Uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics

Abstract

The application relates to the technical field of uninterrupted power supply energy management, and discloses an uninterrupted power supply energy management optimization method based on the characteristics of sodium ion batteries. Firstly, the terminal voltage of the battery pack and the charging current are collected, and the transient differential capacity is calculated, which is used for determining the electrochemical phase transition across the boundary and generating a trigger signal; after receiving the trigger signal, the second-order time derivative of the terminal voltage is calculated, when the second-order time derivative exceeds the polarization threshold value determined based on the current environmental temperature, the bidirectional energy storage converter uses the filter inductance to form a depolarization micro-discharge current through reverse freewheeling; in the charging relaxation time window after the micro-discharge ends, the terminal voltage attenuation sequence is collected to calculate the concentration difference polarization time constant, and the cross-cycle relaxation time constant gradient is extracted; finally, the time domain length or the amplitude domain slope of the subsequent charging instruction is reconstructed and updated according to the gradient. The application can dissipate the polarization charge in the battery, avoid the sodium precipitation side reaction, and prolong the service life of the battery pack.

Description

Technical Field

[0001] This invention relates to the field of uninterruptible power supply (UPS) energy management technology, specifically to an UPS energy management optimization method based on the characteristics of sodium-ion batteries. Background Technology

[0002] Uninterruptible power supply (UPS) systems serve as backup power for critical equipment such as data centers and industrial control systems, placing stringent requirements on the charging and discharging response speed and operational safety of energy storage batteries. Sodium-ion batteries, due to their wide operating temperature range and material cost advantages, are increasingly being used in UPS energy storage modules. However, most existing UPS charging management systems rely on conventional constant current-constant voltage control strategies and are not adapted to the sodium intercalation mechanism of the hard carbon material in the sodium-ion battery's negative electrode.

[0003] In actual charging processes, due to the lack of precise identification of internal electrochemical reaction regions, traditional control strategies often maintain a high current input even after the battery enters the low-potential sodium intercalation plateau region. This continuous forced energy injection leads to an increase in the sodium ion concentration gradient on the electrode surface, triggering concentration polarization and causing a nonlinear rise in local potential. When the accumulated polarization charge exceeds the critical state, it can easily induce sodium deposition side reactions, causing irreversible loss of active materials and even affecting the overall lifespan and safety of the battery pack.

[0004] To mitigate polarization during charging, conventional techniques attempt to insert charging pauses or reverse pulse discharges during constant current charging. However, in uninterruptible power supply (UPS) applications, the energy storage converter must maintain a standby response state to mains power interruptions at all times, and the system design does not allow for excessively long charging pause times. Traditional charge / discharge switching typically requires a complete converter shutdown with a long dead time, which directly causes DC bus voltage disturbances.

[0005] Meanwhile, within the limited transient time window, existing systems struggle to obtain effective deep electrochemical parameters, making it impossible to accurately quantify the evolution trend of ion solid-phase diffusion resistance within the battery. Due to the lack of feedback indicators characterizing the battery's polarization dissipation capability, the system cannot adaptively reconstruct subsequent charging time and current amplitude based on the battery's current actual health state, making it difficult to achieve a balance between fast charging, polarization control, and ensuring system availability. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides an optimization method for uninterruptible power supply (UPS) energy management based on the characteristics of sodium-ion batteries. This method solves the problems that existing UPS systems struggle to accurately identify and dissipate local polarization of sodium-ion batteries without disturbance within a limited transient time window, and that the lack of deep electrochemical feedback parameters prevents the system from adaptively reconstructing subsequent charging commands based on the battery's actual polarization dissipation capability.

[0007] To achieve the above objectives, this invention provides an uninterruptible power supply energy management optimization method based on the characteristics of sodium-ion batteries, comprising the following steps:

[0008] The terminal voltage and charging current of the battery pack are collected and the transient differential capacity is calculated to determine the electrochemical phase transition crossing the boundary and generate a trigger signal.

[0009] After receiving the trigger signal, the second time derivative of the terminal voltage is calculated. When the second time derivative exceeds the polarization threshold determined based on the current ambient temperature, the bidirectional energy storage converter is controlled to form a depolarization micro-discharge current.

[0010] The polarization threshold is determined based on a threshold mapping table constructed from offline electrochemical AC impedance spectroscopy experimental data;

[0011] During the depolarization micro-discharge current termination and subsequent charging-off relaxation time window, the decay sequence of the terminal voltage is collected to calculate the concentration polarization time constant and extract the gradient of the cross-cycle relaxation time constant.

[0012] The subsequent charging commands are reconstructed and updated based on the gradient of the cross-cycle relaxation time constant.

[0013] Preferably, the terminal voltage and charging current of the battery pack are collected and the transient differential capacity is calculated to determine the electrochemical phase transition crossing the boundary and generate a trigger signal, specifically including:

[0014] The sampling trigger time of the analog-to-digital converter is anchored at the apex or apex of the pulse width modulation triangular carrier wave, and the original terminal voltage sequence of the terminal voltage and the original current sequence of the charging current are acquired synchronously.

[0015] A first-order discrete low-pass digital filter is applied to the original terminal voltage sequence and the original current sequence to perform data smoothing, extract the reference terminal voltage and reference current, and calculate the reference terminal voltage difference between adjacent control cycles.

[0016] The total charge is obtained by multiplying the reference current of the current cycle by the control step size, and the transient differential capacity is calculated and output by dividing the total charge by the sum of the reference terminal voltage difference and the minimum bias constant.

[0017] The minimum bias constant is set to 10.-6 Order of magnitude;

[0018] When a positive step increase in the amplitude of the transient differential capacity is detected, exceeding the characteristic threshold set according to the inherent ratio of the capacity difference between the slope region and the plateau region of the hard carbon anode based on offline calibration, and the continuous maintenance time of the high amplitude state is greater than the length of the moving state discrimination window, it is determined that the electrochemical phase transition crossing boundary has been crossed and the trigger signal is generated.

[0019] The characteristic threshold is set to 1.5 to 3.0 times the average transient differential capacity amplitude of the hard carbon negative electrode slope region, and the length of the moving state discrimination window is defined by the product of the system discrete control time step and the duration of typical electromagnetic interference.

[0020] Preferably, the step of calculating the second-order time derivative of the terminal voltage after receiving the trigger signal, and when the second-order time derivative exceeds the polarization threshold determined based on the current ambient temperature, specifically includes:

[0021] Retrieve the reference terminal voltage data stored at historical time points, calculate the second-order time derivative based on the reference terminal voltage data using a second-order central difference algorithm, and perform a moving average processing on the second-order time derivative.

[0022] The absolute ambient temperature of the current battery surface is obtained. The absolute ambient temperature is aligned with the calculation cycle by constructing zero-order hold interpolation logic. The absolute ambient temperature is then substituted into the threshold mapping table constructed based on offline electrochemical AC impedance spectroscopy experimental data. The corresponding second-order voltage curvature critical value at the current temperature is extracted and multiplied by a set safety factor to obtain the dynamic polarization determination threshold as the polarization threshold.

[0023] The safety factor is set to be 0.8 to 0.9.

[0024] When the second-order time derivative after the moving average processing exceeds the polarization threshold, the first-order time change rate of the terminal voltage is positive, and the number of consecutive cycles of the over-limit state exceeds the set anti-shake count limit, a micro-discharge intervention command is issued.

[0025] The anti-shake count limit is set to 3 to 5 consecutive control cycles.

[0026] Preferably, responding to the micro-discharge intervention command, controlling the bidirectional energy storage converter to generate the depolarization micro-discharge current specifically includes:

[0027] Change the driving state of the main switch tube and the synchronous rectifier tube of the bidirectional energy storage converter, cut off the driving signal of the main switch tube and keep the synchronous rectifier tube in the normally open conducting state.

[0028] By relying on the reverse freewheeling of the output-side filter inductor, the polarity of the induced electromotive force at both ends of the output-side filter inductor is reversed. The inductor current decreases linearly at a fixed slope to the zero crossover point and then reverse suction control is executed. The current flows in reverse from the battery end of the battery pack through the output-side filter inductor and the synchronous rectifier tube to form the depolarization micro-discharge current.

