CN116936009B - Electric field distribution regulation and control method and system for high-voltage insulating dielectric functionally-graded material - Google Patents
Electric field distribution regulation and control method and system for high-voltage insulating dielectric functionally-graded material Download PDFInfo
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Abstract
Description
技术领域Technical field
本发明属于电场分布调控领域，尤其涉及高压绝缘介电功能梯度材料的电场分布调控方法及系统。The invention belongs to the field of electric field distribution control, and in particular relates to an electric field distribution control method and system for high-voltage insulating dielectric functional gradient materials.
背景技术Background technique
本部分的陈述仅仅是提供了与本发明相关的背景技术信息，不必然构成在先技术。The statements in this section merely provide background technical information related to the present invention and do not necessarily constitute prior art.
随着国家电网的快速发展和高压开关柜的广泛使用，高压开关柜事故也屡见不鲜，主要表现在绝缘事故、载流故障、机械事故、误动事故和拒动事故等，其中绝缘事故尤为突出。由于绝缘件中材料电导、介电常数等无法实现连续过渡，导致高压开关柜中绝缘件所承担的电场分布极不均匀，而设备长期运行在高场强下，局部电场畸变严重，甚至达到平均场强的数倍以上，电场畸变会导致局部放电，容易使绝缘材料发生老化，耐电性能降低，最终使高压电力设备绝缘系统发生沿面闪络、体击穿等故障，降低设备可靠性，增大运维难度。With the rapid development of the State Grid and the widespread use of high-voltage switchgear, high-voltage switchgear accidents are also common, mainly manifested in insulation accidents, current-carrying faults, mechanical accidents, malfunction accidents and refusal to move accidents, among which insulation accidents are particularly prominent. Since the conductivity and dielectric constant of the materials in the insulating parts cannot achieve continuous transition, the electric field distribution borne by the insulating parts in the high-voltage switch cabinet is extremely uneven. When the equipment operates under high field strength for a long time, the local electric field distortion is serious and even reaches the average level. At several times the field strength, electric field distortion will lead to partial discharge, which will easily cause the insulation material to age and reduce its electrical resistance. Eventually, faults such as surface flashover and body breakdown will occur in the insulation system of high-voltage power equipment, reducing equipment reliability and increasing Great operation and maintenance difficulty.
现有技术通常采用单独调节材料介电常数或单独调节电导率空间分布的方法，实现电场分布调控，这两种方法虽然在一定程度上可以缓和局部高电场强度，改善绝缘子的沿面电场分布，但调控效果有限，且若只调节介电常数或电导率空间分布容易导致结缘结构更为复杂，增加设备制造的复杂性、困难度及成本。Existing technology usually adopts the method of individually adjusting the dielectric constant of the material or individually adjusting the spatial distribution of conductivity to achieve electric field distribution control. Although these two methods can alleviate local high electric field intensity to a certain extent and improve the electric field distribution along the surface of the insulator, they The control effect is limited, and if you only adjust the dielectric constant or the spatial distribution of conductivity, it will easily lead to a more complex junction structure, increasing the complexity, difficulty and cost of equipment manufacturing.
发明内容Contents of the invention
为克服上述现有技术的不足，合理优化气固界面整体电场分布，改善局部电场畸变程度，本发明提供了高压绝缘介电功能梯度材料的电场分布调控方法及系统，通过优化介电常数与电导率实现电场调控，有效缓解局部电场过高的情况，均化沿面电场分布，抑制电场畸变，提升了电场利用率和绝缘系统的耐电性能，改善了介电参数空间分布优化问题。In order to overcome the shortcomings of the above-mentioned existing technologies, reasonably optimize the overall electric field distribution at the gas-solid interface, and improve the degree of local electric field distortion, the present invention provides an electric field distribution control method and system for high-voltage insulating dielectric functional gradient materials, by optimizing the dielectric constant and conductance. Efficiently realize electric field control, effectively alleviate the situation of excessive local electric field, homogenize the electric field distribution along the surface, suppress electric field distortion, improve the electric field utilization rate and the electrical resistance performance of the insulation system, and improve the spatial distribution optimization problem of dielectric parameters.
为实现上述目的，本发明的一个或多个实施例提供了如下技术方案：To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions:
本发明第一方面提供了高压绝缘介电功能梯度材料的电场分布调控方法。A first aspect of the present invention provides a method for regulating electric field distribution of high-voltage insulating dielectric functionally graded materials.
高压绝缘介电功能梯度材料的电场分布调控方法，包括：Electric field distribution control methods for high-voltage insulating dielectric functionally graded materials include:
对待调控的高压绝缘介电功能梯度材料进行网格划分，得到多个单元；The high-voltage insulating dielectric functional gradient material to be regulated is meshed to obtain multiple units;
基于单元的当前介电常数分布，计算单元的电位值，并确定电场的不均匀程度；Based on the current dielectric constant distribution of the unit, calculate the potential value of the unit and determine the degree of unevenness of the electric field;
当电场的不均匀程度超过预设阈值，则通过迭代的电场分布优化，直到满足电场分布的综合评价函数；When the unevenness of the electric field exceeds the preset threshold, the electric field distribution is optimized through iteration until the comprehensive evaluation function of the electric field distribution is satisfied;
其中，所述电场分布优化，包括介电常数分布优化与电导率优化，所述介电常数分布优化，是根据电场畸变系数及电场稳定系数优化介电常数分布，所述电导率优化是根据电场梯度调整电场强度优化电导率。Wherein, the electric field distribution optimization includes dielectric constant distribution optimization and conductivity optimization. The dielectric constant distribution optimization is to optimize the dielectric constant distribution based on the electric field distortion coefficient and the electric field stability coefficient. The conductivity optimization is based on the electric field. Gradient adjustment of electric field strength optimizes conductivity.
