gauging algorithm comparisons · 2016. 10. 10. · m := cell mass . c. p:= specific heat . h. c :=...
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TI Information – Selective Disclosure 2010 Dallas BMS Deep Dive 2011 Dallas Deep Dive 1
Gauging Algorithm Comparisons
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Agenda • Basic Vocabulary Review
• How to estimate battery capacity? – Voltage lookup – Current integration
• Factors affecting capacity estimation (Or, why you may not want to try this at home!)
• Deeper dive into CEDV – Learning Before Fully Discharged – Learning Before Fully Discharged with CEDV – CEDV Model Visualization
• Deeper dive into Impedance Track – Current Direction and Relaxation mode – OCV profiles – Resistance learning – Qmax learning – FCC and Remaining Capacity simulation
• IT-DVC
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Basic Vocabulary Review • Capacity
– Design Capacity [mAh] – Qmax, Chemical Capacity [mAh] – FCC, Usable Capacity [mAh] – RM, Remaining Capacity [mAh] – RSOC [%] – DOD [%] – DOD0 [%]
• Voltages – OCV [mV] – OCV(DOD) [mV] – EDV [mV] – EDV 2 [mV] – EDV 0 [mV] – CEDV [mV]
• Current – C-rate [mA] – Coulomb Counting
∫ ⋅+= dttIqtq )()( 0
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• External battery voltage (blue curve) V = V0CV – I • RBAT • Higher C-rate EDV is reached earlier (higher I • RBAT)
EDV
Full chemical capacity: Qmax Usable capacity : FCC
0 1 2 3 4 6
3.0
3.5
4.0
4.5
Capacity, Ah
Voltage, V
How Much Capacity is Really Available?
Open circuit voltage (OCV)
I • RBAT
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How to estimate battery capacity?
• Measure change in capacity –Voltage lookup –Coulomb counting –Combination of both
• Develop a cell model –Circuit model –Table Lookup
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Voltage lookup
)(tq
mL marks
V(t)
I(t)
• One can tell how much water is in a glass by reading the water level – Accurate water level reading should
only be made after the water settles (no ripple, etc)
• One can tell how much charge is in a battery by reading well-rested cell voltage – Accurate voltage should only be made
after the battery is well rested (stops charging or discharging)
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OCV curve
Level rises same rate
Level rises same rate
Volta
ge
Fullness
OCV Curve Full charge voltage
End of discharge voltage
0% 100% Capacitor
Level rises faster
Level rises slower
Volta
ge
Fullness
OCV Curve Full charge voltage
End of discharge voltage
0% 100% Battery
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OCV voltage table: DOD representation
OCV(DOD)
2900
3100
3300
3500
3700
3900
4100
4300
0 0.2 0.4 0.6 0.8 1 1.2
DOD
Volta
ge_a
(DO
D)
Voltage_a
Poly_a(DOD)
Flat Zone
Vmax Vmin
DOD = Depth of Discharge SOC = State of Charge DOD = 100% - SOC
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Current integration
• One can also measure how much water goes in and out
• In batteries, battery capacity changes can be monitored by tracking the amount of electrical charges going in/out
• But how do you know the amount of charge, , already in the battery at the start?
