Online prediction method for long-term thermal safety power boundary of lithium battery of ship facing emission control area

Abstract

The present application relates to the technical field of power battery management, and is an online prediction method for long-time domain thermal safety power boundary of lithium battery of ship in emission control area, comprising: constructing a simplified electrochemical model of thermal coupling of lithium ion battery; using a lumped parameter heat transfer model, simplifying the lithium ion battery monomer into a uniform heating body to represent the battery temperature by surface temperature; in the case of close arrangement of multiple batteries, correcting the lumped parameter heat transfer model according to the heat dissipation environment; according to the simplified electrochemical model, constructing a terminal voltage prediction proxy model based on a Kriging model, and obtaining a future terminal voltage prediction sequence; using a model predictive control algorithm to solve the maximum continuous charging and discharging power boundary of the battery under the thermal safety constraint according to the future terminal voltage prediction sequence. The present application aims to realize fast and accurate online prediction of the maximum continuous charging and discharging power boundary allowed by the battery in the future long-time scale.

Description

Technical Field

[0001] This invention relates to the field of power battery management technology, and in particular to an online prediction method for the long-term thermal safety power boundary of lithium batteries for ships in emission control areas. Background Technology

[0002] As a pillar of global trade, the international shipping industry faces increasingly stringent international regulations on its greenhouse gas and pollutant emissions. Emission Control Areas (ECAs) have emerged and are continuously expanding to protect densely populated and ecologically sensitive coastal and port areas. Compared to high seas standards, ECAs impose significantly lower limits on emissions of harmful pollutants such as sulfur oxides (SOx), nitrogen oxides (NOx), and particulate matter (PM). For example, fuel sulfur content limits within ECAs are typically below 0.1%. Therefore, once ships enter an ECA, they must switch to low-sulfur fuels, use exhaust aftertreatment systems, or, more fundamentally, adopt cleaner alternative power modes. Thus, ECA regulations have become the most direct and mandatory policy driver for achieving ultra-low or zero emissions on specific shipping routes.

[0003] Within the ECA, typical ship operating conditions (such as port entry / exit maneuvers, berthing and unberthing operations, and low-speed cruising in restricted waters) place unique power demands on propulsion systems, whose load characteristics are inherently high-power, transient, and involve frequent start-stop cycles. For example, during collision avoidance or course correction, the propulsion system needs to output enormous torque and power in a short period; while berthing operations involve frequent micro-speed adjustments and braking. To mitigate the impact of these operating conditions on the ship's electrical system and meet ECA emission requirements, hybrid power systems typically require the power lithium-ion batteries to undergo frequent high-rate charging and discharging.

[0004] However, such prolonged, intermittent high-rate charging and discharging generates significant Joule heating and reaction heat, leading to continuous heat accumulation. Over the entire ECA (Extended Cautionary Range) timescale (typically tens of minutes to several hours), battery temperature exhibits a slow rise, with its thermal state evolution far exceeding the transient temperature rise range of seconds to minutes. Limited by the computational complexity of battery models, existing lithium-ion battery thermal safety boundary prediction methods primarily focus on short-term overheating assessments within the next 60 seconds, failing to capture the risk of temperature exceeding limits due to cumulative thermal effects and dynamic changes in heat dissipation boundary conditions over long timescales. Without the ability to predict thermal safety power boundaries over long timescales, ship energy management strategies will be forced to adopt conservative power limits, sacrificing the ship's ability to navigate purely on electric power within the ECA. Conversely, insufficient prediction may trigger output power limitations or even disconnection due to continuous high-temperature operation, increasing the risk of thermal runaway and performance degradation, and potentially preventing the ship from completing its planned voyage or mission, thereby triggering emissions compliance risks and operational disruptions. Therefore, there is an urgent need to develop an online prediction method for the thermal safety power boundary of lithium batteries that can cover the entire ECA flight and be oriented towards long time scales. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides an online prediction method for the long-term thermal safety power boundary of lithium batteries for ships in emission control areas. This invention addresses the issue that traditional short-term prediction methods fail due to the significant battery thermal accumulation effect during the entire ECA voyage (typically lasting tens of minutes to several hours). The invention aims to achieve rapid and accurate online prediction of the maximum permissible continuous charge and discharge power boundary of the battery over a long future timescale.

[0006] The technical means employed in this invention are as follows:

[0007] A long-term online prediction method for the thermal safety power boundary of lithium-ion batteries for ships in emission control areas includes: constructing a simplified electrochemical model of lithium-ion batteries with thermal coupling; simplifying a single lithium-ion battery cell into a uniform heat source using a lumped-parameter heat transfer model, with surface temperature representing battery temperature; modifying the lumped-parameter heat transfer model according to the heat dissipation environment when multiple batteries are closely arranged; constructing a terminal voltage prediction proxy model based on the Kriging model according to the simplified electrochemical model, and obtaining a future terminal voltage prediction sequence; and using a model predictive control algorithm to solve online for the maximum continuous charge-discharge power boundary of the battery under thermal safety constraints based on the future terminal voltage prediction sequence.

