A method for optimizing the geometry of a thermoelectric arm of a thermoelectric power generation system

Abstract

This invention discloses a method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system, relating to the field of thermoelectric power generation. The method includes: constructing a three-dimensional steady-state multiphysics coupled model of the thermoelectric power generation system; incorporating the height and cross-sectional area of ​​the thermoelectric arm as core geometric parameters to be optimized; and configuring the Seebeck coefficient, electrical conductivity, and thermal conductivity parameters corresponding to the thermoelectric material; setting boundary conditions for the model, including the target temperature at the hot end of the thermoelectric arm, the fluid velocity boundary corresponding to the cold end heat dissipation, and the system load resistance boundary, to ensure the model remains consistent with the actual working scenario. This invention improves model adaptation accuracy by constructing a multiphysics coupled model that fits the actual working conditions and dynamically adjusting material-related parameters. Combined with a parameterized scanning strategy with dynamic step sizes, it improves scanning efficiency while ensuring optimization effectiveness. The dual-objective optimization based on dynamic weights can flexibly adapt to different power supply requirements.

Description

Technical Field

[0001] This invention relates to the field of thermoelectric power generation technology, specifically to a method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system. Background Technology

[0002] Thermoelectric generators can convert solar energy, heat generated by nuclear radiation, industrial waste heat, etc. into electrical energy through the Seebeck effect. They have advantages such as small size, no moving parts, maintenance-free operation, no limitation by ambient temperature, and reliable operation. In recent years, people have conducted extensive research on thermoelectric technology and its materials.

[0003] The invention patent application with application number 202410302936.3 discloses a method for optimizing the geometric structure of a segmented thermoelectric power generation module. This application aims to solve the problem that "in the current segmented thermoelectric power generation module, the shape of the thermocouple arms in the segmented design is rectangular or cylindrical. Such a geometric design makes the cross-sectional area of ​​different segmented levels of the thermocouple arm the same everywhere, which leads to a serious deviation between the relative current density u value of the local thermocouple arm and the compatibility factor s, reducing the overall thermoelectric conversion efficiency of the thermoelectric material and failing to maximize the thermoelectric performance of each level of thermoelectric material."

[0004] However, in existing technologies, how to achieve the dual objectives of maximizing the output power and optimizing the area power density of a thermoelectric power generation system by optimizing the height and cross-sectional area parameters of the thermoelectric arm under extreme temperature environments such as plateaus and actual heat dissipation and power supply requirements, while ensuring the net output power and continuous operation stability of the system, remains an unresolved technical problem.

[0005] To address this, we propose a method for optimizing the geometric parameters of the thermoelectric arm in a thermoelectric power generation system. Summary of the Invention

[0006] In view of the above-mentioned shortcomings of the prior art, the present invention provides a method for optimizing the geometric parameters of the thermoelectric arm of a thermoelectric power generation system, which can effectively solve the problems of the prior art.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solutions; This invention discloses a method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system, comprising: A three-dimensional steady-state multiphysics coupled model of the thermoelectric power generation system was constructed. The height and cross-sectional area of ​​the thermoelectric arm were incorporated into the model as core geometric parameters to be optimized, and the Seebeck coefficient, electrical conductivity, and thermal conductivity parameters of the thermoelectric material were configured. Boundary conditions of the model were set, including the target temperature of the hot end of the thermoelectric arm, the fluid velocity boundary corresponding to the heat dissipation at the cold end, and the system load resistance boundary, to ensure that the model is consistent with the actual working scenario. Parametric scanning of multiple parameter combinations was performed on the thermoelectric arm with a height ranging from 0.6 mm to 4.6 mm and a cross-sectional area ranging from 1.42 mm² to 16 mm². Based on the parametric scanning data, the temperature difference between the hot and cold ends, open-circuit voltage, output power, and area power density corresponding to each parameter combination were calculated. With the dual objectives of maximizing output power and optimizing area power density, the optimal geometric parameter combination of the thermoelectric arm was selected based on the current power supply requirements. The thermoelectric arm and the supporting thermoelectric power generation system were fabricated using the optimal parameter combination, and their net output power and continuous operation stability under the target operating conditions were tested simultaneously to verify the effectiveness of the optimized parameters. The decision to refresh the operating cycle was based on the effectiveness verification results.

[0008] Furthermore, the three-dimensional steady-state multiphysics coupling model includes the coupling of thermoelectric field, solid heat transfer field, fluid flow field and circuit field; The thermoelectric field is based on the Seebeck effect, Peltier effect and Joule effect to construct the energy conversion equation. The solid heat transfer field includes the heat conduction and contact thermal resistance of the thermoelectric arm, ceramic substrate and conductive strip. The fluid flow field corresponds to the fluid heat transfer and flow resistance in the flow channel of the cold end water cooling heat dissipation system. The circuit field includes the series and parallel connection relationship of the thermoelectric arm and the adaptation relationship between the load and the internal resistance of the thermoelectric system.

