Performance Analysis of a Novel High Frequency Self-Reconfigurable Battery - MDPI

Article
Performance Analysis of a Novel High Frequency
Self-Reconfigurable Battery
Rémy Thomas *, Fanny Lehmann , Jérôme Blatter , Ghislain Despesse and Vincent Heiries

 CEA, Minatec Campus, Université Grenoble Alpes, F-38000 Grenoble, France;
 fanny.lehmann@ens-paris-saclay.fr (F.L.); jerome.blatter@cea.fr (J.B.); ghislain.despesse@cea.fr (G.D.);
 vincent.heiries@cea.fr (V.H.)
 * Correspondence: remy.thomas@cea.fr

 Abstract: Self-reconfigurable battery architectures have gained a lot of interest recently in the litera-
 ture, with more and more advanced functionalities. This paper describes the performance analysis of
 our proposed High Frequency Self-Reconfigurable Battery (HF SRB). To evaluate specific features
 with long-term dependencies of our system, a full functional behavioral simulator was developed.
 A comparison with a real 128-level HF SRB validated the simulator operation. The balancing per-
 formances obtained on vehicle test cycles showed the cell capacity discrepancy that the HF SRB
 is capable of handling in a single complete charge or discharge cycle. The magnitude of this gap
 demonstrated the extent to which the HF SRB is capable of operating with second life cells or even
 different chemistry mixes.

 Keywords: active balancing; Self-Reconfigurable Battery (SRB); modelling; simulation; charge equalization

 


 1. Introduction
 

 In most of classical Li-Ion electrical storage systems, the battery pack is composed
Citation: Thomas, R.; Lehmann, F.;
 of a certain number of unitary battery cells arranged in series and/or parallel, according
Blatter, J.; Despesse, G.; Heiries, V.
 to a fixed arrangement. A traditional li-ion battery system is limited by the weakest
Performance Analysis of a Novel
 cell of the battery pack whatever is the charge balancing mechanism [1]. Consequently,
High Frequency Self-Reconfigurable
Battery. World Electr. Veh. J. 2021, 12,
 battery manufacturers must use cells having perfectly homogeneous characteristics and
10. https://doi.org/10.3390/
 must implement advanced thermal management to maintain this homogeneity as long as
wevj12010010 possible. This kind of limitation makes it difficult to build a battery mixing different cells
 characteristics as with reusing second life battery cells because the system will be always
Received: 30 November 2020 limited by the cell having the smallest capacity and/or the highest impedance.
Accepted: 31 December 2020 Not being able to use the full energy contained in all cells of the battery is one of the
Published: 11 January 2021 aspects that led to the development of Self-Reconfigurable Batteries (SRB) [2]. The key idea
 of those batteries is to introduce individual control of each cell in the battery pack thanks
Publisher’s Note: MDPI stays neu- to dedicated half-bridge chopper switches. With such a management, it becomes possible
tral with regard to jurisdictional clai- to disconnect only the weakest or damaged cells and supply the required power with the
ms in published maps and institutio- remaining ones. Moreover, bypassing switches offer the capability to adjust the number N
nal affiliations. of cells placed in serial and thus to adjust the output voltage of the battery.
 Optimal cell connection strategies were widely studied for well-determined power
 profiles ([3,4]). Those algorithms generally consist in exploring all the combinations of cells
Copyright: © 2021 by the authors. Li-
 through the power profile and choosing the one that minimizes a certain criterion such
censee MDPI, Basel, Switzerland.
 as the total capacity loss. However, those methods were not applicable when the SRB is
This article is an open access article
 also used to provide an AC output voltage, to directly drive a motor [5] or to recharge the
distributed under the terms and con- battery directly on the electric grid ([6,7]).
ditions of the Creative Commons At- The generation of an AC waveform voltage from an SRB rely on the sequential
tribution (CC BY) license (https:// superimposition of each cell voltages Ulevel resulting in a staircase shape signal of period
creativecommons.org/licenses/by/ T and nominal root mean square voltage Urms , as shown in Figure 1. A cell insertion
4.0/). increases the output voltage of one cell voltage, we name that voltage increment a “Level”,

World Electr. Veh. J. 2021, 12, 10. https://doi.org/10.3390/wevj12010010 https://www.mdpi.com/journal/wevj

ctr. Veh. J. 2021, 12, x 2 of 12

 World Electr. Veh. J. 2021, 12, 10 2 of 12
 and nominal root mean square voltage Urms, as shown in Figure 1. A cell insertion in-
 creases the output voltage of one cell voltage, we name that voltage increment a “Level”,
 Level 1 being theLevel
 first step,
 1 beingandtheLevel
 first n, the and
 step, nth step.
 LevelAn,level is not
 the nth step.attached
 A leveltoisanot
 particular
 attached to a particular
 cell, any cell of the
 cell, any cell of the battery pack can ensure that level. As shown onlevel
 battery pack can ensure that level. As shown on Figure 1, each Figure 1, each level
 performs four switching
 performsoperations
 four switching within a sinusoidal
 operations withinperiod, while a H-bridge
 a sinusoidal period, whileallows a H-bridge allows
 the voltage to bethereversed
 voltageby toswitching
 be reversed twobytimes less. Therefore,
 switching two timesinless. order to generate
 Therefore, a
 in order to generate
 50-Hz sinusoidala waveform, the switching
 50-Hz sinusoidal waveform, frequency of a level
 the switching is 200 Hzofwhen
 frequency a levelthose
 is 200of Hz when those
 the H-bridge is 100 Hz. H-bridge
 of the However,isin100 orderHz.to However,
 generate aninaccurate
 order towaveform
 generate inanitsaccurate
 steepestwaveform in its
 part, it is necessary to respect
 steepest part,aitminimum
 is necessary time toTimeStep
 respect amin between time
 minimum two level changes.
 TimeStep In
 min between two level
 the case of a sinechanges.
 wave, the minimum
 In the case of atime sine step
 wave,must be less than
 the minimum timeor step
 equal to the
 must period
 be less than or equal to the
 of the fundamental harmonic
 period of the voltageharmonic
 of the fundamental over more of than six times
 the voltage themore
 over numberthanofsixlevels
 times the number of
 Nmax. When taking EU N
 levels electrical
 max . When network
 takingvoltage as an example,
 EU electrical network whichvoltageisas230anVexample,
 RMS +/− 10% which is 230 VRMS
 with a frequency+/of−50 Hz,with
 10% and ausing cells which
 frequency the specified
 of 50 Hz, and usingend cellsofwhich
 discharge thresholdend of discharge
 the specified
 is 2800 mV, Nmaxthreshold
 reaches 128 is and
 2800the mV, Nmax minimum
 related reaches 128 andstep
 time theisrelated minimum
 then about 25 µs,time
 which step is then about
 corresponds to an 25 µs, which corresponds
 equivalent to an equivalent
 switching frequency of 40 kHz.switching frequency can
 This frequency of 40bekHz.
 re- This frequency
 duced if more thancan one
 be reduced
 level canif bemore than one
 switched level control
 at each can be switched
 time step.atNote eachthat
 control time step. Note that
 the bat-
 tery pack could include additional cells that could be used to provide the maximum volt- the maximum
 the battery pack could include additional cells that could be used to provide
 age output in casevoltage
 of celloutput
 failures;intherefore,
 case of cell thefailures;
 number therefore, the number
 of cells could of cells
 be greater thancould
 Nmax be greater than
 without affectingNTimeStep
 max without min. affecting
 StaircaseTimeStep min . Staircase
 shape waveform shape waveform
 are usually generated arefrom usually
 mul- generated from
 tilevel convertersmultilevel converters
 using carrier phase shiftusing carrier
 Pulse phase
 Width shift Pulse(PWM)
 Modulation Width orModulation
 carrier cas- (PWM) or carrier
 cascaded PWM
 caded PWM implemented on Fieldimplemented
 Programmable on Field Programmable
 Gate Arrays (FPGA) and GateDigital
 Arrays (FPGA) and Digital
 Signal
 Processor (DSP) Signal
 targetsProcessor
 [8]. (DSP) targets [8].