进一步的，所述计算单元的电位值，具体为：Further, the potential value of the calculation unit is specifically:
利用有限元方法，以单元当前的介电常数分布为输入参数，计算单元的绝缘子沿面电场分布；Using the finite element method, the current dielectric constant distribution of the unit is used as the input parameter to calculate the electric field distribution along the surface of the insulator of the unit;
通过插值函数，计算得出单元面积内的电场对整个区域的贡献，明确单元的电位值。Through the interpolation function, the contribution of the electric field within the unit area to the entire area is calculated, and the potential value of the unit is clarified.
进一步的，所述电场的不均匀程度，计算公式为：Further, the calculation formula for the unevenness of the electric field is:
其中，B i表示第i个单元的绝缘子沿面电场分布，表示第i个单元的电位值，N表示单元的总个数。Among them, B i represents the electric field distribution along the surface of the insulator of the i- th unit, represents the potential value of the i -th unit, and N represents the total number of units.
进一步的，所述根据电场畸变系数及电场稳定系数优化介电常数分布，具体为：Further, the dielectric constant distribution is optimized according to the electric field distortion coefficient and the electric field stability coefficient, specifically:
通过控制闪络电压抑制电场畸变，得到电场畸变系数；Suppress the electric field distortion by controlling the flashover voltage and obtain the electric field distortion coefficient;
基于电场畸变系数，计算电场稳定系数；Based on the electric field distortion coefficient, calculate the electric field stability coefficient;
利用电场稳定系数，计算介电常数，并判断介电常数分布是否在约束范围内；Use the electric field stability coefficient to calculate the dielectric constant and determine whether the dielectric constant distribution is within the constraint range;
若超出约束范围，则对介电常数分布进行线性缩放。If the constraint range is exceeded, the dielectric constant distribution is linearly scaled.
进一步的，所述控制闪络电压的公式为：Further, the formula for controlling flashover voltage is:
其中，q为电荷量，U C为闪络电压，为电压偏转角，s用于调整控制速率的系数；Among them, q is the charge amount, U C is the flashover voltage, is the voltage deflection angle, s is the coefficient used to adjust the control rate;
所述电场畸变系数的公式为：The formula of the electric field distortion coefficient is:
其中，g为单元边界条件确定量，r为单元的边界长度，E max为单元最大电场强度，E min为单元最小电场强度，E obj为单元优化目标场强，ε i为第i个单元u i的最优介电常数；Among them, g is the unit boundary condition determination quantity, r is the boundary length of the unit, E max is the maximum electric field intensity of the unit, E min is the minimum electric field intensity of the unit, E obj is the unit optimization target field intensity, ε i is the i- th unit u The optimal dielectric constant of i ;
所述电场稳定系数的公式为：The formula of the electric field stability coefficient is:
其中，E max为单元最大电场强度，E min为单元最小电场强度，E kp为单元临界电场强度，E kp与电场的不均匀程度以及绝缘体的厚薄等因素有关，f为电场的不均匀系数，d为单元范围大小；Among them, E max is the maximum electric field intensity of the unit, E min is the minimum electric field intensity of the unit, E kp is the critical electric field intensity of the unit, E kp is related to factors such as the unevenness of the electric field and the thickness of the insulator, f is the uneven coefficient of the electric field, d is the unit range size;
所述计算介电常数的具体公式为：The specific formula for calculating the dielectric constant is:
其中，ρ为虚拟密度，U为给材料施加的交流电压，s表示电场稳定系数，N表示单元的总个数，表示第i个单元的电位值，ε i表示第i个单元当前的介电常数分布。Among them, ρ is the virtual density, U is the AC voltage applied to the material, s represents the electric field stability coefficient, N represents the total number of units, represents the potential value of the i-th unit, and ε i represents the current dielectric constant distribution of the i-th unit.
进一步的，所述根据电场梯度调整电场强度优化电导率，具体为：Further, adjusting the electric field intensity according to the electric field gradient to optimize the conductivity is specifically:
根据电场不均匀对电场变化造成的影响，对电场梯度进行调整；Adjust the electric field gradient according to the impact of uneven electric field on electric field changes;
判断电场梯度的范围是否满足条件，并对电场强度进行调整；Determine whether the range of the electric field gradient meets the conditions and adjust the electric field intensity;
优化电导率。Optimize conductivity.
