CN112068000A - Peak power prediction method considering power battery durability influence - Google Patents

Peak power prediction method considering power battery durability influence Download PDF

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CN112068000A
CN112068000A CN202011034157.8A CN202011034157A CN112068000A CN 112068000 A CN112068000 A CN 112068000A CN 202011034157 A CN202011034157 A CN 202011034157A CN 112068000 A CN112068000 A CN 112068000A
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battery
current
peak current
temperature
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CN112068000B (en
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于全庆
黄永和
万长江
张昕
林野
李�昊
俄立新
秦梦迪
孙逸臣
李俊夫
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Harbin Institute of Technology Weihai
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
    • G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • 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 invention provides a peak power prediction method considering the durability influence of a power battery, and compared with the prior art, the peak power prediction method takes the highest temperature value of the battery as a constraint and also increases the change rate constraint and the aging constraint of the battery temperature. The temperature rise change rate of the battery can well reflect the health change condition of the battery when the battery is at any environmental temperature, so the invention can better reflect the health change condition of the battery, reduce the capacity loss and improve the durability. In addition, considering that the current multiplying power can influence the capacity fading track of the battery, the method starts from the capacity loss model to deduce the relation between the current multiplying power and the capacity fading constraint, and takes the capacity fading limit value as the constraint to predict the continuous charging and discharging peak current so as to predict the continuous charging and discharging peak power of the battery, thereby having important significance on the durability of the battery.

Description

Peak power prediction method considering power battery durability influence
Technical Field
The invention relates to the technical field of power battery systems, in particular to a peak power prediction method research of a power battery.
Background
The peak power of the electric automobile directly influences the climbing acceleration performance and the regenerative braking energy recovery capability. The peak power is too low, and the energy provided by the battery cannot meet the requirement; when the peak power is too high, irreversible damage can be caused to the battery, and the service life of the battery is shortened. In view of the indirectly measurable characteristic of peak power, it is necessary to accurately predict the peak power.
Currently, in the process of predicting the peak power of a power battery, a means of predicting the peak current by using the State of charge (SOC) of the battery, the terminal voltage, the temperature and the maximum current of the battery design as constraints is mostly adopted, so as to predict the peak power. However, in practice, the rate of change in the battery temperature during charging and discharging can better reflect the change in the health of the battery than the temperature value of the battery. Too fast temperature rise means that side reactions occur inside the battery, resulting in a decrease in the amount of available lithium ions and an increase in the aging rate of the battery. In addition, excessive peak current can cause part of lithium ions to be accumulated on the surface of an active material before the positive electrode and the negative electrode of the battery are combined with electrons, so that the consumption of available lithium ions is caused, the aging speed of the battery is accelerated, and the quality guarantee mileage and the quality guarantee time of the battery are influenced. Therefore, for the improvement of the durability of the battery, besides the conventional constraints of SOC, terminal voltage, temperature and factory current limit, the temperature rise change rate and the aging constraint are also important factors to be considered in peak power prediction, but the research on the aspect is still lacked in the prior art.
Disclosure of Invention
In view of this, the present invention provides a peak power prediction method considering the durability influence of a power battery, which specifically includes the following steps:
step one, recording current I and terminal voltage U in the charging and discharging process of a batterytBattery surface temperature T and external environment temperature Tex；
Step two, establishing a first-order RC equivalent circuit model of the power battery; based on the relationship among the external environment temperature, the open-circuit voltage and the state of charge, the open-circuit voltage (OCV) -state of charge (SOC) -environment temperature (T) is established in a fitting mannerex) A three-dimensional response surface model; acquiring a thermal model of the power battery by using the three-dimensional response surface model;
step three, taking the SOC as constraint to calculate corresponding continuous charge-discharge peak current
Figure BDA0002704714590000011
And
Figure BDA0002704714590000012
identifying model parameters of the first-order RC equivalent circuit model, taking terminal voltage as constraint, and calculating corresponding continuous charge-discharge peak current based on the first-order RC equivalent circuit model
Figure BDA0002704714590000013
And
Figure BDA0002704714590000014
and fifthly, calculating corresponding continuous charging peak current by using the thermal model and using the temperature and the temperature change rate of the battery as constraints
Figure BDA0002704714590000015
And sustained discharge peak current
Figure BDA0002704714590000016
Step six, taking the capacity loss caused by the peak current to the battery aging process as a constraint, and calculating the corresponding continuous charging peak current
Figure BDA0002704714590000021
And sustained discharge peak current
Figure BDA0002704714590000022
Seventhly, obtaining the continuous charging peak current of the battery under multiple constraints based on the continuous charging and discharging peak current and the battery delivery current limit value obtained through multiple constraints
Figure BDA0002704714590000023
And sustained discharge peak current
Figure BDA0002704714590000024
Substituting the voltage into the first-order RC battery equivalent circuit model to calculate the terminal voltage corresponding to the continuous peak current, thereby calculating the charge-discharge continuous peak power.
