CN109164398A - Cell capacity evaluation method in a kind of Li-ion batteries piles - Google Patents
Cell capacity evaluation method in a kind of Li-ion batteries piles Download PDFInfo
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
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Abstract
The present invention proposes cell capacity evaluation method in a kind of Li-ion batteries piles.The discharge process of charging process and single battery of the implementation of this method based on Li-ion batteries piles, it include N number of battery cell in same ageing state in Li-ion batteries piles, this method comprises: calculating approximation Q-OCV curve QV according to charging and discharging curve using single battery fully charged at first in Li-ion batteries piles as reference battery0；Its approximation Q-OCV curve QV is calculated according to the charging and discharging curve of i-th capacity single battery to be estimatedi；Respectively to QV0And QViDifferential calculation is carried out, differential capacity curve D is obtained0And Di, by D0And DiAfter normalization, to DiCarrying out translation makes itself and D0It is overlapped；Record DiThe approximate OCV at middle charge cutoff momenti(End of Curve value)；According to curve VQ0The approximate SOC-OCV curve S of calculating benchmark battery0；In curve S0Middle determination and OCViCorresponding SOCiValue；According to the partial discharge capacity and SOC of i-th single batteryiValue calculates the actual capacity of i-th single battery.
Description
Technical field
The invention belongs to automobile-used and stored energy power battery technology field, monomer electricity in a kind of Li-ion batteries piles is related generally to
The evaluation method of tankage.
Background technique
As country vigorously advocates new energy, the development of electric car is a dark horse, and becomes substitution conventional fuel oil vehicle
Optimal selection.Heart of the lithium ion battery as electric car, mileage travelled and power characteristic to electric car play decision
Property effect.Battery capacity be measure battery performance an important indicator, and determine electric automobile during traveling mileage it is important because
One of element.Demand due to electric car to the energy content of battery, the battery for electric car be all by a large amount of single batteries simultaneously
Therefore the battery pack form for joining and being connected in series can understand the active volume of Li-ion batteries piles for automobile batteries management
For it is most important.
Since there are inconsistency, the available appearances of Li-ion batteries piles between single battery each in Li-ion batteries piles
It is had differences between amount and single battery active volume.When certain battery reaches charge cutoff voltage in Li-ion batteries piles,
Li-ion batteries piles charging terminates, and the electricity that Li-ion batteries piles are filled at this time is the charging capacity of Li-ion batteries piles, this
When, other batteries for not reaching charge cutoff voltage have only been filled with part electricity, lead to charging voltage upper capacity not
It can use；Similarly, when certain battery reaches discharge cut-off voltage in Li-ion batteries piles, Li-ion batteries piles electric discharge terminates,
The electricity that Li-ion batteries piles are released at this time is the discharge capacity of Li-ion batteries piles, is cut at this point, other do not reach electric discharge
Only the battery of voltage has only released part electricity, and guiding discharge voltage lower portion capacity is unavailable.So that being bound to cause
The waste of capacity of Li-ion batteries piles.Therefore, it needs to carry out balanced management to Li-ion batteries piles in use, and it is balanced
The formulation of strategy is carried out based on cell capacity and single battery residual capacity (SOC) state, it follows that understanding single
Capacity volume variance is most important between body battery, and in other words, cell capacity is for formulating lithium in grasp Li-ion batteries piles
Ion battery group balance policy has important directive significance.
It is different currently, there are many research of capacity estimation for single battery and SOC estimation, but due to single battery
Cause property, in groups after active volume before in groups compared to there is some difference, therefore, according to the method for cell capacity estimation
It is worthless for carrying out Li-ion batteries piles capacity estimation.It is maximally utilized to reach the energy content of battery on electric car, needs to slap
Each cell capacity is held, to lay the foundation to formulate the balance policy of Li-ion batteries piles.