进一步的，所述电场梯度定义为：Further, the electric field gradient is defined as:
其中，表示电场的不均匀程度，Q为介质损耗功率，f为电场的不均匀系数，C i为第i个单元所含有的电容量，/>为绝缘材料的导热系数，S为单元面积，j为每次测量电场梯度的次数，/>表示第i个单元的电位值；in, Indicates the degree of unevenness of the electric field, Q is the dielectric loss power, f is the uneven coefficient of the electric field, C i is the capacitance contained in the i- th unit,/> is the thermal conductivity of the insulating material, S is the unit area, j is the number of times the electric field gradient is measured each time,/> Represents the potential value of the i -th unit;
所述电场强度的公式为：The formula for the electric field strength is:
其中，b为场强关联系数，U为外部施加稳定电压的大小，f为电场的不均匀系数，r为单元的边界长度，表示第i个单元的电位值，G为电场强度调控系数；Among them, b is the field strength correlation coefficient, U is the magnitude of the externally applied stable voltage, f is the uneven coefficient of the electric field, r is the boundary length of the unit, represents the potential value of the i- th unit, G is the electric field intensity control coefficient;
所述电导率的公式所示：The formula for conductivity is shown as:
其中，为绝缘材料电导率的上限，/>为绝缘材料电导率的下限，E i表示第i个单元的电场强度，/>表示第i个单元的电位值，r为单元的边界长度，N表示单元的总个数。in, is the upper limit of electrical conductivity of insulating materials,/> is the lower limit of the electrical conductivity of the insulating material, E i represents the electric field intensity of the i -th unit,/> represents the potential value of the i- th unit, r is the boundary length of the unit, and N represents the total number of units.
进一步的，所述电场分布的公式为：Further, the formula of the electric field distribution is:
其中，p为优化系数，表示绝缘材料电导率，/>表示第i个单元的电位值，ε表示第i个单元的介电常数分布。Among them, p is the optimization coefficient, Represents the conductivity of insulating materials,/> represents the potential value of the i- th unit, and ε represents the dielectric constant distribution of the i- th unit.
进一步的，所述综合评价函数，具体为：Further, the comprehensive evaluation function is specifically:
其中，B表示优化后的电场分布，N表示单元的总个数，B i表示优化前第i个单元的电场分布。Among them, B represents the electric field distribution after optimization, N represents the total number of units, and Bi represents the electric field distribution of the i -th unit before optimization.
本发明第二方面提供了高压绝缘介电功能梯度材料的电场分布调控系统。A second aspect of the present invention provides an electric field distribution control system for high-voltage insulating dielectric functionally graded materials.
高压绝缘介电功能梯度材料的电场分布调控系统，包括网格划分模块、不均匀计算模块和迭代优化模块：The electric field distribution control system of high-voltage insulating dielectric functionally graded materials includes a meshing module, a non-uniform calculation module and an iterative optimization module:
网格划分模块，被配置为：对待调控的高压绝缘介电功能梯度材料进行网格划分，得到多个单元；The meshing module is configured to: mesh the high-voltage insulating dielectric functional gradient material to be controlled to obtain multiple units;
不均匀计算模块，被配置为：基于单元的当前介电常数分布，计算单元的电位值，并确定电场的不均匀程度；The non-uniformity calculation module is configured to: calculate the potential value of the unit based on the current dielectric constant distribution of the unit, and determine the degree of non-uniformity of the electric field;
迭代优化模块，被配置为：当电场的不均匀程度超过预设阈值，则通过迭代的电场分布优化，直到满足电场分布的综合评价函数；The iterative optimization module is configured to: when the unevenness of the electric field exceeds the preset threshold, the electric field distribution is optimized through iteration until the comprehensive evaluation function of the electric field distribution is satisfied;
其中，所述电场分布优化，包括介电常数分布优化与电导率优化，所述介电常数分布优化，是根据电场畸变系数及电场稳定系数优化介电常数分布，所述电导率优化是根据电场梯度调整电场强度优化电导率。Wherein, the electric field distribution optimization includes dielectric constant distribution optimization and conductivity optimization. The dielectric constant distribution optimization is to optimize the dielectric constant distribution based on the electric field distortion coefficient and the electric field stability coefficient. The conductivity optimization is based on the electric field. Gradient adjustment of electric field strength optimizes conductivity.
以上一个或多个技术方案存在以下有益效果：One or more of the above technical solutions have the following beneficial effects:
（1）本发明通过网格划分将复杂的区域等效成若干个有限的、简单的、易求的子单元，使得处理过程更加简单，插值函数的引入使得单元的计算更加精确。(1) The present invention equates a complex area into a number of limited, simple, and easy-to-find sub-units through grid division, making the processing process simpler. The introduction of the interpolation function makes the calculation of the unit more accurate.
（2）本发明在优化介电常数分布时，通过引入电场畸变系数与电场稳定系数，有效降低了电场畸变严重程度，减少了闪络发生的频率，提升了电场利用率。(2) When optimizing the dielectric constant distribution, the present invention effectively reduces the severity of the electric field distortion, reduces the frequency of flashover, and improves the electric field utilization rate by introducing the electric field distortion coefficient and the electric field stability coefficient.
（3）本发明在优化电导率时，通过调整电场梯度，有利于分析整个电场中电导率的梯度分布，便于对电场强度的调整，有效降低了场强过大导致的绝缘击穿现象。(3) When optimizing the electrical conductivity, the present invention facilitates the analysis of the gradient distribution of electrical conductivity in the entire electric field by adjusting the electric field gradient, facilitates the adjustment of the electric field intensity, and effectively reduces the insulation breakdown phenomenon caused by excessive field intensity.
本发明附加方面的优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本发明的实践了解到。Additional advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
附图说明Description of the drawings
构成本发明的一部分的说明书附图用来提供对本发明的进一步理解，本发明的示意性实施例及其说明用于解释本发明，并不构成对本发明的不当限定。The description and drawings that constitute a part of the present invention are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention.
图1为第一个实施例的方法流程图。Figure 1 is a method flow chart of the first embodiment.