 U delay
 N cells
 N
 … Ulevel
 n+1 cells
 Level n+1
 n cells Control time step
 Level n
 n–1 cells Level n–1
 …
 1 cell
 Level 1
 Level –1
 0 (H-Bridge toggle @ T/2 and T) T/2 T t

 Staircaseshape
 Figure1.1.Staircase
 Figure shapesine
 sinewaveform
 waveformgenerated
 generatedby
 byN-level
 N-levelSelf-Reconfigurable
 Self-ReconfigurableBatteries
 Batteries(SRB).
 (SRB).

 A High Frequency Self-Reconfigurable Battery (HF SRB) was recently proposed in [9].
 A High Frequency Self-Reconfigurable Battery (HF SRB) was recently proposed in
 This SRB relies on a Nearest Level Control (NLC) to allow the integration of the switches
 [9]. This SRB relies on a Nearest Level Control (NLC) to allow the integration of the
 control in low cost microcontrollers. This study demonstrated the operation of a prototype
 switches control in low cost microcontrollers. This study demonstrated the operation of a
 of 128 cells recharging directly on the electrical grid without charger, while perfectly
 prototype of 128 cells recharging directly on the electrical grid without charger, while per-
 balancing the cells in real-time. Its operating principle is detailed in Section 2.
 fectly balancing the cells in real-time. Its operating principle is detailed in Section 2.
 Cell balancing in this SRB relies on individual control of the utilization rate of each
 Cell balancing in this SRB relies on individual control of the utilization rate of each
 cell in the overall power generation and/or absorption. This variation in the utilization
 cell in the overall power generation and/or absorption. This variation in the utilization
 rate is achieved by modifying the order of use of the cells to generate the staircase shape
 rate is achieved by modifying the order of use of the cells to generate the staircase shape
 sinusoidal waveform. The average current supplied or absorbed by a cell decreases with
 sinusoidal waveform. The average current supplied or absorbed by a cell decreases with
 the number of the level at which the cell is introduced. The balancing is then performed in
 the number of the level at which the cell is introduced. The balancing is then performed
 real time with a large dynamic thanks to the use of the nominal power usage. Moreover,
 in real time withthe
 a large dynamic
 balancing thanks
 criteria aretonot
 thelimited
 use of the nominal
 to the voltage power usage. of
 balancing Moreover,
 the cells or their state of
 the balancing criteria are not limited to the voltage balancing of the cells
 charge. Indeed, by adjusting the utilization rate of each cell, it is also or their statepossible
 of to balance
 charge. Indeed, cell
 by adjusting
 temperature,the utilization rate of(SoC),
 State of Charge each State
 cell, itofisHealth
 also possible to balance
 (SoH), or any other characteristic
 cell temperature,that
 State
 mayof be
 Charge (SoC),
 observed orState of Health
 estimated as the(SoH), or anycapacity;
 remaining other characteristic
 or a weighted combination
 that may be observed or estimated as the remaining capacity; or a weighted
 of them. The assessment of balancing algorithms and their validation combination requires the use of a
 of them. The assessment
 large numberof balancing algorithms
 of cells and multipleand theirorvalidation
 charge discharge requires
 cycles. Inthe use of the variation of
 addition,
 a large number of cells and
 several multiple
 criteria, such charge or discharge
 as the power profile cycles. In addition, the
 or the temperature variation
 profile, increases the number
 of several criteria,
 ofsuch
 testsas the power
 tenfold. Thisprofile
 can be ortime
 the temperature
 consuming and profile,
 evenincreases
 introducethe safety
 num- constraints. In
 ber of tests tenfold. This can
 addition, be time
 initial cellsconsuming
 states mustand evenknown.
 be well introduce Allsafety constraints.
 this makes In
 it preferable to carry on
 addition, initial this
 cellsstudy
 statesinmust be well known. All this makes it preferable to carry on
 simulation. Thus, in order to evaluate correctly the trends of some balancing
 features, many trials can be performed concurrently without requiring the supply of many

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 World Electr. Veh. J. 2021, 12, 10 3 of 12
 this study in simulation. Thus, in order to evaluate correctly the trends of some balancing
 features, many trials can be performed concurrently without requiring the supply of many
 expensive batteries. However, the simulation results have first to be compared with those
 expensive batteries. However, the simulation results have first to be compared with those
 produced by a real system in order to validate the reliability of the simulator results.
 produced by a real system in order to validate the reliability of the simulator results.
 The first aim of this study is to evaluate the balancing capability of the HF SRB. For
 The first aim of this study is to evaluate the balancing capability of the HF SRB. For
 this purpose, a simulator is created and used aside a real demonstrator to validate its op-
 this purpose, a simulator is created and used aside a real demonstrator to validate its
 eration. Once validated, the simulator is used to study the running time gain achieved by
 operation. Once validated, the simulator is used to study the running time gain achieved
 the HF SRB over different standardized driving cycles from heterogeneous distributions
 by the HF SRB over different standardized driving cycles from heterogeneous distributions
 of the SoC and total capacities of the cells.
 of the SoC and total capacities of the cells.
 This document is composed as follows: the Section 2 describes the main operating
 This document is composed as follows: the Section 2 describes the main operating
 principles of the HF SRB. Then the Section 3 details the simulator with the description of
 principles of the HF SRB. Then the Section 3 details the simulator with the description of
 its constitutive blocks. The Section 4 details the validation of the simulator, with respect
 its constitutive blocks. The Section 4 details the validation of the simulator, with respect
 to the demonstrator
 to theofdemonstrator
 a real system,ofasawellrealassystem,
 its operation
 as well with testoperation
 as its driving cycles.
 with Then
 test driving cycles.
 a following section presents the results obtained from the simulator. The
 Then a following section presents the results obtained from the simulator. balancing per-The balancing
 formance of the State of Charge (SoC) is evaluated on the New European Driving Cycle
 performance of the State of Charge (SoC) is evaluated on the New European Driving Cycle
 (NEDC) with an initial with
 (NEDC) SoC imbalance
 an initial SoCof 56%. The impact
 imbalance of 56%.of The
 the balancing
 impact of criteria used, criteria used,
 the balancing
 such as cells’ voltage or SoC, is then evaluated on a profile consisting of repeated alternat-
 such as cells’ voltage or SoC, is then evaluated on a profile consisting of repeated alternating
 ing NEDC cycles NEDCand recharging
 cycles and phases.
 recharging Subsequently, the improvement
 phases. Subsequently, in battery lifein
 the improvement is battery life is
 evaluated withevaluated
 a Worldwide harmonized Light Vehicles Test Procedure (WLTP) driving
 with a Worldwide harmonized Light Vehicles Test Procedure (WLTP) driving
 cycle based oncycle
 an initial
 basedcells’
 on ancapacity
 initial dispersion of +/−dispersion
 cells’ capacity 10%. Finally,
 of +/the
 − Section 5 con- the Section 5
 10%. Finally,
 cludes on the performances
 concludes on the demonstrated
 performances by the results obtained
 demonstrated by theand develops
 results the per-
 obtained and develops the
 spectives that follow.
 perspectives that follow.

 2. HF SRB Operating Principle
 2. HF SRB Operating Principle
 The HF SRB consists
 The HFof SRBa distributed
 consists of system divided
 a distributed into remote
 system dividedmodules named
 into remote modules named
 “Slave” and a “Slave” and a central
 central module namedmodule
 “Master”.named “Master”.
 An overview of An overview
 the overall of the overall
 hardware ar- hardware
 architecture
 chitecture is given in Figureis 2.
 given in Figure 2.

