Hierarchical State-of-Charge Balancing and Second-Harmonic Current Suppressing Control With a Scalable DC Reconfigurable Battery Pack

This article presents a hierarchical balancing architecture for the dc reconfigurable battery pack (RBP) with a modular design. The battery cells in the RBP are divided into several modules, and each module is equipped with a slave controller that is only responsible for a subset of cells. The system controller performs the closed-loop control and allocates the desired voltage steps into battery modules. The proposed architecture can significantly reduce communication and computation requirements for large-scale applications. Moreover, considering the second-harmonic current (SHC) widely existing in a single-phase dc/ac system, which may induce the aging of battery cells, the dc RBP is used to suppress the SHC for the first time without an additional central dc/dc converter. Due to the high output voltage quality and low-frequency operation of the dc RBP, the filter size can be significantly reduced. Experimental validation of the proposed control scheme is demonstrated through the utilization of a dc RBP comprising 48 3-Ah 18 650 lithium-ion cells. The experimental results demonstrate that the proposed method achieves effective battery cell balancing and SHC suppression.

Abstract-This article presents a hierarchical balancing architecture for the dc reconfigurable battery pack (RBP) with a modular design.The battery cells in the RBP are divided into several modules, and each module is equipped with a slave controller that is only responsible for a subset of cells.The system controller performs the closed-loop control and allocates the desired voltage steps into battery modules.The proposed architecture can significantly reduce communication and computation requirements for large-scale applications.Moreover, considering the secondharmonic current (SHC) widely existing in a single-phase dc/ac system, which may induce the aging of battery cells, the dc RBP is used to suppress the SHC for the first time without an additional central dc/dc converter.Due to the high output voltage quality and low-frequency operation of the dc RBP, the filter size can be significantly reduced.Experimental validation of the proposed control scheme is demonstrated through the utilization of a dc RBP comprising 48 3-Ah 18 650 lithium-ion cells.The experimental results demonstrate that the proposed method achieves effective battery cell balancing and SHC suppression.Index Terms-Battery management system (BMS), cell balancing, multilevel converter, reconfigurable battery pack (RBP), second-harmonic current (SHC).