• How do you count charges accurately? )(tq
mL marks
Voltage
I(t) ∫ ⋅+= dttIqtq )()( 0
∑⋅∆+=k kk Itqq 0
0q
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Basic Smart Battery System
Batte
ry Mo
del
Gas Gauge
Rs Ibatt
Vbatt
Load
Char
ger
VCHG
ICHG
comm
CHG DSG
IDSG
VDSG
VPACK
Tbatt
∑⋅∆+=k kk Itqq 0
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Circuit model • VOC a function of SOC
• Rint is internal resistance
• Rs and Cs model the short term transient response
• RL and CL model the long term transient response
• Vbatt and Ibatt are the battery voltage and current
• All parameters are function of temperature and battery age
Voc(SOC)
Rint RL
CS CL
RS Vbatt
Ibatt
DC model
Voc(SOC)
Rint RL
CS CL
RS Vbatt
Ibatt
Transient model
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Table lookup
• Large, multi-dimensional table relating capacity to – Voltage – Current – Temperature – Aging
• No cell model
• Apply linear interpolation to make lookup “continuous”
• Memory intensive
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Factors affecting capacity estimation
• PCB component accuracy
• Instrumentation accuracy
• Cell model fidelity
• Aging
• Temperature
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PCB component accuracy
• Example – Current sensing resistor – Trace length (resistance)
sRtItV ⋅= )()(
Gas Gauge
Rs )(tI
rsRtVtIε±
=)()(
R+ R-
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Instrumentation accuracy
ADC count
Volta
ge
• ADC Resolution
• Sampling rate
• Voltage drift / calibration
• Noisy immunity
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Battery model fidelity
• Steady-state (DC)
• Transient (AC)
• Capacity degradation – Aging – Overcharge
Voc(SOC)
Rint RL
CS CL
RS Vbatt
Ibatt
Transient model
Voc(SOC)
Rint RL
CS CL
RS Vbatt
Ibatt
DC model
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Model parameter extraction
• Extract battery model parameter values using actual collected battery data – Open circuit voltage (OCV) – Transient parameters (RC) – DC parameters (Ri)
• Least square minimization
• Extraction process can be hard and time consuming
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Temperature
• Temperature is important for – Capacity estimation – Safety – Charging control
• Temperature impacts model parameters – Resistance – Capacitance – OCV – Max capacity
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Modeling temperature
Voc(Vsoc)
R i
C
R
Vbatt
Ibatt
[ ] ( )acibattocbattibattp TTAhRIVVR
RIdtTdcm −−−−+= 22 1
m := cell mass cp := specific heat
hc := heat transfer coef A := cell surface area
Ta := ambient temp
Heating Cooling
• Based on a heating / cooling model **
• Heating is from the internal resistance
• Cooling is from heat transfer to the environment, i.e.,
• How many thermistors?
** “Dynamic Lithium-Ion Battery Model for System Simulation”, L. Gao, S. Liu and R. A. Dougal, IEEE Transaction on Components and Packaging Technologies, vol. 25, no. 3, September 2002.
( )aTT −
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What Does A Fuel Gauge Do?
3V
4.2V
Which route is the battery taking?
Suppose we are here
0%
• What is the remaining capacity at current load?
• What is the State of charge (SOC)?
• How long can the battery run?
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Current Integration Based Fuel-gauging • Battery is fully charged
• During discharge capacity is integrated
• State of charge (SOC) at each moment is RM/FCC
• FCC is updated every time full discharge occurs
0% 3V RM = FCC - Q
SOC = RM/FCC
4.2V
Q
FCC
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Learning Before Fully Discharged – fixed voltage thresholds
7% 3%
0% EDV0
FCC
4.2V
• It is too late to learn when 0% capacity is reached Learning FCC before 0%
• We can set voltage threshold that correspond to given percentage of remaining capacity
• However, true voltage corresponding to 7% depends on current and temperature
EDV2
EDV1
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Learning before fully discharged - with current and temperature compensation
4.2V
EDV2 (I1)
EDV2 (I2)
OCV
• Modeling last part of discharge allows to calculate function V(SOC, I, T)
• Substituting SOC=7% allows to calculate in real time CEDV2 threshold that corresponds to 7% capacity at any current and temperature
CEDV Model: Predict V(SOC) under any current and temperature
CEDV
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CEDV Formula
CEDV = CV - I*[EDVR0/4096]*[1 + EDVR1*Cact/16384]* [1 – EDVT0*(10T - 10Tadj)/(256*65536)]*[1+(CC*EDVA0)/(4*65536)] * age
Where: CV = EMF*[1 – EDVC0*(10T)*log(Cact)/(256*65536)] Cact = 256/(2.56*RSOC + EDVC1) – 1 for (2.56*RSOC + EDVC1) > 0 Cact = 255 for (2.56*RSOC + EDVC1) = 0 EDVC1 = 2.56 * Residual Capacity (%) + “Curve Fit” factor Tadj = EDVTC*(296-T) for T< 296oK and Tadj < T Tadj = 0 for T > 296 oK and Tadj max value = T age = 1 + 8 * CycleCount * A0 / 65536.
