV applications, and the proposed architecture offered several advantages over existing equalizer designs.Prospective future research developments may include improvement of the magnetic part design, further investigation on possible balancing algorithms, and the usage of artificial intelligence techniques.

Fig. 2 .
Fig. 2. Equivalent circuit of the MWT in p2c mode.This model is valid also to the c2c operation.

Fig. 3 .
Fig. 3. Key waveforms for a DAB.(a) Voltages at the transformer terminals.(b) Current across the transformer leakage inductances.
C where I C = I O − I S with I O the output current of HB and I S the string current, as shown in Fig. 1.Considering unitary efficiency (i.e., V S I S = V C I O ), the power transferred to the cell P p2c

Fig. 8 .
Fig. 8. p2c cell current as a function of phase shift ϕ with V S = 26.9V and V C = 4.1 V.

Fig. 9 .
Fig. 9. Efficiency curves as a function of transferred power for different switching frequencies in the c2c operating mode with cells at 4.2 V and 4.1 V.

Fig. 10 .
Fig. 10.Efficiency curves as a function of cell voltages in the c2c operating mode.

Fig. 11 .
Fig. 11.Efficiency curves as a function of cell voltages in the p2c operating mode.

Fig. 12 .
Fig. 12. Experimental waveforms in the c2c mode with a phase shift of 20 • .(a) HB output voltages.(b) Current on the primary and on the secondary winding of the transformer and the output current injected into the cell.

Fig. 13 .
Fig. 13.Experimental waveforms in the p2c mode with a phase shift of 20 • .(a) HB output voltages.(b) Current on the primary and on the secondary winding of the transformer and the output current injected into the cell.

Fig. 14 .
Fig. 14. Results of the balancing test in the c2c operating mode.

Fig. 16 .
Fig. 16.Results of the balancing test in the p2c operating mode.

Fig. 18 .
Fig. 18.EIS test performed in a singular Li-ion cell with different current amplitudes.The test is carried out in 21 points between 5 Hz and 1.2 kHz.

TABLE I SPECIFICATIONS
OF SAMSUNG LI-ION BATTERY CELL ICR18650-26JM