A battery gradient heating and charging combined optimization method suitable for low temperature environment

Abstract

The application discloses a battery gradient heating and charging combined optimization method suitable for a low-temperature environment and relates to the technical field of batteries. The method divides a low-temperature heating-charging combined control process into multiple control segments according to time, and the external heating power and the charging current of each control segment are all to-be-optimized variables; for each control segment, based on a pre-determined fast electric heating model, the external heating net temperature rise amount caused only by the external heating is obtained, and then the segmented heating efficiency index is obtained; and a constraint penalty field is constructed; the segmented heating efficiency index and the constraint penalty field are taken as the guiding information of particle swarm search, an improved particle swarm algorithm is used for iterative optimization, and the optimal segmented external heating power sequence and the optimal segmented charging current sequence are obtained. The application can avoid misjudging the self-heating of the charging current as the effective action of the external heating, and improve the safety and the optimization search efficiency of the low-temperature charging.

Description

Technical Field

[0001] This invention relates to the field of battery technology, and in particular to a combined optimization method for gradient heating and charging of batteries adapted to low-temperature environments. Background Technology

[0002] In low-temperature environments, lithium-ion batteries experience increased internal resistance and enhanced polarization, exhibiting a strong coupling relationship between external heating power, charging current, battery temperature, and state of charge. Battery temperature rise stems not only from active heating by external heaters but also from electrochemical internal heat generated by the charging current, including irreversible ohmic heat and reversible entropy heat, both of which jointly influence the battery temperature trajectory. Simultaneously, the negative electrode potential may approach or fall below the lithium metal equilibrium potential during low-temperature charging, posing a risk of lithium plating. Therefore, synergistic optimization between external heating and charging is necessary to achieve efficient and rapid low-temperature charging while ensuring both thermal and lithium plating safety.

[0003] In existing technologies, when evaluating low-temperature heating efficiency, the total temperature rise of the battery is usually used directly for evaluation. This can easily lead to the misjudgment of parasitic self-heating caused by a large charging current as the effective effect of the external heater, resulting in optimization results biased towards high-current charging schemes and increasing the risk of lithium plating in the battery.

[0004] Furthermore, existing technologies often use fixed upper limits for charging current or terminal voltage as safety constraints, which makes it difficult to accurately describe the lithium plating risk boundary that changes dynamically with the state of charge and battery temperature, and lacks constraints on the thermal safety corridor that requires the battery temperature to rise synchronously with the state of charge.

[0005] Meanwhile, conventional optimization algorithms often fail to effectively utilize segmented heating efficiency information and comprehensive safety constraint information to guide the search in low-temperature heating-charging joint optimization scenarios, resulting in low search efficiency for feasible solutions in high-dimensional non-convex constraint spaces. Summary of the Invention

[0006] The purpose of this invention is to provide a joint optimization method for battery gradient heating and charging adapted to low-temperature environments, solving the technical problems of distorted heating efficiency evaluation, inaccurate safety constraint description, and low optimization search efficiency.

[0007] In a first aspect, the present invention provides a battery gradient heating and charging joint optimization method adapted to low-temperature environments, comprising: The low-temperature heating-charging joint control process is divided into multiple control segments according to time; in each control segment, the external heating power and charging current are variables to be optimized. For each control segment, based on a predetermined fast electrothermal model, the apparent temperature rise of the battery within the control segment is calculated. Then, the electrochemical internal heat temperature rise caused by irreversible ohmic heat and reversible entropy heat is subtracted to obtain the net external heating temperature rise caused only by external heating. Based on the ratio of the net external heating temperature rise to the input energy of the external heater, the segment heating efficiency index of the control segment is obtained. Based on the pre-calibrated lithium plating risk margin surface, the lower boundary of the thermal safety corridor that increases with the state of charge, and the preset upper limit of the terminal voltage, a constraint penalty field is constructed for the control strategies corresponding to multiple control segments; wherein, the constraint penalty field includes lithium plating cumulative risk penalty, thermal safety corridor deviation penalty, and terminal voltage overrun penalty; Using the segmented heating efficiency index and the constraint penalty field as guiding information for particle swarm search, an improved particle swarm algorithm is used to iteratively optimize the external heating power and charging current of each control segment, thereby obtaining the optimal segmented external heating power sequence and the optimal segmented charging current sequence for controlling the external heater and charger.

[0008] In some preferred embodiments of the present invention, for each control segment, based on a predetermined fast electrothermal model, the apparent temperature rise of the battery within the control segment is calculated, and then the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropy heat is subtracted to obtain the net external heating temperature rise caused only by external heating. Based on the ratio of the net external heating temperature rise to the input energy of the external heater, the segmented heating efficiency index of the control segment is obtained, including: Within each control segment, calculate the apparent temperature rise of the battery between adjacent discrete time points; Based on the current charging current, ohmic internal resistance, and open-circuit voltage temperature coefficient, calculate the irreversible ohmic thermal power and the reversible entropy thermal power; multiply the sum of the irreversible ohmic thermal power and the reversible entropy thermal power by the discrete time step and divide by the cell's equivalent heat capacity to obtain the electrochemical internal heat temperature rise. Subtract the electrochemical internal heat temperature rise from the apparent temperature rise to obtain the net external heating temperature rise. The net temperature rise from external heating at all discrete time steps within the control segment is summed up and then divided by the total energy input from the external heaters within the control segment to obtain the segmented heating efficiency index of the control segment.

[0009] In some preferred embodiments of the present invention, based on a pre-calibrated lithium plating risk margin surface, a thermal safety corridor lower boundary that increases with increasing state of charge, and a preset terminal voltage upper limit, a constraint penalty field is constructed for the control strategies corresponding to multiple control segments, including: The lithium plating risk margin value at each discrete moment is obtained by using the lithium plating risk margin surface. The lithium plating risk margin values ​​that are greater than zero are multiplied by a preset temperature rise reduction factor and then summed over time to obtain the cumulative lithium plating risk value. Construct the lower boundary of the thermal safety corridor based on the state of charge trajectory, which increases with the state of charge, and calculate the deviation of the battery temperature from the lower boundary of the thermal safety corridor. The amount by which the terminal voltage exceeds the preset terminal voltage upper limit is calculated based on the terminal voltage trajectory. The constraint penalty field is obtained by multiplying the cumulative risk value of lithium plating, the deviation of the lower boundary of the thermal safety corridor, and the overstepping of the upper limit of the terminal voltage by their respective penalty weights.

[0010] In some preferred embodiments of the present invention, the particle swarm optimization algorithm is improved, including: Based on a pre-built historical pattern library and segmented heating efficiency index, heuristic particle swarm initialization is performed; Particle velocity and position are updated using segmented efficiency-aware dimensional inertial weights and lithium plating potential field repulsion terms. Perform a two-mode mutation refinement on the elite particle to generate candidate new positions for the elite particle. If the fitness of the candidate new position is better than that of the original elite particle position, then replace the original elite particle position with the candidate new position.

[0011] In some preferred embodiments of the present invention, heuristic particle swarm initialization is performed based on a pre-built historical pattern library and a segmented heating efficiency index, including: Match similar historical successful control strategies from the historical pattern library based on the current operating condition label; For the external heating power dimension, the benchmark heating power corrected by the segmented heating efficiency index is used as the sampling center for truncated normal sampling; For the charging current dimension, the initial value is generated by superimposing random disturbances on the charging current of the corresponding segment in the historical successful control strategy as a reference value. If the terminal voltage constraint and lithium plating risk constraint are not met, the charging current is gradually reduced until the safety conditions are met.

[0012] In some preferred embodiments of the present invention, the dimensional inertia weight is obtained by mapping according to the segmented heating efficiency index; wherein, the inertia weight obtained by the low-efficiency segment is greater than the inertia weight obtained by the high-efficiency segment. The lithium plating potential field repulsion term is constructed by the finite difference gradient of the cumulative lithium plating risk value on the decision variable, so that the particle obtains a velocity correction amount away from the lithium plating risk direction when it is close to the lithium plating risk region.

[0013] In some preferred embodiments of the present invention, dual-mode mutation refining includes: Based on the dimensional efficiency index, the Levy flight continuous perturbation generates the first candidate new position of the elite particle, and the low-efficiency dimension obtains a larger perturbation amplitude. With a preset segment replacement probability, a continuous time segment is selected from the historical pattern library, and the external heating power and charging current of the corresponding continuous control segment in the elite particle are replaced with the external heating power and charging current of the corresponding control segment in the continuous time segment to generate the second candidate new position of the elite particle; wherein, the continuous time segment includes the external heating power and charging current of at least one control segment. Boundary correction, rate of change correction, and augmented fitness evaluation are performed on the first and second candidate new positions, respectively. If the fitness of any candidate new position is better than that of the original elite particle position, the original elite particle position is replaced by the candidate new position with the best fitness.

[0014] In some preferred embodiments of the present invention, the rapid electrothermal model adopts a single-node lumped heat capacity model, and obtains the open-circuit voltage, open-circuit voltage temperature coefficient, and ohmic internal resistance under the current state from a pre-calibrated parameter table through piecewise linear interpolation, and calculates the battery temperature, state of charge, and terminal voltage according to the following recursive formula: ; ; ; in, Let be the battery temperature at the (k+1)th discrete time. Let be the battery temperature at the k-th discrete time. For discrete time steps, The equivalent heat capacity of the battery cell, External heating power, This is the charging current. The internal resistance in ohms is obtained by looking up a table based on battery temperature and charging current direction. The open-circuit voltage temperature coefficient is obtained by looking up a table based on the state of charge and battery temperature. The convective heat transfer coefficient is... For effective heat dissipation area, For ambient temperature, For surface emissivity, The Stefan-Boltzmann constant is... This is the fourth-power temperature difference between the battery temperature and the ambient temperature. For the first State of charge at discrete moments, For the first State of charge at discrete moments, This refers to the battery's nominal capacity. For the first Terminal voltage at discrete moments Open circuit voltage, For current Direction markers.

[0015] In some preferred embodiments of the present invention, the method further includes: The optimal segmented external heating power sequence and the optimal segmented charging current sequence are sent to the external heater and charger; Real-time acquisition of battery temperature, terminal voltage, and charging current, and correction of state of charge based on real-time acquisition results; If the difference between the real-time terminal voltage and the preset terminal voltage upper limit is less than the preset voltage threshold, or if the real-time battery temperature is lower than the lower boundary of the thermal safety corridor, then adjust the charging current or external heating power. Using a scrolling window approach, the real-time state is used as the new initial state to regenerate the optimized control strategy for the remaining time period.

[0016] In some preferred embodiments of the present invention, before dividing the low-temperature heating-charging combined control process into multiple control segments according to time, the method further includes: Collect heating-charging joint control samples with different combinations of external heating power and charging current under low temperature environment; Calibrate open-circuit voltage two-dimensional table, open-circuit voltage temperature coefficient two-dimensional table, ohmic internal resistance parameter table, heat transfer parameters and lithium plating risk margin surface; Control strategies that meet safety conditions are selected from the samples to build a historical pattern library.