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CEDV Model Visualization
3% 4% 5% 6% 7% 8% 9%
Actual battery voltage curve
Voltage OCV curve defined
by EMF, C0
OCV corrected by I*R (R is defined by
R0, R1, T0) I*R
Further correction by low temperature (TC)
Reserve Cap: C1 shifts fit curve laterally Battery Low
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Impedance Track Fuel Gauging
• Combine advantages of voltage correlation and coulomb counting methods
• State of charge (SOC) update: – Read fully relaxed voltage to determine initial SOC and capacity
decay due to self-discharge – Use current integration when under load
• Parameters learning on-the-fly: – Learn impedance during discharge – Learn total capacity Qmax without full charge or discharge – Adapt to spiky loads (delta voltage)
• Usable capacity learning: – Calculate remaining run-time at typical load by simulating voltage
profile do not have to pass 7% knee point
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Current Direction Thresholds and Delays
Example of the Algorithm Operation Mode Changes With Varying SBS.Current( )
1
2
3
4
5
6
7
1. CHG relaxation timed 2. Enter RELAX mode 3. Start discharging 4. Enter DSG mode 5. DSG relaxation timed 6. Enter RELAX mode 7. Start charging 8. Enter CHG mode
8
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What is Impedance Track? 1. Chemistry table in Data Flash:
OCV = f (dod) dod = g (OCV)
2. Impedance learning during discharge:
R = OCV – V
I
Or, for bq78PL114/116: R = dv/di (Simultaneous Meas)
3. Update Max Chemical Capacity for each cell
Qmax = PassedCharge / (SOC1 – SOC2)
4. Temperature modeling allows for temperature-compensated impedance to be used in calculating remaining capacity and FCC
5. Run periodic simulation to predict Remaining and Full Capacity
10,000 foot View
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Close OCV profile for the Same Base-Electrode Chemistry
• OCV profiles close for all tested manufacturers
• Most voltage deviations from average are below 5mV
• Average DOD prediction error based on average voltage/DOD dependence is below 1.5%
• Same OCV database can be used with batteries produced by different manufacturers as long as base chemistry is same
• Generic database allows significant simplification of fuel-gauge implementation at user side
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13.4
3.67
3.93
4.2
Manufacturer ABCDE
DOD, fraction
Vo
lta
ge,
V
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Resistance Update
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
100
200
300
400
dod
Ra
Before Update
Discharge direction
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Ra Table: Interpolation and Scaling Operation • R = (OCV – V) / Avg Current. Averaging
method is selectable
• Resistance updates require updating 15 values for each cell
• A new resistance measurement represents the resistance at an exact grid point. Exact value found by interpolation
• All 14 grid points are ratiometrically updated from any valid gridpoint measurement. Changes are weighted according to confidence in accuracy
• Resistance updates in bq78PL114/116 are very much different – see the technical reference manual for details.
Grid
0
Grid
14
k: P
rese
nt g
rid
m:
Last
vis
ited
grid
Ra_new Ra_old
Step 1
Step 2
Step 3
Interpolation
Scale “After”
Scale “Before”
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Timing of Qmax Update
QMAX is learned from the change in SOC and Passed Charge between two qualified points in time, P1 and P2.
The learning occurs when two consecutive relaxation periods are separated by a period of current flow.