 Iout > 0 I out Vout
 Inverter L1
 Local U, I, T° 100 µH
 H-bridge Master F1
 Controller sensors
 C4 VG
 U, T° SW 1
 Insulated internal
 data bus

 L2
 C3 sensors M aster Controller 1 mH F2
 C2
 Switch VN
 drivers Voltages/current SW 2 VN
 management
 C1 Half-bridge
 S lave 1 Chopper circuits
 Cell selector
 External data bus
 S lave 2 ensuring BM S
 … Voltage/current requirements
 S lave N
 Neutral (com)

 Figure 2.
 Figure 2. High
 High Frequency
 Frequency Self-Reconfigurable
 Self-ReconfigurableBattery
 Battery(HF
 (HFSRB)
 SRB)hardware
 hardwarearchitecture.
 architecture.

 Each Slave is composed
 Each Slaveofis four serial cells
 composed of four connected through
 serial cells half-bridge
 connected through chopper
 half-bridge chopper
 circuits, an H-Bridge
 circuits,toaninvert the module
 H-Bridge to invertpolarity,
 the moduleand apolarity,
 local controller. Thecontroller.
 and a local number ofThe number of
 serial stages associated to each
 serial stages local controller
 associated to each localis limited to reduce
 controller the electrical
 is limited to reduceconstraints
 the electrical constraints
 of the implemented
 of theswitches
 implemented (low voltage
 switches MOSFET) as wellMOSFET)
 (low voltage as the complexity
 as well ofasthe
 thenum-
 complexity of the
 ber of switchesnumber
 and cellsof to
 switches
 manageand (lowcells
 costto CPU).
 manage (lowSlaves
 Then cost CPU). Then Slaves
 are chained to reacharethe
 chained to reach
 the required
 required output voltage. output voltage.
 The Master
 The Master module module
 is in charge ofismanaging
 in chargeall of slave
 managingmodulesall slave
 thanksmodules thanks to a master
 to a master
 controller.
 controller. It estimates theItstate
 estimates
 of eachthe cellstate
 and of each cell
 manages theand manages
 safety accordingthe to
 safety
 data according
 col- to data
 lected throughcollected
 the remote through
 modulesthe (mainly
 remote modules
 voltage and (mainly voltage and
 temperature temperature
 of the of itthe cells). Then,
 cells). Then,
 it performs
 performs a centralized a centralized
 calculation calculation
 to define whichtocell define
 needwhich
 to becell need to be activated/deactivated
 activated/deactivated
 and send orders to the slaves to apply the new
 and send orders to the slaves to apply the new states. The change of a serial states. The change of a serial
 level state is level state
 is then translated at the slave node level by the driving
 then translated at the slave node level by the driving of the related local switches as well of the related local switches as
 well as its inverting H-bridge if necessary. The slave
 as its inverting H-bridge if necessary. The slave controller is supplied by the local cellscontroller is supplied by the local
 cells sharing a same local ground potential reference, simplifying the transistors driving
 and voltages measurements. Indeed, the latter have to withstand a common-mode voltage

ectr. Veh. J. 2021, 12, x 4 of 12

 World Electr. Veh. J. 2021, 12, 10 4 of 12

 sharing a same local ground potential reference, simplifying the transistors driving and
 voltages measurements. Indeed, the latter have to withstand a common-mode voltage
 limited to only four
 limitedlevels of cell
 to only voltages,
 four levels of which let usingwhich
 cell voltages, classicalletmethods of differential
 using classical methods of differential
 measurement. measurement.
 Concerning the Mosfet driving,
 Concerning we driving,
 the Mosfet use the we principle
 use the described in [10], in [10], which
 principle described
 which operatesoperates
 properlyproperly
 up to 4 cells
 up toin4series without
 cells in need of galvanic
 series without insulation.
 need of galvanic insulation.
 Cells balancingCells
 is achieved
 balancing by isactivating
 achievedthe bycells according
 activating to anaccording
 the cells order of priority
 to an order of priority
 based on their state. A first part of those state parameters is directly measured and trans- measured and
 based on their state. A first part of those state parameters is directly
 transmitted
 mitted by the local by thesuch
 controllers, localascontrollers,
 voltages and suchtemperatures.
 as voltages and temperatures.
 The The rest of the cells
 rest of the cells
 state indicators,state
 suchindicators,
 as SoC, SoH, such oras SoC,
 SoE, areSoH, or SoE,atare
 estimated estimated
 master at master
 controller level.controller level.
 The AC waveform The AC waveform
 generated by the generated
 HF SRBby is the HF SRB
 obtained by is obtained
 a Near LevelbyControl
 a Near Level Control
 (NLC) method.(NLC) method.
 The number of The
 serialnumber
 levels toof activate
 serial levels to activate
 at each at each
 time instant time instant is determined
 is determined
 in real-time by in real-time
 rounding upbytorounding
 the nearest upinteger
 to the nearest
 the realinteger the real
 value given byvalue given by a closed-loop
 a closed-loop
 control. The voltage waveforms generated with
 control. The voltage waveforms generated with this system are similar to those from this system are similar
 car- to those from
 carrier-cascaded PWM. The control loop updates
 rier-cascaded PWM. The control loop updates a reference voltage in real time, which al- a reference voltage in real time, which
 lows a forthwithallows a forthwith
 management of themanagement of the voltage
 electrical network electrical network voltage
 perturbations while perturbations
 regu- while
 regulating
 lating the exchanged the at
 current exchanged
 a set value current
 [9]. at a set value [9].
 As shown
 As shown on Figure onFirst
 3, the Figure In 3, the Out
 First First (FIFO)
 In Firstprinciple
 Out (FIFO) is principle
 applied tois connect
 applied to connect and
 and disconnect the cells. The selection of the cell to be connected or disconnected is per- is performed
 disconnect the cells. The selection of the cell to be connected or disconnected
 on in
 formed on the fly thea fly in a priority
 priority order X(t) order X(t) provided
 provided by a balancing
 by a balancing algorithm. algorithm.
 The failing The failing cells
 cells are handled forthwith without disturbing the generated waveform thanks to a cell to a cell swap
 are handled forthwith without disturbing the generated waveform thanks
 swap operation.operation. A largerofnumber
 A larger number cells thanof cells
 those than those required
 required to provide to the
 provide the AC waveform can be
 AC waveform
 can be integrated in order to maintain the continuity of service capabilities offered offered
 integrated in order to maintain the continuity of service capabilities by the by the bypass
 bypass circuits circuits as operated
 as operated in DCThe
 in DC SRBs. SRBs. The additional
 additional cells arecells
 thenare thenasused
 used as hot redundancy so
 hot redun-
 that their capacity contributes to the total capacity
 dancy so that their capacity contributes to the total capacity of the HF SRB [11]. of the HF SRB [11].

 (Swap 2) New cell ranking
 U Cell G “OFF”, Cell J “ON” Cell X X X
 (Cell B fault)
 (Swap 1) Cell J “OFF” order t < t4 t 4< t < t 6 t > t6
 Cell B “OFF” Cell D “ON” 1 Cell A Cell A Cell A
 4th level Cell C “OFF”

 cells number
 Available
 Cell G “ON” Cell B “ON” 2 Cell C Cell C Cell D
 3rd level Cell D “OFF”
 Cell C “ON” 3 Cell B Cell D Cell C
 2nd level Cell A “OFF” 4 Cell D Cell G Cell J
 Cell A “ON”
 1st level 5 Cell G Cell J Cell G
 t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 6 Cell J
 t

 Figure
 Figure 3. HF SRB cells switch 3. HF
 control SRB cells switch control principle.
 principle.