Summary of the invention
A kind of lithium-ion electric is proposed in the invention patent to solve the technical problem in above-mentioned power battery application
Cell capacity evaluation method in the group of pond, comprising the following steps:
S1: using single battery fully charged at first in Li-ion batteries piles as reference battery, according to the filling of reference battery,
The approximate Q-OCV curve QV of discharge curve calculating benchmark battery0；
S2: the approximate Q- of capacity single battery to be estimated is calculated according to the charge and discharge curve of i-th capacity single battery to be estimated
OCV curve QVi；
S3: respectively to QV0And QViDifferential calculation is carried out, the differential capacity curve D of reference battery is obtained0With capacity list to be estimated
The differential capacity curve D of body batteryi, by D0And DiAfter normalization, to DiCarrying out translation makes DiWith D0It is overlapped；
S4: record DiThe approximate OCV value OCV at middle charge cutoff momenti(End of Curve value)；
S5: according to curve QV0The approximate SOC-OCV curve S of calculating benchmark battery0；
S6: in curve S0Middle determination and OCViCorresponding SOC value SOCi；
S7: according to the partial discharge capacity Q of i-th capacity single battery to be estimatediAnd SOCiCalculate i-th capacity list to be estimated
The actual capacity Q of body batteryir。
It comprising N single battery, N >=2 in the Li-ion batteries piles, and is integer on the basis of above scheme.
On the basis of above scheme, the battery in the Li-ion batteries piles can be new battery, or experience
The echelon in identical aging path is crossed using battery, or uses used batteries after a period of time.
On the basis of above scheme, the approximate Q-OCV curve QV of the reference battery0By the charge and discharge of reference battery
Curve and charge-discharge magnification are calculated and are obtained；Assuming that the rate of charge of battery is m C, discharge-rate is n C, reference battery charging
Voltage value in curve when a certain moment t is Vtc, the voltage value in discharge curve mutually in the same time is Vtd, then the meter of approximation OCV value
Calculation formula is OCV (V)=Vtc-[m/(m+n)]×(Vtc-Vtd)=Vtd+[n/(m+n)]×(Vtc-Vtd), wherein m ∈ (0,
k1], n ∈ (0, k2], k1、k2The respectively maximum allowable rate of charge and maximum allowable discharge-rate of battery.
On the basis of above scheme, the approximate Q-OCV curve QV of capacity single battery to be estimated described in step S2iMeter
Calculation and acquisition methods Q-OCV curve QV approximate with reference battery0Calculating it is identical with acquisition methods.
On the basis of above scheme, the Li-ion batteries piles are discharged to single single battery first and reach electric discharge cut-off
Voltage is recharged to single single battery and reaches charge cutoff voltage, is then discharged to electric discharge cut-off electricity to every single battery
Pressure.
On the basis of above scheme, the single battery for reaching discharge cut-off voltage at first and arrival charging at first are cut
Only the single battery of voltage is not necessarily same battery.
On the basis of above scheme, a variety of differential calculation modes of differential capacity curve negotiating described in the step S3 are obtained
It takes, including but not limited to immediate derivation, voltage interpolation etc..
On the basis of above scheme, the DiNormalization include peak intensity and peak position normalization.
On the basis of above scheme, in step S5 after reference cell voltage reaches charge cutoff voltage, one is added
The step of 2.5V blanking voltage is discharged to every capacity single battery to be estimated, it can thus be concluded that the actual discharge capacity of reference battery
Q0With the partial discharge capacity Q of capacity single battery to be estimatedi, the actual discharge capacity Q based on reference battery0By QV0In curve
Capacity Q is converted into SOC, it is assumed that the capacity of t moment reference battery is Qt, then the moment corresponding SOC value SOCt=Qt/Q0×
100%, obtain the SOC-OCV curve S of reference battery0。
On the basis of above scheme, the partial discharge capacity Q of i-th capacity single battery to be estimated is utilized in step S7i
And SOCiEstimate the actual capacity Q of capacity single battery to be estimatedir, calculation formula Qir=Qi/SOCi；Further, it is also possible to be based on
SOC-OCV curve calculates the actual capacity Q of capacity single battery to be estimated using the thought of Δ Q/ Δ SOCir, Qir=Δ Q/ Δ
SOC, Δ Q are the difference of the corresponding battery capacity of the section OCV two-end-point, and Δ SOC is the difference of the corresponding SOC of the section OCV two-end-point.
On the basis of above scheme, the Δ SOC is not limited to [0, SOCi], it can be any one son in this section
Section；Preferably, the section SOC is chosen between 10%-95%.