Qmax = PassedCharge soc1 – soc2
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FCC Learning
0 0.2 0.4 0.6 0.87200
7400
7600
7800
8000
8000
9000
1 .104
1.1 .104
1.2 .104
1.3 .104
SMB FCCtrue FCC
Ra gridsVoltage
SMB FCCtrue FCC
Ra gridsVoltage
DOD
FCC
, mA
h
V, m
V
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RemCap Simulation (concept)
Constant Load Example
I
Qstart ΔQ ΔQ ΔQ
ΔQ/2
ΔQ/4
. . . . . RsvCap
Vterm
Δ V > 250mV
EDV
V
(loaded)
Start of discharge
RemCap
Time
Time
OCV I*R
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Z-track Accuracy in Battery Cycling Test
0 50 100 150 200 250 3001.5
1
0.5
0
0.5
1
error at 10%error at 5%error at 3%
Cycle Number
Rem
aini
ng C
apac
ity E
rror
, %
• Error is shown at 10%, 5% and 3% points of discharge curve
• For all 3 cases, error stays below 1% during entire 250 cycles
• It can be seen that error somewhat decreases from 10 to 3% due to adaptive nature of IT algorithm
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Property CEDV Impedance Track
Worst error new, learned +/-2% +/-1%
Worst error aged, learned +30% (+/- 15% with age data) +/-2%
Data collection 3 temperatures, 2 rates,
Fitting to obtain parameters.
2 weeks
Chemistry selection test,
Optimization cycle
1 week
Instruction flash small large
Voltage accuracy requirement 20mV/pack 3mV/pack
State of charge initialization (host side requirement)
No
Yes
FCC temperature compensation
No (with rare exceptions)
Yes
FCC rate compensation No (with rare exceptions) Yes
Learning cycle in production required Not required
CEDV, Impedance Track Comparison
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37
bq27620 Impedance Track™ with Dynamic Voltage Correlation (IT-DVC)
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bq27620 System Side IT-DVC Fuel Gauge
• Patented Impedance TrackTM battery fuel gauging technology.
• Patent pending Impedance Track – Dynamic Voltage Correlation (IT-DVC) developed to estimate the battery states in real time by using voltage and temperature only without current sensing resistor.
• The current-voltage relationship of battery is modeled to estimate current.
• The estimated current is used in Impedance Track Algorithm to calculate State of Charge.
• Integrated 2.5V LDO regulator • Calculates remaining charge under all
conditions of discharge rate, temperature, and cell age.
38
Host System
Single Cell Li-IonBattery Pack
PACK-
PROTECTIONIC
CHGDSG
BatteryGood
I2CT
PACK+VoltageSense
BatteryLow
FETs
bq27620
Power Management
Controller
LDOREG25 REGIN
VCC
DATABI/TOUT
TS
1.75
2.69
0.62
5 (m
ax)
0.30
0.50
WCSP
• Package options: – WCSP 15-ball, 1.75 x 2.69 mm, 0.625 max thickness, 0.5mm pitch
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IT-DVC: Principles and Algorithm
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IT-DVC Introduction
• Development target: battery fuel gauge without the current sensing resistor
Current sensor
Idea: replace this with algorithms and firmware
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Circuit model
• VOC a function of SOC
• Rint is internal resistance
• Rs and Cs model the short term transient response
• RL and CL model the long term transient response
• Vbatt and Ibatt are the battery voltage and current
• All parameters are function of temperature and battery age
Voc(SOC)
Rint RL
CS CL
RS Vbatt
Ibatt
Transient model
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IT-DVC Introduction
• IT-DVC was developed to estimate the battery states in real time by measuring voltage and temperature only
• The current-voltage relationship of batteries was modeled as a piecewise linear system
