WO2023274194A1 - 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 - Google Patents
一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 Download PDFInfo
- Publication number
- WO2023274194A1 WO2023274194A1 PCT/CN2022/101756 CN2022101756W WO2023274194A1 WO 2023274194 A1 WO2023274194 A1 WO 2023274194A1 CN 2022101756 W CN2022101756 W CN 2022101756W WO 2023274194 A1 WO2023274194 A1 WO 2023274194A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- lithium
- battery
- rich manganese
- order
- internal resistance
- Prior art date
Links
- PWHULOQIROXLJO-UHFFFAOYSA-N Manganese Chemical compound [Mn] PWHULOQIROXLJO-UHFFFAOYSA-N 0.000 title claims abstract description 105
- 229910052748 manganese Inorganic materials 0.000 title claims abstract description 105
- 239000011572 manganese Substances 0.000 title claims abstract description 105
- WHXSMMKQMYFTQS-UHFFFAOYSA-N Lithium Chemical compound [Li] WHXSMMKQMYFTQS-UHFFFAOYSA-N 0.000 title claims abstract description 104
- 229910052744 lithium Inorganic materials 0.000 title claims abstract description 104
- 238000000034 method Methods 0.000 title claims abstract description 65
- 230000010287 polarization Effects 0.000 claims abstract description 41
- 230000000694 effects Effects 0.000 claims abstract description 15
- 239000003990 capacitor Substances 0.000 claims description 38
- 238000007600 charging Methods 0.000 claims description 36
- 238000012360 testing method Methods 0.000 claims description 25
- 238000004458 analytical method Methods 0.000 claims description 9
- 230000003068 static effect Effects 0.000 claims description 8
- 239000002131 composite material Substances 0.000 claims description 5
- KLARSDUHONHPRF-UHFFFAOYSA-N [Li].[Mn] Chemical compound [Li].[Mn] KLARSDUHONHPRF-UHFFFAOYSA-N 0.000 claims description 4
- 150000001875 compounds Chemical class 0.000 claims description 3
- 238000007599 discharging Methods 0.000 description 7
- 238000004088 simulation Methods 0.000 description 7
- 238000010586 diagram Methods 0.000 description 6
- HBBGRARXTFLTSG-UHFFFAOYSA-N Lithium ion Chemical compound [Li+] HBBGRARXTFLTSG-UHFFFAOYSA-N 0.000 description 5
- 238000004364 calculation method Methods 0.000 description 5
- 229910001416 lithium ion Inorganic materials 0.000 description 5
- 230000007423 decrease Effects 0.000 description 3
- 238000002474 experimental method Methods 0.000 description 3
- 230000015572 biosynthetic process Effects 0.000 description 2
- 238000004422 calculation algorithm Methods 0.000 description 2
- 238000013461 design Methods 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 230000018109 developmental process Effects 0.000 description 2
- GELKBWJHTRAYNV-UHFFFAOYSA-K lithium iron phosphate Chemical compound [Li+].[Fe+2].[O-]P([O-])([O-])=O GELKBWJHTRAYNV-UHFFFAOYSA-K 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000003786 synthesis reaction Methods 0.000 description 2
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 description 1
- 230000032683 aging Effects 0.000 description 1
- 229910052799 carbon Inorganic materials 0.000 description 1
- 230000002925 chemical effect Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000003247 decreasing effect Effects 0.000 description 1
- 238000003487 electrochemical reaction Methods 0.000 description 1
- 238000004146 energy storage Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 239000005543 nano-size silicon particle Substances 0.000 description 1
- 238000003062 neural network model Methods 0.000 description 1
- 230000003647 oxidation Effects 0.000 description 1
- 238000007254 oxidation reaction Methods 0.000 description 1
- 238000011056 performance test Methods 0.000 description 1
- 230000000750 progressive effect Effects 0.000 description 1
- 238000010278 pulse charging Methods 0.000 description 1
- 230000000630 rising effect Effects 0.000 description 1
Images
Classifications
-
- 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]
- G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02E60/10—Energy storage using batteries
Definitions
- the invention relates to the technical field of battery parameter identification, in particular to a high-order model parameter identification method and system suitable for lithium-rich manganese-based batteries.
- lithium-ion batteries With the large-scale application of lithium-ion batteries in fields such as electric vehicles and energy storage markets, improving energy density is the continuous development goal of lithium-ion batteries. At present, mass-produced lithium-ion batteries have almost reached the limit of technology. Ultra-high specific energy lithium-ion batteries will be the future development direction. Ultra-high specific energy lithium-ion batteries using lithium-rich manganese-based positive electrodes and nano-silicon carbon negative electrodes have very good performance. application prospects. However, because the battery system is a very complex system, especially for higher specific energy lithium-rich manganese-based batteries, the electrochemical reaction process presents highly nonlinear characteristics.
- the equivalent circuit model is based on the working principle of the battery and uses a circuit network composed of capacitors and resistors to describe the working characteristics of the battery.
- the equivalent circuit model has a clear physical meaning, can be analytically expressed by a mathematical model, and the model parameters are easy to identify. It can model the battery within the full capacity range. Therefore, there are many studies on the equivalent circuit and its applications are also extensive.
- the variable SOC needs to be considered in the battery model; in order to improve the accuracy of the model, the model should well reflect the dynamics of the battery Performance; the battery model should eventually generate code and embed it into the battery management system.
- the model structure should not be too complex to reduce the calculation load of the processor and facilitate engineering implementation.
- the battery model is actually a very complex nonlinear system, which contains a large number of unknown parameters.
- a large amount of prior knowledge is required in advance, such as model order, model structure, various unknown constants, etc., and these prior knowledge are usually difficult to obtain, especially for high-energy-rich batteries.
- the acquisition of their characteristic parameters requires the design of targeted experiments.
- the parameters of the battery model change accordingly, and this change over time also changes.
- the purpose of the present invention is to provide a high-order model parameter identification method and system suitable for lithium-rich manganese-based batteries, which have the advantages of good versatility, high practical value, and high parameter identification accuracy.
- the present invention provides the following scheme:
- a high-order model parameter identification method suitable for lithium-rich manganese-based batteries including:
- An equivalent circuit model suitable for lithium-rich manganese-based batteries is established based on the characteristics of lithium-rich manganese-based batteries; The resistance characteristics of lithium-manganese-based battery voltage, and the circuit model for equivalently simulating the polarization effect of lithium-rich manganese-based batteries with RC inertial links;
- the battery model parameters are obtained; the identified battery model parameters are high-order model parameters suitable for lithium-rich manganese-based batteries; the identified battery model parameters include: open circuit voltage, battery Ohmic internal resistance, first-order polarization internal resistance, second-order polarization internal resistance, first-order time constant, and second-order time constant.
- the identification of battery model parameters based on the equivalent circuit model includes:
- the open circuit voltage is determined according to the voltage value of the static set time period after charging and the voltage value of the set time period after discharge according to the equivalent circuit model;
- the identification of battery model parameters based on the equivalent circuit model further includes:
- the identification of battery model parameters based on the equivalent circuit model further includes:
- the terminal voltage of the equivalent circuit model is fitted by the least square method to obtain a first-order time constant and second-order time constant;
- the terminal voltage of the equivalent circuit model is simulated by the least square method. Combined to obtain the first-order polarization internal resistance and the second-order polarization internal resistance.
- an equivalent circuit model suitable for lithium-rich manganese-based batteries based on the characteristics of lithium-rich manganese-based batteries also includes:
- the performance of the lithium-rich manganese-based battery is obtained experimentally; the performance includes load changes and capacity changes;
- the characteristics of the lithium-rich manganese-based battery are analyzed.
- the invention discloses the following technical effects:
- the high-order model parameter identification method suitable for lithium-rich manganese-based batteries provided by the present invention is based on the characteristics of lithium-rich manganese-based batteries to establish an ideal voltage source equivalent to simulate the open circuit voltage of lithium-rich manganese-based batteries suitable for lithium-rich manganese-based batteries , using the internal resistance to equivalently simulate the resistance characteristics of the lithium-rich manganese-based battery voltage, using the RC inertial link to equivalently simulate the equivalent circuit model of the polarization effect of the lithium-rich manganese-based battery, and then using the equivalent circuit model to identify the suitable for rich manganese-based battery
- the present invention also provides the following implementation system:
- a high-order model parameter identification system suitable for lithium-rich manganese-based batteries including:
- the equivalent circuit model building module is used to establish an equivalent circuit model suitable for lithium-rich manganese-based batteries based on the characteristics of lithium-rich manganese-based batteries; Open-circuit voltage, using internal resistance to equivalently simulate the resistance characteristics of lithium-rich manganese-based battery voltage, and using RC inertial links to equivalently simulate the circuit model of the polarization effect of lithium-rich manganese-based batteries;
- the high-order model parameter identification module is used to obtain battery model parameters based on the equivalent circuit model identification; the identified battery model parameters are high-order model parameters suitable for lithium-rich manganese-based batteries; the identified The battery model parameters include: open circuit voltage, battery ohmic internal resistance, first-order polarization internal resistance, second-order polarization internal resistance, first-order time constant, and second-order time constant.
