Comparison of Battery Architecture Dependability - MDPI

batteries Article

Comparison of Battery Architecture Dependability Christophe Savard *

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, Pascal Venet

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, Éric Niel, Laurent Piétrac and Ali Sari

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Univ Lyon, Université Claude Bernard Lyon 1, École Centrale de Lyon, INSA Lyon, CNRS, Ampère, F-69622 Villeurbanne, France; [email protected] (P.V.); [email protected] (É.N.); [email protected] (L.P.); [email protected] (A.S.) * Correspondence: [email protected] Received: 14 May 2018; Accepted: 7 June 2018; Published: 3 July 2018







Abstract: This paper presents various solutions for organizing an accumulator battery. It examines three different architectures: series-parallel, parallel-series and C3C architecture, which spread the cell output current flux to three other cells. Alternatively, to improve a several cell system reliability, it is possible to insert more cells than necessary and soliciting them less. Classical RAMS (Reliability, Availability, Maintainability, Safety) solutions can be deployed by adding redundant cells or by tolerating some cell failures. With more cells than necessary, it is also possible to choose active cells by a selection algorithm and place the others at rest. Each variant is simulated for the three architectures in order to determine the impact on battery-operative dependability, that is to say the duration of how long the battery complies specifications. To justify that the conventional RAMS solutions are not deployed to date, this article examines the influence on operative dependability. If the conventional variants allow to extend the moment before the battery stops to be operational, using an algorithm with a suitable optimization criterion further extend the battery mission time. Keywords: battery; operative dependability; selection algorithm

1. Context An electrical energy storage systems (EESS) may be an electrochemical cell association in a battery [1]. These cells can belong to different technologies and chemistries. The oldest are lead–acid cells. Then, there are the cells using alkaline metals. Finally, for a quarter of a century, lithium cells have been marketed. Lithium-ion cells are more stable than the first lithium cells and have higher energy and power densities than the lead–acid and nickel-based technologies [2]. They also have a higher lifespan, which partly explains their strong growth. The lithium-ion battery market continues to grow, to the point that their unit manufacturing price decreases steadily because of the growing number of units produced [3]. Naturally, in a battery, all cells belong to the same technology. This paper presents three architectures that can be used in cell batteries: two classics, using permanent series and parallel connections between cells, and one innovative, described later and allowing different connections between the cells. On these architectures, different variants are tested: common solutions (balancing between cells, using of more cells than necessary to provide the nominal power), other conventional but not deployed in best industrial solutions (failure tolerance of some cells with over-solicitation of others, addition of redundant cells to replace the first failing cells) and a new variant (redundant cells management with a control law using cells fundamental states as a choice criterion). The performances of the architectures and their variants are compared by simulation under Matlab, by resorting to a cell model that including aging phenomena. The cell main electrical characteristic is its maximum storable capacity Q0 . It is well known that this capacity decrease with aging. When a cell is new, this capacity is optimal. It is noted in this paper as Q*. The battery physical behavior can be modeled by a second order Thevenin model scheme [4] as

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seen in Figure 1. In this, a cell is represented as a series association of an open-circuit voltage (OCV), an an equivalent equivalent series series resistance resistance (ESR) (ESR) and and aa parallel parallel RC RC circuit. circuit. The The ESR ESR corresponds corresponds to to the the battery battery terminals , only if it is measured without an external load connection and with the cell at terminals voltage voltage V Vcell cell, only if it is measured without an external load connection and with the cell at rest rest for for an an adequate adequate time. time. This This time time is is necessary necessary for for balancing balancing internal internal electrical electrical charges charges (relaxation (relaxation phenomenon). A double-layer capacitance (C ) and a charge transfer resistance phenomenon). A double-layer capacitance (Cww) and a charge transfer resistance (R (Rww)) complete complete the the model by describing relaxation. Other internal phenomena such as a hysteresis voltage can also model by describing relaxation. Other internal phenomena such as a hysteresis voltage can also be be modeled by additional additionalsubcircuits. subcircuits.Hysteresis Hysteresisconsists consists a shifting open-circuit voltage for modeled by inin a shifting onon thethe open-circuit voltage for the the same contained charge between current direction,ananupward upwardoffset offsetwith with aa negative negative current in same contained charge between current direction, current IIcell cell in charging phase and a downset offset with a positive current in the discharge phase. charging phase and a downset offset with a positive current in the discharge phase.

Figure 1. Cell second order Thevenin model. Figure 1. Cell second order Thevenin model.

To express physical state in which a cell is, two indicators are commonly used: SoC and SoH, To express state inand which a cellofis,health two indicators aredescribes, commonly used: SoC SoH, respectively, thephysical state of charge the state [5]. The SoC in percent, theand amount respectively, the state of it charge andatthe state compared of health [5]. The SoC describes, in percent, amount of electrical charge Q(t) contains t time, to its maximum storable capacity.the The SoC is of electrical charge Q(t) it contains at t time, compared to its maximum storable capacity. The SoC is determined by Equation (1). Moreover, when a cell ages, it cannot store as much electrical charge determined by Equation (1). Moreover, when a cell ages, it cannot store as much electrical charge than than when it is new. The maximum storable capacity Q0 decreases over time continuously and when it is new. maximum storable capacity Q0 decreases time continuously and gradually fromThe its optimal capacity Q*. So, a cell’s State of over Health (SoH) is defined bygradually the ratio from its optimal capacity Q*. So, a cell’s State of Health (SoH) is defined by the ratio between these between these two capacity values, as shown by Equation (2). For applications requiring significant two capacity values, as shown by Equation (2). For applications requiring significant power more power more than a willingness to deliver energy, SoH can also be defined relative to the ESR [6].than a willingness to deliver energy, SoH can also be defined 𝑄(𝑡) relative to the ESR [6]. (1) 𝑆𝑜𝐶(𝑡) = 𝑄 (𝑡) Q(t) 𝑄 (𝑡) (1) SoC (t) = (2) 𝑆𝑜𝐻(𝑡) = Q (t) 𝑄∗ 0 The ISO 12405-2 standard for electric vehiclesQ0[7] (t) specifies test procedures for lithium-ion SoH (t) = (2) batteries and electrically propelled road vehicles. It specifies that a cell enters the old age phase when Q∗ its SoH tostandard 80%. Manufacturers communicate a lifetime value for cells that incorporate, as Thegoes ISO down 12405-2 for electric vehicles [7] specifies test procedures for lithium-ion batteries specified in their datasheet, the two aging modes that a cell faces: an age-related calendar mode [8] and electrically propelled road vehicles. It specifies that a cell enters the old age phase when its SoH and adown cyclictomode to cell use [9]. These two phenomena [10]cells can that be described by aascombined goes 80%. related Manufacturers communicate a lifetime value for incorporate, specified evolution of a linear aging and an “aging” power of time whose principles are described Equation in their datasheet, the two aging modes that a cell faces: an age-related calendar mode [8]by and a cyclic (3), where thetoaging parameter is between 0.5 and [10] 2 and A1be and A2 are two mode related cell use [9]. These two phenomena can described by aconstants. combined evolution of a

