A lithium battery soc estimation method based on high-precision ampere-hour integration algorithm

Abstract

The present application belongs to the field of lithium battery SOC calculation, and particularly relates to a lithium battery SOC estimation method based on high-precision ampere-hour integral algorithm. The method comprises establishing an ampere-hour integral mathematical model and solving, and performing Taylor expansion on the solution; the average slope is obtained by means of linear combination of three-point slope by investigating the slope of two points in the interval, so as to ensure that the precision of the third-order Taylor expansion formula and the equivalent formula is the same. When the algorithm is executed, the charge state and the capacity value are initialized first, then the sampling time is obtained according to the sampling frequency, and then the relevant parameters are calculated according to the current sampling value, and finally the current SOC is calculated according to the specific value and the three slopes and is iterated in a loop. This method can improve the ampere-hour integral precision, and weaken the cumulative error and SOC jump.

Description

Technical Field

[0001] This invention belongs to the field of lithium battery SOC calculation, specifically involving a lithium battery SOC estimation method based on a high-precision ampere-hour integration algorithm. Background Technology

[0002] State of Charge (SOC) is a crucial parameter for measuring the remaining capacity of a lithium-ion battery. It represents the percentage of the battery's current charge relative to its maximum capacity. Accurately estimating the SOC of a lithium-ion battery is essential for battery management systems, helping to optimize battery performance, extend battery life, and improve safety. The importance of SOC is mainly reflected in three aspects: First, battery management: accurate SOC estimation helps prevent overcharging and over-discharging, extending battery life and ensuring the battery operates within safe limits; second, energy management: in electric vehicles or energy storage systems, SOC information helps optimize energy distribution, improving system efficiency and reliability; and finally, user experience: accurate SOC display helps users understand the remaining battery capacity, rationally plan charging and usage, and improve ease of use. Lithium-ion battery SOC estimation is a complex and important task involving various technologies and methods. By appropriately selecting and optimizing estimation methods, high-precision and high-reliability SOC estimation can be achieved, thereby improving the overall performance of the battery system and the user experience.

[0003] Existing SOC algorithms mainly include the open-circuit voltage method, model estimation method, and ampere-hour integration method. The open-circuit voltage method is primarily used in static scenarios, with very limited start-up conditions; the model estimation method suffers from high model complexity, difficulty in obtaining model parameters, and high computational resource requirements; and the ampere-hour integration method is susceptible to accumulated errors. Therefore, this patent proposes a method to improve the accuracy of ampere-hour integration, thereby reducing long-term accumulated errors and, through a hybrid algorithm, mitigating SOC jumps. Summary of the Invention

[0004] This invention addresses the technical problems existing in the background art by proposing a method that is reasonably designed, simple in method, theoretically sound, and capable of improving the accuracy of ampere-hour integration in estimating battery state of charge (SOC).

[0005] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0006] S1. First, establish the mathematical model of the ampere-hour integral. Where i is the current, soc is the state of charge, cap is the battery capacity, soc′ is the first derivative of soc, and the changes of each variable with time are omitted. f represents the relationship between the first derivative of soc and the current i and soc, and soc0 represents the initial state of the state of charge soc.

[0007] S2. Then, the solution to the mathematical model of the ampere-hour integral is obtained as soc = soc(i), and this solution is then subjected to a Taylor expansion. Where soc′(i n ), soc″(i n ), soc″′(i n ) are the first, second, and third derivatives of soc(i), respectively, and Δ represents the unit time difference, i.e., Δ = t n+1 -t n i n This represents the current value measured at the nth time. To ensure accuracy and minimize computational complexity, only the first four terms of the Taylor formula are used.

[0008] S3, Next, examine the interval (i) n i n+1 Two points Where i n+p i n+q Let x be two points in the interval, and let K2 and K3 be the slopes between them. Let K1 be a value of x. n The slope at point i, from which we can obtain K1 = f(i) n ,soc n According to the improved Euler scheme, K2 = f(i) n +pΔ,soc n +pΔK1) and then K3=f(i n +qΔ,soc n +qΔ(rK1+sK2)), where r and s are parameters used to adjust the slope combination method;

[0009] S4, Finally, using three points x n ,x n+p ,x n+q The average slope is obtained by linearly combining the slopes K1, K2, and K3. In this case, the Taylor formula is equivalent to soc. n+1 =soc n +Δ(λ1K1+λ2K2+λ3K3), where λ1, λ2, and λ3 are linear coefficients. To ensure that the third-order Taylor expansion and the equivalent formula have the same accuracy, the following equation must be satisfied. Solving the equation, we find a special case that satisfies the following equation:

[0010] As a preferred option, the detailed execution flow of the algorithm is as follows:

[0011] Step 1: First, initialize the value of the charge state soc0. Generally, this value is read from non-volatile memory. Based on the individual cell capacity and pack configuration of the battery pack, calculate the theoretical capacity value, i.e., the cap value.