Further, the second step specifically includes:
the first-order RC equivalent circuit model specifically adopts the following form:
Figure BDA0002704714590000025
in the formula, a subscript k represents a kth sampling time, and Δ t is a sampling period; r0Expressing ohmic internal resistance; i represents a current; tau is1Is a time constant and1＝R1C1，R1and C1Respectively the polarization internal resistance and polarization capacitance of the battery; u shape1Represents the cell polarization voltage; u shapetIs terminal voltage; model parameter R0、R1And C1On-line by recursive least square method with forgetting factorIdentification is carried out; u shapeocvRepresents the open-circuit voltage OCV of the battery and can pass through the OCV-SOC-TexObtaining a three-dimensional response surface model;
the OCV-SOC-TexThe three-dimensional response surface model construction method comprises the following steps:
at different ambient temperatures TexRespectively carrying out OCV test to obtain corresponding relations between SOC and OCV at different external environment temperatures, respectively fitting the relations between SOC and OCV at different external environment temperatures according to the following formula to obtain each temperature TexAlpha of0,α1,…,α6Parameter value, then parameter α is corrected by quadratic function0,α1,…,α6And temperature TexThe relationship of (2) is fitted to complete the establishment of the three-dimensional response surface:
Uocv(Tex,z)＝α0+α1z+α2z2+α3z3+α4/z+α5ln(z)+α6ln(1-z)
[α0 α1 α2 α3 α4 α5 α6]T＝Λ×[Tex 2 Tex 1]T
in the formula of Uocv(TexZ) represents the function of the open circuit voltage OCV in terms of TexA function of SOC; alpha is alpha0,α1,…,α6Fitting coefficients for the model; Λ is a 7 × 3 constant matrix; z represents the state of charge SOC of the battery and can be calculated by the ampere-hour integration method as follows:
Figure BDA0002704714590000026
in the formula, z0Is the SOC value at the initial moment; η represents the cell coulombic efficiency; q represents a battery capacity;
the thermal model is established on the assumption that the temperature T and the heat generation rate q of the battery surface at any time are uniformly distributed:
the temperature of the battery at time k +1 can be expressed as:
Figure BDA0002704714590000031
in the formula, RthAnd CthThermal resistance and thermal capacity, τ, of the cell, respectivelythIs a thermal time constant, andth＝RthCththe thermal resistance and capacity can be measured by adiabatic calorimetry, and q is composed mainly of irreversible heat and reversible heat and can be expressed as:
Figure BDA0002704714590000032
wherein (U)t-Uocv) I represents the irreversible heat generation rate of the battery;
Figure BDA0002704714590000033
represents a reversible heat generation rate;
Figure BDA0002704714590000034
is entropy coefficient of heat, about equal to
Figure BDA0002704714590000035
Passing OCV-SOC-TexAnd obtaining a three-dimensional response surface model.
Further, the third step specifically includes:
taking the SOC of the battery as a constraint condition, predicting the step length L into a plurality of sampling periods, and deducing a continuous charge-discharge peak current expression of the battery according to an ampere-hour integration method:
Figure BDA0002704714590000036
in the formula (I), the compound is shown in the specification,
Figure BDA0002704714590000037
and
Figure BDA0002704714590000038
respectively the peak charging current and the peak discharging current of the battery under the SOC constraint; z is a radical ofmax、zminThe maximum SOC value and the minimum SOC value are respectively set as 90 percent and 10 percent when the battery is charged and discharged; z is a radical ofkCan be obtained by ampere-hour integration.