[0009] Furthermore, the Seebeck coefficient, electrical conductivity, and thermal conductivity of the thermoelectric material are dynamically adjusted with temperature: ; In the formula: These are the dynamic Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively, taking into account temperature and temperature gradient. , , The materials at the reference temperature Initial parameters; , , These are the Seebeck coefficient, electrical conductivity, and temperature sensitivity coefficient, respectively; This represents the current actual temperature of the thermoelectric arm. , , These are the Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively, representing the temperature gradient response coefficients. This represents the temperature gradient inside the thermoelectric arm.

[0010] Furthermore, in the parametric scanning stage, based on a preset range of thermoelectric arm height and cross-sectional area, an initial scanning grid is divided and a first round of parameter combination tests is performed. Then, the performance sensitivity coefficient corresponding to each parameter combination is calculated, and the subsequent scanning step size is dynamically adjusted based on the sensitivity coefficient. ; In the formula: The performance sensitivity coefficient corresponding to the parameter combination; For the current scan parameters, thermoelectric arm height or cross-sectional area; The first-order partial derivative of the output power with respect to the current scan parameters; This serves as the step size for subsequent scans; This is the initial scan step size; This is the historical error correction coefficient; This represents the relative error of the previous scan results; This is the sensitivity weighting coefficient.

[0011] Furthermore, during the calculation of the cold and hot end temperature difference, open-circuit voltage, output power, and area power density for each parameter combination, the net output power is calculated simultaneously. With mass power density ; In the formula: This refers to the output power of a thermoelectric power generation system. This refers to the power consumption of the water pump in the water-cooled heat dissipation system. This refers to the power consumed by the cooling fan; The total mass of the thermoelectric power generation system; in, This includes the total mass of the thermoelectric module, heat dissipation system, and power supply control unit in a thermoelectric power generation system.

[0012] Furthermore, during the application phase, the net output power is adjusted based on the user's autonomous decision at the system end: No, then Directly for use Calculation; Yes, then Synchronous correction, in which net output power The corrected logic is as follows: ; Among them, contact thermal resistance power loss Power loss corresponding to local head loss ; In the formula: The temperature difference between the contact surface between the thermoelectric arm and the conductive strip; Contact area; The total contact thermal resistance of the contact surface; The density of the cooling fluid; The average flow rate of the cooling fluid; This is the equivalent length of the flow channel; The flow area of ​​the channel; It is the equivalent diameter of the flow channel.

[0013] Furthermore, the bi-objective optimization employs a dynamic weight allocation strategy, namely: Based on the current power supply demand, determine the weights for maximizing output power and optimizing area power density: ; In the formula: Weights for maximizing output power; This is the demand adaptation coefficient; This represents the current power supply demand. This represents the system's theoretical maximum output power. This is the urgency coefficient of demand; The weights are used to optimize the area power density.

[0014] Furthermore, the process of selecting the optimal combination of geometric parameters for the thermoelectric arm based on dynamic weights, with the goal of maximizing the normalized comprehensive performance index, specifically includes: The output power and areal power density of each parameter combination are normalized: Normalized output power: ,in This represents the system's theoretical maximum output power. Normalized value of area power density: ,in The maximum area power density is calculated for all parameter combinations in a parametric scan. Calculate the comprehensive performance index for each parameter combination. ,in , Dynamic weights; Filtering: When there are no additional constraints, directly select the parameter combination with the largest comprehensive performance index J as the optimal geometric parameter combination; If preset constraints exist, including but not limited to the system volume limit Total mass limit First, filter those that satisfy V≤ and ≤ A subset of parameter combinations is defined, where V is the accumulated sum of the external components of the thermoelectric module, heat dissipation system, and power supply control unit. The parameter combination with the largest J is then selected from this subset. The total mass of the heat extraction arm module, the total mass of the heat dissipation / heat absorption components, the total mass of the power supply control unit, the temperature sensor, and the connecting wires.

[0015] Furthermore, the continuous operation stability verification includes a quantitative evaluation based on power attenuation rate and fluctuation coefficient: Under the target operating conditions, the system runs continuously for a preset duration, records the output power at fixed time intervals, calculates the power attenuation rate and fluctuation coefficient, and determines that the stability of the parameter combination meets the requirements when the power attenuation rate is less than the preset attenuation threshold and the fluctuation coefficient is less than the preset fluctuation threshold. The formulas for calculating the power attenuation rate and the fluctuation coefficient are as follows: ; In the formula: Power attenuation rate; This represents the output power at the initial moment of continuous operation. This refers to the output power at the end of continuous operation. Preset duration; This is the volatility coefficient; The number of power data points recorded; Let k be the output power at the k-th recording time. Indicates a fixed time interval; This represents the average output power during continuous operation.