 3. HF SRB Simulator
 3. HF SRB Simulator
 This section focuses
 This on the simulator
 section focuses on of the
 theHF SRB developed
 simulator of the HFin order to study thor-
 SRB developed in order to study
 oughly its various performance,
 thoroughly and particularly
 its various performance, its and
 capability in terms
 particularly its of voltage, in
 capability tem-
 terms of voltage,
 perature, SoC, or remaining capacity
 temperature, balancing.capacity
 SoC, or remaining These balancing
 balancing. capabilities
 These balancingare measur-
 capabilities are mea-
 able over operating periods
 surable that can beperiods
 over operating limitedthatto acanfewbe complete
 limited tobattery
 a fewcycles.
 complete battery cycles.
 The study of HF SRB capability in terms of SoH estimation improvement
 The study of HF SRB capability in terms of SoH estimation improvement and SoH and SoH cells
 cells balancing is beyond the scope of this paper. It would require the simulation
 balancing is beyond the scope of this paper. It would require the simulation of a very of a very large
 large number of cycles, of
 number which would
 cycles, which imply
 would theimply
 use ofthe another
 use of version
 another of this simulator
 version of this simulator with a
 with a very simplified operation. Moreover, this simulator would have
 very simplified operation. Moreover, this simulator would have to integrate to integrate gen-generalizations
 eralizations on onthethe
 balancing capability over operating periods of a few
 balancing capability over operating periods of a few cycles such as cycles such as those obtained
 those obtained inin this
 this study.
 study.
 The HF SRB simulator
 The HFwas SRBdeveloped
 simulatorinwas MATLAB.
 developed Its structure
 in MATLAB. is illustrated in
 Its structure is illustrated in
 Figure 4. The lowest
 Figuresimulation
 4. The lowesttimesimulation
 step is based timeonstep theiscontrol
 based time
 on the step of thetime
 control serial
 step of the serial
 levels used in the realused
 levels system (50real
 in the µs) system
 in order(50 to µs)
 be able to compare
 in order to be ablethetoresults
 compare obtained
 the results obtained
 with the latter. with
 The equivalent frequency
 the latter. The of execution
 equivalent frequency forofeach block of
 execution forthe
 eachsimulator
 block ofarethe simulator are
 reported in Figure 4. The
 reported in simulator
 Figure 4. isThedetailed
 simulator hereafter through
 is detailed the description
 hereafter through the of description
 its of its
 building blocks.building blocks.

World Electr. Veh. J. 2021, 12, 10 5 of 12
lectr. Veh. J. 2021, 12, x 5 of 12

 Cells Priority (10 Hz) Cells Cells SoC
 Balancing
 I Batt (20 KHz) (100 Hz)
 U/I cells
 Cells Active cells Cell U/I cells Measurement measures SoC
 Nb of active SoX Batt.
 selection model error models Estimation
 levels (20 KHz)
 (20 KHz) (20 KHz)

 Available Cells security
 cells check ∑ U Batt.

 Figure 4. HighFigure
 Frequency Self-Reconfigurable
 4. High Battery model Battery
 Frequency Self-Reconfigurable synoptic.
 model synoptic.

 3.1. Cell Selection
 The role of3.1.
 thisCell Selection
 block is to simulate the cell selection from the set point of the number
 of active serial levels The role of this
 required andblock is tousage
 the cell simulate
 ordertheofcell selection
 priority. from
 Then, thetheactivation
 set point of the number
 state of the cells is directly updated according to this selection. The order in which the
 of active serial levels required and the cell usage order of priority. Then, theactivation state
 cells are used is generated by the balancing function. For example, when discharging, the the cells are
 of the cells is directly updated according to this selection. The order in which
 usedsorts
 balancing function is generated
 the cellsby the balancing
 according to their function. For example,
 SoC so that the most when
 chargeddischarging,
 cells are the balancing
 discharged first.function
 In this sorts
 study, thethecells according
 balancing to their
 criteria areSoC so that
 limited the most
 to either thecharged cells are discharged
 cell voltage,
 first. In this study,
 the SoC, or the remaining capacity. the balancing criteria are limited to either the cell voltage, the SoC, or
 the remaining capacity.
 The selection function also needs to take care about unavailable cells. Those cells are
 the ones exhibiting The selection function
 a temperature also needs
 or a voltage exceedingto take
 the care about
 security unavailable
 thresholds. cells. Those cells
 Thus,
 are the ones exhibiting a temperature or a voltage
 knowing the required number of active serial levels determined by the regulation func- exceeding the security thresholds.
 Thus, knowing the required number of active serial levels
 tion, the selection function connects the cells satisfying the availability and priority crite- determined by the regulation
 function, the selection function connects the cells satisfying
 ria. If there are not enough cells to meet the demand, all cells are disconnected and the the availability and priority
 criteria. In
 system stops working. If real
 thereuse arecase,
 not enough
 a monitoringcells to
 of meet the number
 the total demand,ofall cells
 cells are disconnected and
 available
 the system stops working. In real use case, a monitoring of the total number of cells
 could be sufficient to anticipate this situation in order to warn the driver that the remain-
 available could be sufficient to anticipate this situation in order to warn the driver that
 ing energy is limited. As a matter of principle, all cells must reach their end of dis-
 the remaining energy is limited. As a matter of principle, all cells must reach their end
 charge/operability at the same time thanks to the fine management of cells during the
 of discharge/operability at the same time thanks to the fine management of cells during
 operation, and finally the battery pack is not any more stopped by the poorest cell (by the
 the operation, and finally the battery pack is not any more stopped by the poorest cell (by
 first fully discharged/unavailable cell). The selection function is used at the operation fre-
 the first fully discharged/unavailable cell). The selection function is used at the operation
 quency, which can be up to 20 kHz in the case of a 50 Hz 230 VRMS sinusoidal waveform
 frequency, which can be up to 20 kHz in the case of a 50 Hz 230 VRMS sinusoidal waveform
 from a HF SRB of 128 serial levels as shown in [9].
 from a HF SRB of 128 serial levels as shown in [9].
 Two other functions need to be executed at this high frequency as they are closely
 Two other functions need to be executed at this high frequency as they are closely
 linked to the selection function: the “cell model” function that simulates the cells evolution
 linked to the selection function: the “cell model” function that simulates the cells evolution
 and the “control and loop” function,
 the “control non-represented
 loop” on Figure 4,on
 function, non-represented adjusting
 Figure 4,the numberthe
 adjusting ofnumber of cells
 cells to connect.to connect.

 3.2. Cell Model 3.2. Cell Model
 A cell model reproduces
 A cell model thereproduces
 behavior of thethe cells (voltage,
 behavior temperature,
 of the cells instantane- instantaneous
 (voltage, temperature,
 ous capacity, total capacity, internal impedance) with respect to external solicitations
 capacity, total capacity, internal impedance) with respect to external solicitations such such as
 as exchanged currents,
 exchanged and externaland
 currents, temperatures. As usually As
 external temperatures. done to limit
 usually thetocomputa-
 done limit the computational
 tional cost, each celleach
 cost, of the
 cellbattery is modelled
 of the battery by an equivalent-circuit
 is modelled by an equivalent-circuitmodel [12].
 model De-
 [12]. Depending
 pending on theon complexity we arewe
 the complexity looking for, thefor,
 are looking cellthe
 electrical equivalent
 cell electrical circuit used
 equivalent circuit used can be
 can be parameterized in the simulator.
 parameterized This cellThis
 in the simulator. modelcell goes
 model from
 goes the simplest
 from model of
 the simplest a of a voltage
 model
 voltage source source
 and anandinternal resistance
 an internal to more
 resistance complex
 to more models
 complex including
 models four series-
 including four series-connected
 connected resistor-capacitor parallel
 resistor-capacitor circuits.
 parallel For example,
 circuits. For example, in theincase of using
 the case the internal
 of using the internal resistance
 resistance R0 and
 R0 aand
 single resistor-capacitor
 a single pair pair
 resistor-capacitor R1C1,Rthe
 1 C1evolution equations
 , the evolution are: are:
 equations