[0017] This invention brings the following beneficial effects: This invention provides a joint optimization method for gradient heating and charging of batteries adapted to low-temperature environments. By subtracting the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropic heat from the apparent temperature rise of the battery, a segmented heating efficiency index reflecting only the external heating effect is extracted. This avoids misjudging parasitic self-heating caused by charging current as the effective effect of the external heater, thus making the heating efficiency evaluation more accurate. By integrating the lithium plating risk margin surface, the lower boundary of the thermal safety corridor, and the preset terminal voltage upper limit into a constraint penalty field, the optimization process can simultaneously perceive the triple safety boundaries of lithium plating risk, insufficient temperature, and voltage overshoot, improving the safety of low-temperature charging. By using the segmented heating efficiency index and the constraint penalty field as guiding information for particle swarm search, and employing an improved particle swarm algorithm for iterative optimization, the search stability and feasible solution ratio can be improved in a high-dimensional non-convex constraint space, ultimately obtaining a low-temperature heating-charging joint control strategy that balances safety, energy consumption, and charging time. Attached Figure Description

[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 A flowchart of a battery gradient heating and charging joint optimization method adapted to low-temperature environments provided in an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the segmented heating efficiency index extraction based on electrochemical internal thermal disturbance, provided in an embodiment of the present invention. Figure 3 A schematic diagram of a rapid reconstruction of low-temperature electrothermal response based on lumped thermal resistance network and piecewise linearization is provided for an embodiment of the present invention. Figure 4 A schematic diagram of the generation of a constraint penalty field that integrates a lithium plating risk margin surface and a thermal safety corridor, provided for an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the online execution of a low-temperature heating-charging combined control strategy provided in an embodiment of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0022] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0023] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0024] Furthermore, terms such as "horizontal," "vertical," and "sag" do not imply that components must be absolutely horizontal or suspended, but rather that they can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0025] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0026] In low-temperature environments, lithium-ion batteries experience increased internal resistance and enhanced polarization, exhibiting a strong coupling relationship between external heating power, charging current, battery temperature, and state of charge (SOC). Battery temperature rise stems not only from active heating by external heaters but also from electrochemical internal heat generated by the charging current, including irreversible ohmic heat and reversible entropy heat, both of which jointly influence the battery temperature trajectory. Simultaneously, the negative electrode potential may approach or fall below the lithium metal equilibrium potential during low-temperature charging, posing a risk of lithium plating. Therefore, synergistic optimization between external heating and charging is necessary to achieve efficient and rapid low-temperature charging while ensuring thermal and lithium plating safety. Current technologies typically evaluate low-temperature heating efficiency directly using the total battery temperature rise, which can easily misjudge parasitic self-heating caused by large charging currents as the effective effect of external heaters. This leads to optimization results biased towards high-current charging schemes, increasing the risk of lithium plating. Furthermore, existing technologies often employ fixed upper limits for charging current or terminal voltage as safety constraints, making it difficult to accurately describe the lithium plating risk boundary that dynamically changes with SOC and battery temperature, and lacking constraints on the thermal safety corridor that requires the battery temperature to rise synchronously with the SOC. Conventional optimization algorithms typically employ random initialization in low-temperature heating-charging joint optimization scenarios and use the same search parameters for all control segments. They cannot inherit verified safety control strategies and do not distinguish the differences in heating efficiency and safety costs among different control segments, resulting in low search efficiency for feasible solutions in high-dimensional non-convex constraint spaces.

[0027] This invention extracts a segmented heating efficiency index that reflects only the effect of external heating by subtracting the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropic heat from the apparent temperature rise of the battery. This avoids misjudging parasitic self-heating caused by charging current as the effective effect of the external heater, thus making the heating efficiency evaluation more accurate. By integrating the lithium plating risk margin surface, the lower boundary of the thermal safety corridor, and the preset terminal voltage upper limit into a constraint penalty field, the optimization process can simultaneously perceive the triple safety boundaries of lithium plating risk, insufficient temperature, and voltage overrun, improving the safety of low-temperature charging. By using the segmented heating efficiency index and the constraint penalty field as guiding information for particle swarm search and using an improved particle swarm algorithm for iterative optimization, the search stability and feasible solution ratio can be improved in a high-dimensional non-convex constraint space, ultimately obtaining a low-temperature heating-charging joint control strategy that takes into account safety, energy consumption, and charging time.

[0028] The following detailed description of some embodiments of the present invention is provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0029] This invention provides a joint optimization method for battery gradient heating and charging adapted to low-temperature environments. See [link to relevant documentation]. Figure 1 The flowchart shown in this embodiment of the invention provides a joint optimization method for battery gradient heating and charging adapted to low-temperature environments. The method includes: Step S102: The heat-charging joint control process is divided into multiple control segments according to time; wherein, the external heating power and charging current of each control segment are variables to be optimized.

[0030] Specifically, the low-temperature heating-charging joint control process refers to the complete control process of a lithium-ion battery under the combined action of external heating and charging in a low-temperature environment. Dividing the low-temperature heating-charging joint control process into multiple control segments according to time aims to discretize the continuous control process into several time intervals, facilitating the determination of external heating power and charging current for each time interval in subsequent optimization. In this embodiment, the total number of control segments is denoted as S, which is determined based on the total control duration and the required control granularity, and can be between 10 and 50. The start time of the s-th control segment is denoted as... The termination time of the s-th control segment is denoted as . , This represents the duration of the s-th control segment. When s=1, This indicates the start time of the entire cryogenic heating-charging combined control process, which can be taken as... =0 seconds. For example, if the total duration of the low-temperature heating-charging combined control is 600 seconds, and the total number of control segments is 10, then... =0 seconds, =600 seconds, with each control segment lasting 60 seconds.

[0031] In this embodiment, according to the discrete time step The collected data is discretized to obtain the external heating power at the k-th discrete time. Charging current Battery temperature Terminal voltage and state of charge .in, This refers to the time interval between adjacent discrete moments, in seconds, which can be 1 second; k represents the discrete moment index, k=0,1,…,K; K represents the number of discrete simulation steps in a single low-temperature heating-charging joint control process, which can be the total control time and the sampling step size. The ratio, i.e. . This represents the external heating power at the k-th discrete time point, in watts. The charging current at the k-th discrete moment is expressed in amperes. In this embodiment, a positive charging current indicates an increase in the state of charge of the lithium-ion battery. This represents the battery temperature at the k-th discrete time, in Kelvin. This represents the terminal voltage at the k-th discrete moment, in volts. This represents the state of charge (SOC) at the k-th discrete time, characterizing the proportion of the remaining capacity of the lithium-ion battery to its nominal capacity. It is dimensionless and ranges from 0 to 1. In one implementation, the SOC... The state of charge (SOC) can be obtained through ampere-hour integration and initialized before the experiment using the resting open-circuit voltage or the battery management system's estimate. If charging current sampling noise exists during the experiment, the charging current can be low-pass filtered before performing ampere-hour integration to avoid transient noise causing fluctuations in the SOC trajectory. It should be noted that ampere-hour integration is a method for estimating the SOC by accumulating charge, assuming the initial SOC is known. Then, the charging current in each discrete time step is... Integrating (accumulating) the total charged amount, and then dividing by the battery's nominal capacity, yields the current state of charge (SOC). Its discretized calculation method is expressed as follows: ,in, This represents the state of charge at the (k+1)th discrete time. This indicates the battery's nominal capacity, measured in ampere-seconds; charging current. A positive value corresponds to an increase in the state of charge.

[0032] In this embodiment, the external heating power and charging current of each control segment are variables to be optimized, meaning that the position vector of each particle in the subsequent improved particle swarm optimization algorithm is composed of the external heating power components and charging current components of all control segments. The cryogenic heating-charging joint control strategy to be evaluated is defined as the control strategy vector X, where X refers to the sequence of segmented external heating power... and segmented charging current sequence The decision variable vector is composed of... .in, This represents the external heating power of the s-th control segment, in watts. Let represent the charging current of the s-th control segment, in amperes. If the k-th discrete time step belongs to the s-th control segment, then let . and order This transforms the control strategy vector X into a discrete simulation input for the fast electrothermal model.

[0033] Furthermore, in some preferred embodiments of the present invention, before dividing the low-temperature heating-charging joint control process into multiple control segments according to time, the method further includes: collecting heating-charging joint control samples with different combinations of external heating power and charging current under low-temperature conditions; calibrating the two-dimensional table of open-circuit voltage, the two-dimensional table of open-circuit voltage temperature coefficient, the table of ohmic internal resistance parameters, heat transfer parameters, and the lithium plating risk margin surface; and screening control strategies that meet safety conditions from the samples to construct a historical pattern library.

[0034] Specifically, under low-temperature conditions, the internal resistance of lithium-ion batteries increases and polarization intensifies, and there is a strong coupling relationship between external heating power, charging current, battery temperature, and state of charge. This embodiment first collects samples of low-temperature heating-charging joint control, and then establishes an electrothermal parameter table, a lithium plating risk margin surface, and a historical pattern library, providing a directly callable data foundation for subsequent control strategy optimization.

[0035] Temperature, voltage, current, and state of charge (SOC) data of lithium-ion batteries under different low-temperature conditions and combined external heating and charging were collected to form a low-temperature heating-charging joint control sample set. This sample set was used to calibrate the rapid electrothermal model, extract the segmented heating efficiency index, verify the lithium plating risk margin surface, and construct a historical pattern library. Lithium-ion batteries, battery surface temperature sensors, ambient temperature sensors, external heaters, chargers, and data acquisition devices were deployed in a constant temperature chamber or low-temperature environment chamber, and heating-charging joint experiments were performed under multiple low-temperature conditions. The ambient temperature is denoted as... , This refers to the temperature of the low-temperature environment surrounding a lithium-ion battery, measured in Kelvin; battery temperature is denoted as Kelvin. , Refers to time The equivalent average temperature of the lithium-ion battery body, measured in Kelvin; external heating power is denoted as... , Refers to time The heating power input to the lithium-ion battery from the external heater, measured in watts; the charging current is denoted as... , Refers to time The input charging current for the lithium-ion battery, in this embodiment, a positive charging current indicates an increase in the state of charge of the lithium-ion battery, and the unit is amperes; the terminal voltage is denoted as... , Refers to time The voltage between the positive and negative terminals of a lithium-ion battery, measured in volts.

[0036] The battery temperature can be obtained by weighting the measurements from multiple surface temperature sensors. If the sensor output is in Celsius, it is first converted to Kelvin before relevant calculations are performed. Using multiple temperature sensors, the temperatures near the tab area, the middle of the casing, and the heating contact area can be collected separately, and then a weighted average can be taken as the battery temperature T(τ), reducing local deviations caused by single-point temperature measurements. The sampling frequency can be from 1 Hz to 10 Hz, and a higher sampling frequency can be used in rapidly changing pulse heating experiments. In one embodiment, as an example, if the temperature sensor readings at the battery tab, the middle of the casing, and the heating contact surface are 263.65 Kelvin (i.e., -9.5 degrees Celsius), 263.15 Kelvin (i.e., -10.0 degrees Celsius), and 263.35 Kelvin (i.e., -9.8 degrees Celsius), respectively, and the preset weighting coefficients are 0.2, 0.5, and 0.3, then the battery temperature at that moment is... Kelvin (i.e. -9.84 degrees Celsius).

[0037] The combined heating-charging experiment involves simultaneously acquiring electrical and thermal response data of lithium-ion batteries under different combinations of external heating power and charging current in a controlled low-temperature environment. First, the lithium-ion battery is placed in a low-temperature chamber and left to stand for a sufficient time to allow the battery temperature to reach equilibrium with the ambient temperature. Then, the data acquisition device is activated to record the initial battery temperature, terminal voltage, and state of charge (SOC). Next, according to a preset heating-charging control curve, the external heater and charger are simultaneously activated. Throughout the heating-charging process, the data acquisition device records the ambient temperature, readings from various surface temperature sensors, external heating power, charging current, terminal voltage, and timestamps at a fixed sampling frequency. The experiment continues until the battery SOC reaches the target value, the total charging time ends, or safety protection conditions are triggered (such as battery temperature exceeding limits or terminal voltage exceeding limits), at which point heating and charging are stopped. The acquired electrical and environmental parameters constitute a complete heating-charging combined control sample.

[0038] The data obtained from each low-temperature heating-charging combined experiment were combined to form a low-temperature heating-charging combined control sample. Multiple low-temperature heating-charging joint control samples were combined to form a low-temperature heating-charging joint control sample set. Where n represents the sample index, N represents the total number of samples under the combined low-temperature heating-charging control, which can be 50 to 200. This represents the nth low-temperature heating-charging joint control sample, including the ambient temperature trajectory, external heating power trajectory, charging current trajectory, battery temperature trajectory, terminal voltage trajectory, state of charge trajectory, initial battery temperature, initial state of charge, and target state of charge; This refers to a dataset consisting of different low-temperature environments, different initial battery temperatures, different initial states of charge, and different heating-charging control curves. The low-temperature heating-charging joint control sample set should cover typical low-temperature operating conditions, such as 253.15 Kelvin (i.e., -20 degrees Celsius), 263.15 Kelvin (i.e., -10 degrees Celsius), and 273.15 Kelvin (i.e., 0 degrees Celsius), as well as different initial state of charge ranges, so that the optimization strategy is not limited to a single low-temperature condition.

