Lithium iron phosphate battery SOC estimation method based on electric-thermal-force multi-source signals

Abstract

The invention provides a lithium iron phosphate battery SOC estimation method based on electric-thermal-force multi-source signals, and belongs to the technical field of lithium ion battery management. Establishing a first-order equivalent circuit model of the battery; identifying parameters in the equivalent circuit model; establishing an equivalent mechanical model of the battery; identifying a free expansion curve, a rigidity coefficient and a thermal expansion coefficient in the equivalent mechanical model; performing battery SOC estimation by using voltage, current and temperature signals measured by the battery in real time to obtain an electrical SOC estimation result; sOC estimation is carried out by using expansion force, temperature and current signals measured by the battery in real time, and a mechanical SOC estimation result is obtained; and carrying out adaptive weighting calculation on the electrical SOC estimation result and the mechanical SOC estimation result to obtain a final SOC result. According to the method, a dual-channel SOC estimation system is constructed based on the electrical characteristics and mechanical characteristics of the battery, and high-precision and high-robustness SOC online calculation is realized through an adaptive fusion method.

Description

Technical Field

[0001] This invention provides a method for estimating the state of charge (SOC) of lithium iron phosphate batteries based on multi-source electrical-thermal-mechanical signals, belonging to the field of lithium-ion battery management technology. Background Technology

[0002] With the rapid growth of applications such as electric vehicles and energy storage power stations, the safety, lifespan, and available energy management of lithium-ion batteries during use are becoming increasingly important. State of Charge (SOC), as one of the most critical state variables in a Battery Management System (BMS), directly impacts energy management strategies, charge / discharge protection, battery equalization control, and overall battery life prediction. Therefore, improving the real-time accuracy of battery SOC estimation is a key research direction in current battery management technology.

[0003] Currently, commercial battery management systems (BMS) primarily rely on two types of electrical signal methods for State of Charge (SOC) estimation: the Coulomb integration method and the Extended Kalman Filter (EKF) method based on the Equivalent Circuit Model (ECM). The Coulomb integration method obtains SOC by integrating the current, but it is highly sensitive to current measurement bias and prone to estimation errors accumulating over time. While the ECM-EKF method introduces a dynamic model to suppress error propagation and can utilize terminal voltage to correct SOC to some extent, it still fundamentally relies on the open-circuit voltage (OCV) – SOC mapping relationship for state correction. For LFP batteries widely used in electric vehicles and energy storage systems, their OCV-SOC curves are extremely flat over a wide SOC range, resulting in very low sensitivity of terminal voltage changes to SOC. In this case, the correction capability of the ECM-EKF method is significantly reduced, making it difficult to effectively use voltage to inversely estimate SOC. In summary, traditional SOC estimation methods that rely solely on voltage and current signals (including coulomb integration and ECM-EKF) generally suffer from poor identifiability and difficulty in error correction in LFP batteries, making it difficult to meet the current engineering requirements for high-precision SOC estimation in electric vehicles and energy storage systems.

[0004] In recent years, with the development of the "smart battery" concept, researchers have begun to explore using multiple physical quantities such as mechanical stress and expansion displacement during battery charging and discharging as auxiliary signals. Lithium-ion insertion and extraction cause changes in the lattice volume of the active material, resulting in measurable expansion force or deformation displacement. Studies have shown that the expansion force signal has a high correlation with SOC (State of Charge) and is an important supplement to the electrical signal. However, most existing mechanical models rely on empirical fitting, failing to accurately characterize the stress characteristics of the battery cell under assembly preload and mechanical constraints, making it difficult to achieve interpretable, portable, and real-time engineering deployment at the BMS (Battery Management System) level.

[0005] In the prior art, patent CN119936685A discloses a method for estimating the state of charge (SOC) of lithium iron phosphate batteries based on static stress and dynamic electrochemical impedance spectroscopy (DEIS). This method involves using a force sensor placed externally to collect total stress in real time, and decomposing the total stress into dynamic stress and static stress, which is mainly related to SOC, based on a pre-calibrated stress-current relationship. Subsequently, candidate SOC values ​​are obtained using a "static stress-SOC lookup table relationship" established during the calibration phase. Since the static stress-SOC relationship is not monotonic, this method further utilizes the trend of static stress change over time to determine whether the battery is in the rising, falling, or plateau region, thereby narrowing down the candidate range. When the SOC still cannot be uniquely determined, the equivalent series capacitance extracted from the mid-frequency band of DEIS is introduced, which changes monotonically with SOC, to ultimately distinguish between high and low SOC regions. SOC estimation is completed through the joint determination of static stress, its changing trend, and impedance spectrum characteristics.

[0006] 1. This method fits the "empirical relationship between dynamic stress and current" through a large number of charge-discharge experiments and separates the static stress accordingly. However, this dynamic stress model does not distinguish between electrochemical expansion and mechanical response, nor does it introduce physical mechanisms such as structural constraints. It relies solely on data fitting for inference, which lacks physical interpretability and is difficult to reflect the actual electro-mechanical coupling behavior of the battery.