Further, the fourth step specifically includes:
obtaining model parameter R at moment k by recursive least square method with forgetting factor0,k、R1,kAnd C1,kAssuming that the model parameters of the battery are unchanged in L sampling periods, when the working current is IkThe terminal voltage at time k + L can be expressed as:
Ut,k+L＝Uocv,k+L+U1,k+L+Ik+L·R0
the open circuit voltage value and the polarization voltage value of the battery at the time k + L can be expressed as:
Figure BDA0002704714590000039
Figure BDA00027047145900000310
order to
Figure BDA0002704714590000041
Then U istAt time k + L can be expressed as:
Figure BDA0002704714590000042
based on the above formula, the peak current of the battery during continuous charging and discharging is respectively:
Figure BDA0002704714590000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002704714590000044
and
Figure BDA0002704714590000045
respectively representing a continuous charging peak current and a continuous discharging peak current which are constrained by voltage; u shapet,maxAnd Ut,minThe upper and lower cut-off voltages are set according to specifications of the selected battery.
Further, the fifth step specifically includes:
obtaining the surface temperature T of the battery at the k + L moment according to the thermal model of the batteryk+L：
Figure BDA0002704714590000046
In the formula, τthRepresents the thermal time constant of the battery; t isex,k+LThe ambient temperature at time k + L;
order to
Figure BDA0002704714590000047
The highest temperature T of the surface of the batterymaxNot more than 60 ℃ as a constraint, obtaining the maximum heat generation rate q of the battery1：
Figure BDA0002704714590000048
Changing the temperature of the battery
Figure BDA0002704714590000049
As a constraint, the maximum heat generation rate q of the battery is obtained assuming that the temperature change rate does not exceed the limit of 2 ℃/s2：
Figure BDA00027047145900000410
Get qmax＝min(q1,q2) The heat generation rate of a lithium ion battery can be approximated as:
Figure BDA0002704714590000051
in the formula, RtIs the sum of ohmic internal resistance and polarization internal resistance of the battery;
assuming that the entropy thermal coefficient of the battery is constant in L sampling periods, let q be qmaxThe peak charging current under the temperature and temperature change rate constraints can be obtained
Figure BDA0002704714590000052
And peak discharge current
Figure BDA0002704714590000053
Respectively as follows:
Figure BDA0002704714590000054
further, the sixth step specifically includes:
obtaining a capacity loss model according to a battery aging experiment:
Figure BDA0002704714590000055
in the formula, QlossIs a loss of battery capacity; n is the number of charge-discharge cycles; b is a coefficient influenced by the discharge rate C according to Q under different discharge rateslossDetermining the value of B under different multiplying powers C, and performing polynomial fitting on the value of B to obtain an expression of B changing along with the charging and discharging multiplying power C:
B(C)＝β0+β1C+β2C2
in the formula, beta0,β1,β2Fitting coefficients for the polynomial;
when the battery is subjected to N1During each charge-discharge cycle, Q x% of the capacity is lost, and if the battery continues to operate at peak current, the battery capacity is satisfied at the Nth*The decay of each cycle is Q x 20%,the following expression holds:
Figure BDA0002704714590000056
B*(C)＝β0+β1C*+β2(C*)2
in the formula, N*For the delivery quality assurance cycle number of the electric automobile, T represents the battery temperature when the electric automobile works at the peak current, C is the current multiplying power corresponding to the peak current, and C is obtained by solving the above formula by a Newton iteration method*The specific flow is as follows:
order:
Figure BDA0002704714590000057
the original equation can be: [ beta ]0+β1C*+β2(C*)2]·exp(αC*+β)-λ＝0。
Applying Newton iteration method to solve the iteration formula as follows:
Figure BDA0002704714590000061
in the formula, the initial value C of the multiplying power0For the ratio of the current value acquired by the current sensor of the battery to the capacity, the iteration end condition is that the absolute value of the difference of the multiples obtained twice before and after is less than 2% of the given precision, namely | C%k+1-Ck|/|CkWhen | < 2%, let Ck+1Is C*And further obtaining the peak current of continuous charge and discharge:
Figure BDA0002704714590000062
further, the seventh step specifically includes:
the continuous charging peak current and the continuous discharging peak current based on the above multiple constraints are:
Figure BDA0002704714590000063
in the formula IchgAnd IdchgRespectively designing a maximum charging current and a maximum discharging current for battery delivery;
and further obtaining the peak power of continuous charge and discharge by combining the terminal voltage of the battery:
Figure BDA0002704714590000064
compared with the prior art, the invention at least has the following beneficial effects:
1. the surface temperature and the environment temperature of the battery in actual operation have uncertainty, and can be at any temperature between-10 ℃ and 50 ℃, and the peak current prediction constraint of the battery is only applicable to the peak current prediction of the battery in the environment with higher temperature by adopting a single highest temperature value. When the temperature of the battery is low, the irreversible capacity loss of the battery can be caused even if the highest temperature of the battery caused by charging and discharging with large current does not reach the set highest temperature. And the temperature rise change rate of the battery can well reflect the health change condition of the battery when the battery is at any environmental temperature. Therefore, the invention also increases the temperature change rate constraint of the battery besides taking the highest temperature value as the constraint, and can better reflect the change condition of the health state of the battery, reduce the capacity loss and improve the durability compared with the prior art.
