A novel mechanical analogy based battery model for SoC estimation using a multi-cell EKF

1.2 MB·

by  Maurizio Paschero

1
A novel mechanical analogy based battery model
for SoC estimation using a multi-cell EKF
Maurizio Paschero, Gian Luca Storti, Antonello Rizzi, Fabio Massimo Frattale Mascioli
and Giorgio Rizzoni, IEEE Fellow
Abstract—The future evolution of technological systems dedi- definitions for any objective function acting as the fitness of
6 cated toimproveenergyefficiencywillstronglydependoneffec- each technological subsystem in this evolving scenario. From
1 tiveandreliableEnergyStorageSystems,askeycomponentsfor
this point of view, just to cite an example, the revolution in
0 Smart Grids, microgrids and electric mobility. Besides possible
2 improvementsinchemicalmaterialsandcellsdesign,theBattery transportationsystemsdue to the introductionof plug-inelec-
n ManagementSystemisthemostimportantelectronicdevicethat tricvehicles(EVs)willcontributeindrivingthedesignofnext
a improvesthereliabilityofabatterypack.Infact,apreciseState generationof Smart Grids [1], [2], [3], since electric mobility
J of Charge (SoC) estimation allows the energy flows controller will be a huge additional load for both energygeneration and
to exploit better the full capacity of each cell. In this paper,
4 distribution systems. At the same time, the massive introduc-
we propose an alternative definition for the SoC, explaining the
1 tion of EVs will yield a true reduction of CO emissions
rationales by a mechanical analogy. We introduce a novel cell 2

model, conceived as a series of three electric dipoles, together only if supportedby a modelof distributed energygeneration
]
Y with a procedure for parameters estimation relying only on fromrenewablesources.Inturn,thestochasticnatureofsome
voltage measures and a given current profile. The three dipoles promising renewable sources (photovoltaics plants and wind
S
representthequasi-stationary,thedynamicsandtheistantaneous
generators, for example) demands the presence of stationary
.
s components of voltage measures. An Extended Kalman Filer
energystoragesystems(ESSs)toexploitfullytheavailableen-
c (EKF) is adopted as a nonlinear state estimator. Moreover,
[ we propose a multi-cell EKF system based on a round-robin ergy,allowingthespreadofMicroGrids.AMicroGridcanin

approach to allow the same processing block to keep track of factbedefinedasasub-networkcharacterizedbythepresence
1
many cellsat thesame time. Performance testswith aprototype of autonomous (often renewable) energy sources buffered by
v
batterypackcomposedby18A123cellsconnectedinseriesshow
4 some type of ESS and locally controlled in order to achieve
encouraging results.
5 smartenergyflowsmanagement[4].Inthisscenario,theSmart
5 IndexTerms—Nonlinearcircuits,MechanicalAnalogy,Battery Grid will evolve into a System of Systems (SoS), where most
4 modeling, Parameter identification, State of Charge estimation,
of the loads and energy sources will be localized into Micro
0 Extended Kalman Filter.
Grids, organized as a hierarchical territorial granulation, and
.
1 acting as cooperative/competitiveagents in a complex energy
0 I. INTRODUCTION tradingnetwork. The key componentsfor the full deployment
6
MODERN engineeringisalreadyfacingthefundamental of this future technological setting are ESSs. Nowadays the
1
: challenge of improving energetic, environmental and most promising technology is represented by Li-Ion (Lithium
v
socialsustainabilityinthewayenergyisproduced,distributed, Ion) and Li-Po (Lithium Polymer) battery systems, controlled
i
X deliveredandevenconsumedbythefinalusers.Manysystems by suited BMSs (Battery Management Systems). The BMS
r and technical components are on the verge of a disruptive represents the key component of every chemical ESS, since
a
transformation, driven by a complex multidisciplinary co- this electronic device is conceived and designed to manage,
evolutionprocess,wheremanyvitalsubsystemsarecloselyre- protect, monitor, balance and estimate the State of Charge
latedoneanother.Thisrevolutionmustbefacedandperformed (SoC) of rechargeable batteries. An accurate SoC determi-
taking into account a systemic point of view, able to drive nation in Li-Ion batteries is the most important aspect for
technicaladvancementsassequencesofsystematicandcoher- maximizingthebatterypackusageandtoevaluateandmonitor
ent transformations. Urban areas planning and development, correctly its State of Health (SoH). Determining the exact
buildings design, electric generation and distribution systems, amountofenergyavailableinabatteryisanextremelydifficult
advanced telecommunication systems, intelligent multimodal endeavor, due to the lack of deep knowledge of the electro-
transportation systems, cloud computing systems and intel- chemical behavior of a cell. The only available option is
ligent processing systems (just to cite some instances) will to perform an estimation of the SoC based on an external
benefit each other of advances and technical improvements. characterization of the cell, i.e. based on current and voltage
Sustainability is the key term to drive and define precise measurements. In the literature there exits several techniques
toperformthisestimation:opencircuitvoltage(OCV)calcula-
M.Paschero,A.RizziandF.M.FrattaleMascioliarewiththeInformation,
tion, coulomb counting, and/or more sophisticated techniques
ElectronicandTelecommunicationDepartment(DIET)-POMOSLabsofthe
University ofRome‘Sapienza’, Italy. that employ state estimators such as the Extended Kalman
G.L. Storti and G. Rizzoni are with the Center for Automotive Re- Filter (EKF). In the paper, we propose a new battery model
search (CAR), Ohio State University, Columbus, OH, 43211 USA e-mail:
and a procedure to characterize a cell, by estimating models
[email protected].