On the basis of above scheme, the battery types of the Li-ion batteries piles are existing various commercial li-ion electricity
Pond, including cathode be graphite, just extremely cobalt acid lithium, LiFePO4, LiMn2O4, nickel-cobalt-manganese ternary battery, further include that cathode is
Lithium titanate, the battery of the just extremely above a variety of materials, but it is not limited to this few class battery.
Beneficial effects of the present invention are as follows:
The method that cell capacity is estimated is applied in Li-ion batteries piles, realizes by the proposition of the invention patent
The volume calculation of single battery in Li-ion batteries piles has been established the balance policy formulation of lithium ion battery for electric vehicle good
Basis, there is critically important realistic meaning, the invention method can be used for battery pack in cyclic process in different agings
Cell capacity estimation when the stage.
Detailed description of the invention
Specific embodiments of the present invention will be described in further detail with reference to the accompanying drawing；
Fig. 1 is the flow chart of cell capacity evaluation method in Li-ion batteries piles of the invention；
Fig. 2 is the approximate Q-OCV curve graph of the reference battery of the embodiment of the present invention；
Fig. 3 is the approximate Q-OCV curve graph of the capacity single battery to be estimated of the embodiment of the present invention；
Fig. 4 is the benchmark of the embodiment of the present invention and the Differential Capacity curve graph of capacity single battery to be estimated；
Fig. 5 is the benchmark of the embodiment of the present invention and the Differential Capacity curve normalization figure of capacity single battery to be estimated；
Fig. 6 is the approximate SOC-OCV figure of the reference battery of the embodiment of the present invention；
Fig. 7 is the volume calculation result figure of the embodiment of the present invention；
Fig. 8 is the relative error figure of the volume calculation of the embodiment of the present invention.
Specific embodiment
Below in conjunction with attached drawing, invention is further described in detail, is exemplary by reference to the embodiment that attached drawing describes
, it is intended to it is used to explain the present invention, and is not considered as limiting the invention.
Fig. 1 show the flow chart of cell capacity evaluation method in Li-ion batteries piles according to the present invention.This hair
Bright thought is identical based on the aging path that N single battery in Li-ion batteries piles is undergone, and the SOC-OCV of each single battery
The consistent hypothesis of curve, it is believed that the OCV formed when each single batteries of Li-ion batteries piles is in identical SOC state is also identical,
SOC-OCV curve i.e. in Li-ion batteries piles between each single battery can be overlapped, it is believed that internal resistance inconsistency is to the curve
It influences little.The case where for not being overlapped, can realize coincidence by way of normalizing or translating.
In an embodiment of the present invention, the monomer electricity of identical ageing state is only substantially in Li-ion batteries piles comprising N
Pond, comprising the following steps:
S1: using single battery fully charged at first in Li-ion batteries piles as reference battery, according to the filling of reference battery,
The approximate Q-OCV curve QV of discharge curve calculating benchmark battery0。
Fig. 2 show the approximate Q-OCV curve graph of the reference battery of the embodiment of the present invention, by Li-ion batteries piles at first
The single battery of charge cutoff voltage is charged to as reference battery, abscissa is the capacity of benchmark battery, when by charge cutoff
It carves and is aligned with the capacity of electric discharge initial time, the approximate OCV value of reference battery is calculated by charge-discharge magnification or electric current, it
Thus it is approximate OCV value, is the not true OCV of reference battery obtained because of thus method, but it is different to ignore internal resistance
The approximate open-circuit voltage that the different influence that causes and polarize obtains.Assuming that the rate of charge of battery is m C, discharge-rate is n C, base
Voltage value in quasi- battery charging curve when a certain moment t is Vtc, the voltage value in discharge curve mutually in the same time is Vtd, then closely
Calculation formula like OCV value is OCV (V)=Vtc-[m/(m+n)]×(Vtc-Vtd)=Vtd+[n/(m+n)]×(Vtc-Vtd),
In, m ∈ (0, k1], n ∈ (0, k2], k1、k2The respectively maximum allowable rate of charge and maximum allowable discharge-rate of battery.It is false
If the charging current or discharge current of known battery, can convert the current to charge-discharge magnification, then calculated according to above formula approximate
OCV value.