图2为第一个实施例具体方法的流程图。Figure 2 is a flow chart of a specific method of the first embodiment.
图3 为第一个实施例的单元划分示意图。Figure 3 is a schematic diagram of unit division in the first embodiment.
图4为第一个实施例介电常数分布优化的具体过程图。Figure 4 is a specific process diagram of dielectric constant distribution optimization in the first embodiment.
图5 为第一个实施例电导率优化的具体过程图。Figure 5 is a specific process diagram of conductivity optimization in the first embodiment.
图6为第二个实施例的系统结构图。Figure 6 is a system structure diagram of the second embodiment.
具体实施方式Detailed ways
应该指出，以下详细说明都是例示性的，旨在对本申请提供进一步的说明。除非另有指明，本发明使用的所有技术和科学术语具有与本申请所属技术领域的普通技术人员通常理解的相同含义。It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meanings commonly understood by one of ordinary skill in the art to which this application belongs.
需要注意的是，这里所使用的术语仅是为了描述具体实施方式，而非意图限制根据本申请的示例性实施方式。如在这里所使用的，除非上下文另外明确指出，否则单数形式也意图包括复数形式，此外，还应当理解的是，当在本说明书中使用术语“包含”和/或“包括”时，其指明存在特征、步骤、操作、器件、组件和/或它们的组合。It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular forms are also intended to include the plural forms unless the context clearly indicates otherwise. Furthermore, it will be understood that when the terms "comprises" and/or "includes" are used in this specification, they indicate There are features, steps, operations, means, components and/or combinations thereof.
实施例一Embodiment 1
在一个或多个实施方式中，公开了高压绝缘介电功能梯度材料的电场分布调控方法，如图1所示，包括如下步骤：In one or more embodiments, a method for regulating electric field distribution of high-voltage insulating dielectric functionally graded materials is disclosed. As shown in Figure 1, it includes the following steps:
步骤S1：对待调控的高压绝缘介电功能梯度材料进行网格划分，得到多个单元；Step S1: Mesh the high-voltage insulating dielectric functionally graded material to be regulated to obtain multiple units;
步骤S2：基于单元的当前介电常数分布，计算单元的电位值，并确定电场的不均匀程度；Step S2: Based on the current dielectric constant distribution of the unit, calculate the potential value of the unit and determine the degree of unevenness of the electric field;
步骤S3：当电场的不均匀程度超过预设阈值，则通过迭代的电场分布优化，直到满足电场分布的综合评价函数；Step S3: When the unevenness of the electric field exceeds the preset threshold, the electric field distribution is optimized through iteration until the comprehensive evaluation function of the electric field distribution is satisfied;
其中，所述电场分布优化，包括介电常数分布优化与电导率优化，所述介电常数分布优化，是根据电场畸变系数及电场稳定系数优化介电常数分布，所述电导率优化是根据电场梯度调整电场强度优化电导率。Wherein, the electric field distribution optimization includes dielectric constant distribution optimization and conductivity optimization. The dielectric constant distribution optimization is to optimize the dielectric constant distribution based on the electric field distortion coefficient and the electric field stability coefficient. The conductivity optimization is based on the electric field. Gradient adjustment of electric field strength optimizes conductivity.
进一步的，所述计算单元的电位值，具体为：Further, the potential value of the calculation unit is specifically:
利用有限元方法，以单元当前的介电常数分布为输入参数，计算单元的绝缘子沿面电场分布；Using the finite element method, the current dielectric constant distribution of the unit is used as the input parameter to calculate the electric field distribution along the surface of the insulator of the unit;
通过插值函数，计算得出单元面积内的电场对整个区域的贡献，明确单元的电位值。Through the interpolation function, the contribution of the electric field within the unit area to the entire area is calculated, and the potential value of the unit is clarified.
进一步的，所述电场的不均匀程度，计算公式为：Further, the calculation formula for the unevenness of the electric field is:
其中，B i表示第i个单元的绝缘子沿面电场分布，表示第i个单元的电位值，N表示单元的总个数。Among them, B i represents the electric field distribution along the surface of the insulator of the i- th unit, represents the potential value of the i -th unit, and N represents the total number of units.
进一步的，所述根据电场畸变系数及电场稳定系数优化介电常数分布，具体为：Further, the dielectric constant distribution is optimized according to the electric field distortion coefficient and the electric field stability coefficient, specifically:
通过控制闪络电压抑制电场畸变，得到电场畸变系数；Suppress the electric field distortion by controlling the flashover voltage and obtain the electric field distortion coefficient;
基于电场畸变系数，计算电场稳定系数；Based on the electric field distortion coefficient, calculate the electric field stability coefficient;
利用电场稳定系数，计算介电常数，并判断介电常数分布是否在约束范围内；Use the electric field stability coefficient to calculate the dielectric constant and determine whether the dielectric constant distribution is within the constraint range;
若超出约束范围，则对介电常数分布进行线性缩放。If the constraint range is exceeded, the dielectric constant distribution is linearly scaled.