[0012] Step 2: Next, obtain the sampling time Δ based on the sampling frequency of the current sensor by the battery management system (BMS).

[0013] Step 3: Next, calculate the value of K1 based on the current sample value i0 at the current moment and using the ampere-hour integral mathematical model and a special case that satisfies the equation. The value of K2 can be calculated based on the Δ value. The value of K3 can be calculated based on the values ​​of K1 and K2.

[0014] Step 4: Finally, based on the current SOC0 value and the three slopes K1, K2, K3, the current SOC1 value can be calculated. Then, the current current value i1 is sampled again. Using the three slopes K1, K2, K3, and the known SOC1 value, SOC2 can be calculated. This process is repeated iteratively to calculate the current SOC of the lithium battery.

[0015] Compared with existing technologies, the advantages and positive effects of this invention are that it proposes a lithium battery SOC estimation method based on a high-precision ampere-hour integration algorithm, which can improve the accuracy of ampere-hour integration and reduce long-term accumulated errors. Under the hybrid algorithm, it can reduce SOC jumps and more accurately estimate the lithium battery SOC. Estimating the slope at two points within the interval reduces the SOC error, resulting in a smaller error compared to the forward Euler algorithm that only considers the first two terms of the Taylor formula. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 An integral model for ampere-hours;

[0018] Figure 2 Flowchart of the high-precision algorithm model;

[0019] Figure 3 Error analysis diagram for high-precision ampere-hour algorithm; Detailed Implementation

[0020] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0021] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the invention is not limited to the specific embodiments disclosed in the following specification.

[0022] In lithium battery applications, accurate estimation of its State of Charge (SOC) is crucial. Existing SOC algorithms, such as the open-circuit voltage method, model estimation method, and ampere-hour integration method, all have certain limitations. The open-circuit voltage method is mainly applicable to static conditions with limited opening conditions; the model estimation method has high model complexity, is difficult to obtain parameters, and requires high computational resources; the ampere-hour integration method is easily affected by accumulated errors. To overcome these problems, this invention proposes a lithium battery SOC estimation method based on a high-precision ampere-hour integration algorithm. This method aims to improve the accuracy of ampere-hour integration, reduce long-term accumulated errors, and minimize SOC jumps under a hybrid algorithm, thereby more accurately estimating the lithium battery's SOC and improving the performance and reliability of the battery management system.

[0023] First, we establish the mathematical model for the ampere-hour integral, by... Figure 1 It can be known Where i is the current, soc is the state of charge, cap is the battery capacity, soc′ is the first derivative of soc, and the changes of each variable with time are omitted. f represents the relationship between the first derivative of soc and the current i and soc, and soc0 represents the initial state of the state of charge soc.

[0024] Then, the solution to the mathematical model of the ampere-hour integral is obtained as soc = soc(i), and this solution is then subjected to a Taylor expansion. Where soc′(i n ), soc″(i n ), soc″′(i n ) are the first, second, and third derivatives of soc(i), respectively, and Δ represents the unit time difference, i.e., Δ = t n+1 -t n i n This represents the current value measured at the nth time. To ensure accuracy and minimize computational complexity, only the first four terms of the Taylor formula are used.