linear aging and an “aging” power of𝑆𝑜𝐻(𝑡) time whose the = 1 −principles 𝐴 𝑡 − 𝐴 𝑡 are described by Equation (3), where(3) aging parameter is between 0.5 and 2 and A1 and A2 are two constants. Cyclic aging is aggravated mainly by three parameters: the operating temperature [11], the amount of electrical charge extracted in a cycle [12] and the current [13]. Despite the cell SoH (t) = 1 − A1 t − A2 t aging (3) manufacturing standardization, disparities can occur between cells from the same batch. These are Cyclic is aggravated by three parameters: the operating temperature amount reflected inaging an optimal capacitymainly Q* variability and in an equivalent series resistances[11], ESRthe variability of electrical charge extracted in a cycle [12] and the current [13]. Despite the cell manufacturing [14]. Thus, when cells are associated in an EESS, their disparities should lead to imbalances in standardization, disparitiesand canthen occur between from the same batch. reflected currents, cell temperatures in their aging.cells Consequently, a battery mayThese remainare operational in an optimal capacity Q* variability and in an equivalent series resistances ESR variability [14]. for a shorter time than a cell lifetime. Thus,Operative when cells are associated inisandefined EESS, their shouldinlead to imbalances in of currents, dependability Odep as thedisparities time, expressed hours or in number cycles, cell temperatures and then in their aging. a battery remain operational for a shorter during which a multi-cellular battery canConsequently, meet the external loadmay specifications [15]. In other words, time than cell lifetime. Odep is theatime before a downtime related to a full discharge or a too high age. That is to say, it Operative dependability Odep is therequested time, expressed hours or incell, number cycles, contains enough operational cells to defined provideasthe power. in For a single this of cessation during which a multi-cellular battery can meet the external load specifications [15]. In other words, comes from: -

a cell aging failure, resulting in a SoH of less than 0.8; a sudden random failure (open or short circuit); a complete discharge, SoC drops down to zero in operating phase.

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Odep is the time before a downtime related to a full discharge or a too high age. That is to say, it contains enough operational cells to provide the requested power. For a single cell, this cessation comes from:

− − −

a cell aging failure, resulting in a SoH of less than 0.8; a sudden random failure (open or short circuit); a complete discharge, SoC drops down to zero in operating phase.

For a battery, Odep depends on the architecture (how cells are connected); if some cells are in redundancy for the current mission and if failed cells can be isolated or not. It is therefore necessary to monitor the cell states. In order to monitor cells, in particular to control end of charging and to prevent overheating, EESS cells are managed by a BMS (Battery Management System) [16]. Today, multi-cellular EESS are constituted according to two conventional architectures (series-parallel and parallel-series) and sometimes include variants, as explained in the next section, to improve their availability. From a formal point of view, the operative dependability Odep is defined by the equation set (4), according to SoC and SoH cells.

Odep = min{SoH (χ) > 0.8, SoC (χ) > 0}

   su f f icient number o f cells with provide power > needed power;   χ = f ( architecture, structure)

(4)

In the next section, different architectures and possible variants to improve the battery operative dependability are presented. Then, part III presents simulations performed on each variant, whatever the cell technology, in order to determine the impact on operative dependability, for LiFePO4 cell example. The next part presents and compares the simulation results, especially for operative dependability. 2. Architectures and Variants In the literature, to improve the operative dependability, various solutions for reconfiguration of the internal structure are proposed, such as the power tree solution presented in [17] or the DESA architecture (Dependable, efficient, scalable architecture) [18]. The first solution does not allow use of a battery at full power and the second only improves the operative dependability of a similar order to the amount of additional cell number (typically 50% with 50% of additional cells). Three architectures are compared to determine which has the best operative dependability: two conventionally used and a new one. These architectures are reconfigurables by using a limited number of switches associated with a cell. To increase the battery voltage, the cells are associated in series. To increase the current, they are associated in parallel. Thus, batteries are generally associated in a SP (series-parallel) architecture, as described in Figure 2, which presents a n-rows m-columns structure, noted (n, m). Switches allow to isolate a column, following one of its cell failure, for instance. By duality, the same structure can be inserted into a PS (parallel-series) architecture, as shown in Figure 3. One switch for each cell is needed in order to isolate a failed cell. In an SP architecture, same-column cell voltage disparities can appear. In a PS architecture, the same-row cell currents can be different. To deliver the same power, by keeping the same structure, another architecture is possible: the C3C [19], depicted in Figure 4. The architecture consists of an element association. Each C3C element comprises a cell and three switches, as shown by Figure 5. Each includes an upstream connection and three downstream. The A indexed switch is placed on the upstream connection. Switch B is on the first downstream connection, C on the third. The middle connection is intended to be connected with the same-column downstream-row cell upstream connection. The C3C architecture combines the advantages of both conventional architectures, as PS’ self-balancing and allows a series association of some cells located on different columns. The current that leaves the Celli,j in the ith row and the jth column can be directed to one of the three following row cells: Celli+1,j−1 , Celli+1,j , Celli+1,j+1 , in a

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recharge phase, respectively by the switches Si,j B, Si+1,j A and Si,j C or to one of the three upstream row cells: Celli−1,j−1 , Celli−1,j , Celli−1,j+1 , in a discharge phase. This is made by activating the appropriate Batteries 2018, 4, x FOR PEER REVIEW switches, respectively Si−1,j−1 C, Si,j A and Si−1,j+1 B. Thanks to the architecture, the mth column cells are connected those ofREVIEW the first column. Batteries 2018,with 4, x FOR PEER 4 of 12

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Figure 2. SP (series-parallel) architecture.

