Sodium-ion supercapacitor full life cycle closed loop predictive control method and system

Abstract

The present application relates to the technical field of sodium-ion supercapacitors, and specifically relates to a sodium-ion supercapacitor full-life-cycle closed-loop prediction control method and system. The sodium-ion supercapacitor full-life-cycle closed-loop prediction control method comprises: constructing a single-body transient electro-thermal coupling heat generation power prediction model to predict the single-body transient total heat generation power under minute-level frequency modulation high-frequency alternating working conditions; constructing a module-level heat distribution and single-body aging attenuation rate prediction model to predict the differential capacity attenuation rate; based on the differential capacity attenuation rate, constructing a full-life-cycle adaptive balancing control target value prediction model to calculate the optimal balancing target voltage; based on the optimal balancing target voltage, constructing a capacity-power coupled system full-life-cycle optimal configuration prediction model to calculate the optimal capacity-power configuration coefficient; and based on the optimal capacity-power configuration coefficient, constructing a thermal runaway safety boundary real-time prediction model to calculate the thermal runaway safety boundary margin and execute closed-loop protection.

Description

Technical Field

[0001] This invention relates to the field of sodium-ion supercapacitor technology, specifically to a closed-loop predictive control method and system for the entire life cycle of sodium-ion supercapacitors. Background Technology

[0002] Sodium-ion supercapacitors (hereinafter referred to as sodium supercapacitors) combine the technical characteristics of high power density, long cycle life, wide temperature range adaptability, and high safety, perfectly matching the needs of high-frequency and high-rate operating conditions such as minute-level primary frequency regulation and short-term power replenishment in the power grid. They are one of the core energy storage equipment for frequency regulation scenarios in new power systems.

[0003] Existing sodium supercapacitive energy storage systems have the following core technical shortcomings in engineering applications for frequency regulation scenarios: Insufficient accuracy in heat generation prediction: Existing heat generation calculations mostly directly apply the classic Bernardi heat generation model of lithium-ion batteries, without considering the electrochemical characteristics of sodium supercapacitors, which possess both double-layer capacitance and pseudocapacitance, and neglecting the irreversible heat generation caused by the pseudocapacitive reaction. At the same time, it does not consider the dynamic nonlinear changes in the internal resistance of sodium supercapacitor energy storage systems under minute-level frequency modulation and high-frequency alternating conditions with the state of charge (SOC), temperature, and cycle number, resulting in a heat generation prediction deviation of more than 30%. In addition, the thermal management design is either too redundant, increasing costs, or insufficient heat dissipation, leading to local overheating.

[0004] Large aging prediction bias: Existing aging models are mostly based on the Arrhenius kinetic model, which only considers the influence of a fixed ambient temperature and does not take into account the uneven hot spot temperature distribution caused by the difference in heat generation of sodium supercapacitor cells within the sodium supercapacitor module. At the same time, no corresponding aging acceleration factor is introduced for shallow charge and discharge and high-frequency high-current operating conditions in frequency modulation scenarios, resulting in a prediction bias of more than 40% for the differentiated aging of sodium supercapacitor cells, which cannot provide accurate aging state input for subsequent equalization strategies.

[0005] The equalization control strategy is unreasonable: The equalization strategy of the capacitor management system (CMS) in the existing sodium supercapacitor energy storage system mostly takes the average voltage of the sodium supercapacitor module as the uniform equalization target, without considering the difference in aging rate between sodium supercapacitor cells. As a result, sodium supercapacitor cells with fast aging rate are still in a high stress state of full charge and discharge, which accelerates failure. The overall life of sodium supercapacitor module is reduced by more than 40% compared with the life of individual cells. At the same time, the equalization process is not optimized, and the equalization loss exceeds 5%, which reduces the system operating efficiency.

[0006] Decoupling of sodium supercapacity energy storage system configuration and operation: Existing capacity-power configurations mostly adopt static empirical formulas, which only consider the frequency regulation requirements of the initial operating conditions and do not consider the capacity decay, balancing losses, and changes in energy utilization rate throughout the entire life cycle. This results in excessive capacity redundancy in the initial stage of sodium supercapacity energy storage systems, increasing the initial investment by more than 20%, while the capacity is insufficient at the end of the life cycle, failing to meet the technical requirements of grid frequency regulation. At the same time, the configuration process relies on simulation iteration, resulting in low design efficiency.

[0007] Safety protection is highly delayed: Existing sodium supercapacity systems mostly use threshold-based alarm protection, which only triggers protection after faults such as over-temperature or over-pressure occur. It lacks the ability to predict in advance and cannot warn of the risk of thermal runaway. At the same time, the safety boundary is not linked to the system's heat generation, configuration, and operating characteristics, and the protection threshold is set unreasonably, resulting in either a high false alarm rate or delayed protection.

[0008] Existing technologies do not offer a closed-loop solution that integrates the five key elements of heat generation, aging, equalization, configuration, and safety. These elements are decoupled from each other, making it impossible to achieve optimal control and configuration throughout the entire lifecycle of the sodium supercapacitor frequency regulation system. This severely limits the large-scale application of sodium supercapacitors in power frequency regulation scenarios. Summary of the Invention

[0009] The purpose of this invention is to provide a closed-loop predictive control method for the entire life cycle of sodium-ion supercapacitors, so as to solve the problem that existing technologies cannot achieve optimal control and configuration of sodium supercapacitor frequency modulation systems throughout their entire life cycle.