进一步的，所述控制闪络电压的公式为：Further, the formula for controlling flashover voltage is:
其中，q为电荷量，U C为闪络电压，为电压偏转角，s用于调整控制速率的系数；Among them, q is the charge amount, U C is the flashover voltage, is the voltage deflection angle, s is the coefficient used to adjust the control rate;
所述电场畸变系数的公式为：The formula of the electric field distortion coefficient is:
其中，g为单元边界条件确定量，r为单元的边界长度，E max为单元最大电场强度，E min为单元最小电场强度，E obj为单元优化目标场强，ε i为第i个单元u i的最优介电常数；Among them, g is the unit boundary condition determination quantity, r is the boundary length of the unit, E max is the maximum electric field intensity of the unit, E min is the minimum electric field intensity of the unit, E obj is the unit optimization target field intensity, ε i is the i- th unit u The optimal dielectric constant of i ;
所述电场稳定系数的公式为：The formula of the electric field stability coefficient is:
其中，E max为单元最大电场强度，E min为单元最小电场强度，E kp为单元临界电场强度，E kp与电场的不均匀程度以及绝缘体的厚薄等因素有关，f为电场的不均匀系数，d为单元范围大小；Among them, E max is the maximum electric field intensity of the unit, E min is the minimum electric field intensity of the unit, E kp is the critical electric field intensity of the unit, E kp is related to factors such as the unevenness of the electric field and the thickness of the insulator, f is the uneven coefficient of the electric field, d is the unit range size;
所述计算介电常数的具体公式为：The specific formula for calculating the dielectric constant is:
其中，ρ为虚拟密度，U为给材料施加的交流电压，s表示电场稳定系数，N表示单元的总个数，表示第i个单元的电位值，ε i表示第i个单元当前的介电常数分布。Among them, ρ is the virtual density, U is the AC voltage applied to the material, s represents the electric field stability coefficient, N represents the total number of units, represents the potential value of the i-th unit, and ε i represents the current dielectric constant distribution of the i-th unit.
进一步的，所述根据电场梯度调整电场强度优化电导率，具体为：Further, adjusting the electric field intensity according to the electric field gradient to optimize the conductivity is specifically:
根据电场不均匀对电场变化造成的影响，对电场梯度进行调整；Adjust the electric field gradient according to the impact of uneven electric field on electric field changes;
判断电场梯度的范围是否满足条件，并对电场强度进行调整；Determine whether the range of the electric field gradient meets the conditions and adjust the electric field intensity;
优化电导率。Optimize conductivity.
进一步的，所述电场梯度定义为：Further, the electric field gradient is defined as:
其中，表示电场的不均匀程度，Q为介质损耗功率，f为电场的不均匀系数，C i为第i个单元所含有的电容量，/>为绝缘材料的导热系数，S为单元面积，j为每次测量电场梯度的次数，/>表示第i个单元的电位值；in, Indicates the degree of unevenness of the electric field, Q is the dielectric loss power, f is the uneven coefficient of the electric field, C i is the capacitance contained in the i- th unit,/> is the thermal conductivity of the insulating material, S is the unit area, j is the number of times the electric field gradient is measured each time,/> Represents the potential value of the i -th unit;
所述电场强度的公式为：The formula for the electric field strength is:
其中，b为场强关联系数，U为外部施加稳定电压的大小，f为电场的不均匀系数，r为单元的边界长度，表示第i个单元的电位值，G为电场强度调控系数；Among them, b is the field strength correlation coefficient, U is the magnitude of the externally applied stable voltage, f is the uneven coefficient of the electric field, r is the boundary length of the unit, represents the potential value of the i- th unit, G is the electric field intensity control coefficient;
所述电导率的公式所示：The formula for conductivity is shown as:
其中，为绝缘材料电导率的上限，/>为绝缘材料电导率的下限，E i表示第i个单元的电场强度，/>表示第i个单元的电位值，r为单元的边界长度，N表示单元的总个数。in, is the upper limit of electrical conductivity of insulating materials,/> is the lower limit of the electrical conductivity of the insulating material, E i represents the electric field intensity of the i -th unit,/> represents the potential value of the i- th unit, r is the boundary length of the unit, and N represents the total number of units.
进一步的，所述电场分布的公式为：Further, the formula of the electric field distribution is:
其中，p为优化系数，表示绝缘材料电导率，/>表示第i个单元的电位值，ε表示第i个单元的介电常数分布。Among them, p is the optimization coefficient, Indicates the conductivity of insulating materials,/> represents the potential value of the i- th unit, and ε represents the dielectric constant distribution of the i- th unit.
进一步的，所述综合评价函数，具体为：Further, the comprehensive evaluation function is specifically:
其中，B表示优化后的电场分布，N表示单元的总个数，B i表示优化前第i个单元的电场分布。Among them, B represents the electric field distribution after optimization, N represents the total number of units, and Bi represents the electric field distribution of the i -th unit before optimization.
下面对本实施例高压绝缘介电功能梯度材料的电场分布调控方法的实现过程进行详细说明。The implementation process of the electric field distribution control method of the high-voltage insulating dielectric functionally graded material of this embodiment will be described in detail below.
本发明的主要目的是为了提供一种适用于高压绝缘介电功能梯度材料的电场分布调控实现方法，通过优化介电常数与电导率实现电场调控，有效抑制了电场畸变，提升了电场利用率，改善了介电参数空间分布优化问题，提升了绝缘系统的耐电性能。The main purpose of the present invention is to provide a method for regulating electric field distribution suitable for high-voltage insulating dielectric functional gradient materials. Electric field regulation is achieved by optimizing dielectric constant and conductivity, which effectively suppresses electric field distortion and improves electric field utilization. It improves the spatial distribution optimization problem of dielectric parameters and improves the electrical resistance performance of the insulation system.
