A Battery Management Method, Device, Equipment and Medium Based on Graph Theory

Through the battery management and control method based on graph theory, the battery model is established and the energy path is optimized, which solves the problem that traditional battery management systems are difficult to effectively utilize the remaining energy of the battery, and realizes flexible management and energy balance of the battery system, extends battery life and improves the stability of energy supply.

CN114330226BActive Publication Date: 2025-06-24STATE GRID BEIJING ELECTRIC POWER CO +2
View PDF 3 Cites 0 Cited by

Patent Information

Application Number
CN202111679217.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-12-31
Publication Date
2025-06-24
Estimated Expiration
2041-12-31

AI Technical Summary

Technical Problem

In a system where multiple battery cells or modules are fixed in series and parallel, it is difficult to effectively utilize the remaining energy of each battery cell or module, resulting in overvoltage or undervoltage of some batteries, affecting the protection and energy management efficiency of the entire battery system.

Method used

Using a graph theory-based battery control method, by establishing a battery model G=(P,ε,ω), obtaining the vertex set P and edge set ε, computing the weight of each energy path, and obtaining the optimal energy path through an optimization algorithm to achieve flexible battery system management and energy equalization.

Benefits of technology

It realizes flexible control of each battery unit in the battery system, improves energy management efficiency, eliminates the impact of battery differences on the operation of the battery pack, extends the life of the battery system, and improves the stability and sustainability of the energy supply of the battery energy storage system.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN114330226B_ABST
    Figure CN114330226B_ABST
Patent Text Reader

Abstract

The present invention belongs to the technical field of battery management, and specifically discloses a battery control method, device, equipment and medium based on graph theory. The method includes the following steps: S1. Based on the graph theory method, mathematically abstract the connection relationship and energy path characteristics of each battery unit in the target battery system to establish a battery model; S2. According to the battery model, obtain a vertex set and an edge set; the vertex set is each battery unit with an independent control function; the edge set is the connection relationship of the battery units formed under the same independent control logic, that is, the energy path from the initial battery unit to the terminal battery unit; S3. According to the vertex set and the edge set, use the battery energy path optimization algorithm to calculate the weight of each energy path in the edge set to obtain the weight; S4. Sort the weight values in the weight to obtain the optimal energy path. By using the graph theory method, the present invention regards the battery system as an energy path network and realizes the safe and efficient use of the battery at the same time.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention belongs to the technical field of battery management, and particularly relates to a battery control method, device, equipment and medium based on graph theory. Background Technique

[0002] With the breakthrough of energy storage battery material technology, the application of new energy has seen great development. The energy storage battery system is an important part of the new energy application. As the core component of the energy storage system, the battery is the main detection object and control target of the entire energy storage system. The main electrical performance indicators and control basis of the battery are voltage, current, and remaining energy, and the magnitudes of the three will fluctuate and be correlated with the charge and discharge states. During charging, the voltage and remaining energy will continuously increase throughout the process, and the voltage at a certain moment is proportional to the current; during discharging, the voltage and remaining energy will continuously decrease throughout the process, and the voltage at a certain moment is inversely proportional to the current; there is no direct mathematical calculation relationship between the charge and discharge voltage or current and the remaining energy of the battery.

[0003] In a traditional battery management system, each battery cell or module is fixedly connected, and it is assumed that the remaining energies of each battery cell or module are the same or similar. The traditional battery management system realizes the charging or discharging current by detecting and controlling the DC voltage. However, in actual use, due to the electrochemical differences of each battery cell or module, there are inconsistencies in their remaining energies. Especially after several charge and discharge cycles, the differences in the remaining energies will initially expand. On the other hand, the traditional battery energy algorithm makes logical judgments based on voltage. Therefore, in a system where multiple battery cells or modules are fixedly connected in series or parallel, there will inevitably be a protection of the entire battery system due to overvoltage or undervoltage of some battery cells or modules, and at this time, there is still a large amount of remaining energy in other battery cells or modules that cannot be used. These are the specific problems of the inflexibility of the traditional battery management system and energy algorithm and the low energy management efficiency. Summary of the Invention

[0004] The purpose of the present invention is to provide a battery control method, device, equipment and medium based on graph theory to solve the technical problem that it is difficult to fully charge all battery cells / modules when there are large differences in battery cells / modules in the traditional battery management method.