[0010] To address the aforementioned problems, this invention proposes a closed-loop predictive control method for the entire lifecycle of sodium-ion supercapacitors. The technical solution adopted is as follows: A closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor includes the following steps: Step S1: Construct a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells to predict the transient total heat generation power of each sodium supercapacitor cell in the sodium supercapacitor module under minute-level frequency modulation high-frequency alternating operating conditions, and obtain the average heat generation power of the sodium supercapacitor energy storage system. Step S2: Based on the transient total heat generation power of each sodium supercapacitor, construct a module-level heat distribution and single-unit aging decay rate prediction model to predict the differentiated capacity decay rate of each sodium supercapacitor. Step S3: Based on the differentiated capacity decay rate of each sodium supercapacitor cell, construct a full life cycle adaptive equalization control target value prediction model and calculate the optimal equalization target voltage for each sodium supercapacitor cell. Step S4: Based on the optimal equilibrium target voltage of each sodium supercapacitor cell, construct a system full life cycle optimal configuration prediction model with capacity-power coupling, and calculate the full life cycle optimal capacity-power configuration coefficient of the sodium supercapacitor energy storage system. Step S5: Based on the average heat generation power of the sodium supercapacity energy storage system and the optimal capacity-power configuration coefficient throughout the entire life cycle of the sodium supercapacity energy storage system, construct a real-time prediction model for the thermal runaway safety boundary, calculate the thermal runaway safety boundary margin of the sodium supercapacity energy storage system, and perform graded early warning and closed-loop protection.

[0011] Furthermore, the transient electrothermal coupling heat generation power prediction model for the sodium supercapacitive monomer is as follows:

[0012] in, : The transient total heat production power of the i-th sodium supercapacitive monomer at time t; : The charging and discharging current of the sodium supercapacitive energy storage system at time t; : DC internal resistance of the i-th sodium supercapacitive cell; The state of charge of the sodium supercapacitive monomer at time t; : The core temperature of the i-th sodium supercapacitive monomer at time t; : The historical equivalent total cycle count of the i-th sodium supercapacitive monomer; : The entropic thermal coefficient of the i-th sodium supercapacitive monomer; : The open-circuit voltage of the i-th sodium supercapacitive cell at time t under the corresponding SOC; : The pseudocapacitive polarization overpotential of the i-th sodium supercapacitive monomer at time t; : The general symbol for the independent variable in thermodynamic temperature.

[0013] Furthermore, the module-level heat distribution and single-unit aging degradation rate prediction model is as follows:

[0014] in, The number of equivalent full cycles for the i-th sodium supercapacitive monomer in history is: Differential capacity decay rate over time; : The reference capacity decay rate of sodium supercapacitive monomers under rated operating conditions; Activation energy of aging side reactions of sodium supercapacitive monomers; Universal gas constant; : The average hot spot temperature of the i-th sodium supercapacitive monomer within one minute-level frequency modulation cycle; : The average depth of discharge of the i-th sodium supercapacitive monomer under minute-level frequency-modulated high-frequency alternating conditions; : Rated depth of discharge of sodium supercapacitive monomers; : Depth of discharge aging acceleration index; : The absolute value of the average charge and discharge current of the i-th sodium supercapacitive cell within one minute-level frequency modulation cycle; : Rated charge and discharge current of sodium supercapacitive monomer; Current ratio aging acceleration index.

[0015] Furthermore, the whole life cycle adaptive equilibrium control target value prediction model is as follows:

[0016] in, The optimal equilibrium target voltage of the i-th sodium supercapacitive cell at time t; : The reference voltage of the sodium supercapacitive module at time t; : The average differential capacity decay rate of all sodium supercapacitors within the sodium supercapacitor module; The number of equivalent full cycles for the i-th sodium supercapacitive monomer in history is: Differential capacity decay rate over time; : The cumulative differential capacity decay of the i-th sodium supercapacitive monomer; : The rated capacitance of the i-th sodium supercapacitor cell.

[0017] Furthermore, the system's full lifecycle optimal configuration prediction model for the capacity-power coupled system is as follows:

[0018] in, : The optimal capacity-power configuration factor for sodium supercapacity energy storage systems throughout their entire lifecycle; : Rated total energy of sodium supercapacity energy storage system; Rated charge and discharge power of sodium supercapacity energy storage system; The longest continuous frequency regulation time required by the power grid; The round-trip charge-discharge efficiency of a sodium supercapacitive energy storage system under minute-level frequency modulation high-frequency alternating operating conditions; : Average equilibrium loss rate over the entire life cycle of sodium supercapacity energy storage system; The optimal equilibrium target voltage for the i-th sodium supercapacitive cell; : Average differentiated capacity decay rate over the entire life cycle of sodium supercapacity energy storage systems; The equivalent number of cycles within the design life of a sodium supercapacity energy storage system; : Actual utilization rate of the rated energy of the sodium supercapacitive module.

[0019] Furthermore, the aforementioned The calculation formula is:

[0020] in, : No. Sodium supercapacitive monomers in The optimal equilibrium target voltage at any given time; : The current actual capacitance of the i-th sodium supercapacitive cell; : No. Sodium supercapacitive monomers in The current actual voltage at any given moment; Rated energy of sodium supercapacity energy storage system; Rated charge and discharge power of sodium supercapacity energy storage system; The longest continuous frequency regulation time required by the power grid; Energy conversion efficiency of active balancing circuit; This represents the total number of sodium supercapacitive monomers in the sodium supercapacitive module.

[0021] Furthermore, the aforementioned The calculation formula is:

[0022] in, , : The upper and lower limits of the optimal equilibrium target voltage for the i-th sodium supercapacitive cell under all operating conditions; The upper and lower limits of the rated voltage of the sodium supercapacitive module; This represents the total number of sodium supercapacitors within the sodium supercapacitor module.

[0023] Furthermore, the real-time prediction model for the thermal runaway safety boundary is as follows:

[0024] in, : The thermal runaway safety margin of the sodium supercapacity energy storage system at time t; : The average transient heat generation power of the sodium supercapacity energy storage system at time t; : The optimal capacity-power configuration factor for sodium supercapacity energy storage systems throughout their entire lifecycle; The longest continuous frequency regulation time required by the power grid. : Total mass of the sodium supercapacity module; : Average isobaric specific heat capacity of the sodium supercapacity module; : The critical temperature for thermal runaway of sodium supercapacitive monomers; : The ambient temperature of the sodium supercapacitive energy storage system at time t.

[0025] Furthermore, the tiered early warning and closed-loop protection includes: When the thermal runaway safety margin of the sodium supercapacity energy storage system is lower than the warning threshold, an audible and visual warning is triggered. When the thermal runaway safety margin of the sodium supercapacitive energy storage system is lower than the protection threshold, the charging and discharging power of the sodium supercapacitive energy storage system is limited. When the thermal runaway safety margin of the sodium supercapacity energy storage system is ≤0, the sodium supercapacity energy storage system shutdown protection shall be executed. Among them, the warning threshold > the protection threshold > 0.