[0007] 2. Battery expansion originates not only from the insertion / extraction of lithium ions in the active material but is also affected by ambient temperature and self-heating. With temperature changes, the cell experiences significant thermal expansion, which in turn alters the total stress measured by the force sensor. However, this technology does not model or compensate for the effect of temperature on the force signal, making the static stress-SOC lookup table relationship prone to inaccuracy under varying temperature conditions, and difficult to adapt to the temperature fluctuations commonly found in real vehicles or energy storage systems.

[0008] 3. The total stress, dynamic stress, and static stress of the battery are all affected by the battery clamps and preload. Currently, it is difficult in the industry to guarantee completely consistent preload; even with the same tooling and assembly methods, different preload magnitudes can occur. Therefore, this method requires calibration of the "dynamic stress-current relationship" and "static stress-SOC curve" for each battery, resulting in high experimental costs and long cycles, making it difficult to promote on a large scale.

[0009] 4. The core of this existing technology is to calculate dynamic stress through real-time current and then subtract the dynamic stress from the total stress to obtain the static stress. Therefore, the calculation of dynamic and static stresses is entirely dependent on the measurement accuracy of the force and current sensors. Once the sensors are affected by noise, temperature drift, mechanical loosening, current bias, or transient disturbances, the dynamic stress will be incorrectly estimated, further leading to unavoidable deviations in the static stress. Because this method uses a fixed static stress-SOC calibration lookup table relationship, when errors occur in the static stress, the lookup results cannot be automatically corrected, and the SOC output will subsequently exhibit a systematic deviation. Therefore, this method is highly sensitive to sensor quality, installation conditions, and environmental stability, making it difficult to maintain stable and reliable SOC accuracy under complex operating conditions such as in actual vehicles or energy storage.

[0010] Patent CN120522566A proposes a method for estimating and correcting the State of Charge (SOC) of solid-state batteries based on an equivalent stress model. This method first establishes a mapping table between the battery's mechanical static stress and SOC using test data. Then, it equates the battery and fixture system to a rod-spring-elastic damping mechanical model and identifies the model parameters. Next, it calculates the battery's thermal and mechanical dynamic stresses in real time, and uses the total stress to inversely deduce the mechanical static stress, thereby obtaining the initial SOC value from the mapping table. Finally, it applies mechanical and temperature corrections to the initial value to compensate for the effects of environmental changes and mechanical constraints, ultimately obtaining a high-precision SOC estimation result.

[0011] 1. This method requires obtaining the "first stress," "second stress," and total stress under different SOC, temperature, and initial preload conditions, and establishing a mechanical static stress-SOC relationship table. This table is strongly correlated with ambient temperature, chamber temperature, and initial preload. If the fixture structure, preload, or installation conditions change, the entire relationship table and model parameters must be recalibrated, making rapid migration between different modules and platforms difficult.

[0012] 2. This method takes the measured total stress and temperature as inputs, and directly calculates the SOC by substituting them into the equivalent mechanical model and looking up table relationships. It is highly sensitive to the accuracy of the force sensor, temperature sensor and previous test data. Once the actual measured signal has bias or noise, it is difficult to avoid causing errors in the calculated mechanical static stress, thus affecting the accuracy of SOC estimation.

[0013] 3. This method is designed for solid-state batteries. When applied to LFP batteries, the expansion signal does not change monotonicly with SOC. That is, the same static stress may correspond to multiple SOC values, which can easily lead to non-convergence of model results. Therefore, this method is not suitable for LFP battery systems. Summary of the Invention

[0014] This invention provides a method for estimating the state of charge (SOC) of lithium iron phosphate batteries based on multi-source electro-thermal-mechanical signals, addressing the following technical problems:

[0015] 1. Address the issue of insufficient accuracy of voltage-based SOC estimation algorithms in LFP batteries.

[0016] Because the OCV-SOC curve of LFP batteries exhibits a flat characteristic over a wide range and also displays a significant hysteresis effect (i.e., the charge-discharge OCV curves do not completely overlap), traditional coulomb integration methods and ECM-EKF based on voltage and current signals are difficult to effectively correct, resulting in poor SOC identifiability and limited estimation accuracy. This invention aims to improve the SOC estimation accuracy of LFP batteries across the entire range by introducing an additional expansion force signal for SOC estimation.

[0017] 2. Solve the problem that force signals are severely affected by temperature changes, making them difficult to use stably for SOC estimation.

[0018] The expansion force signal of LFP batteries is not only caused by lithium-ion insertion / extraction, but also by changes in the battery's own temperature, which can lead to expansion or contraction and consequently, changes in expansion force. This invention introduces a thermal expansion coefficient into the mechanical model to correct for battery expansion at a temperature, compensating for the influence of temperature on expansion force and enabling it to be used for SOC stability estimation.

[0019] 3. Address the issues of existing force signal-assisted SOC estimation algorithms lacking physical foundation and having poor transferability.