Manuscript received Dec15,2015;revisedJuneXX,2015. parameters, finalized to enhance SoC estimation. We explain
2
the procedure relying on a mechanical (hydraulics) analogy. B. A mechanical analogy
Once performed the parameters estimation, by a suited data
Theproblemofestimatingtheamountofchargestoredina
driven external characterization, an EKF is employed to lock
cellbasedonvoltageandcurrentmeasurementsisquitesimilar
and track the status of the system. Moreover, we propose a
to the problem of estimating the volume of the water stored
round-robin approach to keep track of the states of multiple
in a reservoir based on pressure and flow rate measurements.
cells, by relying on a single implementation of the EKF
As well known, the pressure at a given point is proportional
block.Thesystem isdesignedtofullyexploitalltheavailable
computational power of the embedded system running the
SoC procedure, and it is based on the fact that in practical
applications currents are band-limited signals, characterized
by very low maximum frequencies, and thus allowing low
sampling rates. This paper is organizedas follows. In Sect. II
we describe a novel way to define the SoC of a rechargeable
cell, while in Sect. III we explain the proposed cell model,
defined as a series of three dipoles, each one defined to
model contributions affecting the cell behavior at different
time scales. Sect. IV depicts the parameters identification
procedure, conceived to isolate and compute the quasi-static,
dynamical and istantaneou contributions, by feeding the cell
with a suited current profile. The Muli-cell EKF is presented
in Sect. V. Test setups and results for both the model and
the Multi-cell EKF are reported in Sect. VI. Finally, our
Figure 1: Mechanical analogy of a cell.
conclusions are drown in Sect. VII.
totheheightofthecolumnoffluidbetweenthispointandthe
water surface; for this reason from now on we will use the
II. CONSDERATIONS ON THESTATEOFCHARGE
term pressure instead of height.
A. Introduction It should be notedthat differentamountsof water stored in
two reservoirs having different internal shape can provide the
The SoC is a time dependent quantity representing the samepressureatthemeasurementpoint,asshowninFigure1
percentage of the total storable charge still drainable from a parts (a) and (b). In other words, when the internal shape
cell at a given instant of time [5]. Assuming for convenience of the reservoir is unknown, it is not possible to determine
an unitary efficiency, it is usually defined as the amount of water contained in the tank based on pressure
1 t measures only.
SoC(t)=SoC(t0)+ Iin(τ)dτ (1) In fact, the infinitesimal increment in the water volume
C
n Zt0 dV and the consequent pressure variation dp are related one
where Iin is the inputcurrentand Cn is the nominalcapacity another through the reservoir cross section area C(p) by the
of the cell, i.e. the amount of charge drainable, in an hour, relation
froma fullychargedcell ata givencurrentrate.A cellissaid dV
C(p)= (2)
to be fully charged if a given maximum reference voltage is dp
permanently measured between its terminals in open circuit Unfortunately,we don’tknowthereservoirinternalshape,i.e.
condition. Even though (1) is quite clear from a theoretical the variation of the internal cross section area C(p) with the
point of view, it is difficult to apply it in actual practice. In pressure measuredat the gauge(see Figure 1), but we can try
fact there are at least three problems with it: to estimate it experimentally.
1) we do not know the SoC value SoC(t ) at time t
0 0
2) we do not know exactly how the nominal capacity C ,
n C. Internal shape estimation procedure
which could be different cell to cell, is related to the
maximum and the minimum voltage of the cell. In order to develop a procedure capable to estimate the
3) itisveryhardtomeasuretheinputcurrentI accurately reservoir internal shape, first of all we need to clarify which
in
actionswecanperformonthereservoir.ReferringtoFigure1,
It should be noted that most of the problems listed above
there are only three actions we can carry out
are due to the insufficient semantic correlation of (1) with
the physical parameters of the cell. In fact the only cell • open or close the replenishment control
parameterinvolvedin (1) is C and all the differencesamong • open or close the emptying control
n
cells are flatten in the initial condition SoC(t0). In order to • read and acquire the pressure Pout at the gauge
overpass these limits, the SoC definition should be tailored Moreover, we should realize that when we act on the re-
cell by cell. An alternative SoC definition, capable to solve plenishment and the emptying control, the water movement
the problems related to (1) will be introduced based on a producestheformationofwavesonthestationarywaterlevel.
mechanical analogy. Consequently, the pressure P read at the gauge will be
out
3
the summation of a quasi-statical contribution P and a time t by
qst
dynamical contribution P .
dyn 1 Vqst(t)
The proposedprocedureis composedof two macro phases: SoC(V (t))= C(ν)dν, V (t)∈[V ,V ]
qst qst min max
∆Q
aninitializationphaseandanacquisitionphase(seeFigure2). ZVmin (3)
Each macro phase is composed of three steps, detailed in the
Equation (3) offers an alternative definition of SoC which
overcomes most of the limits of (1). In fact,
• it does notrequire the knowledgeof the previoushistory
of the cell (i.e. the initial conditions)
• The amount of charge ∆Q is well related to Vmax and
V .
min
• itdoesnotneedanaccuratecurrentmeasurementbecause
it is based on voltage only.