[0039] Regarding the calibration of the electrothermal parameter table, a constant-temperature static test was performed at multiple state of charge points and multiple battery temperature points to obtain a two-dimensional table of open-circuit voltage. , Open-circuit voltage (OCV) refers to the open-circuit voltage of a lithium-ion battery when its state of charge (SOC) is z and its temperature is T. It characterizes the equilibrium potential of a lithium-ion battery in a state of no current or near-no current, and is measured in volts (V). SOC sampling points can be 0.1, 0.2, 0.3, ..., 0.9, and battery temperature sampling points can be 253.15 Kelvin (-20°C), 263.15 Kelvin (-10°C), 273.15 Kelvin (0°C), 283.15 Kelvin (10°C), and 298.15 Kelvin (25°C). The rate of change of open-circuit voltage with respect to battery temperature is calculated between adjacent battery temperature points to obtain a two-dimensional table of open-circuit voltage temperature coefficient. , Entropy coefficient refers to the partial derivative of the open-circuit voltage with respect to the battery temperature when the state of charge is z and the battery temperature is T. It is also called the entropy coefficient and is used to characterize the direction and magnitude of the reversible entropy-heat of an electrochemical reaction. Its unit is volts per Kelvin. In one embodiment, as an example, if the battery temperature is measured at the state of charge z = 0.5... Open circuit voltage at Kelvin (i.e., 0 degrees Celsius) Fu, Open circuit voltage at Kelvin (i.e., 10 degrees Celsius) The open-circuit voltage temperature coefficient in this range is... Vol. Kelvin.

[0040] By applying short-time pulsed currents under different battery temperatures and current directions, the ohmic internal resistance parameters are identified based on the voltage changes before and after the pulse. , This refers to a battery temperature of T and a current direction of [missing information]. The equivalent ohmic resistance at time t is expressed in ohms. The current direction marker is used to distinguish between charging and discharging directions. This method assumes the charging current direction is positive, and low-temperature charging optimization mainly utilizes the ohmic internal resistance corresponding to the charging direction. In practice, a pulse charging current of 5 to 10 seconds can be applied after the battery temperature stabilizes. The voltage transition at the start of the pulse is read, and the ohmic internal resistance is obtained by dividing the voltage transition by the pulse current. The ohmic internal resistance changes significantly with battery temperature at low temperatures. For example, the charging direction ohmic internal resistance might be calibrated as 75 milliohms at 263.15 Kelvin (i.e., -10 degrees Celsius), and as 45 milliohms at 273.15 Kelvin (i.e., 0 degrees Celsius). Using a table of ohmic internal resistance parameters for different temperatures avoids underestimating ohmic heat and voltage rise during low-temperature charging optimization.

[0041] Heat transfer parameters are obtained through natural cooling experiments, constant power heating experiments, or parameter identification methods. These parameters include the equivalent heat capacity of the battery cell. The convective heat transfer coefficient h, effective heat dissipation area A, and surface emissivity ε are also mentioned. Among these, the equivalent heat capacity of the battery cell is also considered. This term represents the amount of heat required to raise the temperature of a lithium-ion battery by 1 Kelvin, measured in joules per Kelvin (J / K). Here, m represents the cell mass in kilograms. The equivalent specific heat capacity of the battery cell is expressed in joules per kilogram per Kelvin; the convective heat transfer coefficient h characterizes the intensity of convective heat transfer between the lithium-ion battery surface and the ambient air, expressed in watts per square meter per Kelvin; the effective heat dissipation area A represents the equivalent area of ​​heat exchange between the lithium-ion battery and the environment, expressed in square meters; and the surface emissivity ε characterizes the ability of the lithium-ion battery surface to emit thermal radiation, and is dimensionless. These heat transfer parameters are not fixed theoretical constants, but are related to the battery pack structure (e.g., cell size, module structure, insulation materials) and the installation method of the external heater, and should preferably be obtained through calibration using actual equipment.

[0042] Establishing a lithium plating risk margin surface , This refers to the lithium plating risk margin value, measured in volts, when the state of charge (SOC) is z, the battery temperature is T, and the charging current is I. A lithium plating risk margin value greater than 0 indicates that the negative electrode potential has entered the lithium plating risk zone, while a value less than or equal to 0 indicates that the negative electrode potential still has a safety margin. In one implementation, the negative electrode potential against lithium is first obtained under different SOCs, battery temperatures, and charging currents through low-temperature constant current charging experiments, three-electrode battery tests, or offline electrochemical model simulations. Then, the threshold value of the negative electrode potential against lithium below 0 volts is used as the lithium plating risk margin value, forming a three-dimensional interpolation surface with SOC, battery temperature, and charging current as inputs and the lithium plating risk margin value as the output. If the negative electrode potential against lithium is 0.03 volts, the operating condition still has a safety margin, and the lithium plating risk margin value can be set to -0.03 volts; if the negative electrode potential against lithium is -0.02 volts, the operating condition has crossed the lithium plating boundary, and the lithium plating risk margin value can be set to 0.02 volts. Based on this, it is possible to directly determine whether to enter the lithium plating risk zone based on the positive or negative value of the lithium plating risk margin.

[0043] This embodiment compiles the safety-verified cryogenic heating-charging joint control curves into a historical pattern library. This library is used for particle swarm initialization and elite mutation processes, enabling the optimization algorithm to inherit verified safe heating-charging control strategies and reducing infeasible control strategies caused by completely random search. Regarding the construction of the historical pattern library, it is derived from the cryogenic heating-charging joint control sample set. Samples that meet safety conditions are selected, and the corresponding external heating power trajectory and charging current trajectory are stored in the historical pattern library. Historical pattern library This refers to a dataset composed of multiple sets of historical successful control strategies. Each set of historical successful control strategies includes ambient temperature, initial battery temperature, initial state of charge (SOC), target SOC, allowable charging time, external heating power curve, charging current curve, final external heating energy consumption, final SOC, and safety verification results. Safety conditions include terminal voltage not exceeding the terminal voltage limit, battery temperature not exceeding the maximum allowable temperature, and the lithium plating risk margin not showing a positive value or the cumulative lithium plating risk value being lower than the preset limit. For example, if a historical sample, although having a short charging time, shows a significant positive lithium plating risk margin in the early stages of low temperature, then that historical sample will not be stored in the historical pattern library as a historical successful control strategy. The values ​​of the terminal voltage limit, maximum allowable temperature, and cumulative lithium plating risk limit are given by the battery datasheet and safety design documents. For example, the terminal voltage limit can be 4.2 volts, the maximum allowable temperature can be 318.15 Kelvin (i.e., 45 degrees Celsius), and the cumulative lithium plating risk limit can be 0.

[0044] For historical pattern library Each group of historical successful control strategies is assigned a condition label. These labels are used to quickly identify historical successful control strategies similar to the current task during initialization. The condition label for the b-th group of historical successful control strategies is denoted as... , This refers to a task description vector composed of ambient temperature, initial battery temperature, initial state of charge (SBC), target SBC, and allowed charging time, with a dimension of 5; 'b' represents the index of historical successful control strategies. In one implementation, min-max normalization is first performed on each variable in the operating condition label, mapping all variable values ​​to the [0,1] interval. Then, the weighted distance between the current operating condition and all successful control strategy operating condition labels in the historical pattern library is calculated to find the historical successful control strategy closest to the current operating condition. Since the initial battery temperature and initial SBC have a more significant impact on low-temperature lithium plating risk, heating requirements, and charging acceptance, these two variables can be assigned higher weights. For example, the weight of the initial battery temperature can be 0.3, the weight of the initial SBC can be 0.3, and the weights of the ambient temperature, target SBC, and allowed charging time can each be 0.1. Through weighted operating condition label matching, the erroneous migration of historical charging curves under high temperature or high SBC conditions to low temperature and low SBC tasks can be avoided. In one embodiment, as an example, if the ambient temperature weight is 0.1, the initial battery temperature weight is 0.3, the initial state of charge weight is 0.3, the target state of charge weight is 0.1, and the allowable charging time weight is 0.1, then the current task's condition label after min-max normalization is... The working condition label of a certain historical strategy after min-max normalization is: The weighted distance between the two is calculated to be... .

[0045] This invention provides a directly callable data foundation for subsequent optimization by constructing a historical pattern library, including the parameters required for the rapid electrothermal model, the criteria for judging lithium plating risk, and historical successful control strategy templates, supporting the implementation of the subsequently determined rapid electrothermal model, the pre-calibrated lithium plating risk margin surface, and the pre-constructed historical pattern library.

[0046] Step S104: For each control segment, based on a predetermined fast electrothermal model, calculate the apparent temperature rise of the battery within the control segment, and then subtract the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropy heat to obtain the net external heating temperature rise caused only by external heating. Based on the ratio of the net external heating temperature rise to the input energy of the external heater, obtain the segmented heating efficiency index of the control segment.

[0047] Specifically, when lithium-ion batteries are subjected to combined external heating and charging control in low-temperature environments, the battery temperature rise comes not only from the external heater but also from irreversible ohmic heat and reversible entropy heat caused by the charging current. If the total temperature rise is directly used to evaluate the external heating efficiency, it is easy to misjudge the parasitic self-heating caused by the large charging current as the effective influence of the external heater, leading to an optimization process biased towards high-current charging schemes, increasing the risk of low-temperature lithium plating and accelerated aging. This embodiment separates electrochemical internal heat disturbances through a rapid electrothermal model and extracts the segmented heating efficiency index affected only by the external heating power, enabling particle swarm optimization to identify high-efficiency heating regions. This embodiment first estimates the impact of electrochemical internal heat on the battery temperature rise based on the external heating power, charging current, and battery temperature trajectory. Then, it subtracts the electrochemical internal heat influence from the temperature rise reconstructed from the rapid electrothermal model to obtain the net external heating temperature rise caused by the external heating power. Finally, it calculates the segmented heating efficiency index for each control segment, thereby avoiding the misjudgment of charging current self-heating as heating system efficiency.

[0048] The rapid electrothermal model is a simplified model established to quickly evaluate control strategies during optimization iterations. Based on the assumption of single-node lumped heat capacity, it uses a pre-calibrated electrothermal parameter table and heat transfer parameters to quickly calculate the battery temperature, state of charge, and terminal voltage response under a given control strategy using algebraic recursion, avoiding the solution of complex partial differential equations. Single-node lumped heat capacity refers to treating the entire battery as a point mass with a uniform temperature distribution and only the equivalent heat capacity of a single cell, ignoring the internal temperature gradient and requiring only the battery temperature to describe its thermal state. In some preferred embodiments of this invention, the rapid electrothermal model can also employ a two-node lumped heat capacity model, dividing the battery into internal cell nodes and external casing nodes, establishing separate thermal balance equations to describe the temperature difference between the battery's interior and surface, suitable for scenarios with larger battery sizes or higher heating power.

[0049] Furthermore, in some preferred embodiments of the present invention, for each control segment, based on a predetermined fast electrothermal model, the apparent temperature rise of the battery within the control segment is calculated, and then the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropy heat is subtracted to obtain the net external heating temperature rise caused only by external heating. Based on the ratio of the net external heating temperature rise to the input energy of the external heater, the segmented heating efficiency index of the control segment is obtained, including: within each control segment, calculating the apparent temperature rise of the battery between adjacent discrete moments; Based on the current charging current, ohmic internal resistance, and open-circuit voltage temperature coefficient, calculate the irreversible ohmic thermal power and the reversible entropy thermal power; multiply the sum of the irreversible ohmic thermal power and the reversible entropy thermal power by the discrete time step and divide by the cell's equivalent heat capacity to obtain the electrochemical internal heat temperature rise; subtract the electrochemical internal heat temperature rise from the apparent temperature rise to obtain the external heating net temperature rise; accumulate the external heating net temperature rise of all discrete time steps within the control segment, and then divide by the total energy input to the external heaters within the control segment to obtain the segmented heating efficiency index of the control segment.

[0050] For details, see Figure 2 The illustrated embodiment of the present invention provides a schematic diagram of segmented heating efficiency index extraction based on electrochemical internal thermal perturbation. The low-temperature heating-charging joint control process to be analyzed is segmented, and the control segment to which each discrete moment belongs is determined. The set of discrete moments corresponding to the s-th control segment is denoted as... , Refers to the start time Until the end time The set of indices of all discrete times in between; if the k-th discrete time belongs to the s-th control segment, then Battery temperature was read from a low-temperature heating-charging joint control sample. Charging current External heating power Ohmic internal resistance and open-circuit voltage temperature coefficient .in, This represents the equivalent ohmic internal resistance at the k-th discrete moment, obtained by looking up a table based on the current battery temperature and current direction. This represents the open-circuit voltage temperature coefficient at the k-th discrete moment, obtained by looking up a table based on the current state of charge and current battery temperature. By reading parameters at discrete moments, the nonlinear characteristics of the ohmic internal resistance and entropy thermal coefficient as a function of battery temperature and state of charge under low-temperature conditions can be preserved.