[0016] Furthermore, when the optimization parameter verification result is valid, a refresh step is executed based on a preset cycle. When the optimization parameter verification result is invalid, it is simultaneously identified whether the optimal geometric parameter combination of the thermoelectric arm is unique. If it is unique, the refresh step is executed immediately. If it is not unique, another optimal geometric parameter combination of the thermoelectric arm is applied, and the validity verification of the new application parameters is performed again.

[0017] Compared with the known prior art, the technical solution provided by this invention has the following beneficial effects: This invention improves model adaptation accuracy by constructing a multiphysics coupling model that fits actual working conditions and dynamically adjusting material-related parameters. Combined with a parameterized scanning strategy with dynamic step size, it improves scanning efficiency while ensuring optimization effect. The dual-objective optimization based on dynamic weights can flexibly adapt to different power supply requirements and achieve an optimal balance between output power and area power density. By calculating net output power and correcting losses, it reduces ineffective energy consumption. Furthermore, quantitative indicators verify the continuous operation stability of the system, effectively avoiding operational risks and extending the service life. It not only adapts to the different needs of different application scenarios but also comprehensively improves the overall operating efficiency of the thermal power generation system. Attached Figure Description

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

[0019] Figure 1 This is a flowchart illustrating a method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] The present invention will be further described below with reference to embodiments.

