CN109408885B - Insulator space charge density model optimization method under high voltage direct current - Google Patents
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Abstract
Description
技术领域technical field
本发明涉及电力领域，尤其是涉及一种高压直流下绝缘子空间电荷密度模型优化方法。The invention relates to the field of electric power, in particular to an optimization method for an insulator space charge density model under high-voltage direct current.
背景技术Background technique
随着中国高压直流输电建设工程的日益加快，对高压直流下一些关键问题的研究显得至关重要。长期处于直流高压作用下的绝缘子内部容易积聚电荷，从而影响绝缘子内部的电场分布，降低了绝缘子的耐受电压，严重时可能导致绝缘强度的下降，给绝缘系统带来隐患。因此，建立一种计算绝缘子内部空间电荷密度的数学模型显得至关重要。With the acceleration of China's high-voltage direct current transmission construction projects, it is very important to study some key issues under high-voltage direct current. Insulators under the action of DC high voltage for a long time tend to accumulate charges inside, which affects the electric field distribution inside the insulator and reduces the withstand voltage of the insulator. In severe cases, it may lead to a decrease in dielectric strength and bring hidden dangers to the insulation system. Therefore, it is very important to establish a mathematical model to calculate the space charge density inside the insulator.
直流电场作用下，积累在绝缘子内部的空间电荷能显著影响电场分布和绝缘系统的绝缘性能。尽管目前国际上对于绝缘子空间电荷密度有一定研究，但多是通过仿真以及试验，现有文献中建立的理论模型也比较简化，忽略了很多外在的环境条件的影响，因此在理论研究上依旧存在许多未解决的问题。Under the action of DC electric field, the space charge accumulated inside the insulator can significantly affect the electric field distribution and the insulation performance of the insulation system. Although there is currently some research on the space charge density of insulators in the world, most of them are through simulation and experiments. The theoretical models established in the existing literature are also relatively simplified, ignoring the influence of many external environmental conditions, so the theoretical research is still There are many unresolved issues.
目前在针对于绝缘子的研究中，大多以固定的电导率来做为研究基础。实际上，直流输电系统中运行电流很大，输电通道会出现明显的发热现象。温度变化引起绝缘子电学性能的变化，进而引起电导率变化。固体介质的电导率除了会受温度的影响外，也依赖于场强的变化。绝缘子表面电荷积聚，会使绝缘子电场分布发生畸变，从而使得电导率发生变化。在绝缘子表面电荷积聚与消散的过程中，存在着很多弛豫现象，介电弛豫对于该过程的时间常数起着重要的作用，因此，介电弛豫的影响，也是至关重要的研究内容。At present, in the research on insulators, most of them use fixed conductivity as the research basis. In fact, the operating current in the DC transmission system is very large, and the transmission channel will have obvious heating phenomenon. Temperature changes cause changes in the electrical properties of insulators, which in turn cause changes in electrical conductivity. In addition to being affected by temperature, the conductivity of solid media also depends on the change of field strength. The accumulation of charges on the surface of the insulator will distort the electric field distribution of the insulator, thereby causing the conductivity to change. In the process of charge accumulation and dissipation on the surface of insulators, there are many relaxation phenomena, and dielectric relaxation plays an important role in the time constant of the process. Therefore, the influence of dielectric relaxation is also a crucial research content .
现有试验研究中很少考虑温度、时变电场、介电弛豫等对电荷密度的影响，难以获得用于实际工程中的直流绝缘子电荷积聚情况。为此，针对上述问题，需要探索出一种新的关于绝缘子空间电荷密度的数学模型。The effects of temperature, time-varying electric field, and dielectric relaxation on charge density are rarely considered in existing experimental studies, and it is difficult to obtain the charge accumulation of DC insulators used in practical engineering. Therefore, in view of the above problems, it is necessary to explore a new mathematical model for the space charge density of insulators.
发明内容Contents of the invention
本发明的目的就是为了克服上述现有技术存在的缺陷而提供一种高压直流下绝缘子空间电荷密度模型优化方法。The object of the present invention is to provide a method for optimizing the space charge density model of an insulator under high voltage direct current in order to overcome the defects of the above-mentioned prior art.
本发明的目的可以通过以下技术方案来实现：The purpose of the present invention can be achieved through the following technical solutions:
一种高压直流下绝缘子空间电荷密度模型优化方法，包括：A method for optimizing an insulator space charge density model under high-voltage direct current, comprising:
步骤S1：以温度和时变电场为自变量，得到电导率数学模型，并得到电导电流密度；Step S1: Using temperature and time-varying electric field as independent variables, obtain a mathematical model of conductivity, and obtain the conductance current density;
步骤S2：建立介电弛豫函数，并得到驰豫极化电流密度；Step S2: establishing a dielectric relaxation function, and obtaining a relaxation polarization current density;
步骤S3：将电导电流密度、驰豫极化电流密度和瞬时极化电流密度求和得到体积电流密度；Step S3: summing the conductance current density, relaxation polarization current density and instantaneous polarization current density to obtain the volume current density;
步骤S4：将体积电流密度求积分得到空间电荷密度数据模型。Step S4: Integrate the volume current density to obtain a space charge density data model.