为达上述目的，本实施例提出了一种适用于高压绝缘介电功能梯度材料的电场分布调控实现方法，如图2所示，方法如下所述：In order to achieve the above purpose, this embodiment proposes a method for regulating electric field distribution suitable for high-voltage insulating dielectric functionally graded materials, as shown in Figure 2. The method is as follows:
步骤一：完成网格划分，明确单元的电位值；Step 1: Complete the meshing and clarify the potential value of the unit;
（1）运用有限元网格划分方法对材料进行处理，如图3所示，采样网格长度r=5cm，(x,y)表示第i个单元u i中心位置的坐标，划分得到的单元集合表示为：,其中,N表示单元的总个数。(1) Use the finite element meshing method to process the material, as shown in Figure 3, the sampling grid length r =5cm, (x, y) represents the coordinates of the center position of the i -th unit u i , and the divided unit is The set is expressed as: ,where N represents the total number of units.
（2）利用有限元方法，以第i个单元u i当前的介电常数分布ε i为输入参数，计算第i个单元u i绝缘子沿面电场分布B i。(2) Use the finite element method and use the current dielectric constant distribution ε i of the i- th unit u i as the input parameter to calculate the electric field distribution B i along the surface of the insulator of the i -th unit u i .
（3）通过插值函数，计算得出单元面积内的电场对整个区域的贡献，明确单元的电位值。(3) Through the interpolation function, calculate the contribution of the electric field in the unit area to the entire area and clarify the potential value of the unit.
插值函数定义为：The interpolation function is defined as:
其中，v(x,y)表示单元面积内的电场强度，(x,y)表示第i个单元u i中心位置的坐标，、/>为待求常数，具体公式为：Among them, v(x,y) represents the electric field intensity within the unit area, (x,y) represents the coordinates of the center position of the i- th unit u i , ,/> is the constant to be found, the specific formula is:
其中，B i表示第i个单元u i绝缘子沿面电场分布，ε i表示第i个单元u i当前的介电常数分布。Among them, B i represents the electric field distribution along the surface of the insulator of the i -th unit u i , and ε i represents the current dielectric constant distribution of the i -th unit u i .
由此，计算得出单元面积内的电场强度v(x,y)对整个材料区域的贡献g i，具体公式为：From this, the contribution g i of the electric field intensity v(x,y) in the unit area to the entire material area is calculated. The specific formula is:
其中,v(x,y)表示单元面积内的电场强度，(x,y)表示第i个单元u i中心位置的坐标。Among them, v(x,y) represents the electric field intensity within the unit area, and (x,y) represents the coordinates of the center position of the i- th unit u i .
综上，可得单元u i的电位值，公式为：In summary, the potential value of unit u i can be obtained , the formula is:
其中，B i表示第i个单元u i绝缘子沿面电场分布,g i表示第i个单元u i的电场强度对整个区域的贡献。Among them, B i represents the electric field distribution along the surface of the i- th unit u i insulator, and g i represents the contribution of the electric field intensity of the i -th unit u i to the entire area.
步骤二：确定材料电场的不均匀程度，改善介电常数与电导率；Step 2: Determine the unevenness of the material’s electric field and improve the dielectric constant and conductivity;
（1）根据单元的电位值，确定电场的不均匀程度。(1) Determine the degree of unevenness of the electric field based on the potential value of the unit.
其中，B i表示第i个单元u i绝缘子沿面电场分布，表示第i个单元u i的电位值，N表示单元的总个数。Among them, B i represents the electric field distribution along the surface of the i -th unit u i insulator, represents the potential value of the i- th unit u i , and N represents the total number of units.
将电场的不均匀程度分为R级，,每个级别有自己的不均匀度数值范围，依据得到的电场的不均匀程度，判断电场的不均匀程度级别。The degree of unevenness of the electric field is classified into R level, ,Each level has its own non-uniformity value range, and the unevenness level of the electric field is judged based on the obtained unevenness of the electric field.
（2）完成介电常数分布与电导率优化。(2) Complete the optimization of dielectric constant distribution and conductivity.
如果计算得出不均匀程度大于1级，便对介电常数分布与电导率进行迭代优化。If the calculated unevenness is greater than level 1, the dielectric constant distribution and conductivity will be iteratively optimized.
介电常数分布优化的具体过程，如图4所示，具体为：The specific process of dielectric constant distribution optimization is shown in Figure 4, specifically:
1）电场的不均匀使得电场发生畸变，导致电场分布发生变化，对电场分布的均匀程度造成不良的影响；因此通过降低电场畸变系数来提高电场利用率，具体如下所示：1) The unevenness of the electric field distorts the electric field, causing changes in the electric field distribution and adversely affecting the uniformity of the electric field distribution; therefore, by reducing the electric field distortion coefficient To improve the electric field utilization, the details are as follows:
电场发生畸变的同时，闪络电压也随之变化，因此通过控制闪络电压抑制电场畸变，减少电场畸变系数。When the electric field is distorted, the flashover voltage also changes accordingly. Therefore, by controlling the flashover voltage, the electric field distortion is suppressed and the electric field distortion coefficient is reduced.
控制闪络电压的公式如下所示：The formula controlling flashover voltage is as follows:
其中，q为电荷量，U C为闪络电压，为电压偏转角，范围为/>~/>，s用于调整控制速率的系数，数值越大代表对闪络电压的调整幅度越大，收敛速度越快；为了保证较快的控制速度，本实施例将系数s设置为2。Among them, q is the charge amount, U C is the flashover voltage, is the voltage deflection angle, the range is/> ~/> , s is used to adjust the coefficient of the control rate. The larger the value, the greater the adjustment amplitude of the flashover voltage and the faster the convergence speed; in order to ensure a faster control speed, this embodiment sets the coefficient s to 2.