[0020] Existing SOC estimation methods based on expansion forces mostly rely on empirical fitting or data-driven models, lacking physical modeling of electrochemical expansion, thermal expansion, and mechanical constraints in cell assembly. This makes them difficult to transfer and apply to different cells and tooling fixtures, and also difficult to deploy in real-time within a Battery Management System (BMS). This invention introduces an equivalent mechanical model with clear physical meaning and a corresponding parameter identification algorithm. All model parameters can be obtained through simple experiments, enabling the method to possess both clear physical interpretability and rapid portability.

[0021] 4. Address the technical issues of SOC estimation being overly sensitive to single sensor signals, lacking noise suppression, and having poor model robustness.

[0022] Existing SOC estimation algorithms based on mechanical signals typically rely heavily on instantaneous measurements from force sensors. Once the force signal is affected by factors such as noise, temperature drift, installation deviations, structural loosening, or external mechanical disturbances, the calculated static stress will deviate, directly causing SOC estimation errors. Furthermore, existing methods often employ lookup tables or fixed mapping relationships for SOC calculation, lacking self-correction capabilities when force signals are abnormal, deviate, or unreliable. This makes the estimation results prone to instability or jumps under complex operating conditions such as in actual vehicles or energy storage. This invention introduces a joint estimation framework of mechanical and electrical models, combined with an extended Kalman filter algorithm and an adaptive weighting mechanism, to effectively suppress force signal noise. Simultaneously, when a signal channel experiences a sudden change or an increase in error, the weight of that channel can be actively reduced, thereby improving the robustness and stability of SOC estimation under complex operating conditions and interference.

[0023] This invention constructs a dual-channel SOC estimation system based on the electrical and mechanical characteristics of batteries, and achieves high-precision and robust online SOC calculation through an adaptive fusion method.

[0024] The specific technical solution is as follows:

[0025] A method for estimating the state of charge (SOC) of lithium iron phosphate batteries based on multi-source electro-thermal-mechanical signals includes the following steps:

[0026] S1. Establish the first-order equivalent circuit model of the battery;

[0027] S2. Identify the parameters in the equivalent circuit model based on signals such as current, voltage, and temperature from the hybrid pulse power characteristic test.

[0028] S3. Establish an equivalent mechanical model of the battery;

[0029] S4. Based on the expansion force, current, and temperature signals combined with the parameter identification algorithm, the free expansion curve, stiffness coefficient, and thermal expansion coefficient in the equivalent mechanical model are identified.

[0030] S5. Combine the extended Kalman filter algorithm with the equivalent circuit model to estimate the battery SOC using the real-time measured voltage, current and temperature signals of the battery, and obtain the electrical SOC estimation result.

[0031] S6. Combining the extended Kalman filter algorithm and the equivalent mechanical model, the SOC is estimated using the real-time measured expansion force, temperature, and current signals of the battery to obtain the mechanical SOC estimation result.

[0032] S7. Using an adaptive weighting algorithm, the electrical SOC estimation results and the mechanical SOC estimation results are weighted and calculated to obtain the final SOC result.

[0033] Specifically:

[0034] S1, the equivalent circuit model includes the open-circuit voltage source U. OC Ohmic resistor R0 and polarization resistor R P and polarization capacitor C P The parallel RC network, composed of these components, collectively describes the dynamic polarization characteristics of the battery. This model takes the load current I(t) as input and the terminal voltage U... L (t) represents the output, which is controlled by the following equation, where t is the operating time:

[0035] (1)

[0036] (2)

[0037] S2, the parameters in the equivalent circuit model include the open-circuit voltage source U. OC Ohmic resistor R0, polarization resistor R p and polarization capacitor C P All of these parameters are functions of SOC and temperature. To obtain the relationship between these parameters and SOC and temperature, offline identification was performed using hybrid pulse power characteristic testing (HPPC). Specifically, standard charge and discharge pulse sequences were applied to the battery at different SOC points and temperatures, and voltage and current response data were collected. Based on the pulse response data, the model parameters were determined according to the following relationship:

[0038] (3)

[0039] (4)

[0040] (5)

[0041] Among them, I Dis with I Cha These are the discharge pulse and charging pulse currents, respectively; τ is the relaxation time constant of the battery polarization voltage, defined as the time consumed for the voltage change during the resting phase to reach 63% of its total change; U1, U2, U3, U4, and U5 are the HPPC test voltage characteristic points at this SOC and temperature, respectively, and the battery voltage after being fully rested at different SOC points is the open circuit voltage at that SOC.

[0042] S3. Establish a phenomenological mechanical model, which considers the battery as consisting of parallel wound electrodes and a casing. During charging and discharging, the insertion and extraction of lithium ions cause volume changes in the wound electrodes, characterized by the following nonlinear relationship:

[0043] (6)

[0044] Wherein: F aFor the expansion force of the wound electrode, k a1 and k a2 These represent the linear and nonlinear stiffness components of the wound electrode, respectively. The expansion and deformation of the wound electrode caused by lithium-ion intercalation.

[0045] In reality, the wound electrode is constrained by the outer shell, which can be characterized by the following relationship:

[0046] (7)

[0047] Wherein: F c For the reaction force of the shell constraint, k c This is the equivalent stiffness of the battery casing. The initial deformation of the casing is 0. The deformation of the outer shell due to the interaction between the outer shell and the wound electrodes.