- the high-order model parameter identification module includes:
- the open-circuit voltage determination unit is used for, within a compound pulse power test HPPC cycle, according to the voltage value of the set time period after charging and the voltage value of the set time period after discharge according to the equivalent circuit model Determine the open circuit voltage;
- the first functional relationship determining unit is configured to establish a functional relationship between the open circuit voltage and the SOC value after acquiring the SOC value corresponding to the open circuit voltage.
- the high-order model parameter identification module also includes:
- a resistance characteristic acquisition unit configured to acquire the resistance characteristic of the equivalent circuit model after the discharge point is stopped
- a battery ohmic internal resistance determining unit configured to determine the battery ohmic internal resistance according to the resistance characteristics
- the second functional relationship determination unit is configured to establish a functional relationship between the battery ohmic internal resistance and the SOC value after obtaining the SOC value corresponding to the ohmic internal resistance of the battery.
- the high-order model parameter identification module also includes:
- the capacitor initial value acquisition unit is used to obtain the initial voltage value of the first capacitor and the initial voltage value of the second capacitor in the RC inertia link;
- a time constant determination unit configured to use the least squares method to calculate the equivalent circuit model according to the functional relationship between the open circuit voltage and the SOC value, the initial voltage value of the first capacitor and the initial voltage value of the second capacitor The terminal voltage is fitted to obtain the first-order time constant and the second-order time constant;
- the polarization internal resistance determination unit is configured to use the least square method to calculate the The terminal voltage of the equivalent circuit model is fitted to obtain the first-order polarization internal resistance and the second-order polarization internal resistance.
- it also includes:
- the performance acquisition module is used to obtain the performance of the lithium-rich manganese-based battery in an experimental manner; the performance includes load changes and capacity changes;
- the characteristic analysis module of the lithium-rich manganese-based battery is used to analyze the characteristics of the lithium-rich manganese-based battery according to the performance.
- Fig. 1 is a flow chart of the high-order model parameter identification method suitable for lithium-rich manganese-based batteries provided by the present invention
- Fig. 2 is an overall framework diagram of implementing a high-order model parameter identification method suitable for lithium-rich manganese-based batteries in an embodiment of the present invention
- FIG. 3 is a structural diagram of an equivalent circuit model provided by an embodiment of the present invention.
- FIG. 4 is a battery test waveform diagram provided by an embodiment of the present invention.
- Fig. 5 is the cftools tool fitting curve diagram that the embodiment of the present invention provides
- FIG. 6 is a simulation result diagram provided by an embodiment of the present invention.
- FIG. 7 is a schematic structural diagram of a high-order model parameter identification system suitable for lithium-rich manganese-based batteries provided by the present invention.
- the purpose of the present invention is to provide a high-order model parameter identification method and system suitable for lithium-rich manganese-based batteries, which have the advantages of good versatility, high practical value, and high parameter identification accuracy.
- the high-order model parameter identification method suitable for lithium-rich manganese-based batteries provided by the present invention includes:
- Step 100 Establish an equivalent circuit model suitable for the lithium-rich manganese-based battery based on the characteristics of the lithium-rich manganese-based battery.
- the equivalent circuit model is to equivalently simulate the open circuit voltage of lithium-rich manganese-based batteries with an ideal voltage source, the equivalent simulation of the resistance characteristics of the voltage of lithium-rich manganese-based batteries with internal resistance, and the equivalent simulation of the poles of lithium-rich manganese-based batteries with an RC inertial link. 2nd-order equivalent circuit model of lithium-rich manganese-based battery based on oxidation effect.
- Step 200 Obtain battery model parameters based on equivalent circuit model identification.
- the identified battery model parameters are high-order model parameters suitable for lithium-rich manganese-based batteries.
- the identified battery model parameters include: open circuit voltage, battery ohmic internal resistance, first-order polarization internal resistance, second-order polarization internal resistance, first-order time constant, and second-order time constant.
- the specific implementation process of obtaining battery model parameters based on equivalent circuit model identification in step 200 includes:
- the open circuit voltage OCV is the most important parameter in the battery model.
- the battery voltage When the battery is left standing after charging, the battery voltage will drop slowly after an instant drop. In theory, after a long enough time, the battery voltage will eventually be equal to the OCV value corresponding to the SOC point. Similarly, when the battery is left to stand after being discharged, the battery voltage will rise slowly after an instant, gradually approaching the corresponding SOC value.
- the OCV value corresponding to the SOC value is within the interval determined by the gradually decreasing voltage value after charging and the gradually rising voltage value after discharging, and the true value of OCV should be close to the average value of this interval. In a compound pulse power test HPPC cycle, because the pulse charge and discharge time is very short, the SOC change is small and can be considered basically unchanged.
- the voltage value of 40s after charging and the voltage value of 40s after discharge are used.
- the average value of the SOC point is used to determine the OCV value corresponding to the SOC point, and the parameter table is established according to the corresponding relationship between OCV and SOC. Based on this implementation principle, the steps to identify the open circuit voltage are as follows:
- Step 1-1 In a composite pulse power test HPPC cycle, according to the equivalent circuit model, the voltage value of the static set time period (40s) after charging and the voltage value of the static set time period (40s) after discharge Determine the open circuit voltage.
- step 1-2 after obtaining the SOC value corresponding to the open circuit voltage, a functional relationship between the open circuit voltage and the SOC value is established.
- the battery voltage will rise instantaneously, which reflects the internal resistance characteristics of the battery.
- the discharge internal resistance of the battery can be calculated. Based on this, the identification steps of the battery ohmic internal resistance are as follows:
- Step 2-1 Obtain the resistance characteristics of the equivalent circuit model after the discharge stops.
- Step 2-2 Determine the ohmic internal resistance of the battery according to the resistance characteristics.
- Step 2-3 After obtaining the SOC value corresponding to the ohmic internal resistance of the battery, a functional relationship between the ohmic internal resistance of the battery and the SOC value is established.
- u t1 is the voltage at time t1
- u t2 is the voltage at time t2
- R 0 is the discharge internal resistance of the battery
- t is the time.
- the battery voltage will drop momentarily, and the charging internal resistance of the battery can also be calculated.
- the charging internal resistance and discharging internal resistance of lithium iron phosphate batteries are relatively close, and the difference in battery internal resistance corresponding to different SOC values is very small.
- the change of the internal resistance of the battery has an approximate linear relationship with the SOC, the smaller the SOC, the greater the internal resistance of the battery. With the decrease of SOC, the discharge internal resistance changes more obviously than the charge internal resistance.
- Step 3-1 Obtain the initial voltage value of the first capacitor and the initial voltage value of the second capacitor in the RC inertia link. Both the initial voltage value of the first capacitor and the initial voltage value of the second capacitor include the initial voltage value at the moment of stopping the discharge and the initial value of the voltage at the moment of stopping the charging.
- Step 3-2 according to the functional relationship between the open circuit voltage and the SOC value, the initial value of the voltage of the first capacitor and the initial value of the voltage of the second capacitor, the least square method is used to fit the terminal voltage of the equivalent circuit model to obtain the first-order time constants and second-order time constants.
- Step 3-3 According to the functional relationship between the first-order time constant, the second-order time constant, the battery ohmic internal resistance, the open circuit voltage and the SOC value, the least square method is used to fit the terminal voltage of the equivalent circuit model to obtain the first-order pole Polarized internal resistance and second-order polarized internal resistance.
- u 1 and u 2 are the voltages across the first capacitor C 1 and the second capacitor C 2 in the RC inertia link respectively, i is the current flowing through the battery load, and the charging current is assumed to be positive.
- ⁇ 1 R 1 C 1
- a single RC inertial link is equivalent to a first-order circuit, its zero-input response is given by equation (3), and its zero-state response is given by equation (4):
- the discharge direction can be calculated by using the least squares fitting method
- OCV can be obtained by fitting interpolation according to the previously measured OCV (SOC) parameter table, u 1 (0), u 2 (0) are the first capacitor C 1 and the second capacitor C 2 at the moment of discharge stop The initial value of the voltage.