Moreover, (3) is based on the function C(V ) which is a
qst
physical property of the cell allowing a cell to cell tailoring
of SoC definition.
Figure 2: Internal shape extimation procedure.
Unfortunately the successful application of (3) requires the
knowledge of the quasi-statical voltage V whereas we are
qst
following list. able to measure the output voltage V only. For this reason
out
step 1 fill the tank until the pressure at the gauge reachs a we areforcedtodevelopa cellmodelwellsuited to employa
desired value stateobserverinordertoisolatethequasi-staticalcontribution
step 2 waitforthewavesproducedbythewater injectionhave from the dynamical one.
been damped
step 3 recordthestationaryvalueofpressurePmaxatthegauge III. PROPOSED CELLMODEL
step 4 empty the reservoir of a known amount of water ∆V
A Thevenin equivalent circuit model (ECM) is said to be
for a specified period of time T at a constant flow
empty realistic if it is able to reproduce within a given error the
rate equalt to ∆V/T
empty voltagesorthe currentsmeasuredattherealcomponentwhen
step 5 wait forthe wavesproducedby the water bleedinghave
it is driven by any current or voltage waveform. The ECM
been damped
accuracy depends strongly on the choice of the foundational
step 6 recordthestationaryvalueofpressureP atthegauge
min circuit elements [6]. In fact, trying to model a nonlinear
ItshouldbenotedthatthevaluesofP ,∆V andT can
max empty device through linear components implies the introduction of
notbe chosenin a completelyarbitraryway,butthey mustbe
mathematicalartifices,asSoCdependentresistors[7],[8],[9],
set accordinglywith a previsionalknowledgeof the reservoir,
that do not reflect any physical component.
whereas the value of P is defined by the procedure itself.
min In this paper, each cell has been modeled as a nonlinear
Furthermore,theprocedurecanberepeatedcyclically,i.e.,step
two terminal device. According with the argumentsdiscussed
1 can be consistently applied after step 6, even if in this case
in section II-B, the voltage measured at the cell terminals
steps 1 to 3 also will be acquisition steps.
hasbeenmodeledas thesummationofcontributionsaffecting
It is important to realize that, during step 5, the emptying
the cell behavior at different time scales. In order to include
controlis closed and, consequently,the stationary levelof the
in the model a direct dependence between input current
water does not change and the pressure variation acquired at
I and output voltage V , an instantaneous contribution
in out
thegaugeduringthisstepisduetothedampingofthedynamic V = Vˆ (I ) has been added to the quasi-stationary V
ist ist in qst
contribution only. This portion of the acquired pressure can
and the dynamicV contributionsdescribedin section II-B.
dyn
be used to model the waves dynamics. For this reason the
Accordingwiththepreviousargumentsitcanbestatedthat:
time period T must be set large enough to ensure that
empty
the waves have spanned all their dynamic during the step Vout(t)=Vqst(t)+Vdyn(t)+Vˆist(Iin(t)) (4)
4. Afterward, the waves model can be used to clean the
Relation (4) can be considered as the output equation of
outputpressureP acquiredduringstep 4fromthedynamic
out the state form representation of the cell model. In order to
contribution,allowingustoderivetherelationshipbetweenthe
complete the state form representation of the cell model we
volume V(P ) and the quasi-stationary pressure P . Once
qst qst need to chose appropriate state variables. According with the
this relationship is available, the internal shape C(p) can be
mechanicalanalogydescriptiongiveninsectionII-B,itseems
estimeted accordig with (2).
reasonable to select V and V to represent the internal
qst dyn
state of the cell.
D. An alternative SoC definition In order to derive the time evolution of V (t), we can
qst
consider (2) in the electric domain. Solving for the voltage
Now we are ready to come back to the electrical domain.
variation and taking the time derivative, we obtain
Replacing pressure with voltage and volume with charge we
can express the percentage of the total charge ∆Q available dV (t) 1 dQ(t) I (t)
qst = = in (5)
in the voltagerange[Vmin,Vmax] still storedin the cellat the dt Cqst(Vqst(t)) dt Cqst(Vqst(t))
4
It should be noted that C (V (t)) in (5) represents the 0.6 step3
nonlinear stationary capaciqtsyt oqfstthe cell (i.e. its ‘internal [A]00..24 step2 step4 step5 ∆Q
shape’). ,()tn−0.02 ∆Q
staIgne,otrhdeerdytonakmeiecpctohmepmonoednetlVas si(mt)plweilalsbpeocsosnibsliedeartedthaiss Ii−−00..640 6 12 Tempty 18 Time24,[h] ste3p06step1 36 ste42p2 48
dyn (a)
the summation of N linear first order filters.