[0022] Example: This embodiment presents a method for optimizing the geometric parameters of the thermoelectric arm in a thermoelectric power generation system, such as... Figure 1 As shown, it includes: A three-dimensional steady-state multiphysics coupling model of a thermoelectric power generation system is constructed. The height and cross-sectional area of ​​the thermoelectric arm are included in the model as core geometric parameters to be optimized, and the Seebeck coefficient, electrical conductivity and thermal conductivity parameters of the thermoelectric material are configured. The three-dimensional steady-state multiphysics coupling model includes the coupling of thermoelectric field, solid heat transfer field, fluid flow field and circuit field; The thermoelectric field is based on the Seebeck effect, Peltier effect and Joule effect to construct the energy conversion equation. The solid heat transfer field includes the heat conduction and contact thermal resistance of the thermoelectric arm, ceramic substrate and conductive strip. The fluid flow field corresponds to the fluid heat transfer and flow resistance in the flow channel of the cold end water cooling heat dissipation system. The circuit field includes the series and parallel connection relationship of the thermoelectric arm and the matching relationship between the load and the internal resistance of the thermoelectric system. The model also considers the temperature-dependent properties of thermoelectric material parameters, namely, the Seebeck coefficient, electrical conductivity, and thermal conductivity are dynamically adjusted with temperature as a variable, enabling the model to accurately match the actual working conditions under extreme temperature environments at high altitudes. The dynamic adjustment of the Seebeck coefficient, electrical conductivity, and thermal conductivity of thermoelectric materials with temperature: ; In the formula: These are the dynamic Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively, taking into account temperature and temperature gradient. , , The materials at the reference temperature Initial parameters; , , These are the Seebeck coefficient, electrical conductivity, and temperature sensitivity coefficient, respectively; This represents the current actual temperature of the thermoelectric arm. , , These are the Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively, representing the temperature gradient response coefficients. The internal temperature gradient of the thermoelectric arm; The above formula takes into account that the Seebeck coefficient, electrical conductivity and thermal conductivity of thermoelectric materials are not fixed values ​​and will change with the actual temperature and internal temperature gradient. Therefore, based on the initial parameters at the reference temperature, the temperature sensitivity coefficient and temperature gradient response coefficient are introduced. The correction term is constructed by the two together to realize the dynamic adjustment of these core parameters. It should be noted that the above formula is a simplified expression. In practical applications, the constant term has been incorporated into the correction term coefficient, meaning that the correction term is assumed to be 1 at the reference temperature. In actual implementation, if the thermoelectric arm temperature is exactly equal to the reference temperature and the internal temperature gradient is zero, a constant term of 1 should be added before the square brackets on the right side of the formula, for example, α(T, )=α0·[1+K S ·(T-T0)+K G · This ensures that the material parameters accurately return to their initial values ​​under the reference conditions. However, in the target application scenario of high-altitude extreme temperature environment, the operating temperature of the thermoelectric arm usually deviates significantly from the reference temperature and there is a clear temperature gradient inside. The above extreme cases will not actually occur. Therefore, the simplified expression adopted in this invention not only meets the actual needs, but also facilitates the calculation and processing in subsequent parameter scanning. The range of values ​​for different coefficients is set according to the material's own characteristics. For example, the more significant the Seebeck coefficient changes with temperature, the larger the corresponding temperature sensitivity coefficient becomes. The smaller the temperature gradient's influence on conductivity, the smaller the corresponding gradient response coefficient becomes. This setting allows the material parameter calculations to accurately adapt to the complex working conditions in the extreme temperature environment of the plateau, and to better fit the parameter change patterns in actual working scenarios. in, The preset value range is [0.001, 0.01]. The value is larger when the Seebeck coefficient of the thermoelectric material changes more significantly with the increase of temperature in the target application temperature range, and smaller when the change is more gradual. The preset value range is [0.0005, 0.008]. The value is larger when the conductivity of the thermoelectric material decreases with increasing temperature, and smaller when the decrease rate is slower or basically stable. The preset value range is [0.0008, 0.009]. The value is larger when the thermal conductivity of the thermoelectric material fluctuates with temperature, and smaller when the fluctuation is smaller and the thermal conductivity is more stable. The preset value range is [0.0002, 0.002]. The value is larger when the internal temperature gradient of the thermoelectric arm modulates the Seebeck coefficient more strongly, and smaller when the modulation effect is weaker. The preset value range is [0.0001, 0.0015]. The larger the value is when the temperature gradient causes a more significant change in the conductivity of the thermoelectric material, the smaller the value is when the temperature gradient has almost no effect on the conductivity. The preset value range is [0.0003, 0.0025]. The value is larger when the temperature gradient has a greater impact on the thermal conductivity of the thermoelectric material, and smaller when the impact is smaller. Set boundary conditions for the model, including the target temperature of the hot end of the thermoelectric arm, the fluid velocity boundary corresponding to the heat dissipation at the cold end, and the system load resistance boundary, so that the model is consistent with the actual working scenario. Parametric scanning with multiple parameter combinations was performed on the thermoelectric arm with a height in the range of 0.6 mm to 4.6 mm and a cross-sectional area in the range of 1.42 mm² to 16 mm². In the parametric scanning phase, based on the preset range of thermoelectric arm height and cross-sectional area, an initial scanning grid is defined and the first round of parameter combination tests is performed. Then, the performance sensitivity coefficient corresponding to each parameter combination is calculated, and the subsequent scanning step size is dynamically adjusted based on the sensitivity coefficient. ; In the formula: The performance sensitivity coefficient corresponding to the parameter combination; For the current scan parameters, thermoelectric arm height or cross-sectional area; The first-order partial derivative of the output power with respect to the current scan parameters; This serves as the step size for subsequent scans; This is the initial scan step size; This is the historical error correction coefficient; This represents the relative error of the previous scan results; This is the sensitivity weighting coefficient; To make parametric scanning more targeted, the above formula first calculates the first partial derivative of the output power with respect to the current scanning parameter (thermoelectric arm height or cross-sectional area), and combines the parameter itself to obtain the performance sensitivity coefficient, thereby judging the degree of influence of the parameter on the output power. Then, based on the initial scanning step size, the relative error of historical scanning results and sensitivity weight coefficient are incorporated to dynamically adjust the subsequent scanning step size. When the parameter sensitivity is high, the step size will be reduced accordingly to achieve dense scanning, and when the sensitivity is low, the step size will be increased to achieve sparse scanning. This method not only ensures the optimization accuracy of the region that has a significant impact on the output power, but also avoids repeated scanning of invalid regions, greatly improving the overall efficiency of parametric scanning. It is important to emphasize that the aforementioned dynamic adjustment mechanism of material parameters based on temperature gradient response provides a more accurate computational foundation for the dynamic step-size scanning strategy in this step. Because material parameter correction improves the adaptability of the multiphysics coupling model under extreme temperature environments, the output power values ​​obtained from the simulation of each parameter combination are closer to actual operating conditions. This ensures that the calculated performance sensitivity coefficient can truly reflect the degree of influence of geometric parameters on system performance. When guiding dynamic step-size adjustment, this high-precision sensitivity information can accurately identify high-sensitivity regions requiring dense scanning and low-sensitivity regions that can be sparsely scanned, avoiding wasted scanning resources or decreased optimization accuracy due to sensitivity misjudgment caused by insufficient model accuracy. Therefore, the synergistic cooperation between temperature gradient response correction and dynamic step-size scanning forms an efficient optimization strategy adapted to extreme temperature environments. in, The preset value range is [0.1, 0.8], representing the relative error of the previous scan result. The larger the value, the larger the value; conversely, the smaller the value, the smaller the value. The preset value range is [0.3, 1.2]. When it is desired to scan more densely in high-sensitivity areas to improve optimization accuracy, the value should be larger, and vice versa. The above strategy enables dense scanning of high-sensitivity regions that significantly affect output power, and sparse scanning of low-sensitivity regions that have a negligible impact, thereby improving the efficiency of parametric scanning while ensuring optimization accuracy. Based on parametric scanning data, calculate the cold and hot end temperature difference, open circuit voltage, output power and area power density corresponding to each set of parameters; During the calculation of the cold and hot end temperature difference, open-circuit voltage, output power, and area power density for each parameter combination, the net output power is calculated simultaneously. With mass power density ; In the formula: This refers to the output power of a thermoelectric power generation system. This refers to the power consumption of the water pump in the water-cooled heat dissipation system. This refers to the power consumed by the cooling fan; The total mass of the thermoelectric