Battery capacity estimation method, device and computer storage medium

Abstract

A battery capacity estimation method, device and computer storage medium, the method comprising: obtaining a voltage-capacity curve of a battery in real time during the battery charging process; performing differentiation on the voltage-capacity curve to obtain a voltage differential-capacity curve; determining a voltage inflection point in the voltage-capacity curve according to the voltage differential-capacity curve; obtaining a reference capacity value corresponding to a pre-calibrated voltage inflection point; obtaining the amount of charge charged to the battery from the voltage inflection point to a fully charged state; and obtaining the actual capacity of the battery based on the sum of the reference capacity value and the charge-in amount. The present invention estimates the capacity of a battery according to the voltage inflection point on the voltage-capacity curve during the battery charging process, can improve the estimation accuracy of the battery capacity, and does not require the battery to be discharged, which is in line with the user's usage habits.

Description

Technical Field

[0001] The present invention relates to the technical field of battery management, and more specifically, to a method and device for estimating battery capacity and a computer storage medium. Background Art

[0002] The strong demand for new renewable energy solutions, such as electric cars, electric aircraft and electric ships, has led to the rapid development of lithium-ion batteries. Batteries used in the above systems will face more severe working conditions: higher power demand and energy demand, as well as greater temperature changes, all of which accelerate battery aging. Therefore, it is necessary to track the state of health (SOH) of the battery and determine when to terminate its service life. SOH is usually defined as the ratio between the actual capacity of the battery and its initial capacity at a given time.

[0003] At present, when calculating battery capacity, the total amount of electricity in the charging or discharging stage is mainly calculated by fully charging and discharging the battery, or charging and discharging in a certain battery state of charge (SOC) interval, and the total battery capacity is calculated based on the charging or discharging amount and the corresponding SOC interval. The accuracy of this method's estimation depends entirely on the accuracy of SOC. If the SOC estimation error is large, it will affect the estimation accuracy of the battery capacity. Especially for lithium iron phosphate batteries, the accumulated SOC error will affect the accuracy of the battery capacity, and the battery capacity error will in turn affect the accuracy of the SOC, forming a cross-effect, and ultimately making the battery capacity estimation completely invalid.

[0004] If the method of benchmarking with the laboratory is adopted, there are two disadvantages: first, laboratory testing is very time-consuming, labor-intensive, and costly, and it is impossible to cover all working conditions; second, benchmarking with laboratory data in actual use will be too dogmatic and unable to estimate the actual battery capacity. Summary of the invention

[0005] A series of simplified concepts are introduced in the Summary of the Invention, which will be further described in detail in the Detailed Description of the Invention. The Summary of the Invention does not mean to attempt to define the key features and essential technical features of the claimed technical solution, nor does it mean to attempt to determine the scope of protection of the claimed technical solution.

[0006] In view of the shortcomings of the prior art, a first aspect of an embodiment of the present invention proposes a method for estimating battery capacity, comprising: obtaining a voltage-capacity curve of the battery in real time during battery charging; performing differentiation on the voltage-capacity curve to obtain a voltage difference-capacity curve; identifying multiple peaks in the voltage difference-capacity curve; calculating a first height and a first width between each peak and an adjacent valley on its left side, and a second height and a second width between each peak and an adjacent valley on its right side; calculating a determination index based on the first height, the first width, the second height and the second width, wherein p =2(h1+w1) / (h1·w1)+2(h2+w2) / (h2·w2), p represents the determination index, h1 represents the first height, w1 represents the first width, h2 represents the second height, and w2 represents the second width; the voltage inflection point in the voltage-capacity curve is determined according to the peak with the minimum determination index; a reference capacity value corresponding to the voltage inflection point in the pre-calibrated voltage-capacity curve is obtained; when the battery reaches a fully charged state, the amount of charge charged to charge the battery from the voltage inflection point to the fully charged state is obtained; the actual capacity of the battery is obtained based on the sum of the reference capacity value and the charged amount.