[0005] In the first aspect, a battery control method based on graph theory includes the following steps:

[0006] S1. Based on the graph theory method, mathematically abstract the connection relationship and energy path characteristics of each battery unit in the target battery system, and establish a battery model G=(P, ε, ω);

[0007] S2. According to the battery model G=(P, ε, ω), obtain the vertex set P={n1, n2, n3…n n}, and the edge set ε = {ε1, ε2, ε3…ε m};

[0008] The vertex set P = {n1, n2, n3…n n} is each battery cell with an independent control function;

[0009] The edge set ε = {ε1, ε2, ε3…ε m} is the connection relationship of the battery cells formed under the same independent control logic, that is, the energy path from the initial battery cell to the terminal battery cell;

[0010] S3. According to the vertex set P = {n1, n2, n3…n n} and the edge set ε = {ε1, ε2, ε3…ε m}, use the battery energy path optimization algorithm to calculate the weight of each energy path in the edge set ε = {ε1, ε2, ε3…ε m} to obtain the weight ω = {ε1, ε2, ε3…ε m};

[0011] S4. Sort the weight values in the weight ω = {ε1, ε2, ε3…ε m} to obtain the optimal energy path.

[0012] A further improvement of the present invention is that: the battery cell is a battery monomer or module on the energy path node, and its performance characteristics include remaining capacity, maximum capacity, charge and discharge cut-off voltage, and charge and discharge limiting current.

[0013] A further improvement of the present invention is that: in the edge set ε = {ε1, ε2, ε3…ε m} and the weight ω = {ε1, ε2, ε3…ε m}, m represents the total number of feasible remaining energy conversion paths searched exhaustively.

[0014] A further improvement of the present invention is that: the battery energy path optimization algorithm includes the remaining capacity control boundary condition and the electrical condition based on Kirchhoff's law.

[0015] A further improvement of the present invention is that: the remaining capacity control boundary condition refers to the total energy expectation and consistency expectation of the remaining capacity of each battery cell, including the following steps:

[0016] Select all energy paths with a total energy greater than the energy required by the electrical system load;

[0017] Judge the remaining capacity control relationship of all battery cells on each energy path whose total energy is greater than the energy required by the electrical system load. The energy paths where the remaining energy of each battery cell meets the remaining capacity control relationship are further screened by the electrical conditions based on Kirchhoff's law.

[0018] A further improvement of the present invention lies in that: the electrical conditions based on Kirchhoff's law, that is, the safe operating ranges of the battery cell voltage and current, are restricted by the charge and discharge cut-off conditions;

[0019] Among the energy paths that meet the remaining capacity control relationship, the energy paths where the sum of the currents at each node is equal to zero and the sum of the loop voltages is equal to zero meet the electrical conditions based on Kirchhoff's law.

[0020] A further improvement of the present invention lies in that according to:

[0021] Remaining energy of each battery cell ≥ average value of remaining capacities of all battery cells on this energy path ± preset energy consistency correction value, judge the remaining capacity control relationship of all battery cells on each energy path whose total energy is greater than the energy required by the electrical system load.

[0022] In a second aspect, a battery control device based on graph theory includes:

[0023] Battery model establishment module: used to mathematically abstract the connection relationship and energy path characteristics of each battery cell in the target battery system based on graph theory methods, and establish a battery model;

[0024] Vertex set and edge set acquisition module: used to obtain the vertex set and edge set according to the battery model;

[0025] Weight calculation module: used to calculate the weight of each energy path in the edge set by using the battery energy path optimization algorithm according to the vertex set and edge set, and obtain the weight;

[0026] Optimal energy path acquisition module: used to sort the weights to obtain the optimal energy path.

[0027] In a third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned battery control method based on graph theory.

[0028] In a fourth aspect, a computer-readable storage medium stores a computer program, characterized in that when the computer program is executed by a processor, it implements the above-mentioned battery control method based on graph theory.

[0029] Compared with the prior art, the present invention has at least the following beneficial effects:

[0030] 1. In the present invention, the original battery pack with unified management and fixed control is composed of individual battery cells, which are regarded as individual energy points. The differences between battery cells are manifested as the magnitudes of each energy point. The electrical connections of the positive electrode, energy points, and negative electrode are regarded as variable paths, and the sum of the battery energy and voltage on different paths is taken as the result of the graph. In the traditional technical solution, the energy path is fixed, and the number of energy points of the batteries passed by the path is also fixed, so the internal optimization of the battery pack cannot be carried out. The present invention realizes flexible control of each battery unit in the battery system and improves the energy management efficiency;

[0031] 2. In the present invention, the energy path is controlled to change through the remaining capacity control boundary conditions. The change and selection of the path will be based on external energy requirements (voltage, current, power, duration, etc.) as boundary conditions, and the energy path with the shortest necessary path, the smallest sum of the passed energy points, and the smallest difference between energy points will be calculated, that is, internal optimization of enabling or disabling will be carried out according to the differences in the states of each battery cell, and finally the effect of using the batteries with strong capabilities first and then the batteries with weak capabilities will be achieved, eliminating the influence of battery differences on the operation of the battery pack.