3,3729
3,35945
V (t)= N V (t), dVi(t) = 1 (R I (t)−V (t)) (6) [V]3V,33,m3321a59x5 1 Vmax Vout(t)
Thedyvnalue aXis=su1meid by thdetdynamτiic ciominponent iafter the ,()Vtout3333,,,,33V2223,,257022m418569in987652 555532 Vmin Vd∞yn VVViqdssyttn((tt())t+)+VmVminin
exhaustion of the transient can be evaluated to be 3,21150 6 12 18 Tim2e4,[h] 30 36 42 48
N (b)
V∞ = R I (t) (7)
dyn i in Figure 4: Experimental parameters identification procedure: (a) as-
!
Xi=1 signedcurrentprofileIin(t),(b)measuredvoltageprofileVout(t)on
Equation (4), (5) and (6) can be interpreted, as shown in anAH32113M1Ultra-B Cylindricalcellanditsdecompositioninthe
Figure 3, as the series connection of a nonlinear capacitor, contributions Vqst(t), Vdyn(t) and Vist(t).
a non linear resistor and a cascade of a certain numberof RC
groups.
coordinatesandthetimetasaparameter,sothataninteresting
Vout(t) plotcanbeobtainedinthe(I,V)plane,asshowninFigure5.
It is easy to understand that the oblique lines in Figure 5
I (t)
in
0.5
0.4 Vist
Vqst(t) Figure 3:VEdqyuniv(atl)ent circuit ofVthiset(cte)ll It,[A]()in−−00000.....012321 Vist Vd∞yn Vmax−Vmin Vd∞ynVist
−0.3
−0.4 Vist
−03.,52035 3,2213 Vmin 3,2569 3,2747 3,2925 3,3103 3,3281 Vmax 3,3637 33,,33881156
Vout(t),[V]
IV. PARAMETER IDENTIFICATION Figure 5: (Vout,Iin) parametric plot
In order to determine the model parameters introduced in
represent a simultaneous jump in both the current and the
section III, we should apply the characterization procedure
voltagethatcorrespondtotheinstantaneouscontributionofthe
described in section II-B to determine the reservoir’s shape
outputvoltage.Theslopeofthoselinesrepresentsthevalueof
to a specific cell. The cell taken into consideration in this
the internal resistance at the specified current values. Similar
paperistheA123NanophosphateAHR32113M1Ultra-B.The
testsperformedatdifferentcurrentvaluescanbeusedtoderive
main characteristics of this cell are given in Table I. The
the characteristic Vˆ (I ) representing, from circuital point
ist in
of view, a nonlinear resistor. On the midline of Figure 5,
Variable Setting
together with the instantaneous contributions, the variation
Cell Dimensions (mm) 32x113
ranges of V and V are labeled with V −V and
qst dyn max min
Cell Weight (g) 205 V∞ , respectively.
Cell Capacity (nominal/minimum,Ah) 4.4 dyn
The values of circuital components related to the dynamic
Energy Content (nominal, Wh) 14.6
portion of the output voltage can be obtained by fitting the
Discharge Power (nominal, W) 550
measured voltage shown in Figure 4 part (b) acquired in
Voltage (nominal, V) 3.3
correspondenceofzerocurrentafterthecurrentpulsehasbeen
Specific Power (nominal, W/kg) 2700
removed(i.e. from hour 18 to 30 and 36 to 48). As expected,
Specific Energy (nominal, Wh/kg) 71
these portions of the V (t) curve correspond to a low-pass
out
Energy Density (nominal, Wh/L) 161
behavioranditcanbeidentifiedwithacertainnumberofRC
Operating Temperature(C) -30 to 55
groupsconnectedinseriesasstatedin(6).Moreover,asstated
Storage Temperature (C) -40 to 60
by (7), the total resistive contribution can be estimated from
Table I: A123 Nanophosphate AHR32113M1Ultra-B specifications. the difference V∞ between the output voltage measured at
dyn
the30-thandatthe18-thhour.Accordingwith(4),onceboth
experimental parameters identification is based on the proce- the instantaneousand the dynamic componentsVist and Vdyn
dure described in the mechanicaldomain in section II-B. The ofthecircuitshavebeenidentifiedthequasi-staticportionVqst
current input profile and the output voltage measured on the of output voltage Vout can be obtained by subtraction.
celltakenintoconsiderationareshowninFigure4part(a)and
V (t)=V (t)−V (t)−Vˆ (I (t)) (8)
(b), respectively. The values of circuital components related qst out dyn ist in
to the instantaneous portion of the voltage can be obtained The proposed technique is quite different from the identifi-
by interpreting the current I (t) and the voltage V (t) as cation techniques present in the litterature based on linear
in out
5
combinationsof nonlinearfunctions[10], [11], pointby point V. MULTI-CELLEXTENDEDKALMANFILTER
[12] or on averaging charge and discharge curves [13], [14].