 ( )
 . η (t)
 ( ) = − ( ) z(t) = −i (t) (1) (1)
 Q

 v(t) = OCV (z(t)) − R0 i (t) − R1 i R1 (t) (2)
 ( ) = ( ) − ( ) − ( ) (2)
 ∂i R1 (t) 1 1
 =− i R1 ( t ) + i (t) (3)
 ( ) ∂t R C R 1 C1
 1 1
 1 1
 =− ( ) + ( ) (3)
 

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 where z denotes the SoC, i the current in the cell, η the coulombic efficiency, Q the cell
 nominal
 where capacity,
 z denotesvthe theSoC,
 cell voltage, OCVin
 i the current the
 theOpen
 cell, Circuit Voltage, Refficiency,
 η the coulombic 0 the cell internal
 Q the cell
 resistance, R and C the resistor and capacitor values of the
 nominal capacity, v the cell voltage, OCV the Open Circuit Voltage, R0 the
 1 1 parallel circuit, iR1 the
 cellcurrent
 internal
 through the resistor
 resistance, R1 and R C11. the
 Cellresistor
 parameters are identified
 and capacitor valuesonofan Arbin
 the testcircuit,
 parallel bench at iR1some dis-
 the current
 crete breakpoints.
 through ThenRit1 .isCell
 the resistor necessary to interpolate
 parameters each parameter
 are identified on an Arbin at the
 testSoC
 benchpoints of
 at some
 interest. Tobreakpoints.
 discrete avoid interpolation
 Then itcomputations
 is necessary to at interpolate
 each time step,
 eachinterpolated
 parameter at parameters are
 the SoC points
 stored along a To
 of interest. discretized SoC grid. Thecomputations
 avoid interpolation validity of thisatapproach
 each time is step,
 confirmed in Section
 interpolated 4.1.
 parame-
 ters are stored along a discretized SoC grid. The validity of this approach is confirmed
 3.3.inControl
 SectionLoop
 4.1. Function
 A control loop function is used to determine the instantaneous number of required
 active Control
 3.3. Loop from
 serial levels Functiona Root Mean Square (RMS) set point of a sinusoidal voltage, cur-
 rent, orAoutput
 control loop function
 power (see Sectionis used
 3.7).to determine
 First, a temporalthe instantaneous
 reference signal number
 of the ofsetrequired
 value
 active serial levels from a Root Mean Square (RMS) set point of a sinusoidal
 is generated from its RMS set point. Then, a control loop compares the actual output value voltage, current,
 or the
 with output power
 required (see
 one and Section
 deduces 3.7).
 theFirst,
 numbera temporal
 of cells toreference signal of the set value is
 be connected.
 generated from its RMS set point. Then, a control loop compares the actual output value
 3.4.with the required
 Measurement Errorone and deduces the number of cells to be connected.
 Models

 3.4.The value of each
 Measurement parameter
 Error Models is perfectly known in a battery simulator. This block is
 used to reproduce the biases from the real measuring circuits used to observe parameters
 The value of each parameter is perfectly known in a battery simulator. This block is
 such as voltage, current, and temperature.
 used to reproduce the biases from the real measuring circuits used to observe parameters
 such as voltage, current, and temperature.
 3.5. SoC Estimator
 3.5.AsSoC
 theEstimator
 simulator is designed to faithfully reproduce the behavior of a real battery,
 the SoCAs hastheto simulator
 be estimated from the to
 is designed electrical data
 faithfully measuredthe
 reproduce onbehavior
 the battery,of aasreal
 it would
 battery,
 be the
 done on a real system. The SoC is one of the state indicators commonly
 SoC has to be estimated from the electrical data measured on the battery, as it would monitored by
 a BMS,
 be doneleading
 on aus to system.
 real implement Thea SoC
 well-documented Extended
 is one of the state Kalman
 indicators Filter to this
 commonly pur-
 monitored
 pose. Indeed, Kalman Filters are widely used for SoC estimation [13]
 by a BMS, leading us to implement a well-documented Extended Kalman Filter to this due to an efficient
 compromise between
 purpose. Indeed, modelFilters
 Kalman complexity and used
 are widely accuracy. The
 for SoC SoC error[13]
 estimation hasduebeen assessed
 to an efficient
 bycompromise
 comparing the estimated SoC value with the real SoC used in the cell
 between model complexity and accuracy. The SoC error has been assessedmodel for differ-by
 entcomparing
 estimator thefrequency
 estimated during a discharge
 SoC value with theunder
 real SoC100used
 s of in
 a the
 normalized
 cell model NEDC profilees-
 for different
 (Figure
 timator5).frequency
 In our situation,
 during aa discharge
 frequencyundercomprised between
 100 s of 20 Hz and
 a normalized NEDC 200profile
 Hz allows
 (Figurere- 5).
 ducing
 In ourthe calculation
 situation, time while
 a frequency providingbetween
 comprised a very reasonable
 20 Hz andSoC 200 error lowerreducing
 Hz allows than 1.6%the
 forcalculation
 the worst time
 case.while
 The frequency
 providinguseda very toreasonable
 perform the SoCSoC estimator
 error is then
 lower than 1.6%fixed to 100
 for the worst
 Hz.case. The frequency used to perform the SoC estimator is then fixed to 100 Hz.

 Figure 5. Mean
 Figure error
 5. Mean and
 error maximal
 and error
 maximal between
 error real
 between and
 real estimated
 and SoC
 estimated over
 SoC 100
 over s of
 100 a normal-
 s of a normalized
 ized New European Driving Cycle (NEDC) profile with 20 NMC cells.
 New European Driving Cycle (NEDC) profile with 20 NMC cells.

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 3.6. Cell
 3.6. Cell Balancing
 Balancing
 The cell balancing function is in charge of providing
 providing the cells
 cells usage
 usage order
 order from
 from aa
 parameter to
 parameter to balance.
 balance. This order has to be refreshed
 refreshed with
 with a time dynamic
 dynamic correlated
 correlated to
 to the
 the
 parameter evolution.
 parameter evolution. A 10-Hz frequency
 frequency is used
 used for
 for the cells’
 cells’ voltage
 voltage balancing
 balancing as
 as well
 well as
 as
 for their SoC balancing.

 3.7. Implementation
 The simulator
 simulatorimplements
 implementsthethe model
 model of SRB described
 of SRB previously
 described with either
 previously with aeither
 modela
 of load of
 model orload
 a load
 or profile
 a load such as such
 profile vehicle
 as test profiles.
 vehicle The model
 test profiles. Theof HF SRB
 model computes
 of HF SRB com-its
 overall voltage from incoming current and the number of activated levels.
 putes its overall voltage from incoming current and the number of activated levels. In In turn, the
 simulator computescomputes
 turn, the simulator the next number
 the nextofnumber
 levels toofactivate
 levels toasactivate
 well as the coming
 as well current
 as the comingin
 the HF SRB from the voltage applied on the load or ordered by a temporal
 current in the HF SRB from the voltage applied on the load or ordered by a temporal current/voltage
 load profile likeload
 current/voltage the normalized vehicle
 profile like the test profile,
 normalized vehicleastest
 illustrated in illustrated
 profile, as Figure 6. in Figure 6.

 Current

 P, U, I
 + Nb of levels HF SRB Voltage Simulated
 Corrector
 set points to active model Load
 -
 P, U, I

 simulator.
 Figure 6. HF SRB model implementation in the simulator.