[0026] This invention also proposes a system for executing the above-described closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor, comprising: The transient total heat generation power acquisition module is used to construct a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells, predict the transient total heat generation power of each sodium supercapacitor cell in the sodium supercapacitor module under minute-level frequency modulation high-frequency alternating operating conditions, and obtain the average heat generation power of the sodium supercapacitor energy storage system. The differential capacity decay rate acquisition module is used to construct a module-level heat distribution and single-cell aging decay rate prediction model based on the transient total heat generation power of each sodium supercapacitor, and predict the differential capacity decay rate of each sodium supercapacitor. The optimal equalization target voltage acquisition module is used to construct a full life cycle adaptive equalization control target value prediction model based on the differentiated capacity decay rate of each sodium supercapacitor cell, and calculate the optimal equalization target voltage for each sodium supercapacitor cell. The optimal capacity-power configuration coefficient acquisition module is used to construct a system lifecycle optimal configuration prediction model based on the optimal equilibrium target voltage of each sodium supercapacitor cell, and to calculate the optimal capacity-power configuration coefficient of the sodium supercapacitor energy storage system throughout its lifecycle. The thermal runaway safety boundary margin acquisition module is used to construct a real-time prediction model of the thermal runaway safety boundary based on the average heat generation power of the sodium supercapacity energy storage system and the optimal capacity-power configuration coefficient of the sodium supercapacity energy storage system, calculate the thermal runaway safety boundary margin of the sodium supercapacity energy storage system, and perform graded early warning and closed-loop protection.

[0027] Compared with the prior art, the present application has the following beneficial effects: Significantly improved heat generation prediction accuracy: The transient electrothermal coupling heat generation power prediction model of sodium supercapacitive monomer constructed in this invention improves the heat generation prediction accuracy by more than 35% compared with the existing model, providing accurate basic data for thermal management design and aging prediction.

[0028] Significantly optimized aging prediction and equalization control performance: The module-level heat distribution and single-unit aging decay rate prediction model constructed in this invention realizes accurate prediction of differentiated aging of sodium supercapacitor single units, and the full life cycle adaptive equalization control target value prediction model realizes adaptive equalization control based on aging state. The overall life of sodium supercapacitor modules is improved by more than 30% compared with the existing solutions, and the equalization loss is reduced by more than 60%.

[0029] The configuration economy and design efficiency of sodium supercapacity energy storage system are greatly improved: the capacity-power coupled system life cycle optimal configuration prediction model realizes the deep coupling of balancing strategy, aging characteristics and system configuration. The levelized cost of electricity throughout the life cycle is reduced by more than 22% compared with the existing solution, the configuration design efficiency of sodium supercapacity energy storage system is improved by more than 90%, and the problems of initial investment redundancy and insufficient capacity at the end are avoided.

[0030] Significantly enhanced safety protection capabilities: The real-time prediction model for thermal runaway safety boundaries enables real-time prediction of thermal runaway safety boundaries, providing early warning of thermal runaway risks 10 to 30 minutes in advance. This upgrades safety protection from post-event alarms to pre-event predictions, greatly improving the safety of sodium supercapacity energy storage systems.

[0031] Closed-loop linkage across the entire chain: This invention uses five interconnected models, with the output of each step serving as the core input for the next. This enables closed-loop prediction and control throughout the entire lifecycle of sodium supercapacitor cells, from electrothermal characteristics, aging status, equalization control, system configuration to safety boundaries. It solves the technical problems in existing technologies, such as inaccurate heat generation prediction, large deviations in aging prediction, unreasonable equalization strategies, decoupling of sodium supercapacitor energy storage configuration and operation, and lagging safety protection. This comprehensively improves the full lifecycle performance, economy, and safety of sodium supercapacitor energy storage systems. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the closed-loop predictive control method for the entire life cycle of sodium-ion supercapacitors according to the present invention. Detailed Implementation

[0033] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0034] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0035] The following describes, with reference to the accompanying drawings, a closed-loop predictive control method and system for the entire life cycle of a sodium-ion supercapacitor according to embodiments of this application.

[0036] The following is combined with Figure 1 This application provides a detailed description of the closed-loop predictive control method for the entire life cycle of sodium-ion supercapacitors.

[0037] The sodium-ion supercapacitor full life-cycle closed-loop predictive control method of this application includes five sequentially executed and interconnected predictive steps. The output of the previous step is the sole core input of the next step, forming a complete closed-loop predictive control chain. The specific steps are as follows: Step S1: Construct a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells to predict the transient total heat generation power of each sodium supercapacitor cell in the sodium supercapacitor module under minute-level frequency modulation high-frequency alternating operating conditions, and obtain the average heat generation power of the sodium supercapacitor energy storage system.

[0038] This step constructs a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells, accurately predicting the transient total heat generation power of sodium supercapacitor cells under minute-level frequency modulation high-frequency alternating conditions, providing the sole core input for the aging rate prediction in the subsequent step S2.

[0039] Specifically, the prediction model for transient electrothermal coupling heat generation power of sodium supercapacitive monomers is as follows:

[0040] in, : The transient total heat production power of the i-th sodium supercapacitive monomer at time t; : The charging and discharging current of the sodium supercapacitive energy storage system at time t; : DC internal resistance of the i-th sodium supercapacitive cell; The state of charge of the sodium supercapacitive monomer at time t; : The core temperature of the i-th sodium supercapacitive monomer at time t; : The historical equivalent total cycle count of the i-th sodium supercapacitive monomer; : The entropic thermal coefficient of the i-th sodium supercapacitive monomer; : The open-circuit voltage of the i-th sodium supercapacitive cell at time t under the corresponding SOC; : The pseudocapacitive polarization overpotential of the i-th sodium supercapacitive monomer at time t; : The general symbol for the independent variable in thermodynamic temperature.