A. Framework
ThethreecomponentsofV (t)havebeenplottedtogether
out
As well known in the literature, the EKF is a powerful
on Figure 5 part (b). In order to improve the readability
method to estimate the states of a nonlinear system such
of the plot both V (t) and V (t) have been added to
ist dyn
as internal parameters and SoC of a battery. However, this
V . From Figure 5, it is possible to realize that the only
min
approachpresentsseveralweakpoints:(i) theprecisionofthe
voltage contribution for zero currentis the dynamical one i.e.
modelimplementedintotheobservercanheavilyinfluencethe
V (t) = V (t) for I (t) = 0. This property is really
out dyn in
estimationprecision;(ii)dependingontheapplicationthetime
useful to identify V (i.e. the wave dynamics). Moreover,it
dyn
convergenceto reacha reasonableestimationcan betoolong;
should be noted that when subject to positive and to negative
(iii) the initialization of the auto-covariance Q matrix can be
current pulses, V exhibits a non symmetrical behavior
dyn
difficult;(iv)theEKFisabletoestimatethestatesofonlyone
resulting in an error in the open circuit voltage estimation
system (i.e. a single cell). In order to improve the robustness
when the mean value between the charge and the discharge
and the reliability of this methodology, regarding points (i),
branches is considered [13], [14].
(ii) and (iii), it is possible to increase the complexity of the
Accordingwiththeliterature,theestimatedV (t)exhibits
qst battery model, perform a better initial condition estimation
different behaviour during charge and discharge. In fact,
and empirically find the best Q matrix values, respectively.
plotting the current integral Q(t) versus this portion of the
Consideringpoint(iv), to our best knowledge,to date has not
outputvoltage,thecharacteristicQ(V )showninFigure6is
qst been proposed any approach allowing the estimation of the
obtained.Accordingwiththe argumentsgivenin sectionII-B,
states of multiple cells using only one observer (i.e. EKF).
Thus, in a real system composed by dozens of cells, as many
1.1 EKFs have to be implemented, exacerbating the complexity
∆Q00..189 of the system and the used memory space. For these reasons,
)/00..67 in the last year the University of Rome Sapienza and the
Vqst000...345 Ohio State University have worked together in order to find a
(Q00..12
0 way to developa novelmethodologydefinedMulti-Cell EKF.
V−0m.1in 3,252 3,264 3,276 V3,2q88st,[V]Vn 3,312 3,324 3.336 Vmax The idea is quite simple and it is based on the well known
Figure 6: Q(Vqst) characteristic. Mean value in red. round-robin strategy, where time slices are assigned to each
process in equal portions and in circular order, handling all
processeswithout priority.Starting from this idea, it has been
forapplying(3)weneedtoestimatethestaticalcapacitanceof
implementedaframeworkthatallowsasingleEKFtoperform
the cell. The hystereticbehaviorof the cell producesdifferent
thestatesestimationofdifferentbatteries.Indeed,considering
capacitances(shapes)forthechargeandthedischargeprocess.
the “slow” evolution of voltage and current during normal
In order to simplify the model, we are forced to consider
applications, it is reasonable to expectsimilarly slow changes
an average between the charge and the discharge behaviors.
ofbatteryconditions.Theblockdiagramexplainingtheround-
Consequently, the static capacitance of the cell C (V )
qst qst
robinapproachisreportedinFigure8.Eventhoughtheround-
can be estimated applying (2) to the mean curve shown in
robin strategy is well known, some relevant comment can be
red in Figure 6. The curve obtained for C (V ) is plotted
qst qst
made.Usingthisnovelapproach,theestimationofcellseither
in Figure 7. From the plot it is evident that most of the
with the same chemistry or not residing either in the same
batterypackor in differentonesis possible.Indeed,as shown
200 in Figure 8, the EKF receivesonly voltage and currentvalues
[F] ∆Vn
,)150 ignoring any other information of the cells (i.e. chemistry
st
Vq100 and position in the battery pack). In order to simplify the
(
st50 descriptionofthisnovelMulti-CellEKF,weconsiderabattery
Cq
Vm0in 3.252 3.264 3.276 V3.2q88st,[V]Vn 3.312 3.324 3.336 Vmax packconstitutedbytheconnectioninseriesofcellsallhaving
the same chemistry.
Figure 7: Estimated nonlinear statical capacity
charge is accumulated around a single statical voltage value
correspondingto the maximumvalue of the capacitance. This
argument can be used as a constructive definition of the
nominal voltage V and it strengthens the choice made in
n
this paper to use V and V values closer to V with
min max n
respect to the values given by the constructor. Moreover,it is
interestingtonotethatfollowingtheproposedprocedurethere
is just a small shift ∆V between the nominal voltage given
n
by the cell constructor and the peak of the estimated statical
capacitance. Figure 8: General block diagram of the Multi-Cell EKF framework.
6
Eventhoughtheround-robinconceptshowninFigure8can be used for every EKF state (i.e. V and V ). The block
qst dyn
appear quite simple, its correct implementation is not trivial diagram of a single MEM is reported in Figure 10. For each
due to the recursivestructure of the observer.In fact the EKF
algorithm is composed by two steps defined Prediction and
Correction. The first step involves projecting both the most
recentstatesestimationandanestimateoftheerrorcovariance
(from the previous time period) forwards in time to compute
a predicted (or a-priori) estimate of the states at the current
time. The second step involves correcting the predicted states
calculated in the first step by incorporating the most recent
process measurement to generate an updated (or a-posteriori)
state estimation. Thus, applying the round-robin strategy, for
each time slice the Prediction step has to be fed by suitable
data from the Correction step at the previous time period.
Figure 10: Inner part of the MEM block.
