CN112464518B - An Equivalent Circuit and a Calculation Method for Steady-State Current in Human-Vehicle Contact - Google Patents
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Abstract
本发明公开了一种等效电路和人与车辆接触时稳态电流计算方法，属于高压输电线路技术领域，包括客车的对地电容CC、客车的开路电压Uoc、轮胎对地电容Ct、轮胎的电阻Rt、接触电阻Rg、人体等效电容Cb和人体等效电阻Rb；轮胎对地电容Ct和轮胎的电阻Rt组成第一并联电路；人体等效电容Cb和人体等效电阻Rb组成第二并联电路；客车的开路电压Uoc的正极端依次通过客车的对地电容CC、第一并联电路后接地；客车的开路电压Uoc的正极端依次通过客车的对地电容CC、开关S、接触电阻Rg与第二并联电路的一端连接，第二并联电路的另一端接地。本发明使得输电线路电场的计算不受客车停车位置的影响，同时大大减少了计算量。
The invention discloses an equivalent circuit and a method for calculating steady-state current when a person is in contact with a vehicle, belonging to the technical field of high - voltage transmission lines . , the resistance R t of the tire, the contact resistance R g , the equivalent capacitance C b of the human body and the equivalent resistance R b of the human body; the capacitance C t of the tire to the ground and the resistance R t of the tire form the first parallel circuit; the equivalent capacitance of the human body C b and the human body equivalent resistance R b to form a second parallel circuit; the positive terminal of the open-circuit voltage U oc of the passenger car passes through the ground capacitance C C of the passenger car and the first parallel circuit in turn; the positive terminal of the open-circuit voltage U oc of the passenger car passes through The ground capacitance C C , the switch S and the contact resistance R g of the passenger car are connected to one end of the second parallel circuit, and the other end of the second parallel circuit is grounded. The invention makes the calculation of the electric field of the transmission line not affected by the parking position of the passenger car, and at the same time greatly reduces the calculation amount.
Description
技术领域technical field
本发明属于高压输电线路技术领域，具体涉及一种等效电路和人与车辆接触时稳态电流计算方法。The invention belongs to the technical field of high-voltage transmission lines, and in particular relates to an equivalent circuit and a method for calculating steady-state current when a person is in contact with a vehicle.
背景技术Background technique
近年来，对于交流高压输电线路下汽车接触电流的计算，越来越受到人们的重视。传统的研究方法是采用模拟电荷法与表面电荷法相结合计算汽车表面的开路电压与对地电容，再构造人体触摸汽车时的等效电路，从而求解基础电流。但由于输电线路与汽车表面电荷产生的电场之间存在耦合，加上场景尺寸庞大，导致直接求解计算量非常大。并且一次长时间的数值计算只能得到汽车与输电线一种相对位置情况下汽车的接触电流，当汽车移动位置时，需要重复进行繁冗的数值计算。In recent years, more and more attention has been paid to the calculation of vehicle contact current under AC high-voltage transmission lines. The traditional research method is to use the analog charge method and the surface charge method to calculate the open-circuit voltage and the capacitance to ground of the car surface, and then construct the equivalent circuit when the human body touches the car, so as to solve the basic current. However, due to the coupling between the transmission line and the electric field generated by the surface charge of the car, and the huge size of the scene, the direct solution is very computationally intensive. In addition, a long-term numerical calculation can only obtain the contact current of the car in a relative position between the car and the transmission line. When the car moves, it is necessary to repeat the tedious numerical calculation.
发明内容SUMMARY OF THE INVENTION
本发明为解决公知技术中存在的技术问题，提供一种等效电路和人与车辆接触时稳态电流计算方法，基于互易定理求出客车的开路电压，使得输电线路电场的计算不受客车停车位置的影响，同时大大减少了计算量。In order to solve the technical problems existing in the known technology, the present invention provides an equivalent circuit and a method for calculating steady-state current when a person is in contact with a vehicle. Based on the reciprocity theorem, the open-circuit voltage of the passenger car is obtained, so that the calculation of the electric field of the transmission line is not affected by the passenger car. The impact of the parking location, while greatly reducing the amount of calculation.