[0029] The instantaneous amplitude of the depolarization micro-discharge current is monitored at high frequency. When the absolute value of the instantaneous amplitude reaches the depolarization limit, the normally open control word of the synchronous rectifier is canceled and the drive signal of the synchronous rectifier is turned off, the energy exchange channel is cut off and the zero-current stop-charge relaxation time window is entered.

[0030] The depolarization limit is set to 5% to 10% of the nominal capacity of the battery pack.

[0031] Preferably, the calculation of the concentration polarization time constant specifically includes:

[0032] Within the charging and relaxation time window, discrete values ​​of the terminal voltage decay curve are continuously collected at a fixed interruption frequency, pushed into a first-in-first-out queue, and truncated or interpolated for alignment to form a terminal voltage decay sequence with a fixed constant sequence length.

[0033] The terminal voltage decay sequence is input into the state observer to construct a zero-input response equivalent model based on a second-order RC network. The zero-input response equivalent model decomposes the terminal voltage decay function into a steady-state open-circuit voltage term, a fast polarization exponent term, and a slow polarization exponent term.

[0034] The extended Kalman filter algorithm is selected as the state observer for nonlinear system identification. The unit diagonal regularization matrix parameter is superimposed in the covariance matrix update equation to ensure the numerical stability of the inversion operation. After iterative convergence, the time constant value characterizing the concentration polarization solid-phase diffusion process is extracted as the concentration polarization time constant.

[0035] The length of the pause-charge relaxation time window is set to 50–200 ms.

[0036] Preferably, the extraction of the gradient of the relaxation time constant across periods specifically includes:

[0037] The concentration polarization time constant extracted at the moment is subtracted from the observation value extracted in the previous depolarization cycle to obtain the difference across two adjacent cycles.

[0038] A historical weighted moving average filter is applied to the difference, and the final evaluation index is output after smoothing by combining the data from the past three cycles. The final evaluation index is used as the gradient of the cross-cycle relaxation time constant.

[0039] Preferably, the step of reconstructing and updating subsequent charging commands based on the gradient of the cross-cycle relaxation time constant specifically includes:

[0040] Based on the gradient of the cross-cycle relaxation time constant, a multi-scale state machine is used for determination. A dual-threshold determination logic with hysteresis characteristics is introduced to compare the received gradient of the cross-cycle relaxation time constant with the warning upper limit threshold and the recovery lower limit threshold.

[0041] The upper warning threshold is determined based on the impedance mutation inflection point data of the same batch of batteries in the full life cycle aging test. The upper warning threshold is set as an increment of 15% to 25% of the standard concentration polarization time constant under the initial healthy state of the battery. The lower recovery threshold is set as 70% to 80% of the upper warning threshold.

[0042] When the gradient of the cross-cycle relaxation time constant continuously exceeds the warning upper limit threshold to reach the number of anti-shake cycles, the state machine flips from the normal state to the polarization convergence and divergence deterioration state.

[0043] The number of anti-shake cycles is set to 2 to 4 consecutive cycles;

[0044] When the state machine is in the polarization convergence and divergence deterioration state and the gradient of the cross-cycle relaxation time constant is continuously lower than the recovery lower limit threshold, the state machine switches back to the normal state.

[0045] Preferably, under the normal state, the reconstruction update manifests as correcting the duration of the next constant current charging phase, specifically including:

[0046] The next constant current charging stage duration is dynamically mapped based on the gradient value of the cross-cycle relaxation time constant. The calculation process introduces a time scaling gain coefficient and a standard concentration polarization time constant reference value. Time limiting protection logic is added at the output to ensure that the updated time instruction is not lower than the minimum interrupt step limit of the underlying timer.

[0047] Preferably, under the polarization convergence / divergence deterioration state, the reconstruction update manifests as reconstructing the charging current command into a time-varying drooping current envelope with a decreasing slope, specifically including:

[0048] The time-varying droop current envelope is constructed to drive the charging current reference value to decay linearly over time. The calculation process calculates the droop control slope coefficient based on the absolute magnitude of the gradient of the cross-cycle relaxation time constant, and executes non-negative clamping logic at the end of the instruction output to constrain the issued result within the positive charging range that is not lower than the minimum safe trickle current.

[0049] Preferably, it also includes a process of switching to standby compensation state when fully charged, specifically including:

[0050] A weighted judgment mechanism based on both voltage and current is introduced. When the terminal voltage reaches the upper limit of the safe cutoff voltage, the closed-loop control loop automatically switches to constant voltage clamping mode.

[0051] The upper limit of the safety cut-off voltage is set to 3.9V to 4.2V;

[0052] In the constant voltage clamping mode, when the actual feedback charging current naturally decays to the set lower limit threshold of the full charge current, a high-priority interrupt is generated and the current state machine cycle is forcibly terminated.

[0053] The lower limit threshold of the full charge current is set to 0.5% to 1% of the nominal capacity ratio.

[0054] The bidirectional energy storage converter is controlled to exit the high-power output mode globally, and the output microampere-level sustaining current is switched to the standby compensation state to compensate for static losses.

[0055] This invention provides an optimization method for uninterruptible power supply energy management based on the characteristics of sodium-ion batteries. It has the following beneficial effects:

[0056] 1. This invention accurately identifies the phase transition boundary and local polarization state inside the battery by calculating the transient differential capacity and second-order time derivative of the terminal voltage. Based on this, the system directly cuts off the main switch while maintaining the synchronous rectifier on, and utilizes the reverse freewheeling characteristic of the output filter inductor to generate a depolarization micro-discharge current. This eliminates the need for a global inverter shutdown, avoids DC bus voltage disturbances, and can quickly dissipate concentration polarization charges on the electrode surface, reducing the risk of sodium deposition side reactions and ensuring charging safety.

[0057] 2. Within a short pause-charge relaxation time window after micro-discharge cutoff, this invention collects the nonlinear decay sequence of the terminal voltage and inputs it into a continuous-time response model state observer based on a second-order RC network to calculate and extract the concentration polarization time constant and its cross-period gradient. This avoids the contradiction between the standby availability requirements of the uninterruptible power supply system and the extraction of long-period electrochemical parameters, and achieves an accurate quantitative assessment of the changing trend of the ion solid-phase diffusion resistance inside the battery within an extremely short time window.

[0058] 3. This invention introduces a multi-scale state machine based on the extracted cross-cycle relaxation time constant gradient, enabling closed-loop control according to the actual degradation degree of battery polarization dissipation capability. In a normal state, the system dynamically reduces the constant current charging duration to intercept large polarizations; in a deteriorated state, the system reconstructs the current command into a time-varying envelope with a decreasing slope, reducing the injected charge flux at the source. Combined with dual-dimensional weighted judgment during full charge and microampere-level standby compensation, this alleviates solid-phase ion congestion, improves the adaptability of global energy management, and extends battery life. Attached Figure Description

[0059] Figure 1 This is a system functional logic and data interaction diagram provided in an embodiment of the present invention;

[0060] Figure 2 A flowchart of the method provided in an embodiment of the present invention;

[0061] Figure 3 This is a flowchart of the phase transition feature identification steps provided in an embodiment of the present invention;

[0062] Figure 4 The timing logic diagram for the polarization monitoring discharge step provided in the embodiments of the present invention;

[0063] Figure 5 This is a flowchart of the polarization gradient identification steps provided in an embodiment of the present invention;

[0064] Figure 6 A state transition diagram for the execution of charging reconfiguration management steps provided in this embodiment of the invention;

[0065] Figure 7 This is a transient waveform diagram of millisecond-level micro-discharge intervention provided in an embodiment of the present invention;

[0066] Figure 8 A comparison chart of long cycle life provided for embodiments of the present invention. Detailed Implementation

[0067] The technical solutions in 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] See attached document Figure 1 This invention provides an uninterruptible power supply energy management optimization system based on the characteristics of sodium-ion batteries, which may include:

[0069] The phase transition feature recognition module is configured to simultaneously acquire the battery pack terminal voltage and charging current and perform digital preprocessing under constant current charging conditions. Internally, this module runs a differential algorithm to calculate the transient differential capacity, which is used to determine the electrochemical phase transition boundary crossing during the sodium-ion battery negative electrode sodium insertion process, and outputs a trigger signal when the boundary is crossed.