Along this line, the general framework block diagram shown
inFigure8hasbeenmodifiedasshowninFigure9,wherethe
time step, the single variable coming from the Correction
actualEKFhasbeenusedasanenginetoperformcalculations,
block is properly addressed to the specific delay block and
whereastheframeworkhasbeenusedtochangethecellunder
stored,whereasits previousvalueis sent as outputvariableto
test every time slice.
thePredictionblock.Thisupdatingoperationis performedon
asinglecellatthetime,drivenbytheclockrate,whileallthe
other data are left unchanged.
B. Determining the maximum number of cells
As discussed in the previous section, the proposed frame-
work gives the possibility to perform states estimation of
differentcellsimplementingasingleEKF.Aimedtodetermine
themaximumnumberofcellsthattheMulti-CellEKFcandeal
withinarealscenario,arealisticcurrentprofilehasbeenused.
The current profile, shown in Figure 11 part (a), is derived
fromthewellknownUS06drivingprofile,whereamaximum
Figure9:BlockdiagramofthedevelopedMulti-CellEKFframework.
current limitation of 44 [A] (10 C-Rate) is considered. This
constraint has been applied only for safety reasons, based on
In the block diagram reported in Figure 9, it is possible the cell characteristics of the cell used in the actual test (see
to see how the round-robin structure is implemented using Table I). The spectrum of the input signal I (t) is reported
in
multiplexers (MUXs), demultiplexers (DEMUXs), memories
(MEMs) driven by a common clock signal. MUXs have been 50
used to select suitable data for each time slice, MEMs have A]
[
been used to store real time data of each cell, DEMUXs have ,()t 0
been used to properly separate variables contained in arrays Iin
and the clock has been used to set the sampling time T .
slice −50
0 100 200 300 400 500 600
The EKF Prediction and Correction blocks are two common t,[s]
processing blocks with known latencies. This modular design (a)
allows to modify, tune and improve the latter blocks, without 5x 104
modifyingthe remainderof the system. Furthermore,as men- As] 4
[
tioned before in cases where cells have different chemistry, ,)|3
it is possible to customize, for instance, the battery internal (ωn2
Ii1
parameters increasing the versatility of the proposed method. |0
−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5
The MUXs and DEMUXs blocks shown in Figure 9 perform ω,[Hz]
(b)
standard functions, so they can be implemented using built-
in blocks or custom functions according to the programming Figure 11: Current profile derived from the standard US06 driving
environment available. These blocks have been used to sepa- cycle: (a) time evolution, (b) spectrum.
rate or concatenate the variablesto or from the MEMs blocks
that represent the states and the auto-covariance Q matrix, in Figure 11 part (b), where the maximum frequency can
respectively. MEMs blocks, used to properly store data, have be cautiously fixed to 2 Hz. The maximum number of the
been implemented using a custom solution. These blocks, cells that the Multi-Cell EKF can manage is dictated by the
playing a vital role, constitute the most important part of the input signal maximum frequency (i.e. current and voltage)
entire Multi-Cell EKF structure. A single MEM block has to as well described in the Nyquist-Shannon sampling theorem.
7
By setting the time slot T (slice time of each process modelin describinghysteresisphenomena.Evenif the results
slot
in the round-robin strategy) equal to 10 ms to allow the achieved with the actual model are encouraging, we believe
correct computation of the data with the available hardware, that a better modeling of the hysteresis phenomena should
themaximumnumberofthecellssupportedbytheMulti-Cell reduce the mean value of the error.
EKF is computed as follows:
1 1 B. Multi-Cell EKF Validation
#CellsT ≤ ⇒#Cells≤ =25 (9)
slot
2f 2f T Once the model is validated, in order to verify the effec-
max max slot
According with (9), where a current profile derived from a tiveness of the Multi-Cell EKF in a real operative scenario,
standardUS06drivingcycleis applied,theMulti-CellEKFis wedecidedtoexploitthesamecurrentprofileusedtovalidate
abletoperformtheSoCestimationupto25cells.Considering themodel,onaprototypebatterypackcomposedby18A123
thathundredsofcellsarenormallypresentinaregularbattery Nanophosphate AHR32113M1Ultra-B connected in series.
pack,thereductionofthecomputinghardwarecostsusingthis Before starting the test all the 18 cells have been prepared
approach is remarkable. to ensure the condition Vqst = Vmax. The Multi-Cell EKF
registershavebeensetwithaninitialV valuecorresponding
qst
toaboutthe80%ofthetotalstorablecharge.Beingtheactual
VI. TESTSAND RESULTS
cells charged at V = V the initial error on the state
qst max
A. Model Validation estimation is about 20%. The results of the SoC estimation
In order to validate the cell model described in sections III performed by the Multi-Cell EKF are reported in Figure 13,
and IV, we use a custom current profile having a total time wheretheCoulombcountinghasbeenused asSoCreference.