Figure 2. SP (series-parallel) architecture. Figure 2. SP (series-parallel) architecture.

Figure 2. SP (series-parallel) architecture.

Figure 3. PS (parallel-series) architecture.

Figure 3. PS (parallel-series) architecture. Figure 3. PS (parallel-series) architecture. Figure 3. PS (parallel-series) architecture.

Figure 4. C3C architecture.

Figure 4. C3C architecture. Figure 4. C3C architecture.

Figure 4. C3C architecture. Figure 5. C3C element.

The C3C architecture involves two particularities. Firstly, to take advantage of its very large possible configuration number [20], it must be managed by an algorithm that chooses the best cell combination, with a cell-aging-reducingFigure aim. The cells selection parameters can be chosen to define 5. C3C element. the optimal combination. Only two are considered in this paper: SoC and SoH. Secondly, whatever The C3C architecture two particularities. Firstly, to of take advantagemust of itsbevery large the architecture, to increase involves battery reliability, a minimum amount redundancy included possible number of [20], it must be managed by the an algorithm that chooses the best cell [21]. This configuration minimal part consists using a column (especially mth) as a redundant column. Thus, Figure 5. C3C element. a cell-aging-reducing aim. Thepower cells selection acombination, (n, m) batterywith is calibrated to provide a nominal Pn givenparameters by Equationcan (5).be chosen to define

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Figure 4. C3C architecture.

Figure 5. C3C element. Figure 5. C3C element.

The C3C architecture involves two particularities. Firstly, to take advantage of its very large The configuration C3C architecture involves particularities. to take advantage of itsthe very possible number [20], two it must be managedFirstly, by an algorithm that chooses bestlarge cell possible configuration number [20], it must be managed by an algorithm that chooses the best cell combination, with a cell-aging-reducing aim. The cells selection parameters can be chosen to define combination, with a cell-aging-reducing aim. The cells selection can Secondly, be chosen whatever to define the optimal combination. Only two are considered in this paper:parameters SoC and SoH. the combination. Only two are considered in this paper: SoCof and SoH. Secondly, the the optimal architecture, to increase battery reliability, a minimum amount redundancy mustwhatever be included architecture, to increase battery reliability, a minimum amount of redundancy must be included [21]. [21]. This minimal part consists of using a column (especially the mth) as a redundant column. Thus, This part consists of to using a column (especially thePnmth) as by a redundant Thus, a (n, m) a (n, minimal m) battery is calibrated provide a nominal power given Equation column. (5). battery is calibrated to provide a nominal power Pn given by Equation (5). 𝑃 = 𝑛(𝑚 − 1) 𝑉 𝐼 (5)

Pn = (n(m − 1))Vcell Icell Batteries 2018, 4, x FOR PEER REVIEW

(5) 5 of 12

As a result, if the conventional architectures include a redundant column, they can also be managed the same algorithm that chooses the best cell combination. The possible combination As by a result, if the conventional architectures include a redundant column, they can also be number is nevertheless lower. if the must supply nominal current Inom , managed by the same much algorithm thatTherefore, chooses the bestbattery cell combination. Theitspossible combination depict in Equation (6), onemuch cell in each Therefore, row stays at rest.battery In PS and architectures, cell can number is nevertheless lower. if the mustC3C supply its nominalthis current Inom,be anydepict of theinmEquation cells of each row.cell In in SP,each all the cells at rest. To dothis this, it can requires (6), one rowsame-column stays at rest. In PS are andplaced C3C architectures, cell be any ofa the m cells of eachwith row.each In SP, allin thePS same-column are placed at shown rest. To in doFigures this, it requires adding switch in series cell and one by cells column in SP, as 2 and 3. adding a switch in series with each cell in PS and one by column in SP, as shown in Figures 2 and 3.

Inom = (m − 1) Icell 𝐼

= (𝑚 − 1)𝐼

(6)

(6)

If SP and batteriesinclude includeaaredundant redundant column, column, it If SP and PSPS batteries it becomes becomespossible possibletotouse usethis thisredundancy redundancy classically. That batterycan canwork workwith withits itsbase base cells, cells, corresponding corresponding to columns, classically. That is,is, thethe battery tothe thefirst first(m−1) (m−1) columns, until them stops operational.ItItis is thus thus replaced replaced by the mth until oneone of of them stops totobebeoperational. by the thespare sparecell. cell.InInthis thisvariant, variant, the mth switches in the Figure 3 are off in the beginning for a PS architecture. For an SP architecture, in Figure switches in the Figure 3 are off in the beginning for a PS architecture. For an SP architecture, in Figure 2, all cells the mth column are redundant. all 2, cells in theinmth column are redundant. Another variant can also examined,tolerating tolerating aa cell circuit Another variant can also bebeexamined, cell failure failureby byreplacing replacingititwith witha short a short circuit in SP architecture and allowing the battery to continue to fulfill its mission, even if it requires the in SP architecture and allowing the battery to continue to fulfill its mission, even if it requires the active active cells to afford a greater current than their nominal current. To do so, two switches should be cells to afford a greater current than their nominal current. To do so, two switches should be placed placed around each cell: one in series and one in parallel as Si,jA is being open and Si,jB closed when around each cell: one in series and one in parallel as Si,j A is being open and Si,j B closed when celli,j celli,j must be isolated, as depicted for cell22, as shown by Figure 6. In this example, cell22 fails, the must be isolated, as depicted for cell22 , as shown by Figure 6. In this example, cell22 fails, the current current of the second column passes through S22B. The cell is marked with a red cross to symbolize of the second column passes through S22 B. The cell is marked with a red cross to symbolize its failure. its failure. This variant does not require redundancy cells. The same power as in Equation (5) is This variant does not require redundancy cells. The same power as in Equation (5) is obtained with a obtained with a (n, m−1) structure. In a PS architecture, the cell may just be disconnected by only one (n, switch, m−1) structure. a PS the cell may just be disconnected by only one switch, as shown as shownIn for cellarchitecture, 22 in Figure 7, in which cell1m−1 and cell22 are faulty and marked with a red forcross. cell22 in Figure 7, in which cell1m−1 and cell22 are faulty and marked with a red cross.