[0008] Furthermore, the simplified electrochemical model uses the battery terminal voltage. This indicates that the battery terminal voltage is the result of the combined effects of the internal electrode thermodynamic processes, lithium ion diffusion processes in the solid-liquid phases, ohmic processes, and electrochemical reaction processes. Represented as:

[0009] in, Indicates the battery open-circuit voltage. Indicates concentration polarization overpotential, Indicates the Ohmic polarization overpotential. Indicates the reaction polarization overpotential; The lithium intercalation concentration fraction of the positive and negative electrode active materials directly affects the open-circuit voltage of the battery through the electrode potential curve, and the open-circuit voltage of the battery is expressed as:

[0010] in, This indicates the open-circuit voltage of the battery's positive terminal. This indicates the open-circuit voltage of the battery's negative terminal. This indicates the lithium intercalation concentration fraction on the surface of the positive electrode active material. This indicates the lithium intercalation concentration fraction on the surface of the negative electrode active material; Solid-phase diffusion of lithium ions in the active particles of the electrode causes changes in the lithium intercalation concentration fraction on the positive and negative electrode surfaces, which in turn affects the open-circuit voltage of the battery.

[0011] in, This represents the average lithium intercalation concentration fraction of the positive electrode active material. This represents the average lithium intercalation concentration fraction of the negative electrode active material. This represents the difference between the surface area of ​​the positive electrode active material and the average lithium intercalation concentration fraction. This represents the difference between the surface area of ​​the negative electrode active material and the average lithium intercalation concentration fraction. The lithium-ion concentration distribution during solid-phase diffusion is solved using a three-parameter parabolic approximation:

[0012] in, and As an intermediate variable, This represents the negative electrode solid-phase diffusion time constant. This represents the solid-phase diffusion time constant of the positive electrode. This indicates the positive electrode capacity of a lithium-ion battery. This indicates the capacity of the negative electrode in a lithium-ion battery. Indicates the battery operating current; intermediate variables and The discretization formula is expressed as:

[0013] in, Indicates the first kThe time corresponding to each discrete time point Indicates the first k +1 discrete time points corresponding to the time; The liquid-phase diffusion process leads to a significant difference in lithium-ion concentration inside the battery, which in turn generates the concentration polarization overpotential, expressed as:

[0014] in, Represents the ideal gas constant. Denotes Faraday's constant. This indicates the initial lithium-ion concentration in the electrolyte. This represents the difference in lithium ion concentration at the positive and negative electrodes. Indicates the number of charges transferred. Indicates that the battery is in t Temperature at any moment; The lithium ion concentration difference of the electrolyte at the positive and negative electrodes Represented as:

[0015] in, Represents the liquid phase diffusion time constant. Indicates the liquid phase diffusion coefficient; The ohmic effects of each part of the simplified electrochemical model are lumped together, and the combined effect of each ohmic process is characterized by the ohmic internal resistance. The ohmic polarization overpotential is then calculated. Represented as:

[0016] in, Indicates the internal resistance of the ohm; The polarization effect of an electrochemical reaction generates a reaction polarization overpotential, which will reduce the reaction polarization overpotential. Represented as:

[0017] in, and As an intermediate variable, This represents the reaction polarization constant.

[0018] Furthermore, the lumped parameter heat transfer model, based on the law of conservation of energy and the lumped parameter assumption, is derived from... Battery temperature at all times calculate Temperature at any time :

[0019] in, Indicates the battery's heating power. Indicates the battery's heat dissipation power. Indicates battery quality. Represents the integral variable. Indicates the battery's specific heat capacity; The heating power of the battery The heat generation power of the battery is calculated using the Bernardi heat generation equation, which consists of two parts: reversible heat and irreversible heat. The irreversible heat part is equal to the product of the battery overpotential and the current; the reversible heat part is the product of the battery temperature, the current, and the entropy coefficient. The heat generation power of the battery can be expressed as:

[0020] in, Indicates the battery open-circuit voltage. Indicates the battery terminal voltage. Indicates the battery operating current. This represents the entropy coefficient of the battery. Indicates battery temperature; Based on Newton's law of cooling and the lumped-parameter heat transfer model, the heat dissipation power of the battery can be expressed as:

[0021]

[0022] in, This indicates the temperature of the air surrounding the battery. This indicates the thermal resistance between the battery and the air. This indicates the heat dissipation coefficient between the battery and the air. This indicates the area of ​​the battery that dissipates heat.

[0023] Furthermore, the lumped parameter heat transfer model is modified, and the modified temperature discretization recursive formula is expressed as:

[0024] in, This indicates the total heat dissipation power of a single battery cell. Indicates the coolant temperature. Indicates air temperature. Indicates battery quality. Indicates the battery's specific heat capacity. Indicates the sampling step size. This represents the equivalent thermal resistance between the battery and the coolant. This represents the equivalent thermal resistance between the battery and the air.

[0025] Furthermore, the terminal voltage prediction proxy model decomposes long-time-domain multi-step prediction into a combined architecture of single-step prediction and recursive iteration. The terminal voltage prediction proxy model selects current... Terminal voltage and state of charge As input feature vector The output is the terminal voltage at the next discrete time step. :

[0026] in, This is a nonlinear mapping function determined through offline training; The input vector is scaled using the Min-Max scaling method. The features of each dimension are uniformly mapped to a preset standard range. The mathematical transformation equation is expressed as follows:

[0027] in, This represents the value after scaling the original value. Indicates the first i Dimensional features in k The original value at time, and For the first i Minimum and maximum values ​​of the dimensional features throughout the entire training sequence; The original data matrix is ​​divided into two overlapping subsets with temporal misalignment along the time axis, which respectively constitute the input feature matrix. and output target vector :

[0028] Based on the input feature matrix and output target vector The terminal voltage prediction surrogate model is trained offline to establish a nonlinear mapping relationship from the current state to the terminal voltage at the next time step. The terminal voltage prediction surrogate model will then predict the system response. It can be viewed as the superposition of a global trend term and a local random fluctuation term, and its mathematical expression is as follows:

[0029] in, Represents a global regression model. For the regression basis function vector, This is the corresponding regression coefficient vector; It is a function with a mean of zero and a variance of . It is a stochastic process with non-zero covariance; At the prediction starting point, the measured initial state vector As input, a single-step prediction is performed using an offline-trained terminal voltage prediction surrogate model to obtain the predicted terminal voltage for the first time step in the future. The measured terminal voltage at the current moment is replaced with the predicted terminal voltage, and combined with the current and state of charge at the next moment to form a new input feature vector. This vector is then input into the terminal voltage prediction proxy model to obtain the predicted terminal voltage value for the next time step. This process is repeated recursively until the preset prediction time domain is covered, thereby generating a future terminal voltage prediction sequence.