本发明的第一目的是提供一种等效电路，包括：The first object of the present invention is to provide an equivalent circuit comprising:
客车的对地电容CC、客车的开路电压Uoc、轮胎对地电容Ct、轮胎的电阻Rt、接触电阻Rg、人体等效电容Cb和人体等效电阻Rb；其中：The ground capacitance C C of the passenger car, the open circuit voltage U oc of the passenger car, the tire-to-ground capacitance C t , the tire resistance R t , the contact resistance R g , the human body equivalent capacitance C b and the human body equivalent resistance R b ; where:
所述轮胎对地电容Ct和轮胎的电阻Rt组成第一并联电路；The tire-to-ground capacitance C t and the tire resistance R t form a first parallel circuit;
所述人体等效电容Cb和人体等效电阻Rb组成第二并联电路；The human body equivalent capacitance C b and the human body equivalent resistance R b form a second parallel circuit;
所述客车的开路电压Uoc的负极端接地，客车的开路电压Uoc的正极端依次通过客车的对地电容CC、第一并联电路后接地；The negative terminal of the open circuit voltage U oc of the passenger car is grounded, and the positive terminal of the open circuit voltage U oc of the passenger car is grounded through the ground capacitance C C of the passenger car and the first parallel circuit in sequence;
所述客车的开路电压Uoc的正极端依次通过客车的对地电容CC、开关S、接触电阻Rg与第二并联电路的一端连接，所述第二并联电路的另一端接地。The positive terminal of the open circuit voltage U oc of the passenger car is sequentially connected to one end of the second parallel circuit through the ground capacitance C C , the switch S and the contact resistance R g of the passenger car, and the other end of the second parallel circuit is grounded.
优选地，Rt>>1/ωCt，所述接触电阻Rg一侧的戴维南等效电压UThevinin为：Preferably, R t >>1/ωC t , the Thevenin equivalent voltage U Thevinin on the side of the contact resistance R g is:
所述接触电阻Rg一侧的等效阻抗Zeq为：The equivalent impedance Z eq on one side of the contact resistance R g is:
根据欧姆定律，流过开关S的稳态接触电流Ig的表达式为：According to Ohm's law, the expression for the steady-state contact current I g flowing through the switch S is:
本发明的第二目的是提供一种基于上述等效电路的人与车辆接触时稳态电流计算方法，包括：The second object of the present invention is to provide a method for calculating steady-state current when a person is in contact with a vehicle based on the above-mentioned equivalent circuit, including:
S1、计算悬浮导体对地电压；具体为：S1. Calculate the voltage of the suspended conductor to the ground; specifically:
交流高压输电线路下悬浮导体对地电压的表达式如下：The expression of the ground voltage of the suspended conductor under the AC high voltage transmission line is as follows:
将悬浮导体表面剖分为有限单元，在单元内选择某些积分点，求出被积函数在这些积分点上的数值，然后乘以权因子，再求综合，得到积分值；Divide the surface of the suspended conductor into finite elements, select some integration points in the element, obtain the value of the integrand at these integration points, multiply the weight factor, and then integrate to obtain the integral value;
S2、构建等效电路；S2, build an equivalent circuit;
S3、通过欧姆定理计算人与客车稳态接触电流Ig的大小。S3. Calculate the magnitude of the steady-state contact current I g between the person and the passenger car through Ohm's theorem.
优选地，在S1中，所述有限单位为三角形；此时，二维高斯积分的公式为：Preferably, in S1, the finite unit is a triangle; at this time, the formula of the two-dimensional Gaussian integral is:
优选地，采用积分点数为1的三角形单元二维高斯积分方法，式(4)的连续积分化为式(6)的数值积分：Preferably, a two-dimensional Gaussian integration method with a triangular element with 1 integration point is used, and the continuous integration of formula (4) is transformed into the numerical integration of formula (6):
其中，Si为三角形单元i的面积，Vi表示单元i上的积分点处的电压，
本发明具有的优点和积极效果是：The advantages and positive effects that the present invention has are:
本发明通过将交流高压输电线路电场的计算，与客车表面电荷密度的计算解耦合，使交流高压输电线路的电场计算不受客车停车位置的影响，降低了求解的复杂度，提高了输电线路下方的人体接触客车稳态电流的计算效率。The invention decouples the calculation of the electric field of the AC high-voltage transmission line from the calculation of the surface charge density of the passenger car, so that the calculation of the electric field of the AC high-voltage transmission line is not affected by the parking position of the passenger car, reduces the complexity of the solution, and improves the efficiency of the lower part of the transmission line. The computational efficiency of the steady-state current of the human body contacting the passenger car.