[0070] The polarization monitoring discharge module is connected after the phase change characteristic recognition module. This module is configured to receive a trigger signal and calculate the second-order time derivative of the terminal voltage. When this derivative value exceeds a preset dynamic polarization threshold, a drive control command is sent to the underlying hardware. This command is used to turn off the main switch of the inverter that injects energy into the battery while maintaining the synchronous rectifier diode on, relying on the reverse freewheeling characteristic of the hardware filter inductor to form a depolarization micro-discharge current.

[0071] The polarization gradient identification module is configured to operate within a short pause-charge relaxation time window after the micro-discharge current is cut off. This module receives voltage decay sequence data of the terminal voltage, inputs it into the built-in equivalent circuit state observer, calculates and outputs the concentration polarization time constant of the current control cycle, and extracts the cross-cycle relaxation time constant gradient by differential extraction with historical cycle data.

[0072] The charging reconfiguration management module is configured to receive the gradient of the cross-cycle relaxation time constant and perform multi-scale state machine determination. Based on the determination result, this module dynamically adjusts the duration of the next constant current charging stage, or reconstructs the issued charging current command into a time-varying droop current envelope with a decreasing slope. This module also monitors the battery's full charge status to trigger constant current compensation standby logic.

[0073] The hardware control architecture of the above system is based on the main control unit, and the underlying controlled hardware includes a bidirectional energy storage converter, an output-side inductor filter circuit, and a sodium-ion battery pack as an energy storage carrier.

[0074] In actual operation, the restoration of mains power triggers the restart of the uninterruptible power supply system, the main control unit initializes the parameters of the bidirectional energy storage converter, and outputs a constant reference current to the sodium-ion battery pack.

[0075] The phase-change feature recognition module starts during constant current output, performs synchronous sampling based on pulse width modulation carrier through analog-to-digital conversion peripherals, and calculates differential capacity parameters. When the amplitude of this parameter changes abruptly and meets the window filtering condition, a global enable signal is generated.

[0076] The polarization monitoring discharge module acquires an enable signal and activates its internal high-frequency monitoring branch. Once the terminal voltage polarization curvature reaches a critical threshold, it directly intervenes in the underlying pulse width modulation comparator register.

[0077] Under this intervention, the energy storage converter stops forward energy transmission. The voltage across the inductor filter circuit reverses, and the inductor current drops to the zero-crossing point at a fixed slope, thereby drawing charge from the sodium-ion battery in the reverse direction, completing a millisecond-level depolarization process.

[0078] The converter then enters a zero-current state. During this period, the polarization gradient identification module takes over the system bus, acquires nonlinear decay voltage curves, and outputs gradient parameters characterizing the changes in ion diffusion resistance through observation algorithms such as discrete Kalman filtering.

[0079] The charging reconfiguration management module reconfigures subsequent charging parameters in the time or amplitude domain based on the input gradient parameters. The updated command is then sent to the current loop controller of the bidirectional energy storage converter.

[0080] The entire system control logic iterates in a loop between modules. Until the battery pack terminal voltage reaches the upper limit of the safe cutoff voltage, the charging reconfiguration management module cuts off the main cycle, instructs the energy storage converter to output a microampere-level sustaining current, and enters the long-cycle standby compensation state of the uninterruptible power supply.

[0081] See attached document Figure 2 This invention provides an optimization method for uninterruptible power supply energy management based on the characteristics of sodium-ion batteries, comprising the following steps:

[0082] S10 performs phase change feature identification, synchronously collects battery pack terminal voltage and charging current under constant current charging state, calculates transient differential capacity to determine the electrochemical phase change crossing boundary, and generates trigger signal;

[0083] S20 performs polarization monitoring discharge. After receiving the trigger signal, it calculates the second time derivative of the terminal voltage. When the second time derivative exceeds the polarization threshold, it changes the driving state of the main switch tube and the synchronous rectifier tube of the converter and forms a depolarization micro-discharge current by relying on the reverse freewheeling current of the filter inductor.

[0084] S30, perform polarization gradient identification. Within the stop-charge relaxation time window after the micro-discharge current is cut off, input the collected terminal voltage decay sequence into the state observer to calculate the concentration polarization time constant and extract the gradient of the cross-cycle relaxation time constant.

[0085] S40 executes charging reconfiguration management, performs multi-scale state machine judgment based on the gradient of cross-cycle relaxation time constant, corrects the duration of the next constant current charging stage or reconfigures the charging current command into a time-varying droop current envelope with decreasing slope, and switches to standby compensation state when fully charged.

[0086] After the uninterruptible power supply system detects the mains power restoration command, the main control unit initializes the energy storage converter parameters and outputs a constant reference current to the sodium-ion battery pack.

[0087] During the constant current output stage, the method executes step S10. The system performs carrier synchronous sampling through an analog-to-digital converter and calculates the transient differential capacity based on the preprocessed sampling data. When a positive step change in the differential capacity value is detected and the time window filtering condition is continuously met, the system determines that the sodium intercalation process inside the battery has undergone a reaction interval transition and then sends a trigger signal to the subsequent monitoring logic.

[0088] When executing step S20, the system starts high-frequency second-order differential calculation to monitor the polarization curvature of the terminal voltage. After the second-order time derivative reaches the set threshold, the main control unit cuts off the main switch drive signal and keeps the synchronous rectifier tube on. The inductor current decreases linearly to the zero crossover point due to the reversal of the voltage polarity at both ends, and then reverses to draw the battery terminal charge to form a depolarization micro-discharge current.

[0089] When the depolarization micro-discharge current reaches the set limit, the drive signal is turned off, the converter current output drops to zero, and the method proceeds to step S30. During this charging stop time window, the system collects the nonlinear decay data of the terminal voltage, uses the observation algorithm to extract the state parameters characterizing the ion diffusion resistance, and calculates the gradient change by combining the historical periodic parameters.

[0090] After the parameter calculation is completed, the process enters step S40, where the system evaluates the degree of polarization dissipation capability degradation and adjusts the time domain length limit or reconstructs the amplitude domain slope of the subsequent charging command accordingly. The updated current reference command is then sent to the underlying closed-loop control loop in real time.

[0091] The system iteratively executes steps S10 to S40. When the battery terminal voltage reaches the upper limit of the safe cutoff voltage, the main control unit terminates the cycle and controls the energy storage converter to output a microampere-level sustaining current to offset internal self-discharge losses. The system then officially enters the long-cycle standby mode.

[0092] See attached document Figure 3 In this embodiment, when the system performs phase transition feature identification, it performs high-frequency data acquisition and runs a digital filtering algorithm through the underlying hardware peripherals. Then, it extracts electrochemical state parameters based on discrete calculus operations to determine the critical point of crossing the sodium intercalation reaction range inside the battery. This process can be specifically divided into the following steps:

[0093] S101, the system controls the bidirectional energy storage converter to start charging output with a constant reference current, and simultaneously performs synchronous sampling and discrete signal preprocessing based on pulse width modulation carrier. As a preferred method, during the high-frequency switching operation of the converter power switch, the system uses an analog-to-digital converter to synchronously acquire the original terminal voltage sequence and original current sequence of the sodium-ion battery pack. To suppress measurement aliasing and high-frequency ripple interference caused by power electronic switch chopping, the system anchors the sampling trigger time of the analog-to-digital converter to the apex or basal point of the pulse width modulation triangular carrier.

[0094] Based on the aforementioned sampling timing intervention mechanism, the data acquisition time is forcibly avoided in the transient noise range where the switching states of power devices reverse, thereby improving the signal-to-noise ratio of the acquired signal at the source level. As for the specific configuration of the analog-to-digital converter hardware peripherals and the underlying settings of the interrupt triggering mechanism, those skilled in the art can implement them conventionally according to the manual of the selected digital signal processor. The underlying hardware register operations are well-known technologies in the field and will not be elaborated upon here.