2. The invention derives the relation between the current multiplying power and capacity fading constraint from a capacity loss model, and carries out continuous charging and discharging peak current prediction by taking a capacity fading limit value as constraint so as to realize the continuous charging and discharging peak power prediction of the battery, thereby having important significance on the durability of the battery.
Drawings
FIG. 1 is a schematic flow diagram of a method provided by the present invention;
FIG. 2 is a schematic diagram of a first-order RC equivalent circuit model employed in the method of the present invention;
figure 3 is a schematic of the thermal model architecture employed in the process of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In a preferred embodiment of the present invention, the method provided by the present invention is performed on the basis of a LiFePO4 battery to continuously predict peak power. LiFePO of the battery4The battery parameters were as follows:
the rated voltage is 3.6V, the nominal capacity is 20A, the upper and lower limit cut-off voltages are 4.2V and 2.5V, the highest current is 100A, the recommended temperature use range is 0-50 ℃, the vehicle quality guarantee is 10 years or the battery is degraded by Q multiplied by 20 after passing 3500 circulation capacities.
The flow of the battery continuous peak power prediction method is shown in fig. 1, and the specific steps are as follows:
step one, recording current I and terminal voltage U in the charging and discharging process of a batterytBattery surface temperature T and external environment temperature Tex；
Step two, establishing a first-order RC equivalent circuit model of the power battery; based on the relationship among the external environment temperature, the open-circuit voltage and the state of charge, the open-circuit voltage (OCV) -state of charge (SOC) -temperature (T) is established in a fitting mannerex) A three-dimensional response surface model; acquiring a thermal model of the power battery by using the three-dimensional response surface model;
a first-order RC equivalent circuit model shown in FIG. 2 is established, and the mathematical expression is as follows:
Figure BDA0002704714590000071
in the formula, a subscript k represents a kth sampling time, and Δ t is a sampling period; r0Expressing ohmic internal resistance; r1And C1Respectively the polarization internal resistance and polarization capacitance of the battery; tau is1Is a time constant and1＝R1C1；U1represents the cell polarization voltage; u shapetIs terminal voltage; parameter R0、R1And C1The method is obtained by on-line identification through a recursive least square method with forgetting factors; u shapeocvRepresents the open-circuit voltage OCV of the battery and can pass through the OCV-SOC-TexAnd obtaining a three-dimensional response surface model.
OCV-SOC-TexThe three-dimensional response surface model construction method comprises the following steps:
performing OCV test at-10 deg.C, 0 deg.C, 10 deg.C, 20 deg.C, 30 deg.C, 40 deg.C, 50 deg.C and 60 deg.C respectively to obtain corresponding relationship between SOC and OCV at different temperatures, and fitting the relationship between SOC and OCV at different temperatures according to the following formula to obtain each temperature TexAlpha of0,α1,…,α6Value, then using a quadratic function pair alpha0,α1,…,α6And temperature TexFitting the relation to complete the establishment of the three-dimensional response surface model:
Uocv(Tex,z)＝α0+α1z+α2z2+α3z3+α4/z+α5ln(z)+α6ln(1-z)
[α0 α1 α2 α3 α4 α5 α6]T＝Λ×[Tex 2 Tex 1]T
in the formula of Uocv(TexZ) represents the open circuit voltage OCV function, which is TexA function of SOC; alpha is alpha0,α1,…,α6Fitting coefficients for the model; superscript T represents the transpose of the matrix; Λ is a 7 × 3 constant matrix; z represents the state of charge SOC of the battery and can be calculated by the ampere-hour integration method as follows:
Figure BDA0002704714590000081
in the formula, z0Is the SOC value at the initial moment; η represents the cell coulombic efficiency; q represents a battery capacity;
a thermal model of the battery as shown in fig. 3 was established, assuming that the temperature T and the heat generation rate q of the battery surface at any time were uniformly distributed. RthAnd CthThermal resistance and thermal capacity, τ, of the cell, respectivelythIs a thermal time constant, andth＝RthCthand q is the heat generation rate of the battery.