[0030] Furthermore, the model predictive control algorithm uses the battery operating current as the control variable and the temperature of the middle battery in the battery pack as the controlled variable. Under the premise that the battery temperature does not exceed a set threshold, it solves for the maximum allowable charging and discharging current of the system. The objective function of the model predictive control algorithm is expressed as:

[0031] in, Represent the objective function; Indicates the current weighting factor; Indicates the temperature penalty factor; This indicates the maximum operating current within the current solution cycle; This indicates the preset upper limit of the battery's safe temperature. This indicates the future number calculated by the prediction model. Step battery temperature; Indicates the number of steps in the prediction time domain; The temperature penalty factor Designed as a dynamically adjustable parameter, the temperature penalty factor is adjusted online based on the deviation between the predicted battery temperature and the set temperature.

[0032] When the predicted temperature does not exceed the set value hour, Take the smaller value This causes the optimization process to prioritize increasing the operating current; when the predicted temperature reaches or exceeds the set value... Take the larger value This forces the current to be limited, thus preventing the temperature from rising further.

[0033] Furthermore, the objective function of the model predictive control algorithm is solved using a bisection method, with the comparison between the predicted maximum temperature and the temperature setpoint serving as the core criterion for the direction of current adjustment. In each control cycle, the current current value is substituted into the model predictive control algorithm to calculate the maximum temperature in the predicted time domain. If the highest temperature If the current is low, decrease it; otherwise, increase it. The current search interval is continuously narrowed using a bisection method until the maximum current that satisfies the thermal safety constraints is obtained. .

[0034] Compared with the prior art, the present invention has the following advantages: This invention establishes a simplified electrochemical model with coupled thermal characteristics to describe the core dynamic behavior of a battery under multi-physics conditions, avoiding the computational burden of online solutions for complex models while ensuring the description of heat generation and heat transfer processes. Building upon this, to address the bottleneck issue of inefficient terminal voltage calculation in the simplified electrochemical model, this invention integrates simulation and measured data generated by the simplified electrochemical model to construct a surrogate model for rapid terminal voltage calculation. This surrogate model reproduces the voltage response characteristics of the physical model in a data-driven manner, achieving an order-of-magnitude improvement in computational speed and laying the foundation for iterative prediction and solution over long time scales. Furthermore, the surrogate model is embedded as a prediction model within a model predictive control framework; within each control time domain, using a preset thermal safety temperature threshold as a hard constraint, a rolling optimization algorithm is used to solve online for the maximum continuous charge-discharge power boundary that will prevent the battery from overheating over future long time scales. Finally, an experimental platform was built to verify the effectiveness and superiority of the proposed method.

[0035] This invention employs a simplified physical model, a data-driven proxy model, and an online solution for model predictive control. This approach preserves the interpretability and generalization capability of the physical model for battery thermal behavior while overcoming the timeliness bottleneck of online calculation of the full physical model through a data-driven method. It enables online prediction of the thermal safety power boundary of lithium batteries over a long timescale at the ECA full-range level, providing reliable time-varying safety constraints for the energy management strategy of hybrid-powered ships, thereby balancing the zero-emission compliance of ships within the ECA with the thermal safety of the power battery. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a flowchart of the online prediction method for long-time thermal safety power boundary of marine lithium batteries in emission control areas according to the present invention.

[0038] Figure 2 This is a schematic diagram of the lumped parameter heat transfer model of the square aluminum-cased battery in this invention.

[0039] Figure 3 This is a schematic diagram of the lumped parameter thermal model of a single cell in the liquid-cooled battery module of the present invention.

[0040] Figure 4 This is a schematic diagram of the input-output relationship of the terminal voltage prediction proxy model in this invention.

[0041] Figure 5 This is a schematic diagram of the time series misalignment mapping of the training dataset in this invention.

[0042] Figure 6 This is a flowchart of the voltage multi-step prediction process based on a recursive iteration strategy in this invention.

[0043] Figure 7 This is a framework diagram of the model predictive control algorithm in this invention.

[0044] Figure 8 This is a schematic diagram of the actual five-cell battery liquid cooling system structure in an embodiment of the present invention.

[0045] Figure 9 This is a graph showing the prediction time-domain result for 600 seconds under the charging condition in an embodiment of the present invention.

[0046] Figure 10 This is a graph showing the predicted time-domain result for 900 seconds under the charging condition in an embodiment of the present invention.

[0047] Figure 11 This is a curve showing the predicted time-domain result for 600s under the discharge condition in an embodiment of the present invention.

[0048] Figure 12 This is a curve showing the predicted time-domain result of 900s under the discharge condition in an embodiment of the present invention. Detailed Implementation

[0049] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0050] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. 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.