I. INTRODUCTION
I N CONVENTIONAL battery packs, cells are fixedly con- nected in series and parallel to satisfy high capacity and voltage requirements [1].However, due to variations in manufacturing processes and operational circumstances, there are inconsistencies in the parameters, such as the capacity and internal resistance among cells [2], [3].It is therefore that the battery pack's performance is limited by the weakest cell [4], and extra passive or active balancing circuits are required in conventional battery management systems (BMSs) to improve the battery pack's performance [3].However, these balancing circuits typically have a slow balancing speed to reduce cost and volume [5], and there is additional energy lost during the equalization processes.
In recent studies, large-scale reconfigurable battery packs (RBPs) and associated BMSs are an emerging solution to replace hard-wired HV battery packs and conventional BMSs [1], [6].Individual battery cells in RBPs are equipped with additional power switches, allowing the change of battery interconnection pattern during operation [7].The reconfigurable design enables active balancing by adjusting the duty cycle of each cell according to their relative state-of-charge (SOC) [8], enhances fault tolerance by bypassing the defective cell [9], and has been proven to have better performance compared to conventional energy redistribution balancing methods [8].In addition, the reconfigurable design has been confirmed to have higher efficiency compared to a conventional battery pack with a power converter for high-power applications [10], [11], [12].
A variety of reconfigurable topologies have been proposed [1], which can be divided into AC RBPs [13], [14], and dc RBPs [15], [16] by the output voltage.The typical dc RBP equips each cell with a half-bridge circuit, which is the most widely studied and applied due to its low complexity [11], [17], [18].An additional central dc-ac converter is required for grid applications.The ac RBPs usually use the cascaded H-bridge topology to eliminate the need for a monolithic DC-AC converter, which features excellent output quality, low-frequency operation, and flexible management of batteries [13], [14], [19].However, the ac RBPs implement a string of battery cells per phase, so the second harmonic current (SHC) will penetrate battery cells [20], [21].According to earlier studies, the ac harmonic currents will cause indirect aging of cells by raising their temperature [22], and the increased charge throughput may also shorten the life of cells [23].Moreover, in ac RBPs, four-quadrant circuits are required for each module to form a bipolar output voltage, but in dc RBPs, only unipolar circuits are required, reducing the cost and complexity of the system.Due to the above-mentioned advantages, there have been emerging studies on the DC RBPs in recent years.However, most of them are verified by a laboratory prototype including a small number of battery cells and a flat BMS [17], [18], [24].A centralized controller is in charge of keeping track of each cell's state (cell voltage, SOC, etc.), processing the data, and supplying the switching signals for the active switches in the flat BMS.However, this type of architecture is unable to manage hundreds and thousands of battery cells in practical applications, where the computational burden and communication delay increase to an unacceptable level [25].The modular BMS, which has a system controller and several module controllers, each controlling only a subset of battery cells, provides simple scalability [7].In previous studies, many hierarchical SOC balancing algorithms have been developed for hard-wired battery packs and conventional BMSs [26], [27], [28].In conventional battery systems, additional passive or active balancing circuits are used to achieve SOC balancing, with operations being independent of the main circuit.In addition, the SOCs of batteries do not change quickly.Consequently, this type of hierarchical SOC balancing algorithm does not require a high data throughput between controllers.For the RBPs, the SOC balancing operations are achieved by adjusting the equivalent operating duty cycle of battery cells according to their SOCs [8].In recent studies, hierarchical SOC balancing schemes have been proposed for the dc RBPs [29], [30].However, the adopted dc RBPs do not function as converters, making them unable to be used for stabilizing bus voltage and suppressing harmonics.For the dc RBPs that function as multilevel converters, the switching signals need to be updated at a relatively high rate and with low latency to accurately track the reference and maintain stability.As a result, the hierarchical SOC balancing algorithms for the dc RBPs have stricter requirements compared to those for conventional battery systems.These include high data throughput, real-time capability, and time-synchronous switching.To the best of the author's knowledge, no research has been conducted on the hierarchical SOC balancing algorithm specifically designed for dc RBPs with a modular architecture.
To fill this research gap, in this article, a hierarchical SOC balancing control scheme for the scalable dc RBP working as a multilevel converter is proposed, as shown in Fig. 1.It can be seen that the battery cells and corresponding half-bridges are divided into several modules, and each module is equipped with module controller.The module controller is responsible for monitoring the cells' states, processing the data, and supplying the switching signals for the active switches in the module.The SOC balancing control can be divided into the module layer and cell layer, where the module layer balancing is performed by distributing the voltage steps for each module in proportion to their average SOC, and the cell layer balancing is achieved by choosing the cells in the module to be engaged and bypassed according to the SOC sorting result.The system controller is used to produce the overall voltage steps for the whole system and then distribute them to each module.Therefore, there is limited information exchanged between the system controller and module controllers, which reduces the communication loads and thus makes the system easy to scale.
Moreover, the SHC problem in ac RBPs also exists in dc RBPs when they are connected with a single-phase dc/ac converter for grid applications [20], [21].In previous studies, a central dc/dc converter, which connects the battery pack and the dc/ac converter is most commonly used to suppress the SHC [31], [32].However, the additional dc/dc converter increases the cost, loss, and volume of the system.Considering that the dc RBP is, in essence, a modular multilevel dc/dc converter [24], [33], the SHC suppression method implemented by the dc RBPs is then developed for the first time, which greatly saves the inductor's volume and weight by reducing the inductor's current ripple [24].The main contributions of this article can be summarized as follows.
1) A specifically designed hierarchical SOC balancing scheme is developed for the dc RBPs functioning as converters, reducing the computational and communication loads of controllers.
2) The SHC suppression method is implemented with the dc RBPs for the first time, reducing the volume and weight of the system.The rest of this article is organized as follows.Section II describes the principle of SOC balancing using a dc RBP with nearest-level control pulsewidth modulation (NLC-PWM).Section III explains the hierarchical SOC balancing algorithm based on the proposed dc RBP.Section IV describes the SHC suppression method using the proposed dc RBP.In Section V, a laboratory prototype containing 48 3-Ah 18 650 lithium-ion cells that are divided into three modules is developed to validate the proposed approach.Finally, Section VI concludes this article.