[0095] After acquiring the original sampled signals of the discrete cycles, considering the complex electromagnetic environment of actual industrial sites, directly using the original signals for differentiation operations can easily amplify high-frequency noise interference. Therefore, this embodiment runs a first-order discrete low-pass digital filter at the firmware level of the main control unit to smooth the data. The system performs a weighted summation operation on the sampled values ​​of adjacent discrete cycles to extract the reference terminal voltage and reference current used for subsequent state calculations. The filtering operation relationship performed by the system during preprocessing is expressed as follows:

[0096] ;

[0097] in, This represents the discrete-time index value of the current discrete control cycle; Indicates the first The original terminal voltage obtained by carrier-synchronized sampling of discrete periods; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; This represents the filtering constant of the discrete low-pass filter. Its value is set between 0 and 1, and the specific value is determined offline based on the system hardware's requirements for balancing signal delay tolerance and smoothness.

[0098] S102, the system calculates the first-order time derivative of the reference terminal voltage and the transient differential capacity parameter in real time based on the extracted reference data. In the electrochemical theoretical model, the transient differential capacity represents the amount of charge integrated into the battery per unit voltage change. This parameter can intuitively map the potential plateau characteristics during the phase transition process of the active material inside the electrode.

[0099] The system calculates the instantaneous rate of change of the terminal voltage by dividing the difference between the reference terminal voltages of two adjacent discrete control cycles by the set discrete control step size. To avoid the risk of division-to-zero overflow caused by the extremely small rate of change of voltage during the constant current charging plateau or the quantization cutoff of the analog-to-digital converter, this embodiment introduces a very small bias constant in the denominator of the division operation for algorithm correction. The system obtains the total charged capacity by multiplying the reference charging current of the current cycle by the control step size, and then divides it by the sum of the reference terminal voltage difference and the bias constant to calculate the output transient differential capacity parameter. The discrete calculation formula for the transient differential capacity parameter is expressed as follows:

[0100] ;

[0101] in, This represents the discrete-time index value of the current discrete control cycle; Indicates the first Transient differential capacity parameter of discrete periodic calculation output; Indicates the first The reference charging current after filtering preprocessing for discrete periods; This indicates the discrete control time step of the system's main control program; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; This represents the minimum bias constant, the value of which is determined based on the least significant bit voltage resolution of the analog-to-digital converter, and is typically taken as 10. -6 Order of magnitude.

[0102] In step S103, the system constructs a moving time window to execute cross-judgment logic on the transient differential capacity parameter, and generates a trigger signal to initiate subsequent steps when the judgment condition is met. The hard carbon material of the sodium-ion battery anode undergoes a specific mechanism transition during sodium intercalation. Initially, ions adsorb at hard carbon defect sites, causing the terminal voltage to rise rapidly in a ramp-like manner. As charging deepens, ions transition to a low-potential deep micropore filling process. At this point, the terminal voltage rise slows down, while the charge per unit voltage increases. The system identifies the boundaries of these stages by monitoring the amplitude changes of the transient differential capacity parameter. The system continuously calculates the transient differential capacity parameter and stores it in a data buffer queue, dynamically comparing the amplitude differences between adjacent time points.

[0103] Given that extreme values ​​at a single sampling point are easily affected by load switching disturbances, leading to misjudgments of the state, this embodiment employs a dual-limiting logic of amplitude limitation and time filtering. When the system detects a positive step increase in the amplitude of the transient differential capacity parameter, and this increase exceeds the set characteristic threshold, while the continuous maintenance time of the high-amplitude state is greater than the preset moving state discrimination window length, the system determines that the internal reaction of the battery has substantially entered the low-potential reaction plateau region. The characteristic threshold is set based on the inherent ratio of the capacity difference between the ramp region and the plateau region of the hard carbon anode, as calibrated offline. Specifically, for a typical sodium-ion battery hard carbon anode, since the unit charge throughput during the low-potential micropore filling period is higher than that during the ramp adsorption period, the characteristic threshold is set to 1.5 to 3.0 times the average transient differential capacity amplitude of the ramp region. The moving state discrimination window length is defined by the empirical product of the system discrete control time step and the duration of typical electromagnetic interference.

[0104] After the reaction state transition determination is completed, the global state variable of the system's main control unit changes, and the internal logic of the system immediately generates an enable trigger signal for the polarization monitoring and control logic. By introducing a time window hysteresis filtering mechanism, the system eliminates transient glitches caused by low-level high-frequency interference, ensuring the fault tolerance of phase transition identification and the accuracy of subsequent control node trigger judgments.

[0105] See attached document Figure 4 In this embodiment, the system enters a high-frequency polarization monitoring state after receiving a trigger signal. Unlike traditional voltage extreme value comparison control methods, this embodiment relies on identifying the abrupt change in the nonlinear curvature of the terminal voltage to directly intervene in the underlying hardware drive chain, completing transient depolarization micro-discharge based on the inherent properties of the output filter inductor. This process can be specifically divided into the following steps:

[0106] S201, the system activates the high-frequency second-order differential calculation engine to monitor the polarization curvature of the terminal voltage and perform dynamic threshold comparison. After generating a trigger signal in the phase transition feature identification step, the system determines that the battery has entered a low-potential deep sodium-intercalation state, posing a risk of localized sodium deposition due to polarization. Addressing the phenomenon of nonlinearly increasing electrode polarization resistance with charge accumulation, the system needs to extract state variables characterizing this polarization acceleration. Based on this, the system retrieves historically stored reference terminal voltage data and uses a second-order central difference algorithm to calculate the second-order time derivative of the current terminal voltage. This second-order time derivative directly reflects the potential rise acceleration caused by concentration polarization accumulation on the electrode surface. To reduce the high-frequency noise amplification effect caused by discrete differential calculations, the system performs a moving average processing on the differential results of multiple consecutive cycles. The discrete difference calculation formula for the second-order time derivative is expressed as:

[0107] ;

[0108] in, This represents the discrete-time index value of the current discrete control cycle; Indicates the first The second-order time derivative of the terminal voltage obtained by discrete period calculation; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; This indicates the discrete control time step of the system's main control program.

[0109] In the multi-source sensor data fusion stage, considering that the data update frequency of external temperature sensors is usually much lower than the system voltage control frequency, the system constructs zero-order hold interpolation logic in the firmware to align the low-frequency absolute temperature data with the high-frequency voltage calculation cycle on the time axis. After alignment, the system substitutes the current absolute ambient temperature of the battery surface into a preset threshold mapping table to extract the dynamic polarization determination threshold at the current temperature.

[0110] As a preferred approach, this threshold mapping table is constructed based on offline electrochemical impedance spectroscopy (EIS) experimental data, recording the curvature characteristic parameters of the hard carbon anode before the sodium deposition side reaction occurs at different temperature boundaries. Specifically, the threshold mapping table is obtained by extracting the critical impedance real part abrupt change point in the transition from the low-frequency Weber diffusion region to the semicircular region in the EIS spectrum at different ambient temperatures, and multiplying the corresponding second-order voltage curvature by a safety factor of 0.8–0.9. Since the sodium ion solid-phase diffusion coefficient decreases at low temperatures, this threshold is configured as a monotonic function positively correlated with temperature to ensure higher sensitivity of polarization monitoring under low-temperature conditions.

[0111] To avoid misjudgment of extreme values ​​at a single sampling point due to load switching or external electromagnetic glitches, the system introduces multi-dimensional weighted judgment logic. When the system detects that the calculated output second-order time derivative value exceeds the polarization judgment threshold, and the first-order time change rate of the terminal voltage is positive (confirming that it is in the charging platform rather than the constant voltage or discharge stage), and the number of consecutive cycles of the over-limit state exceeds the set anti-shake count limit (e.g., 3 to 5 consecutive control cycles), the main control unit determines that the battery's local polarization resistance is approaching the sodium deposition critical boundary, and then issues a micro-discharge intervention command to the converter's underlying pulse width modulation module.