附图说明Description of drawings
图1为本发明优选实施例中人触摸客车时的等效电路图；1 is an equivalent circuit diagram when a person touches a passenger car in a preferred embodiment of the present invention;
图2为本发明优选实施例中客车表面网格剖分图；Fig. 2 is the grid division diagram of the passenger car surface in the preferred embodiment of the present invention;
具体实施方式Detailed ways
为能进一步了解本发明的发明内容、特点及功效，兹例举以下实施例，并配合附图详细说明如下：In order to further understand the content of the invention, features and effects of the present invention, the following embodiments are exemplified and described in detail with the accompanying drawings as follows:
本发明的技术方案为：The technical scheme of the present invention is:
请参阅图1，一种等效电路，包括：See Figure 1, an equivalent circuit consisting of:
客车的对地电容CC、客车的开路电压Uoc、轮胎对地电容Ct、轮胎的电阻Rt、接触电阻Rg、人体等效电容Cb和人体等效电阻Rb；其中：The ground capacitance C C of the passenger car, the open circuit voltage U oc of the passenger car, the tire-to-ground capacitance C t , the tire resistance R t , the contact resistance R g , the human body equivalent capacitance C b and the human body equivalent resistance R b ; where:
所述轮胎对地电容Ct和轮胎的电阻Rt组成第一并联电路；The tire-to-ground capacitance C t and the tire resistance R t form a first parallel circuit;
所述人体等效电容Cb和人体等效电阻Rb组成第二并联电路；The human body equivalent capacitance C b and the human body equivalent resistance R b form a second parallel circuit;
所述客车的开路电压Uoc的负极端接地，客车的开路电压Uoc的正极端依次通过客车的对地电容CC、第一并联电路后接地；The negative terminal of the open circuit voltage U oc of the passenger car is grounded, and the positive terminal of the open circuit voltage U oc of the passenger car is grounded through the ground capacitance C C of the passenger car and the first parallel circuit in sequence;
所述客车的开路电压Uoc的正极端依次通过客车的对地电容CC、开关S、接触电阻Rg与第二并联电路的一端连接，所述第二并联电路的另一端接地。The positive terminal of the open circuit voltage U oc of the passenger car is sequentially connected to one end of the second parallel circuit through the ground capacitance C C , the switch S and the contact resistance R g of the passenger car, and the other end of the second parallel circuit is grounded.
一种基于上述等效电路的人与车辆接触时稳态电流计算方法，包括：A method for calculating steady-state current when a person is in contact with a vehicle based on the above-mentioned equivalent circuit, comprising:
S1、计算悬浮导体对地电压；具体为：S1. Calculate the voltage of the suspended conductor to the ground; specifically:
根据现有的经验公式，交流高压输电线路下悬浮导体对地电压的表达式如下：According to the existing empirical formula, the expression of the ground voltage of the suspended conductor under the AC high voltage transmission line is as follows:
对式(4)中的积分，采用高斯积分法。即将悬浮导体表面剖分为若干单元，在单元内选择某些积分点，求出被积函数在这些积分点上的数值，然后乘以权因子，再求综合，便可得到积分值。以有限元单元为三角形为例，二维高斯积分的一般公式为：For the integral in formula (4), the Gauss integral method is used. That is, the surface of the suspended conductor is divided into several units, some integral points are selected in the unit, the value of the integrand at these integral points is obtained, and then multiplied by the weight factor, and then integrated, the integral value can be obtained. Taking the finite element element as a triangle as an example, the general formula of the two-dimensional Gaussian integral is:
本文采用积分点数为1的三角形单元二维高斯积分方法，式(4)的连续积分可化为式(6)的数值积分：In this paper, the triangular element two-dimensional Gauss integration method with 1 integration point is adopted, and the continuous integral of Eq. (4) can be transformed into the numerical integration of Eq. (6):
其中，Si为三角形单元i的面积，
S2、构建等效电路；当人触摸输电线路下的客车时，考虑汽车的对地电容、轮胎对地电容、人的对地电容和电阻，不考虑人与汽车之间的耦合关系以及人的开路电压，可构成如图1所示的等效电路，开关S闭合后，电路达到稳态时，流过S的电流Ig即为人与客车的稳态接触电流。S2. Build an equivalent circuit; when a person touches a passenger car under the transmission line, consider the car's ground capacitance, tire-to-ground capacitance, human's ground capacitance and resistance, regardless of the coupling relationship between the person and the car and the human The open-circuit voltage can form an equivalent circuit as shown in Figure 1. After the switch S is closed, when the circuit reaches a steady state, the current Ig flowing through S is the steady-state contact current between the person and the passenger car.