[0048] In engineering, batteries are often placed in rigid battery clamps, with cushioning material placed between them and a preload applied. In this configuration, the force acting on the wound electrode is equal to the sum of the constraint force of the battery casing and the expansion force of the cushioning material, which can be characterized by the following relationship:

[0049] (8)

[0050] Wherein: F c and F s These represent the constraint force from the battery casing and the expansion force from the cushioning material, respectively. For the deformation of the battery casing under the action of cushioning material, rigid clamps, and preload, k s Let s0 be the equivalent stiffness of the buffer material, and s0 be the deformation of the buffer material under the preload F0. In actual use, the force sensor is deployed between the buffer material and the rigid clamp. The battery expansion force measured by the sensor is equal to the force on the buffer material, and the expansion force F0 is... m It is represented by the following relation:

[0051] (9)

[0052] Considering the effect of temperature changes on battery expansion, the following formula is used to describe the expansion displacement of the wound electrode. Make corrections:

[0053] (10)

[0054] in: F represents the temperature-corrected expansion displacement of the wound electrode. T The coefficient of thermal expansion, T is the actual temperature of the battery, T ref For reference battery temperature; The battery's state of charge (SOC) and temperature (T) are related to the battery's energy level (T), thus establishing an equivalent mechanical model with SOC and temperature as inputs and battery expansion force as output.

[0055] S4, regarding the coefficient of thermal expansion F T At various SOCs, the batteries were placed in constant temperature chambers at different temperatures. After thermal equilibrium was reached, the maximum expansion of the batteries was recorded. The coefficient of thermal expansion at different SOCs was calculated according to Equation 10. The expansion displacement of the wound electrodes was then considered. Because the aluminum-plastic soft-pack battery casing has low rigidity, the expansion of the battery after being left to stand for a sufficient period of time at different SOCs is directly measured under standard temperature conditions. This allows us to obtain the free expansion displacement of the wound electrodes related to the battery's SOC. .

[0056] For each equivalent stiffness parameter in the equivalent circuit model, it is obtained quickly either by disassembling and measuring them one by one, or by identifying the parameters using quasi-static force test results. Quasi-static force testing involves installing the battery in a fixture, fully charging it to 100% SOC, allowing it to stand for a period of time, then discharging it at a rate of 0.33C to 5% SOC, allowing it to stand for a period of time, and recording the expansion force at each step. This process is repeated until the battery is discharged to 0% SOC, thus obtaining the open-circuit expansion force curve of the battery. Then, an optimization algorithm is used to identify the stiffness parameters using the SOC and expansion force data. The loss function F(θ) is shown below:

[0057] (11)

[0058] in The battery expansion force is predicted by the equivalent mechanical model. F represents the initial preload predicted by the equivalent mechanical model, where F is the battery expansion force and F0 is the battery preload. , The weight parameters are set.

[0059] S5 combines the equivalent circuit model with the extended Kalman filter algorithm to obtain the electrical SOC estimation result. The extended Kalman filter process mainly includes two stages: prediction and update.

[0060] S6 combines the corresponding equivalent mechanical model with the extended Kalman filter algorithm to obtain the mechanical SOC estimation result. Similarly, this extended Kalman filter process mainly includes two stages: prediction and update.

[0061] S7, the mechanical SOC estimation results and the electrical SOC estimation results are adaptively weighted in the following manner:

[0062] (12)

[0063] (13)

[0064] (14)

[0065] (15)

[0066] (16)

[0067] Where: ΔF represents the difference between the expansion force estimated by the equivalent mechanical model and the expansion force measured by the sensor; ΔF lim This is the maximum allowable upper limit for the difference; This represents the weights assigned to the equivalent electrophysiological model; ΔV represents the weights pre-assigned to the equivalent circuit model; ΔV represents the difference between the battery terminal voltage estimated by the equivalent circuit model and the battery voltage measured by the sensor; ΔV lim This is the maximum allowable upper limit for the difference; This represents the weights assigned to the equivalent circuit model; This represents the weights pre-assigned to the equivalent circuit model; The above mechanical SOC estimation results; Based on the above electrical SOC estimation results, The final SOC estimation result is given by k1 and k2, which are proportional conversion coefficients.

[0068] The beneficial effects of the technical solution of this invention are as follows:

[0069] 1. This invention introduces an expansion force signal as an additional observable measurement in addition to traditional electrical signals. By mapping the mechanical response to the state of charge (SOC), it effectively compensates for the lack of discernibility of the flat OCV range of LFP batteries, enabling the SOC to obtain stable estimation accuracy across the entire range.

[0070] 2. This invention explicitly introduces a thermal expansion term into the mechanical model and compensates for the influence of thermal expansion on the total expansion force of the battery based on synchronously collected data from temperature sensors. This significantly reduces the error caused by the force signal changing with temperature, enabling the mechanical channel to be used stably in a wide temperature range.