[0032] 3. The present invention abandons the rough judgment of the battery state through charge and discharge voltage and current in traditional battery management. The battery system is regarded as an energy path network, and the energy paths of the remaining energy of each battery are exhaustively calculated and analyzed from the perspective of the transient system. The feasibility and safety of the energy path calculation results are constrained through control limit conditions, realizing the function of dynamically balancing the energy of each battery unit while safely and stably meeting the energy requirements of the system, and finally realizing the maximum utilization of the energy of the target battery system. It decouples the energy supply stability and persistence of the battery energy storage system from the battery consistency, and prolongs the service life of the battery system. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings forming a part of this specification are used to provide a further understanding of the present invention. The schematic embodiments and descriptions thereof of the present invention are used to explain the present invention and do not constitute an improper limitation to the present invention. In the drawings:

[0034] Figure 1 is a schematic diagram of the model construction of a battery control method based on graph theory according to the present invention;

[0035] Figure 2 is a flowchart of a battery control method based on graph theory according to the present invention;

[0036] Figure 3 is a system block diagram of a battery control device based on graph theory according to the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0037] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments may be combined with each other.

[0038] The following detailed descriptions are all exemplary descriptions, aiming to provide further details of the present invention. Unless otherwise specified, all technical terms used in the present invention have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. The terms used in the present invention are only for describing specific embodiments, and are not intended to limit the exemplary embodiments according to the present invention.

[0039] Embodiment 1

[0040] As Figure 1-2 shown, a battery management and control method based on graph theory includes the following steps:

[0041] S1. Based on graph theory, mathematically abstract the connection relationship and energy path characteristics of each battery unit in the target battery system to establish a battery model G = (P, ε, ω). This graph theory algorithm consists of vertices, an edge set, and weights. The vertices are battery monomers or battery modules with each independent control function; the edge set represents the connection relationship of battery units formed under different independent control logics; the weights are the feasibility of the battery system under each edge set scheme.

[0042] The purpose of establishing the battery model is to obtain information with higher frequency and resolution, and at the same time represent the energy flow.

[0043] S2. According to the battery model G = (P, ε, ω), obtain the vertex set P = {n1, n2, n3... n n} and the edge set ε = {ε1, ε2, ε3... ε m};

[0044] The vertex set P = {n1, n2, n3... n n} is the remaining energy of each battery unit. The battery unit is a battery monomer or module on the energy path node, and their performance characteristics such as remaining capacity, maximum capacity, charge and discharge cut-off voltage, charge and discharge limit current, etc. are known parameters;

[0045] The edge set ε = {ε1, ε2, ε3... ε m} is the connection path from the initial battery unit to the terminal battery unit. The battery units on the connection path form a battery system for supporting energy output, which is used to characterize the flexibility of the remaining energy configuration. m represents the total number of feasible remaining energy conversion paths obtained by exhaustive search;

[0046] Calculate the edge set ε = {ε1, ε2, ε3... ε n} according to the vertex set P = {n1, n2, n3... nm The feasible weight of each energy path in}, and the weight set of m energy paths is the weight ω = {ε1, ε2, ε3…ε m}, the weight ω = {ε1, ε2, ε3…ε m} represents the safe operation of the remaining energy, voltage, and current control values of the corresponding edge set;

[0047] S3. Calculate each energy path through the battery energy path optimization algorithm to obtain the weight value corresponding to each energy path;

[0048] The battery energy path optimization algorithm includes the remaining capacity control boundary condition and the electrical condition based on Kirchhoff's law;

[0049] The remaining capacity control boundary condition refers to the total energy expectation and consistency expectation of the remaining capacity of each battery cell;

[0050] The electrical condition based on Kirchhoff's law refers to the condition that the voltage operating range of each battery cell is limited by the cut-off voltage and the full voltage;