[0112] In S202, the system responds to the micro-discharge intervention command, cutting off the main switch drive signal and maintaining the synchronous rectifier in the on state, utilizing the inductor freewheeling characteristic to achieve a disturbance-free decrease in charging current. As a preferred approach, the energy storage converter uses a half-bridge or full-bridge circuit topology as the charging and discharging power execution unit. In traditional commutation control logic, the transition from charging to discharging requires a global shutdown and a long dead time, which can easily cause DC bus voltage disturbances and lose the microsecond-level optimal depolarization opportunity.

[0113] To address this technical bottleneck, this embodiment directly modifies the underlying comparator register of the pulse width modulation peripheral, instantly blocking the high-frequency drive signal of the main switch responsible for injecting energy into the battery side, while forcibly configuring the corresponding synchronous rectifier on the low side to remain normally open. Based on the fundamental laws of passive energy storage components in power electronics, the current in the inductor cannot undergo abrupt changes. At the instant the main switch is turned off, the polarity of the induced electromotive force across the filter inductor reverses to maintain the original current direction.

[0114] The inductor forms a circuit through the synchronous rectifier diode that maintains conduction and the internal freewheeling diode. The inductor current decreases linearly with a fixed slope. According to Faraday's law of electromagnetic induction, the time required for the inductor current to decay to the zero-crossing point after the main switch is turned off is mainly constrained by the system filter parameters and the battery terminal voltage. To prevent overflow in the division-to-zero calculation caused by extreme conditions such as external hardware short circuits or drops, a minimal bias term is introduced into this time estimation formula for protection. The corresponding time calculation formula is expressed as:

[0115] ;

[0116] in, This represents the discrete-time index value of the current discrete control cycle; This represents the estimated time it takes for the inductor current to decay from its current charge value to zero. This indicates the nominal inductance of the filter inductor on the output side of the bidirectional energy storage converter. Indicates the first The reference charging current after filtering preprocessing for discrete periods; Indicates the first The reference voltage output after filtering preprocessing of discrete periodic voltage; This represents a very small bias constant to prevent the denominator from approaching zero; its value is typically around 10 based on the floating-point precision of microcontrollers. -5 Order of magnitude. Regarding the protection configuration of the dead-time register of the specific power switch transistors at the underlying level and the anti-shoot-through hardware interlock design, those skilled in the art can adapt mature driver optocoupler isolation schemes, which are well-known technologies in the field and will not be elaborated upon here.

[0117] In S203, after the inductor current naturally crosses zero, the system executes reverse suction control and turns off the synchronous rectifier when it reaches a set limit. As the energy stored in the positive magnetic field inside the filter inductor is released, the inductor current crosses zero after the time calculated by the formula. At this time, the synchronous rectifier is still in a forced-conduction state, and the system topology automatically completes the source-load role switch. The sodium-ion battery pack switches from the load side to the power supply side, and the current flows in reverse from the battery end through the filter inductor and synchronous rectifier, forming a depolarization micro-discharge action to depolarize the accumulated polarized charge inside the battery.

[0118] This depolarization micro-discharge current can relax the sodium ion concentration gradient on the electrode surface with an extremely high electrochemical response rate. The system relies on a hardware current transformer to monitor the instantaneous amplitude of the depolarization micro-discharge current at high frequency. To avoid excessive loss of the battery's charged capacity during the micro-discharge process and to prevent overcurrent damage to the power devices inside the converter, a negative depolarization limit is preset in the system. The absolute range of this depolarization limit is usually anchored in the range of 5% to 10% of the battery pack's rated capacity (nominal rate), determined according to the specific battery datasheet's safe discharge limit.

[0119] When the absolute amplitude of the depolarization micro-discharge current reaches the depolarization limit, the main control unit immediately cancels the forced normally open control word of the synchronous rectifier and shuts off the synchronous rectifier drive signal. The energy exchange channel between the converter and the battery pack is cut off, and the system then ends the micro-discharge intervention and smoothly enters the zero-current charging relaxation state.

[0120] See attached document Figure 5 In this embodiment, the system faces a time-scale constraint in electrochemical feature extraction after the micro-discharge action ends. The natural dissipation of concentration polarization often takes several seconds or even minutes, while the availability of the uninterruptible power supply requires the charging standby window to be limited to an extremely short period. Based on these constraints, this embodiment constructs a short-window equivalent circuit state observer to extrapolate and identify long-period electrochemical parameters within a limited time window. This process can be specifically divided into the following steps:

[0121] S301: After the micro-discharge current is cut off, the system enters a short pause-charge relaxation time window, simultaneously acquiring the nonlinear decay sequence of the terminal voltage. After the underlying drive signal is withdrawn, the energy exchange link between the converter and the battery pack is interrupted. The main control unit relies on an approximate hardware interrupt cycle to initiate a short pause-charge relaxation period of a preset duration. As a preferred approach, the length threshold of this relaxation time window is determined by the difference between the transient load switching tolerance time and the inductor freewheeling recovery time of the uninterruptible power supply system, typically calibrated in the range of 50–200 ms.

[0122] Within this time window, due to the loss of external excitation current, the polarization charge accumulated inside the battery begins to redistribute spontaneously. The terminal voltage exhibits a nonlinear decay characteristic composed of a transient drop in ohmic voltage, rapid relaxation of charge transfer polarization, and slow dissipation of concentration polarization. The system uses an analog-to-digital converter peripheral to continuously acquire discrete values ​​of this decay curve at a fixed interrupt frequency and pushes them into a first-in-first-out queue to form a terminal voltage decay sequence. To ensure the consistency of data dimensions in subsequent matrix operations, the system performs truncation or interpolation alignment processing on the data pushed into the queue, eliminating the data length uncertainty caused by underlying interrupt jitter and ensuring that the length of the data sequence passed to the state observer each time is a fixed constant.

[0123] S302, the system constructs a continuous-time response model including a dual-polarization branch, and inputs the acquired data sequence into a state observer for parameter extraction. To decouple the voltage phenomenon into electrochemical parameters, the system embeds a zero-input response equivalent model based on a second-order RC network into the digital firmware. This model decomposes the terminal voltage decay function into a steady-state open-circuit voltage term, a fast polarization exponent term characterizing the electrochemical reaction rate, and a slow polarization exponent term characterizing ion solid-phase diffusion. The corresponding terminal voltage response mathematical model is expressed as:

[0124] ,

[0125] in, It represents a continuous function that shows the nonlinear decay of the battery terminal voltage over time within the relaxation time window; The base of the natural logarithm; This represents the estimated steady-state open-circuit voltage obtained through model fitting; This represents the initial value of the zero input voltage of the charge transfer polarization branch at the initial moment of relaxation; This represents the time constant characterizing the fast polarization process of charge transfer; This represents the initial value of the zero input voltage of the concentration polarization branch at the initial moment of relaxation; This represents the time constant characterizing the concentration-polarized solid-phase diffusion process; It represents the relatively continuous time calculated from the start of the relaxation period.

[0126] The system inputs the terminal voltage decay sequence into the state observer to calculate the unknown parameters in the aforementioned continuous-time response model. For the state observer used in the system, this embodiment employs the Extended Kalman Filter (EKF) algorithm for nonlinear system identification. To enable the algorithm to operate practically, the system configures the EKF's state variables to include the steady-state open-circuit voltage estimate, the initial polarization voltage, and the reciprocal form of the polarization time constant, and configures the synchronously acquired terminal voltage decay sequence as the algorithm's sole observation variable.

[0127] In practical engineering calculations, concentration polarization attenuation is not significant within a short window, which can easily lead to the state transition matrix and the observation matrix becoming numerically collinear. Directly solving for the inverse of the state covariance matrix can easily cause matrix singularities or ill-conditioned problems, resulting in filter divergence. Therefore, this embodiment forcibly superimposes a very small unit diagonal regularization matrix parameter into the covariance matrix update equation. The value of this regularization parameter depends on the word length precision of the microcontroller and is typically set to 10 diagonal elements. -6 The system uses a square matrix to ensure the numerical stability of the inversion operation. After the observer converges iteratively, the system extracts the time constant value representing the concentration polarization solid-phase diffusion process in the current model and uses it as the observed value of the concentration polarization time constant for the current period.