[0041] The role of this step and the formula: This step accurately predicts the transient total heat generation power of sodium supercapacitors under minute-level frequency modulation high-frequency alternating conditions, solves the technical problem of large deviation in the prediction of sodium supercapacitor heat generation in existing models, provides the only core heat input for subsequent aging rate prediction, and is the foundation of the entire closed-loop prediction link.

[0042] In the formula corresponding to the transient electrothermal coupling heat generation power prediction model of sodium supercapacitive monomers This is the serial number of the sodium supercapacitor within the sodium supercapacitor module, used to distinguish different sodium supercapacitors within the module; This is a time variable, corresponding to the real-time execution moment; Charging is positive, discharging is negative, and under frequency modulation conditions, it is a high-frequency alternating current on the order of minutes; SOC, i-th sodium supercapacitive monomer core temperature The historical equivalent total cycle count of the i-th sodium supercapacitive monomer The three-dimensional nonlinear function accurately characterizes the dynamic change of DC internal resistance under frequency modulation conditions; The remaining charge of a sodium supercapacitor cell is the percentage of its rated capacity, and the value ranges from 0 to 1. Characterizing the historical usage intensity of sodium hypercapacitive monomers; For the first The entropic thermal coefficient of a sodium supercapacitive monomer, i.e. the rate of change of open-circuit voltage with temperature, is a function of SOC. Characterizes the polarization voltage drop caused by pseudocapacitive reaction; This is the irreversible thermal term of pseudocapacitive polarization, covering the polarization heat generation of the pseudocapacitive reaction. The absolute value is adapted to the bidirectional charging and discharging conditions of high-frequency alternating current.

[0043] Step S2 involves constructing a module-level heat distribution and individual cell aging decay rate prediction model based on the transient total heat generation power of each sodium supercapacitor cell, predicting the differentiated capacity decay rate of each sodium supercapacitor cell. This step accurately predicts the differentiated capacity decay rate of each sodium supercapacitor cell within the sodium supercapacitor module, providing the sole core input for the adaptive equilibrium target value prediction in the subsequent step S3.

[0044] Specifically, the prediction model for module-level thermal distribution and individual cell aging degradation rate is as follows:

[0045] in, The number of equivalent full cycles for the i-th sodium supercapacitive monomer in history is: The capacity decay rate at that time; : The reference capacity decay rate of sodium supercapacitive monomers under rated operating conditions; Activation energy of aging side reactions of sodium supercapacitive monomers; Universal gas constant; : The average hot spot temperature of the i-th sodium supercapacitive monomer within one minute-level frequency modulation cycle; : The average depth of discharge of the i-th sodium supercapacitive monomer under minute-level frequency-modulated high-frequency alternating conditions; : Rated depth of discharge of sodium supercapacitive monomers; : Depth of discharge aging acceleration index; : The absolute value of the average charge and discharge current of the i-th sodium supercapacitive cell within one minute-level frequency modulation cycle; : Rated charge and discharge current of sodium supercapacitive monomer; Current ratio aging acceleration index.

[0046] The role of this step and formula: This step realizes the linkage prediction of heat generation, hot spot temperature and aging rate, accurately predicts the differentiated capacity decay rate of sodium supercapacitor cells in sodium supercapacitor modules, solves the technical problems of large prediction deviation and incompatibility with frequency modulation conditions in existing aging models, provides the only core aging state input for subsequent adaptive balancing strategies, and is a key link connecting sodium supercapacitor cell characteristics and system control.

[0047] In the formula corresponding to the module-level heat distribution and the individual unit aging degradation rate prediction model, Characterizes the capacity decay rate of sodium supercapacitive monomers per historical equivalent full cycle; The historical equivalent total cycle number of sodium supercapacitive monomers; The reference capacity decay rate characterizes sodium supercapacitive monomers at rated temperature, rated depth of discharge (DOD), and rated current rate. Characterize the temperature sensitivity of aging side reactions; The value is 8.314 J / (mol·K); The actual operating temperature of each sodium supercapacitor cell was characterized, which solved the problem of missing aging acceleration prediction caused by local hot spots in the sodium supercapacitor module; Characterizes the degree to which the depth of discharge accelerates aging; The value ranges from 0 to 1, representing the charge-discharge depth of sodium supercapacitive monomers; The value range is 0 to 1, which represents the maximum permissible depth of discharge specified in the sodium supercapacitive monomer datasheet. It characterizes the degree to which the charge / discharge current rate accelerates aging.

[0048] The formula corresponding to the module-level thermal distribution and individual cell aging degradation rate prediction model introduces two power-law aging acceleration factors: DOD fluctuation acceleration factor. Characterizing the accelerating effect of discharge depth on aging; current rate acceleration factor. It characterizes the accelerating effect of charge / discharge current ratio on aging and accurately adapts to the aging characteristics of frequency modulation conditions.

[0049] Step S3 involves constructing a lifecycle adaptive equalization control target value prediction model based on the differentiated capacity decay rate of each sodium supercapacitor cell, and calculating the optimal equalization target voltage for each sodium supercapacitor cell. This step provides two core necessary inputs for the subsequent step S4, which predicts the optimal capacity-power configuration of the sodium supercapacitor energy storage system throughout its lifecycle.

[0050] Specifically, the prediction model for the target value of the full life-cycle adaptive equilibrium control is as follows:

[0051] in, The optimal equilibrium target voltage of the i-th sodium supercapacitive cell at time t; The reference voltage of the sodium supercapacitive module at time t is used as the reference value for the balancing target. : The average capacity decay rate of all sodium supercapacitor cells within the sodium supercapacitor module; The number of equivalent full cycles for the i-th sodium supercapacitive monomer in history is: Differential capacity decay rate over time; : The cumulative differential capacity decay of the i-th sodium supercapacitor, which is the difference between the rated capacity and the actual remaining capacity of the sodium supercapacitor; : The rated capacitance of the i-th sodium supercapacitor cell.

[0052] The role of this step and formula: This step realizes the adaptive linkage between aging state and equalization target. Based on the differentiated aging state of sodium supercapacitor cells, the optimal equalization target voltage is calculated, which solves the technical problems of existing equalization strategies not considering aging differences, short module life and high loss. At the same time, it provides two core necessary inputs for the system configuration calculation in the subsequent step S4. It is the core link connecting cell control and system configuration.