S2: the approximate Q- of capacity single battery to be estimated is calculated according to the charge and discharge curve of i-th capacity single battery to be estimated
OCV curve QVi。
Fig. 3 is the approximate Q-OCV curve graph QV of the capacity single battery to be evaluated of the embodiment of the present inventioni, abscissa be to
Estimate the capacity of capacity single battery, capacity single battery QV to be estimatediCalculating and acquisition methods Q-OCV approximate with reference battery
The calculating of curve graph is identical with acquisition methods, only the V in formulatcAnd VtdCapacity single battery respectively to be evaluated is charged and is put
In electric curve in moment t corresponding voltage value, if not otherwise specified, remaining parameter is no difference with reference battery.
S3: respectively to QV0And QViDifferential calculation is carried out, the differential capacity curve D of reference battery is obtained0With capacity list to be estimated
The differential capacity curve D of body batteryi, by D0And DiAfter normalization, to DiCarrying out translation makes DiWith D0It is overlapped.
Since battery charge and discharge process Instrumental data record also can there are inconsistent between error or single battery
Error is brought, therefore, it is necessary to pairing approximation OCV values to be corrected, using curve differential calculus-normalization-shifting method.
Fig. 4 be the embodiment of the present invention benchmark and capacity single battery to be estimated Differential Capacity curve graph, in the present invention,
The acquisition methods of Differential Capacity curve graph have very much, including directly to QV0And QViDerived function is carried out, further includes being inserted using voltage
The method calculating of value acquires, and interpolation voltage spaces range value Δ V is 1mV~10mV, it is preferable that Δ V takes [2mV, 5mV]；With
On be merely illustrative and can be used derivation or voltage interpolation method is differentiated capacity curve, but be not limited to both methods.
Since capacity has differences between different monomers battery, the peak intensity and peak area of differential curve also can be poor
Not, therefore, it is necessary to which the differential capacity curve of capacity single battery to be estimated and reference battery to be normalized, curve can be selected
In any one peak peak intensity as normalized benchmark, it is preferable that be to be normalized according to the peak intensity of highest peak, make most
The peak intensity at strong peak is converted into 1, and the peak intensity at remaining peak accordingly proportionally changes.In order to reduce data record and battery not
Consistency bring error, it is also necessary to the normalized Differential Capacity curve of capacity single battery to be estimated is subjected to left and right translation, made
The Differential Capacity curve co-insides of itself and reference battery determine that the standard being overlapped is completely heavy for peak center position in Differential Capacity curve
Close, Fig. 5 be the embodiment of the present invention in after estimating the normalized Differential Capacity curve of capacity single battery and being overlapped with reference battery
Effect picture.
S4: record DiThe approximate OCV value OCV at middle charge cutoff momenti(End of Curve value).
Since reference battery is the battery for being charged to charge cutoff voltage in Li-ion batteries piles at first, when reference battery arrives
When up to charge cutoff voltage, charge cutoff voltage is had not yet been reached in remaining battery, therefore, the approximation of remaining single battery in battery pack
OCV value is less than the approximate OCV value of reference battery, that is to say, that in Differential Capacity curve after normalization, capacity monomer to be estimated
Approximate OCV value (OCV when battery charge cutoffi) be less than reference battery charge cutoff when approximate OCV value (OCV0), record to
Estimate capacity single battery DiThe approximate OCV value OCV at charge cutoff moment in curvei, i.e. End of Curve value.
S5: according to curve QV0The approximate SOC-OCV curve S of calculating benchmark battery0。
Fig. 6 is the approximate SOC-OCV figure of the reference battery of the embodiment of the present invention, because reference battery has been filled in charging process
Electricity is to charge cutoff voltage, it is therefore contemplated that being 100%SOC when reference battery charge cutoff.In the present embodiment, work as lithium
After certain single battery (reference battery) voltage reaches charge cutoff voltage in ion battery group, additional one is held every wait estimate
The step of amount single battery is discharged to 2.5V blanking voltage, it can thus be concluded that the actual discharge capacity Q of reference battery0With capacity to be estimated
The partial discharge capacity Q of single batteryi, the actual discharge capacity Q based on reference battery0, can be by QV0Capacity Q in curve turns
Turn to SOC, it is assumed that the capacity of t moment reference battery is Qt, then the moment corresponding SOC value SOCt=Qt/Q0× 100%, it obtains
The SOC-OCV curve of reference battery, is denoted as S0。
S6: in curve S0Middle determination and OCViCorresponding SOC value SOCi。
OCV increases the relationship that monotonic increase is presented with SOC in the SOC-OCV curve that step S5 is obtained, it can be seen that OCV
It is correspondingly, to give an OCV value, then there is a unique SOC value to correspond with SOC.It mentions in step s 4,
Approximate OCV value of the capacity single battery to be estimated at the charge cutoff moment is less than reference battery in approximate OCV value mutually in the same time, base
SOC-OCV curve is consistent it is assumed that the OCV determined in step S4 between different monomers battery in Li-ion batteries pilesiIn step
SOC-OCV curve S obtained in rapid S50In can arrive and find a corresponding SOC value, be denoted as SOCi, it should be noted that
SOCi< 100%.