[0007] In one embodiment, before differentiating the voltage-capacity curve, a step of smoothing and filtering the voltage-capacity curve is also included.

[0008] In one embodiment, the reference capacity value is calibrated in the following manner: after discharging the battery, the battery is charged to a full charge state at a constant current, a reference voltage-capacity curve of the battery during the constant current charging process is recorded, and the reference capacity value is calibrated according to the voltage-capacity curve during the constant current charging process.

[0009] In one embodiment, obtaining the charged amount of the battery from the voltage inflection point to the fully charged state includes: recording the charging time used to charge the battery from the voltage inflection point to the fully charged state; and calculating the charged amount based on the charging time and the charging current.

[0010] In one embodiment, the method further comprises: estimating a health status of the battery according to the actual capacity and a pre-calibrated initial capacity of the battery.

[0011] In one embodiment, the battery is a lithium iron phosphate battery.

[0012] A second aspect of an embodiment of the present invention provides a battery capacity estimation device, the device comprising a memory and a processor, the memory storing a computer program executed by the processor, and the computer program executing the battery capacity estimation method as described above when executed by the processor.

[0013] A third aspect of an embodiment of the present invention provides a computer storage medium having a computer program stored thereon, wherein the computer program implements the battery capacity estimation method as described above when executed.

[0014] The battery capacity estimation method and device of the embodiment of the present invention estimates the battery capacity according to the voltage inflection point on the voltage-capacity curve during the battery charging process, does not involve the absolute value of SOC, can improve the estimation accuracy of the battery capacity, and does not need to discharge the battery, which is in line with the user's usage habits. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above and other purposes, features and advantages of the present invention will become more apparent by describing the embodiments of the present invention in more detail in conjunction with the accompanying drawings. The accompanying drawings are used to provide a further understanding of the embodiments of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings, the same reference numerals generally represent the same components or steps.

[0016] Figure 1 is a schematic flow chart of a method for estimating battery capacity according to an embodiment of the present invention;

[0017] Figure 2 is a schematic diagram of a voltage-capacity curve according to an embodiment of the present invention;

[0018] Figure 3 is a schematic diagram of a voltage difference-capacity curve according to an embodiment of the present invention;

[0019] Figure 4 FIG. 4 is a schematic block diagram of a device for estimating battery capacity according to an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the present application more obvious, the example embodiments according to the present application will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application, and it should be understood that the present application is not limited to the example embodiments described herein. Based on the embodiments of the present application described in the present application, all other embodiments obtained by those skilled in the art without creative work should fall within the scope of protection of the present application.

[0021] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present application. However, it is apparent to those skilled in the art that the present application can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present application, some technical features well known in the art are not described.

[0022] It should be understood that the present application can be implemented in different forms and should not be interpreted as being limited to the embodiments set forth herein. On the contrary, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0023] The purpose of the terms used herein is only to describe specific embodiments and is not intended to be limiting of the present application. When used herein, the singular forms "one", "an" and "said / the" are also intended to include plural forms, unless the context clearly indicates otherwise. It should also be understood that the terms "consisting of" and / or "comprising", when used in this specification, determine the presence of the features, integers, steps, operations, elements and / or parts, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, parts and / or groups. When used herein, the term "and / or" includes any and all combinations of the relevant listed items.

[0024] In order to thoroughly understand the present application, a detailed structure will be proposed in the following description to illustrate the technical solution proposed by the present application. The optional embodiments of the present application are described in detail as follows, but in addition to these detailed descriptions, the present application may also have other implementation methods.