Figure 6. Fault tolerant SP architecture. Figure 6. Fault tolerant SP architecture.

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Figure 6. Fault tolerant SP architecture.

Figure 7. Fault tolerant PS architecture. Figure 7. Fault tolerant PS architecture.

It is also possible to use a battery comprising m columns to provide a power corresponding to It is also power possible use a battery comprising columns provide a power corresponding to the the the nominal oftoEquation (5). In this way, mthe batterytohas an over-capacity compared to nominal power of Equation (5). In this way, the battery has an over-capacity compared to the external external load specifications. load Moreover, specifications. in order to reduce the disparities between the SoCs when cells are associated in series, Moreover, in orderbalancing to reduce circuits the disparities between SoCs whentocells are associated in series, in an SP architecture, are often used. the They enable homogenize the electrical in an SP architecture, balancing circuits are often used. They enable to homogenize the electrical charges2018, in all in theREVIEW string [22]. These balancing circuits are controlled by a BMS [23]. They6allow Batteries 4, xcells FOR PEER of 12 charges in all cells in the string [22]. These balancing circuits are controlled by a BMS [23]. They allow better stored stored energy energy use use [24] [24] and and aa battery batteryoperative operativedependability dependability improvement improvement [25,26]. [25,26]. To To evaluate evaluate better balancing impact, impact, basic basic SP SP of of Figure Figure 22 (with −1)columns) columns)with withand andwithout withoutbalancing balancing circuits circuits are are balancing (with (m (m−1) simulated. All All compared compared batteries batteries must must provide provide the the same same Equation Equation (5) (5) power. power. So, So, this this structure structure only only simulated. includes (m−1) (m−1)columns. columns.Several Severalbalancing balancingtechniques techniquesexist existininan anSP SParchitecture: architecture: includes -− -−

dissipative balancing balancing [27], [27], consisting consisting of of balancing balancing the the electrical electrical charges charges from from below below by byremoving removing dissipative excess energy energy by by Joule Joule effect; effect; excess redistributive balancingtotosend send excess energy the most charging cell(s) to the least redistributive balancing excess energy fromfrom the most charging cell(s) to the least charging charging cell(s) in column the same column [28]. Itsisprinciple described by 8the Figurerelating 8 scheme, cell(s) in the same [28]. Its principle describedisby the Figure scheme, to a relating to a single column j in an SP architecture. When a,j is more than Cellb,j, the single column j in an SP architecture. When Cella,j is moreCell charged thancharged Cellb,j , the intermediate intermediate associate toj,this column is placed parallel on by the switching onSthe capacitor Cbjcapacitor , associateCb toj,this column is placed in j,parallel by in switching Sa,j + and a,j− Sswitches. a,j+ and Sa,j− switches. Then, these switched and the Sb ,j + and Sb ,j− switches are Then, these switches are switches switched are off and the Sboff + and Sb switches are switched on. ,j ,j− switched on. At the end, Cell aj electric charge have been reduced and Cell aj one have been At the end, Cellaj electric charge have been reduced and Cellaj one have been increased. increased.

Figure 8. Balancing circuit for an SP architecture’s column j. Figure 8. Balancing circuit for an SP architecture’s column j.

In this study, only redistributive balancing circuits from one cell to another are considered. This only redistributive balancingeach circuits from one cell to another aretoconsidered. leadsIn to this add study, two switches by cell in SP schemes, connecting a terminal of the cell a terminal This leads to add two switches by cell in SP schemes, each connecting a terminal ofthis theway, cell to of an intermediate capacitor, used to temporarily store the energy to be transferred. By thea terminal of an intermediate capacitor, used to temporarily store the energy to be transferred. By this different variants combining architecture and improvement are listed in Table 1. The structure column number mc and the cell-associated switch number are also specified. For the basic PS and the over-capacity PS variants, the switches in Figure 3 are not useful because cells are not managed individually. The cells are all active or all inactive. In the same way, those of Figure 2 are not useful in the without-balancing SP variant. Apart from the variant reported without balancing, all other SPs include balancing circuits, which add two switches per cell. The variants deployed in present

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Figure 8. 8. Balancing Balancing circuit circuit for for an an SP SP architecture’s architecture’s column column j.j. Figure