S7: according to the partial discharge capacity Q of i-th capacity single battery to be estimatediAnd SOCiCalculate i-th capacity list to be estimated
The actual capacity Q of body batteryir。
In the present embodiment, it can use the partial discharge capacity Q of i-th capacity single battery to be estimatediIt estimates and holds wait estimate
Measure the actual capacity Q of single batteryir, calculation formula Qir=Qi/SOCi.Based on SOC-OCV curve, Δ Q/ Δ can be used
The thought of SOC calculates the actual capacity of battery.In the present embodiment, also have chosen in charging process the different sections OCV (or
The section SOC) and volume change estimate that the actual capacity of battery, the code in different sections are expressed as digital 1-7.
Specific embodiment is to choose D in step s 4iCurved portion section records the approximation of section beginning and end
OCV value, is denoted as OCVi1And OCVi2.Not every single battery has all reached discharge cut-off voltage before starting due to charging, because
This, the approximate OCV value of charging each single battery of initial time is also not quite similar, and estimates the reliable of selected section for guaranteed capacity
Property, the range of approximate OCV value should be in 3.0V~OCViBetween；In step s 6 determine respectively with OCVi1And OCVi2It is corresponding
SOCi1And SOCi2Value；Simultaneously determine respectively with OCVi1And OCVi2Corresponding capability value Qi1And Qi2Value；It is estimated according to above-mentioned each value
I-th capacity cell capacity to be estimated, calculation formula Qir=Δ Qi/ΔSOCi, wherein QirFor i-th capacity list to be estimated
The actual capacity of body battery, Δ QiFor section [OCVi1,OCVi2] the corresponding battery capacity of two-end-point difference, Δ SOCiFor section
[OCVi1,OCVi2] the corresponding battery SOC of two-end-point difference, Δ Qi=Qi2-Qi1, Δ SOCi=SOCi2-SOCi1。
It should be noted that if without specified otherwise, for estimating that the section OCV or the section SOC of battery capacity can be with
It is any to choose.
According to the volume calculation result figure of the embodiment of the present invention and the relative error figure of volume calculation, as a result Fig. 7 and Fig. 8 is
Show that the estimated capacity of single battery and experimental data have high consistency, relative error base in ferric phosphate lithium cell group
This is less than 2%.
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention may be used also on the basis of the above description for those of ordinary skill in the art
To make other variations or changes in different ways, all embodiments can not be exhaustive here, it is all to belong to this hair
The obvious changes or variations that bright technical solution is extended out are still in the scope of protection of the present invention.
The content being not described in detail in this specification belongs to the prior art and name well known to professional and technical personnel in the field
Word.
Claims (10)
1. cell capacity evaluation method in a kind of Li-ion batteries piles, which comprises the following steps:
S1: using single battery fully charged at first in Li-ion batteries piles as reference battery, according to the charge and discharge of reference battery
The approximate Q-OCV curve QV of curve calculating benchmark battery0；
S2: the approximate Q-OCV of capacity single battery to be estimated is calculated according to the charge and discharge curve of i-th capacity single battery to be estimated
Curve QVi；
S3: respectively to QV0And QViDifferential calculation is carried out, the differential capacity curve D of reference battery is obtained0With capacity monomer electricity to be estimated
The differential capacity curve D in pondi, by D0And DiAfter normalization, to DiCarrying out translation makes DiWith D0It is overlapped；
S4: record DiThe approximate OCV value OCV at middle charge cutoff momenti；
S5: according to curve QV0The approximate SOC-OCV curve S of calculating benchmark battery0；
S6: in curve S0Middle determination and OCViCorresponding SOC value SOCi；
S7: according to the partial discharge capacity Q of i-th capacity single battery to be estimatediAnd SOCiCalculate i-th capacity monomer electricity to be estimated
The actual capacity Q in pondir。
2. cell capacity evaluation method in Li-ion batteries piles as described in claim 1, which is characterized in that the lithium from
It comprising N single battery, N >=2 in sub- battery pack, and is integer；Battery in the Li-ion batteries piles includes new battery, warp
The echelon in identical aging path was gone through using battery and using used batteries after a period of time.