 For a vehicle test profile as thethe Worldwide
 Worldwide harmonized
 harmonized LightLight vehicles Test
 Test Cycle
 Cycle
 (WLTC), the vehicle speed is translated
 (WLTC), the vehicle speed is translated intointo power consumption according
 consumption according to to the relations
 relations
 (4)
 (4) and
 and (5)
 (5) and
 and using
 using the
 the dataset
 dataset shown
 shown in in Table
 Table 11 [12].
 [12]. Then
 Then the
 the instant
 instant power
 power is
 is used
 used to
 to
 determine
 determine the
 the corresponding
 correspondingcurrent
 currentconsumption
 consumptionaccording
 accordingto to
 thethe
 battery output
 battery outputvoltage.
 volt-
 age.  
 d v(t) 1 2
 P(t) = v(t) me + Cr m g + ρ air S f rontal Cd v(t) (4)
 
 dt ( ) 21
 ( ) = ( ) + + ( ) (4)
 
 22
 1  
 me = m + Jmotor + Jgear N + nwheel Jwheel (5)
 Rwheel
 1
 = + ( + + ) (5)
 
 Table 1. Dataset used to translate the vehicle speed into power consumption.

 Values Description
 Table 1. Dataset used to translate the vehicle speed into power consumption.
 Cr 0.0111 Rolling friction coefficient
 g Values 9.81 N/kg Description
 Acceleration of gravity
 ρ air 0.0111 1.225 kg/m3 Rolling frictionAir density
 coefficient
 S f rontal 1.84 m2 Aerodynamic frontal area
 9.81 N/kg Acceleration of gravity
 Cd 0.22 Drag coefficient
 m 1.225 kg/m 3
 1425 kg Air density
 Vehicle masse
 Rwheel 1.84 m2 0.35 m Aerodynamic Wheel
 frontalradius
 area
 Jmotor 0.22 0.2 kg m 2
 Drag coefficient
 Motor inertia
 Jgear 1425 kg 0.05 kg m2 Gear inertia
 Vehicle masse
 N 4 Gear ratio
 0.35 m Wheel radius
 nwheel 4 Number of wheels
 Jwheel 0.2 kg m2 8 kg m2 Motor inertia
 Wheel inertia
 0.05 kg m2 Gear inertia
 Validation
 4. Simulator 4 Gear ratio
 4
 4.1. Arbitrary Waveform Generation Validation Number of wheels
 8 kg m2 Wheel inertia
 First, the ability of the HF SRB model to follow an arbitrary waveform signal is
 assessed. To do so, a recorded signal of a real electrical grid voltage is directly injected as a
 set voltage in the control loop performed at 20 kHz with no output current. This signal is

4. Simulator Validation
 4.1.J. Arbitrary
World Electr. Veh. 2021, 12, 10 Waveform Generation Validation 8 of 12
 First, the ability of the HF SRB model to follow an arbitrary waveform signal is as-
 sessed. To do so, a recorded signal of a real electrical grid voltage is directly injected as a
 set voltage in the control loop performed at 20 kHz with no output current. This signal is
 rectified to match therectified to match behavior.
 real prototype the real prototype behavior.
 Indeed, this Indeed,
 prototype this prototype
 integrates integrates a rectifier
 a rectifier
 diode stage at its charging input to prevent outputting current on its connector.
 diode stage at its charging input to prevent outputting current on its connector.
 The results are shown on Figure 7. The small differences between the battery voltage
 The results are shown on Figure 7. The small differences between the battery voltage
 and the electrical grid voltage show the proper operation of the closed-loop control. One
 and the electrical grid voltage show the proper operation of the closed-loop control. One
 can also see that the 20-kHz control frequency is well adapted to follow the electrical
 can also see that the 20-kHz control frequency is well adapted to follow the electrical net-
 network voltage.
 work voltage.

 −

 Figure 7. Output voltage control loop tracking the electrical grid.
 Figure 7. Output voltage control loop tracking the electrical grid.
 In order to pursue the simulator validation, it is now necessary to check the fidelity of
 In order to pursue the simulator
 the model validation,
 with respect it is nowofnecessary
 to the behavior the cells ittosimulates.
 check the fidelity
 of the model with respect to the behavior of the cells it simulates.
 4.2. Comparison to a Real Battery
 4.2. Comparison to a RealABattery
 comparison of the simulator output with a real prototype of the HF SRB is required
 A comparisonto ofvalidate its proper
 the simulator outputoperation.
 with a real The real battery
 prototype of thedemonstrator
 HF SRB is requiredwe designed is made of
 128 operation.
 to validate its proper SONY VTC6 The18,650 cells (Lithium-ion
 real battery demonstrator NMC cells, 3.6-V
 we designed is nominal
 made of voltage and 3-Ah
 128 SONY VTC6 18,650 capacity).
 cellsAs(Lithium-ion
 explained before,
 NMCone of the
 cells, aims
 3.6-V of self-reconfigurable
 nominal voltage and 3-Ah batteries is to balance
 cells’ before,
 capacity). As explained State ofone
 Charge.
 of theTo validate
 aims the ability of our batteries
 of self-reconfigurable system toisperform
 to balancean efficient balancing,
 cellsTo
 cells’ State of Charge. have been heavily
 validate unbalanced
 the ability prior to perform
 of our system the recording. After abalanc-
 an efficient one-hour rest, we started
 ing, cells have been toheavily
 monitorunbalanced
 the cells’ voltage
 prior while
 to the the battery is
 recording. charging
 After under rest,
 a one-hour a 230weVRMS 50 Hz voltage.
 started to monitor the cells’ voltage while the battery is charging under a 230 VRMS 50 Circuit Voltage to
 The initial voltages were used as a good approximation of the Open
 initialize
 Hz voltage. The initial the simulator.
 voltages were usedThen, the initial
 as a good SoC are deduced
 approximation from Circuit
 of the Open the relationship between
 OCV and SoC. This leads to a strong 56% discrepancy between
 Voltage to initialize the simulator. Then, the initial SoC are deduced from the relationship the SoC of the cells, in both
 between OCV andreal SoC. and simulated
 This leads to battery.
 a strongThe 56%theoretical
 discrepancy endbetween
 of charge voltage
 the SoC ofisthe4.2 V but it has been
 reduced
 cells, in both real and to 4 Vbattery.
 simulated for safety
 Thereasons.
 theoretical end of charge voltage is 4.2 V but
 it has been reduced to 4ItVhas forto be noticed
 safety reasons.from Figure 8 that the real battery stopped charging after 1 h and
 29 min, although the voltage
 It has to be noticed from Figure 8 that the real is still below
 battery 4 V. This
 stopped comesafter
 charging from1the fact that the voltages
 h and
 29 min, although the voltage is still below 4 V. This comes from the fact that the voltages voltage increases
 represented are filtered over 20-ms periods to avoid seeing irrelevant
 when aover
 represented are filtered cell 20-ms
 is connected
 periods(because
 to avoid of the resistive
 seeing 0 × I added
 term Rvoltage
 irrelevant to the OCV when a cell
 increases
 is connected). Thus, the unfiltered voltages reached 4
 when a cell is connected (because of the resistive term R0 x I added to the OCV when a cellV, causing the BMS to stop charging
 is connected). Thus, thethebattery.
 unfiltered voltages reached 4 V, causing the BMS to stop charging
 the battery.

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 Figure 8. Simulated and experimental results of the HF SRB charging over the national power grid with a 56% initial State
 Figure 8. Simulated and experimental results of the HF SRB charging over the national power grid with a 56% initial State
 of Charge (SoC) unbalancing.
 of Charge (SoC) unbalancing.