[0071] 3. The equivalent mechanical model constructed in this invention simultaneously considers chemical expansion, thermal expansion, and assembly constraints. The model parameters can be identified through a small number of experiments, exhibiting good portability and engineering adaptability, and is suitable for real-time deployment and operation in vehicle-mounted BMS.

[0072] 4. This invention uses extended Kalman filtering to synchronously estimate electrical and mechanical signals, and uses an adaptive weighting mechanism to adjust the contribution of each channel according to the real-time error. It can automatically suppress abnormal inputs under sensor noise, temperature drift, structural disturbance or non-ideal force signal conditions, and ensure the continuity, stability and reliability of SOC output. Attached Figure Description

[0073] Figure 1 This is a flowchart of the present invention;

[0074] Figure 2 This is a schematic diagram of the equivalent circuit model of the present invention;

[0075] Figure 3 This is a battery voltage diagram after being allowed to settle at different SOC points according to the present invention;

[0076] Figure 4 This is a schematic diagram of the phenomenological mechanical model of the present invention. Detailed Implementation

[0077] like Figure 1 As shown, the SOC estimation method for lithium iron phosphate batteries based on multi-source electro-thermal-mechanical signals of the present invention mainly includes the following steps:

[0078] In step S1, a first-order equivalent circuit model of the battery is established, and in step S2, the parameters in the equivalent circuit model are identified based on the current, voltage, temperature and other signals in the hybrid pulse power characteristic test.

[0079] In step S3, an equivalent mechanical model of the battery is established. In step S4, based on signals such as expansion force, current, and temperature, a parameter identification algorithm is used to identify the free expansion curve, stiffness coefficient, thermal expansion coefficient, etc. in the equivalent mechanical model.

[0080] In step S5, the battery SOC is estimated by combining the extended Kalman filter algorithm and the equivalent circuit model with the real-time measured voltage, current, temperature and other signals of the battery to obtain the electrical SOC estimation result; in step S6, the battery SOC is estimated by combining the extended Kalman filter algorithm and the equivalent mechanical model with the real-time measured expansion force, temperature, current and other signals of the battery to obtain the mechanical SOC estimation result.

[0081] In step S7, the electrical SOC estimation result and the mechanical SOC estimation result are weighted and calculated using an adaptive weighting algorithm to obtain the final SOC result.

[0082] For step S1, establish as follows Figure 2 The equivalent circuit model shown includes an open-circuit voltage source U. OC An ohmic resistor R0 and a polarization resistor R P and polarization capacitor C P The parallel RC network, composed of these components, collectively describes the dynamic polarization characteristics of the battery. This model takes the load current I as input and the terminal voltage U as input. L The output is controlled by the following equation.

[0083] (1)

[0084] (2)

[0085] For step S2, the parameters in the equivalent circuit model include the open-circuit voltage source U. OC Ohmic resistor R0, polarization resistor R p and polarization capacitor C P All of these are functions of SOC and temperature. To obtain the relationship between these parameters and SOC and temperature, this invention uses hybrid pulse power characteristic testing (HPPC) for offline identification. Specifically, standard charge and discharge pulse sequences are applied to the battery at different SOC points and temperatures, and voltage and current response data are collected. Based on the pulse response data, model parameters are determined according to the following relationship:

[0086] (3)

[0087] (4)

[0088] (5)

[0089] Among them, I Dis with I Cha These are the discharge pulse and charging pulse currents, respectively; τ is the relaxation time constant of the battery polarization voltage, defined as the time consumed for the voltage change during the resting phase to reach 63% of its total change; such as Figure 3 U1, U2, U3, U4, and U5 are shown as characteristic points of the HPPC test voltage at the given SOC and temperature. The battery voltage after being allowed to rest at different SOC points is U at that SOC. OC .

[0090] For step S3, establish as follows Figure 4 The phenomenological mechanical model shown treats the battery as a series of parallel wound electrodes and a casing. During charging and discharging, the insertion and extraction of lithium ions cause volume changes in the wound electrodes, which can be characterized by the following nonlinear relationship:

[0091] (6)

[0092] Wherein: F a For the expansion force of the wound electrode, k a1 and k a2 These represent the linear and nonlinear stiffness components of the wound electrode, respectively. This represents the expansion displacement of the wound electrode caused by lithium-ion intercalation (in the unconstrained state). However, in reality, the wound electrode is constrained by the battery casing, forming a parallel mechanical system. The force exerted by the wound electrode on the casing is equal in magnitude and opposite in direction to the force exerted by the casing on the wound electrode. Therefore, for a battery model constrained by the casing, the following relationship characterizes it:

[0093] (7)

[0094] Wherein: F c For the reaction force of the shell constraint, k c This is the equivalent stiffness of the battery casing. The initial deformation of the casing is 0. This refers to the deformation of the battery casing due to the interaction between the casing and the wound electrodes. In practical applications, batteries are often placed in rigid battery clamps, with cushioning material placed between them and a preload applied. Under this configuration, the force acting on the wound electrodes is equal to the sum of the battery casing constraint force and the expansion force of the cushioning material, which can be characterized by the following relationship:

[0095] (8)