• Battery current is estimated by using the model. Other battery states (SOC,TimeToEmpty, etc) are derived by using the estimated current instead of measured current inside the Impedance Track Algorithm
• The SOC estimation is still current based (using estimated current)
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Impedance Track Algorithm
Work Flow
Battery test data
Identify the parameters of dynamic battery model
Difference equations for current estimation
Offline algorithms; Have been implemented in MATCHCAD
Impedance update
IT-DVC algorithm
TimeToEmpty,FCC etc
Iest,DOD
Real time algorithms, in Firmware
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Estimating battery current and DOD estimation result
0.1 1.06008 103× 2.12006 103× 3.18004 103× 4.24002 103× 5.3 103×1−
0.6−
0.2−
0.2
0.6
1
DOD error(%)
1
1−
CIest_2RC CI−( )→
100⋅
Qmax
5300t1 t
1.291 104× 1.327 104× 1.362 104× 1.398 104× 1.433 104× 1.468 104×150−
130−
110−
90−
70−
50−
30−
10−
10
Estimated Current(mA)True Current(mA)
10
150−
f_Iest_2RC
I
1468512911 AG_SET rows I( ) 1−( )
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Pulsed load - 1700mAh capacity battery
Estimate Current in Real Time
3.6 103×
3.72 103×
3.84 103×
3.96 103×
4.08 103×
4.2 103×
4.194 103×
3.658 103×
V
4.137 104×0 index2
0 3.6 104× 7.2 104× 1.08 105× 1.44 105× 1.8 105×255−
188−
121−
54−
13
80
Estimated CurrentTrue Current
Iest_best 0⟨ ⟩
I
t
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0 3.6 104× 7.2 104× 1.08 105× 1.44 105× 1.8 105×0.01−
6− 10 3−×
2− 10 3−×
2 10 3−×
6 10 3−×
0.01Error of DOD
0.01
0.01−
Iest_best 1⟨ ⟩ CI−
Qmax
→
1800000 t
Error of DOD< 1%
Initial Verification: Sanyo 1700mAh battery
0 3.6 104× 7.2 104× 1.08 105× 1.44 105× 1.8 105×0
0.2
0.4
0.6
0.8
1Estimated DODTrue DOD
1
0
Iest_best 1⟨ ⟩−
Qmax
CI−
Qmax
1800000 t
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Verification: Handset load
0 5 103× 1 104× 1.5 104× 2 104× 2.5 104×0.02−
0.014−
8− 10 3−×
2− 10 3−×
4 10 3−×
0.010.01
0.02−
Iest 1⟨ ⟩ CI
Qmax+
250000 t
DOD error<2%
0 5 103× 1 104× 1.5 104× 2 104× 2.5 104×355−
274−
193−
112−
31−
50
Estimeated CurrentTrue Current
50
355−
Iest 0⟨ ⟩
I
250000 t
Sanyo 898 mAh battery
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Estimated Current vs True Current – portable electronic device
1 104× 1.5 104× 2 104×400−
300−
200−
100−
0Estimated CurrentTrue Current
20
347−
A ein⟨ ⟩
A in⟨ ⟩
238578787 A tn⟨ ⟩
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0 4 103× 8 103× 1.2 104× 1.6 104× 2 104×3.2 103×
3.4 103×
3.6 103×
3.8 103×
4 103×
4.2 103×
0
20
40
60
80
100
RSOCVoltage
Temperature=25C; Load=C/5; Voltage vs RSOC
Logged SOC vs True SOC
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0 10 20 30 40 50 60 70 80 90 1002−
0
2
4
SMB RSOC
RSOC
RSO
C e
rror
Temperature=25C; RSOC error
Logged SOC vs True SOC
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Summary
• IT-DVC works as a firmware implemented coulomb counter
• Regular Impedance Track™ is applied with these estimated variables
• SOC error <3%
• bq27620 with IT-DVC is scheduled for samples & RTM in Q4 2011
• Systems that benefit most from this device: – Need small board size (no sense resistor space) – Need low cost (no sense resistor cost) – Need high current support, can not afford losing power for sense resistor – Requires high accuracy provided by Impedance Track framework – Need short development time provided by chemical ID database support for
most new cells without characterization time
51
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Q & A