[0051] The remaining capacity control boundary condition includes the total energy and the energy consistency of the battery cells; according to the charge and discharge energy requirements of the target battery system, the total energy of all battery cells on the path under different energy path schemes should meet the transient demand of external energy. For example, if the electrical system load requires 1000W of energy demand and there are 4 battery cells on a possible energy path in the target battery system, then the total energy ΣP n should be greater than or equal to 1000W, where (n = 1, 2, 3, 4). The energy consistency of the battery cells is used for the problem of selecting the battery energy among multiple possible energy paths. There may be multiple energy paths in the target battery system that satisfy the total energy ΣP mn ≥1000W, (m = 1, 2, 3, 4; n = 1, 2, 3, 4) and other energy paths. It is necessary to judge the remaining capacity control relationship of the four battery cells on different P 1n 、P 2n 、P 3n and other energy paths. The remaining energy of each battery cell needs to meet the requirements of the mathematical average value of the remaining capacity of all four battery cells ± the energy consistency correction value. Through the analysis of the remaining capacity control boundary of the battery cells, the possible path of the optimal battery balance combination that meets the external power consumption conditions can be obtained.

[0052] The electrical conditions based on Kirchhoff's laws, namely the safe operating ranges of the battery cell voltage and current, are restricted by the charge and discharge cut-off conditions; in a lower-frequency electrical topology, the static supply voltage and current involved in the circuit need to satisfy Kirchhoff's laws, that is, the sum of the node currents is equal to zero and the sum of the loop voltages is equal to zero; in addition, when the independent switches in the vertices operate dynamically according to an appropriate duty cycle, it is necessary to consider the high-frequency range that these switches can withstand, as well as the maximum energy storage limits of the inductor and the supercapacitor as energy buffers;

[0053] S4. According to the magnitude of each weight value in the weight ω = {ε1, ε2, ε3…ε m}, sort the energy paths corresponding to each weight value to obtain the optimal energy path.

[0054] Embodiment 2

[0055] As Figure 3 shown, a battery management and control device based on graph theory, based on a battery management and control method based on graph theory in Embodiment 1, includes:

[0056] Battery model establishment module: used to mathematically abstract the connection relationships and energy path characteristics of each battery cell in the target battery system based on graph theory methods to establish a battery model;

[0057] Vertex set and edge set acquisition module: used to acquire the vertex set and the edge set according to the battery model;

[0058] Weight calculation module: used to calculate the weight of each energy path in the edge set by using a battery energy path optimization algorithm according to the vertex set and the edge set to obtain the weight;

[0059] Optimal energy path acquisition module: used to sort the weights to obtain the optimal energy path.

[0060] Embodiment 3

[0061] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements a battery management and control method based on graph theory in Embodiment 1.

[0062] Embodiment 4

[0063] The present invention also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, it implements a battery management and control method based on graph theory in Embodiment 1.

[0064] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0065] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one or more of the processes Figure 1 or multiple processes and / or blocks.

[0066] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means implement the functions specified in Figure 1 one or more of the processes Figure 1 or multiple processes and / or blocks.

[0067] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one or more of the processes Figure 1 or multiple processes and / or blocks.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the specific implementation manners of the present invention can still be modified or equivalently replaced, and any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention.

Claims

1. A battery management and control method based on graph theory, characterized in that, It includes the following steps: S1. Based on the graph theory method, mathematically abstract the connection relationship of each battery unit and its energy path characteristics in the target battery system, and establish a battery model G = (P, ε, ω); S2. According to the battery model G = (P, ε, ω), obtain the vertex set P = {n1, n2, n3…n n} and the edge set ε = {ε1, ε2, ε3…ε m}; The vertex set P = {n1, n2, n3…n n} is each battery cell with an independent control function; Edge set ε = {ε1, ε2, ε3…ε m} is the connection relationship of battery cells formed under the same independent control logic, that is, the energy path from the initial battery cell to the terminal battery cell; S3. According to the vertex set P = {n1, n2, n3…n n} and the edge set ε = {ε1, ε2, ε3…ε m}, use the battery energy path optimization algorithm to calculate the weight of each energy path in the edge set ε = {ε1, ε2, ε3…ε m}, and obtain the weight ω = {ε1, ε2, ε3…ε m}; S4. Sort the weight values in the weight ω = {ε1, ε2, ε3…ε m}, so as to obtain the optimal energy path; The battery unit is a battery monomer or module on the energy path node, and its performance characteristics include remaining capacity, maximum capacity, charge and discharge cut-off voltage, and charge and discharge limiting current; The edge set ε = {ε1, ε2, ε3…ε m} and the weight ω = {ε1, ε2, ε3…ε m}, where m represents the total number of feasible remaining energy conversion paths for exhaustive search; The battery energy path optimization algorithm includes the remaining capacity control boundary condition and the electrical condition based on Kirchhoff's law; The remaining capacity control boundary condition refers to the total energy expectation and consistency expectation of the remaining capacity of each battery unit, including the following steps: Select all energy paths with a total energy greater than the energy required by the electrical system load; Judge the remaining capacity control relationship of all battery units on each energy path with a total energy greater than the energy required by the electrical system load. The energy paths where the remaining energy of each battery unit meets the remaining capacity control relationship are further screened by the electrical condition based on Kirchhoff's law; The electrical condition based on Kirchhoff's law means that the safe operating range of the battery unit voltage and current is restricted by the charge and discharge cut-off conditions; The energy paths where the sum of the currents at each node in the energy paths that meet the remaining capacity control relationship is equal to zero and the sum of the loop voltages is equal to zero meet the electrical condition based on Kirchhoff's law; According to: the remaining energy of each battery unit ≥ the average remaining capacity of all battery units on this energy path ± a preset energy consistency correction value, judge the remaining capacity control relationship of all battery units on each energy path with a total energy greater than the energy required by the electrical system load.