[0051] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0052] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0053] like Figure 1 As shown, this invention provides an online prediction method for the long-term thermal safety power boundary of lithium batteries for ships in emission control areas. The method includes: establishing a lithium-ion battery electrothermal coupling mathematical model that combines computational efficiency and prediction accuracy. This model describes the coupled dynamic behavior of the battery's electrical and thermal characteristics during charging and discharging, providing a physical basis for subsequent power boundary prediction. The model consists of two parts: a simplified electrochemical model and a lumped-parameter heat transfer model.

[0054] A simplified electrochemical model of a lithium-ion battery with thermal coupling is constructed. Specifically, as a preferred embodiment of this invention, the simplified electrochemical model uses the battery terminal voltage. This indicates that the battery terminal voltage is the result of the combined effects of the internal electrode thermodynamic processes, lithium ion diffusion processes in the solid-liquid phases, ohmic processes, and electrochemical reaction processes. Represented as:

[0055] in, Indicates the battery open-circuit voltage. Indicates concentration polarization overpotential, Indicates the Ohmic polarization overpotential. Indicates the reaction polarization overpotential; The lithium intercalation concentration fraction of the positive and negative electrode active materials directly affects the battery open-circuit voltage through the electrode potential curve. The battery open-circuit voltage is expressed as:

[0056] in, This indicates the open-circuit voltage of the battery's positive terminal. This indicates the open-circuit voltage of the battery's negative terminal. This indicates the lithium intercalation concentration fraction on the surface of the positive electrode active material. This indicates the lithium intercalation concentration fraction on the surface of the negative electrode active material; Solid-phase diffusion of lithium ions in the active particles of the electrode causes changes in the lithium intercalation concentration fraction on the positive and negative electrode surfaces, which in turn affects the open-circuit voltage of the battery.

[0057] in, This represents the average lithium intercalation concentration fraction of the positive electrode active material. This represents the average lithium intercalation concentration fraction of the negative electrode active material. This represents the difference between the surface area of ​​the positive electrode active material and the average lithium intercalation concentration fraction. This represents the difference between the surface area of ​​the negative electrode active material and the average lithium intercalation concentration fraction. The lithium-ion concentration distribution during solid-phase diffusion is solved using a three-parameter parabolic approximation:

[0058] in, and As an intermediate variable, This represents the negative electrode solid-phase diffusion time constant. This represents the solid-phase diffusion time constant of the positive electrode. This indicates the positive electrode capacity of a lithium-ion battery. This indicates the capacity of the negative electrode in a lithium-ion battery. Indicates the battery operating current; intermediate variables and The discretization formula is expressed as:

[0059] in, Indicates the first k The time corresponding to each discrete time point Indicates the first k +1 discrete time points corresponding to the time The liquid-phase diffusion process leads to a significant difference in lithium-ion concentration inside the battery, which in turn generates a concentration polarization overpotential. This concentration polarization overpotential can be expressed as:

[0060] in, Represents the ideal gas constant. Denotes Faraday's constant. This indicates the initial lithium-ion concentration in the electrolyte. This represents the difference in lithium ion concentration at the positive and negative electrodes. Indicates the number of charges transferred. Indicates that the battery is in t Temperature at any moment; The lithium ion concentration difference of the electrolyte at the positive and negative electrodes Represented as:

[0061] in, Represents the liquid phase diffusion time constant. Indicates the liquid phase diffusion coefficient; The ohmic interactions within the battery lead to the generation of ohmic polarization overpotential. By lumping the ohmic interactions of each component in the simplified electrochemical model and using the ohmic internal resistance to characterize the combined effect of these processes, the ohmic polarization overpotential is calculated. Represented as:

[0062] in, Indicates the internal resistance of the ohm; The polarization effect of an electrochemical reaction generates a reaction polarization overpotential, which will reduce the reaction polarization overpotential. Represented as:

[0063] in, and As an intermediate variable, This represents the reaction polarization constant.

[0064] Using a lumped-parameter heat transfer model, the lithium-ion battery cell is simplified as a uniform heat-generating body, ignoring internal temperature gradients and differences in material heat capacity, with surface temperature representing the battery temperature; for example... Figure 2 As shown, the battery is considered as a single point mass, through thermal resistance R d It exchanges heat with the surrounding air via convection. In a preferred embodiment of this invention, the lumped-parameter heat transfer model, based on the law of conservation of energy and the lumped-parameter assumption, is derived from... Battery temperature at all times calculate Temperature at any time :

[0065] in, Indicates the battery's heating power. Indicates the battery's heat dissipation power. Indicates battery quality. Represents the integral variable. This indicates the battery's specific heat capacity.

[0066] Battery heat dissipation power The heat generation equation, derived from Bernardi's equation, consists of two parts: reversible heat and irreversible heat. The irreversible heat part equals the product of the battery's overpotential and current; the reversible heat part is the product of the battery's temperature, current, and entropy coefficient. The battery's heat generation power can be expressed as:

[0067] in, Indicates the battery open-circuit voltage. Indicates the battery terminal voltage. Indicates the battery operating current. This represents the entropy coefficient of the battery. Indicates battery temperature; Based on Newton's law of cooling and the lumped-parameter heat transfer model, the heat dissipation power of the battery can be expressed as:

[0068]

[0069] in, This indicates the temperature of the air surrounding the battery. This indicates the thermal resistance between the battery and the air. The coefficient of heat dissipation between the battery and the air can be identified by performing nonlinear least squares fitting on the temperature change data during the experiment. This indicates the area of ​​the battery that dissipates heat.