[0025] The following describes the battery capacity estimation method and battery capacity estimation device proposed in the embodiments of the present invention with reference to the accompanying drawings. Figure 1 , Figure 1 FIG. 1 is a schematic flow chart of a method 100 for estimating battery capacity according to an embodiment of the present invention. Figure 1 As shown, the battery capacity estimation method 100 includes:

[0026] In step S110, during the battery charging process, a voltage-capacity curve of the battery is obtained in real time;

[0027] In step S120, the voltage-capacity curve is differentiated to obtain a voltage difference-capacity curve;

[0028] In step S130, a plurality of peaks are identified in the voltage difference-capacity curve;

[0029] In step S140, a first height and a first width between each wave crest and an adjacent wave valley on its left side, and a second height and a second width between each wave crest and an adjacent wave valley on its right side are calculated;

[0030] In step S150, a determination index is calculated according to the first height, the first width, the second height and the second width, wherein p=2(h1+w1) / (h1·w1)+2(h2+w2) / (h2·w2), p represents the determination index, h1 represents the first height, w1 represents the first width, h2 represents the second height, and w2 represents the second width;

[0031] In step S160, a voltage inflection point in the voltage-capacity curve is determined according to a peak with a minimum determination index;

[0032] In step S170, a reference capacity value corresponding to a voltage inflection point in a pre-calibrated voltage-capacity curve is obtained;

[0033] In step S180, when the battery reaches a fully charged state, the amount of electricity charged to charge the battery from the voltage inflection point to a fully charged state is obtained;

[0034] In step S190, the actual capacity of the battery is obtained based on the sum of the reference capacity value and the charged power.

[0035] The battery capacity estimation method 100 of the embodiment of the present invention detects the voltage-battery capacity curve in real time during the battery charging process, analyzes the curve characteristics, finds the voltage inflection point, and estimates the actual capacity of the battery based on the voltage inflection point. The method intelligently estimates the actual capacity of the battery based on the characteristic properties of the material itself during the battery charging process, does not need to deeply discharge the battery, and can accurately calculate the actual capacity of the battery when the initial SOC state of the battery is unknown. Moreover, since the calculation process does not involve the absolute value of SOC, it will not have a cross-influence with the calculation of SOC. The battery capacity estimation method 100 of the embodiment of the present invention can not only greatly save the laboratory testing cost, but also can significantly improve the efficiency and accuracy of battery capacity calculation.

[0036] Specifically, during the battery charging process, the voltage-capacity curve of the battery is obtained in real time, and the voltage inflection point is determined in the voltage-capacity curve. The battery includes a lithium-ion battery, specifically a lithium iron phosphate battery. The voltage inflection point is one of the points where the voltage changes fastest with capacity. Figure 2 and Figure 3 The characteristics of the voltage-capacity curve and the voltage inflection point are explained.

[0037] First refer to Figure 2 , Figure 2The voltage-capacity curve of a lithium-ion battery is shown. Generally speaking, the voltage-capacity curve of a lithium-ion battery has three intervals where the voltage changes slowly with the capacity, which are called voltage platform areas. There is a region between each two adjacent voltage platform areas where the voltage changes rapidly with the capacity. The point where the voltage changes fastest in this region is called the voltage inflection point. The voltage inflection point used to estimate the battery SOH in the embodiment of the present invention is located between the second and third voltage platform areas, which is the point where the voltage changes fastest with the capacity in this interval.

[0038] Research has found that as lithium-ion batteries age, the capacity difference between the battery capacity value corresponding to the voltage inflection point and the battery capacity value corresponding to SOC=0 (i.e., the capacity value is 0) remains unchanged. The embodiment of the present invention estimates the actual capacity of the battery based on this characteristic of the voltage inflection point. After estimating the actual capacity of the battery, the battery's state of health (SOH) can be calculated based on the actual capacity of the battery. The battery's SOH is the ratio between the actual capacity of the battery and its initial capacity. The initial capacity of the battery can be obtained through calibration before leaving the factory. Specifically, the battery can be discharged and then charged to a full charge state at a constant current, and the initial capacity of the battery (denoted as Q new ). The embodiment of the present invention calculates the actual capacity of the battery according to the characteristics of the voltage inflection point, avoiding calculating the actual capacity of the battery according to the SOC, thereby avoiding the problem that the estimation accuracy of the SOH is affected by the accumulated SOC error and the SOH error affects the accuracy of the SOC.