length of about 37 hours. It is composed by: AsvisibleintheFigure13part(a),theMulti-CellEKFisable
• 6 hours of discharging at a constant 0.4 [A] rate
• 12 hours of rest 0.9
0.7
• 6 hours of charging at a constant 0.4 [A] rate oC 0.5
• 12 hours of rest S
0.3
• 1hourofvariablecurrentcomposedbytheconcatenation 0.1
of 6 US06 current profiles shown in Figure 11 part (a)
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38
Duringthe first 36 hoursthe currentprofile is quite similar to Time,[h]
(a)
the one shown in Figure 4 part (a) used in the identification
procedure.We take this choiceto verifythatthe modelworks 1
well in a slow dynamic situation. Conversely, for the latter 0.8
hour of the current profile, we take a high dynamic behavior oC 0.6
S
in ordertostress themodel.Acomparisonbetweenthe actual
0.4
voltage acquired from the cell and the one estimated by the
0.2
modelandtheir absoluteerroris reportedin Figure12for the 36 36.22 36.44 36.66 36.88 37.1
latter hour. Inspecting Figure 12 part (b) a few considerations Time,[h]
(b)
3.45 Figure 13: Comparison between Coulomb counting (blue) and the
3.38 Actual SoC of the 18 cells estimated by the Multi-Cell EKF (red): (a) full
Model
V] test, (b) zoom of the US06 section.
[ 3.31
,out3.24
V
3.17 toengagetheSoCreferenceasatraditionalEKFshowinghow
3.1 the proposed framework does not alter its functioning. In the
36 36.2 36.4 36.6 36.8 37 37.2
Time,[h] part (b) of the same figure is depicted a zoom of the latter
(a) hour of the test showing that in high dynamicalcondition the
32 SoCestimatedofeachcellisslightlydifferentfromtheothers
V] 24 with a maximum difference up to 10% with the reference.
m
or,[ 16 This behavior is expected since in an operative scenario the
Err 8 cells differ one to each other in terms of internal parameters,
age, etc.. In order to perform a better estimation, authors are
0
36 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8 36.9 37
Time,[h] actually workingon an improvedround-robinstrategy able to
(b) include cell to cell tailored parameters.
Figure12: Comparison betweenmodel andactual voltage: (a) Com-
parison, (b) absolute difference. VII. CONCLUSIONS
An alternative SoC definition, based on a mechanical anal-
can be made. First of all it should be noted that the voltage ogy,has been introducedin orderto avercomea few limits of
produced by the model is almost always less than the actual the standard definition. Based on the same analogy, a novel
one. This behavior is probably due to the inability of the equivalent nonlinear circuit model of a cell has been derived
8
together with a suitable parameters identification procedure Maurizio Paschero is a post doctoral research as-
which avoid the use of nonphysicalcomponentssuch as SoC sociate at the Information Engineering, Electronics
and Telecommunications Department of the Uni-
dependantresistors.Amulti-cellSoCestimationusingasingle
versity of Rome ”La Sapienza” since September
EKFmakinguseofaround-robinapproachhasbeendescribed 2008, where he works in the Polo per la Mobilita`
and a design procedure to extimate the maximum number of Sostenibile(POMOS)Laboratories. Hereceivedhis
M.S in Electronic Engineering 2003 and the Ph.D
cellit is possible to menagewith a singolEKF filter hasbeen
in Information and Communication Engineering in
derived. The tests conducted to validate the model show a 2006 from the University ”La Sapienza” of Rome
good accuracy in SoC estimation, even in very challenging and the Ph.D in Mechanical Engineering in 2008
fromVirginiaPolytechnicInsituteandStateUniver-
conditions.Similartestconductedona prototypebatterypack
sity. His major fields of interest include Smart Grids, circuital modeling of
composed of 18 cells connected in series show the ability multi-physicsystems,intelligent signalprocessing, andbattery modeling.
of the proposed EKF to prerform an accurate multi-cell SoC
estimation.
REFERENCES
[1] X. Yu, C. Cecati, T. Dillon, and M. G. Simoes, “The new frontier of Gian Luca Storti is a post doctoral research as-
smart grids,” Industrial Electronics Magazine, IEEE,vol. 5, no. 3, pp. sociate at Center for Automotive Research ofOhio
49–63,2011. State University since May 2015. He received his
[2] E. De Santis, L. Livi, A. Sadeghian, and A. Rizzi, “Modeling and B.SandhisM.SinElectronicEngineeringfrom”La
recognitionofsmartgridfaultsbyacombinedapproachofdissimilarity Sapienza”University,Rome,Italy,in2008and2011,
learning and one-class classification,” Neurocomputing, vol. 170, pp. respectively. He received his Ph.D. in the Informa-
368–383,2015. tion Engineering, Electronics and Telecommunica-
[3] G.L.Storti,M.Paschero,A.Rizzi,andF.M.FrattaleMascioli,“Com- tionsDepartmentin2015fromthesameuniversity.
parison between time-constrained and time-unconstrained optimization Hismajorfieldofinterest include theSmartGrids,
forpowerlossesminimizationinsmartgridsusinggeneticalgorithms,” intelligent signal processing, modeling and control
Neurocomputing, vol.170,pp.353–367,2015. ofhybridpowertrain,designofautomotiveelectrical
[4] E.DeSantis,A.Rizzi,A.Sadeghiany, andF.M.F.Mascioli,“Genetic systemandbatterymodeling.
optimization of a fuzzy control system for energy flow management
inmicro-grids,” inIFSAWorldCongressandNAFIPSAnnualMeeting
(IFSA/NAFIPS),2013Joint. IEEE,2013,pp.418–423.