In this this study, study, only only redistributive redistributive balancing balancing circuits circuits from from one one cell cell to to another another are are considered. considered. This This In

way, theleads different combining andconnecting improvement are of listed in to Table 1. The structure to add add variants two switches switches by cell cell in in architecture SP schemes, schemes, each each terminal the cell cell terminal leads to two by SP connecting aa terminal of the to aa terminal columnof number m and the cell-associated switch number are also specified. For the basic PS and of an an intermediate intermediate capacitor, used used to to temporarily temporarily store store the the energy energy to to be be transferred. transferred. By By this this way, way, the the c capacitor, different variants combining architecture and improvement are listed in Table 1. The structure the over-capacity PS variants, switchesand in Figure 3 are not usefulinbecause are not managed different variants combiningthe architecture improvement are listed Table 1. cells The structure column The number mcc are and all the active cell-associated switch number number are same also specified. specified. For the the basic PS and and the not useful column number m and the cell-associated switch are also For PS the individually. cells or all inactive. In the way, those ofbasic Figure 2 are over-capacity PS PS variants, variants, the the switches switches in in Figure Figure 33 are are not not useful useful because because cells cells are are not not managed managed over-capacity in the without-balancing SP variant. Apart fromInthe variant reported without balancing, all other individually. The The cells cells are are all all active active or or all all inactive. inactive. In the same same way, way, those those of of Figure Figure 22 are are not not useful useful individually. the SPs include balancing circuits, whichApart addfrom twothe switches per cell. The balancing, variants all deployed in the the without-balancing without-balancing SP variant. variant. Apart from the variant reported reported without balancing, all other SPs SPs in present in SP variant without other industrial solutions are PS-base, SP-base with or without balancing and over-capacity variants. include balancing circuits, which add two switches per cell. The variants deployed in present include balancing circuits, which add two switches per cell. The variants deployed in present industrial solutions solutions are are PS-base, PS-base, SP-base SP-base with with or or without without balancing balancing and and over-capacity over-capacity variants. variants. industrial

Table 1. Simulated architectures and variants. Table 1. 1. Simulated Simulated architectures architectures and and variants. variants. Table

Architecture Architecture Architecture

Electric Electric Electric Scheme Scheme Scheme

Switches per per ColumnColumn Switches Column Switches (mc ) Cell per CellNumber NumberNumber (mcc)) Cell (m basic (m−1) (m−1) basic 00 (m−1) basic 0 over-capacity m over-capacity 00 m over-capacity 0 m With redundancy redundancy m With redundancy 1 m With 11 m With SoC-based optimization optimization 3 With SoC-based With SoC-based 1 m 1 m m optimization algorithm 1 algorithm algorithm SoH-based With SoH-based SoH-based With optimization With optimization 1 m m m optimization algorithm 11 algorithm algorithm

Fig. Fig. Fig.

PS PS PS

33

PS PS PS

77

7

Variant Variant Variant

Fault tolerant tolerant Fault tolerant Fault

11

1

(m−1) (m−1) (m−1)

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7 of 12 of 12 12 77 of 7 of 12

SP SP SP SP SP

2 22 2

SP SP SP SP SP

2& & 22 & 28& 88 8

SP SP SP SP SP

C3C C3C C3C C3C C3C

6 66 6

5 55 5

Without balancing Without balancing Without balancing balancing Without Without balancing Basic, with balancing Basic, with balancing Basic, with balancing Withwith redundancy Basic, with balancing Basic, balancing With redundancy With redundancy over-capacity With redundancy With redundancy over-capacity over-capacity over-capacity over-capacity 2& 8 SoH-based With optimization With SoH-based With SoH-based optimization With SoH-based optimization algorithm With SoH-based optimization optimization algorithm algorithm algorithm algorithm

2

6

Fault tolerant Fault tolerant tolerant Fault Fault tolerant Fault tolerant

With SoC-based optimization With SoC-based SoC-based optimization With optimization algorithm With SoC-based optimization algorithm algorithm With SoC-based algorithm optimization algorithm With SoH-based optimization 5With SoH-based SoH-based optimization With optimization With SoH-based algorithm With SoH-based optimization algorithm algorithm optimization algorithm algorithm

0 00 0 2 22 2 2 22 2 2 22 2 4 44 4 3 33 3 3 33 3

0

2 2 2

4

3 3

(m−1) (m−1) (m−1) (m−1) (m−1) (m−1) (m−1) (m−1) (m−1) (m−1) m m m m m m m m m m (m−1) (m−1) (m−1) (m−1) (m−1) m m m m m m m m