[0070] During implementation, the excitation-response analysis method was used to identify the model parameters offline. The identified parameters included open-circuit voltage-related parameters, solid-liquid phase diffusion time constant, ohmic internal resistance, and reaction polarization constant. The parameter identification results are shown in Table 1. Simultaneously, considering the high temperature sensitivity of the battery's electrochemical characteristics, temperature corrections were applied to key parameters based on the Arrhenius equation to maintain the model's predictive accuracy under environmental fluctuations.

[0071] Table 1 Parameter Identification Results

[0072] When multiple batteries are closely arranged to form a battery pack and a liquid cooling system is added, the simplified electrochemical model does not change due to the battery pack arrangement. However, the heat dissipation environment changes. Specifically, heat flows simultaneously to surrounding batteries, the liquid cooling system, and the air, rather than flowing unidirectionally to the air. Therefore, the lumped parameter heat transfer model in the electro-thermal coupling model needs to be modified. The modified lumped parameter heat transfer model has the following heat transfer path: Figure 3 As shown. Taking battery #3, which has the worst heat dissipation in a 5-cell liquid-cooled battery module, as an example, the corrected temperature discretization recursive formula is expressed as:

[0073] in, This indicates the total heat dissipation power of a single battery cell. Indicates the coolant temperature. Indicates air temperature. Indicates battery quality. Indicates the battery's specific heat capacity. Indicates the sampling step size. This represents the equivalent thermal resistance between the battery and the coolant. This represents the equivalent thermal resistance between the battery and the air.

[0074] like Figure 3 As shown, battery #3 dissipates heat from the outside in three directions: X, Y, and Z. Figure 3 As shown in (a). In the X direction, the battery transfers heat to the liquid cooling plate; in the Y direction, battery #3 transfers heat to its adjacent batteries #2 and #4; in the Z direction, the battery transfers heat to the air. The lumped thermal resistance parameters corresponding to the heat transfer processes in the above three directions are represented by Rx, Ry, and Rz, respectively.

[0075] Since the temperature difference between batteries is typically limited to within 5°C, and the thermal conductivity of the insulating plates between individual battery cells is relatively low (approximately 0.2 W / (m·°C), the heat transfer in the Y direction is minimal. A lumped thermal resistance model that neglects the Y-direction heat transfer process is as follows: Figure 3 As shown in (b).

[0076] While the thermally coupled simplified electrochemical model can generate high-precision simulation data under various operating conditions, its iterative solution of partial differential equations takes seconds, making it difficult to meet real-time requirements. This step fuses the generated simulation data with a small amount of measured data to form a training sample set for training the terminal voltage prediction surrogate model. This model transforms the time-domain differential iterative solution process into spatial static interpolation, achieving online computation time of less than milliseconds and possessing optimal unbiased estimation characteristics, effectively suppressing error accumulation in multi-step prediction processes. Therefore, using the high-fidelity training samples provided by the thermally coupled simplified electrochemical model, the terminal voltage prediction surrogate model can achieve millisecond-level fast prediction capabilities; the two work together to constitute a fast terminal voltage prediction surrogate model.

[0077] Based on a simplified electrochemical model, a terminal voltage prediction proxy model is constructed using the Kriging model to obtain a future terminal voltage prediction sequence. In a preferred embodiment of this invention, to achieve multi-step advance prediction of the terminal voltage, the terminal voltage prediction proxy model decomposes the long-time-domain multi-step prediction into a combined architecture of single-step prediction and recursive iteration. The terminal voltage prediction proxy model is used as a single-step state transition operator, and the terminal voltage prediction proxy model selects the current... Terminal voltage and state of charge As input feature vector The output is the terminal voltage at the next discrete time step. :

[0078] in, The nonlinear mapping function is determined through offline training; the relationship between the input and output is as follows: Figure 4 As shown.

[0079] A hybrid training set is constructed by fusing a large amount of simulation data generated from a thermally coupled simplified electrochemical model with a small amount of measured data to enhance the model's reliability and predictive universality. The fusion process employs a two-step Kriging algorithm: First, the large amount of generated simulation data is used as low-precision training data to construct an approximate terminal voltage prediction surrogate model; second, the small amount of measured data is used as high-precision training data to correct the prediction bias of the approximate model, establishing a mapping relationship from low-precision output to high-precision true values, thus obtaining the final high-precision terminal voltage prediction surrogate model. This two-step fusion approach—first constructing a low-precision model and then correcting for bias using measured data—significantly reduces the cost of acquiring high-precision training data and the model training time while ensuring prediction accuracy.

[0080] The original data is truncated to remove initially unstable data. A Min-Max scaling method is used to scale the input vector. The features of each dimension are uniformly mapped to a preset standard range. Within this range, the interval is set to [0, 1], and the mathematical transformation equation is expressed as:

[0081] in, This represents the value after scaling the original value. Indicates the first i Dimensional features in k The original value at time, and For the first i Minimum and maximum values ​​of the dimensional features throughout the entire training sequence; To form the autoregressive time series relationship required for single-step prediction, the original data matrix is ​​divided into two overlapping subsets with temporal misalignment along the time axis, which respectively constitute the input feature matrix. and output target vector :

[0082] Through this data misalignment and recombination, a mapping relationship is established between the input characteristics at time k and the terminal voltage response at time k+1, such as... Figure 5 As shown.