[0096] Wherein: F c and F s These represent the constraint force from the battery casing and the expansion force from the cushioning material, respectively. For the deformation of the battery casing under the action of cushioning material, rigid clamps, and preload, k s Let s0 be the equivalent stiffness of the buffer material, and s0 be the deformation of the buffer material under the preload F0. In actual use, the force sensor is deployed between the buffer material and the rigid clamp. The battery expansion force measured by the sensor is equal to the force on the buffer material; therefore, the expansion force F0 is... m It can be represented by the following relation:

[0097] (9)

[0098] Considering the effect of temperature changes on battery expansion, the following formula is used to describe the expansion displacement of the wound electrode. Make corrections:

[0099] (10)

[0100] in: F represents the temperature-corrected expansion displacement of the wound electrode. T The coefficient of thermal expansion, T is the actual temperature of the battery, T ref For reference battery temperature (T) ref =25℃). Related to the battery's state of charge (SOC) and temperature T, an equivalent mechanical model was established with SOC and temperature as inputs and battery expansion force as output.

[0101] For step S4, regarding the coefficient of thermal expansion F T The battery can be placed in a constant temperature chamber at different temperatures under various SOCs. After thermal equilibrium is reached, the maximum expansion of the battery is recorded, and the thermal expansion coefficient under different SOCs is calculated according to formula (10). For the expansion displacement of the wound electrode, (Unconstrained state), due to the low rigidity of the aluminum-plastic soft-pack battery casing, it can be directly used in a standard temperature environment (T=T). ref The expansion of the battery after being allowed to stand for a sufficient period of time (SOC) was measured at 25℃ to obtain the free expansion displacement of the wound electrode related to the battery SOC. All the above parameters are measured at the battery level, without the need for installation in a tooling fixture. Furthermore, since batteries in the same batch have high consistency, the results of a single test can effectively reflect the overall characteristics of that batch of batteries.

[0102] For each equivalent stiffness parameter in the equivalent circuit model, it can be obtained quickly by disassembling and measuring them one by one, or by identifying the parameters using quasi-static force test results. Quasi-static force testing involves installing the battery in a fixture, fully charging it to 100% SOC, allowing it to stand for a while, then discharging it at a rate of 0.33C to 5% SOC, allowing it to stand for a while, and recording the expansion force at each step. This process is repeated until it discharges to 0% SOC, thus obtaining the battery's open-circuit expansion force curve. Then, particle swarm optimization, genetic algorithms, least squares methods, or other optimization algorithms are used to identify the stiffness parameters using the SOC and expansion force data. The loss function F(θ) is shown below:

[0103] (11)

[0104] in The battery expansion force is predicted by the equivalent mechanical model. F represents the initial preload predicted by the equivalent mechanical model, where F is the battery expansion force and F0 is the battery preload. , The weight parameters are set.

[0105] In step S5, the corresponding equivalent circuit model is combined with the extended Kalman filter algorithm to obtain the electrical SOC estimation result. The extended Kalman filter algorithm involved in this invention is a well-known algorithm to those skilled in the art, and its specific steps can be found in relevant technical literature. In short, the extended Kalman filter process mainly includes two stages: prediction and update.

[0106] 1. Prediction phase: Based on the SOC estimate, current information and real-time battery temperature of the previous moment, the prior SOC estimate and the prior terminal voltage estimate of the current moment are predicted through the state equation of the equivalent circuit model.

[0107] 2. Update Phase: The obtained prior estimate of the terminal voltage is compared with the actual measured value. The Kalman gain is calculated, and this gain is used to correct the prior estimate of the SOC, obtaining the optimal posterior estimate of the SOC at the current moment, which is used as the mechanical SOC estimation result. Through this closed-loop feedback correction mechanism, measurement noise and model errors can be effectively suppressed, achieving high-precision and stable SOC estimation.

[0108] For step S6, the corresponding equivalent mechanical model is combined with the extended Kalman filter algorithm to obtain the mechanical SOC estimation result. Similarly, this extended Kalman filter process mainly includes two stages: prediction and update.

[0109] 1. Prediction phase: Based on the SOC estimate of the previous moment and the real-time battery temperature, the prior SOC estimate and the prior expansion force estimate of the current moment are predicted through the state equation of the equivalent mechanical model.

[0110] 2. Update phase: The obtained prior estimate of expansion force is compared with the actual measured value, the Kalman gain is calculated, and the prior estimate of SOC is corrected using the gain to obtain the optimal posterior estimate of SOC at the current time, which is used as the mechanical SOC estimation result.