[0039] Specifically, as described above, since the battery capacity value corresponding to the voltage inflection point remains unchanged, after the voltage inflection point is identified according to the voltage-capacity curve, the embodiment of the present invention calculates the charged capacity of the battery in the interval from the voltage inflection point to the full charge of the battery (denoted as Q HVP ), the capacity value corresponding to the voltage inflection point (denoted as Q HVTP ) and then we can get the actual capacity Q of the battery, Q = Q HVP +Q HVTP , and based on the actual capacity Q of the battery and the pre-calibrated initial capacity Q new Calculate the battery's SOH, SOH = Q / Q new *100%.

[0040] Among them, since the battery capacity in the voltage-capacity curve is calculated by the battery management system based on the SOC, in order to avoid introducing errors in the SOC, the embodiment of the present invention uses a pre-calibrated reference capacity value corresponding to the voltage inflection point to calculate the actual capacity of the battery. Exemplarily, before the battery leaves the factory, the battery is emptied and then charged to a full-charge state at a constant current, and the voltage-capacity curve during the battery charging process is recorded. By analyzing the characteristics of the voltage-capacity curve, the reference capacity value corresponding to the voltage inflection point is determined by offline calibration. When calculating the amount of charge from the voltage inflection point to the fully charged state, the time to reach the voltage inflection point and the charging time to reach the fully charged state can be recorded, and calculated based on the actual charging current and the charging time used to charge the battery from the voltage inflection point to the fully charged state. Since the reference capacity value corresponding to the voltage inflection point is an accurate value, the charge amount is also an accurate value, and the sum of the two can obtain a more accurate actual capacity of the battery.

[0041] The embodiment of the present invention does not involve the absolute value of SOC in the process of estimating the actual capacity of the battery, which can avoid the disadvantage of over-reliance on the accuracy of SOC estimation when calculating the actual capacity of the battery using the traditional method. In addition, the embodiment of the present invention does not need to empty the battery, which is in line with the usage habits of ordinary users. Experiments have shown that the actual capacity of the battery can be accurately calculated when charging starts at less than 60% SOC.

[0042] Exemplarily, since the voltage inflection point is the point where the voltage changes fastest with the capacity, the voltage inflection point can be determined according to the voltage differential-capacity curve, and the voltage inflection point corresponds to the peak of the voltage differential-capacity curve. Specifically, the voltage-capacity curve is differentiated to obtain a voltage differential-capacity (dV / dQ-Q) curve, and the capacity value corresponding to the voltage inflection point is determined according to the peak of the voltage differential-capacity curve.

[0043] There are generally multiple peaks in the voltage difference-capacity curve. In order to determine the voltage inflection point, it is necessary to determine a characteristic peak, that is, a peak corresponding to the voltage inflection point. The embodiment of the present invention searches for a characteristic peak based on the ratio of the perimeter to the area of ​​each peak. The voltage inflection point determined based on the characteristic peak is the voltage inflection point that satisfies the capacity invariance characteristic.

[0044] Specifically, see Figure 3 First, multiple peaks are identified in the voltage difference-capacity curve, and the first height and first width between each peak and the adjacent valley on its left, and the second height and second width between each peak and the adjacent valley on its right are calculated. The first height is the difference in voltage difference between each peak and the adjacent valley on its left, and the first width is the difference in capacity between each peak and the adjacent valley on its left; the second height is the absolute value of the difference in voltage difference between each peak and the adjacent valley on its right, and the second width is the absolute value of the difference in capacity between each peak and the adjacent valley on its right.

[0045] Afterwards, a determination index is calculated for each peak according to the first height, the first width, the second height and the second width, and the sum of the ratios of the perimeter and the area of ​​the two half peaks on the left and right sides of each peak is used as the determination index. Specifically, the determination index p=2(h1+w1) / (h1·w1)+2(h2+w2) / (h2·w2), where h1 represents the first height, w1 represents the first width, h2 represents the second height, and w2 represents the second width. After the determination index is calculated for each peak, the peak with the smallest determination index is used as the characteristic peak to determine the voltage inflection point.