[0083] Based on the input feature matrix and output target vector The DACE toolbox was used to train the terminal voltage prediction surrogate model offline to establish a nonlinear mapping relationship from the current state to the terminal voltage at the next time step. The terminal voltage prediction surrogate model will then predict the system response. It can be viewed as the superposition of a global trend term and a local random fluctuation term, and its mathematical expression is as follows:

[0084] in, Represents a global regression model. For the regression basis function vector, This is the corresponding regression coefficient vector; It is a function with a mean of zero and a variance of . It is a stochastic process with non-zero covariance; This invention selects a first-order polynomial @regpoly1 as the global regression basis function to capture the linear baseline trend of terminal voltage variation with charge / discharge depth; and selects a Gaussian correlation function @corrgauss as the covariance kernel function of the stochastic process. Parameter optimization is performed through maximum likelihood estimation, and offline model training is completed. This model possesses the characteristics of optimal unbiased estimation, with a zero expected value for its prediction error and a minimized prediction variance.

[0085] At the prediction starting point, the measured initial state vector As input, a single-step prediction is performed using an offline-trained terminal voltage prediction surrogate model to obtain the predicted terminal voltage for the first time step in the future. The measured terminal voltage at the current moment is replaced with the predicted terminal voltage, and combined with the current and state of charge at the next moment to form a new input feature vector. This new feature vector is then input into the terminal voltage prediction surrogate model to obtain the predicted terminal voltage value for the next time step. This process is repeated recursively until the preset prediction time domain is covered, generating a future terminal voltage prediction sequence. The process is as follows: Figure 6 As shown.

[0086] Based on the terminal voltage prediction results output by the terminal voltage prediction surrogate model, the maximum continuous charge-discharge power boundary of the battery under thermal safety constraints is solved online using the Model Predictive Control (MPC) algorithm. MPC employs a rolling time-domain optimization strategy, directly incorporating safety limits such as temperature into the optimization problem, which can effectively address the relatively lagging temperature response of liquid cooling systems.

[0087] This invention employs MPC as its core optimization framework. Within each sampling period, MPC, based on the current state of the controlled object and the prediction model, solves for the optimal control sequence within the finite prediction time domain under physical constraints, but only executes the first term of the sequence. In the next period, instead of using previously unexecuted control commands, the prediction starting point is reset with the latest measured state, and the optimization problem is solved again. This iterative process of prediction, execution, measurement, and re-prediction is repeated in each control period, thus forming a rolling time-domain closed-loop feedback mechanism. The MPC algorithm framework is as follows: Figure 7 As shown, the framework consists of three core components: a prediction model (the constructed temperature prediction model), rolling optimization, and feedback correction (updating the initial state based on real-time temperature measurements).

[0088] The model predictive control algorithm is used to solve the maximum continuous charge / discharge power boundary of the battery under thermal safety constraints online based on the predicted future terminal voltage sequence. Specifically, in a preferred embodiment of this invention, the model predictive control algorithm uses the battery operating current as the control variable and the temperature of the middle battery in the battery pack as the controlled variable. Under the premise that the battery temperature does not exceed a set threshold, it solves for the maximum allowable charge / discharge current of the system. The objective function of the model predictive control algorithm is expressed as:

[0089] in, Represent the objective function; Indicates the current weighting factor; Indicates the temperature penalty factor; This indicates the maximum operating current within the current solution cycle; This indicates the preset upper limit of the battery's safe temperature. This indicates the future number calculated by the prediction model. Step battery temperature; Indicates the number of steps in the prediction time domain; To effectively control battery temperature rise while increasing the operating current amplitude, the temperature penalty factor is... Designed as a dynamically adjustable parameter, the temperature penalty factor is adjusted online based on the deviation between the predicted battery temperature and the set temperature.

[0090] When the predicted temperature does not exceed the set value hour, Take the smaller value This causes the optimization process to prioritize increasing the operating current; when the predicted temperature reaches or exceeds the set value... Take the larger value This is done to forcibly limit the current and suppress further temperature increases. Simultaneously, the above optimization process must meet preset constraints on current, voltage, and temperature.

[0091] In a preferred embodiment of this invention, considering the positive correlation between current amplitude and the predicted maximum battery temperature, the objective function of the model predictive control algorithm is solved using a bisection method. The comparison between the predicted maximum temperature and the temperature setpoint is used as the core criterion for the direction of current adjustment. In each control cycle, the current current value is substituted into the model predictive control algorithm to calculate the maximum temperature in the predicted time domain. If the highest temperature If the current is low, decrease it; otherwise, increase it. The current search interval is continuously narrowed using a bisection method until the maximum current that satisfies the thermal safety constraints is obtained. .

[0092] Example like Figure 8 As shown, this invention constructs an experimental platform for a five-cell battery liquid cooling system to verify the technical rationality and effectiveness of the proposed method. Figure 8 (a) is a liquid cooling loop diagram. Figure 8 (b) shows the data acquisition and control equipment. The experiment used a 50Ah square ternary lithium-ion battery cell, and its design parameters are shown in Table 2.

[0093] Table 2 Main parameters of CATL-NCM27E892-50AH battery

[0094] When the control system detects that the real-time battery temperature has reached the preset safe temperature threshold, it immediately starts the water pump and keeps the water pump running until the end of the current charging or discharging process.

[0095] Under charging conditions, the safe temperature threshold is set at 32℃, and the maximum allowable charging current is set at 50A. The curves showing the changes in charging current, battery temperature, and the start / stop status of the liquid cooling system are as follows, with prediction time domains of 600s and 900s respectively. Figure 9 and Figure 10 As shown. Figure 9 (a) is a graph showing the changes in charging current and battery temperature over a predicted time domain of 600 s. Figure 9 (b) is a state diagram of the liquid cooling system during charging in the predicted time domain of 600s. Figure 10(a) is a graph showing the changes in charging current and battery temperature over a predicted time domain of 900 s. Figure 10 (b) is the state diagram of the liquid cooling system during charging in the predicted time domain of 900s.