- the time constants ⁇ 1 and ⁇ 2 corresponding to the battery standing still for 40 seconds after charging can also be calculated by using the least squares fitting method.
- the calculation method of OCV is the same as above, and the discharge internal resistance R 0 can also be obtained by fitting and interpolation according to the previously calculated discharge internal resistance parameter table. Using the least square method to fit the curve of the terminal voltage u L of the equivalent circuit model, the resistances R 1 and R 2 in the discharge direction can be obtained.
- the calculation method of discharge internal resistance R 0 is the same as above.
- An approximate method is used to determine the zero-input response of the RC inertial link for the initial voltage values of the first capacitor C 1 and the second capacitor C 2 at the time of charging stop.
- the zero-input response of the RC inertial link during charging is a continuation of the zero-input response of the static RC inertial link after discharge.
- the initial voltage values u 1 (0), u 2 (0) of the capacitors C 1 and C 2 at the moment of discharge stop and the time constants ⁇ 1 , ⁇ during the discharge process 2 can calculate the zero input response during the charging process, and then get the resistances R 1 and R 2 in the charging direction according to the least square algorithm.
- step 100 it also includes:
- the performance of lithium-rich manganese-based batteries was obtained experimentally. Performance includes load changes and capacity changes. The purpose of this step in real time is to obtain the parameters of the battery model, so the battery performance test is carried out to fully reflect the changes in battery load and capacity.
- Analyzing the characteristics of the lithium-rich manganese-based battery according to the performance facilitates the establishment of an equivalent circuit model suitable for the lithium-rich manganese-based battery based on the analysis of the characteristics of the lithium-rich manganese-based battery in the above step 100 .
- the 12Ah lithium-rich manganese-based positive electrode battery was tested at a normal temperature of 25°C.
- the test instrument is a special battery charge and discharge test equipment produced by Arbin Company. Considering that different charging and discharging directions correspond to different battery parameters, the original HPPC cycle test has been improved, and the design scheme is as follows: test the SOC points of the battery at equal intervals, the whole process takes 100 seconds, and the first is 10 seconds of 2C rate pulse discharge, as shown in Figure 4 from t0 to t1, then the battery is left to stand for 40 seconds, as shown in Figure 4 from t1 to t2, and then pulsed at a rate of 1.5C for 10 seconds, as shown in Figure 4 from t2 to t3, and finally rested 40 seconds, as shown from t3 to t4 in Figure 4. Based on this, the specific identification steps are as follows:
- the SOC points selected for the test are 0.95, 0.90, 0.85, 0.8, 0.75, ..., 0.15 and 0.10. Such a process can express the complex chemical reactions inside the battery through the external characteristics, and the model parameters for the same charge and discharge process identification at different SOC points are more reasonable.
- the equivalent circuit model uses an ideal voltage source to equivalently simulate the open circuit voltage of the battery, uses an internal resistance R 0 to equivalently simulate the resistance characteristics of the battery voltage, and uses an inertial RC link to equivalently simulate the polarization effect of the battery. From the analysis of the model structure, the use of two RC links in series can not only improve the accuracy of the model, but also the model structure is not too complicated, and it is easy to perform real-time calculations on the actual microprocessor, and finally establish a second-order lithium-rich manganese base Battery equivalent circuit model.
- the battery model used needs to identify the following parameters: OCV, R 0 , R 1 , R 2 , ⁇ 1 and ⁇ 2 (that is, open circuit voltage, battery ohmic internal resistance, first-order polarization internal resistance , second-order polarization internal resistance, first-order time constant, and second-order time constant).
- OCV open circuit voltage
- R 0 , R 1 , R 2 , ⁇ 1 and ⁇ 2 that is, open circuit voltage, battery ohmic internal resistance, first-order polarization internal resistance , second-order polarization internal resistance, first-order time constant, and second-order time constant.
- the open circuit voltage OCV is the most important parameter in the battery model. When the battery is left standing after charging, the battery voltage will drop slowly after an instant drop. In theory, after a long enough time, the battery voltage will eventually be equal to the OCV value corresponding to the SOC point. Similarly, when the battery is left to stand after being discharged, the battery voltage will rise slowly after an instant, gradually approaching the corresponding SOC value.
- the OCV (open circuit voltage) value corresponding to SOC is within the range determined by the voltage value that gradually decreases after charging and the voltage value that gradually rises after discharging. The true value of OCV should be close to average value of this range.
- the battery voltage will rise instantaneously, which reflects the internal resistance characteristics of the battery. This characteristic of the battery is used to calculate the discharge internal resistance of the battery, as shown in the above formula (1).
- the battery voltage will drop momentarily, and the charging internal resistance of the battery can also be calculated.
- the least square fitting method can be used to calculate the discharge direction. Time constants ⁇ 1 , ⁇ 2 .
- the same method can be used to calculate the time constant corresponding to the battery standing still for 40s after charging.
- the initial voltage values u 1 (0), u 2 (0) of capacitors C1 and C2 at the moment of discharge stop and the time constants ⁇ 1 and ⁇ 2 during discharge can be Calculate the zero-input response during the charging process, and then get the resistances R 1 and R 2 in the charging direction according to the least squares algorithm.
- Figure 5 shows the fitting process of calculating the time parameters ⁇ 1 and ⁇ 2 when the battery is left standing after discharge when the SOC is 0.10.
- a battery model is established in Matlab/Simulink for simulation analysis, as shown in Figure 6.
- the input mat file of the model is organized according to the experimental data, including recording time, current, voltage and SOC.
- the variables that the model needs to input are the measured current and SOC.
- the SOC reference value is calculated based on the ampere hours recorded in the test data.
- the output variable of the model is the output voltage, which is compared with the measured voltage in the Scope module. It can be seen from the error curve that the SOC estimation accuracy is within 5%.
- the present invention also provides a high-order model parameter identification system suitable for lithium-rich manganese-based batteries, as shown in Figure 7, the high-level
- the high-order model parameter identification system includes: an equivalent circuit model establishment module 1 and a high-order model parameter identification module 2 .
- the equivalent circuit model building module 1 is used to establish an equivalent circuit model suitable for lithium-rich manganese-based batteries based on the characteristics of lithium-rich manganese-based batteries.
- the equivalent circuit model is to equivalently simulate the open circuit voltage of lithium-rich manganese-based batteries with an ideal voltage source, the equivalent simulation of the resistance characteristics of the voltage of lithium-rich manganese-based batteries with internal resistance, and the equivalent simulation of the poles of lithium-rich manganese-based batteries with an RC inertial link.
- a circuit model of the chemical effect is used to establish an equivalent circuit model suitable for lithium-rich manganese-based batteries based on the characteristics of lithium-rich manganese-based batteries.
- the equivalent circuit model is to equivalently simulate the open circuit voltage of lithium-rich manganese-based batteries with an ideal voltage source, the equivalent simulation of the resistance characteristics of the voltage of lithium-rich manganese-based batteries with internal resistance, and the equivalent simulation of the poles of lithium-rich manganese-based batteries with an RC inertial link.
- the high-order model parameter identification module 2 is used to obtain battery model parameters based on equivalent circuit model identification.
- the identified battery model parameters are high-order model parameters suitable for lithium-rich manganese-based batteries.
- the identified battery model parameters include: open circuit voltage, battery ohmic internal resistance, first-order polarization internal resistance, second-order polarization internal resistance, first-order time constant, and second-order time constant.
- the high-order model parameter identification module 2 adopted above preferably includes: an open circuit voltage determination unit, a first functional relationship determination unit, a resistance characteristic acquisition unit, a battery ohmic internal resistance determination unit, a second functional relationship determination unit, and an initial capacitance acquisition unit. Unit, time constant determination unit and polarization internal resistance determination unit.
- the open circuit voltage determination unit is used to determine the open circuit voltage according to the voltage value of the static set time period after charging and the voltage value of the static set time period after discharge of the equivalent circuit model in a composite pulse power test HPPC cycle .
- the first functional relationship determining unit is configured to establish a functional relationship between the open circuit voltage and the SOC value after obtaining the SOC value corresponding to the open circuit voltage.
- the resistance characteristic obtaining unit is used for obtaining the resistance characteristic of the equivalent circuit model after the discharge stops.
- the battery ohmic internal resistance determination unit is used to determine the battery ohmic internal resistance according to the resistance characteristics.
- the second functional relationship determining unit is configured to establish a functional relationship between the battery ohmic internal resistance and the SOC value after obtaining the SOC value corresponding to the ohmic internal resistance of the battery.