所述步骤S1具体为：The step S1 is specifically:
步骤S11：以温度和时变电场为自变量，得到电导率数学模型：Step S11: Taking temperature and time-varying electric field as independent variables, the mathematical model of electrical conductivity is obtained:
σ＝σ0eαT+βE(t) (1)σ＝σ 0 e αT+βE(t) (1)
其中：σ为电介质的电导率，σ0为初始电导率，T为温度，E(t)为电场强度，α为温度系数，β为场强系数。Among them: σ is the conductivity of the dielectric, σ 0 is the initial conductivity, T is the temperature, E(t) is the electric field strength, α is the temperature coefficient, and β is the field strength coefficient.
步骤S12：基于得到的电导率数学模型得到电导电流密度：Step S12: Obtain the conductance current density based on the obtained conductivity mathematical model:
j1(t)＝σ0eβE(t)+αTE(t)j 1 (t)=σ 0 e βE(t)+αT E(t)
其中：j1(t)为电导电流密度。Where: j 1 (t) is the conductance current density.
所述场强系数和温度系数通过实验数据拟合得到。The field strength coefficient and temperature coefficient are obtained by fitting experimental data.
所述步骤S2具体包括：Described step S2 specifically comprises:
步骤S21：测量绝缘子材料在不同温度和绝缘子体积电导率下随时间变化的驰豫值；Step S21: measuring the relaxation value of the insulator material as a function of time at different temperatures and insulator bulk conductivity;
步骤S22：根据测量得到的驰豫系数，并建立介电弛豫函数f(t)：Step S22: According to the measured relaxation coefficient, and establish a dielectric relaxation function f(t):
f(t)＝At-n f(t)=At -n
其中：A和n为拟合得到的弛豫系数，t为时间；Where: A and n are the relaxation coefficients obtained by fitting, and t is the time;
步骤S23：根据建立的介电弛豫函数与电场强度的卷积得到驰豫极化电流密度：Step S23: obtain the relaxation polarization current density according to the convolution of the established dielectric relaxation function and electric field intensity:
其中：j3(t)为驰豫极化电流密度，ε0为真空介电常数，τ为t之前的时间。Where: j 3 (t) is the relaxation polarization current density, ε 0 is the vacuum permittivity, and τ is the time before t.
所述瞬时极化电流密度具体为：The instantaneous polarization current density is specifically:
其中：j2(t)为瞬时极化电流密度，ε∞为光频介电常数。Where: j 2 (t) is the instantaneous polarization current density, ε ∞ is the optical frequency permittivity.
所述方法还包括：The method also includes:
步骤S5：仿真并验证得到的空间电荷密度数据模型。Step S5: Simulate and verify the obtained space charge density data model.
与现有技术相比，本发明具有以下有益效果：Compared with the prior art, the present invention has the following beneficial effects:
1)综合考虑了温度、电场、介电弛豫对空间电荷密度的影响，解决了现有模型对环境因素的考虑不周的问题，并仿真分析了各项因素对空间电荷密度的影响程度，可作为高压直流绝缘子材料选择、结构设计的参考。1) The effects of temperature, electric field, and dielectric relaxation on space charge density are considered comprehensively, and the problem of insufficient consideration of environmental factors in existing models is solved, and the degree of influence of various factors on space charge density is simulated and analyzed. It can be used as a reference for material selection and structural design of high-voltage DC insulators.
2)通过建立三种电流密度的特殊的数学模型，可以在提高精度的同时确保计算负荷不过大。2) By establishing special mathematical models of three current densities, it is possible to ensure that the calculation load is not too large while improving the accuracy.
3)租后进行仿真验证，可以为后续的改进作指导，进一步提高优化效果。3) Carry out simulation verification after renting, which can provide guidance for subsequent improvement and further improve the optimization effect.
附图说明Description of drawings
图1为本发明方法的主要步骤流程示意图。Fig. 1 is a schematic flow chart of the main steps of the method of the present invention.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明进行详细说明。本实施例以本发明技术方案为前提进行实施，给出了详细的实施方式和具体的操作过程，但本发明的保护范围不限于下述的实施例。The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is carried out on the premise of the technical solution of the present invention, and detailed implementation and specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.