[0096] Under discharge conditions, the safe temperature threshold is set at 35℃, and the maximum allowable discharge current is set at 100A. The curves showing the changes in discharge current, battery temperature, and the start-stop status of the liquid cooling system are as follows: (The curves are not provided in the original text.) Figure 11 and Figure 12 As shown. Figure 11 (a) is a graph showing the changes in charging current and battery temperature over a predicted time domain of 600 s. Figure 11 (b) is a state diagram of the liquid cooling system during charging in the predicted time domain of 600s. Figure 12 (a) is a graph showing the changes in charging current and battery temperature over a predicted time domain of 900 s. Figure 12 (b) is the state diagram of the liquid cooling system during charging in the predicted time domain of 900s.

[0097] Experimental results show that when a long prediction time domain of 900s is used, the control system can proactively reduce the current in the early stage of operation based on the risk of future temperature rise, so that the temperature rises smoothly to the set threshold and remains stable without overshoot. At the same time, the long prediction time domain can delay the start-up time of the water pump, thereby reducing the system energy consumption.

[0098] The method proposed in this invention can obtain reliable thermal safety power boundaries online, and is applicable to the two typical operating conditions of ships in emission control areas: charging and discharging. It provides a key safety constraint method for ship energy management strategies.

[0099] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for online prediction of the long-term thermal safety power boundary of marine lithium batteries in emission control areas, characterized in that, include: Constructing a simplified electrochemical model of thermal coupling for lithium-ion batteries; Using a lumped parameter heat transfer model, the lithium-ion battery cell is simplified into a uniform heat-generating body, with surface temperature representing battery temperature. When multiple batteries are closely arranged, the lumped parameter heat transfer model is modified according to the heat dissipation environment; Based on the simplified electrochemical model, a proxy model for terminal voltage prediction is constructed using the Kriging model, and a future terminal voltage prediction sequence is obtained. The maximum continuous charge and discharge power boundary of the battery under thermal safety constraints is solved online using a model predictive control algorithm based on the predicted future terminal voltage sequence.

2. The online prediction method for long-term thermal safety power boundary of ship lithium batteries in emission control areas according to claim 1, characterized in that, The simplified electrochemical model uses battery terminal voltage. This indicates that the battery terminal voltage is the result of the combined effects of the internal electrode thermodynamic processes, lithium ion diffusion processes in the solid-liquid phases, ohmic processes, and electrochemical reaction processes. Represented as: in, Indicates the battery open-circuit voltage. Indicates concentration polarization overpotential, Indicates the Ohmic polarization overpotential. Indicates the reaction polarization overpotential; The lithium intercalation concentration fraction of the positive and negative electrode active materials directly affects the open-circuit voltage of the battery through the electrode potential curve, and the open-circuit voltage of the battery is expressed as: in, This indicates the open-circuit voltage of the battery's positive terminal. This indicates the open-circuit voltage of the battery's negative terminal. This indicates the lithium intercalation concentration fraction on the surface of the positive electrode active material. This indicates the lithium intercalation concentration fraction on the surface of the negative electrode active material; Solid-phase diffusion of lithium ions in the active particles of the electrode causes changes in the lithium intercalation concentration fraction on the positive and negative electrode surfaces, which in turn affects the open-circuit voltage of the battery. in, This represents the average lithium intercalation concentration fraction of the positive electrode active material. This represents the average lithium intercalation concentration fraction of the negative electrode active material. This represents the difference between the surface area of ​​the positive electrode active material and the average lithium intercalation concentration fraction. This represents the difference between the surface area of ​​the negative electrode active material and the average lithium intercalation concentration fraction. The lithium-ion concentration distribution during solid-phase diffusion is solved using a three-parameter parabolic approximation: in, and As an intermediate variable, This represents the negative electrode solid-phase diffusion time constant. This represents the solid-phase diffusion time constant of the positive electrode. This indicates the positive electrode capacity of a lithium-ion battery. This indicates the capacity of the negative electrode in a lithium-ion battery. Indicates the battery operating current; intermediate variables and The discretization formula is expressed as: in, Indicates the first k The time corresponding to each discrete time point Indicates the first k +1 discrete time points corresponding to the time; The liquid-phase diffusion process leads to a significant difference in lithium-ion concentration inside the battery, which in turn generates the concentration polarization overpotential, expressed as: in, Represents the ideal gas constant. Denotes Faraday's constant. This indicates the initial lithium-ion concentration in the electrolyte. This represents the difference in lithium ion concentration at the positive and negative electrodes. Indicates the number of charges transferred. Indicates that the battery is in t Temperature at any moment; The lithium ion concentration difference of the electrolyte at the positive and negative electrodes Represented as: in, Represents the liquid phase diffusion time constant. Indicates the liquid phase diffusion coefficient; The ohmic effects of each part of the simplified electrochemical model are lumped together, and the combined effect of each ohmic process is characterized by the ohmic internal resistance. The ohmic polarization overpotential is then calculated. Represented as: in, Indicates the internal resistance of the ohm; The polarization effect of an electrochemical reaction generates a reaction polarization overpotential, which will reduce the reaction polarization overpotential. Represented as: in, and As an intermediate variable, This represents the reaction polarization constant.