power generation system; in, This includes the total mass of the thermoelectric module, heat dissipation system, and power supply control unit in the thermoelectric power generation system; During the application phase, the net output power is adjusted based on the user's decision at the system end: No, then Directly for use Calculation; Yes, then Synchronous correction, in which net output power The corrected logic is as follows: ; Among them, contact thermal resistance power loss Power loss corresponding to local head loss ; In the formula: The temperature difference between the contact surface between the thermoelectric arm and the conductive strip; Contact area; The total contact thermal resistance of the contact surface; The density of the cooling fluid; The average flow rate of the cooling fluid; This is the equivalent length of the flow channel; The flow area of ​​the channel; The equivalent diameter of the flow channel; The above formula is designed for scenarios where some users have higher requirements for the accuracy of net output power. It allows users to choose whether to make further corrections. During the correction process, contact thermal resistance and local head loss, which are easily overlooked, are taken into account. The power loss due to contact thermal resistance is calculated using the temperature difference, contact area, and total contact thermal resistance between the thermoelectric arm and the conductive strip. The power loss corresponding to local head loss is derived by considering fluid characteristic parameters such as coolant density, average flow velocity, and equivalent channel length. Subtracting these two types of losses from the original net output power allows for a more detailed and accurate calculation of the net output power. Simultaneously, the mass power density is also corrected to meet the precision requirements of different users. The formula for local head loss power is derived from the Darcy-Weisbach pressure drop relationship in fluid mechanics, combined with pump power consumption. The equivalent channel length and equivalent channel diameter in the formula comprehensively consider factors such as channel friction coefficient and local resistance coefficient. This equivalence process transforms complex channel losses into a unified form suitable for engineering calculations. This formula is applicable to laminar or transitional flow water-cooled systems and can accurately estimate the additional pump power consumption corresponding to pressure drop losses caused by local bends, diameter changes, and other structural features. In practical applications, and The value of should be determined by empirical formulas or CFD simulation based on the specific flow channel geometry and Reynolds number range to ensure the accuracy of loss estimation. This invention, based on system-level net output power optimization, offers significant advantages over traditional methods that only optimize the output power of thermoelectric devices. Traditional methods typically aim to maximize the output power of the thermoelectric module itself when optimizing geometric parameters, neglecting the power consumption of auxiliary equipment such as pumps and fans during actual system operation. This can lead to optimized geometric parameters that result in higher device output power, but the net output power after deducting the power consumption of auxiliary equipment may be unsatisfactory. In some parameter combinations, excessive power consumption of auxiliary equipment can even significantly reduce the actual usable power of the system. This invention, by incorporating the power consumption of auxiliary equipment into the optimization objective, ensures that the selected optimal geometric parameters maximize the net output power of the entire thermoelectric power generation system, better meeting practical application requirements. Especially in extreme environments such as high altitudes, where the power consumption of the heat dissipation system accounts for a large proportion, the advantages of system-level optimization are even more pronounced, effectively avoiding the problem of the overall system performance deviating from the optimal state due to device-level optimization. With the dual objectives of maximizing output power and optimizing area power density, the optimal combination of geometric parameters for the thermoelectric arm is selected based on the current power supply requirements. The bi-objective optimization employs a dynamic weight allocation strategy, namely: Based on the current power supply demand, determine the weights for maximizing output power and optimizing area power density: ; In the formula: Weights for maximizing output power; This is the demand adaptation coefficient; This represents the current power supply demand. This represents the system's theoretical maximum output power. This is the urgency coefficient of demand; Weights are used to optimize area power density. In the dual-objective optimization process, the above formula adjusts the influence of the two on the weight of maximizing output power by combining the ratio of the current actual power demand to the theoretical maximum output power of the system with the demand urgency coefficient and the demand adaptation coefficient. The area power density optimization weight complements the former to ensure that the sum of the two weights is always 1. The demand adaptation coefficient will be dynamically adjusted according to the closeness of the power demand to the maximum output power and the priority requirements of the output power. The demand urgency coefficient takes a higher value in emergency power supply scenarios and a lower value in continuous power supply scenarios. This setting allows the dual-objective optimization to adapt more flexibly to different power supply scenarios and demand priorities. in, , The range of all of them is (0,1), and , The sum is always 1; The value of ∈ (0,1) is larger when the ratio of the current power demand to the theoretical maximum output power of the system is closer to 1 and the priority requirement of output power is higher than that of area power density; otherwise, the value is smaller. ∈(0,1], The value is greater than 0.5 in emergency power supply scenarios and less than 0.5 in continuous power supply scenarios. The process of selecting the optimal combination of geometric parameters for the thermoelectric arm based on dynamic weighting, with the goal of maximizing the normalized comprehensive performance index, specifically includes: The output power and areal power density of each parameter combination are normalized: Normalized output power: ,in This represents the system's theoretical maximum output power. Normalized value of area power density: ,in The maximum area power density is calculated for all parameter combinations in a parametric scan. Calculate the comprehensive performance index for each parameter combination. ,in , Dynamic weights; Filtering: When there are no additional constraints, directly select the parameter combination with the largest comprehensive performance index J as the optimal geometric parameter combination; If preset constraints exist, including but not limited to the system volume limit Total mass limit First, filter those that satisfy V≤ and ≤ A subset of parameter combinations is defined, where V is the accumulated sum of the external components of the thermoelectric module, heat dissipation system, and power supply control unit. The parameter combination with the largest J is then selected from this subset. The total mass of the thermoelectric arm module, the total mass of the heat dissipation / heat absorption components, the total mass of the power supply control unit, the temperature sensor, and the connecting wires; In the normalization process, if a certain combination of parameters... =0 or If the value is 0, the corresponding normalized value is 0, and the optimal candidate qualification of this parameter combination is directly excluded. The thermoelectric arm and its supporting thermoelectric power generation system were prepared using the optimal parameter combination. The net output power and continuous operation stability under the target operating conditions were tested simultaneously to verify the effectiveness of the optimized parameters. Based on the effectiveness verification results, the operating cycle was refreshed. Continuous operation stability verification includes a quantitative evaluation based on power attenuation rate and fluctuation coefficient: Under the target operating conditions, the system runs continuously for a preset duration, records the output power at fixed time intervals, calculates the power attenuation rate and fluctuation coefficient, and determines that the stability of the parameter combination meets the requirements when the power attenuation rate is less than the preset attenuation threshold and the fluctuation coefficient is less than the preset fluctuation threshold. The formulas for calculating the power attenuation rate and the fluctuation coefficient are as follows: ; In the formula: Power attenuation rate; This represents the output power at the initial moment of continuous operation. This refers to the output power at the end of continuous operation. Preset duration; This is the volatility coefficient; The number of power data points recorded; Let k be the output power at the k-th recording time. Indicates a fixed time interval; This represents the average output power during continuous operation. The above formula is used to quantitatively evaluate the continuous operation stability of a thermal power generation system. By combining the difference in output power between the initial and final moments of continuous operation with the preset operating time, the relative attenuation of output power per unit time is calculated, which intuitively reflects the power attenuation. At the same time, by recording output power data at fixed time intervals, the square root of the sum of squares of the deviations of all data from the average value is calculated, and then compared with the average value to obtain the fluctuation coefficient, which characterizes the dispersion of output power. These two indicators comprehensively measure stability from two dimensions: attenuation trend and fluctuation. Only when both are lower than the corresponding preset thresholds can the stability of the parameter combination be determined to meet the requirements, thus providing a quantitative basis for verifying the effectiveness of the optimized parameters. Among them, power attenuation rate The physical meaning of is the relative attenuation of output power per unit time, expressed as % / h, and is the fluctuation coefficient. Used to characterize the stability and dispersion of output power; When the optimization parameter verification result is valid, the refresh step is executed based on the preset cycle. When the optimization parameter verification result is invalid, the optimal geometric parameter combination of the thermoelectric arm is simultaneously identified as unique. If it is unique, the refresh step is executed immediately. If it is not unique, another optimal geometric parameter combination of the thermoelectric arm is applied, and the validity verification of the new application parameters is performed again.