电场畸变系数公式如下所示：The electric field distortion coefficient formula is as follows:
其中，g为单元边界条件确定量，r为单元的边界长度，E max为单元最大电场强度，E min为单元最小电场强度，E obj为单元优化目标场强，ε i为第i个单元u i的最优介电常数。Among them, g is the unit boundary condition determination quantity, r is the boundary length of the unit, E max is the maximum electric field intensity of the unit, E min is the minimum electric field intensity of the unit, E obj is the unit optimization target field intensity, ε i is the i- th unit u The optimal dielectric constant of i .
2）基于电场畸变系数，提出了电场稳定系数s，其公式为：2) Based on the electric field distortion coefficient, the electric field stability coefficient s is proposed, and its formula is:
其中，E max为单元最大电场强度，E min为单元最小电场强度，E kp为单元临界电场强度，E kp与电场的不均匀程度以及绝缘体的厚薄等因素有关，f为电场的不均匀系数，定义为常数，d为单元范围大小。Among them, E max is the maximum electric field intensity of the unit, E min is the minimum electric field intensity of the unit, E kp is the critical electric field intensity of the unit, E kp is related to factors such as the unevenness of the electric field and the thickness of the insulator, f is the uneven coefficient of the electric field, Defined as a constant, d is the unit range size.
3）计算介电常数，并判断介电常数分布是否在约束范围内。3) Calculate the dielectric constant and determine whether the dielectric constant distribution is within the constraint range.
介电常数分布的计算公式，如下所示：The calculation formula of dielectric constant distribution is as follows:
其中，ρ为虚拟密度，该变量可将材料进行归一化，数据范围为(0~1)，U为给材料施加的交流电压，s表示电场稳定系数，N表示单元的总个数，表示第i个单元u i的电位值，ε i为第i个单元u i当前的介电常数分布。Among them, ρ is the virtual density. This variable can normalize the material. The data range is (0~1). U is the AC voltage applied to the material. s represents the electric field stability coefficient. N represents the total number of units. represents the potential value of the i- th unit u i , and ε i is the current dielectric constant distribution of the i- th unit u i .
判断判断介电常数分布是否在约束范围内，若超出约束范围，对其进行线性缩放，并重新计算电场分布。Determine whether the dielectric constant distribution is within the constraint range. If it exceeds the constraint range, linearly scale it and recalculate the electric field distribution.
缩放公式如下所示：The scaling formula is as follows:
其中，ε和分别为缩放前和缩放后介电常数分布；/>和/>分别为缩放前介电常数分布的最大值与最小值；60和3分别为介电常数约束范围的上、下限。Among them, ε and They are the dielectric constant distribution before scaling and after scaling respectively;/> and/> are respectively the maximum value and the minimum value of the dielectric constant distribution before scaling; 60 and 3 are respectively the upper and lower limits of the dielectric constant constraint range.
缩放后，利用介电常数分布的计算公式重新计算介电常数分布，直到满足约束范围。After scaling, the dielectric constant distribution is recalculated using the calculation formula of the dielectric constant distribution until the constraint range is satisfied.
电导率优化的具体过程，如图5所示，具体为：The specific process of conductivity optimization is shown in Figure 5, specifically:
1）根据电场不均匀对电场变化造成的影响，对电场梯度进行调整。1) Adjust the electric field gradient according to the impact of uneven electric field on electric field changes.
根据电场梯度的变化，相应的电场强度也会发生变化，因此可将电场梯度定义为：According to the change of the electric field gradient, the corresponding electric field intensity will also change, so the electric field gradient can be defined as:
其中，表示电场的不均匀程度，Q为介质损耗功率，f为电场的不均匀系数，C i为第i个单元u i所含有的电容量，/>为绝缘材料的导热系数，S为单元面积，j为每次测量电场梯度的次数，/>表示第i个单元u i的电位值。in, Represents the degree of unevenness of the electric field, Q is the dielectric loss power, f is the uneven coefficient of the electric field, C i is the capacitance contained in the i -th unit u i ,/> is the thermal conductivity of the insulating material, S is the unit area, j is the number of times the electric field gradient is measured each time,/> Represents the potential value of the i -th unit u i .
2）判断电场梯度的范围是否满足条件，并对电场强度进行调整。2) Determine whether the range of the electric field gradient meets the conditions and adjust the electric field intensity.
电场梯度需满足以下条件：The electric field gradient needs to meet the following conditions:
其中，Y j为前一次的测量值，Y j-1为本次的测量值，k为误差。Among them, Y j is the previous measurement value, Y j-1 is the current measurement value, and k is the error.