The temperature of the battery at time k +1 can be expressed as:
Figure BDA0002704714590000082
in the formula, RthAnd CthAs measured by adiabatic accelerated calorimetry, q consists primarily of irreversible heat and reversible heat and can be expressed as:
Figure BDA0002704714590000083
wherein (U)t-Uocv) I represents the irreversible heat generation rate of the battery;
Figure BDA0002704714590000084
represents a reversible heat generation rate;
Figure BDA0002704714590000085
is entropy coefficient of heat, about equal to
Figure BDA0002704714590000086
Passing OCV-SOC-TexAnd obtaining a three-dimensional response surface model.
Step three, taking the SOC as constraint to calculate corresponding continuous charge-discharge peak current
Figure BDA0002704714590000087
And
Figure BDA0002704714590000088
taking the SOC of the battery as a constraint condition, predicting the step length L to be 360 sampling periods, and deducing a continuous charge-discharge peak current expression of the battery according to an ampere-hour integration method:
Figure BDA0002704714590000091
in the formula (I), the compound is shown in the specification,
Figure BDA0002704714590000092
and
Figure BDA0002704714590000093
respectively a continuous charging peak current and a continuous discharging peak current under the constraint of the SOC of the battery; z is a radical ofmax、zminThe maximum SOC value and the minimum SOC value are respectively set as 90 percent and 10 percent when the battery is charged and discharged; z is a radical ofkCan be obtained by ampere-hour integration.
Identifying model parameters of the first-order RC equivalent circuit model, taking terminal voltage as constraint, and calculating corresponding continuous charge-discharge peak current based on the first-order RC equivalent circuit model
Figure BDA0002704714590000094
And
Figure BDA0002704714590000095
obtaining model parameter R at moment k by recursive least square method with forgetting factor0,k、R1,kAnd C1,kR is measured by adiabatic acceleration calorimeterthAnd Cth. Assuming that the model parameters of the battery are unchanged in L sampling periods, when the working current is IkThe terminal voltage at time k + L can be expressed as:
Ut,k+L＝Uocv,k+L+U1,k+L+Ik+L·R0
the open circuit voltage value and the polarization voltage value of the battery at the time k + L can be expressed as:
Figure BDA0002704714590000096
Figure BDA0002704714590000097
order to
Figure BDA0002704714590000098
UtAt time k + L can be expressed as:
Figure BDA0002704714590000099
based on the above formula, the peak current of the battery during continuous charging and discharging is respectively:
Figure BDA00027047145900000910
in the formula (I), the compound is shown in the specification,
Figure BDA00027047145900000911
and
Figure BDA00027047145900000912
respectively representing a continuous charging peak current and a continuous discharging peak current which are constrained by voltage; u shapet,maxAnd Ut,minThe upper and lower cut-off voltages were set to 4.2V and 2.5V according to the specifications of the battery.
Step five, calculating corresponding continuous charging peak current by using the thermal model and taking temperature and temperature change rate as constraints
Figure BDA0002704714590000101
And sustained discharge peak current
Figure BDA0002704714590000102
Obtaining the surface temperature T of the battery at the k + L moment according to the thermal model of the batteryk+L：
Figure BDA0002704714590000103
Order to
Figure BDA0002704714590000104
The highest temperature T of the surface of the batterymaxNot more than 60 ℃ as a constraint, obtaining the maximum heat generation rate q of the battery1：
Figure BDA0002704714590000105
Changing the temperature of the battery
Figure BDA0002704714590000106
As a constraint, the maximum heat generation rate q of the battery is obtained assuming that the temperature change rate does not exceed the limit of 2 ℃/s2：
Figure BDA0002704714590000107
Get qmax＝min(q1,q2)，
The heat generation rate of a lithium ion battery can be approximated as:
Figure BDA0002704714590000108
in the formula, RtIs the sum of the ohmic internal resistance and the polarization internal resistance of the battery.