II. PRINCIPLES OF SOC BALANCING USING A DC RBP WITH NLC-PWM
The basic unit in the dc RBP is the combination of a battery cell and half-bridge, which is referred to as a submodule (SM) in this article.The switches of each SM operate in complementary conduction mode.When the upper switch is turned ON, the battery cell can be charged or discharged, and the battery cell is always bypassed when the lower switch is turned ON.The dc RBP is in essence a multilevel buck converter [16].Thus, all existing multilevel modulation techniques can be implemented on the dc RBP [34].When selecting the modulation technique for the RBP, a tradeoff should be made between effectiveness, computational complexity, and filter volume.The Initialize the sum of the average SOC of all unallocated modules SOC sum = 0; 5: end for 8: Read the ID of the module to be allocated in this Calculate the engaged cell number for the idth module by Update the available cell number in the idth module Update the unallocated voltage levels N cell = N cell −n id ; 15: end for 16: Step 2: Distribute the switching cell; 17: Set the ID of the module where the switching cell is located break; 21 end if 22: end for phase-shifted carrier pulsewidth modulation (PS-PWM) can increase the effective switching frequency of the system, thus significantly decreasing the filter size.However, the RBP consists of hundreds of SMs in real battery energy storage systems (BESSs), the total switching losses increase by the factor of the number of SMs with PS-PWM.In addition, the high-frequency operations of massive SMs will reduce the reliability of the system.The nearest level control (NLC) is a promising choice that stands out for easy digital implementation and low switching losses [35].However, the NLC scheme is in fact no modulation technique since no averaging processes take place [34].Consequently, suppression of harmonics is not feasible with the NLC method [36].
Based on the above-mentioned analysis, the NLC-PWM method proposed in [37] is adopted in this article.With the NLC-PWM method, there is only one SM that operates at a high switching frequency, making it easy to implement and reducing switching losses.Meanwhile, the introduced averaging processes make it possible for the dc RBP to implement harmonic suppression methods.As demonstrated in Fig. 2, a dc RBP comprised of three battery cells is used to illustrate the principle of SOC balancing with NLC-PWM.First, the number of engaged battery cells m in the control cycle is calculated by where v c is the control voltage calculated by the voltage loop of the RBP, and V e is the rated value of cell voltage.There is another battery cell is regulated by PWM, with a duty cycle as follows: Therefore, there are three optional states for battery cells in a control cycle T s with NLC-PWM in the RBP, which can be expressed as where i is the number of the corresponding cell, and k is the number of the control cycle.The SOC of the ith cell at k + 1th cycle is a function of the pack current and the cell state as follows: where SOC i (k + 1) is the SOC of the ith cell at kth cycle, i(k) is the pack current at the kth cycle, T s is the duration time of one control cycle, and Q i is the rated capacity of the ith cell.From ( 3) and ( 4), it can be found that the SOC of cells can be regulated by controlling the cell states.The states of the cells in the RBP are ascertained by using a priority list L where all the available battery cells are sorted in accordance with their relative SOC.When the system is discharging, cells are arranged in descending order by SOC and the first m cells are engaged, the m + 1th cell is regulated by PWM with a duty cycle d from (2), and the other cells are bypassed.When the system is charging, cells are arranged in ascending order, and the other steps are the same.Therefore, the SOC balancing can be achieved by the independent control of each cell.
For an RBP with a relatively small number of battery cells, balancing operations can be implemented by using a central controller to calculate the SOC of each cell, sort cells according to their SOC, and produce the switching signals for all power switches.However, there will be hundreds or even more cells required to provide high dc voltage in real applications.This implies a heavy computational load for the central controller.Since a single controller does not have enough IO ports to supply the necessary switching signals, expansion calls for several external modules.In the centralized architecture, the switching signals calculated in the central controller have to be transferred to external modules via the communication bus, which also implies a heavy communication load for the controller.
To address these problems, a scalable dc RBP with modular design and the associated hierarchical SOC balancing control structure is presented in Section III.