- the capacitor initial value acquisition unit is used to acquire the initial voltage value of the first capacitor and the initial voltage value of the second capacitor in the RC inertia link.
- the time constant determination unit is used to fit the terminal voltage of the equivalent circuit model by the least square method according to the functional relationship between the open circuit voltage and the SOC value, the initial voltage value of the first capacitor and the initial voltage value of the second capacitor to obtain a first-order time constant and second-order time constant.
- the polarization internal resistance determination unit is used to fit the terminal voltage of the equivalent circuit model by the least square method according to the functional relationship between the first-order time constant, the second-order time constant, the battery ohmic internal resistance, and the open circuit voltage and SOC value.
- First-order polarization internal resistance and second-order polarization internal resistance are used to fit the terminal voltage of the equivalent circuit model by the least square method according to the functional relationship between the first-order time constant, the second-order time constant, the battery ohmic internal resistance, and the open circuit voltage and SOC value.
- the high-order model parameter identification system suitable for lithium-rich manganese-based batteries provided by the present invention also includes: a performance acquisition module and a characteristic analysis module for lithium-rich manganese-based batteries.
- the performance acquisition module is used to obtain the performance of the lithium-rich manganese-based battery through experiments.
- Performance includes load changes and capacity changes.
- the characteristic analysis module of lithium-rich manganese-based batteries is used to analyze the characteristics of lithium-rich manganese-based batteries according to their performance.
- each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other.
- the description is relatively simple, and for the related information, please refer to the description of the method part.
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Tests Of Electric Status Of Batteries (AREA)
- Secondary Cells (AREA)
Abstract
一种适用于富锂锰基电池的高阶模型参数辨识方法和系统。适用于富锂锰基电池的高阶模型参数辨识方法基于富锂锰基电池特性建立适用于富锂锰基电池的以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的等效电路模型（100），再采用等效电路模型辨识得到适用于富锂锰基电池的高阶模型参数（200），以在提高参数辨识精度的同时，使得整个高阶模型参数辨识方法具有通用性好和实用价值高的特点。
Description
本申请要求于2021年06月28日提交中国专利局、申请号为202110720961.X、发明名称为“一种适用于富锂锰基电池的高阶模型参数辨识方法和系统”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
本发明涉及电池参数识别技术领域，特别是涉及一种适用于富锂锰基电池的高阶模型参数辨识方法和系统。
随着锂离子电池在电动汽车和储能市场等领域的大规模应用，提高能量密度是锂离子电池持续的发展目标。目前量产的锂离子电池几乎已经达到了技术的极限，超高比能锂离子电池将是未来发展方向，采用富锂锰基正极、纳米硅碳负极的超高比能锂离子电池具有非常良好的应用前景。但是由于电池系统是一个非常复杂的系统，尤其是针对更高比能量的富锂锰基电池电化学反应过程呈现出高度的非线性特性。
对于传统的电池模型结构，研究人员进行了大量的研究，从各个研究角度，提出了多种多样的电池模型，可大致分为以下几类：电化学模型、经验模型、神经网络模型、等效电路模型等。其中等效电路模型是基于电池工作原理利用电容电阻等器件构成的电路网络来描述电池的工作特性。等效电路模型物理意义明晰，能够用数学模型解析表达，模型参数辨识方便，可对电池进行全容量范围内建模，因此等效电路的研究较多，应用也比较广泛。采用等效电路模型需要考虑以下几个因素：由于电池管理系统中需用于SOC的估算，在电池模型中需要考虑SOC这个变量；为了提高模型的精确度，模型应该很好地体现电池的动态性能；电池模型最终要生成代码嵌入到电池管理系统，模型结构不能过于复杂，以减少处理器的计算量，易于工程实现。
对于电池模型实际是一个非常复杂的非线性系统，它包含了大量的未知参数。对电池模型进行辨识，需要事先掌握大量的先验知识，如模型阶次、模型结构、各种未知常量等，而这些先验知识通常是很难获得的，特 别是针对比能量更高的富锂锰基电池，其特性参数的获取需要设计有针对性的试验。其次，在电池的实际使用过程中，随着电池剩余容量SOC和老化状态SOH的不断变化，电池模型的参数是随之变化的，并且这种随时间变化的规律也是变化的。有鉴于此，迫切需要提出一种通用性好、实用价值高的适用于富锂锰基电池的高阶模型参数辨识方法或系统，以提高参数辨识精度高。
发明内容
本发明的目的是提供一种具有通用性好、实用价值高、参数辨识精度高等优点的适用于富锂锰基电池的高阶模型参数辨识方法和系统。
为实现上述目的，本发明提供了如下方案：
一种适用于富锂锰基电池的高阶模型参数辨识方法，包括：
基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型；所述等效电路模型为以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的电路模型；
基于所述等效电路模型辨识得到电池模型参数；辨识得到的所述电池模型参数即为适用于富锂锰基电池的高阶模型参数；辨识得到的所述电池模型参数包括：开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数。
优选地，所述基于所述等效电路模型辨识得到电池模型参数，包括：
在一个复合脉冲功率测试HPPC循环内，根据所述等效电路模型的充电后静置设定时间段的电压值和放电后静置所述设定时间段的电压值确定开路电压；
获取与所述开路电压对应的SOC值后，建立开路电压和SOC值间的函数关系。
优选地，所述基于所述等效电路模型辨识得到电池模型参数，还包括：
获取放点停止后所述等效电路模型的电阻特性；
根据所述电阻特性确定电池欧姆内阻；
获取与所述电池欧姆内阻对应的SOC值后，建立电池欧姆内阻和SOC值间的函数关系。
优选地，所述基于所述等效电路模型辨识得到电池模型参数，还包括：
获取RC惯性环节中第一电容的电压初值和第二电容的电压初值；
根据所述开路电压和SOC值间的函数关系、所述第一电容的电压初值和第二电容的电压初值，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶时间常数和二阶时间常数；
根据所述一阶时间常数、所述二阶时间常数、所述电池欧姆内阻和所述开路电压和SOC值间的函数关系，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶极化内阻和二阶极化内阻。
优选地，所述基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型，之前还包括：
采用实验方式获取富锂锰基电池的性能；所述性能包括负载变化和容量变化；
根据所述性能对所述富锂锰基电池特性进行分析。