[0046] In some embodiments, in order to reduce the error, before differentiating the voltage-capacity curve, a step of smoothing and filtering the voltage-capacity curve is also included. After determining the voltage inflection point, the actual capacity of the battery can be estimated according to the method described above.

[0047] The embodiment of the present invention detects and analyzes the voltage-capacity curve in real time during the battery charging process. It does not need to deeply discharge the battery, which is in line with the user's usage habits and has great technical advantages and market value. In the calculation process, it is not necessary to determine the initial SOC of the battery, nor does it involve the absolute value of the SOC. It only needs to identify the voltage inflection point during the charging process to calculate the actual capacity of the battery, thereby improving the accuracy of the actual capacity estimation of the battery. Furthermore, the SOH of the battery can also be obtained, which improves the estimation accuracy and speed of the SOH. In addition, when identifying the voltage inflection point, the perimeter / area feature is used to achieve automatic identification, and there is no need to manually set thresholds according to different vehicle models and different aging degrees, which is more universal.

[0048] The embodiment of the present invention further provides a battery capacity estimation device, which can be used to implement the battery capacity estimation method 100 described above. Figure 4 , Figure 4 FIG. 4 is a schematic block diagram of a battery capacity estimation device 400 according to an embodiment of the present invention.

[0049] like Figure 4As shown, the battery capacity estimation device 400 includes a memory 410, a processor 420, and a computer program stored in the memory 410 and running on the processor 420. When the processor 420 executes the computer program, the battery capacity estimation method 100 described above can be implemented. The processor 420 can be implemented by software, hardware, firmware, or a combination thereof, and can use at least one of a circuit, a single or multiple application-specific integrated circuit (ASIC), a digital signal processor (DSP), a digital signal processing device (DSPD), a programmable logic device (PLD), a field programmable gate array (FPGA), a central processing unit (CPU), a controller, a microcontroller, and a microprocessor, so that the device can execute some steps or all steps of the battery capacity estimation method 100 in various embodiments of the present application or any combination of the steps therein.

[0050] The embodiment of the present invention further provides a computer storage medium on which a computer program is stored. When the computer program is executed, the method 100 for estimating the battery capacity of the embodiment of the present invention can be implemented.

[0051] The battery capacity estimation device 400 and the computer storage medium according to the embodiment of the present invention are used to implement the battery capacity estimation method 100 described above, and thus also have similar advantages.

[0052] Although example embodiments have been described herein with reference to the accompanying drawings, it should be understood that the above example embodiments are merely exemplary and are not intended to limit the scope of the present application thereto. Various changes and modifications may be made therein by one of ordinary skill in the art without departing from the scope and spirit of the present application. All such changes and modifications are intended to be included within the scope of the present application as required by the appended claims.

[0053] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0054] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic, for example, the division of the units is only a logical function division, and there may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another device, or some features can be ignored or not executed.

[0055] In the description provided herein, a large number of specific details are described. However, it is understood that the embodiments of the present application can be practiced without these specific details. In some instances, well-known methods, structures and techniques are not shown in detail so as not to obscure the understanding of this description.

[0056] Similarly, it should be understood that in order to streamline the present application and help understand one or more of the various inventive aspects, in the description of the exemplary embodiments of the present application, the various features of the present application are sometimes grouped together into a single embodiment, figure, or description thereof. However, the method of the present application should not be interpreted as reflecting the following intention: the claimed application requires more features than the features clearly stated in each claim. More specifically, as reflected in the corresponding claims, the inventive point is that the corresponding technical problem can be solved with features less than all the features of a single disclosed embodiment. Therefore, the claims following the specific embodiment are hereby explicitly incorporated into the specific embodiment, wherein each claim itself serves as a separate embodiment of the present application.

[0057] It will be understood by those skilled in the art that, except for mutually exclusive features, all features disclosed in this specification (including the accompanying claims, abstracts and drawings) and all processes or units of any method or device disclosed in this specification may be combined in any combination. Unless otherwise expressly stated, each feature disclosed in this specification (including the accompanying claims, abstracts and drawings) may be replaced by an alternative feature that provides the same, equivalent or similar purpose.