 To beas
 To be asrealistic
 realisticasaspossible,
 possible, each
 each modelled
 modelled cellcell is parameterized
 is parameterized withwith slightly
 slightly dif-
 different
 ferent capacity and impedance parameters. According to
 capacity and impedance parameters. According to [14], the disparity among the capacities [14], the disparity among the
 capacities of cells coming from a same manufacturer is usually
 of cells coming from a same manufacturer is usually around 2.5%. As the exact capacities around 2.5%. As the exact
 capacities
 of the cellsofusedthe cells
 in theused real in the real
 battery arebattery
 unknown, are unknown,
 simulated simulated
 cells have cells
 their have their
 capacities
 capacities distributed according to a normal distribution
 distributed according to a normal distribution with a 0.025C variance (with C denoting with a 0.025C variance (with C
 denoting
 the nominal the capacity).
 nominal capacity).
 Moreover, Moreover,
 the workthe work
 of [15] of [15]
 states thatstates
 a 20% that a 20% mismatch
 mismatch in internal in
 internal
 impedance impedance is a reasonable
 is a reasonable maximum maximum
 for cellsfor
 fromcellsthefrom
 same the sameand
 batch, batch, andusleads
 leads to addus
 to add a normal
 a normal random random
 variable variable of variance
 of variance 0.1 ×0.1Zi ×toZieachto each impedance
 impedance value
 value Zi (where
 Zi (where Zi
 Zi is the mean of the impedance Zi over the SoC grid).
 is the mean of the impedance Zi over the SoC grid). As a compromise between model As a compromise between model
 accuracy
 accuracy and and computation
 computation time, time, aa RR − − 2RC
 2RC model
 model is is chosen
 chosen for for each
 each cell,
 cell, leading
 leading toto five Zi
 five Zi
 parameters:
 parameters: R00,, R R11,, C
 C11, , RR22, ,CC22. .This
 Thiscell
 celldescription
 descriptionallowsallows us us to
 to compare the balancing
 balancing
 dynamics of the simulated battery and the real one.
 As there
 there exists
 existsno noexactexactmodelmodelofofthe the cell,
 cell, wewe cannot
 cannot expect
 expect thethe simulator
 simulator to repro-
 to reproduce
 duce the exact
 the exact behavior
 behavior of theofbattery.
 the battery. Keeping
 Keeping this consideration
 this consideration in mind
 in mind explains
 explains whywhy it is
 it is acceptable that the simulated battery works 8% longer
 acceptable that the simulated battery works 8% longer than the real one. The main result than the real one. The main
 result to observe
 to observe in Figure in Figure
 8 is that 8 isthethat the simulator
 simulator behavesbehavesin the samein theway sameas way as the
 the real real
 battery
 battery with tendencies.
 with similar similar tendencies.
 Both systems Both present
 systemsapresent
 56% SoC a 56%
 mismatchSoC mismatch at the begin-
 at the beginning of the
 ning
 chargingof the charging
 process andprocess
 becomeand become completely
 completely balanced at balanced
 the end ofatcharge.
 the endFor of charge.
 the sakeFor of
 simplicity,
 the sake ofasimplicity,
 voltage balancing
 a voltage is balancing
 performedisinperformed
 both casesin andbothproduces
 cases anda perfect balancing
 produces a per-
 in less
 fect than 1 hinand
 balancing less40than
 min1for h and an average charging
 40 min for current
 an average of C/2.current of C/2.
 charging

 5. Simulations
 5. Simulations Results
 Results
 Now we
 Now we have
 have validated
 validated the
 the simulator,
 simulator, and
 and assessed
 assessed its
 its fidelity
 fidelity to
 to the
 the real
 real system,
 system, we
 we
 can use it to simulate some use cases.
 can use it to simulate some use cases.
 5.1. Application to the New European Driving Cycle (NEDC)
 5.1. Application to the New European Driving Cycle (NEDC)
 To begin with, the New European Driving Cycle (NEDC) was used as a reference
 To begin with, the New European Driving Cycle (NEDC) was used as a reference
 current and voltage signal to assess the balancing capability over a vehicle test cycle. To do
 current and voltage signal to assess the balancing capability over a vehicle test cycle. To
 this, the same cells SoC imbalance of 56% from Section 4.2 is used as initial SoC distribution.
 do this, the same cells SoC imbalance of 56% from Section 4.2 is used as initial SoC distri-
 The simulator is set to use 20 NMC cells of 3 Ah in series in order to provide a rated voltage
 bution. The simulator is set to use 20 NMC cells of 3 Ah in series in order to provide a
 of 48 V. The current provided by the NEDC is then normalized to take this into account.
 rated voltage of 48 V. The current provided by the NEDC is then normalized to take this
 The vehicle driving cycle is used until a first cell reaches the end of discharge. A SoC
 into account. The vehicle driving cycle is used until a first cell reaches the end of discharge.
 balancing is performed during all the operation.
 A SoC balancing is performed during all the operation.

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 Figure 99 shows
 Figure shows at at left
 left the
 the normalized
 normalized NEDCNEDC cycle
 cycle used
 used by
 by the
 the simulator
 simulator andand at
 at right
 right
 Figure 9 shows at left the normalized NEDC cycle used by the simulator and at right
 the SoC of each cell during a discharge following the NEDC cycle. The figure shows that that
 the SoC of each cell during a discharge following the NEDC cycle. The figure shows the
 the
 theSoC of each
 complete cell during
 energy a discharge
 contained followingbethe NEDC cycle. Theof figure shows
 SoCthat
 complete energy contained in theincells
 the can
 cells
 becan exploited
 exploited inofspite
 in spite an SoC
 an initial initial
 imbalanceim-
 the complete energy contained in the cells can be exploited in spite of an initial SoC im-
 balance
 of 56%. of 56%.
 balance of 56%.

 Figure 9.
 Figure 9. SoC
 SoC dispersion
 dispersion balancing
 balancing with
 with New
 New European
 European Driving
 DrivingCycle
 Cycle(NEDC)
 (NEDC)profile.
 profile.
 Figure 9. SoC dispersion balancing with New European Driving Cycle (NEDC) profile.
 5.2. Effect of the Balancing Criterion
 5.2.
 5.2. Effect
 Effect of
 of the
 the Balancing
 Balancing Criterion
 Criterion
 The impact of the balancing criterion was assessed through the comparison between
 The
 Theofimpact
 the use impact of
 of the
 cell voltage balancing
 theand the usecriterion
 balancing criterion was
 was assessed
 assessed
 of its estimated through
 through
 SoC during the
 the comparison
 several alternancesbetween
 comparison of driv-
 the
 the use of cell voltage and the use of its estimated SoC during several
 ing NEDC cycles and charging periods. The effect of the chemistry of the cellofwas
 use voltage and the use of its estimated SoC during several alternances
 alternances of driv-
 driving
 also
 NEDC
 ing NEDCcycles and
 cycles charging
 and periods.
 charging The
 periods. effect
 The of the
 effect chemistry
 of the of
 chemistry
 assessed by comparing the behavior of NMC cells and LiFePO4 cells. The mean SoC andthe cell
 of was
 the also
 cell assessed
 was also
 by comparing
 assessed
 spread between the
 thebehavior
 by comparing minimal of NMC
 the behavior
 SoC and ofcells
 theNMC andcells
 maximumLiFePO4
 and iscells.
 SoCLiFePO4
 shown The formean
 cells. SoC
 Thecase
 each mean and
 in spread
 SoC
 Figureand
 10.
 between
 spread the minimal
 between SoC and
 the minimal SoCthe
 andmaximum
 the maximum SoC is shown
 SoC for each
 is shown casecase
 for each in Figure 10. 10.
 in Figure