[0023] The methods described in the above embodiments can accurately match actual working scenarios. Through reasonable parameter scanning and dynamic optimization, they can improve output power while optimizing power density, reducing operating losses, and balancing the flexibility of power supply demand with the stability of continuous operation. This can effectively improve the practical value and adaptability of the power generation system.

[0024] Application example: Company XX needs to equip its small emergency power supply equipment with a thermoelectric power generation system for extreme temperature environments in high-altitude areas. The optimal geometric parameters of the thermoelectric arm are determined using the method in Example 1.

[0025] First, a three-dimensional steady-state multiphysics coupling model was constructed, incorporating thermoelectric field, solid heat transfer field, fluid flow field, and circuit field. The height and cross-sectional area of ​​the thermoelectric arm were set as core optimization parameters. A thermoelectric material suitable for the high-altitude environment was selected, with an initial Seebeck coefficient of 200 μV / K and an electrical conductivity of 1 × 10⁻⁶ at the reference temperature. 5 S / m, thermal conductivity 2W / The model dynamically adjusts these parameters according to material properties, ultimately yielding a Seebeck coefficient of 208 μV / K and an electrical conductivity of 9.8 × 10⁻⁶ under operating temperature and temperature gradient conditions. 4 S / m, thermal conductivity 2.03W / .

[0026] Set the model boundary conditions: target temperature of the hot end of the thermoelectric arm is 300℃, fluid flow rate of the cold end water cooling system is 2m / s, and system load resistance is 5Ω to ensure consistency with the actual working scenario at high altitude.

[0027] Parametric scanning was then performed. The initial scanning grid was divided into sections with a thermoelectric arm height of 0.6 mm to 4.6 mm and a cross-sectional area of ​​1.42 mm² to 16 mm². The first scan step size was set to a height of 0.5 mm and a cross-sectional area of ​​2 mm². After calculating the performance sensitivity coefficients of each parameter combination, the scanning step size in the high-sensitivity area was adjusted to a height of 0.2 mm and a cross-sectional area of ​​1 mm², while the first scan step size was maintained in the low-sensitivity area, thereby improving scanning efficiency and accuracy.