Assuming that the entropy thermal coefficient of the battery is constant in L sampling periods, let q be qmaxThe peak charging current under the temperature and temperature change rate constraints can be obtained
Figure BDA0002704714590000109
And peak discharge current
Figure BDA00027047145900001010
Respectively as follows:
Figure BDA00027047145900001011
step six, taking the capacity loss caused by the peak current to the aging process as the constraint, and calculating the corresponding continuous charging peak current
Figure BDA00027047145900001012
And sustained discharge peak current
Figure BDA00027047145900001013
Obtaining a capacity loss model according to a battery aging experiment:
Figure BDA0002704714590000111
in the formula, QlossIs a loss of battery capacity; n is the number of charge-discharge cycles; b is a coefficient influenced by discharge rate according to Q under different discharge rateslossDetermining the values of the coefficients B under different multiplying powers C, and performing polynomial fitting on the values to obtain an expression of B changing along with the charging and discharging multiplying power C:
B(C)＝β0+β1C+β2C2
in the formula, beta0,β1,β2Fitting coefficients for the polynomial.
Assuming that the battery has been subjected to 1500 charge-discharge cycles and the battery capacity has lost Q × 8%, if the battery reaches Q × 20% after the capacity loss reaches 3500 th cycle, the following equation holds:
Figure BDA0002704714590000112
B*(C)＝β0+β1C*+β2(C*)2
t represents the battery temperature when working with peak current, C is the current multiplying power corresponding to the peak current, and C is obtained by Newton iteration method*The method comprises the following steps:
order to
Figure BDA0002704714590000113
The original equation can be:
[β0+β1C*+β2(C*)2]·exp(αC*+β)-λ＝0。
applying Newton iteration method to solve the iteration formula as follows:
Figure BDA0002704714590000114
in the formula, the initial value of multiplying power C0For the ratio of the current value collected by the current sensor of the battery to the capacity, the iteration end condition is that the absolute value of the difference of the time rates obtained in two times before and after is less than 2% of the given precision:
|Ck+1-Ck|/|Ckless than or equal to 2 percent, namely Ck+1≈C*And further obtaining the peak current of continuous charge and discharge:
Figure BDA0002704714590000121
seventhly, obtaining the continuous charging peak current of the battery under multiple constraints based on the continuous charging and discharging peak current and the battery delivery current limit value obtained through multiple constraints
Figure BDA0002704714590000122
And sustained discharge peak current
Figure BDA0002704714590000123
Substituting the voltage into the first-order RC battery equivalent circuit model to calculate the terminal voltage corresponding to the continuous peak current so as to calculate the charge-discharge continuous peak power;
the continuous charging peak current and the continuous discharging peak current based on the above multiple constraints are:
Figure BDA0002704714590000124
in the formula IchgAnd IdchgThe maximum charging current and the maximum discharging current are respectively designed for battery factory production.
And further obtaining the continuous charge and discharge peak power by combining the voltage of the battery terminal:
Figure BDA0002704714590000125
it should be understood that, the sequence numbers of the steps in the embodiments of the present invention do not mean the execution sequence, and the execution sequence of each process should be determined by the function and the inherent logic of the process, and should not constitute any limitation on the implementation process of the embodiments of the present invention.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (7)

1. A peak power prediction method considering the durability influence of a power battery is characterized by comprising the following steps: the method specifically comprises the following steps:
step one, recording current I and terminal voltage U in the charging and discharging process of a batterytBattery surface temperature T and external environment temperature Tex；
Step two, establishing a first-order RC equivalent circuit model of the power battery; based on the relationship among the external environment temperature, the open-circuit voltage and the state of charge, fitting and establishing an open-circuit voltage-state of charge-environment temperature three-dimensional response surface model; acquiring a thermal model of the power battery by using the three-dimensional response surface model;
step three, taking the SOC interval as constraint, and calculating corresponding continuous charge-discharge peak current
Figure FDA0002704714580000011
And
Figure FDA0002704714580000012
identifying model parameters of the first-order RC equivalent circuit model, taking terminal voltage as constraint, and calculating corresponding continuous charge-discharge peak current based on the first-order RC equivalent circuit model
Figure FDA0002704714580000013
And
Figure FDA0002704714580000014
and fifthly, calculating corresponding continuous charging peak current by using the thermal model and taking the surface temperature and the temperature change rate of the battery as constraints
Figure FDA0002704714580000015
And sustained discharge peak current
Figure FDA0002704714580000016
Step six, taking the capacity loss caused by the peak current to the aging process as the constraint, and calculating the corresponding continuous charging peak current
Figure FDA0002704714580000017
And sustained discharge peak current
Figure FDA0002704714580000018
Seventhly, obtaining the continuous charging peak current of the battery under multiple constraints based on the continuous charging and discharging peak current and the battery delivery current limit value obtained through multiple constraints
Figure FDA0002704714580000019
And sustained discharge peak current
Figure FDA00027047145800000110
Substituting the voltage into the first-order RC battery equivalent circuit model to calculate the terminal voltage corresponding to the continuous peak current, thereby calculating the charge-discharge continuous peak power.