3. cell capacity evaluation method in Li-ion batteries piles as described in claim 1, which is characterized in that the lithium from
The battery types of sub- battery pack are existing various commercial li-ion batteries, including cathode is graphite, just extremely cobalt acid lithium, ferric phosphate
The battery of lithium, LiMn2O4 or nickel-cobalt-manganese ternary, further include cathode be lithium titanate, just extremely cobalt acid lithium, LiFePO4, LiMn2O4 or
The battery of nickel-cobalt-manganese ternary.
4. cell capacity evaluation method in Li-ion batteries piles as described in claim 1, which is characterized in that the benchmark
The approximate Q-OCV curve QV of battery0It is calculated by the charge and discharge curve and charge-discharge magnification of reference battery and is obtained；Assuming that battery
Rate of charge be m C, discharge-rate is n C, and the voltage value in reference battery charging curve when a certain moment t is Vtc, electric discharge
Voltage value in curve mutually in the same time is Vtd, then the calculation formula of approximation OCV value is OCV (V)=Vtc-[m/(m+n)]×(Vtc-
Vtd)=Vtd+[n/(m+n)]×(Vtc-Vtd), wherein m ∈ (0, k1], n ∈ (0, k2], k1、k2Respectively battery is maximum allowable
Rate of charge and maximum allowable discharge-rate.
5. cell capacity evaluation method in Li-ion batteries piles as claimed in claim 4, which is characterized in that in step S2
The approximate Q-OCV curve QV of the capacity single battery to be estimatediCalculating and acquisition methods Q-OCV approximate with reference battery it is bent
Line QV0Calculating it is identical with acquisition methods.
6. cell capacity evaluation method in Li-ion batteries piles as described in claim 1, which is characterized in that the step
The a variety of differential calculation modes of differential capacity curve negotiating described in S3 obtain, including immediate derivation and voltage interpolation.
7. cell capacity evaluation method in Li-ion batteries piles as described in claim 1, which is characterized in that the Di's
Normalization includes the normalization of peak intensity and peak position.
8. cell capacity evaluation method in Li-ion batteries piles as described in claim 1, which is characterized in that in step S5
After reference cell voltage reaches charge cutoff voltage, additional one is discharged to 2.5V cut-off to every capacity single battery to be estimated
Thus the step of voltage, obtains the actual discharge capacity Q of reference battery0With the partial discharge capacity Q of capacity single battery to be estimatedi, base
In the actual discharge capacity Q of reference battery0By QV0Capacity Q in curve is converted into SOC, it is assumed that the capacity of t moment reference battery
For Qt, then the moment corresponding SOC value SOCt=Qt/Q0× 100%, obtain the SOC-OCV curve S of reference battery0。
9. cell capacity evaluation method in Li-ion batteries piles as claimed in claim 8, which is characterized in that in step S7
Utilize the partial discharge capacity Q of i-th capacity single battery to be estimatediAnd SOCiEstimate the actual capacity of capacity single battery to be estimated
Qir, calculation formula Qir=Qi/SOCi；Based on SOC-OCV curve, capacity monomer to be estimated is calculated using the thought of Δ Q/ Δ SOC
The actual capacity Q of batteryir, Qir=Δ Q/ Δ SOC, Δ Q are the difference of the corresponding battery capacity of the section OCV two-end-point, and Δ SOC is
The difference of the corresponding SOC of the section OCV two-end-point.
10. cell capacity evaluation method in Li-ion batteries piles as claimed in claim 9, which is characterized in that the Δ
SOC is [0, SOCi] any one subinterval in section.
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