[0028] Based on the scan data, the performance indicators of each set of parameters were calculated: the temperature difference between the hot and cold ends of a certain parameter combination is 220℃, the open circuit voltage is 4.5V, the output power is 12W, and the area power density is 1.6W / mm²; the net output power was calculated simultaneously, and after deducting the 0.3W consumed by the water pump and the 0.2W consumed by the cooling fan, the net output power is 11.5W. The total system mass is 2kg, and the mass power density is 5.75W / kg. No additional corrections were performed in this application.

[0029] Because this device is used in emergency power supply scenarios, the current power demand is 8W, and the theoretical maximum output power of the system is 15W. With a demand adaptation coefficient of 0.7 and a demand urgency coefficient of 0.6, the weight for maximizing output power is 0.62, and the weight for optimizing area power density is 0.38. After normalizing the output power and area power density of all parameter combinations, the comprehensive performance index is calculated, and the optimal parameter combination with a thermoelectric arm height of 2.8mm and a cross-sectional area of ​​7.5mm² is finally selected.

[0030] The thermoelectric arm and its supporting system were prepared according to the optimal parameter combination and tested by continuous operation for 24 hours under the target conditions: the initial output power was 12.2W, the final output power was 11.9W, the power decay rate was 0.125% / h, the average output power was 12.05W, and the fluctuation coefficient was 0.03. Both indicators were less than the preset threshold, verifying the effectiveness of the optimized parameters. Subsequently, the operating parameters were refreshed according to the preset cycle of once a month.

[0031] In summary, the methods described in the above embodiments improve model adaptation accuracy by constructing a multiphysics coupling model that fits actual working conditions and dynamically adjusting material-related parameters. Combined with a parameterized scanning strategy with dynamic step size, the methods improve scanning efficiency while ensuring optimization effects. The dual-objective optimization based on dynamic weights can flexibly adapt to different power supply requirements and achieve an optimal balance between output power and area power density. Furthermore, the methods reduce ineffective energy consumption through net output power calculation and loss correction. The methods also verify the continuous operation stability of the system through quantitative indicators, effectively avoiding operational risks and extending the service life. This approach not only adapts to the different needs of various application scenarios but also comprehensively improves the overall operational efficiency of the thermal power generation system.

[0032] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system, characterized in that, include: A three-dimensional steady-state multiphysics coupling model of a thermoelectric power generation system is constructed. The height and cross-sectional area of ​​the thermoelectric arm are included in the model as core geometric parameters to be optimized, and the Seebeck coefficient, electrical conductivity and thermal conductivity parameters of the thermoelectric material are configured. Set boundary conditions for the model, including the target temperature of the hot end of the thermoelectric arm, the fluid velocity boundary corresponding to the heat dissipation at the cold end, and the system load resistance boundary, so that the model is consistent with the actual working scenario. Parametric scanning with multiple parameter combinations was performed on the thermoelectric arm with a height in the range of 0.6 mm to 4.6 mm and a cross-sectional area in the range of 1.42 mm² to 16 mm². Based on parametric scanning data, calculate the cold and hot end temperature difference, open circuit voltage, output power and area power density corresponding to each set of parameters; With the dual objectives of maximizing output power and optimizing area power density, the optimal combination of geometric parameters for the thermoelectric arm is selected based on the current power supply requirements. The thermoelectric arm and its supporting thermoelectric power generation system were prepared using the optimal parameter combination. The net output power and continuous operation stability under the target operating conditions were tested simultaneously to verify the effectiveness of the optimized parameters. Based on the effectiveness verification results, the operating cycle was refreshed.

2. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 1, characterized in that, The three-dimensional steady-state multiphysics coupling model includes the coupling of thermoelectric field, solid heat transfer field, fluid flow field and circuit field; The thermoelectric field is based on the Seebeck effect, Peltier effect and Joule effect to construct the energy conversion equation. The solid heat transfer field includes the heat conduction and contact thermal resistance of the thermoelectric arm, ceramic substrate and conductive strip. The fluid flow field corresponds to the fluid heat transfer and flow resistance in the flow channel of the cold end water cooling heat dissipation system. The circuit field includes the series and parallel connection relationship of the thermoelectric arm and the adaptation relationship between the load and the internal resistance of the thermoelectric system.

3. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 1, characterized in that, The Seebeck coefficient, electrical conductivity, and thermal conductivity of the thermoelectric material dynamically adjust with temperature: ； In the formula: These are the dynamic Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively, taking into account temperature and temperature gradient. , , The materials at the reference temperature Initial parameters; , , These are the Seebeck coefficient, electrical conductivity, and temperature sensitivity coefficient, respectively; This represents the current actual temperature of the thermoelectric arm. , , These are the Seebeck coefficient, electrical conductivity, and thermal conductivity, respectively, representing the temperature gradient response coefficients. This represents the temperature gradient inside the thermoelectric arm.

4. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 1, characterized in that, In the parametric scanning stage, based on a preset range of thermoelectric arm height and cross-sectional area, an initial scanning grid is divided and the first round of parameter combination tests is performed. Then, the performance sensitivity coefficient corresponding to each parameter combination is calculated, and the subsequent scanning step size is dynamically adjusted based on the sensitivity coefficient. ； In the formula: The performance sensitivity coefficient corresponding to the parameter combination; For the current scan parameters, thermoelectric arm height or cross-sectional area; The first-order partial derivative of the output power with respect to the current scan parameters; This serves as the step size for subsequent scans; This is the initial scan step size; This is the historical error correction factor; This represents the relative error of the previous scan results; This is the sensitivity weighting coefficient.

5. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 1, characterized in that, During the calculation of the cold and hot end temperature difference, open-circuit voltage, output power, and area power density for each parameter combination, the net output power is calculated simultaneously. With mass power density ; In the formula: This refers to the output power of a thermoelectric power generation system. This refers to the power consumption of the water pump in the water-cooled heat dissipation system. This refers to the power consumed by the cooling fan; The total mass of the thermoelectric power generation system; in, This includes the total mass of the thermoelectric module, heat dissipation system, and power supply control unit in a thermoelectric power generation system.

6. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 5, characterized in that, During the application phase, the net output power is adjusted based on the user's decision at the system end: No, then Directly for use Calculation; Yes, then Synchronous correction, in which net output power The corrected logic is as follows: ； Among them, contact thermal resistance power loss Power loss corresponding to local head loss ; In the formula: The temperature difference between the contact surface between the thermoelectric arm and the conductive strip; Contact area; The total contact thermal resistance of the contact surface; The density of the cooling fluid; The average flow rate of the cooling fluid; This is the equivalent length of the flow channel; The flow area of ​​the channel; It is the equivalent diameter of the flow channel.

7. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 1, characterized in that, The dual-objective optimization employs a dynamic weight allocation strategy, namely: Based on the current power supply demand, determine the weights for maximizing output power and optimizing area power density: ； In the formula: Weights for maximizing output power; This is the demand adaptation coefficient; This represents the current power supply demand. This represents the system's theoretical maximum output power. This is the urgency coefficient of demand; The weights are used to optimize the area power density.

8. A method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 6 or 7, characterized in that, The process of selecting the optimal combination of geometric parameters for the thermoelectric arm based on dynamic weights aims to maximize the normalized comprehensive performance index, and specifically includes: The output power and areal power density of each parameter combination are normalized: Normalized output power: ,in This represents the system's theoretical maximum output power. Normalized value of area power density: ,in The maximum area power density is calculated for all parameter combinations in a parametric scan. Calculate the comprehensive performance index for each parameter combination. ,in , Dynamic weights; Filtering: When there are no additional constraints, directly select the parameter combination with the largest comprehensive performance index J as the optimal geometric parameter combination; If preset constraints exist, including but not limited to the system volume limit Total mass limit First, filter those that satisfy V≤ and ≤ A subset of parameter combinations is defined, where V is the accumulated sum of the external components of the thermoelectric module, heat dissipation system, and power supply control unit. The parameter combination with the largest J is then selected from this subset. The total mass of the heat extraction arm module, the total mass of the heat dissipation / heat absorption components, the total mass of the power supply control unit, the temperature sensor, and the connecting wires.

9. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 1, characterized in that, The continuous operation stability verification includes a quantitative evaluation based on power attenuation rate and fluctuation coefficient: Under the target operating conditions, the system runs continuously for a preset duration, records the output power at fixed time intervals, calculates the power attenuation rate and fluctuation coefficient, and determines that the stability of the parameter combination meets the requirements when the power attenuation rate is less than the preset attenuation threshold and the fluctuation coefficient is less than the preset fluctuation threshold. The formulas for calculating the power attenuation rate and the fluctuation coefficient are as follows: ； In the formula: Power attenuation rate; This represents the output power at the initial moment of continuous operation. This refers to the output power at the end of continuous operation. Preset duration; This is the volatility coefficient; The number of power data points recorded; Let k be the output power at the k-th recording time. Indicates a fixed time interval; This represents the average output power during continuous operation.

10. The method for optimizing the geometric parameters of a thermoelectric arm in a thermoelectric power generation system according to claim 9, characterized in that, When the optimization parameter verification result is valid, the refresh step is executed based on the preset cycle. When the optimization parameter verification result is invalid, the optimal geometric parameter combination of the thermoelectric arm is simultaneously identified as unique. If it is unique, the refresh step is executed immediately. If it is not unique, another optimal geometric parameter combination of the thermoelectric arm is applied, and the validity verification of the new application parameters is performed again.

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