[0051] Within the s-th control segment, the battery temperature change at adjacent discrete time steps is progressively decomposed. First, the apparent temperature rise is calculated, then the electrochemical internal heat temperature rise is calculated, and finally, the net external heating temperature rise is obtained. The apparent temperature rise refers to the actual increase in battery temperature between adjacent discrete time steps; the electrochemical internal heat temperature rise refers to the temperature rise caused by irreversible ohmic heat and reversible entropy heat within that discrete time step; the net external heating temperature rise refers to the temperature rise affected by external heating power after deducting the electrochemical internal heat disturbance. In one implementation, first use... To obtain the apparent temperature rise at the k-th discrete time step, use... To calculate the irreversible ohmic heat power at the k-th discrete time, use... Calculate the reversible entropy heat power at the k-th discrete time step; then multiply the sum of the irreversible ohmic heat power and the reversible entropy heat power by... and divide by We obtain the electrochemical internal heat temperature rise at the k-th discrete time step; finally, we subtract the electrochemical internal heat temperature rise from the apparent temperature rise to obtain the net external heating temperature rise at the k-th discrete time step.

[0052] The formula for calculating the electrochemical internal heat temperature rise is: ; in, For discrete time steps, The equivalent heat capacity of the battery cell, Let be the charging current at the k-th discrete time. Let be the ohmic internal resistance at the k-th discrete time. Let be the battery temperature at the k-th discrete time. Let be the open-circuit voltage temperature coefficient at the k-th discrete time.

[0053] The net temperature rise from external heating is obtained by summing up the net temperature rise from external heating for all discrete time steps within the s-th control segment. The calculation method is expressed as follows: ; in, This represents the net temperature rise due to external heating in the s-th control segment, referring to the battery temperature rise affected by external heating power after deducting electrochemical internal thermal disturbances. If reversible entropy heat is endothermic in a certain state of charge range, then... The value is negative, and it is directly used in the calculation to ensure that the electrochemical internal heat subtraction result is consistent with the actual electrochemical reaction direction.

[0054] In one embodiment, for example, if the apparent temperature rise is within a certain control segment... It is 2.0 Kelvin. Second, =1000 joules per Kelvin; Ohm heat at all times The total is 500 joules, and the reversible entropy heat is present at all times. The total sum is -100 J (manifesting as endothermic); therefore, the total electrochemical internal heat rise is Kelvin; then the net temperature rise due to external heating of that segment. Kelvin.

[0055] First, the external heating power within the s-th control segment is accumulated over time to obtain the external heating input energy of the s-th control segment. ,Right now Then divide the net temperature rise of external heating by the external heating input energy to obtain the segmented heating efficiency index of the s-th control segment. ,Right now .in, This refers to the total actual heat input to the internal and external heaters of the s-th control segment, in joules; This refers to the net temperature rise effect of external heating caused by a unit of external heating input energy within the s-th control segment. The larger the value, the more effective the external heating power is in raising the temperature of the lithium-ion battery body within the control segment. The unit is Kelvin per joule.

[0056] The calculations of net external heating temperature rise, external heating input energy, and segment heating efficiency index are repeated for all control segments. All segment heating efficiency indices are then arranged in order of control segment number to obtain a segment heating efficiency index sequence. , t is due to The efficiency characteristic sequence is used to characterize the actual performance differences of the external heating system under different battery temperatures and different states of charge. Furthermore, the segmented heating efficiency index sequence... By performing lower bound truncation and min-max normalization, a normalized piecewise heating efficiency index sequence is obtained. Normalized piecewise heating efficiency index sequence All elements are in the range of 0 to 1. When the battery temperature in a certain control segment experiences a net drop due to strong heat dissipation, It can be a negative value. In this case, the corresponding segmented heating efficiency index is truncated to 0 or normalized to a preset stable range, which can avoid negative efficiency values ​​interfering with particle velocity updates.

[0057] This embodiment isolates the irreversible ohmic heat and reversible entropic heat caused by the charging current from the total temperature rise of the battery, and obtains a segmented heating efficiency index that only reflects the actual effect of the external heater. This avoids misjudging the self-heating of the charging current as the effective effect of external heating, prevents the optimization process from being biased towards high-current charging schemes, and reduces the risk of low-temperature lithium plating.

[0058] Furthermore, in some preferred embodiments of the present invention, the rapid electrothermal model adopts a single-node lumped heat capacity model, and obtains the open-circuit voltage, open-circuit voltage temperature coefficient, and ohmic internal resistance under the current state from a pre-calibrated parameter table through piecewise linear interpolation, and calculates the battery temperature, state of charge, and terminal voltage according to the following recursive formula: ; ; ;in, Let be the battery temperature at the (k+1)th discrete time. Let be the battery temperature at the k-th discrete time. For discrete time steps, The equivalent heat capacity of the battery cell, External heating power, This is the charging current. The internal resistance in ohms is obtained by looking up a table based on battery temperature and charging current direction. The open-circuit voltage temperature coefficient is obtained by looking up a table based on the state of charge and battery temperature. The convective heat transfer coefficient is... For effective heat dissipation area, For ambient temperature, For surface emissivity, The Stefan-Boltzmann constant is... This is the fourth-power temperature difference term between the battery temperature and the ambient temperature, used to characterize the driving force of radiative heat transfer. For the first State of charge at discrete moments, For the first State of charge at discrete moments, This refers to the battery's nominal capacity. For the first Terminal voltage at discrete moments Open circuit voltage, For current Direction markers.

[0059] For details, see Figure 3 The illustrated embodiment of the present invention provides a schematic diagram of rapid reconstruction of low-temperature electrothermal response based on a lumped thermal resistance network and piecewise linearization. The rapid electrothermal model uses single-node lumped heat capacity to describe the thermal behavior of a lithium-ion battery, and employs open-circuit voltage lookup tables, ohmic internal resistance lookup tables, open-circuit voltage temperature coefficient lookup tables, and state of charge recursion to describe the electrical behavior. Piecewise linear interpolation preserves the nonlinear characteristics of battery parameters changing with battery temperature and state of charge under low-temperature conditions. This embodiment, by constructing a rapid electrothermal model, can quickly evaluate the battery temperature trajectory, state of charge trajectory, and terminal voltage trajectory corresponding to different external heating power sequences and charging current sequences during optimization iterations.

[0060] At the k-th discrete time, based on the current state of charge Current battery temperature and current charging current Piecewise linear interpolation was used to obtain the open-circuit voltage from a two-dimensional table. Two-dimensional table of open-circuit voltage temperature coefficient And Ohmic internal resistance parameter table The parameter values ​​under the current state are read from the table. Piecewise linear interpolation refers to first finding the adjacent grid points surrounding the current state of charge and the current battery temperature in the parameter table, and then linearly weighting them according to the distance between the current point and the adjacent grid points to obtain the parameter values ​​under the current operating condition. In one embodiment, as an example, if the current state of charge... The current battery temperature is between 0.40 and 0.50. If the open-circuit voltage is located between 263.15 Kelvin (i.e., -10 degrees Celsius) and 273.15 Kelvin (i.e., 0 degrees Celsius), the open-circuit voltage at the intersection of these four grid points is first taken, and then linearly weighted along the direction of charge state and battery temperature to obtain the current open-circuit voltage. Similarly, by looking up the ohmic internal resistance parameter table based on the current battery temperature and charging current direction, the current ohmic internal resistance can be obtained. .

[0061] Based on the external heating power, charging current, battery temperature, state of charge, and lookup table parameters at the k-th discrete time step, the heat budget for that discrete time step is calculated, and the battery temperature at the (k+1)-th discrete time step is recursively obtained. The heat budget includes external heating power, irreversible ohmic heat power, reversible entropy heat power, convective heat dissipation power, and radiative heat dissipation power. Convective heat dissipation power describes the heat exchange between the lithium-ion battery and the ambient air, while radiative heat dissipation power describes the heat loss from the lithium-ion battery surface to the low-temperature environment. The item represents the heat power input to the battery by the external heater; The term represents the irreversible Joule heat power generated by the charging current across the ohmic internal resistance of the battery. The term represents the reversible entropy-heat power caused by entropy change in electrochemical reactions; The item represents the convective heat dissipation power between the battery surface and the surrounding ambient air; The term represents the radiative heat dissipation power from the battery surface to the environment.

[0062] The state of charge is recursively calculated based on the ampere-hour integral principle, and the calculation method is expressed as follows: .in, This represents the state of charge at the (k+1)th discrete time. The nominal capacity of a lithium-ion battery refers to the rated amount of electricity required to charge it from a 0% state of charge to a fully charged state, measured in ampere-seconds (APS). In this embodiment, the charging current... When the value is positive, the state of charge increases with time; therefore, the recursive formula for the state of charge uses a plus sign. If the actual control system uses a current sign indicating discharge as positive, then it is uniformly converted to a current sign indicating charging as positive during the data input stage.

[0063] Calculate the terminal voltage based on the sum of the current open-circuit voltage and the ohmic voltage drop. The calculation method is expressed as .in, This represents the terminal voltage at the k-th discrete moment.

[0064] From initial battery temperature and initial state of charge Initially, parameter lookup, heat budget calculation, battery temperature recursion, state of charge recursion, and terminal voltage calculation are repeatedly performed for all discrete time points to obtain the battery temperature trajectory T, state of charge trajectory z, and terminal voltage trajectory V corresponding to the control strategy vector X. Here, T refers to the trajectory sequence composed of the battery temperatures at each discrete time point, used to determine the thermal safety corridor constraint; z refers to the trajectory sequence composed of the state of charge at each discrete time point, used to determine the charging progress and lithium plating risk; and V refers to the trajectory sequence composed of the terminal voltages at each discrete time point, used to determine the upper limit constraint of the charging voltage.

[0065] The rapid electrothermal model reconstructs the low-temperature electrothermal response simply by looking up tables, piecewise linear interpolation, and algebraic recursion. It does not require repeatedly solving complex partial differential equations in the optimization iteration and can provide a unified data source for the extraction of piecewise heating efficiency index, the calculation of lithium plating risk, and the evaluation of particle swarm fitness.

[0066] This invention achieves rapid algebraic recursive calculation of low-temperature electrothermal response through a single-node lumped heat capacity model and piecewise linear interpolation lookup table. It eliminates the need to solve partial differential equations in each optimization iteration, providing a unified and efficient data foundation for subsequent extraction of piecewise heating efficiency index, calculation of lithium plating risk, and evaluation of particle swarm fitness.

[0067] Step S106: Based on the pre-calibrated lithium plating risk margin surface, the lower boundary of the thermal safety corridor that increases with the state of charge, and the preset upper limit of the terminal voltage, a constraint penalty field is constructed for the control strategies corresponding to multiple control segments; wherein, the constraint penalty field includes lithium plating cumulative risk penalty, thermal safety corridor deviation penalty, and terminal voltage overrun penalty.

[0068] Specifically, during low-temperature charging, lithium plating is prone to occur when the negative electrode potential is close to or below the lithium metal equilibrium potential. Relying solely on the upper limits of charging current and terminal voltage is insufficient to accurately describe this risk boundary. This embodiment calculates the lithium plating risk margin value at each discrete moment using a pre-calibrated lithium plating risk margin surface and constructs a cumulative lithium plating risk value based on the battery temperature rise rate. Simultaneously, it introduces a lower boundary of the thermal safety corridor and a penalty for exceeding the terminal voltage limit to prevent increased safety risks due to insufficient battery temperature or excessively high terminal voltage during the increase of state of charge. This embodiment constructs a constraint penalty field by combining the lithium plating risk margin, thermal safety corridor deviation, and terminal voltage exceedance, enabling particle swarm optimization to simultaneously identify high-efficiency heating regions and high-risk control regions. The constraint penalty field is obtained by summing the cumulative lithium plating risk value, thermal safety corridor deviation, and terminal voltage exceedance value after multiplying them by their respective penalty weights. In some preferred embodiments of the present invention, the constraint penalty field can also take the form of a piecewise penalty function, that is, when the safety index is within the safety range, the penalty is zero, and when it exceeds the safety boundary, the penalty value increases linearly or quadratically with the amount of the out-of-bounds, which can also unify the three types of safety constraints into the same penalty field.