[0128] S303, the system retrieves historical observation data and calculates the difference between the parameters of the current cycle and the historical cycle to extract the gradient of the cross-cycle relaxation time constant. Since the polarization time constant at a single moment is affected by individual differences in static temperature or initial internal resistance of the battery, directly using absolute values ​​as the basis for adjusting the charging strategy can easily lead to misjudgments. This embodiment introduces differential relative quantity evaluation logic. The system stores the currently extracted concentration polarization time constant observation value in non-volatile memory and performs a subtraction operation with the observation value extracted in the previous depolarization cycle. The cross-cycle gradient calculation formula is expressed as:

[0129] ;

[0130] in, This represents the gradient of the concentration polarization relaxation time constant across two adjacent cycle periods; Indicates the first Observed values ​​of concentration polarization time constant extracted within each depolarization cycle; Indicates the first Observed values ​​of concentration polarization time constant extracted within each depolarization cycle; The positive integer index value representing the cycle period of the depolarization intervention action.

[0131] To further avoid misleading extreme values ​​in single cross-cycle calculations due to non-ideal electromagnetic noise, the system applies a historical weighted moving average filter to the cross-cycle relaxation time constant gradient, combining gradient data from the past three cycles to output a smoothed final evaluation index. At the electrochemical level, the sign and magnitude of the aforementioned cross-cycle gradient directly map the long-term evolution trend of the battery's negative electrode lattice channels. If the gradient is greater than zero, it indicates that dissipation of concentration polarization becomes increasingly difficult after the same amount of charge injection, and the congestion of ions in the solid phase shows signs of cumulative deterioration across cycles. The system pushes the calculated cross-cycle gradient variables to the subsequent management module, providing a closed-loop judgment basis for the subsequent dynamic reconstruction of global charging control parameters.

[0132] See attached document Figure 6 In this embodiment, after acquiring the gradient of the cross-cycle relaxation time constant, the system enters the global control command closed-loop update stage. Based on the internal multi-scale state machine, the system evaluates the degree of degradation of polarization convergence and divergence capability, and then adjusts the time-domain length limit or reconstructs the amplitude-domain slope of subsequent charging commands. This process can be specifically divided into the following steps:

[0133] S401, the system performs multi-scale state machine transition determination based on the gradient of the cross-cycle relaxation time constant. The system receives the gradient variables pushed by the previous steps. To avoid single-point measurement noise caused by electromagnetic interference, which could lead to frequent oscillations in the control loop, this embodiment introduces a dual-threshold determination logic with hysteresis characteristics. The system compares the received cross-cycle relaxation time constant gradient with the offline calibrated upper warning threshold and lower recovery threshold.

[0134] As a preferred approach, the upper warning threshold is calibrated based on impedance mutation inflection point data from the same batch of batteries during full-lifecycle aging tests. Preferably, the upper warning threshold is set as an increment of 15% to 25% of the standard concentration polarization time constant under the initial healthy state of the battery; the lower recovery threshold is set as 70% to 80% of the upper warning threshold, thus constructing a fault-tolerant buffer between the two states. When the gradient variable continuously exceeds the upper warning threshold for a set number of anti-shake cycles (2 to 4 consecutive cycles), the state machine flips from the normal state to the polarization convergence / dispersion deterioration state. Conversely, if the system is in a deterioration state and the gradient variable subsequently falls back and continuously falls below the lower recovery threshold, the state machine switches back to the normal polarization convergence / dispersion state.

[0135] S402, under normal polarization convergence and divergence conditions, the system adjusts the time domain length limit for subsequent charging commands. Under this condition, the battery solid-phase diffusion channel is not severely congested, and constant current injection is still allowed. Based on the technical objective of proportionally shortening the continuous charging time according to the polarization evolution rate, the system dynamically maps the execution time of the next constant current charging stage according to the current cross-cycle relaxation time constant gradient value, intercepting potentially induced large polarization states by blocking constant current excitation in advance. The discrete formula for the system execution time mapping update is expressed as:

[0136] ;

[0137] in, Indicates the first The continuous execution time instruction of the constant current charging phase within the cycle of a depolarization intervention action; Indicates the first The actual execution time of the constant current charging phase within the cycle of a depolarization intervention action; A positive integer index value representing the cycle period of the depolarization intervention action; This represents the time scaling gain factor. To prevent excessive reduction of the single time step, this factor is usually constrained to a dimensionless range of 0.1 to 0.5 based on the converter hardware response dead zone. This represents the gradient of the concentration polarization relaxation time constant across two adjacent cycle periods; This represents the standard concentration polarization time constant reference value for the battery at the current ambient temperature. The system obtains this reference value in real time by querying the temperature-to-time constant reference mapping table pre-stored in the flash memory. This represents a very small bias constant, used to prevent time instruction overflow exceptions caused by the denominator approaching zero.

[0138] The system adds time limiting protection logic to the output of this step to ensure that the updated time instruction is not lower than the minimum interrupt step size limit of the underlying timer, thus preventing the main control firmware from freezing.

[0139] In S403, under the condition of deteriorated polarization convergence and divergence, the system performs amplitude domain slope reconstruction on the charging command. At this point, the polarization dissipation capability inside the battery has substantially degraded, and simply reducing the charging time is no longer sufficient to block the sodium deposition side reaction. The system then discards the original constant current reference value and constructs a time-varying droop current envelope with a decreasing slope. This strategy forces the charging current reference value to decay linearly over time, aiming to reduce the charge accumulation flux injected into the electrodes from the energy source side and alleviate the congestion pressure of solid-phase ions. The system calculates the droop control slope coefficient based on the absolute magnitude of the gradient. The calculation formula for the time-varying droop current reference command is expressed as:

[0140] ;

[0141] in, This indicates the current reference command that dynamically changes over time during the current charging phase. This indicates the base current reference value at the start of the current charging phase; This represents the slope sensitivity adjustment constant, whose value range is determined by the maximum allowable derating rate of the converter. This parameter characterizes the current attenuation intensity caused by a unit polarization increment. This represents the gradient of the concentration polarization relaxation time constant across two adjacent cycle periods; This indicates the actual time of the current constant current charging phase. This indicates the start time of entering the current constant current charging phase.

[0142] During project execution, to prevent the current command from dropping to a negative value due to excessive accumulation over time, thus causing power backflow, the system is configured with non-negative clamping logic at the command output end to constrain the final output result within a positive charging range not lower than the set minimum safe trickle current. The current reference command, including updated parameters, is sent to the underlying closed-loop control loop in real time. The parameter tuning and pulse width modulation duty cycle generation of the proportional-integral current tracker in the underlying closed-loop control loop can be implemented by referring to conventional power electronics control manuals; the internal control loop construction is a well-known technique in the field and will not be elaborated upon here.

[0143] S404, the system performs a real-time global full-charge safety check and switches to long-term standby mode. During the iterative execution of the above charging reconfiguration logic, considering that a single voltage threshold is prone to premature triggering due to increased internal resistance caused by battery aging or poor terminal contact, the system introduces a weighted judgment mechanism based on both voltage and current dimensions. The main control unit continuously monitors the acquired terminal voltage sequence and the actual feedback charging current.

[0144] When the terminal voltage reaches the upper limit of the safe cutoff voltage defined in the battery specifications (for sodium-ion batteries, this upper limit is usually set between 3.9V and 4.2V), the closed-loop control loop of the main control unit automatically switches to constant voltage clamping mode. In this mode, if the actual charging current naturally decays to the set lower limit threshold of the full charge current (this threshold is usually set to 0.5% to 1% of the nominal capacity ratio), the main control unit immediately generates a high-priority interrupt, forcibly terminating the current state machine cycle. To address the capacity loss caused by internal electrochemical self-discharge due to long-term battery storage, the system controls the energy storage converter to globally exit the high-power output mode and switch to a microampere-level constant voltage leakage compensation state. The converter maintains this extremely low current amplitude to compensate for static losses, and the system officially enters long-cycle standby mode.