[0053] The full lifecycle adaptive equilibrium control target value prediction model introduces a capacity decay correction term. The equilibrium target voltage is adjusted based on the actual remaining capacity of the sodium supercapacitor cell to adapt to the capacity characteristics of the sodium supercapacitor cell after aging, avoiding overcharging and over-discharging. The analytical solution for the optimal equilibrium target voltage obtained by this invention requires no iteration, improves computational efficiency by more than 10 times, and can be directly run in real time in CMS.

[0054] Step S4: Based on the optimal equilibrium target voltage of each sodium supercapacitor cell, construct a system lifecycle optimal configuration prediction model with capacity-power coupling, and calculate the lifecycle optimal capacity-power configuration coefficient of the sodium supercapacitor energy storage system.

[0055] The optimal configuration prediction model for the entire lifecycle of a capacity-power coupled system is as follows:

[0056] in, The optimal capacity-power configuration factor for the entire life cycle of a sodium supercapacitor energy storage system represents the ratio of the rated energy of the sodium supercapacitor energy storage system to the energy required for frequency regulation. : Rated total energy of sodium supercapacity energy storage system; The rated charging and discharging power of the sodium supercapacity energy storage system matches the power requirements of grid frequency regulation; The longest continuous frequency regulation time required by the power grid; The round-trip charge-discharge efficiency of a sodium supercapacitive energy storage system under minute-level frequency modulation high-frequency alternating operating conditions; : Average equilibrium loss rate over the entire life cycle of sodium supercapacity energy storage system; The optimal equilibrium target voltage for the i-th sodium supercapacitive cell; : Average differentiated capacity decay rate over the entire life cycle of sodium supercapacity energy storage systems; The equivalent number of cycles within the design life of a sodium supercapacity energy storage system; : Actual utilization rate of the rated energy of the sodium supercapacitive module.

[0057] The role of this step and formula: This step realizes the full-chain linkage of balancing strategy, aging characteristics and system configuration, accurately calculates the optimal capacity-power configuration coefficient of sodium supercapacitor system throughout its entire life cycle under frequency regulation scenario, solves the technical problems of static configuration method, decoupling of sodium supercapacitor energy storage system configuration and operation, substandard performance throughout life cycle and low design efficiency, and provides the only core configuration parameter input for subsequent safety boundary prediction. It is a key link connecting system control and safety protection.

[0058] Specifically, The calculation formula is:

[0059] in, : No. Sodium supercapacitive monomers in The optimal equilibrium target voltage at any given time; : The current actual capacitance of the i-th sodium supercapacitive cell; : No. Sodium supercapacitive monomers in The current actual voltage at any given moment; Rated energy of sodium supercapacity energy storage system; Rated charge and discharge power of sodium supercapacity energy storage system; The longest continuous frequency regulation time required by the power grid; Energy conversion efficiency of active balancing circuit; : The total number of sodium supercapacitors in the sodium supercapacitor module.

[0060] The calculation formula is:

[0061] in, , : The upper and lower limits of the optimal equilibrium target voltage for the i-th sodium supercapacitive cell under all operating conditions; The upper and lower limits of the rated voltage of the sodium supercapacitive module; : The total number of sodium supercapacitors in the sodium supercapacitor module.

[0062] In the capacity-power coupled system lifecycle optimal configuration prediction model, Output from step S3 The calculated value is the equalization loss rate correction term; Output from step S3 The calculation yields a utilization correction term, achieving deep coupling between the balancing strategy and system configuration, thus solving the core pain point of decoupling system configuration and operation in existing technologies. The usable energy of the sodium supercapacitor module is determined by the voltage window of the series-connected sodium supercapacitor cells, and the output of step S3 is... The dynamic optimal voltage upper and lower limits for each sodium supercapacitor cell directly determine the actual usable voltage window of the sodium supercapacitor module. Simultaneously, a new full-lifecycle capacity degradation correction term is introduced. This approach achieves the coupling of aging characteristics with the configuration of sodium supercapacity energy storage systems, solving the problem that traditional solutions do not consider capacity decay throughout the entire life cycle.

[0063] The analytical solution for the optimal capacity-power configuration coefficient of a sodium supercapacity energy storage system throughout its entire life cycle, derived in this invention, replaces the traditional simulation iteration method, improving configuration design efficiency by more than 90%, and can be directly used in engineering design.

[0064] Step S5 involves constructing a real-time prediction model for the thermal runaway safety boundary based on the average heat generation power of the sodium supercapacitor energy storage system and its optimal capacity-power configuration factor throughout its entire lifecycle. This model calculates the thermal runaway safety boundary margin of the sodium supercapacitor energy storage system and implements tiered early warning and closed-loop protection. This step achieves early warning and closed-loop control of safety risks.

[0065] Specifically, the real-time prediction model for the thermal runaway safety boundary is as follows:

[0066] in, The thermal runaway safety margin of the sodium supercapacitive energy storage system at time t represents the degree of safety redundancy of the sodium supercapacitive energy storage system. : The average transient heat generation power of the sodium supercapacity energy storage system at time t; : The optimal capacity-power configuration factor for sodium supercapacity energy storage systems throughout their entire lifecycle; The longest continuous frequency regulation time required by the power grid. : Total mass of the sodium supercapacity module; : Average isobaric specific heat capacity of the sodium supercapacity module; : The critical temperature for thermal runaway of sodium supercapacitive monomers; : The ambient temperature of the sodium supercapacitive energy storage system at time t.

[0067] The purpose of this step is to achieve full-link linkage between heat generation, configuration, and safety boundary, and to quantitatively predict the thermal runaway safety boundary margin of the sodium supercapacity energy storage system in real time. This solves the technical problems of existing safety protection lag, lack of early prediction capability, and decoupling from system characteristics, realizes early warning of thermal runaway risk, significantly improves the safety of the sodium supercapacity energy storage system, and forms a closed-loop control link for the entire method.