 Figure 10. State of Charge dispersion over NEDC profile.
 Figure
 Figure 10.
 10. State
 State of
 of Charge
 Charge dispersion
 dispersion over
 over NEDC
 NEDC profile.
 profile.
 It appears that the balancing criterion have no effect on the battery autonomy for both
 ItIt appears
 appears
 chemistries. Inthat
 that the
 otherthe balancing
 balancing
 word, criterion
 criterion
 the cell voltage have
 have no
 no effect
 effect
 balancing is on
 as the
 on the battery
 battery
 efficient as autonomy
 autonomy for
 for both
 both
 the SoC balancing,
 chemistries.
 chemistries. In
 In other
 other word,
 word, the
 the cell
 cell voltage
 voltage balancing
 balancing is
 is as
 as efficient
 efficient
 even for LiFePO4 cells, which have a lower correlation between their output voltage and as
 as the
 the SoC
 SoC balancing,
 balancing,
 even
 theirfor
 even for
 stateLiFePO4
 LiFePO4
 of charge. cells,
 In which
 cells, which
 fact, have
 have aa lower
 LiFePO4 correlation
 lowershows
 cells a largebetween
 correlation their output
 SoC imbalance voltage
 between 20%and and
 their
 their state
 state ofofcharge.
 charge. In fact,
 In LiFePO4
 fact, LiFePO4 cells shows
 cells a
 shows large
 a SoC
 large imbalance
 SoC imbalance
 80% of their capacity in the case of voltage balancing. But the balancing capability is so between 20%
 between and
 20%
 and
 high80%
 80% of that,ofastheir
 their sooncapacity
 capacity in cell
 as the thein voltage
 the case
 case of voltage
 of voltage balancing.
 balancing.
 correlation becomes But But
 the the
 stronger balancing
 balancing
 outside capability
 capability
 of constant is
 isvolt-
 so
 so
 highhigh
 that, that,
 as as
 soon soon
 as as
 the the
 cell cell voltage
 voltage correlation
 correlation
 age window, the SoC imbalance was forthwith compensated. becomes
 becomes stronger
 stronger outside
 outside of of constant
 constant volt-
 voltage
 age window, window, the SoC
 the SoC imbalance
 imbalance waswas forthwith
 forthwith compensated.
 compensated.

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 5.3. Cells
 5.3. CapacityDispersion
 Cells Capacity Dispersion andand Battery
 Battery Lifetime
 Lifetime Improvement
 Improvement over WLTC over WLTC
 Since we
 Since we know
 know that
 that the
 the simulator
 simulator efficiently
 efficiently reproduces
 reproduces the the behavior
 behavior of of aa real
 real battery,
 battery,
 the point of interest is now to use it to evaluate the performance of
 the point of interest is now to use it to evaluate the performance of the self-reconfigurablethe self-reconfigurable
 battery compared
 battery compared to to aa classical
 classical static
 static battery.
 battery. To To this
 this purpose,
 purpose, thethe HF
 HF SRB SRB and
 and aa classical
 classical
 static battery
 static battery are
 are compared
 compared using using aa WLTC
 WLTC driving
 driving cycle.
 cycle.
 simulatedbatteries
 Both simulated batteriesare areparameterized
 parameterized to to
 useuse128128
 NMC NMC cellscells
 of 3 of
 Ah3inAh in series
 series with
 awith a cell voltage
 cell voltage end of discharge
 end of discharge threshold threshold
 of 2.9 V. The of WLTC
 2.9 V.driving
 The WLTC cycle is driving cycle
 translated is
 into
 translated into a power profile normalized for a 360-V battery
 a power profile normalized for a 360-V battery and applied to discharge both simulated and applied to discharge
 both simulated
 batteries throughbatteries through
 a control-loop a control-loop
 (see Section 3.7). A (see
 cellSection 3.7). A dispersion
 total capacity cell total capacity
 of +/−
 dispersion
 10% around of2.696
 +/- 10% Aharound
 is created2.696asAh is created
 initial as initial cell
 cell conditions for conditions
 both batteries for both
 while batteries
 all are
 while all are
 initialized initialized
 to 100% of theirto SoC.
 100%Thus,of their
 eachSoC. Thus,
 battery eachwith
 starts battery starts with
 an overall an overall
 capacity of 345
 capacity
 Ah takingofinto345account
 Ah taking into account
 the applied dispersion.the applied dispersion.
 The simulation The simulation
 is performed with SoC is
 performedaswith
 balancing wellSoC balancing capacity
 as remaining as well as remaining
 balancing capacity balancing
 to compare their effectto oncompare their
 the behavior
 of the on
 effect HFthe
 SRB.behavior of the HF SRB.
 Before
 Before analyzing
 analyzingthe theresults of the
 results of simulation
 the simulationshownshownon Figure
 on 11, the energy
 Figure 11, the delivered
 energy
 by each battery
 delivered by each is compared to ensure ato
 battery is compared similar
 ensure use. The difference
 a similar use. Thebetween
 difference thebetween
 cumulatedthe
 energy
 cumulatedof both batteries
 energy havebatteries
 of both to be compared
 have to when the first battery
 be compared when the is fully
 first discharged. For
 battery is fully
 both balancing
 discharged. Forstrategies,
 both balancing the static batterythe
 strategies, stops its battery
 static discharge at time
 stops t1 where at
 its discharge 2.208
 timeAht1
 have been used when 2.22 Ah have been used for the HF SRB,
 where 2.208 Ah have been used when 2.22 Ah have been used for the HF SRB, which which shows the similar use
 of boththe
 shows batteries
 similarwith use aofdifference
 both batteriesof less thana 0.5%.
 with difference of less than 0.5%.

 +/- 10%

 +10.5%
 t1 t2

 Figure 11.
 Figure 11. Comparison
 Comparison of
 of charge
 charge dispersions
 dispersions between
 between aa static
 static battery
 battery and
 and aa self-reconfiguring
 self-reconfiguring battery
 battery discharging
 discharging with
 with
 Worldwideharmonized
 Worldwide harmonizedLight
 Lightvehicles
 vehiclesTest
 TestCycle
 Cycle(WLTC)
 (WLTC)vehicle
 vehiclecycles.
 cycles.

 Thus, 18.1%
 18.1% ofofthe
 thetotal
 totalcapacity
 capacityis is
 unavailable
 unavailable in the static
 in the battery
 static while
 battery the HF
 while the SRB
 HF
 stopsstops
 SRB its discharge at t2 with
 its discharge at t2awith
 totalaoftotal
 2.43 of
 Ah2.43
 provided with thewith
 Ah provided chargethebalancing strategy
 charge balancing
 and 2.505
 strategy andAh for Ah
 2.505 thefor
 SoCthe balancing,
 SoC balancing,which respectively
 which represent
 respectively represent9.87 9.87and
 and 7.1% of
 7.1% of
 unavailable capacity.
 capacity.
 In terms of battery lifetime improvement from a WLTC profile, profile, this
 this leads
 leads toto increase
 increase
 the running time by 10.5%, which is around around half
 half the
 the capacity
 capacity dispersion
 dispersion applied
 applied on on the
 the
 initial state of charge of the cells.
 cells. This demonstrated the ability of the HF SRB to to use
 use the
 the
 energy available in each cell through
 through aa standard
 standard driving
 driving cycle
 cycle as
 as the
 the WLTC.
 WLTC.
 One can note that the strategy of balancing the remaining charge of the the cells
 cells allows
 allows
 to converge much more quickly towards a homogeneous distribution
 to converge much more quickly towards a homogeneous distribution of those charges. of those charges.
 This
 This shows
 shows that
 that aa much
 much greater
 greater dispersion
 dispersion of of cell
 cell capacity
 capacity could
 could be be envisaged
 envisaged without
 without
 impacting
 impacting the power delivered, which paves the way to the use of second life
 the power delivered, which paves the way to the use of second life cells
 cells or
 or even
 even
 of
 of different
 different chemistries
 chemistries mixes.
 mixes.
 6. Conclusions
 6. Conclusions
 In this paper, we evaluated the HF SRB capability to maximize the use of all cells
 In this paper, we evaluated the HF SRB capability to maximize the use of all cells
 when cells are significantly dispersed in terms of state of charge (up to 56%). That was both
 when cells are significantly dispersed in terms of state of charge (up to 56%). That was
 validated by simulation and experimentally.
 both validated by simulation and experimentally.
 A comparison of cell balancing performance between SoC and cell voltage criteria
 A comparison of cell balancing performance between SoC and cell voltage criteria
 were carried out on the basis of this dispersion. It was shown that it is possible to exploit
 were carried out on the basis of this dispersion. It was shown that it is possible to exploit
 the cell voltage to perform SoC balancing even for flat voltage profile chemistries such
 the cell voltage to perform SoC balancing even for flat voltage profile chemistries such as