根据本发明提供的具体实施例，本发明公开了以下技术效果：
本发明提供的适用于富锂锰基电池的高阶模型参数辨识方法，基于富锂锰基电池特性建立适用于富锂锰基电池的以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的等效电路模型，再采用该等效电路模型辨识得到适用于富锂锰基电池的高阶模型参数，以在提高参数辨识精度的同时，使得整个高阶模型参数辨识方法具有通用性好和实用价值高的特点。
对应于上述提供适用于富锂锰基电池的高阶模型参数辨识方法，本发明还提供了如下实施系统：
一种适用于富锂锰基电池的高阶模型参数辨识系统，包括：
等效电路模型建立模块，用于基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型；所述等效电路模型为以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的电路模型；
高阶模型参数辨识模块，用于基于所述等效电路模型辨识得到电池模型参数；辨识得到的所述电池模型参数即为适用于富锂锰基电池的高阶模 型参数；辨识得到的所述电池模型参数包括：开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数。
优选地，所述高阶模型参数辨识模块包括：
开路电压确定单元，用于在一个复合脉冲功率测试HPPC循环内，根据所述等效电路模型的充电后静置设定时间段的电压值和放电后静置所述设定时间段的电压值确定开路电压；
第一函数关系确定单元，用于获取与所述开路电压对应的SOC值后，建立开路电压和SOC值间的函数关系。
优选地，所述高阶模型参数辨识模块还包括：
电阻特性获取单元，用于获取放点停止后所述等效电路模型的电阻特性；
电池欧姆内阻确定单元，用于根据所述电阻特性确定电池欧姆内阻；
第二函数关系确定单元，用于获取与所述电池欧姆内阻对应的SOC值后，建立电池欧姆内阻和SOC值间的函数关系。
优选地，所述高阶模型参数辨识模块还包括：
电容初值获取单元，用于获取RC惯性环节中第一电容的电压初值和第二电容的电压初值；
时间常数确定单元，用于根据所述开路电压和SOC值间的函数关系、所述第一电容的电压初值和第二电容的电压初值，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶时间常数和二阶时间常数；
极化内阻确定单元，用于根据所述一阶时间常数、所述二阶时间常数、所述电池欧姆内阻和所述开路电压和SOC值间的函数关系，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶极化内阻和二阶极化内阻。
优选地，还包括：
性能获取模块，用于采用实验方式获取富锂锰基电池的性能；所述性能包括负载变化和容量变化；
富锂锰基电池特性分析模块，用于根据所述性能对所述富锂锰基电池特性进行分析。
因本发明提供的适用于富锂锰基电池的高阶模型参数辨识系统实现 的技术效果与上述提供的适用于富锂锰基电池的高阶模型参数辨识方法实现的技术效果相同，故在此不再进行赘述。
说明书附图
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1为本发明提供的适用于富锂锰基电池的高阶模型参数辨识方法的流程图；
图2为本发明实施例中实施适用于富锂锰基电池的高阶模型参数辨识方法的整体框架图；
图3为本发明实施例提供的等效电路模型结构图；
图4为本发明实施例提供的电池试验测试波形图；
图5为本发明实施例提供的cftools工具拟合曲线图；
图6为本发明实施例提供的仿真结果图；
图7为本发明提供的适用于富锂锰基电池的高阶模型参数辨识系统的结构示意图。
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
本发明的目的是提供一种具有通用性好、实用价值高、参数辨识精度高等优点的适用于富锂锰基电池的高阶模型参数辨识方法和系统。
为使本发明的上述目的、特征和优点能够更加明显易懂，下面结合附图和具体实施方式对本发明作进一步详细的说明。
如图1所示，本发明提供的适用于富锂锰基电池的高阶模型参数辨识方法，包括：
步骤100：基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型。等效电路模型为以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的2阶富锂锰基电池等效电路模型。
其中，等效电路模型的结构如图3所示，从模型结构上分析，使用2个串联的RC惯性环节，既能提高模型的精确性，同时模型结构又不是过于复杂，易于在实际的微处理器上进行实时运算。
步骤200：基于等效电路模型辨识得到电池模型参数。辨识得到的电池模型参数即为适用于富锂锰基电池的高阶模型参数。辨识得到的电池模型参数包括：开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数。
步骤200中基于等效电路模型辨识得到电池模型参数的具体实施过程包括：
(1)开路电压OCV的快速辨识：
开路电压OCV是电池模型中最重要的参数。电池充电后静置时，电池电压经过一个瞬间下降之后会缓慢下降，理论上经过足够长的时间，电池的电压最终会等于SOC点对应的OCV值。同样，电池放电后静置时，电池电压经过一个瞬间之后会缓慢上升，逐渐逼近对应的SOC值。SOC值所对应的OCV值处于充电后静置逐渐下降的电压值和放电后静置逐渐上升的电压值所确定的区间之内，OCV的真实值应该接近于这个区间的平均值。在一个复合脉冲功率测试HPPC循环内，由于脉冲充放电时间很短，SOC变化很小可以认为基本不变，因此，采用充电后静置40s的电压值和放电后静置40s的电压值二者的均值来确定该SOC点对应的OCV值，依据OCV与SOC对应关系建立参数表。基于这一实施原理，辨识开路电压的步骤如下：
步骤1-1、在一个复合脉冲功率测试HPPC循环内，根据等效电路模型的充电后静置设定时间段(40s)的电压值和放电后静置设定时间段(40s)的电压值确定开路电压。
步骤1-2、获取与开路电压对应的SOC值后，建立开路电压和SOC 值间的函数关系。
(2)电池欧姆内阻R
0辨识：
放电停止后，电池电压会有一个瞬间的上升，体现了电池的内阻特性，利用电池的这个特性就可以计算电池的放电内阻，基于此，电池欧姆内阻的辨识步骤如下：
步骤2-1、获取放电停止后等效电路模型的电阻特性。
步骤2-2、根据电阻特性确定电池欧姆内阻。
步骤2-3、获取与电池欧姆内阻对应的SOC值后，建立电池欧姆内阻和SOC值间的函数关系。
其中，电池的放电内阻计算方式如下式(1)所示：
式中，u
t1为t1时刻电压，u
t2为t2时刻电压，R
0为电池的放电内阻，t为时刻。
类似的，充电停止后，电池电压会有一个瞬间的下降，同样可以计算电池的充电内阻。
磷酸铁锂电池的充电内阻和放电内阻阻值是比较接近的，不同SOC值对应的电池内阻差别很小。电池内阻的变化与SOC成近似的线性关系，SOC越小，电池内阻越大。随着SOC的减小，放电内阻较充电内阻变化明显。
(3)一阶极化内阻R
1、二阶极化内阻R
2、一阶时间常数τ
1和二阶时间常数τ
2的辨识，具体辨识步骤如下：
步骤3-1、获取RC惯性环节中第一电容的电压初值和第二电容的电压初值。第一电容的电压初值和第二电容的电压初值均包括放电停止时刻的电压初值和充电停止时刻的电压初值。
步骤3-2、根据开路电压和SOC值间的函数关系、第一电容的电压初值和第二电容的电压初值，采用最小二乘法对等效电路模型的端电压进行拟合得到一阶时间常数和二阶时间常数。
步骤3-3、根据一阶时间常数、二阶时间常数、电池欧姆内阻和开路 电压和SOC值间的函数关系，采用最小二乘法对等效电路模型的端电压进行拟合得到一阶极化内阻和二阶极化内阻。
具体的，等效电路模型中两个RC惯性环节的电压数学关系式如公式(2)所示：
式中，u
1,u
2分别为RC惯性环节中第一电容C
1和第二电容C
2两端的电压，i为流经电池负载的电流，设充电电流为正。定义一阶时间常数为τ
1＝R
1C
1，二阶时间常数为τ
2＝R
2C
2。单个RC惯性环节相当于一个一阶电路，其零输入响应由式(3)给出，零状态响应由式(4)给出：
在HPPC循环试验中，放电后静置40s这段时间内，电流为0，RC惯性环节的电路响应可以认为是零输入相应，根据式(5)采用最小二乘拟合的方式可以计算放电方向的时间常数τ
1,τ
2：
式(5)中，OCV可以根据前面测得的OCV(SOC)参数表拟合插值得到，u
1(0),u
2(0)为放电停止时刻第一电容C
1，第二电容C
2的电压初值。根据式(5)采用最小二乘拟合的方式同样可以计算充电后电池静置40s对应的时间常数τ
1,τ
2。
利用HPPC循环试验中的放电过程计算RC惯性环节中的电阻R
1，R
2。由于HPPC循环开始之前，电池已经静置足够长的时间，电池的极化效应已经基本消失，可以认为HPPC循环试验放电过程中RC的电路响应为零状态响应，根据式(6)采用最小二乘法计算放电方向的电阻R
1，R
2。
式(6)中，OCV计算方法同上，放电内阻R
0同样可以根据前面算得的放电内阻参数表拟合插值得到。利用最小二乘方法对等效电路模型的端电压u
L的曲线进行拟合，可以得到放电方向的电阻R
1，R
2。
计算充电方向的电阻R
1、R
2时，因为HPPC循环试验中，放电结束后电池仅静置40s，极化效应并未完全消失，这时候RC惯性环节上的电路响应为零输入响应和零状态响应的综合，如式(7)所示：
式(7)中，OCV，放电内阻R
0计算方法同上。
为充电停止时刻第一电容C
1、第二电容C
2的电压初值，采用了近似的方法，确定RC惯性环节的零输入响应。充电过程中RC惯性环节的零输入响应是放电后静置RC惯性环节零输入响应的延续。因此，根据前面辨识的放电后静置的电池模型参数：放电停止时刻电容C
1，C
2的电压初值u
1(0),u
2(0)以及放电过程中的时间常数τ
1,τ
2可以计算充电过程中的零输入响应，然后根据最小二乘算法即可得到充电方向的电阻R
1，R
2。
如图2所示，在步骤100之前还包括：
采用实验方式获取富锂锰基电池的性能。性能包括负载变化和容量变化。实时该步骤的目的是为了获得电池模型的参数，所以进行电池性能试验，以充分体现电池负载的变化和容量的变化。
根据性能对富锂锰基电池特性进行分析，便于上述步骤100中基于对富锂锰基电池特性的分析建立适用于富锂锰基电池的等效电路模型。