III. DESCRIPTION OF THE HIERARCHICAL BALANCING CONTROL
The modular system structure of the dc RBP is illustrated in Fig. 1.The battery cells in the RBP are divided into K modules, and each module contains N cells.Each module is equipped with a module controller, which is responsible for monitoring and balancing the battery cells in the module and producing the switching signals for the respective half-bridges.A system controller is used to carry out the closed-loop control and distribute the engaged and switching cells into modules according to their average SOC.The hierarchical SOC balancing control can be divided into two layers, as demonstrated in Fig. 3.
As illustrated in Section II, the dc RBP is modulated by NLC-PWM, and the engaged cell number m and the duty cycle of the switching cell d in each control cycle can be calculated in the system controller using (1) and (2).To reduce the computational and communication load on the system controller, it only receives the average SOC and the available number of battery cells from each module controller.First, the battery modules are sorted by their average SOC in descending order when discharging or ascending order when charging.A priority array L m [K] is then produced, where K is the total number of modules in the RBP.Each element in the array is composed of three variables: the module's identifier (ID), the module's average SOC, and the number of available cells in the module.The m-engaged cells and the switching cell are then assigned to each module as described in Algorithm 1.On the whole, modular balancing is achieved by dividing the required engaged cells into modules in proportion to their average SOC.When the RBP is discharging, more cells are discharging in the module with a higher average SOC, and vice versa.However, when there is a large difference between the average SOC of modules, the simple proportional distribution method may cause some modules to fail to provide the required level number, while some modules provide too few levels.To address this problem, in Algorithm 1, the engaged cell number for the module is determined by the proportion of the module's average SOC and the sum of the average SOC of all unallocated modules, and the order of allocation is determined by the priority array.As a result, the proposed algorithm can always produce the required output voltage, provided that there are enough cells present throughout the entire system.
It can be seen from Fig. 1 that the information transferred from the system controller to each module controller including the engaged cell number n i , the ID of the module where the switching cell is located n sw , and the duty cycle of the switching cell d, and the information transferred from the module controller to system controller including the average SOC and the available cell number of the module.Therefore, there is only limited information exchanged between the system controller and module controllers, which significantly reduces the communication load.
The SOC balancing control among cells in the module is implemented by the corresponding module controller.First, the battery cells in the module are sorted by their SOC in descending order when discharging or ascending order when charging.A priority array L C [N] is then produced, where N is the total number of cells in the module.Each element in the array is the cell's ID.For the ith module, the n i cells at front positions in the priority array are engaged into the string.If the module's ID is equal to n sw , the n i +1th cell in the priority array is switched at a duty cycle d, and the remaining N i -n i -1 cells are bypassed.Otherwise, the remaining N i -n i cells are bypassed.It can be seen from Fig. 3 that two parallel processes that run at different rates make up the balancing control: a slow sorting process occurring every 2 s and a fast closed-loop control process running at 20 kHz.Sorting operations should not be done frequently for the two reasons listed below: first, the sorting algorithm requires a lot of computation, and frequent sorting will increase the computation load of the controller.Second, frequent sorting will result in engaged battery cells switching at a high rate once all cells have reached equilibrium, raising the system's switching loss.However, on the other hand, long sorting intervals can lead to an increase in the SOC imbalance of the battery cells.Considering the above factors, the execution frequency of the sorting algorithm in this article is set to 0.5 Hz.The frequency of the fast process is determined by the closed-loop control cycle, which depends on the particular implementation.

IV. SHC SUPPRESSING CONTROL USING THE PROPOSED DC RBP
As discussed above, one of the main shortcomings of ac RBPs is the resulting SHC, which may induce the aging of battery cells.However, when dc RBPs are connected to a single-phase dc/ac converter for grid applications [20], [21], the SHC problem also occurs.A central two-level dc/dc converter is most commonly employed between the battery pack and the dc/ac converter to stabilize the dc bus voltage as well as suppress the SHC, as demonstrated in Fig. 4(a).However, the additional dc/dc converter increases the cost, loss, and volume of the system.In this article, the dc RBPs are used to implement the SHC-suppressing method for the first time, as shown in Fig. 4(b).