2. A battery management device based on graph theory, characterized in that It includes: Battery model establishment module: used to mathematically abstract the connection relationship of each battery unit and its energy path characteristics in the target battery system based on the graph theory method, and establish a battery model G = (P, ε, ω); Vertex set and edge set acquisition module: used to obtain the vertex set \(P = \{n_1, n_2, n_3,\cdots, n\}\) and the edge set \(\varepsilon=\{\varepsilon_1, \varepsilon_2, \varepsilon_3,\cdots, \varepsilon\}\) according to the battery model \(G=(P, \varepsilon, \omega)\); n The vertex set \(P = \{n_1, n_2, n_3,\cdots, n\}\) is each battery cell with independent control function; m The edge set \(\varepsilon=\{\varepsilon_1, \varepsilon_2, \varepsilon_3,\cdots, \varepsilon\}\) is the connection relationship of the battery cells formed under the same independent control logic, that is, the energy path from the initial battery cell to the terminal battery cell; n} is the connection relationship of battery cells formed under the same independent control logic, that is, the energy path from the initial battery cell to the terminal battery cell; m} is the connection relationship of the battery cells formed under the same independent control logic, that is, the energy path from the initial battery cell to the terminal battery cell; Weight calculation module: used to calculate the weights of each energy path in the edge set ε = {ε1, ε2, ε3... ε n} according to the vertex set P = {n1, n2, n3... n m}, using the battery energy path optimization algorithm, and obtain the weights ω = {ε1, ε2, ε3... ε m}; m ​ Optimal energy path acquisition module: used to sort the weights ω = {ε1, ε2, ε3…ε m}, so as to obtain the optimal energy path; The battery unit is a battery monomer or module on the energy path node, and its performance characteristics include remaining capacity, maximum capacity, charge and discharge cut-off voltage, and charge and discharge limiting current; The edge set ε = {ε1, ε2, ε3…ε m} and the weight ω = {ε1, ε2, ε3…ε m}, where m represents the total number of feasible remaining energy conversion paths for exhaustive search; The battery energy path optimization algorithm includes the remaining capacity control boundary condition and the electrical condition based on Kirchhoff's law; The remaining capacity control boundary condition refers to the total energy expectation and consistency expectation of the remaining capacity of each battery unit, including the following steps: Select all energy paths with a total energy greater than the energy required by the electrical system load; Judge the remaining capacity control relationship of all battery units on each energy path with a total energy greater than the energy required by the electrical system load. The energy paths where the remaining energy of each battery unit meets the remaining capacity control relationship are further screened by the electrical condition based on Kirchhoff's law; The electrical condition based on Kirchhoff's law means that the safe operating range of the battery unit voltage and current is restricted by the charge and discharge cut-off conditions; The energy paths where the sum of the currents at each node in the energy paths that meet the remaining capacity control relationship is equal to zero and the sum of the loop voltages is equal to zero meet the electrical condition based on Kirchhoff's law; According to: the remaining energy of each battery cell ≥ the average value of the remaining capacities of all battery cells on this energy path ± a preset energy consistency correction value, determine the remaining capacity control relationship of all battery cells on each energy path with a total energy greater than the energy required by the electrical system load.

3. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the graph theory-based battery control method described in claim 1.

4. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the graph theory-based battery control method described in claim 1.

Citation Information

Patent Citations

  • Ring type battery equalization system construction method and device

    CN117040062A

  • Battery energy balanced distribution and optimization method, device, equipment and storage medium

    CN119725825A

  • Battery data processing method and apparatus, and electronic device and storage medium

    WO2024244235A1