下面以对12Ah富锂锰基正极电池的高阶模型参数进行辨识为例，对本发明提供的上述适用于富锂锰基电池的高阶模型参数辨识方法的优点进行说明。在实际应用过程中，本发明上述提供的辨识方法还可应用于其他类型的富锂锰基电池。
将12Ah富锂锰基正极电池，在常温25℃下进行试验。测试仪器为 Arbin公司生产的专用电池充放电测试设备。考虑到充放电方向不同对应的电池参数不同，对原有的HPPC循环试验进行了改进，设计方案如下：对电池等间隔的SOC点进行试验，整个过程共100秒，首先是10秒的2C倍率的脉冲放电，如图4中t0到t1，然后电池静置40秒，如图4中t1到t2，再进行10秒1.5C倍率的脉冲充电，如图4中t2到t3，最后再静置40秒，如图4中t3到t4所示。基于此，其具体识别步骤如下：
1、对富锂锰基电池进行HPPC循环实验：
首先对电池进行恒流恒压充电使电池SOC为1，然后用0.5C倍率放电使SOC为0.95，静置5min后进行一次HPPC循环(对电池等间隔的SOC点进行试验，整个过程共100秒，首先是10秒的2C倍率的脉冲放电，如图4中t0到t1，然后电池静置40秒，如图4中t1到t2，再进行10秒1.5C倍率的脉冲充电，如图4中t2到t3，最后再静置40秒，如图4中t3到t4所示。)，记录电池的电压和电流，然后再将电池放电到SOC为0.9，静置5min后进行下一个HPPC循环，以此类推。试验选取的SOC点为0.95、0.90、0.85、0.8、0.75、……、0.15和0.10。这样的过程能将电池内部的复杂化学反应通过外特性表现出来，且在不同的SOC点做相同的充放电过程辨识的模型参数更具合理性。
2、建立如图3所示的富锂锰基的等效电路模型(常用的电路模型)：
等效电路模型用一个理想电压源等效模拟电池的开路电压，用一个内阻R
0等效模拟电池电压的电阻特性，用惯性RC环节等效模拟电池的极化效应。从模型结构上分析，使用2个串联的RC环节，既能提高模型的精确性，同时模型结构又不是过于复杂，易于在实际的微处理器上进行实时运算，最终建立2阶富锂锰基电池等效电路模型。
3、对电池模型进行参数辨识：
获得电池的试验数据以后，采用的电池模型需要辨识以下几个参数：OCV、R
0、R
1、R
2、τ
1和τ
2(即开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数)。辨识参数考虑到各个参数与SOC的关系，分充放电方向进行辨识。
(1)开路电压OCV快速辨识
开路电压OCV是电池模型中最重要的参数。电池充电后静置时，电池电压经过一个瞬间下降之后会缓慢下降，理论上经过足够长的时间，电池的电压最终会等于SOC点对应的OCV值。同样，电池放电后静置时，电池电压经过一个瞬间之后会缓慢上升，逐渐逼近对应的SOC值。SOC(电池荷电状态)所对应的OCV(开路电压)值处于充电后静置逐渐下降的电压值和放电后静置逐渐上升的电压值所确定的区间之内，OCV的真实值应该接近于这个区间的平均值。在一个复合脉冲功率测试HPPC循环内，由于脉冲充放电时间很短，SOC变化很小可以认为基本不变，采用充电后静置40s的电压值和放电后静置40s的电压值二者的均值来确定该SOC点对应的OCV值，依据OCV数据建立OCV(SOC)函数关系，OCV参数如表1所示：
表1 OCV-SOC参数表
(2)电池欧姆内阻R
0辨识
放电停止后，电池电压会有一个瞬间的上升，体现了电池的内阻特性，利用电池的这个特性计算电池的放电内阻，如上式(1)所示。
类似的，充电停止后，电池电压会有一个瞬间的下降，同样可以计算电池的充电内阻。
建立电池内阻与SOC的关系函数。磷酸铁锂电池的充电内阻和放电内阻阻值是比较接近的，不同SOC值对应的电池内阻差别很小。电池内阻的变化与SOC成近似的线性关系，SOC越小，电池内阻越大。随着SOC的减小，放电内阻较充电内阻变化明显。充放电内阻辨识的结果如表2所示：
表2 放电方向内阻Rd和充电方向内阻Rc参数表
(3)RC惯性环节R
1、R
2、τ
1、τ
2辨识
电池模型中两个RC环节的电压数学关系如上式(2)所示。单个RC环节相当于一个一阶电路，其零输入响应如上式(3)所示，零状态响应如上式(4)所示。
在HPPC循环试验中，放电后静置40s这段时间内，电流为0，RC环节的电路响应可以认为是零输入相应，根据上述(5)采用最小二乘拟合的方式可以计算放电方向的时间常数τ
1,τ
2。
采用同样的方法可以计算充电后电池静置40s对应的时间常数。
利用HPPC循环试验中的放电过程计算RC环节中的电阻R
1，R
2。由于HPPC循环开始之前，电池已经静置足够长的时间，电池的极化效应已经基本消失，可以认为HPPC循环试验放电过程中RC的电路响应为零状态响应，根据上式(6)采用最小二乘法计算放电方向的电阻R
1，R
2。
计算充电方向的电阻R
1，R
2无法采用类似的方法，因为HPPC循环试验中，放电结束后电池仅静置40s，极化效应并未完全消失，这时候RC环节上的电路响应为零输入响应和零状态响应的综合，如上式(7)所示。充电过程中RC环节的零输入响应是放电后静置RC环节零输入响应的延续。因此，根据前面辨识的放电后静置的电池模型参数：放电停止时刻电容C1，C2的电压初值u
1(0),u
2(0)以及放电过程中的时间常数τ
1,τ
2可以计算充电过程中的零输入响应，然后根据最小二乘算法即可得到充电方向的电阻R
1，R
2。
利用最小二乘方法进行参数辨识，采用Matlab软件中的曲线拟合工具箱cftools。图5所示为SOC为0.10时，放电后电池静置时计算时间参 数τ
1,τ
2的拟合过程。
其中，RC环节参数辨识结果汇总如表3，表4所示。
表3 放电方向RC环节参数表
| SOC | τ 1/s | τ 2/s | R 1/Ω | R 2/Ω |
| 1 | 33.7268 | 0.001433 | 0.01262 | 4.1356 |
| 0.946 | 46.8823 | 0.001639 | 0.01476 | 3.0864 |
| 0.846 | 56.1482 | 0.001047 | 0.01293 | 3.251 |
| 0.753 | 59.5238 | 0.0006162 | 0.01297 | 4.4504 |
| 0.662 | 53.8213 | 0.0002531 | 0.01308 | 4.2355 |
| 0.559 | 42.123 | 0.00006633 | 0.01285 | 3.5125 |
| 0.464 | 40.1929 | 0.0002557 | 0.01424 | 3.199 |
| 0.388 | 40.7498 | 0.002395 | 0.01224 | 2.8482 |
| 0.301 | 37.9795 | 0.00125 | 0.01865 | 2.3652 |
| 0.176 | 39.0778 | 0.004533 | 0.01788 | 2.8369 |
| 0 | 53.3333 | 0.005367 | 0.04598 | 3.7355 |
表4 充电方向RC环节参数表
| SOC | τ 1/s | τ 2/s | R 1/Ω | R 2/Ω |
| 1 | 4.9456 | 73.1529 | 0.002788 | 0.01762 |
| 0.949 | 4.0225 | 86.7303 | 0.00324 | 0.01119 |
| 0.849 | 3.7286 | 98.7167 | 0.001081 | 0.02195 |
| 0.755 | 5.277 | 110.8893 | 0.0007381 | 0.02278 |
| 0.665 | 4.8685 | 118.7366 | 0.0008714 | 0.02142 |
| 0.562 | 6.2189 | 149.2092 | 0.001971 | 0.02172 |
| 0.466 | 5.8651 | 154.4402 | 0.002276 | 0.02764 |
| 0.39 | 4.3365 | 137.2684 | 0.002663 | 0.0268 |
| 0.303 | 3.7064 | 124.5175 | 0.00432 | 0.01836 |
| 0.179 | 3.5868 | 109.0275 | 0.007238 | 0.008267 |
| 0.003 | 3.9604 | 123.1679 | 0.01122 | 0.0001746 |
(4)仿真分析
根据以上方法辨识出来的模型参数，在Matlab/Simulink中建立电池模型进行仿真分析，如图6所示。模型的输入mat文件是根据实验数据整理的，包括记录时间、电流、电压和SOC，模型需要输入的变量是实测的电流和SOC，SOC参考值是根据试验数据记载的安时数计算所得。模型的输出变量是输出电压，与实测的电压在Scope模块中进行对比。从误差曲线上可以看出SOC估算精度在5％以内。
此外，对应于上述提供适用于富锂锰基电池的高阶模型参数辨识方法，本发明还提供一种适用于富锂锰基电池的高阶模型参数辨识系统，如图7所示，该高阶模型参数辨识系统包括：等效电路模型建立模块1和高阶模型参数辨识模块2。
其中，等效电路模型建立模块1用于基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型。等效电路模型为以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的电路模型。
高阶模型参数辨识模块2用于基于等效电路模型辨识得到电池模型参数。辨识得到的电池模型参数即为适用于富锂锰基电池的高阶模型参数。辨识得到的电池模型参数包括：开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数。
进一步，上述采用的高阶模型参数辨识模块2优选包括：开路电压确定单元、第一函数关系确定单元、电阻特性获取单元、电池欧姆内阻确定单元、第二函数关系确定单元、电容初值获取单元、时间常数确定单元和极化内阻确定单元。
其中，开路电压确定单元用于在一个复合脉冲功率测试HPPC循环内，根据等效电路模型的充电后静置设定时间段的电压值和放电后静置设定时间段的电压值确定开路电压。
第一函数关系确定单元用于获取与开路电压对应的SOC值后，建立开路电压和SOC值间的函数关系。
电阻特性获取单元用于获取放电停止后等效电路模型的电阻特性。
电池欧姆内阻确定单元用于根据电阻特性确定电池欧姆内阻。
第二函数关系确定单元用于获取与电池欧姆内阻对应的SOC值后，建立电池欧姆内阻和SOC值间的函数关系。
电容初值获取单元用于获取RC惯性环节中第一电容的电压初值和第二电容的电压初值。