2. The method of claim 1, wherein: the second step specifically comprises:
the first-order RC equivalent circuit model specifically adopts the following form:
Figure FDA00027047145800000111
in the formula, a subscript k represents a kth sampling time, and Δ t is a sampling period; r0Expressing ohmic internal resistance; i represents a current; tau is1Is a time constant and1＝R1C1，R1and C1Respectively the polarization internal resistance and polarization capacitance of the battery; u shape1Represents the cell polarization voltage; u shapetIs terminal voltage; model parameter R0、R1And C1The method is obtained by on-line identification through a recursive least square method with forgetting factors; u shapeocvRepresents the battery open circuit voltage OCV;
the OCV-SOC-TexThe three-dimensional response surface model construction method comprises the following steps:
at different ambient temperatures TexRespectively carrying out OCV test to obtain corresponding relations between SOC and OCV at different external environment temperatures, and respectively simulating the relation between SOC and OCV at different external environment temperatures according to the following formulaAre combined to obtain respective temperatures TexAlpha of0,α1,…,α6Parameter value, then parameter α is corrected by quadratic function0,α1,…,α6And temperature TexThe relationship of (2) is fitted to complete the establishment of the three-dimensional response surface:
Uocv(Tex,z)＝α0+α1z+α2z2+α3z3+α4/z+α5ln(z)+α6ln(1-z)
[α0 α1 α2 α3 α4 α5 α6]T＝Λ×[Tex 2 Tex 1]T
in the formula of Uocv(TexZ) represents the function of the open circuit voltage OCV in terms of TexA function of SOC; alpha is alpha0,α1,…,α6Fitting coefficients for the model; Λ is a 7 × 3 constant matrix; z represents the state of charge SOC of the battery, and is calculated based on an ampere-hour integration method:
Figure FDA0002704714580000021
in the formula, z0Is the SOC value at the initial moment; η represents the cell coulombic efficiency; q represents a battery capacity;
the thermal model is established on the assumption that the temperature T and the heat generation rate q of the battery surface at any time are uniformly distributed:
the temperature of the battery at time k +1 can be expressed as:
Figure FDA0002704714580000022
in the formula, RthAnd CthThermal resistance and thermal capacity, τ, of the cell, respectivelythIs a thermal time constant, andth＝RthCthq is mainly composed of irreversible heat and reversible heat, and can be measured by adiabatic accelerated calorimeterExpressed as:
Figure FDA0002704714580000023
wherein (U)t-Uocv) I represents the irreversible heat generation rate of the battery;
Figure FDA0002704714580000024
represents a reversible heat generation rate;
Figure FDA0002704714580000025
is entropy coefficient of heat, about equal to
Figure FDA0002704714580000026
Passing OCV-SOC-TexAnd obtaining a three-dimensional response surface model.
3. The method of claim 2, wherein: the third step specifically comprises:
the SOC of the battery is taken as a constraint condition, a prediction step length L comprising a plurality of sampling periods is specified, and a continuous charge and discharge peak current expression of the battery is deduced according to an ampere-hour integration method:
Figure FDA0002704714580000027
in the formula (I), the compound is shown in the specification,
Figure FDA0002704714580000028
and
Figure FDA0002704714580000029
respectively the peak charging current and the peak discharging current of the battery under the SOC constraint; z is a radical ofmax、zminThe maximum and minimum SOC values at the time of charging and discharging of the battery were set to 90% and 10%, respectively.