[0068] The real-time prediction model for thermal runaway safety boundaries will output the results of step S1. The output of step S4 As a core input, this approach achieves full-link linkage between the safety boundary and the heat generation, configuration, and operational characteristics of the sodium supercapacity energy storage system, solving the problem of unreasonable safety protection threshold settings and decoupling from system characteristics in traditional methods. The thermal runaway safety boundary margin of the sodium supercapacity energy storage system at time t can be directly used for graded early warning and closed-loop control of the CMS, achieving early warning of thermal runaway risk 10-30 minutes in advance, upgrading safety protection from post-event alarm to pre-event prediction.

[0069] In one specific embodiment, the tiered early warning and closed-loop protection includes: When the thermal runaway safety margin of the sodium supercapacity energy storage system is lower than the warning threshold, an audible and visual warning is triggered. When the thermal runaway safety margin of the sodium supercapacity energy storage system is lower than the protection threshold, the charging and discharging power is limited. When the thermal runaway safety margin of the sodium supercapacity energy storage system is ≤0, the sodium supercapacity energy storage system shutdown protection shall be executed. Among them, the warning threshold > the protection threshold > 0.

[0070] In one specific embodiment, this embodiment takes a sodium-ion supercapacitor energy storage system applied to the primary frequency regulation scenario of the power grid as the implementation object. Those skilled in the art can fully implement the method of the present invention based on the content disclosed in this embodiment without any creative effort.

[0071] The implementation object of this embodiment is: a sodium-ion supercapacitor energy storage system for grid minute-level primary frequency regulation. The sodium-ion supercapacitor energy storage system is composed of multiple sodium supercapacitor modules connected in series / parallel. Each sodium supercapacitor module is composed of multiple sodium supercapacitor cells connected in series. The sodium-ion supercapacitor energy storage system is equipped with a capacitor management system, a converter, and a thermal management system. It has the ability to collect voltage, current, and temperature in real time, as well as equalization control and charge / discharge control capabilities.

[0072] The specific implementation steps of this embodiment are as follows: S1: Prediction of transient total heat production power of sodium supercapacitive monomer S11: Complete the basic performance tests of sodium supercapacitive monomers in advance: establish a multi-dimensional mapping table of internal resistance with SOC, temperature and cycle number through mixed pulse power characteristic pulse test; establish OCV-SOC mapping table and entropy-thermal coefficient mapping table through constant temperature chamber multi-temperature zone test; establish a multi-dimensional mapping table of polarization overpotential with current ratio, SOC and temperature through constant current intermittent titration test, and store all mapping tables in the storage unit of CMS; S12: CMS collects the charging and discharging current of the sodium supercapacitive energy storage system at time t in real time. The state of charge of the sodium supercapacitive monomer at time t The core temperature of the i-th sodium supercapacitive monomer at time t The historical equivalent total equivalent cycle count of the i-th sodium hypercapacitive monomer The corresponding DC internal resistance is obtained by interpolation through table lookup. The entropy-heat coefficient of the i-th sodium supercapacitive monomer The pseudocapacitive polarization overpotential of the i-th sodium supercapacitive monomer ; S13: Substitute the above parameters into the formula corresponding to the transient electrothermal coupling heat generation power prediction model of sodium supercapacitor cells, and calculate the transient total heat generation power of each sodium supercapacitor cell in real time. Output to step S2.

[0073] S2: Prediction of Differential Capacity Decay Rate of Sodium Hypercapacitive Monomers S21: Aging characteristic testing of sodium supercapacitors completed ahead of schedule: The reference capacity decay rate of sodium supercapacitors was obtained through rated operating condition cycle life testing. The activation energy of the aging side reaction of sodium supercapacitive monomers was obtained through multi-temperature accelerated aging tests. The depth of discharge aging acceleration index was obtained through cyclic aging tests with different DODs and different current rates. and current ratio aging acceleration index All parameters are stored in the CMS storage unit; S22: Based on the output of step S1 The average hotspot temperature of each sodium supercapacitor cell was calculated using a pre-established thermal resistance model of the sodium supercapacitor module. ; S23: CMS statistically analyzes historical operating data to obtain the average depth of discharge of the i-th sodium supercapacitive cell under minute-level frequency-modulated high-frequency alternating operating conditions. and the absolute value of the average charge and discharge current of the i-th sodium supercapacitive cell within a minute-level frequency modulation cycle. Combined with the results obtained in step S22 Substituting the formulas corresponding to the module-level thermal distribution and monomer aging decay rate prediction model, the differentiated capacity decay rate of each sodium supercapacitor is calculated. Output to step S3.

[0074] S3: Prediction of the optimal equilibrium target voltage for sodium hypercapacitive cells S31: CMS collects the terminal voltages of all sodium supercapacitor cells in the sodium supercapacitor module in real time, and takes the median to obtain the reference voltage of the sodium supercapacitor module at time t. ; S32: Calculate the average differential capacity decay rate of all sodium supercapacitors within the sodium supercapacitor module. Meanwhile, CMS obtains the cumulative differential capacity decay of the i-th sodium hypercapacitive monomer through periodic capacity calibration. ; S33: Output from step S2 and the above , , Substituting the formula corresponding to the full life-cycle adaptive equalization control target value prediction model, calculate the optimal equalization target voltage of the i-th sodium supercapacitive cell at time t. On one hand, it outputs to the equalization control module of CMS to perform active equalization control; on the other hand, it outputs to step S4.

[0075] S4: Prediction of the optimal capacity-power configuration factor throughout the entire life cycle of sodium supercapacity energy storage systems S41: Complete system-level performance testing ahead of schedule: Obtain the reciprocating charge-discharge efficiency of the sodium supercapacitive energy storage system under minute-level frequency-modulated high-frequency alternating conditions through system-level frequency-modulated charge-discharge cycle testing. The energy conversion efficiency of the active equalization circuit is obtained through equalization circuit performance testing. ; S42: Based on the output of step S3 Calculate the average equilibrium loss rate over the entire life cycle of a sodium supercapacity energy storage system. Actual utilization rate of rated energy of sodium supercapacitive module ; S43: Determine the rated charging and discharging power of the sodium supercapacitive energy storage system according to the grid frequency regulation technical requirements. The longest continuous frequency regulation time required by the power grid Combined with the output of step S2 Equivalent cycle count within the design life of a sodium supercapacity energy storage system Substituting the formulas into the system's lifecycle optimal configuration prediction model for capacity-power coupling, the lifecycle optimal capacity-power configuration coefficient of the sodium supercapacity energy storage system is calculated. On the one hand, it is used for the design and configuration optimization of sodium supercapacity energy storage systems; on the other hand, it is output to step S5.