时间常数确定单元用于根据开路电压和SOC值间的函数关系、第一电容的电压初值和第二电容的电压初值，采用最小二乘法对等效电路模型的端电压进行拟合得到一阶时间常数和二阶时间常数。
极化内阻确定单元用于根据一阶时间常数、二阶时间常数、电池欧姆内阻和开路电压和SOC值间的函数关系，采用最小二乘法对等效电路模型的端电压进行拟合得到一阶极化内阻和二阶极化内阻。
再进一步，本发明提供的适用于富锂锰基电池的高阶模型参数辨识系统还包括：性能获取模块和富锂锰基电池特性分析模块。
其中，性能获取模块用于采用实验方式获取富锂锰基电池的性能。性能包括负载变化和容量变化。
富锂锰基电池特性分析模块用于根据性能对富锂锰基电池特性进行分析。
本说明书中各个实施例采用递进的方式描述，每个实施例重点说明的都是与其他实施例的不同之处，各个实施例之间相同相似部分互相参见即可。对于实施例公开的系统而言，由于其与实施例公开的方法相对应，所以描述的比较简单，相关之处参见方法部分说明即可。
本文中应用了具体个例对本发明的原理及实施方式进行了阐述，以上实施例的说明只是用于帮助理解本发明的方法及其核心思想。同时，对于本领域的一般技术人员，依据本发明的思想，在具体实施方式及应用范围上均会有改变之处。综上，本说明书内容不应理解为对本发明的限制。
Claims (10)
- 一种适用于富锂锰基电池的高阶模型参数辨识方法，其特征在于，包括：基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型；所述等效电路模型为以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的电路模型；基于所述等效电路模型辨识得到电池模型参数；辨识得到的所述电池模型参数即为适用于富锂锰基电池的高阶模型参数；辨识得到的所述电池模型参数包括：开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数。
- 根据权利要求1所述的适用于富锂锰基电池的高阶模型参数辨识方法，其特征在于，所述基于所述等效电路模型辨识得到电池模型参数，包括：在一个复合脉冲功率测试HPPC循环内，根据所述等效电路模型的充电后静置设定时间段的电压值和放电后静置所述设定时间段的电压值确定开路电压；获取与所述开路电压对应的SOC值后，建立开路电压和SOC值间的函数关系。
- 根据权利要求2所述的适用于富锂锰基电池的高阶模型参数辨识方法，其特征在于，所述基于所述等效电路模型辨识得到电池模型参数，还包括：获取放点停止后所述等效电路模型的电阻特性；根据所述电阻特性确定电池欧姆内阻；获取与所述电池欧姆内阻对应的SOC值后，建立电池欧姆内阻和SOC值间的函数关系。
- 根据权利要求3所述的适用于富锂锰基电池的高阶模型参数辨识方法，其特征在于，所述基于所述等效电路模型辨识得到电池模型参数，还包括：获取RC惯性环节中第一电容的电压初值和第二电容的电压初值；根据所述开路电压和SOC值间的函数关系、所述第一电容的电压初值和第二电容的电压初值，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶时间常数和二阶时间常数；根据所述一阶时间常数、所述二阶时间常数、所述电池欧姆内阻和所述开路电压和SOC值间的函数关系，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶极化内阻和二阶极化内阻。
- 根据权利要求1所述的适用于富锂锰基电池的高阶模型参数辨识方法，其特征在于，所述基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型，之前还包括：采用实验方式获取富锂锰基电池的性能；所述性能包括负载变化和容量变化；根据所述性能对所述富锂锰基电池特性进行分析。
- 一种适用于富锂锰基电池的高阶模型参数辨识系统，其特征在于，包括：等效电路模型建立模块，用于基于富锂锰基电池特性建立适用于富锂锰基电池的等效电路模型；所述等效电路模型为以理想电压源等效模拟富锂锰基电池的开路电压，以内阻等效模拟富锂锰基电池电压的电阻特性，以RC惯性环节等效模拟富锂锰基电池的极化效应的电路模型；高阶模型参数辨识模块，用于基于所述等效电路模型辨识得到电池模型参数；辨识得到的所述电池模型参数即为适用于富锂锰基电池的高阶模型参数；辨识得到的所述电池模型参数包括：开路电压、电池欧姆内阻、一阶极化内阻、二阶极化内阻、一阶时间常数和二阶时间常数。
- 根据权利要求6所述的适用于富锂锰基电池的高阶模型参数辨识系统，其特征在于，所述高阶模型参数辨识模块包括：开路电压确定单元，用于在一个复合脉冲功率测试HPPC循环内，根据所述等效电路模型的充电后静置设定时间段的电压值和放电后静置所述设定时间段的电压值确定开路电压；第一函数关系确定单元，用于获取与所述开路电压对应的SOC值后，建立开路电压和SOC值间的函数关系。
- 根据权利要求7所述的适用于富锂锰基电池的高阶模型参数辨识系统，其特征在于，所述高阶模型参数辨识模块还包括：电阻特性获取单元，用于获取放点停止后所述等效电路模型的电阻特性；电池欧姆内阻确定单元，用于根据所述电阻特性确定电池欧姆内阻；第二函数关系确定单元，用于获取与所述电池欧姆内阻对应的SOC值后，建立电池欧姆内阻和SOC值间的函数关系。
- 根据权利要求8所述的适用于富锂锰基电池的高阶模型参数辨识系统，其特征在于，所述高阶模型参数辨识模块还包括：电容初值获取单元，用于获取RC惯性环节中第一电容的电压初值和第二电容的电压初值；时间常数确定单元，用于根据所述开路电压和SOC值间的函数关系、所述第一电容的电压初值和第二电容的电压初值，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶时间常数和二阶时间常数；极化内阻确定单元，用于根据所述一阶时间常数、所述二阶时间常数、所述电池欧姆内阻和所述开路电压和SOC值间的函数关系，采用最小二乘法对所述等效电路模型的端电压进行拟合得到一阶极化内阻和二阶极化内阻。
- 根据权利要求6所述的适用于富锂锰基电池的高阶模型参数辨识系统，其特征在于，还包括：性能获取模块，用于采用实验方式获取富锂锰基电池的性能；所述性能包括负载变化和容量变化；富锂锰基电池特性分析模块，用于根据所述性能对所述富锂锰基电池特性进行分析。
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110720961.XA CN113433464A (zh) | 2021-06-28 | 2021-06-28 | 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 |
| CN202110720961.X | 2021-06-28 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| WO2023274194A1 true WO2023274194A1 (zh) | 2023-01-05 |
Family
ID=77755064
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/CN2022/101756 WO2023274194A1 (zh) | 2021-06-28 | 2022-06-28 | 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 |
Country Status (2)
| Country | Link |
|---|---|
| CN (1) | CN113433464A (zh) |
| WO (1) | WO2023274194A1 (zh) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116106750A (zh) * | 2023-01-28 | 2023-05-12 | 上海玫克生储能科技有限公司 | 一种电池温测点辨识及异常检测方法、装置和电子设备 |
| CN116680938A (zh) * | 2023-08-04 | 2023-09-01 | 通达电磁能股份有限公司 | 一种锂电池电热耦合模型的建模方法及系统 |
| CN117310508A (zh) * | 2023-11-30 | 2023-12-29 | 山东科技大学 | 一种快速准确测量锂电池电变量的方法 |
| CN117538760A (zh) * | 2024-01-10 | 2024-02-09 | 广东电网有限责任公司茂名供电局 | 一种铅酸蓄电池参数辨识方法及相关装置 |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113433464A (zh) * | 2021-06-28 | 2021-09-24 | 中国科学院电工研究所 | 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 |
| CN114252772B (zh) * | 2021-12-22 | 2023-09-05 | 中国科学院电工研究所 | 一种锂离子电池内部短路诊断方法及系统 |
Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106250576A (zh) * | 2016-05-20 | 2016-12-21 | 武汉科技大学 | 一种基于动态阻抗的锂电池模型的建模方法 |
| CN106909716A (zh) * | 2017-01-19 | 2017-06-30 | 东北电力大学 | 计及容量损耗的磷酸铁锂电池建模及soc估计方法 |
| CN108254698A (zh) * | 2018-01-29 | 2018-07-06 | 西南交通大学 | 一种基于分数阶电池模型的非脆弱性剩余电量的估计方法 |
| CN110361652A (zh) * | 2019-06-26 | 2019-10-22 | 河南理工大学 | 一种基于模型参数优化的卡尔曼滤波锂电池soc估计方法 |
| WO2019242472A1 (zh) * | 2018-06-19 | 2019-12-26 | 华为技术有限公司 | 一种电池荷电状态的估计方法及装置 |
| CN110704790A (zh) * | 2019-09-06 | 2020-01-17 | 湖北文理学院 | 基于ifa-ekf的锂电池soc估算方法 |