[0111] For step S7, the mechanical SOC estimation results and the electrical SOC estimation results are adaptively weighted in the following manner:

[0112] (12)

[0113] (13)

[0114] (14)

[0115] (15)

[0116] (16)

[0117] Where: ΔF represents the difference between the expansion force estimated by the equivalent mechanical model and the expansion force measured by the sensor; ΔF lim This is the maximum allowable upper limit for the difference; This represents the weights assigned to the equivalent electrophysiological model; ΔV represents the weights pre-assigned to the equivalent circuit model; ΔV represents the difference between the battery terminal voltage estimated by the equivalent circuit model and the battery voltage measured by the sensor; ΔV lim This is the maximum allowable upper limit for the difference; This represents the weights assigned to the equivalent circuit model; This represents the weights pre-assigned to the equivalent circuit model; The above mechanical SOC estimation results; Based on the above electrical SOC estimation results, The final SOC estimation result is represented by k1 and k2, which are scaling factors. This adaptive weighting method can dynamically adjust the prediction accuracy of the two models, avoiding significant impacts on the prediction results due to fluctuations or drift of a single sensor, and ensuring the robustness of the SOC prediction results.

[0118] The structure of the equivalent circuit model of this invention can be configured according to the requirements of estimation accuracy, computational complexity, and application scenarios. The equivalent circuit model includes, but is not limited to: a basic first-order RC model, a second-order RC model that can more accurately describe the dual-polarization effect, and a third-order or higher-order RC model designed to meet extremely high accuracy requirements. Furthermore, for energy storage units such as lithium iron phosphate that have significant voltage hysteresis characteristics, the equivalent circuit model can also be a first-order hysteresis model or a second-order hysteresis model integrating a hysteresis voltage source.

[0119] The parameter identification experiment of the equivalent circuit model of this invention is not limited to the hybrid pulse power characteristic (HPPC) experiment, but can also use other dynamic stress tests (DST), Federal Urban Driving Schedules (FUDS), or custom dynamic operating condition curves for parameter identification. The parameter identification algorithm of the equivalent circuit model is not limited to a specific method, and can use direct calculation methods, or optimization estimation algorithms including least squares methods (such as recursive least squares), particle swarm optimization algorithms, genetic algorithms, Kalman filtering, or combinations thereof for parameter identification.

[0120] The equivalent mechanical model of the present invention is not limited to elastic elements (such as springs), and other mechanical elements such as dampers can also be introduced to construct a more complex mechanical model, thereby more accurately simulating the mechanical characteristics of the battery.

[0121] The adjustment strategies of the adaptive weight optimization algorithm of the present invention include, but are not limited to: adjusting the weights of mechanical signals separately, adjusting the weights of electrical signals separately, or coordinating the adjustment of the weights of mechanical and electrical signals.

[0122] The extended Kalman filter algorithm of this invention can be any filtering method used for nonlinear state estimation, including extended Kalman filter (EKF), unscented Kalman filter (UKF), square root Kalman filter (SR-KF), capacitive Kalman filter (CKF), etc.

Claims

1. A method for estimating the state of charge (SOC) of a lithium iron phosphate battery based on multi-source electro-thermal-mechanical signals, characterized in that, Includes the following steps: S1. Establish the first-order equivalent circuit model of the battery; S2. Identify the parameters in the equivalent circuit model based on signals such as current, voltage, and temperature in the hybrid pulse power characteristic test. S3. Establish an equivalent mechanical model of the battery; S4. Based on the expansion force, current, and temperature signals combined with the parameter identification algorithm, the free expansion curve, stiffness coefficient, and thermal expansion coefficient in the equivalent mechanical model are identified. S5. Combine the extended Kalman filter algorithm with the equivalent circuit model to estimate the battery SOC using the real-time measured voltage, current and temperature signals of the battery, and obtain the electrical SOC estimation result. S6. Combine the extended Kalman filter algorithm and the equivalent mechanical model to estimate the SOC using the real-time measured expansion force, temperature and current signals of the battery, and obtain the mechanical SOC estimation result. S7. Using an adaptive weighting algorithm, the electrical SOC estimation results and the mechanical SOC estimation results are weighted and calculated to obtain the final SOC result.

2. The method for estimating the state of charge (SOC) of a lithium iron phosphate battery based on electro-thermal-mechanical multi-source signals according to claim 1, characterized in that, The equivalent circuit model in S1 includes an open-circuit voltage source U. OC Ohmic resistor R0 and polarization resistor R P and polarization capacitor C P The parallel RC network, composed of these components, collectively describes the dynamic polarization characteristics of the battery. This model takes the load current I(t) as input and the terminal voltage U... L (t) is the output, which is controlled by the following equation, where t is the working time; （1） （2）。 3. The method for estimating the state of charge (SOC) of a lithium iron phosphate battery based on multi-source electro-thermal-mechanical signals according to claim 1, characterized in that, The parameters in the equivalent circuit model in S2 include the open-circuit voltage source U. OC Ohm resistor R0, polarization resistor R p and polarization capacitor C P All of these parameters are functions of SOC and temperature. To obtain the relationship between these parameters and SOC and temperature, offline identification was performed using hybrid pulse power characteristic testing (HPPC). Specifically, standard charge and discharge pulse sequences were applied to the battery at different SOC points and temperatures, and voltage and current response data were collected. Based on the pulse response data, the model parameters were determined according to the following relationship: （3） （4） （5） Among them, I Dis with I Cha These are the discharge pulse and charging pulse currents, respectively; τ is the relaxation time constant of the battery polarization voltage, defined as the time consumed for the voltage change during the resting phase to reach 63% of its total change; U1, U2, U3, U4, and U5 are the HPPC test voltage characteristic points at this SOC and temperature, respectively, and the battery voltage after being fully rested at different SOC points is the open circuit voltage at that SOC.