当电场梯度满足以上条件时，电场强度能够刚好达到绝缘材料的最大工作场强；但电场梯度不满足以上条件时，需对电场强度进行调整，因此定义单元的电场强度公式为：When the electric field gradient meets the above conditions, the electric field intensity can just reach the maximum working field strength of the insulating material; but when the electric field gradient does not meet the above conditions, the electric field intensity needs to be adjusted, so the electric field intensity formula for defining the unit is:
其中，b为场强关联系数，一般取0.8，U为外部施加稳定电压的大小，f为电场的不均匀系数，r为单元的边界长度，表示第i个单元u i的电位值，G为电场强度调控系数，计算公式为：Among them, b is the field strength correlation coefficient, generally 0.8, U is the size of the externally applied stable voltage, f is the uneven coefficient of the electric field, r is the boundary length of the unit, represents the potential value of the i- th unit u i , G is the electric field intensity control coefficient, and the calculation formula is:
其中，U 0为刚开始施加外部电压时的电压，a为电场强度非线性程度的常系数，r为单元的边界长度。Among them, U 0 is the voltage when the external voltage is first applied, a is the constant coefficient of the nonlinear degree of the electric field strength, and r is the boundary length of the unit.
当外部施加电压变大时，电场强度调控系数波动范围变小，电场强度变大，电导率优化的效果也越好。When the externally applied voltage becomes larger, the fluctuation range of the electric field intensity control coefficient becomes smaller, the electric field intensity becomes larger, and the effect of conductivity optimization becomes better.
3）优化电导率3) Optimize conductivity
电导率的公式如下所示：The formula for conductivity is as follows:
其中，为绝缘材料电导率的上限，/>为绝缘材料电导率的下限，/>表示第i个单元u i的电场强度，/>表示第i个单元u i的电位值，r为单元的边界长度，N表示单元的总个数。in, is the upper limit of electrical conductivity of insulating materials,/> is the lower limit of the conductivity of insulating materials,/> Represents the electric field intensity of the i -th unit u i ,/> represents the potential value of the i -th unit u i , r is the boundary length of the unit, and N represents the total number of units.
步骤三：调控电场分布Step 3: Control electric field distribution
（1）通过传感器测量电极及电荷电位，在线监测电场稳定与电场强度的变化。(1) Use the sensor to measure the electrode and charge potential, and monitor the electric field stability and changes in electric field intensity online.
（2）通过对介电常数与电导率的优化与调整，调控电场分布，使其满足综合评价函数。(2) By optimizing and adjusting the dielectric constant and conductivity, the electric field distribution is regulated so that it meets the comprehensive evaluation function.
电场分布的计算公式如下：The calculation formula for electric field distribution is as follows:
其中，p为优化系数，为常数，本实施例取值为1，表示绝缘材料电导率，/>表示第i个单元u i的电位值，ε表示第i个单元u i的介电常数分布。Among them, p is the optimization coefficient, which is a constant. In this embodiment, the value is 1. Indicates the conductivity of insulating materials,/> represents the potential value of the i- th unit u i , and ε represents the dielectric constant distribution of the i -th unit u i .
综合评价函数计算公式如下：The calculation formula of the comprehensive evaluation function is as follows:
其中，B表示优化后的电场分布，N表示单元的总个数，B i表示优化前第i个单元u i的电场分布。Among them, B represents the electric field distribution after optimization, N represents the total number of units, and Bi represents the electric field distribution of the i -th unit u i before optimization.
通过本实施例优化的电场分布比未优化前的电场分布提高25%-30%，便可实现调控电场分布的目的。The electric field distribution optimized by this embodiment is 25%-30% higher than the electric field distribution before optimization, and the purpose of regulating the electric field distribution can be achieved.
（3）若未满足评价函数要求，需不断调整介电常数与电导率，直至满足综合评价函数。(3) If the evaluation function requirements are not met, the dielectric constant and conductivity need to be continuously adjusted until the comprehensive evaluation function is met.
实施例二Embodiment 2
在一个或多个实施例中，公开了高压绝缘介电功能梯度材料的电场分布调控系统，如图6所示，包括网格划分模块、不均匀计算模块和迭代优化模块：In one or more embodiments, an electric field distribution control system for high-voltage insulating dielectric functionally graded materials is disclosed, as shown in Figure 6, including a meshing module, a non-uniform calculation module and an iterative optimization module:
网格划分模块，被配置为：对待调控的高压绝缘介电功能梯度材料进行网格划分，得到多个单元；The meshing module is configured to: mesh the high-voltage insulating dielectric functional gradient material to be controlled to obtain multiple units;
不均匀计算模块，被配置为：基于单元的当前介电常数分布，计算单元的电位值，并确定电场的不均匀程度；The non-uniformity calculation module is configured to: calculate the potential value of the unit based on the current dielectric constant distribution of the unit, and determine the degree of non-uniformity of the electric field;
迭代优化模块，被配置为：当电场的不均匀程度超过预设阈值，则通过迭代的电场分布优化，直到满足电场分布的综合评价函数；The iterative optimization module is configured to: when the unevenness of the electric field exceeds the preset threshold, the electric field distribution is optimized through iteration until the comprehensive evaluation function of the electric field distribution is satisfied;
其中，所述电场分布优化，包括介电常数分布优化与电导率优化，所述介电常数分布优化，是根据电场畸变系数及电场稳定系数优化介电常数分布，所述电导率优化是根据电场梯度调整电场强度优化电导率。Wherein, the electric field distribution optimization includes dielectric constant distribution optimization and conductivity optimization. The dielectric constant distribution optimization is to optimize the dielectric constant distribution based on the electric field distortion coefficient and the electric field stability coefficient. The conductivity optimization is based on the electric field. Gradient adjustment of electric field strength optimizes conductivity.
以上所述仅为本发明的优选实施例而已，并不用于限制本发明，对于本领域的技术人员来说，本发明可以有各种更改和变化。凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.
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