[0069] Furthermore, in some preferred embodiments of the present invention, based on a pre-calibrated lithium plating risk margin surface, a thermal safety corridor lower boundary that increases with the state of charge, and a preset terminal voltage upper limit, a constraint penalty field is constructed for the control strategies corresponding to multiple control segments. This includes: obtaining the lithium plating risk margin value at each discrete moment using the lithium plating risk margin surface; multiplying the lithium plating risk margin values ​​greater than zero by a preset temperature rise reduction factor and summing them over time to obtain the cumulative lithium plating risk value; constructing a thermal safety corridor lower boundary that increases with the state of charge based on the state of charge trajectory; calculating the deviation of the battery temperature from the thermal safety corridor lower boundary; calculating the over-limit of the terminal voltage exceeding the preset terminal voltage upper limit based on the terminal voltage trajectory; and multiplying the cumulative lithium plating risk value, the deviation of the thermal safety corridor lower boundary, and the over-limit of the terminal voltage upper limit by their respective penalty weights and summing them to obtain the constraint penalty field.

[0070] For details, see Figure 4 The illustration shown is a schematic diagram of the constraint penalty field generation of a fusion lithium plating risk margin surface and a thermal safety corridor provided by an embodiment of the present invention. The state-of-charge trajectory z, the battery temperature trajectory T, and the charging current sequence are input into the lithium plating risk margin surface. The lithium plating risk margin value is obtained time-by-time. The lithium plating risk margin value at the k-th discrete time is denoted as... , can be represented as ;in, It refers to the lithium plating risk margin value at the k-th discrete time point under the current state of charge, battery temperature, and charging current.

[0071] The lithium plating risk margin value is truncated to a positive value, retaining only the portion that may cause lithium plating. When, it indicates that the k-th discrete time is within the lithium plating safety zone, and the impact of this time on the cumulative risk value of lithium plating is 0; when The value at time k indicates that the lithium plating risk zone has been entered at the kth discrete moment, and this moment has a positive impact on the cumulative lithium plating risk value. Based on this, the safety margin zone and the risk boundary zone can be clearly distinguished to avoid excessive penalties for normal charging behavior within the safety range. In one embodiment, as an example, if the lithium plating risk margin value at a certain moment is -0.015 volts, it means that the negative electrode potential still has a safety margin, and the risk impact at this moment is 0; if the lithium plating risk margin value at another moment is 0.02 volts, it means that the negative electrode potential has crossed the lithium plating boundary, and this moment needs to have a positive impact on the cumulative lithium plating risk value.

[0072] The battery temperature rise rate at each discrete time step is calculated, and a cumulative lithium plating risk value is generated by combining it with the lithium plating risk margin value. The battery temperature rise rate at the k-th discrete time step is denoted as... , This refers to the rate at which the battery temperature rises between adjacent discrete moments, which can be derived from... Calculations show that, to avoid unreasonable impacts on risk reduction items when the battery cools down, when... When it is less than 0, it can be set Set to 0. The cumulative risk value of lithium plating corresponding to the control strategy vector X is denoted as . , This refers to the risk assessment value of the lithium plating risk margin accumulated over time from the start to the end of charging, expressed in volt-seconds. A higher value indicates a higher cumulative lithium plating risk corresponding to the control strategy vector X. The calculation method is as follows: ; in, represents the temperature rise sensitivity coefficient, used to adjust the degree of reduction of the impact of battery temperature rise rate on lithium plating risk, and the unit is seconds per Kelvin, which can be taken as 50 seconds per Kelvin; max(·) represents the maximum value function; exp(·) represents the natural exponential function; This represents the temperature rise reduction factor. When the battery temperature rise rate is high, the temperature rise reduction factor decreases, reflecting the mitigating effect of the heating process on the low-temperature lithium plating growth conditions.

[0073] The lower boundary of the thermal safety corridor is constructed based on the charged state trajectory, and the deviation of the thermal safety corridor is calculated. The lower boundary of the thermal safety corridor is denoted as... , This refers to the minimum battery temperature required to ensure safe low-temperature charging at the k-th discrete time point, and is calculated as follows: ; in, This indicates the minimum allowable initial battery temperature, which can be taken as 263.15 Kelvin (i.e. -10 degrees Celsius). This represents the forced temperature rise slope, used to control the minimum allowable increase in battery temperature as the state of charge increases. The unit is Kelvin per state of charge, and 10 Kelvin can be used. The lower boundary of the thermal safety corridor increases with increasing state of charge, constraining the lithium-ion battery to maintain a sufficient temperature during the charging process.

[0074] Let the deviation of the thermal safety corridor at the k-th discrete time be denoted as... , This refers to the insufficient amount of time when the battery temperature is below the lower boundary of the thermal safety corridor, which can be expressed as: ; where max(·) represents the maximum value function. When Higher than or equal to hour, This indicates that the thermal safety corridor constraint is satisfied; when Below hour, This indicates that the battery temperature is insufficient during low-temperature charging, and a penalty needs to be applied in the fitness function.

[0075] Calculate the terminal voltage exceedance based on the terminal voltage trajectory. The upper limit of the terminal voltage is denoted as... , This represents the highest permissible terminal voltage during charging, which can be set according to the cell specifications; for example, it can be 4.2 volts. The terminal voltage exceeding the limit at the k-th discrete moment is denoted as... , This refers to the amount by which the terminal voltage exceeds the upper limit of the terminal voltage, and can be expressed as: Where max(·) represents the maximum value function. When the terminal voltage Not exceeding the upper limit of terminal voltage At that time, the terminal voltage exceeds the limit. It is 0; when the terminal voltage is 0. Exceeding the terminal voltage limit At that time, the terminal voltage exceeds the limit. It is a positive value. By controlling the terminal voltage out-of-bounds limit, both charger hardware limitations and battery voltage safety limits can be incorporated into the optimization process.

[0076] The cumulative risk value of lithium plating, deviation from the thermal safety corridor, and over-limit of the terminal voltage are transformed into constraint penalty fields. , This refers to the comprehensive penalty value of the safety constraints corresponding to the control strategy vector X, used to guide particles away from the lithium plating risk region, the insufficient temperature region, and the terminal voltage overrun region. The constraint penalty field is obtained based on the cumulative lithium plating risk value, the thermal safety corridor deviation, and the terminal voltage overrun, and is calculated as follows: ; in, This indicates the upper limit of the allowable cumulative risk of lithium plating, which can be 0 or set to a very small positive value according to the test safety boundary, in volt-seconds; This represents the baseline value for cumulative lithium plating risk, used to perform dimensionless processing on the cumulative lithium plating risk value, and can be taken as 1 volt-second; This represents the temperature reference value, used to dimensionlessly process deviations from the thermal safety corridor; it can be taken as 1 Kelvin. This represents the voltage reference value, used to perform dimensionless processing of the voltage overshoot, and can be taken as 1 volt. This represents the time base value, used to make the integration time dimensionless; it can be 1 second. This represents the lithium plating penalty weight, used to control the influence of the cumulative risk value of lithium plating in the constrained penalty field. It can be taken as... ; This represents the thermal safety penalty weight, used to control the influence of thermal safety corridor deviation on the constraint penalty field. It can be taken as... ; This represents the terminal voltage penalty weight, used to control the influence of the terminal voltage overshoot in the constraint penalty field. It can be taken as... ; This represents a smoothing barrier function, used to smoothly transform the cumulative risk value of lithium plating exceeding the risk limit into a positive penalty, while ensuring that the penalty field changes continuously during the optimization search process.

[0077] It should be noted that, This item is a lithium plating penalty item, which is used to penalize particles when the accumulated risk of lithium plating exceeds a preset limit, and is used to guide particles away from high-risk strategies. This item is a thermal safety penalty item, which applies a time-cumulative penalty to the insufficient amount of battery temperature falling below the lower boundary of the thermal safety corridor, in order to ensure that the battery temperature is sufficient during charging. This term is the terminal voltage penalty term, which applies a time-cumulative penalty to any excess terminal voltage exceeding the upper limit, used to protect the battery and charging equipment. (Based on the constraint penalty field...) It can determine the distance between the control strategy vector X and the risk boundary, and subsequent particle swarm optimization can obtain a more stable search direction in a highly constrained non-convex search space.

[0078] This invention unifies three types of safety constraints—lithium plating risk, thermal safety corridor deviation, and terminal voltage overrun—into a continuous constraint penalty field. This enables the optimization algorithm to sense the distance between the control strategy and various safety boundaries, guiding particles away from high-risk areas and improving the safety of the low-temperature charging process.

[0079] In step S108, the segmented heating efficiency index and the constraint penalty field serve as guiding information for particle swarm search. An improved particle swarm algorithm is used to iteratively optimize the external heating power and charging current of each control segment to obtain the optimal segmented external heating power sequence and the optimal segmented charging current sequence for controlling the external heater and charger.

[0080] Specifically, this embodiment uses a normalized segmented heating efficiency index sequence, a fast electrothermal model, and a constraint penalty field to improve the particle swarm optimization algorithm. The object to be optimized is the low-temperature heating-charging joint control strategy, i.e., the control strategy vector X. The improved particle swarm optimization algorithm improves the initial feasibility by guiding initialization with a historical pattern library, enhances the rationality of the search direction by using segmented efficiency-aware dimensional inertial weights, keeps particles away from high-risk areas by using a lithium plating potential field repulsion term, and deeply refines the local optimum through dual-mode elite mutation.

[0081] Furthermore, in some preferred embodiments of the present invention, the improved particle swarm optimization algorithm includes: performing heuristic particle swarm initialization based on a pre-built historical pattern library and a segmented heating efficiency index; updating particle velocity and position using segmented efficiency-aware dimensional inertial weights and lithium plating potential field repulsion terms; performing dual-mode mutation refinement on elite particles to generate candidate new positions for elite particles; if the fitness of the candidate new position is better than the fitness of the original elite particle position, then the candidate new position replaces the original elite particle position.

[0082] Specifically, the particle swarm size is denoted as , The number of particles participating in the optimization search can be 30 to 80; the dimension of the control strategy vector is denoted as D. Since the control strategy vector X includes S external heating power components and S charging current components, D = 2S. The position vector of the i-th particle in the particle swarm is denoted as... , Let represent the i-th candidate cryogenic heating-charging joint control strategy; let denote the position component of the i-th particle in the d-th dimension as . ,in, , Set an allowable lower limit for each location component. and allowed upper limit , This represents the lower bound of the allowed values ​​for the d-th dimension variable. This represents the upper limit of the allowed values ​​for the d-th dimension variable, determined by both hardware capabilities and safety constraints. If the d-th dimension corresponds to external heating power, then... and These represent the lower and upper limits of the allowable heating power within and outside the control segment, respectively; if the d-th dimension corresponds to the charging current, then... and These represent the lower and upper limits of the allowable charging current within the control segment, respectively. The improved particle swarm optimization algorithm updates particle positions and velocities through multiple iterations, ultimately outputting the globally optimal control strategy vector X. X refers to the cryogenic heating-charging joint control strategy composed of the optimal segmented external heating power sequence and the optimal segmented charging current sequence. The optimal segmented external heating power sequence is used to control the heating power of the external heater in different control segments, and the optimal segmented charging current sequence is used to control the charging current of the charger in different control segments.

[0083] Furthermore, in some preferred embodiments of the present invention, heuristic particle swarm initialization is performed based on a pre-built historical pattern library and a segmented heating efficiency index, including: matching similar historical successful control strategies from the historical pattern library according to the current operating condition label; for the external heating power dimension, performing truncated normal sampling with the benchmark heating power corrected by the segmented heating efficiency index as the sampling center; for the charging current dimension, generating an initial value by superimposing random disturbances with the charging current of the corresponding segment in the historical successful control strategy as the reference value, and if the terminal voltage constraint and lithium plating risk constraint are not met, gradually reducing the charging current until the safety conditions are met.

[0084] Specifically, for the high-dimensional non-convex search space in the joint optimization of low-temperature heating-charging, this embodiment uses a segmented heating efficiency index and a historical pattern library to generate an initial particle swarm. The historical pattern library is used to provide verified safety control strategies, and the segmented heating efficiency index is used to correct the external heating power sampling center, so that the initial particles are both diverse and as close as possible to the feasible safety region.

[0085] Based on the current operating condition labels of the low-temperature heating-charging task, from the historical pattern library Select a control strategy based on similar historical successes. The current task status label is denoted as... , This refers to a task description vector composed of the current ambient temperature, current initial battery temperature, current initial state of charge, target state of charge, and allowed charging time. First, let's consider... and The variables in the process are min-max normalized, and then the weighted distance is calculated. Then, several historical successful control strategies with the smallest weighted distance are selected as candidate historical control strategies. Finally, dynamic time warping is used to align the external heating power curve and charging current curve in the candidate historical control strategies to the total number of current control segments. Dynamic time warping is used to handle the problem that the duration of historical successful control strategies differs from that of the current task, ensuring that the preheating segment, current-increasing segment, and constant-current segment in the historical curve can correspond to the control segments of the current task. In one embodiment, for example, if the current task has 10 control segments, but the matched historical successful strategy has a short duration, containing only 6 segments, dynamic time warping can non-linearly stretch the control sequence of these 6 segments on the time axis, aligning it to the current 10 segments. This allows the initial low-power preheating segment, the intermediate high-power heating segment, and the final power-reducing heat preservation segment in the historical strategy to be mapped to the corresponding stages of the current task.