A. Generation and Propagation of the SHC
First, the generating and propagation mechanism of SHC is briefly introduced.With the switching ripple neglected, the output voltage v ac and current i ac of the single-phase dc/ac converter are expressed as where V ac and I ac are the amplitude of the output voltage and the output current respectively, and ϕ is the load impedance angle.
The instantaneous output power of the dc/ac converter can be then derived as It can be seen from ( 6) that the instantaneous output power of the dc/ac converter can be divided into a dc component and a superimposed ac component pulsating at twice the output frequency.In general, a large dc bus capacitor is employed to achieve a small ripple on the intermediate bus voltage, the bus voltage v bus can be therefore approximated by its mean value V bus .The input current i con of the dc/ac converter is then expressed as Thus, the input current of the dc/ac converter is comprised of a dc component I dc and an ac component i 2nd , which pulsates at twice the output frequency and is therefore referred to as the SHC.The SHC will penetrate the bus capacitor and the battery pack.Since the internal resistance of the battery pack is typically much lower than the impedance of the bus capacitor at twice the output frequency, the majority of the SHC will penetrate the batteries, causing additional heating and hastening the aging of the batteries.

B. Filter Design and Size Reduction
In previous studies, the two-level dc/dc converters were widely utilized to suppress the SHC flowing into the batteries with various control strategies.However, passive filters dominate the size of two-level converters, which restricts the increase in power density.For a typical two-level buck converter, the sizes of the inductor and the capacitor are determined by the desired inductor current ripple proportion Δi L and bus voltage ripple proportion at switching frequency Δv bus _ sw [38].The filter inductor can be designed as where f s is the switching frequency.Since the intermediate bus voltage is constant, it can be seen from ( 8) that when the input voltage is the highest, the required inductance value is maximum.In this article, the inductor current ripple is set to 10% of the rated output current.Using the parameters demonstrated in Table I, the minimum value of the filter inductance for the two-level buck converter can be calculated as 4.165 mH.

TABLE I SYSTEM AND CONTROL PARAMETERS OF THE PROTOTYPE
Similarly, if there is no SHC that needs to be absorbed, the bus capacitor can be designed as where P o is the output power, Δv bus _ sw is typically set to 1%.In single-phase dc/ac systems, the dc bus voltage ripple originates from both the switching harmonics and the SHC.Since the second harmonic frequency (SHF) is typically much lower than the switching frequency, the required bus capacitance is dominated by the voltage ripple at SHF.Assuming that all the SHC [i.e., i 2nd depicted in (7)] flows into the bus capacitor by proper control, the bus voltage ripple proportion at SHF can be calculated as where ω o is the output angular frequency.Therefore, the minimum value of the bus capacitor can be obtained by The bus voltage ripple at SHF will lead to an undesired third harmonic current in the grid current [39].In this article, we set the voltage ripple amplitude to 5% of the rated bus voltage to reduce its impact.Consequently, it can be calculated using the parameters in Table I that the bus capacitor should be larger than 477 μF.Comparing ( 9) and ( 11), the required dc link capacitance increases by a factor of k due to the SHC that needs to be reduced, which can be calculated by It should be noted that the high requirement of dc link capacitance is a common issue in single-phase systems where a large SHC exists and needs to be reduced, and the value is only determined by the system parameters.
For the dc RBP with NLC-PWM proposed in this article, it modulates the demanded output voltage using the two nearest levels: (13) where V m+1 and V m are the nearest higher and lower voltages, respectively, m is the engaged cell number obtained in (1), and V cell is the cell voltage.The current ripple amplitude can be calculated by Based on the principle of inductor volt-second balance, the following equation at the steady state should be met: Combining ( 13)-( 15), the current ripple amplitude can be expressed as It can be observed from ( 16) that Δi LA reaches the maximum when V bus equals the average value of V m+1 and V m , and the maximum value of Δi LA is Therefore, the minimum value of the filter inductor for the dc RBP can be calculated by It is clear that the inductor size is proportional to the cell voltage, which ranges from 2.5 to 4.2 V.With the same current ripple amplitude requirement (i.e., 10% of the rated output current), the minimum value of the filter inductor for the dc RBP can be calculated as 87.5 μH.In comparison with a two-level buck converter, the filter inductor of the dc RBP is reduced by a factor of 48.This reduction is significant and can be attributed to the fine voltage steps offered by the dc RBP system.Specifically, for a dc RBP composed of N cells, the filter inductor can be reduced to 1/N when compared to a conventional two-level buck converter [24], which greatly reduces the volume and weight of the system.
However, since the size of the bus capacitor is primarily determined by the SHC it needs to absorb, and the SHC only depends on the rated parameters of the system, the size requirement of the dc RBP bus capacitor is the same as that of the two-level buck converter (i.e., 477 μF).