3. The online prediction method for long-term thermal safety power boundary of ship lithium batteries in emission control areas according to claim 2, characterized in that, The lumped-parameter heat transfer model is based on the law of conservation of energy and the lumped-parameter assumption. Battery temperature at all times calculate Temperature at any time : in, Indicates the battery's heating power. Indicates the battery's heat dissipation power. Indicates battery quality. Represents the integral variable. Indicates the battery's specific heat capacity; The heating power of the battery The heat generation power of the battery is calculated using the Bernardi heat generation equation, which consists of two parts: reversible heat and irreversible heat. The irreversible heat part is equal to the product of the battery overpotential and the current; the reversible heat part is the product of the battery temperature, the current, and the entropy coefficient. The heat generation power of the battery can be expressed as: in, Indicates the battery open-circuit voltage. Indicates the battery terminal voltage. Indicates the battery operating current. This represents the entropy coefficient of the battery. Indicates battery temperature; Based on Newton's law of cooling and the lumped-parameter heat transfer model, the heat dissipation power of the battery can be expressed as: in, This indicates the temperature of the air surrounding the battery. This indicates the thermal resistance between the battery and the air. This indicates the heat dissipation coefficient between the battery and the air. This indicates the area of ​​the battery that dissipates heat.

4. The online prediction method for long-term thermal safety power boundary of marine lithium batteries in emission control areas according to claim 3, characterized in that, The lumped parameter heat transfer model is modified, and the modified temperature discretization recursive formula is expressed as follows: in, This indicates the total heat dissipation power of a single battery cell. Indicates the coolant temperature. Indicates air temperature. Indicates battery quality. Indicates the battery's specific heat capacity. Indicates the sampling step size. This represents the equivalent thermal resistance between the battery and the coolant. This represents the equivalent thermal resistance between the battery and the air.

5. The online prediction method for long-term thermal safety power boundary of ship lithium batteries in emission control areas according to claim 1, characterized in that, The terminal voltage prediction proxy model decomposes long-time multi-step prediction into a combined architecture of single-step prediction and recursive iteration. The terminal voltage prediction proxy model selects current... Terminal voltage and state of charge As input feature vector The output is the terminal voltage at the next discrete time step. : in, This is a nonlinear mapping function determined through offline training; The input vector is scaled using the Min-Max scaling method. The features of each dimension are uniformly mapped to a preset standard range. The mathematical transformation equation is expressed as follows: in, This represents the value after scaling the original value. Indicates the first i Dimensional features in k The original value at time, and For the first i Minimum and maximum values ​​of the dimensional features throughout the entire training sequence; The original data matrix is ​​divided into two overlapping subsets with temporal misalignment along the time axis, which respectively constitute the input feature matrix. and output target vector : Based on the input feature matrix and output target vector The terminal voltage prediction surrogate model is trained offline to establish a nonlinear mapping relationship from the current state to the terminal voltage at the next time step. The terminal voltage prediction surrogate model will then predict the system response. It can be viewed as the superposition of a global trend term and a local random fluctuation term, and its mathematical expression is as follows: in, Represents a global regression model. For the regression basis function vector, This is the corresponding regression coefficient vector; It is a function with a mean of zero and a variance of . It is a stochastic process with non-zero covariance; At the prediction starting point, the measured initial state vector As input, a single-step prediction is performed using an offline-trained terminal voltage prediction surrogate model to obtain the predicted terminal voltage for the first time step in the future. The measured terminal voltage at the current moment is replaced with the predicted terminal voltage, and combined with the current and state of charge at the next moment to form a new input feature vector. This vector is then input into the terminal voltage prediction proxy model to obtain the predicted terminal voltage value for the next time step. This process is repeated recursively until the preset prediction time domain is covered, thereby generating a future terminal voltage prediction sequence.

6. The online prediction method for long-term thermal safety power boundary of marine lithium batteries in emission control areas according to claim 1, characterized in that, The model predictive control algorithm uses the battery operating current as the control variable and the temperature of the middle battery in the battery pack as the controlled variable. Under the premise that the battery temperature does not exceed a set threshold, it solves for the maximum allowable charging and discharging current of the system. The objective function of the model predictive control algorithm is expressed as: in, Represent the objective function; Indicates the current weighting factor; Indicates the temperature penalty factor; This indicates the maximum operating current within the current solution cycle; This indicates the preset upper limit of the battery's safe temperature. This indicates the future number calculated by the prediction model. Step battery temperature; Indicates the number of steps in the prediction time domain; The temperature penalty factor Designed as a dynamically adjustable parameter, the temperature penalty factor is adjusted online based on the deviation between the predicted battery temperature and the set temperature. When the predicted temperature does not exceed the set value hour, Take the smaller value This causes the optimization process to prioritize increasing the operating current; when the predicted temperature reaches or exceeds the set value... Take the larger value This forces the current to be limited, thus preventing the temperature from rising further.

7. The online prediction method for long-term thermal safety power boundary of marine lithium batteries in emission control areas according to claim 6, characterized in that, The objective function of the model predictive control algorithm is solved using a bisection method. The comparison between the predicted maximum temperature and the temperature setpoint is used as the core criterion for the direction of current adjustment. In each control cycle, the current current value is substituted into the model predictive control algorithm to calculate the predicted maximum temperature in the time domain. If the highest temperature If the current is low, decrease it; otherwise, increase it. The current search interval is continuously narrowed using a bisection method until the maximum current that satisfies the thermal safety constraints is obtained. .

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