[5] Z.Zou,J.Xu,C.Mi,B.Cao,andZ.Chen,“Evaluationofmodelbased
state ofcharge estimation methods forlithium-ion batteries,” Energies,
vol.7,no.8,pp.5065–5082, 2014.
[6] L. O. Chua, “Nonlinear Circuit Foundations for Nanodevices, Part i: Antonello Rizzi (S98-M04) received the Ph.D.
TheFour-ElementTorus,”inProceedings oftheIEEE,vol.91,no.11, in Information and Communication Engineering in
Nov.2003,pp.1830–1859, invited paper. 2000, from the University of Rome La Sapienza.
[7] T.Huria,G.Ludovici,andG.Lutzemberger,“Stateofchargeestimation InSeptember2000hejoinedtheDIETDepartment
ofhighpowerlithiumironphosphatecells,”JournalofPowerSources, of the University ”La Sapienza” of Rome as an
vol.249,pp.92–102,2014. Assistant Professor. His major research interests
[8] A.RahmounandH.Biechl, “Modellingofli-ionbatteries usingequiv- are in the area of non-linear circuits and systems,
alent circuit diagrams,” Electrical Rev. ISSN 0033-2097, R. 88 NR 7b, ComputationalIntelligenceandPatternRecognition,
vol.2,no.7,pp.152–156, 2012. includingadvancedGranularComputingtechniques
[9] H.He,R.Xiong, andJ.Fan,“Evaluation oflithium-ion battery equiv- for Data Mining and Knowledge Discovery. Since
alent circuit models for state of charge estimation by an experimental 2008, he serves as the scientic coordinator and
approach,” Energies,vol.4,no.4,pp.582–598,2011. technicaldirectoroftheR&Dactivities intheIntelligentSystemsLaboratory
[10] G.L.Plett,“Extendedkalmanfilteringforbatterymanagementsystems withinthe‘PoloperlaMobilita`Sostenibile’(POMOS)Laboratories,wherehe
of lipb-based hev battery packs part 2. modeling and identification,” isworkingonthedesignofintelligentsystemsforsustainablemobility,smart
JournalofPowerSources,vol.134,p.262276,2004. gridsandmicro-gridsmodelingandcontrol,andbatterymanagementsystems.
[11] M. Paschero, V. Di Giacomo, G. Del Vescovo, A. Rizzi, and F. Frat- Dr.Rizzi(co-)authoredmorethan110internationaljournal/conferencearticles
taleMascioli,“Estimationoflithiumpolymercellcharacteristic param- andbookchapters.
etersthroughgeneticalgorithms,”inElectricalMachines(ICEM),2010
XIXInternational Conference on,Sept2010,pp.1–6.
[12] C.Birkl,E.McTurk,M.Roberts,P.Bruce,andD.Howey,“Aparametric
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[13] Y.Hu,S.Yurkovich,Y.Guezennec,andB.Yurkovich,“Electro-thermal
battery model identification for automotive applications,” Journal of FabioMassimoFrattaleMascioliProf.FabioMas-
PowerSources,vol.196,no.1,pp.449–457,2011. simo Frattale Mascioli received his MS and PhD
[14] F.Baronti,R.Saletti,andW.Zamboni,“Opencircuitvoltageoflithium- in Information and Communication Engineering in
ion batteries for energy storage in dc microgrids,” in DC Microgrids 1989and 1995, from the University ”La Sapienza”
(ICDCM), 2015 IEEE First International Conference on, June 2015, ofRome.In1996,hejoinedtheDIETDepartmentof
pp.343–348. theUniversity ”LaSapienza” ofRomeasAssistant
Professor. He was promoted toAssociate Professor
of Circuit Theory in 2000 and to Full Professor in
2011. His research interest mainly regards neural
networks and neuro-fuzzy systems and their ap-
plications to clustering, classification and function
approximation problems, circuit modeling for vibration damping, energy
conversionsystemsandelectricandhybridvehicles.Heisauthororco-author
of more than 150 papers. Since 2007, he serves as scientific director of the
‘PoloperlaMobilita` Sostenibile’(POMOS)Laboratories,DIETDepartment.
9
Giorgio Rizzoni received his BS, MS and PhD
in Electrical and Computer Engineering in 1980,
1982 and 1986, from the University of Michigan.
Between 1986 and 1990 he was a post-doctoral
fellow, and then a lecturer and assistant research
scientist at the University of Michigan. In 1990 he
joinedtheDepartmentofMechanical(nowMechan-
icalandAerospace)EngineeringatOhioStateasan
Assistant Professor. He was promoted to Associate
Professor in 1995 and to Professor in 2000. In
1999 he was appointed director of the Center for
Automotive Research. Since 2002 he has held the Ford Motor Company
Chair in Electromechanical Systems, and has also been appointed Professor
in the Department of Electrical and Computer Engineering. Prof. Rizzoni’s
specialization is in dynamic systems and control, and his research activities
arerelatedtosustainableandsafemobility.HeisaFellowoftheInstituteof
ElectricalandElectronicEngineersandFellowoftheSocietyofAutomotive
Engineers,andhasreceivednumerousteachingandresearchawards,including
theStanleyHarrisonAwardforExcellenceinEngineeringEducationandthe
NSFPresidential YoungInvestigator Award.