m m

3. Simulations 3. Simulations Simulations 3. 3. Simulations The different variants and architectures were modeled using Matlab. The program simulates cell 3. Simulations The different different variants variants and and architectures architectures were were modeled modeled using using Matlab. Matlab. The The program program simulates simulates cell cell The associations according to each different (n, m) structures. variant, it submits The different variants andarchitecture architecturesfor were modeled using Matlab. For Theeach program simulates cell associations according to each architecture for forwere different (n, m) m) structures. structures. For each each variant, it submits submits The different variants and architectures modeled using Matlab. The program simulates cell associations according to each architecture different (n, For variant, it the battery to regular cycling, leading the current shown in Figure 9 for a single 10 Ah cell. The battery associations according to each architecture for different (n, m) structures. For each variant, it submits the battery battery to to regular regular cycling, cycling, leading leading the the current current shown shown in in Figure Figure 99 for for aa single single 10 10 Ah Ah cell. cell. The The battery battery the associations according to each architecture for different (n, m) structures. For each variant, it submits is initially full. This cycle consists of firstly, a discharge under a current I equal to the battery nominal the battery to regular cycling, leading the current shown in Figure 9 for a single 10 Ah cell. The battery is initially initially full. full. This This cycle cycle consists consists of of firstly, firstly, aa discharge discharge under under aa current current II equal equal to to the the battery battery nominal nominal is current nomfull. divided by theconsists active column number m c (that isintoaFigure say (m−1) or m) forthe a duration of 2500The battery is initially This cycle of firstly, a discharge under current battery the battery to Iregular cycling, leading the current shown 9I equal for a to single 10 Ahnominal cell. current IInom nom divided divided by by the the active active column column number number m mcc (that (that is is to to say say (m−1) (m−1) or or m) m) for for aa duration duration of of 2500 2500 current s. So, except for over-capacity variants, Inumber = 10 A m inc (that discharging phase. Bym) this way, the battery is current I nom divided by the active column is to say (m−1) or for a duration of 2500 is initially full. This consistsvariants, of firstly, discharge under phase. aphase. current I equal battery s. So, So, except forcycle over-capacity variants, I ==a10 10 A in in discharging discharging By this this way,to thethe battery is nominal s. except for over-capacity I A By way, the battery is discharged 70% of its initial variants, capacity. IThis value is relevant forthis quantifying aging. s. So, exceptbyfor over-capacity = 10discharge A in discharging phase. By way, thecell battery is discharged by 70% of its initial capacity. This discharge value is relevant for quantifying cell aging. currentIndeed, I divided by the active column number m (that is to say (m − 1) or m) for a duration of nom it allows c discharged by 70% 70% of its itsthe initial capacity.phase This before discharge value isdischarge. relevant for for quantifying cell aging. to stop discharging a complete The more Qo(t) cell decreases, discharged by of initial capacity. This discharge value is relevant quantifying aging. Indeed, it allows to stop the discharging phase before a complete discharge. The more Q o (t) decreases, Indeed, itthe allows to stop the discharging discharging phase before complete discharge. The more Qto o(t) decreases, 2500 s. the So,more except for over-capacity variants, I before = 10 A in discharging phase. ByQ this way, the the battery is SoCto atstop the end of discharging phase decreases. Thisdischarge. is because a cell has provide Indeed, it allows the phase aa complete The more o(t) decreases, the more more the the SoC SoC at at the the end end of of discharging discharging phase phase decreases. decreases. This This is is because because aa cell cell has has to to provide provide the the the same amount ofof energy. Then, the cells areThis recharged, for thevalue sameisduration, return to provide full charge. discharged by the 70% discharge is relevant for the more SoC atits theinitial end ofcapacity. discharging phase decreases. This because atocell has quantifying to the cell aging. same amount amount of of energy. energy. Then, Then, the the cells cells are are recharged, recharged, for for the the same same duration, duration, to to return return to to full full charge. charge. same the battery isthe placed at the restcells for an identical duration, allowing the return toThe internal same amount ofstop energy. Then, are recharged, for same duration, to return tomore fullbalance. charge. Indeed,Finally, it allows to discharging phase before a the complete Qo (t) decreases, Finally, the battery battery is placed placed at rest rest for for an an identical duration, allowingdischarge. the return return to to internal internal balance. Finally, the is at identical duration, allowing the balance. Finally, the battery is placed at rest for an identical duration, allowing the return to internal balance. the more the SoC at the end of discharging phase decreases. This is because a cell has to provide the

same amount of energy. Then, the cells are recharged, for the same duration, to return to full charge. Finally, the battery is placed at rest for an identical duration, allowing the return to internal balance.

Figure 9. Current profile during a simulation cycle. Figure 9. 9. Current Current profile profile during during aa simulation simulation cycle. cycle. Figure Figure 9. Current profile during a simulation cycle.

To model a cell, a characteristic equation that describes the OCV evolution as a function of the To model model aa cell, cell, a characteristic characteristic equation equation that that describes the the OCV OCV evolution evolution as as a function function of of the the To SoC isTo used. Thea typical shape of this equation curve is described for anthe amorphous iron phosphate (LiFePO 4) model cell, aa characteristic that describes describes OCV evolution as aa function of the

s. So, except for over-capacity variants, I = 10 A in discharging phase. By this way, the battery is discharged by 70% of its initial capacity. This discharge value is relevant for quantifying cell aging. Indeed, it allows to stop the discharging phase before a complete discharge. The more Qo(t) decreases, the more the SoC at the end of discharging phase decreases. This is because a cell has to provide the same of energy. Then, the cells are recharged, for the same duration, to return to full charge. Batteriesamount 2018, 4, 31 8 of 12 Finally, the battery is placed at rest for an identical duration, allowing the return to internal balance.

Figure 9. Current profile during a simulation cycle. Figure 9. Current profile during a simulation cycle.

To model a cell, a characteristic equation that describes the OCV evolution as a function of the model a cell, a characteristic equation describes evolution asphosphate a function (LiFePO of the SoC SoC isToused. The typical shape of this curve isthat described forthe an OCV amorphous iron 4) is used. The typical shape of this curve is described iron for anphosphate amorphouspositive iron phosphate (LiFePO in 4 ) cell cell in Figure 10. Batteries, with an amorphous electrode support high Figure 10. Batteries, withdischarge an amorphous iron phosphate positive electrode high intensities in intensities in charge and as well as fast charges. These cells have support higher power density and chargefire andrisks discharge as well fast charges. have higher power density lower fire lower than cells withas a lithium cobaltThese oxide cells (LiCoO 2) positive electrode [29]. and On this curve, risks than cells with a lithium cobalt oxide (LiCoO ) positive electrode [29]. On this curve, four points 2 four points are identified by a red dot. These four coordinate points (S0, E0), (SL, EL), (SV, EV) and (SM, are by delimit a red dot. These four coordinate points (S0 , E0 ),it(S , Epossible and (SMpartial , EM ), L ), (SV , E E M),identified respectively, three sectors. The curve being continuous, isLso toV )perform respectively, three sectors. Theof curve being continuous, it is OCV so possible to perform regression. Indelimit the sector where the state charge is low (SoC < SL) and low (OCV < EL), thepartial curve regression. In the sector where the state of charge is low (SoC < S ) and OCV low (OCV < E ), the L > SVcurve can be described by an exponential function. It is the same forL high states of charge (SoC and can be> described by an exponential It is the for high statesUltimately, of charge (SoC SV and OCV OCV EV). The central sector can function. be described by same a linear function. the >characteristic > EV ). Thecan central sector can described linear function. Ultimately, the characteristic equation be described bybe equation setby (7)aas a function of the SoC (explain as a dummy equation variable Batteries 4, x FOR REVIEW of 12 can be 2018, described byPEER equation set (7) as a function of the SoC (explain as a dummy variable x). ν 8and ξ parameters are empirical. ν is between 10 and 20. It corresponds to the rapid growth of the voltage x).  and ξ parameters are empirical.  is between 10 and 20. It corresponds to the rapid growth of when the SoC approaches its maximum. ξ parameter is its complement when the voltage collapses, the voltage when the SoC approaches its maximum. ξ parameter is its complement when the voltage the SoC decreasing towards its minimum. collapses, the SoC decreasing towards its minimum.  EL − EV α𝛼=  S L − SV =     ⎧ SV ( EV − EL − E0 )+S L E0 S0 − x β= OCV ( x ) = β + αx + γ 1 − e ξ + δeυ(x−(S M ) ) with ⎪𝛽 = ( SL −SV) (7) 𝑂𝐶𝑉(𝑥) = 𝛽 + 𝛼𝑥 + 𝛾 1 − 𝑒 + 𝛿𝑒 𝑤𝑖𝑡ℎ (7)  γ = EL − E0  ⎨ 𝛾 = 𝐸 − 𝐸 ⎪ δ = E M − EV ⎩𝛿 = 𝐸 − 𝐸