[0086] Heuristic sampling is performed on the external heating power dimension in the particle swarm. If the d-th dimension corresponds to the external heating power of the s-th control segment, then truncated normal sampling is performed within the allowable external heating power range, using the corrected reference heating power as the sampling center. The sampling method for the external heating power dimension is expressed as follows: ; in, The mean is variance is And cut off within the interval Normal distribution within; This refers to the external heating power required to maintain the minimum allowable temperature rise under the current low-temperature environment. It can be estimated based on steady-state heat dissipation, for example, 20 watts. Based on this, the initial value of the external heating power can fluctuate around a physically reasonable value, rather than being randomly generated across the entire range.

[0087] For the charging current dimension, the initial value is generated by superimposing a random perturbation on the charging current of the corresponding segment in the aligned candidate historical control strategies as a reference value. The magnitude of the random perturbation can be set to 5% to 10% of the allowable range for this dimension to maintain the diversity of the initial population. If the reference charging current is too large, causing the terminal voltage to exceed the preset terminal voltage upper limit or the lithium plating risk margin value to be greater than 0, the charging current is gradually reduced until the terminal voltage and lithium plating risk meet the preset safety conditions. In specific implementation, the charging current of this control segment can be reduced step by step in a 5% increment, and the fast electrothermal model and lithium plating risk margin surface are called for verification after each reduction. Based on this, the initial value of the charging current not only inherits the charging method in the historical successful strategies, but also adapts to the current lithium-ion battery temperature and state of charge conditions. In one embodiment, for example, if the reference charging current for a certain segment in a historically successful strategy is 2 amps, but the fast electrothermal model predicts that the terminal voltage of the current segment will exceed the upper limit of 4.2 volts at this current, the system will automatically reduce the current in steps of 5%, trying 1.9 amps, 1.8 amps, etc., until at 1.8 amps, the predicted terminal voltage is lower than 4.2 volts and the lithium plating risk margin is non-positive, then the charging current for that segment is finally determined to be 1.8 amps.

[0088] For each initial particle that has completed sampling, boundary correction, rate of change correction, and fitness evaluation are performed. Boundary correction refers to truncating external heating power and charging current exceeding the allowable range to the corresponding upper and lower limits; rate of change correction refers to limiting the abrupt changes in external heating power and charging current between adjacent control segments to avoid the external heater or charger being unable to track during actual execution. The upper limit of the abrupt change needs to be set according to the hardware specifications of the heater and charger. In one implementation, the fitness function of the control strategy vector X is denoted as J(X). J(X) is used to evaluate the overall quality of the control strategy vector X. The smaller the fitness function J(X), the better the overall performance of the control strategy vector X in terms of energy consumption, time, target state of charge, and safety constraints. The calculation method is expressed as follows: ; in, This represents the total energy consumption corresponding to the control strategy vector X, including external heating energy consumption and charging loss, in joules; This represents the normalized baseline value for energy consumption, used to convert the total energy consumption term into a dimensionless quantity. It can be taken as an estimated total energy consumed under the specified low-temperature operating conditions, operating continuously at maximum heating power and maximum charging current until the end of the allowable charging time, in joules. For example, if the maximum external heating power is 100 watts, the maximum average charging power is 150 watts, and the allowable charging time is 3600 seconds, then... Desirable scorched; This represents the charging time corresponding to the control strategy vector X, in seconds. This indicates the maximum allowable charging time, which is the upper limit of the allowable time for this low-temperature heating-charging task. It is set according to the actual needs of the low-temperature charging task, and the unit is seconds. It can be 3600 seconds or 7200 seconds. Indicates the target state of charge; This represents the state of charge at the final discrete moment; This represents the energy consumption weight, which can be set to 0.4. This represents the time weight, which can be 0.3. This represents the penalty weight for insufficient target state of charge, which can be set to 100. It should be noted that... The term is the total energy consumption normalization term, used to guide the algorithm in finding energy-saving strategies; The term is the normalization term for the total charging time, which is used to guide the algorithm to shorten the charging time; This term is the terminal constraint penalty term, which is used to impose a larger penalty when the final state of charge does not reach the target; The term is a comprehensive safety constraint penalty term, used to guide the algorithm away from infeasible areas.

[0089] The embodiments of the present invention guide the candidate control strategies in the initial particle swarm to be closer to the feasible safe region by using a historical pattern library and segmented heating efficiency index correction, thereby improving the initial feasibility rate and reducing infeasible searches caused by completely random initialization.

[0090] Furthermore, in some preferred embodiments of the present invention, the dimensional inertial weight is obtained by mapping according to the segmented heating efficiency index; wherein, the inertial weight obtained by the low-efficiency segment is greater than the inertial weight obtained by the high-efficiency segment; the lithium plating potential field repulsion term is constructed by the finite difference gradient of the decision variable with respect to the lithium plating cumulative risk value, so that the particle obtains a velocity correction amount away from the lithium plating risk direction when it is close to the lithium plating risk region.

[0091] Specifically, because traditional particle swarm optimization algorithms use the same inertial weights for all dimensions, they struggle to reflect the differences in physical efficiency across different time segments in the combined cryogenic heating-charging control. This embodiment maps the normalized segmented heating efficiency index to the particle dimension, forming a dimension-level inertial weight. Simultaneously, it treats the accumulated risk value of lithium plating as a safety potential field and constructs a repulsive velocity term using the finite difference gradient of the accumulated risk value with respect to the particle position, causing particles to automatically move away from the risk direction when approaching the lithium plating risk region.

[0092] By mapping the piecewise efficiency information to each dimension of the particle position vector, we obtain the dimensional efficiency index. , This refers to the efficiency evaluation value of the control segment corresponding to the d-th dimension of the decision variable, used to adjust the degree of inertia preservation in particle velocity updates. If the d-th dimension corresponds to the external heating power of the s-th control segment, then... Directly take the normalized piecewise heating efficiency index sequence The s-th element. If the d-th dimension corresponds to the charging current of the s-th control segment, then the charging effectiveness index of control segment s is calculated based on the simulation results of the fast electrothermal model, and used as... .

[0093] In this embodiment, the charging effectiveness index is used to comprehensively evaluate the charging efficiency and safety cost of this segment. First, the increment of state of charge, the amount of voltage exceeding the limit, and the cumulative positive value of lithium plating risk margin within the control segment are normalized using a minimum-maximum normalization method to obtain normalized values ​​for the increment of state of charge, the amount of voltage exceeding the limit, and the cumulative positive value of lithium plating risk margin. Then, by subtracting the normalized values ​​for the voltage exceeding the limit and the cumulative positive value of lithium plating risk margin from 1, the normalized values ​​of the latter two items are converted into a positive index. Finally, a set of preset weights (e.g., [values ​​to be filled in]) are used to... The charging effectiveness index is obtained by performing a weighted summation. In one embodiment, as an example, if the charging current of the d-th dimension corresponds to the s-th control segment, and its normalized value for state of charge increment is 0.5, its normalized value for terminal voltage out-of-bounds is 0, and its normalized value for the cumulative positive value of lithium plating risk margin is 0.02, the preset weights are taken as follows: The effectiveness index of this segmented charging is: .

[0094] Charging current dimension A higher value indicates that the segment is further from the safety boundary while advancing the charging progress, meaning that the segment can achieve high charging capability with a smaller safety cost; conversely, a lower value indicates that the segment's charging strategy is inefficient or risky. Based on this, the external heating power dimension reflects the actual heating efficiency, while the charging current dimension reflects the relative relationship between charging capability and safety cost, avoiding the reliance solely on self-heating from charging current as a basis for efficiency.

[0095] The dimension-level inertia weight is calculated based on the dimension efficiency index. The inertia weight of particle i in the d-th dimension at the q-th iteration is denoted as... , This is used to control the degree to which a particle retains its original velocity in the d-th dimension, and is calculated as follows: ; Where q represents the particle swarm iteration number index; This represents the upper bound of the inertia weight, which can be 0.9; This represents the lower bound of the inertia weight, which can be 0.4; The efficiency mapping slope is used to adjust the influence of the dimensional efficiency index on the decay rate of the inertia weight, and can be set to 3; exp(·) represents the natural exponential function. The higher the dimensional efficiency index, the smaller the inertia weight, indicating that the dimension is already in a relatively efficient region and is more suitable for fine convergence; the lower the dimensional efficiency index, the larger the inertia weight, indicating that the dimension still needs to expand the search range to find more effective heating or charging control values.

[0096] The direction of change of the cumulative risk value of lithium plating with respect to each decision variable is calculated using finite difference methods. The control strategy vector of the i-th particle at the q-th iteration is denoted as... The finite difference gradient of the cumulative lithium plating risk value of the i-th particle with respect to the d-th position component at the q-th iteration is denoted as... , It is used to characterize the direction and magnitude of the impact of the d-th dimension decision variable on the cumulative risk value of lithium plating when it increases or decreases.

[0097] In one implementation, for the i-th particle, a small perturbation is first applied to the d-th position component. The positive disturbance control strategy vector is obtained. and reverse disturbance control strategy vector Then, refer to the aforementioned embodiment to calculate the cumulative risk value of lithium plating after forward perturbation and the cumulative risk value of lithium plating after reverse perturbation; finally, divide the difference between the two risk values ​​by... The finite difference gradient of this dimension is obtained, and the calculation method is expressed as follows: ; in, This refers to the finite difference disturbance amplitude in the d-th dimension, which can be taken as 1% to 3% of the allowable range for that dimension; This refers to adding a small perturbation to the position vector of the i-th particle in the d-th dimension at the q-th iteration. The resulting new position vector; This refers to subtracting a small perturbation from the position vector of the i-th particle in the d-th dimension at the q-th iteration. The resulting new position vector; This refers to the position vector The calculated cumulative risk value of lithium plating; This refers to the position vector The calculated cumulative risk value of lithium plating.

[0098] If the variable exceeds the boundary after either a positive or negative perturbation, a one-sided finite difference is used. For example, if the variable exceeds the boundary after a positive perturbation, the gradient is approximated as follows: ,in, This refers to the position vector The calculated cumulative risk value of lithium plating is used. Based on this, without deriving the analytical gradient of a complex electrochemical risk model, a potential field direction sufficient to guide particles away from the lithium plating risk region can be obtained.

[0099] The particle velocity is updated based on the dimensional inertia weight, the historical best position of the individual and the group, and the gradient of the lithium plating risk potential field. The velocity component of the i-th particle in the d-th dimension at the q-th iteration is denoted as... The velocity component of the i-th particle in the d-th dimension at the (q+1)-th iteration is denoted as... The particle velocity update method is expressed as: ; in, This represents the individual learning factor, which can be 2. This represents the group learning factor, which can be 2. and Both represent uniformly random numbers in the range of 0 to 1; This represents the position component of the i-th particle in the d-th dimension at the q-th iteration; This represents the component of the historical optimal position of the i-th particle in the d-th dimension at the q-th iteration; This represents the component of the current global optimal position in the d-th dimension at the q-th iteration; The repulsion coefficient of the lithium plating potential field is used to control the influence of the finite difference gradient of lithium plating risk on the particle velocity, and can be taken as 0.1. The first three terms of the velocity update are the inertia term, the individual cognition term, and the social learning term, which are used to realize the regular search of the particle swarm. The term is a repulsive term for the lithium plating potential field, used to push particles away from directions that increase the risk of lithium plating, thereby avoiding lithium plating risk areas during the search process.

[0100] It should be noted that units do not need to be substituted during the particle velocity update calculation. The updated particle velocity is a parameter in the particle swarm optimization algorithm, has no physical units, and only represents the amount of position change in each iteration. Optionally, all decision variables can be specified before optimization. Normalized to the [0,1] interval, the velocity update is performed in the dimensionless space, at which point the gradient... Naturally dimensionless, it can be directly added to velocity. The dimensional inertial weights, which are based on segmented efficiency, give low-efficiency control segments stronger search capabilities and enable high-efficiency control segments to converge faster. The repulsive velocity term of the lithium plating potential field causes particles to actively avoid lithium plating risk regions. When these two are combined, the particle swarm can focus more quickly on an efficient and safe cryogenic heating-charging joint control strategy while maintaining global search capabilities.