| CN112098849A (zh) * | 2020-09-19 | 2020-12-18 | 西安科技大学 | 基于求积分卡尔曼滤波的锂电池剩余电量估计方法 |
| CN113433464A (zh) * | 2021-06-28 | 2021-09-24 | 中国科学院电工研究所 | 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP5349250B2 (ja) * | 2008-12-01 | 2013-11-20 | カルソニックカンセイ株式会社 | 電池モデル同定方法 |
| CN108832118A (zh) * | 2018-06-25 | 2018-11-16 | 西南交通大学 | MnO2中间体及其制备方法以及富锂锰基正极材料的制备方法 |
| CN110348062B (zh) * | 2019-06-14 | 2023-05-26 | 湖北锂诺新能源科技有限公司 | 一种锂离子电池等效电路模型的构建方法 |
| CN112345939B (zh) * | 2020-09-15 | 2021-11-09 | 北京交通大学 | 基于连续脉冲响应的锂离子电池模型参数辨识方法 |
-
2021
- 2021-06-28 CN CN202110720961.XA patent/CN113433464A/zh active Pending
-
2022
- 2022-06-28 WO PCT/CN2022/101756 patent/WO2023274194A1/zh unknown
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106250576A (zh) * | 2016-05-20 | 2016-12-21 | 武汉科技大学 | 一种基于动态阻抗的锂电池模型的建模方法 |
| CN106909716A (zh) * | 2017-01-19 | 2017-06-30 | 东北电力大学 | 计及容量损耗的磷酸铁锂电池建模及soc估计方法 |
| CN108254698A (zh) * | 2018-01-29 | 2018-07-06 | 西南交通大学 | 一种基于分数阶电池模型的非脆弱性剩余电量的估计方法 |
| WO2019242472A1 (zh) * | 2018-06-19 | 2019-12-26 | 华为技术有限公司 | 一种电池荷电状态的估计方法及装置 |
| CN110361652A (zh) * | 2019-06-26 | 2019-10-22 | 河南理工大学 | 一种基于模型参数优化的卡尔曼滤波锂电池soc估计方法 |
| CN110704790A (zh) * | 2019-09-06 | 2020-01-17 | 湖北文理学院 | 基于ifa-ekf的锂电池soc估算方法 |
| CN112098849A (zh) * | 2020-09-19 | 2020-12-18 | 西安科技大学 | 基于求积分卡尔曼滤波的锂电池剩余电量估计方法 |
| CN113433464A (zh) * | 2021-06-28 | 2021-09-24 | 中国科学院电工研究所 | 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 |
Non-Patent Citations (1)
| Title |
|---|
| HUANGFU HAI-WEN, AI-CHENG HAN: "Ｒesearch on Lithium-ion Battery Models and Model Parameter Identification Methods", ELECTRIC SWITCHGEAR, no. 3, 31 December 2020 (2020-12-31), pages 37 - 41, XP093019659, ISSN: 1004-289X * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116106750A (zh) * | 2023-01-28 | 2023-05-12 | 上海玫克生储能科技有限公司 | 一种电池温测点辨识及异常检测方法、装置和电子设备 |
| CN116106750B (zh) * | 2023-01-28 | 2023-11-10 | 上海玫克生储能科技有限公司 | 一种电池温测点辨识及异常检测方法、装置和电子设备 |
| CN116680938A (zh) * | 2023-08-04 | 2023-09-01 | 通达电磁能股份有限公司 | 一种锂电池电热耦合模型的建模方法及系统 |
| CN116680938B (zh) * | 2023-08-04 | 2023-10-20 | 通达电磁能股份有限公司 | 一种锂电池电热耦合模型的建模方法及系统 |
| CN117310508A (zh) * | 2023-11-30 | 2023-12-29 | 山东科技大学 | 一种快速准确测量锂电池电变量的方法 |
| CN117310508B (zh) * | 2023-11-30 | 2024-02-27 | 山东科技大学 | 一种快速准确测量锂电池电变量的方法 |
| CN117538760A (zh) * | 2024-01-10 | 2024-02-09 | 广东电网有限责任公司茂名供电局 | 一种铅酸蓄电池参数辨识方法及相关装置 |
| CN117538760B (zh) * | 2024-01-10 | 2024-04-23 | 广东电网有限责任公司茂名供电局 | 一种铅酸蓄电池参数辨识方法及相关装置 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113433464A (zh) | 2021-09-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| WO2023274194A1 (zh) | 一种适用于富锂锰基电池的高阶模型参数辨识方法和系统 | |
| Liu et al. | A new method of modeling and state of charge estimation of the battery | |
| CN106909716B (zh) | 计及容量损耗的磷酸铁锂电池建模及soc估计方法 | |
| CN110286332B (zh) | 一种基于多新息理论的电动汽车动力电池soc估计方法 | |
| Buller et al. | Impedance-based simulation models of supercapacitors and Li-ion batteries for power electronic applications | |
| CN103197251B (zh) | 一种动力锂电池二阶rc等效模型的辨识方法 | |
| CN102937704B (zh) | 一种动力电池rc等效模型的辨识方法 | |
| CN110688808B (zh) | 一种动力电池模型的粒子群及lm优化混合迭代辨识方法 | |
| CN109991548A (zh) | 一种ocv-soc标定实验方法、电池等效模型参数辨识方法及soc估算方法 | |
| CN110824363B (zh) | 一种基于改进ckf的锂电池soc和soe联合估算方法 | |
| CN110007236A (zh) | 一种铝空气电池等效电路模型的参数辨识方法 | |
| CN112345939B (zh) | 基于连续脉冲响应的锂离子电池模型参数辨识方法 | |
| CN109459699A (zh) | 一种锂离子动力电池soc实时监测方法 | |
| Einhorn et al. | Comparison of electrical battery models using a numerically optimized parameterization method | |
| CN107957560A (zh) | 一种基于等效电路的锂离子电池soc估计算法 | |
| CN110568373A (zh) | 锂电池健康状态评估方法、系统、终端及存储介质 | |
| CN110673037B (zh) | 基于改进模拟退火算法的电池soc估算方法及系统 | |
| CN111142025A (zh) | 一种电池soc估算方法、装置、存储介质及电动汽车 | |
| US11579201B2 (en) | Method and system for identifying third-order model parameters of lithium battery based on likelihood function | |
| CN110007238A (zh) | 一种铝空气电池等效电路模型的建立方法 | |
| CN113567861A (zh) | 一种动力电池健康状态的估算方法 | |
| CN114781176B (zh) | 一种锂离子电池储能系统集总参数的等效电路参数辨识方法 | |
| Ceylan et al. | A novel Lithium-Ion-Polymer battery model for hybrid/electric vehicles | |
| CN114720881A (zh) | 一种基于改进初值带遗忘因子递推最小二乘法的锂电池参数辨识方法 | |
| Wang et al. | Modeling, parameterization, and benchmarking of a lithium ion electric bicycle battery |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| 121 | Ep: the epo has been informed by wipo that ep was designated in this application |
Ref document number: 22832008 Country of ref document: EP Kind code of ref document: A1 |
|
| NENP | Non-entry into the national phase |
Ref country code: DE |