C. Description of the SHC Suppressing Control
According to the above-mentioned analyses, the dc/ac converter can be modeled as a dc current source I dc and an SHC source i 2nd .The dc RBP without the bus capacitor can be equivalent to a voltage source V oc and the output impedance Z o (s).Therefore, the equivalent schematic diagram of the single-phase dc/ac system with the dc RBP is depicted in Fig. 5. Hence, the proportion of the SHC flowing into the dc RBP is determined by Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the output impedance Z o (s), and the impedance of C bus at twice the output frequency.In previous studies, an additional central dc/dc converter was most commonly used to suppress the SHC, and a variety of control schemes have been proposed [20], [31], [32].However, the basic principles of these methods are the same, which is forcing nearly all the SHCs in the input current of the dc/ac convert to flow into the intermediate dc bus capacitor by increasing the output impedance of the dc/dc converter [40].
The dc RBP in this article indeed operates as a multilevel buck converter.As a result, any of the known SHC reduction control schemes designed for buck-derived dc/dc converters can be also implemented with the dc RBP.A comprehensive comparison of these methods from the perspective of SHC reduction and dynamic performance was presented in [40].It was verified that the bandpass-filter-incorporated inductor current feedback scheme (BPF-ICFS) has the best performance on SHC reduction as well as a good dynamic performance.Hence, we implemented the BPF-ICFS with the proposed DC RBP to deal with the SHC problem.The control block diagram of the BPF-ICFS first developed in [32] is demonstrated in Fig. 6, where v ref is the bus voltage reference; G v (s) is the voltage regulator; v c is the control voltage; H v is the intermediate bus voltage sensor gain; K PWM is the gain of the modulator, which is determined by the specific modulation technique; and r d is composed of the internal resistors of engaged battery cells, on-state resistance of power switches, and the equivalent series resistor (ESR) of the inductance L, which can serve as a damping resistor to improve the system stability [32].According to Fig. 3, it can be seen that feeding back the filter inductor current to the regulated voltage is equivalent to adding a virtual resistor in series with L. Since only the SHC needs to be suppressed, the output impedance of the RBP is required to be high only at around twice the output frequency f 2nd .Therefore, a bandpass filter (BPF) is introduced into the inductance current feedback path, as shown in Fig. 6.The transfer function of the BPF can be expressed as where ω n = 2πf 2nd , and Q is the quality factor.According to Fig. 3, the output impedance of the DC RBP can be derived as It can be seen from ( 20) that the introduction of virtual impedance r s G BPF (s) increases the output impedance of the dc RBP at f 2nd , whereas the output impedance of the RBP at other frequencies still keeps low.In this article, G v (s) is a proportional-integral regulator, which has the expression as In this article, we built a laboratory prototype consisting of 48 3-Ah 18 650 lithium-ion battery cells to verify the proposed control strategies.The main parameters of the prototype are listed in Table I.The optimized control parameters are calculated using the design methods presented in [32].Fig. 7 shows the Bode diagrams of the uncompensated and compensated voltage loop gain.It can be seen that the phase margin of the compensated voltage loop gain is about 63°, which meets the requirement of stability.The magnitude-frequency plots of the output impedance of the dc RBP Z o (s) and the impedance of the dc bus capacitor Z C (s) are displayed in Fig. 8.It can be found that the magnitude of Z o (s) is much greater than the magnitude of Z C (s) at f 2nd .Therefore, only a few of the SHC in the input current of the dc/ac converter i con will flow into the batteries.
The SHC suppressing control method for the dc RBP can be easily embedded in the hierarchical balancing control scheme, as demonstrated in Fig. 3.