[0101] The particle position components are updated based on the updated velocity components, and boundary corrections, rate of change corrections, and fitness assessments are performed on the updated particle positions. ;in, This represents the position component of the i-th particle in the d-th dimension at the (q+1)-th iteration. If the updated external heating power or charging current exceeds the corresponding allowable range, it is truncated to the allowable range; if the change in external heating power or charging current between adjacent control segments exceeds the allowable rate of change of the actuator, it is smoothed by the maximum allowable rate of change. In one embodiment, as an example, if the heating power of two adjacent segments after the update is 20 watts and 50 watts respectively, with a change of 30 watts, and the maximum allowable rate of change of the hardware is 20 watts / segment, then the power of the latter segment will be corrected to 20 + 20 = 40 watts to meet the constraints of the hardware execution capability. The corrected control strategy vector is used to call the fast electrothermal model to obtain the battery temperature trajectory, state of charge trajectory, and terminal voltage trajectory, and the constraint penalty field is calculated, and then the fitness value is calculated. If the current fitness of a particle is better than its historical best fitness, the historical best position of the particle is updated; if the current fitness of a particle is better than its global best fitness, the global best position is updated.

[0102] In this embodiment of the invention, low-efficiency segmentation obtains a larger inertial weight to expand the search range, while high-efficiency segmentation obtains a smaller inertial weight for fine convergence; the lithium plating potential field repulsion term enables particles to obtain a velocity correction amount away from the risk direction when approaching the lithium plating risk region, taking into account both global search capability and local safety.

[0103] Furthermore, in some preferred embodiments of the present invention, the dual-mode mutation refinement includes: generating a first candidate new position for the elite particle based on the Levy flight continuous perturbation of the dimensional efficiency index, with the low-efficiency dimension obtaining a larger perturbation amplitude; selecting a continuous time segment from the historical mode library with a preset segment replacement probability, and replacing the external heating power and charging current of the corresponding continuous control segment in the elite particle with the external heating power and charging current of the corresponding control segment in the continuous time segment to generate a second candidate new position for the elite particle; wherein, the continuous time segment includes the external heating power and charging current of at least one control segment; performing boundary correction, rate of change correction, and augmented fitness evaluation on the first candidate new position and the second candidate new position respectively, and if the fitness of any candidate new position is better than the fitness of the original elite particle position, then the original elite particle position is replaced by the candidate new position with the best fitness.

[0104] Specifically, in the later stages of particle swarm optimization, the algorithm is prone to getting trapped in local optima, especially under the combined constraints of low-temperature lithium plating, thermal safety, and terminal voltage, resulting in a narrow and non-convex feasible solution space. This embodiment introduces a dual-mode mutation refinement for elite particles. One mode is a continuous perturbation of Lévy flight based on the dimensionality efficiency index, used to overcome the local bottleneck of low-efficiency dimensions; the other mode is continuous time segment replacement based on a historical mode library, used to introduce validated safety control strategies.

[0105] Elite particles are selected from the current particle swarm. Elite particles are those with high fitness values; the top 10% to 20% of particles can be selected as the elite subgroup. The control strategy vector of the e-th elite particle at the q-th iteration is denoted as... The position component of the e-th elite particle in the d-th dimension during the q-th iteration is denoted as... Where 'e' represents the elite particle index. Elite particles typically exhibit good performance in terms of charging time, energy consumption, and safety constraints, but there may still be room for improvement in certain low-efficiency control segments. Based on the dimensional efficiency index... Constructing Dimension Sensitive Factors A larger dimension sensitivity factor indicates lower efficiency or higher security cost for the control segment corresponding to the d-th dimension, requiring a larger mutation amplitude; a smaller dimension sensitivity factor indicates a better control segment corresponding to the d-th dimension, where the original control value should be maintained as much as possible, with only small, fine-grained perturbations. Based on this, the mutation operation no longer applies equal-intensity perturbations to all dimensions, but instead prioritizes modifying inefficient bottleneck segments.

[0106] Applying a Levy flight perturbation to the elite particle generates the first candidate new position. The component of the first candidate new position of the e-th elite particle in the d-th dimension is denoted as... The calculation method is expressed as follows: ; Where ζ represents the variation scaling factor, which is used to control the basic variation amplitude and can be taken as 0.5; This represents the Lévy index, with values ​​ranging from 1.5 to 2. This represents the random step size that follows a Lévy distribution; This represents the component in the d-th dimension of the first reference position randomly selected from the elite subgroup or the historical pattern library; This represents the d-th dimension component of the second reference position randomly selected from the elite subgroup or historical pattern library, where the first and second reference positions are different. The Lévy fly-through random step size mostly produces small perturbations, and in a few cases, large jumps. Inefficient dimensions arise because... Larger dimensions allow for more significant search jumps, and higher efficiency dimensions are due to... The smaller size of the candidate new position, which is close to the original elite particle position, protects the already formed efficient heating and safe charging segments, and thus enables key breakthroughs in local inefficient segments without compromising the overall excellent control strategy.

[0107] Fragment replacement from the historical pattern library is performed using a preset fragment replacement probability to generate a second candidate new position. The fragment replacement probability is denoted as... , This refers to the probability of performing historical mode library segment replacement on elite particles, which can be between 0.2 and 0.4. When segment replacement is triggered, a continuous control segment is first randomly selected from the current control strategy vector, with a length of 1 to 3 control segments; then, the historical segment with the most similar operating conditions or better fitness is selected from the candidate historical control strategies; finally, the external heating power and charging current of the corresponding continuous control segment in the elite particle are simultaneously replaced with the corresponding values ​​in the historical segment, generating a second candidate new position. Segment replacement prioritizes maintaining the time correspondence between external heating power and charging current, and does not replace the charging current or external heating power separately. Since the safety of low-temperature charging is determined by both the heating strategy and the charging strategy, replacing a single control variable may disrupt the original thermo-electric matching relationship. By replacing the entire continuous time segment, historically verified safety modes such as "heat up first, then increase current" or "low-temperature current limiting, and relaxing charging current after temperature reaches the target" can be introduced into elite particles, improving the ability to escape local searches.

[0108] The executability correction and augmented fitness evaluation are performed on candidate new positions generated by continuous perturbations or fragment replacements. The executability correction includes variable boundary correction, adjacent control segment change rate correction, terminal voltage upper limit correction, and minimum battery temperature constraint correction. Augmented fitness evaluation involves adding a constraint penalty field to the original fitness function, ensuring that even if a candidate new position is superior in charging time or energy consumption, it must still meet lithium plating risk, thermal safety, and terminal voltage requirements. The battery temperature trajectory, state of charge trajectory, and terminal voltage trajectory are reconstructed using a fast electrothermal model for each candidate new position. Then, the cumulative lithium plating risk value, thermal safety corridor deviation, terminal voltage overrun, and constraint penalty field are calculated, finally yielding the fitness value of the candidate new position. If the fitness value of the candidate new position is better than that of the original elite particle position, the candidate new position replaces the original elite particle position; if the candidate new position is not better than the original elite particle position, the original elite particle position is retained. By only accepting better candidates, the quality of elite particles is guaranteed not to degrade due to random mutations. In one embodiment, for example, if the fitness value of a candidate new position generated after a certain elite particle undergoes Levy flight mutation decreases from 90.5 to 85.2, then the original elite particle's position is replaced with the new position; if the fitness value of another elite particle increases from 75.8 to 78.1 after being replaced by a historical fragment, this indicates that the replacement has disrupted the excellent structure of the original strategy, so the original elite particle's position is retained and the candidate new position is discarded.

[0109] Repeatedly execute particle swarm velocity updates and elite mutation refinement until a stopping condition is met. The stopping condition can be reaching the maximum number of iterations, a global optimal fitness improvement of less than a preset improvement threshold for several consecutive iterations, or the achievement of a control strategy that satisfies the target state of charge, terminal voltage constraints, thermal safety corridor constraints, and lithium plating risk constraints. The maximum number of iterations can be 100 to 300; the number of consecutive periods without improvement can be 10 to 30; the preset improvement threshold can be... The final output is the globally optimal control strategy vector. , This refers to a low-temperature heating-charging joint control strategy consisting of an optimal segmented external heating power sequence and an optimal segmented charging current sequence. The optimal segmented external heating power sequence is used to control the heating power of the external heater in different control segments, and the optimal segmented charging current sequence is used to control the charging current of the charger in different control segments.

[0110] In one embodiment, as an example, at an ambient temperature of 263.15 Kelvin (i.e., -10 degrees Celsius), a heating-charging joint optimization was performed on a lithium-ion battery with a nominal capacity of 50 Ah and an initial state of charge (SOC) of 0.2. The target SOC was set to 0.8, the number of control segments was set to 10, and the total duration was 3600 seconds. The optimization objective was to minimize total energy consumption and shorten charging time. Using the method of this invention, the optimal strategy output was as follows: the first three segments were heated at maximum power and maintained at 8 APM; in the middle four segments, as the battery temperature increased, the charging current was gradually increased to 35 APM, and the heating power was correspondingly reduced; the last three segments utilized ohmic heat to maintain the temperature and completed charging with a 15 APM current. The optimization results showed that, compared to the baseline strategy of constant power heating + constant current charging, this strategy, while satisfying all safety constraints, reduced charging time by 9% and total energy consumption by 16%.

[0111] This invention addresses the inefficiency of segmentation by using continuous perturbations during Levy flight. It introduces a validated safety control mode by replacing continuous time segments in the historical pattern library, helping the particle swarm escape local optima while ensuring that the established superior strategy structure is not destroyed.

[0112] Furthermore, in some preferred embodiments of the present invention, the method further includes: sending the optimal segmented external heating power sequence and the optimal segmented charging current sequence to the external heater and charger; collecting battery temperature, terminal voltage and charging current in real time, and correcting the state of charge based on the real-time collection results; if the difference between the real-time terminal voltage and the preset terminal voltage upper limit is less than the preset voltage threshold, or the real-time battery temperature is lower than the lower boundary of the thermal safety corridor, adjusting the charging current or external heating power; and regenerating the optimized control strategy for the remaining time period using the real-time state as the new initial state in a rolling window manner.

[0113] For details, see Figure 5 The diagram shown illustrates an online execution schematic of a low-temperature heating-charging joint control strategy provided by an embodiment of the present invention. After optimizing the low-temperature heating-charging joint control strategy, the globally optimal control strategy vector X is... Deployed into the battery management system or charge controller. When running online, the system executes external heating power and charging current in a rolling window manner, and performs safety checks and necessary corrections to the control strategy based on real-time battery temperature, terminal voltage, and state of charge.

[0114] Before starting low-temperature charging, the current ambient temperature, current battery temperature, current state of charge, target state of charge, and allowable charging duration are read to form a current task status label. Furthermore, the maximum power of the external heater, the maximum current of the charger, the upper limit of the terminal voltage, the highest allowable battery temperature, the lowest allowable battery temperature, and the upper limit of the rate of change of adjacent control segments are read to form online execution constraint parameters, so that the optimized control strategy can be consistent with the current hardware capabilities and safety limitations.

[0115] The global optimal control strategy vector X The analysis involves determining the optimal segmented external heating power sequence and the optimal segmented charging current sequence. In practical implementation, if the current discrete moment belongs to the s-th control segment, the optimal external heating power of the s-th control segment is sent to the external heater, and the optimal charging current of the s-th control segment is sent to the charger. Before issuing the control command, slope constraints are applied to the changes in external heating power and charging current between adjacent control segments to ensure smooth tracking between the external heater and the charger.

[0116] During execution, battery temperature, terminal voltage, and charging current are collected in real time, and the state of charge (SOC) is corrected based on the actual collected results. If the difference between the real-time terminal voltage and the preset upper limit of terminal voltage is less than the preset voltage threshold, the current charging current is reduced. The voltage threshold can be set according to the cell specifications and safety margin, for example, any value between 0.05V and 0.2V. When the difference between the real-time terminal voltage and the preset upper limit of terminal voltage is less than the voltage threshold, it indicates that the terminal voltage is close to the upper limit, and the charging current needs to be reduced to allow for a safety margin and prevent the terminal voltage from exceeding the upper limit. If the real-time battery temperature is below the lower boundary of the thermal safety corridor, the external heating power within the allowable range is increased or the current charging current is reduced; if the real-time battery temperature exceeds the maximum allowable battery temperature, the external heating power is reduced and the charging current is limited. Based on this, response deviations caused by model errors, ambient temperature changes, and battery aging can be addressed.