Figure Figure 10. 10. Example Example of of aacharacteristic characteristic curve curve representation representation linking linking the the open-circuit open-circuit voltage voltage to to the the state state of charge for a LiFePO 4 cell. of charge for a LiFePO cell. 4

In these simulations, the cells had an initial capacity Q* = 10 Ah and an average ESR of 20 mΩ. In these simulations, the cells had an initial capacity Q* = 10 Ah and an average ESR of 20 mΩ. The ambient temperature was set to 25 °C. Since the Q0(t) degradation is continuous and progressive, The ambient temperature was set to 25 ◦ C. Since the Q0 (t) degradation is continuous and progressive, it is logical to consider that the SoH, which is a representation of this degradation, also decreases it is logical to consider that the SoH, which is a representation of this degradation, also decreases continuously. This degradation is proportional to the using conditions. At each cycle, a cell ages. This translates into an SoH decrease. The cell temperature evolves as a function of the current flowing through it. By convection, radiation and conduction, this heat can spread to other cells. For simplicity, the used model does not integrate thermal coupling phenomena. Finally, the initial conditions for each cell was given randomly around nominal a value with a

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continuously. This degradation is proportional to the using conditions. At each cycle, a cell ages. This translates into an SoH decrease. The cell temperature evolves as a function of the current flowing through it. By convection, radiation and conduction, this heat can spread to other cells. For simplicity, the used model does not integrate thermal coupling phenomena. Finally, the initial conditions for each cell was given randomly around nominal a value with a variability of more or less 10%. The same Celli,j is used for all variants in all architectures, so as to ensure a true comparison of the variant intrinsic performance. A cell is considered faulty in two cases. First, when it is completely discharged whereas it should still supply energy (SoC = 0). Second, when it is too old and has SoH = 0.8. This corresponds, for a single cell, to the operative dependability definition given above. Depending on the architecture, the variant and the failed cell location(s), the battery may or may not continue to provide the requested power. If, at moment, it is no longer able to provide this power, the Odep worth. Simulation was performed several times with different initial conditions. Only the mean values are reported here, even if the figures illustrating this demonstration are related to a single simulation, among all those performed. From these different simulations, it is possible to extract operative dependability. Odep corresponds to the time when the battery stops fitting to the specifications: delivery of the battery nominal current Inom . According to the variant, some cells may have failed (by aging, random failure or complete discharge) before this time and be isolated or replaced by others. The simulations presented here were carried out for several structures: with n = 2 and m varying from 3 to 10 on the one hand, and on the other hand with m = 3 and n varying from 2 to 4. 4. Results and Comparisons Results from a (3,4) structure simulation performed with a C3C architecture with SoH-based optimization algorithm is illustrated in Figure 11, which presents SoC, SoH, OCV and Q0 evolution. In this example, only the first-row cells are shown because it is in this row that the first two cells fail. Cell14 (cyan curve) fails first. Odep is limited by Cell12 aging (green curve). This simulation was performed willingly in accelerated mode, with an announced cell lifetime of only 50 cycles. In order to read SoC evolution on the curve, the aging parameter has been set to its maximum value (aging = 2) to better differentiate the SoH curves when the battery lifespan approaches. By using this variant, aging control is visible on the curve b). All cells age together, their SoH decreases together. Table 2 records the average operative dependability obtained for the different structures. This average is given for cells with lifetimes of 1000 cycles. In the same way that the reliability of a several identical all-necessary element system decreases if the element number increases, the more a battery contains cells, the lower the operative dependability is. For instance, for a basic PS architecture, with a n = 2 structure, Odep reduces when the column number j increases: respectively, to 772, 754, 750, 748, 747 and 674 cycles when j varies from 4 to 10. The lowest operative dependability variant is the PS architecture without redundant cell (basic PS). For instance, Odep = 772 cycles for a (2,4) structure. Its performance serves as a reference value. Operative dependability for the variants are relative compared (base 100 for basic PS) in the bar graph in Figure 12, drawn for a (3,4) structure. Thus, the performances can be grouped into three clusters: those that are between 100% and 120% of the basic PS operative dependability, those between 120% and 140%, and those higher [30]. Among the less powerful variants are the classic solutions: balancing in SP architecture, redundancy, fault tolerance and over-capacity. In the second family are the SoC-based optimization algorithm variants for the three architectures. Finally, those with the best operative dependability are those that use variant with SoH optimization algorithm, regardless of the architecture. Cluster 3 variants show a different Odep improvement by architecture, as summarized in Table 3. On average, this improvement is close to 36%. Unlike the DESA architecture, whose management cannot be deployed in another architecture, with the optimization algorithm,

between 120% and 140%, and those higher [30]. Among the less powerful variants are the classic solutions: balancing in SP architecture, redundancy, fault tolerance and over-capacity. In the second family are the SoC-based optimization algorithm variants for the three architectures. Finally, those with the best operative dependability are those that use variant with SoH optimization algorithm, regardless of the architecture. Cluster 3 variants show a different Odep improvement by architecture, Batteries 2018, 4, 31 10 of 12 as summarized in Table 3. On average, this improvement is close to 36%. Unlike the DESA architecture, whose management cannot be deployed in another architecture, with the optimization the operative improvement is greater than the share cells. For example, algorithm, thedependability operative dependability improvement is greater than of theredundant share of redundant cells. For for a (2,4) structure, O is improved by 50% for only 33% of redundant cells. In the same way, for a example, for a (2,4) structure, Odep is improved by 50% for only 33% of redundant cells. In the same dep (2,10), Odep is improved by almost by 25% regardless of the architecture for 10% more way, for a (2,10), Odep is improved almost 25% regardless of the architecture for cells. 10% more cells.