[0025] Next, examine the interval (i) n i n+1 Two points Where i n+p i n+q Let x be two points in the interval, and let K2 and K3 be the slopes between them. Let K1 be a value of x. n The slope at point i, from which we can obtain K1 = f(i) n ,soc n According to the improved Euler scheme, K2 = f(i) n +pΔ,socn +pΔK1) and then K3=f(i n +qΔ,soc n +qΔ(rK1+sK2)), where r and s are parameters used to adjust the slope combination method;

[0026] Finally, using three points x n ,x n+p ,x n+q The average slope is obtained by linearly combining the slopes K1, K2, and K3. In this case, the Taylor formula is equivalent to soc. n+1 =soc n +Δ(λ1K1+λ2K2+λ3K3), where λ1, λ2, and λ3 are linear coefficients. To ensure that the third-order Taylor expansion and the equivalent formula have the same accuracy, the following equation must be satisfied. Solving the equation, we find a special case that satisfies the following equation:

[0027] The detailed execution process of the algorithm is as follows: Figure 2 As shown. First, the state of charge (SOC) value is initialized. This value is typically read from non-volatile memory. Based on the individual cell capacity and pack configuration of the battery pack, the theoretical capacity value, i.e., the cap value, is calculated. Second, the sampling time Δ is obtained based on the sampling frequency of the current sensor by the battery management system (BMS). Third, based on the current sampled value i0 at the current moment and using the ampere-hour integral mathematical model and a special case satisfying the equation, the value K1 is calculated. The value K2 can be calculated based on Δ, and the value K3 can be calculated based on K1 and K2. Finally, the current SOC1 value is calculated based on the current SOC value and the three slopes K1, K2, and K3. Then, the current current value i1 is sampled again. Based on the calculated three slopes K1, K2, and K3, and given the known SOC1 value, SOC2 can be calculated. This process is repeated iteratively to calculate the current SOC of the lithium battery.

[0028] When the algorithm ends, the SOC is stored in non-volatile memory. Considering only the first two terms of the Taylor formula, i.e., only the first derivative, the calculation of SOC is a forward Euler problem, and its error is as follows: Figure 3 As shown in the figure, soc(i), soc1(t), and soc3(t) represent the true SOC curve, the Euler method SOC curve, and the SOC curve of this algorithm, respectively. From Figure 3 It can be intuitively seen that the error of the algorithm is smaller than that of Euler's algorithm. This algorithm works for two points i within the interval. p and i q The slope was estimated, which reduced the error of the SOC. Increasing the number of estimates in the intervals would increase the computational accuracy, but it would consume a lot of computational resources. In the end, only two points within two sampling intervals were estimated.

[0029] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A lithium battery SOC estimation method based on a high-precision ampere-hour integration algorithm, characterized in that, The method comprises the following steps: S1. First, establish the mathematical model of the ampere-hour integral. Where i is the current, soc is the state of charge, and cap is the battery capacity. yes The first derivative of f, omitting the time-varying expressions of each variable, is expressed as f. First derivative and current i and Relationship, Indicates charge state The initial state; S2, then the solution to the mathematical model of the ampere-hour integral is: And perform a Taylor expansion on this solution. ,in They are The first, second, and third derivatives, This represents the difference per unit time, i.e. , This represents the current value measured at the nth time. To ensure accuracy and minimize computational complexity, only the first four terms of the Taylor formula are used. S3, Next, examine the interval. Two points ,in Let be two points in the interval, and the slope between the two points is . , yes The slope at that point can be obtained from this. According to the improved Euler form, we can obtain and then , where r,s are parameters used to adjust the slope combination method; S4, Finally, using three points slope The linear combination yields the average slope, at which point the Taylor formula is equivalent to... ,in For linear coefficients, to ensure that the third-order Taylor expansion and the equivalent formula have the same accuracy, the following equations must be satisfied. Solving the equation, we find a special case that satisfies the following equation: .

2. The lithium battery SOC estimation method based on high-precision ampere-hour integration algorithm according to claim 1, characterized in that, The detailed flow of the algorithm execution is as follows: Step one, first initialize the charge state The value is generally read from the non-volatile memory, and the theoretical capacity value, i.e., the cap value, is calculated according to the single capacity of the battery pack and the grouping mode. Step 2: Next, obtain the sampling time based on the sampling frequency of the current sensor according to the Battery Management System (BMS). ; Step 3: Next, based on the current sampling value at the current moment... And using the ampere-hour integral mathematical model and a special case satisfying the equation, the following was calculated: Value, based on The value can be calculated Value, based on value and The value can be calculated ; Step 4: Finally, according to the... Values ​​and three slopes The current can be calculated Value; at this point, the current current value is sampled again. Based on the three slopes calculated first Furthermore, as is known The value can be calculated The process involves iterative iteration to calculate the current SOC of the lithium battery.

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