4. The method for estimating the state of charge (SOC) of a lithium iron phosphate battery based on multi-source electro-thermal-mechanical signals according to claim 1, characterized in that, In S3, a phenomenological mechanical model is established, which considers the battery as consisting of parallel wound electrodes and a casing. During charging and discharging, the insertion and extraction of lithium ions cause volume changes in the wound electrodes, which are characterized by the following nonlinear relationship: （6） Wherein: F a For the expansion force of the wound electrode, k a1 and k a2 These represent the linear and nonlinear stiffness components of the wound electrode, respectively. The expansion and deformation of the wound electrode caused by lithium-ion intercalation; In reality, the wound electrode is constrained by the outer shell, which can be characterized by the following relationship: （7） Wherein: F c For the reaction force of the shell constraint, k c This is the equivalent stiffness of the battery casing; the initial deformation of the casing is 0. The deformation of the outer shell due to the interaction between the outer shell and the wound electrodes; In engineering, batteries are often placed in rigid battery clamps, with cushioning material placed between them and a preload applied. In this configuration, the force acting on the wound electrode is equal to the sum of the constraint force of the battery casing and the expansion force of the cushioning material, which can be characterized by the following relationship: （8） Wherein: F c and F s These represent the constraint force from the battery casing and the expansion force from the cushioning material, respectively. For the deformation of the battery casing under the action of cushioning material, rigid clamps, and preload, k s Let s0 be the equivalent stiffness of the buffer material, and s0 be the deformation of the buffer material under the preload F0. In actual use, the force sensor is deployed between the buffer material and the rigid clamp. The battery expansion force measured by the sensor is equal to the force on the buffer material. Therefore, the measured expansion force F is... m It is represented by the following relation: （9） Considering the effect of temperature changes on battery expansion, the following formula is used to describe the expansion displacement of the wound electrode. Make corrections: （10） in: F represents the temperature-corrected expansion displacement of the wound electrode. T The coefficient of thermal expansion, T is the actual temperature of the battery, T ref For reference battery temperature; The battery's state of charge (SOC) and temperature (T) are related to the battery's state of charge (SOC) and temperature, thus establishing an equivalent mechanical model with SOC and temperature as inputs and battery expansion force as output.

5. The method for estimating the state of charge (SOC) of a lithium iron phosphate battery based on multi-source electro-thermal-mechanical signals according to claim 1, characterized in that, S4 refers to the coefficient of thermal expansion F T At various SOCs, the batteries were placed in constant temperature chambers at different temperatures. After thermal equilibrium was reached, the maximum expansion of the batteries was recorded. The coefficient of thermal expansion at different SOCs was calculated according to Equation 10. The expansion displacement of the wound electrodes was then considered. Because the aluminum-plastic soft-pack battery casing has low rigidity, the expansion of the battery after being allowed to stand for a sufficient period of time at different SOCs is directly measured under standard temperature conditions. This allows us to obtain the free expansion displacement of the wound electrodes related to the battery's SOC. ; For each equivalent stiffness parameter in the equivalent circuit model, the parameters are obtained quickly by either disassembling and measuring them one by one or by identifying the parameters using quasi-static force test results. Quasi-static force testing involves installing the battery into a fixture, fully charging it to 100% SOC, allowing it to stand for a period of time, then discharging it at a rate of 0.33C to 5% SOC, allowing it to stand for a period of time, and recording the expansion force at each step. This process is repeated until the battery is discharged to 0% SOC, thus obtaining the open-circuit expansion force curve of the battery. Then, an optimization algorithm is used to identify the stiffness parameters using the SOC and expansion force data. The loss function F(θ) is shown below: （11） in The battery expansion force is predicted by the equivalent mechanical model. F represents the initial preload predicted by the equivalent mechanical model, where F is the battery expansion force and F0 is the battery preload. , The weight parameters are set.

6. The method for estimating the state of charge (SOC) of a lithium iron phosphate battery based on electro-thermal-mechanical multi-source signals according to claim 1, characterized in that, In S7, the mechanical SOC estimation results and the electrical SOC estimation results are adaptively weighted in the following manner: （12） （13） （14） （15） （16） Where: ΔF represents the difference between the expansion force estimated by the equivalent mechanical model and the expansion force measured by the sensor; ΔF lim This is the maximum allowable upper limit for the difference; This represents the weights assigned to the equivalent electrophysiological model; This represents the weights pre-assigned to the equivalent circuit model; ΔV represents the difference between the battery terminal voltage estimated by the equivalent circuit model and the battery voltage measured by the sensor; ΔV lim This is the maximum allowable upper limit for the difference; This represents the weights assigned to the equivalent circuit model; This represents the weights pre-assigned to the equivalent circuit model; The above mechanical SOC estimation results; Based on the above electrical SOC estimation results, The final SOC estimation result is given by k1 and k2, which are proportional conversion coefficients.

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