Figure 11. Example of simulation result (SoC, SoH, OCV, Q0) for a C3C architecture with variant SoHFigure 11. Example of simulation result (SoC, SoH, OCV, Q0 ) for a C3C architecture with variant based optimization algorithm: (a) SoC; (b) SoH; (c) OCV, in Volts; (d) Q0, in Ah. SoH-based optimization algorithm: (a) SoC; (b) SoH; (c) OCV, in Volts; (d) Q0 , in Ah.

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Table 2. Simulation results: operative dependability.

Architecture PS PS PS PS Architecture Fig PSPS 3 SP PSPS 3 PS 3 SP PS PS SP PS SPSP SP SP SPC3C C3C C3C

C3C

Fig 3 3 33 3 2 3 2& 3 8 3 7 3 2 2& 2&8 8 7 2&8 5 5

5 5

With SoC-based Structure (2,4) Table 2.optimization Simulation results: 1052 algorithm basic 772 With SoH-based optimization WithStructure redundancy 868 1172 (2,4) algorithm over-capacity 804 basic 772 Without balancing 808 With redundancy 868 Fault tolerant 796 over-capacity 804 Basic with balancing 839

Fault tolerant With SoC-based optimization algorithm Fault tolerant With SoH-based optimization algorithm With SoH-based optimization Without balancing Basic algorithm with balancing Fault tolerant With SoC-based optimization With SoH-based optimization algorithm With SoC-basedalgorithm optimization algorithm With SoH-based optimization With SoH-based optimization algorithm

algorithm

754 803 1043 (2,5) 773 754 796 803 777 773 814

750 800 1002 (2,6) 772 750 776 800 768 772 780

748 799 993 (2,7) 775 748 765 799 773 775 790

747 796 968 (2,8) 768 747 762 796 768 768 784

674 702 832 (2,10) 768 674 683 702 694 768 708

(3,4) 946 748 818 1104 (3,4) 754 748 771 818 760 754 791

1052 744

892 813

855 812

786 808

874 788

740 711 832

946 786

1104

808 1192

796 1063

776 1028

765 1001

762 980

683 830

771 1080

1172

1044

1001

984

843

1108

796

1172

839 744 1192 1076 1076 1172

(2,5) (2,6) (2,7) (2,8) operative 892 855dependability. 786 874 (2,10) 740

777

1043

814 813 1063 891 891 1044

768

1002

780 812 1028 899 899 1001

773

993

790 808 1001 884 884 984

768

968

784 788 980 860 860 972

972

694

708 711 830 755 755 843

760

791 786 1080 981 981 1108

(4,4) 1052 746 846 1254 (4,4) 764 746 799 846 772 764 826

Cluster 2 basic 13 Cluster 1 basic 1 12 1 1

1234

3

772 1052 810 1254 799 1228 826 810 1228 1080 1080 1234

2 2 1 3 13 1 1 32 2 3

Figure 12. (3,4) structure Odep improvement. Figure 12. (3,4) structure Odep improvement. Table 3. Simulation results: operative dependability. Table 3. Simulation results: operative dependability. Architecture 2,4) (2,5) (2,6) (2,7) (2,8) (2,10) (3,4) (4,4) 52% 34% 33% 48% (3,4) 68% ArchitecturePS(2,4) (2,5) 38% (2,6) (2,7) 30% (2,8) 23%(2,10) SP 54% 41% 37% 34% 31% 23% 44% 65% PS 52% 38% 34% 33% 30% 23% 48% C3C54% 52% 33% 32% 65% SP 41% 33% 37% 34% 30% 31% 25% 23%48% 44% C3C 52% 33% 33% 32% 30% 25% 48%

5. Conclusions

(4,4) 68% 65% 65%

5. Conclusions In this paper, some variants to improve the operative dependability of EESS are described and compared. this,some a formal model integrating aging ofdependability a cell is used. of The different architectures In this For paper, variants to improve thethe operative EESS are described and and the possible solutions improve the performances duration usedifferent are simulated under compared. For this, a formalto model integrating the aging ofin a cell is used.ofThe architectures Matlab. Whatever the architecture, variants as and the possible solutions to improveclassical the performances in over-capacity duration of useand are balancing simulated only underimprove Matlab. Odep by up to 20%. By using a minimal portion of redundant cells and an SoH-based optimization algorithm, it is possible to improve, on average, the battery operative availability by more than 35%, regardless of its architecture. When the current flowing through the battery is below nominal current, in a C3C architecture, it is possible to perform specific cell-to-cell balancing while using other cells to meet the current

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Whatever the architecture, classical variants as over-capacity and balancing only improve Odep by up to 20%. By using a minimal portion of redundant cells and an SoH-based optimization algorithm, it is possible to improve, on average, the battery operative availability by more than 35%, regardless of its architecture. When the current flowing through the battery is below nominal current, in a C3C architecture, it is possible to perform specific cell-to-cell balancing while using other cells to meet the current demand. No other architecture allows this differentiated use of cells. It is necessary to continue this work by comparing the cost of adding the redundant cells, the switches and the over-cost induced on the BMS in terms of computing capacity with the gain in additional mission time. Author Contributions: C.S. wrote the paper; P.V., L.P., A.S. and É.N. have made corrections; All authors discussed results data and decided on next steps. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflicts of interest.

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