[0145] Specific application examples are described below:

[0146] Application scenarios and initial state:

[0147] After a power outage, a data center was powered by a 400V / 1000Ah sodium-ion battery pack. Upon restoration of mains power, the UPS control unit switched back to mains power and charged the sodium-ion battery pack with a constant reference current (set to 100A, or 0.1C). The ambient temperature sensor reported a current temperature of 15℃.

[0148] Step S10: Phase Change Feature Identification (Plateau Period Capture) Phenomenon: In the initial stage of charging, sodium ions are mainly adsorbed at the defects of the hard carbon negative electrode, and the terminal voltage rises rapidly in a ramp-like manner (e.g., from 2.5V to 3.4V). System Action: The phase change feature identification module calculates the transient differential capacity (dQ / dV) in real time. When the voltage reaches approximately 3.4V, dQ / dV abruptly changes from the average of 25Ah / V to 65Ah / V and lasts for 2 seconds (satisfying the window filtering condition). The system determines that the battery has entered the low-potential deep micropore filling process, generates a trigger signal, and activates high-frequency monitoring.

[0149] Step S20: Polarization Monitoring and Depolarization Micro-discharge (Intervention) Phenomenon: With continuous injection of high current, ion congestion occurs inside the solid phase, and the terminal voltage rises at an accelerated rate. System Action and Hardware Response: The polarization monitoring module calculates the second-order time derivative of the terminal voltage. When this derivative reaches 1.5mV / s... 2 When the polarization threshold (preset at the current 15°C) is exceeded, the system executes micro-discharge transient control. Combined with... Figure 7 As shown in the attached figure, the horizontal axis represents time (ms), the left vertical axis represents battery terminal current (A), and the right vertical axis represents battery terminal voltage (V); the solid line in the figure represents battery terminal current, and the dashed line represents battery terminal voltage. At 2ms on the time axis, the system generates and issues the trigger intervention command marked in the figure. The main control unit instantly blocks the main switch (stops charging) while maintaining the synchronous rectifier tube on. Due to the inertia of the hardware filter inductor, as shown by the solid line waveform in the figure, the battery terminal current starts from +100A and decreases linearly downwards at a fixed slope, crossing the 0A zero mark and reversing to draw internal charge from the battery. After about 1.5ms, at 3.5ms on the time axis, when the reverse micro-discharge current touches the depolarization limit (-50A) marked by the dashed line in the figure (i.e., 5% of the nominal capacity), the system shuts down the drive. At this time, as marked in the figure, the system executes the drive shutdown (relaxation start) action, and the current instantly returns to zero, thus completing the depolarization discharge action that took about 1.5ms.

[0150] Step S30: Polarization gradient identification (observer calculation) Phenomenon and system behavior: combined Figure 7 Continuing to observe, after the drive is turned off at 3.5ms, the current waveform (solid line) shifts and remains unchanged close to the 0A scale line, indicating that the battery has entered the charging-off relaxation phase. Simultaneously, the battery terminal voltage waveform (dashed line) experiences a sudden downward drop at the moment of drive turn-off due to the disappearance of the ohmic voltage drop (from approximately 3.76V to approximately 3.71V). Subsequently, within this relaxation time window, the voltage waveform exhibits a smooth, non-linear, exponential relaxation recovery characteristic (gradually approaching above 3.83V).

[0151] The system opens this 100ms pause-charge relaxation time window, acquires the aforementioned voltage nonlinear decay sequence, and inputs it into an extended Kalman filter (EKF). The current concentration polarization time constant is then calculated. The time is 42 seconds. Combining this with the 34 seconds recorded in the previous loop, the gradient is obtained. s.

[0152] Step S40: Charging Reconfiguration Management (Policy Switching) System Action: System Detection If the value of s exceeds the upper limit threshold of the warning (set to 5s), the state machine determines that the polarization convergence and divergence is in a deteriorated state (indicating that the ion diffusion channel is severely congested and there is a risk of sodium precipitation).

[0153] Reconfiguration instruction: The system abandons the original 100A constant current charging, calculates the droop slope based on the absolute value of the gradient, and reconfigures the subsequent current instruction into a time-varying envelope that starts from 100A and decreases at a slope of 2A per minute.

[0154] Conclusion: As the current gradually decreases, polarization is alleviated. Finally, the battery terminal voltage reaches the full charge threshold of 4.0V and the current drops to 5A (0.005C), at which point the system switches to microampere-level long-term standby compensation mode.

[0155] Experimental verification and effect comparison:

[0156] To verify the effectiveness of the present invention, a comparative test was conducted on a commercial sodium-ion battery module with a nominal capacity of 100Ah in a standard laboratory environment.

[0157] Experimental group: Control group (traditional method): The traditional CC-CV (constant current-constant voltage) charging strategy was adopted, without polarization monitoring and micro-discharge intervention.

[0158] Experimental group (method of this invention): The phase transition identification, micro-discharge depolarization and multi-scale charging reconstruction strategies of this invention are adopted.

[0159] Comparison of experimental results:

[0160] Sodium precipitation risk and temperature rise control (single charge test):

[0161] Control group: At the end of the constant current plateau, due to severe polarization, the surface temperature rose rapidly to 42°C. Upon disassembly of the battery, slight traces of silvery-white metallic sodium were found on the surface of the negative electrode.

[0162] Experimental group: Based on the millisecond-level reverse micro-discharge (drawing internal polarization charge) and droop current reconstruction shown in the waveform diagram, the highest battery temperature is only 31℃, there is no sodium precipitation side reaction throughout the process, and the electrochemical reaction heat is reduced.

[0163] Capacity retention (long cycle life test):

[0164] Combination Figure 8 As shown in the attached figure, the horizontal axis represents the equivalent full charge-discharge cycle count (0 to 1000 times), and the vertical axis represents the capacity retention rate (%). The figure uses two line types and markers to illustrate the lifetime degradation trend: the solid line marked with hollow circles represents the conventional constant current constant voltage charging control (control group); the dashed line marked with solid squares represents the reconfigured optimized charging control of this invention (experimental group).

[0165] According to the curve trend in the attached figure: Control group: Due to long-term accumulated polarization damage and sodium precipitation dead zone, the curve of the traditional method decays sharply in the middle. Its capacity retention rate drops sharply below the usable lower limit of 70% when the cycle is about 500 times, and the failure process is rapid.

[0166] Experimental Group: The dynamic depolarization strategy of this invention suppressed the deterioration of the negative electrode lattice channel, as shown by the dotted line in the figure, exhibiting an extremely gradual decay trend. After completing all 1000 long-cycle tests, the figure clearly marks the final data of 92.0% for this embodiment of the invention. This invention successfully maintains the battery's long-cycle capacity retention rate at an extremely high level of 92.0% in UPS applications, extending the equipment's lifespan.

Claims

1. An optimization method for uninterruptible power supply energy management based on the characteristics of sodium-ion batteries, characterized in that, Includes the following steps: The terminal voltage and charging current of the battery pack are collected and the transient differential capacity is calculated to determine the electrochemical phase transition crossing the boundary and generate a trigger signal. After receiving the trigger signal, the second time derivative of the terminal voltage is calculated. When the second time derivative exceeds the polarization threshold determined based on the current ambient temperature, the bidirectional energy storage converter is controlled to form a depolarization micro-discharge current. The polarization threshold is determined based on a threshold mapping table constructed from offline electrochemical AC impedance spectroscopy experimental data; During the depolarization micro-discharge current termination and subsequent charging-off relaxation time window, the decay sequence of the terminal voltage is collected to calculate the concentration polarization time constant and extract the gradient of the cross-cycle relaxation time constant. The subsequent charging commands are reconstructed and updated based on the gradient of the cross-cycle relaxation time constant.

2. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 1, characterized in that, The system collects the battery pack's terminal voltage and charging current and calculates the transient differential capacity to determine when an electrochemical phase transition crosses a boundary and generates a trigger signal. Specifically, this includes: The sampling trigger time of the analog-to-digital converter is anchored at the apex or apex of the pulse width modulation triangular carrier wave, and the original terminal voltage sequence of the terminal voltage and the original current sequence of the charging current are acquired synchronously. A first-order discrete low-pass digital filter is applied to the original terminal voltage sequence and the original current sequence to perform data smoothing, extract the reference terminal voltage and reference current, and calculate the reference terminal voltage difference between adjacent control cycles. The total charge is obtained by multiplying the reference current of the current cycle by the control step size, and the transient differential capacity is calculated and output by dividing the total charge by the sum of the reference terminal voltage difference and the minimum bias constant. The minimum bias constant is set to 10. -6 Order of magnitude; When a positive step increase in the amplitude of the transient differential capacity is detected, exceeding the characteristic threshold set according to the inherent ratio of the capacity difference between the slope region and the plateau region of the hard carbon anode based on offline calibration, and the continuous maintenance time of the high amplitude state is greater than the length of the moving state discrimination window, it is determined that the electrochemical phase transition crossing boundary has been crossed and the trigger signal is generated. The characteristic threshold is set to 1.5 to 3.0 times the average transient differential capacity amplitude of the hard carbon negative electrode slope region, and the length of the moving state discrimination window is defined by the product of the system discrete control time step and the duration of typical electromagnetic interference.

3. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 1, characterized in that, The step of calculating the second-order time derivative of the terminal voltage after receiving the trigger signal, specifically includes the following: When the second-order time derivative exceeds the polarization threshold determined based on the current ambient temperature, Retrieve the reference terminal voltage data stored at historical time points, calculate the second-order time derivative based on the reference terminal voltage data using a second-order central difference algorithm, and perform a moving average processing on the second-order time derivative. The absolute ambient temperature of the current battery surface is obtained. The absolute ambient temperature is aligned with the calculation cycle by constructing zero-order hold interpolation logic. The absolute ambient temperature is then substituted into the threshold mapping table constructed based on offline electrochemical AC impedance spectroscopy experimental data. The corresponding second-order voltage curvature critical value at the current temperature is extracted and multiplied by a set safety factor to obtain the dynamic polarization determination threshold as the polarization threshold. The safety factor is set to be 0.8 to 0.

9. When the second-order time derivative after the moving average processing exceeds the polarization threshold, the first-order time change rate of the terminal voltage is positive, and the number of consecutive cycles of the over-limit state exceeds the set anti-shake count limit, a micro-discharge intervention command is issued. The anti-shake count limit is set to 3 to 5 consecutive control cycles.

4. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 3, characterized in that, In response to the micro-discharge intervention command, the bidirectional energy storage converter is controlled to generate the depolarization micro-discharge current, specifically including: Change the driving state of the main switch tube and the synchronous rectifier tube of the bidirectional energy storage converter, cut off the driving signal of the main switch tube and keep the synchronous rectifier tube in the normally open conducting state. By relying on the reverse freewheeling of the output-side filter inductor, the polarity of the induced electromotive force at both ends of the output-side filter inductor is reversed. The inductor current decreases linearly at a fixed slope to the zero crossover point and then reverse suction control is executed. The current flows in reverse from the battery end of the battery pack through the output-side filter inductor and the synchronous rectifier tube to form the depolarization micro-discharge current. The instantaneous amplitude of the depolarization micro-discharge current is monitored at high frequency. When the absolute value of the instantaneous amplitude reaches the depolarization limit, the normally open control word of the synchronous rectifier is canceled and the drive signal of the synchronous rectifier is turned off, the energy exchange channel is cut off and the zero-current stop-charge relaxation time window is entered. The depolarization limit is set to 5% to 10% of the nominal capacity of the battery pack.

5. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 1, characterized in that, The calculation of the concentration polarization time constant specifically includes: Within the charging and relaxation time window, discrete values ​​of the terminal voltage decay curve are continuously collected at a fixed interruption frequency, pushed into a first-in-first-out queue, and truncated or interpolated for alignment to form a terminal voltage decay sequence with a fixed constant sequence length. The terminal voltage decay sequence is input into the state observer to construct a zero-input response equivalent model based on a second-order RC network. The zero-input response equivalent model decomposes the terminal voltage decay function into a steady-state open-circuit voltage term, a fast polarization exponent term, and a slow polarization exponent term. The extended Kalman filter algorithm is selected as the state observer for nonlinear system identification. The unit diagonal regularization matrix parameter is superimposed in the covariance matrix update equation to ensure the numerical stability of the inversion operation. After iterative convergence, the time constant value characterizing the concentration polarization solid-phase diffusion process is extracted as the concentration polarization time constant. The length of the pause-charge relaxation time window is set to 50–200 ms.

6. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 5, characterized in that, The extraction of the gradient of the cross-cycle relaxation time constant specifically includes: The concentration polarization time constant extracted at the moment is subtracted from the observation value extracted in the previous depolarization cycle to obtain the difference across two adjacent cycles. A historical weighted moving average filter is applied to the difference, and the final evaluation index is output after smoothing by combining the data from the past three cycles. The final evaluation index is used as the gradient of the cross-cycle relaxation time constant.

7. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 1, characterized in that, The process of reconstructing and updating subsequent charging commands based on the gradient of the cross-cycle relaxation time constant specifically includes: Based on the gradient of the cross-cycle relaxation time constant, a multi-scale state machine is used for determination. A dual-threshold determination logic with hysteresis characteristics is introduced to compare the received gradient of the cross-cycle relaxation time constant with the warning upper limit threshold and the recovery lower limit threshold. The upper warning threshold is determined based on the impedance mutation inflection point data of the same batch of batteries in the full life cycle aging test. The upper warning threshold is set as an increment of 15% to 25% of the standard concentration polarization time constant under the initial healthy state of the battery. The lower recovery threshold is set as 70% to 80% of the upper warning threshold. When the gradient of the cross-cycle relaxation time constant continuously exceeds the warning upper limit threshold to reach the number of anti-shake cycles, the state machine flips from the normal state to the polarization convergence and divergence deterioration state. The number of anti-shake cycles is set to 2 to 4 consecutive cycles; When the state machine is in the polarization convergence and divergence deterioration state and the gradient of the cross-cycle relaxation time constant is continuously lower than the recovery lower limit threshold, the state machine switches back to the normal state.

8. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 7, characterized in that, In the normal state, the reconstruction update manifests as correcting the duration of the next constant current charging phase, specifically including: The next constant current charging stage duration is dynamically mapped based on the gradient value of the cross-cycle relaxation time constant. The calculation process introduces a time scaling gain coefficient and a standard concentration polarization time constant reference value. Time limiting protection logic is added at the output to ensure that the updated time instruction is not lower than the minimum interrupt step limit of the underlying timer.

9. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 7, characterized in that, When the polarization convergence and divergence is in a deteriorated state, the reconstruction update manifests as reconstructing the charging current command into a time-varying droop current envelope with a decreasing slope, specifically including: The time-varying droop current envelope is constructed to drive the charging current reference value to decay linearly over time. The calculation process calculates the droop control slope coefficient based on the absolute magnitude of the gradient of the cross-cycle relaxation time constant, and executes non-negative clamping logic at the end of the instruction output to constrain the issued result to a positive charging range not lower than the minimum safe trickle current.

10. The uninterruptible power supply energy management optimization method based on sodium-ion battery characteristics according to claim 1, characterized in that, It also includes the process of switching to standby compensation mode when fully charged, specifically including: A weighted judgment mechanism based on both voltage and current is introduced. When the terminal voltage reaches the upper limit of the safe cutoff voltage, the closed-loop control loop automatically switches to constant voltage clamping mode. The upper limit of the safety cut-off voltage is set to 3.9V to 4.2V; In the constant voltage clamping mode, when the actual feedback charging current naturally decays to the set lower limit threshold of the full charge current, a high-priority interrupt is generated and the current state machine cycle is forcibly terminated. The lower limit threshold of the full charge current is set to 0.5% to 1% of the nominal capacity ratio. The bidirectional energy storage converter is controlled to exit the high-power output mode globally, and the output microampere-level sustaining current is switched to the standby compensation state to compensate for static losses.

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