A. Experimental Setup
To validate the hierarchical SOC balancing and the SHC suppression control with the proposed dc RBP, an experimental setup of the single-phase BESS was developed.The parameters of the experimental setup are detailed in Table I, and the picture of the whole system is shown in Fig. 9(a).
The RBP comprises 48 lithium-ion cells with a 3-Ah nominal capacity, which are divided evenly into three battery modules.Each cell is connected with two complementary MOSFETs to form an SM in the RBP.Each module is equipped with an independent controller and corresponding sample circuits to measure cell voltages and module current, as shown in Fig. 9(b) and (c).A system controller is utilized to perform the SHC suppression and module-level balancing control.In this article, both these controllers are realized using the TMS320F28386S microcontroller, which includes 416-bit 1.1 M sample/s multichannel ADCs.Since there are 16 cell voltages and a module current needs to be sampled in each module, a sequential sampling is realized with multiplexers.The three module controllers and the system controller are connected by two communication links: a daisy-chain fast serial interface communication link, which transfers the control orders from the system controller to the module controllers at 20 kHz, and a controller area network communication link, which transfers the cell information (SOCs and voltages) from the module controllers to the system controller at 0.5 Hz.It is significant to note that due to the time difference between when different module controllers receive control orders in the daisy chain, appropriate synchronization signals are needed to ensure that the control orders take effect at the same time in different modules.In addition, the system controller also establishes communication with a host computer that runs a MATLAB GUI via RS485 protocol.The GUI is used to monitor cell voltages and SOCs that are broadcast by the module controllers and gathered by the system controller.A bidirectional single-phase dc/ac converter connected to the grid via a transformer was built to charge and discharge the batteries, which is controlled by a microprocessor TMS320F28377D.The charge/discharge current of the RBP is indirectly controlled by adjusting the grid current reference accordingly.

B. Experimental Results With the SHC Suppression Control
To verify the effectiveness of the SHC suppression method using the proposed RBP, the experimental waveforms of RBP under open-loop control and SHC suppression control were tested separately.Fig. 10(a) and (c) shows the experimental waveforms of the RBP under open-loop control, where the battery cells in the RBP are directly connected in series.In this configuration, the RBP is equal to a traditional hard-wired battery pack.Since the experiments were conducted under laboratory conditions in which the grid was weak, the small fluctuations in the ac current can be attributed to the background harmonics present in the grid voltage [41].It can be seen that without SHC suppression control, the amplitude of the SHC flowing into the batteries is large.By FFT calculation, the SHCs flowing into the batteries are 27% (when discharged at 3 A) and 37% (when charged at 1.5 A) of the dc current, respectively.Fig. 10(b) and (d) shows the experimental waveforms of the RBP adopting SHC suppression control.From the steady-state waveforms.It can be observed that the SHC flowing into the batteries is almost eliminated after applying the SHC suppression method, which proves that the RBP can be also utilized to suppress the SHC as conventional two-level dc/dc converters.As shown in Table II, the SHCs flowing into the batteries are reduced to 1.9% (discharging at 3 A) and 1.1% (charging at 1.5 A) of the dc current, respectively.It can also be seen that the bus voltage ripple at SHF increases a little as a consequence of the fact that the bus capacitor provides more SHC when the SHC suppression method is adopted.As displayed in Fig. 11, when the load is stepped between 0% and 100% rated power when discharging, the overshoot and undershoot of the intermediate bus voltage are 19 and 14 V, respectively, and the recovering times during load transient are 70 and 80 ms, respectively.The transient performance of the RBP is similar to the conventional two-level    dc/dc converters with the same SHC suppression method and a much smaller filter inductor [32].