[0117] The low-temperature heating-charging joint control strategy is updated using a rolling window approach. After each or several control segments are executed, the real-time acquired battery temperature, state of charge, and terminal voltage are used as new initial states to regenerate the low-temperature heating-charging joint control strategy for the remaining time periods. The rolling window update allows the control strategy to continuously adapt to the actual battery state during execution, preventing the one-time offline optimization results from gradually deviating from the safety boundary due to model errors.

[0118] When the state of charge (SOC) reaches the target SOC, the allowed charging time ends, the terminal voltage continuously approaches the preset terminal voltage upper limit (i.e., within a preset time period, the difference between the terminal voltage and the preset terminal voltage upper limit is continuously less than a preset voltage threshold; both the preset time period and the preset voltage threshold can be set according to the actual scenario), the lithium plating risk margin value continuously shows a positive value, or the battery temperature exceeds the maximum allowable battery temperature, the current low-temperature heating-charging joint control process is terminated, and the actual execution data is recorded. The actual execution data includes the external heating power trajectory, charging current trajectory, battery temperature trajectory, terminal voltage trajectory, SOC trajectory, final energy consumption, and safety event records. If the execution meets the safety conditions and the control effect is good, the actual execution data is added to the historical mode library for initialization and segment replacement under similar low-temperature conditions.

[0119] The embodiments of the present invention deploy the optimal strategy obtained from offline optimization to the actual system, correct model errors and deviations caused by environmental changes through real-time feedback, ensure thermal safety and lithium plating safety during online execution, and continuously accumulate effective execution data for subsequent optimization.

[0120] The embodiments of this invention obtain a segmented heating efficiency index by separating electrochemical internal thermal perturbations, which can suppress the misleading influence of parasitic self-heating on the evaluation of external heating efficiency; by constructing a constraint penalty field through the lithium plating risk margin surface, thermal safety corridor, and terminal voltage overrun, the optimization algorithm can perceive the proximity of the safety boundary; by perceiving the inertial weight of segmented efficiency, the repulsion of the lithium plating potential field, and the dual-mode elite mutation, the search stability and feasibility of low-temperature heating-charging joint optimization in a highly constrained non-convex space can be improved.

[0121] This invention proposes a joint optimization method for battery gradient heating and charging adapted to low-temperature environments. By subtracting the electrochemical internal heat rise (composed of irreversible ohmic heat and reversible entropic heat) from the apparent temperature rise of the battery, a segmented heating efficiency index reflecting only the external heating effect is extracted, avoiding the misjudgment of the self-heating of the charging current as an effective influence of the external heating system. A pre-calibrated lithium plating risk margin surface is fused with the lower boundary of the thermal safety corridor and the voltage overrun, constructing a constraint penalty field that includes lithium plating cumulative risk penalties, insufficient temperature penalties, and voltage overrun penalties, allowing the optimization search process to be constrained by multiple safety boundaries simultaneously. A historical pattern library guides particle swarm initialization, and a dimensional inertial weight is constructed based on the segmented heating efficiency index. Simultaneously, a potential field repulsion term based on the finite difference gradient of lithium plating risk is introduced, enabling the particle swarm to maintain a stable search direction and feasibility rate in the highly constrained non-convex search space of the low-temperature heating-charging joint optimization.

[0122] This invention provides a joint optimization method for gradient heating and charging of batteries adapted to low-temperature environments. By subtracting the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropic heat from the apparent temperature rise of the battery, a segmented heating efficiency index reflecting only the external heating effect is extracted. This avoids misjudging parasitic self-heating caused by charging current as the effective effect of the external heater, thus making the heating efficiency evaluation more accurate. By integrating the lithium plating risk margin surface, the lower boundary of the thermal safety corridor, and the preset terminal voltage upper limit into a constraint penalty field, the optimization process can simultaneously perceive the triple safety boundaries of lithium plating risk, insufficient temperature, and voltage overshoot, improving the safety of low-temperature charging. By using the segmented heating efficiency index and the constraint penalty field as guiding information for particle swarm search, and employing an improved particle swarm algorithm for iterative optimization, the search stability and feasible solution ratio can be improved in a high-dimensional non-convex constraint space, ultimately obtaining a low-temperature heating-charging joint control strategy that balances safety, energy consumption, and charging time.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for jointly optimizing battery gradient heating and charging to adapt to low-temperature environments, characterized in that, include: The low-temperature heating-charging joint control process is divided into multiple control segments according to time; wherein, the external heating power and charging current of each control segment are variables to be optimized. For each control segment, based on a predetermined fast electrothermal model, the apparent temperature rise of the battery within the control segment is calculated, and then the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropy heat is subtracted to obtain the net external heating temperature rise caused only by external heating. Based on the ratio of the net external heating temperature rise to the input energy of the external heater, the segmented heating efficiency index of the control segment is obtained. Based on the pre-calibrated lithium plating risk margin surface, the lower boundary of the thermal safety corridor that increases with the state of charge, and the preset upper limit of the terminal voltage, a constraint penalty field is constructed for the control strategies corresponding to the multiple control segments; wherein, the constraint penalty field includes lithium plating cumulative risk penalty, thermal safety corridor deviation penalty, and terminal voltage overrun penalty; Using the segmented heating efficiency index and the constraint penalty field as guiding information for particle swarm search, an improved particle swarm algorithm is used to iteratively optimize the external heating power and the charging current of each control segment, thereby obtaining the optimal segmented external heating power sequence and the optimal segmented charging current sequence for controlling the external heater and charger.

2. The method according to claim 1, characterized in that, For each control segment, based on a predetermined fast electrothermal model, the apparent temperature rise of the battery within the control segment is calculated. Then, the electrochemical internal heat rise caused by irreversible ohmic heat and reversible entropic heat is subtracted to obtain the net external heating temperature rise caused solely by external heating. Based on the ratio of the net external heating temperature rise to the input energy of the external heater, the segmented heating efficiency index of the control segment is obtained, including: Within each control segment, the apparent temperature rise of the battery between adjacent discrete moments is calculated; Based on the current charging current, ohmic internal resistance, and open-circuit voltage temperature coefficient, calculate the irreversible ohmic thermal power and the reversible entropy thermal power; multiply the sum of the irreversible ohmic thermal power and the reversible entropy thermal power by the discrete time step and divide by the cell's equivalent heat capacity to obtain the electrochemical internal heat rise. The net temperature rise from external heating is obtained by subtracting the electrochemical internal heat temperature rise from the apparent temperature rise. The net temperature rise of external heating at all discrete time steps within the control segment is summed, and then divided by the total energy input from the external heaters within the control segment to obtain the segmented heating efficiency index of the control segment.

3. The method according to claim 1, characterized in that, Based on a pre-calibrated lithium plating risk margin surface, a thermal safety corridor lower boundary that increases with increasing state of charge, and a preset terminal voltage upper limit, a constraint penalty field is constructed for the control strategies corresponding to the multiple control segments, including: The lithium plating risk margin value at each discrete moment is obtained using the lithium plating risk margin surface. The lithium plating risk margin values ​​that are greater than zero are multiplied by a preset temperature rise reduction factor and then summed over time to obtain the cumulative lithium plating risk value. Construct a lower boundary of the thermal safety corridor based on the state of charge trajectory, which increases with the state of charge, and calculate the deviation of the battery temperature from the lower boundary of the thermal safety corridor. The amount by which the terminal voltage exceeds the preset terminal voltage upper limit is calculated based on the terminal voltage trajectory. The constraint penalty field is obtained by multiplying the cumulative risk value of lithium plating, the deviation of the lower boundary of the thermal safety corridor, and the overstepping of the upper limit of the terminal voltage by their respective penalty weights.

4. The method according to claim 1, characterized in that, The improved particle swarm optimization algorithm includes: Based on a pre-built historical pattern library and the segmented heating efficiency index, heuristic particle swarm initialization is performed; Particle velocity and position are updated using segmented efficiency-aware dimensional inertial weights and lithium plating potential field repulsion terms. Perform a two-mode mutation refinement on the elite particle to generate a candidate new position for the elite particle. If the fitness of the candidate new position is better than that of the original elite particle position, then replace the original elite particle position with the candidate new position.

5. The method according to claim 4, characterized in that, Based on a pre-built historical pattern library and the segmented heating efficiency index, heuristic particle swarm initialization is performed, including: Match similar historical successful control strategies from the historical pattern library based on the current operating condition label; For the external heating power dimension, truncated normal sampling is performed with the benchmark heating power corrected by the segmented heating efficiency index as the sampling center; Regarding the charging current dimension, the initial value is generated by superimposing random disturbances on the charging current of the corresponding segment in the historical successful control strategy as a reference value. If the terminal voltage constraint and lithium plating risk constraint are not met, the charging current is gradually reduced until the safety conditions are met.

6. The method according to claim 4, characterized in that, The dimensional inertia weight is obtained by mapping the segmented heating efficiency index; wherein, the inertia weight obtained by the low-efficiency segment is greater than the inertia weight obtained by the high-efficiency segment. The lithium plating potential field repulsion term is constructed by the finite difference gradient of the cumulative lithium plating risk value on the decision variable, so that the particle obtains a velocity correction amount away from the lithium plating risk direction when it is close to the lithium plating risk region.

7. The method according to claim 4, characterized in that, The dual-mode mutation refining includes: Based on the dimensional efficiency index, the Levy flight continuous perturbation generates the first candidate new position of the elite particle, and the low-efficiency dimension obtains a larger perturbation amplitude. With a preset segment replacement probability, a continuous time segment is selected from the historical pattern library, and the external heating power and charging current of the corresponding continuous control segment in the elite particle are replaced with the external heating power and charging current of the corresponding control segment in the continuous time segment to generate a second candidate new position for the elite particle; wherein, the continuous time segment includes the external heating power and charging current of at least one control segment. Boundary correction, rate of change correction, and augmented fitness evaluation are performed on the first candidate new position and the second candidate new position, respectively. If the fitness of any candidate new position is better than the fitness of the original elite particle position, the original elite particle position is replaced by the candidate new position with the best fitness.

8. The method according to claim 1, characterized in that, The rapid electrothermal model adopts a single-node lumped heat capacity model. It obtains the open-circuit voltage, open-circuit voltage temperature coefficient, and ohmic internal resistance under the current state from a pre-calibrated parameter table through piecewise linear interpolation, and calculates the battery temperature, state of charge, and terminal voltage according to the following recursive formula: ； ； ； in, Let be the battery temperature at the (k+1)th discrete time. Let be the battery temperature at the k-th discrete time. For discrete time steps, The equivalent heat capacity of the battery cell, External heating power, This is the charging current. The internal resistance in ohms is obtained by looking up a table based on battery temperature and charging current direction. The open-circuit voltage temperature coefficient is obtained by looking up a table based on the state of charge and battery temperature. The convective heat transfer coefficient is... For effective heat dissipation area, For ambient temperature, For surface emissivity, The Stefan-Boltzmann constant is... This is the fourth-power temperature difference between the battery temperature and the ambient temperature. For the first State of charge at discrete moments, For the first State of charge at discrete moments, This refers to the battery's nominal capacity. For the first Terminal voltage at discrete moments Open circuit voltage, For current Direction markers.

9. The method according to claim 1, characterized in that, The method further includes: The optimal segmented external heating power sequence and the optimal segmented charging current sequence are sent to the external heater and charger; Real-time acquisition of battery temperature, terminal voltage, and charging current, and correction of state of charge based on real-time acquisition results; If the difference between the real-time terminal voltage and the preset terminal voltage upper limit is less than the preset voltage threshold, or if the real-time battery temperature is lower than the lower boundary of the thermal safety corridor, then adjust the charging current or external heating power. Using a scrolling window approach, the real-time state is used as the new initial state to regenerate the optimized control strategy for the remaining time period.

10. The method according to claim 1, characterized in that, Before dividing the low-temperature heating-charging combined control process into multiple control segments according to time, the method further includes: Collect heating-charging joint control samples with different combinations of external heating power and charging current under low temperature environment; Calibrate open-circuit voltage two-dimensional table, open-circuit voltage temperature coefficient two-dimensional table, ohmic internal resistance parameter table, heat transfer parameters and lithium plating risk margin surface; Control strategies that meet safety conditions are selected from the samples to construct a historical pattern library.

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