一种高压直流下绝缘子空间电荷密度模型优化方法，如图1所示，包括：A method for optimizing the space charge density model of an insulator under high-voltage direct current, as shown in Figure 1, includes:
步骤S1：以温度和时变电场为自变量，得到电导率数学模型，并得到电导电流密度，电导率随温度和电场的增加呈指数形式增加，具体为：Step S1: Using temperature and time-varying electric field as independent variables, the mathematical model of conductivity is obtained, and the conductance current density is obtained. The conductivity increases exponentially with the increase of temperature and electric field, specifically:
步骤S11：以温度和时变电场为自变量，得到电导率数学模型：Step S11: Taking temperature and time-varying electric field as independent variables, the mathematical model of electrical conductivity is obtained:
σ＝σ0eαT+βE(t) (1)σ＝σ 0 e αT+βE(t) (1)
其中：σ为电介质的电导率，σ0为初始电导率，T为温度，E(t)为电场强度，α为温度系数，β为场强系数。Among them: σ is the conductivity of the dielectric, σ 0 is the initial conductivity, T is the temperature, E(t) is the electric field strength, α is the temperature coefficient, and β is the field strength coefficient.
步骤S12：基于得到的电导率数学模型得到电导电流密度：Step S12: Obtain the conductance current density based on the obtained conductivity mathematical model:
j1(t)＝σ0eβE(t)+αTE(t)j 1 (t)=σ 0 e βE(t)+αT E(t)
其中：j1(t)为电导电流密度。Where: j 1 (t) is the conductance current density.
场强系数和温度系数通过实验数据拟合得到。The field strength coefficient and temperature coefficient are obtained by fitting the experimental data.
步骤S2：建立介电弛豫函数，并得到驰豫极化电流密度，具体包括：Step S2: Establish a dielectric relaxation function and obtain the relaxation polarization current density, specifically including:
步骤S21：测量绝缘子材料在不同温度和绝缘子体积电导率下随时间变化的驰豫值；Step S21: measuring the relaxation value of the insulator material as a function of time at different temperatures and insulator bulk conductivity;
步骤S22：根据测量得到的驰豫系数，并建立介电弛豫函数f(t)：Step S22: According to the measured relaxation coefficient, and establish a dielectric relaxation function f(t):
f(t)＝At-n f(t)=At -n
其中：A和n为拟合得到的弛豫系数，t为时间；Where: A and n are the relaxation coefficients obtained by fitting, and t is the time;
步骤S23：根据建立的介电弛豫函数与电场强度的卷积得到驰豫极化电流密度：Step S23: obtain the relaxation polarization current density according to the convolution of the established dielectric relaxation function and electric field intensity:
其中：j3(t)为驰豫极化电流密度，τ为t之前的时间。Where: j 3 (t) is the relaxation polarization current density, τ is the time before t.
步骤S3：将电导电流密度、驰豫极化电流密度和瞬时极化电流密度求和得到体积电流密度；Step S3: summing the conductance current density, relaxation polarization current density and instantaneous polarization current density to obtain the volume current density;
其中，瞬时极化电流密度具体为：Among them, the instantaneous polarization current density is specifically:
其中：j2(t)为瞬时极化电流密度，ε∞为光频介电常数。Where: j 2 (t) is the instantaneous polarization current density, ε ∞ is the optical frequency permittivity.
故体积电流密度为。So the volume current density is .
其中，j1(t)为电导电流密度，j2(t)为瞬时极化电流密度，j3(t)为弛豫极化电流密度，j(t)为体积电流密度，ε0为真空介电常数。Among them, j 1 (t) is the conductance current density, j 2 (t) is the instantaneous polarization current density, j 3 (t) is the relaxation polarization current density, j(t) is the volume current density, ε 0 is the vacuum dielectric constant.
步骤S4：将体积电流密度求积分得到空间电荷密度数据模型。Step S4: Integrate the volume current density to obtain a space charge density data model.
其中，在无外施电场有初始积聚电荷时电荷密度的模型可改写为：Among them, the model of the charge density when there is an initial accumulation of charges in the absence of an applied electric field can be rewritten as:
其中ε为材料的介电常数。where ε is the dielectric constant of the material.
步骤S5：仿真并验证得到的空间电荷密度数据模型，具体的，仿真分析温度、电场、极化、初始电导率等各项因素对空间电荷密度变化趋势的影响，具体是仿真各影响因素下的电荷密度变化趋势，尤其是对电荷积聚或消散的快慢的影响，以及改变单一变量，分别分析其对瞬时极化电流密度、电导电流密度、弛豫极化电流密度和总电流密度产生的影响，以及在此情况下各电流密度组分在总电流密度中的比重。Step S5: Simulate and verify the obtained space charge density data model. Specifically, simulate and analyze the influence of various factors such as temperature, electric field, polarization, and initial conductivity on the change trend of space charge density. The change trend of charge density, especially the influence on the speed of charge accumulation or dissipation, and the influence of changing a single variable on the instantaneous polarization current density, conductance current density, relaxation polarization current density and total current density are analyzed respectively, And in this case the proportion of each current density component in the total current density.
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