[0076] S5: Prediction of thermal runaway safety margin in sodium supercapacitive energy storage systems S51: Complete the thermophysical properties and thermal runaway characteristics tests of the sodium supercapacity module ahead of schedule: Obtain the average isobaric specific heat capacity of the sodium supercapacity module through calorimeter testing. The critical temperature for thermal runaway of sodium hypercapacitive monomers was obtained by accelerated calorimetry testing. ; S52: Based on the output of step S1 Calculate the average transient heat generation power of the sodium supercapacity energy storage system at time t. ; S53: Output from step S4 and the above The ambient temperature of the sodium supercapacity energy storage system at time t, collected in real time. Substituting the formula corresponding to the real-time prediction model of thermal runaway safety boundary, the thermal runaway safety boundary margin of the sodium supercapacity energy storage system is calculated in real time. ; S54: CMS according to Implement tiered early warning and closed-loop control: When When the temperature falls below the warning threshold, an audible and visual warning is triggered; when... When the power is below the protection threshold, the charging and discharging power of the sodium supercapacitive energy storage system is limited; when At that time, the sodium supercapacity energy storage system is triggered to shut down, forming a complete closed-loop control link.

[0077] This embodiment fully implements the closed-loop predictive control method for the entire life cycle of the present invention, realizing accurate prediction of heat generation, adaptive aging balancing, optimal configuration throughout the entire life cycle, and early warning of safety boundaries for the sodium supercapacitive frequency regulation system, significantly improving the performance, economy, and safety of the sodium supercapacitive energy storage system throughout its entire life cycle.

[0078] This application also provides a closed-loop predictive control system for the entire life cycle of a sodium-ion supercapacitor, including: The transient total heat generation power acquisition module is used to construct a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells, predict the transient total heat generation power of each sodium supercapacitor cell in the sodium supercapacitor module under minute-level frequency modulation high-frequency alternating operating conditions, and obtain the average heat generation power of the sodium supercapacitor energy storage system. The differential capacity decay rate acquisition module is used to construct a module-level heat distribution and single-cell aging decay rate prediction model based on the transient total heat generation power of each sodium supercapacitor, and predict the differential capacity decay rate of each sodium supercapacitor. The optimal equalization target voltage acquisition module is used to construct a full life cycle adaptive equalization control target value prediction model based on the differentiated capacity decay rate of each sodium supercapacitor cell, and calculate the optimal equalization target voltage for each sodium supercapacitor cell. The optimal capacity-power configuration coefficient acquisition module is used to construct a system lifecycle optimal configuration prediction model based on the optimal equilibrium target voltage of each sodium supercapacitor cell, and to calculate the optimal capacity-power configuration coefficient of the sodium supercapacitor energy storage system throughout its lifecycle. The thermal runaway safety boundary margin acquisition module is used to construct a real-time prediction model of the thermal runaway safety boundary based on the average heat generation power of the sodium supercapacity energy storage system and the optimal capacity-power configuration coefficient of the sodium supercapacity energy storage system, calculate the thermal runaway safety boundary margin of the sodium supercapacity energy storage system, and perform graded early warning and closed-loop protection.

[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. The scope of patent protection of the present invention shall be determined by the claims. Similarly, any equivalent structural changes made based on the description and drawings of the present invention shall also be included within the scope of protection of the present invention.

Claims

1. A closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor, characterized in that, Includes the following steps: Step S1: Construct a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells to predict the transient total heat generation power of each sodium supercapacitor cell in the sodium supercapacitor module under minute-level frequency modulation high-frequency alternating operating conditions, and obtain the average heat generation power of the sodium supercapacitor energy storage system. Step S2: Based on the transient total heat generation power of each sodium supercapacitor, construct a module-level heat distribution and single-unit aging decay rate prediction model to predict the differentiated capacity decay rate of each sodium supercapacitor. Step S3: Based on the differentiated capacity decay rate of each sodium supercapacitor cell, construct a full life cycle adaptive equalization control target value prediction model and calculate the optimal equalization target voltage for each sodium supercapacitor cell. Step S4: Based on the optimal equilibrium target voltage of each sodium supercapacitor cell, construct a system full life cycle optimal configuration prediction model with capacity-power coupling, and calculate the full life cycle optimal capacity-power configuration coefficient of the sodium supercapacitor energy storage system. Step S5: Based on the average heat generation power of the sodium supercapacity energy storage system and the optimal capacity-power configuration coefficient throughout the entire life cycle of the sodium supercapacity energy storage system, construct a real-time prediction model for the thermal runaway safety boundary, calculate the thermal runaway safety boundary margin of the sodium supercapacity energy storage system, and perform graded early warning and closed-loop protection.

2. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 1, characterized in that, The transient electrothermal coupling heat generation power prediction model for sodium supercapacitive monomers is as follows: in, : The transient total heat production power of the i-th sodium supercapacitive monomer at time t; : The charging and discharging current of the sodium supercapacitive energy storage system at time t; : DC internal resistance of the i-th sodium supercapacitive cell; The state of charge of the sodium supercapacitive monomer at time t; : The core temperature of the i-th sodium supercapacitive monomer at time t; : The historical equivalent total cycle count of the i-th sodium supercapacitive monomer; : The entropic thermal coefficient of the i-th sodium supercapacitive monomer; : The open-circuit voltage of the i-th sodium supercapacitive cell at time t under the corresponding SOC; : The pseudocapacitive polarization overpotential of the i-th sodium supercapacitive monomer at time t; : The general symbol for the independent variable in thermodynamic temperature.

3. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 2, characterized in that, The module-level heat distribution and single-unit aging decay rate prediction model is as follows: in, The number of equivalent full cycles for the i-th sodium supercapacitive monomer in history is: Differential capacity decay rate over time; : The baseline capacity decay rate of sodium supercapacitive monomers under rated operating conditions; Activation energy of aging side reactions of sodium supercapacitive monomers; Universal gas constant; : The average hot spot temperature of the i-th sodium supercapacitive monomer within one minute-level frequency modulation cycle; : The average depth of discharge of the i-th sodium supercapacitive monomer under minute-level frequency-modulated high-frequency alternating conditions; : Rated depth of discharge of sodium supercapacitive monomers; : Depth of discharge aging acceleration index; : The absolute value of the average charge and discharge current of the i-th sodium supercapacitive cell within one minute-level frequency modulation cycle; : Rated charge and discharge current of sodium supercapacitive monomer; Current ratio aging acceleration index.

4. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 3, characterized in that, The whole life cycle adaptive equilibrium control target value prediction model is as follows: in, The optimal equilibrium target voltage of the i-th sodium supercapacitive cell at time t; : The reference voltage of the sodium supercapacitive module at time t; : The average differential capacity decay rate of all sodium supercapacitors within the sodium supercapacitor module; The number of equivalent full cycles for the i-th sodium supercapacitive monomer in history is: Differential capacity decay rate over time; : The cumulative differential capacity decay of the i-th sodium supercapacitive monomer; : The rated capacitance of the i-th sodium supercapacitor cell.

5. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 4, characterized in that, The optimal configuration prediction model for the full lifecycle of the capacity-power coupled system is as follows: in, : The optimal capacity-power configuration factor for sodium supercapacity energy storage systems throughout their entire lifecycle; : Rated total energy of sodium supercapacity energy storage system; Rated charge and discharge power of sodium supercapacity energy storage system; The longest continuous frequency regulation time required by the power grid; The round-trip charge-discharge efficiency of a sodium supercapacitive energy storage system under minute-level frequency modulation high-frequency alternating operating conditions; : Average equilibrium loss rate over the entire life cycle of sodium supercapacity energy storage system; The optimal equilibrium target voltage for the i-th sodium supercapacitive cell; The average differentiated capacity decay rate over the entire life cycle of sodium supercapacity energy storage systems; The equivalent number of cycles within the design life of a sodium supercapacity energy storage system; : Actual utilization rate of the rated energy of the sodium supercapacitive module.

6. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 5, characterized in that, The The calculation formula is: in, : No. Sodium supercapacitive monomers in The optimal equilibrium target voltage at any given time; : The current actual capacitance of the i-th sodium supercapacitive cell; : No. Sodium supercapacitive monomers in The current actual voltage at any given moment; Rated energy of sodium supercapacity energy storage system; Rated charge and discharge power of sodium supercapacity energy storage system; The longest continuous frequency regulation time required by the power grid; Energy conversion efficiency of active balancing circuit; : The total number of sodium supercapacitors in the sodium supercapacitor module.

7. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 5, characterized in that, The The calculation formula is: in, , : The upper and lower limits of the optimal equilibrium target voltage for the i-th sodium supercapacitive cell under all operating conditions; The upper and lower limits of the rated voltage of the sodium supercapacitive module; This represents the total number of sodium supercapacitors within the sodium supercapacitor module.

8. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 1, characterized in that, The real-time prediction model for the thermal runaway safety boundary is as follows: in, : The thermal runaway safety margin of the sodium supercapacity energy storage system at time t; : The average transient heat generation power of the sodium supercapacity energy storage system at time t; : The optimal capacity-power configuration factor for sodium supercapacity energy storage systems throughout their entire lifecycle; The longest continuous frequency regulation time required by the power grid. : Total mass of the sodium supercapacity module; : Average isobaric specific heat capacity of the sodium supercapacity module; : The critical temperature for thermal runaway of sodium supercapacitive monomers; : The ambient temperature of the sodium supercapacitive energy storage system at time t.

9. The closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to claim 8, characterized in that, The tiered early warning and closed-loop protection system includes: When the thermal runaway safety margin of the sodium supercapacity energy storage system is lower than the warning threshold, an audible and visual warning is triggered. When the thermal runaway safety margin of the sodium supercapacitive energy storage system is lower than the protection threshold, the charging and discharging power of the sodium supercapacitive energy storage system is limited. When the thermal runaway safety margin of the sodium supercapacity energy storage system is ≤0, the sodium supercapacity energy storage system shutdown protection shall be executed. Among them, the warning threshold > the protection threshold > 0.

10. A system for implementing the closed-loop predictive control method for the entire life cycle of a sodium-ion supercapacitor according to any one of claims 1-9, characterized in that, include: The transient total heat generation power acquisition module is used to construct a transient electrothermal coupling heat generation power prediction model for sodium supercapacitor cells, predict the transient total heat generation power of each sodium supercapacitor cell in the sodium supercapacitor module under minute-level frequency modulation high-frequency alternating operating conditions, and obtain the average heat generation power of the sodium supercapacitor energy storage system. The differential capacity decay rate acquisition module is used to construct a module-level heat distribution and single-cell aging decay rate prediction model based on the transient total heat generation power of each sodium supercapacitor, and predict the differential capacity decay rate of each sodium supercapacitor. The optimal equalization target voltage acquisition module is used to construct a full life cycle adaptive equalization control target value prediction model based on the differentiated capacity decay rate of each sodium supercapacitor cell, and calculate the optimal equalization target voltage for each sodium supercapacitor cell. The optimal capacity-power configuration coefficient acquisition module is used to construct a system lifecycle optimal configuration prediction model based on the optimal equilibrium target voltage of each sodium supercapacitor cell, and to calculate the optimal capacity-power configuration coefficient of the sodium supercapacitor energy storage system throughout its lifecycle. The thermal runaway safety boundary margin acquisition module is used to construct a real-time prediction model of the thermal runaway safety boundary based on the average heat generation power of the sodium supercapacity energy storage system and the optimal capacity-power configuration coefficient of the sodium supercapacity energy storage system, calculate the thermal runaway safety boundary margin of the sodium supercapacity energy storage system, and perform graded early warning and closed-loop protection.

Images