C. Experimental Results of the Hierarchical Balancing Control
To evaluate the performance of the proposed hierarchical balancing algorithm designed for the RBP, the battery cells are unevenly discharged before the beginning of the test.At the beginning of the test, the initial SOCs of the battery cells are calculated by the measured cell voltages and the SOC dependency on the open-circuit voltage (OCV).The OCV-SOC characteristic of the test battery is obtained by off-line test and demonstrated in Fig. 12.During the test, the RBP is firstly discharged at 3 A for 30 min and then charged at 1.5 A for 60 min, and the SOCs of battery cells are calculated by coulomb counting as described in (4).The SOC balancing process during the test is demonstrated in Fig. 13.At the beginning of the test, the maximum SOC variation among cells is 45%, and the maximum average SOC variation among modules equals 12%.At the end of the test, the maximum SOC Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.variations among cells and modules are 0.3% and 0.2%, respectively.The time interval for sorting operations and the charging and discharging current determine the SOC variations at the steady state, while a larger time interval or charging/discharging current will increase the final SOC imbalance.However, as mentioned in Section III, a tradeoff should be made between the computation load, switching loss, and the balancing requirement when choosing the time interval of sorting operations.In summary, the RBP can effectively overcome SOC imbalance among cells and modules with the proposed hierarchical balancing architecture.

VI. CONCLUSION
This article presents a hierarchical SOC balancing control scheme for the dc RBPs with the modular design.Battery cells and power switches in the dc RBP are divided into several modules, and each module is equipped with a slave controller, which is only responsible for monitoring and managing a subset of cells.The system controller is used to implement the voltage closed-loop control and allocate the desired voltage steps into battery modules to achieve balancing among modules.The hierarchical SOC balancing algorithm reduces the computing and communication demands on the controllers, allowing the RBP to scale easily to fit variable applications.
Considering the SHC problem existing in single-phase dc/ac systems, the dc RBP is used to implement the SHC suppression method for the first time.Compared to conventional two-level dc/dc converters, the RBP's high output voltage significantly reduces the need for a large filter inductor.This reduction in size greatly decreases the overall volume and weight of the system.
The SHC suppression control and hierarchical balancing algorithm are experimentally validated using a laboratory prototype comprising 48 lithium-ion battery cells.The SHC flowing into the batteries is suppressed to less than 2% of the dc component with the RBP.Balancing to within 0.3% and 0.2% among different cells and modules, respectively, is achieved while large initial SOC imbalances exist.

Fig. 1 .
Fig. 1.System architecture of the proposed DC RBP with modular design.

Algorithm 1 : 1 : 1 :
Balancing Control at Module Level.Step Distribute the required voltage levels m into each module; 2: Initialize the unallocated voltage levels N cell = m; 3: for i = 1, K do 4:

Fig. 2 .
Fig. 2. Demonstration of SOC balancing among cells in a DC RBP.

Fig. 4 .
Fig. 4. (a) Conventional configuration of a two-stage single-phase DC/AC system.(b) Proposed single-phase DC/AC system with the DC RBP.

Fig. 7 .
Fig. 7. Bode diagram of the uncompensated and compensated voltage loop gain of the RBP.

Fig. 8 .
Fig. 8. Magnitude-frequency plots of the output impedance of the RBP Zo(s) and the impedance of the DC bus capacitor Z C (s).

Fig. 9 .
Fig. 9. Experimental setup of the single-phase BESS with the RBP.(a) Photograph of the whole system.(b) Top view of the reconfigurable battery module.(c) Side view of the reconfigurable battery module.

Fig. 13 .
Fig. 13.SOC balancing process during the charging and discharging operations.(a) SOC balancing at the cell level.(b) SOC balancing at the module level.
Hierarchical State-of-Charge Balancing and Second-Harmonic Current Suppressing Control With a Scalable DC Reconfigurable Battery Pack Zheng Chen , Graduate Student Member, IEEE, Chang Liu , Graduate Student Member, IEEE, Yikai Zhang , Ranchen Yang , Member, IEEE, and Guozhu Chen , Member, IEEE

TABLE II COMPARATIVE
RESULTS WITH AND WITHOUT THE SHC SUPPRESSION CONTROL