[0058] In addition, those skilled in the art will appreciate that, although some embodiments described herein include certain features included in other embodiments but not other features, the combination of features of different embodiments is meant to be within the scope of the present application and form different embodiments. For example, in the claims, any one of the claimed embodiments can be used in any combination.

[0059] The various component embodiments of the present application can be implemented in hardware, or in software modules running on one or more processors, or in a combination thereof. It should be understood by those skilled in the art that a microprocessor or digital signal processor (DSP) can be used in practice to implement some or all functions of some modules according to the embodiments of the present application. The application can also be implemented as a device program (e.g., computer program and computer program product) for executing a part or all of the methods described herein. Such a program implementing the present application can be stored on a computer-readable medium, or can have the form of one or more signals. Such a signal can be downloaded from an Internet website, or provided on a carrier signal, or provided in any other form.

[0060] It should be noted that the above embodiments illustrate rather than limit the present application, and that those skilled in the art may devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference symbol between brackets should not be constructed as a limitation to the claims. The present application may be implemented by means of hardware including several different elements and by means of a suitably programmed computer. In a unit claim that lists several devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order. These words may be interpreted as names.

[0061] The above is only a specific implementation method or an explanation of a specific implementation method of the present application, and the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. The protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for estimating battery capacity, characterized in that: The method comprises: During the battery charging process, obtaining the voltage-capacity curve of the battery in real time; Differentiating the voltage-capacity curve to obtain a voltage difference-capacity curve; identifying a plurality of peaks in the voltage differential-capacity curve; Calculate a first height and a first width between each wave crest and an adjacent wave valley on its left side, and a second height and a second width between each wave crest and an adjacent wave valley on its right side; Calculate a determination index according to the first height, the first width, the second height, and the second width, wherein p=2(h1+w1) / (h1·w1)+2(h2+w2) / (h2·w2), p represents the determination index, h1 represents the first height, w1 represents the first width, h2 represents the second height, and w2 represents the second width; Determine a voltage inflection point in the voltage-capacity curve according to a peak having a minimum determination index; Obtaining a reference capacity value corresponding to a voltage inflection point in a pre-calibrated voltage-capacity curve; When the battery reaches a fully charged state, obtaining the amount of electricity charged to charge the battery from the voltage inflection point to a fully charged state; The actual capacity of the battery is obtained based on the sum of the reference capacity value and the charged power.

2. The method for estimating battery capacity according to claim 1, characterized in that: Before differentiating the voltage-capacity curve, the method further includes a step of smoothing and filtering the voltage-capacity curve.

3. The method for estimating battery capacity according to claim 1, characterized in that: The reference capacity value is calibrated in the following manner: After the battery is discharged, it is charged to a full-charge state at a constant current, the voltage-capacity curve of the battery during the constant-current charging process is recorded, and the reference capacity value is calibrated according to the voltage-capacity curve of the battery during the constant-current charging process.

4. The method for estimating battery capacity according to claim 1, characterized in that: The obtaining of the amount of electricity charged to the battery from the voltage inflection point to a fully charged state includes: Recording the charging time taken to charge the battery from the voltage inflection point to a fully charged state; The charged amount is calculated according to the charging time and the charging current.

5. The method for estimating battery capacity according to claim 1, characterized in that: Also includes: The health status of the battery is estimated based on the actual capacity and a pre-calibrated initial capacity of the battery.

6. The method for estimating battery capacity according to any one of claims 1 to 5, characterized in that: The battery is a lithium iron phosphate battery.

7. A battery capacity estimation device, characterized in that: The device comprises a memory and a processor, wherein a computer program executed by the processor is stored in the memory, and the computer program, when executed by the processor, executes the battery capacity estimation method according to any one of claims 1 to 6.

8. A computer storage medium having a computer program stored thereon, characterized in that: When the computer program is executed, the battery capacity estimation method according to any one of claims 1 to 6 is implemented.

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