4. The method of claim 3, wherein: the fourth step specifically comprises:
obtaining model parameter R at moment k by recursive least square method with forgetting factor0,k、R1,kAnd C1,kAssuming that the model parameters of the battery are unchanged in L sampling periods, when the working current is IkThe terminal voltage at time k + L is expressed as:
Ut,k+L＝Uocv,k+L+U1,k+L+Ik+L·R0
the open circuit voltage value and the polarization voltage value of the battery at the time k + L can be expressed as:
Figure FDA0002704714580000031
Figure FDA0002704714580000032
order to
Figure FDA0002704714580000033
Then U istAt time k + L can be expressed as:
Figure FDA0002704714580000034
based on the above formula, the peak current of the battery during continuous charging and discharging is respectively:
Figure FDA0002704714580000035
in the formula (I), the compound is shown in the specification,
Figure FDA0002704714580000036
and
Figure FDA0002704714580000037
respectively representing a continuous charging peak current and a continuous discharging peak current which are constrained by voltage; upper limit of voltage Ut,maxAnd lower voltage limit Ut,minThe upper and lower cut-off voltages are set according to specifications of the selected battery.
5. The method of claim 4, wherein: the fifth step specifically comprises:
obtaining the surface temperature T of the battery at the k + L moment according to the thermal model of the batteryk+L：
Figure FDA0002704714580000041
In the formula, τthRepresents the thermal time constant of the battery; t isex,k+LThe ambient temperature at time k + L;
order to
Figure FDA0002704714580000042
The highest temperature of the surface of the battery is not more than TmaxMaximum heat generation rate q of the cell was obtained as a constraint of 60 ℃1：
Figure FDA0002704714580000043
Changing the temperature of the battery
Figure FDA0002704714580000044
The maximum heat generation rate q of the battery is obtained by taking the limit value of 2 ℃/s as a constraint2：
Figure FDA0002704714580000045
Get qmax＝min(q1,q2) The heat generation rate of the lithium ion battery can be closeThe method is as follows:
Figure FDA0002704714580000046
in the formula, RtIs the sum of ohmic internal resistance and polarization internal resistance of the battery;
assuming that the entropy thermal coefficient of the battery is constant in L sampling periods, let q be qmaxObtaining the peak charging current under the temperature and temperature change rate constraints
Figure FDA0002704714580000047
And peak discharge current
Figure FDA0002704714580000048
Respectively as follows:
Figure FDA0002704714580000049
6. the method of claim 5, wherein: the sixth step specifically comprises:
obtaining a capacity loss model according to a battery aging experiment:
Figure FDA00027047145800000410
in the formula, QlossIs a loss of battery capacity; n is the number of charge-discharge cycles; b is a coefficient influenced by discharge rate according to Q under different discharge rateslossDetermining the values of the coefficients B under different multiplying powers C, and performing polynomial fitting on the values to obtain an expression of B changing along with the charging and discharging multiplying power C:
B(C)＝β0+β1C+β2C2
in the formula, beta0,β1,β2Fitting coefficients for the polynomial;
suppose electricityThe pool has performed N1After charging and discharging cycles, the battery capacity is lost by Qx percent, and if the battery continues to work at the peak current, the battery capacity is satisfied at the Nth*The decay of each cycle is Q × 20%, and the following expression holds:
Figure FDA0002704714580000051
B*(C)＝β0+β1C*+β2(C*)2
in the formula, N*For the delivery quality assurance cycle number of the electric automobile, T represents the battery temperature when the electric automobile works at the peak current, C is the current multiplying power corresponding to the peak current, and C is obtained by solving the above formula by a Newton iteration method*The specific flow is as follows:
order: λ ═ Q · (20% -)/[ (N)*-N1)·Q]0.55，
Figure FDA0002704714580000052
The original equation can be: [ beta ]0+β1C*+β2(C*)2]·exp(αC*+β)-λ＝0；
Applying Newton iteration method to solve the iteration formula as follows:
Figure FDA0002704714580000053
in the formula, the initial value of multiplying power C0For the ratio of the current value collected by the current sensor of the battery to the capacity, the iteration end condition is that the absolute value of the difference of the time rates obtained in two times before and after is less than 2% of the given precision:
|Ck+1-Ck|/|Ckless than or equal to 2 percent, namely Ck+1≈C*And further obtaining the peak current of continuous charge and discharge:
Figure FDA0002704714580000054
7. the method of claim 1, wherein: the seventh step specifically comprises:
the continuous charging peak current and the continuous discharging peak current based on the above multiple constraints are:
Figure FDA0002704714580000061
in the formula IchgAnd IdchgRespectively designing a maximum charging current and a maximum discharging current for battery delivery;
and further obtaining the peak power of continuous charge and discharge by combining the terminal voltage of the battery:
Figure FDA0002704714580000062
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