其中，CC为客车的对地电容，Uoc为客车的开路电压，Ct为轮胎对地电容，Rt为轮胎的电阻，Rg为接触电阻，Cb为人体等效电容，Rb为人体等效电阻。Among them, C C is the ground capacitance of the passenger car, U oc is the open circuit voltage of the passenger car, C t is the tire-to-ground capacitance, R t is the resistance of the tire, R g is the contact resistance, C b is the equivalent capacitance of the human body, and R b is the equivalent resistance of the human body.
由于Rt>>1/ωCt，在计算时可视Rt为开路。在已知客车开路电压和Uoc和客车对地电容Cc的前提下，当图1中开关电路达到稳态时，开关左侧的戴维南等效电压UThevinin为：Since R t >>1/ωC t , R t can be regarded as an open circuit during calculation. Under the premise of known bus open circuit voltage and U oc and bus-to-ground capacitance C c , when the switch circuit in Figure 1 reaches a steady state, the Thevenin equivalent voltage U Thevinin on the left side of the switch is:
开关右侧的等效阻抗Zeq为：The equivalent impedance Z eq on the right side of the switch is:
公式(2)中，加号后面的部分代表的是电抗的计算方法，电抗是一个矢量，.j和w是代表矢量中的方向参数In formula (2), the part after the plus sign represents the calculation method of reactance, reactance is a vector, .j and w are the direction parameters in the representative vector
则由欧姆定律，流过开关的稳态接触电流Ig的表达式为：Then according to Ohm's law, the expression of the steady-state contact current I g flowing through the switch is:
S3、通过欧姆定理计算人与客车稳态接触电流Ig的大小。S3. Calculate the magnitude of the steady-state contact current I g between the person and the passenger car through Ohm's theorem.
中选取上海中龙SLK611855AN5型号客车。其尺寸参数为：Select the Shanghai Zhonglong SLK611855AN5 passenger car. Its size parameters are:
车身长度(L)：10995mm；Body length (L): 10995mm;
车身宽度(W)：2500mm；Body width (W): 2500mm;
车身高度(H1)：3695mm；Body height (H1): 3695mm;
整车高度(H2)：3880mm。Vehicle height (H2): 3880mm.
通过ANSYS对客车进行建模，如图2所示。首先在客车的表面施加Vb＝1000V的电压，再将客车表面用38406个三角形单元剖分(图2)。如图2所示，在面电荷密度变化较大的区域进行了网格细化以得到更精确得结果。最后由ANSYS输出在恒定电压为Vb的情况下汽车表面三角形单元顶点的坐标信息和电荷密度信息。The passenger car is modeled by ANSYS, as shown in Figure 2. First, a voltage of Vb=1000V is applied to the surface of the passenger car, and then the surface of the passenger car is divided into 38406 triangular elements (Fig. 2). As shown in Figure 2, mesh refinement was performed in regions with large variations in surface charge density to obtain more accurate results. Finally, ANSYS outputs the coordinate information and charge density information of the vertices of the triangle element on the car surface under the condition of constant voltage Vb.
如上所述，这一步的计算与交流高压输电线路电场的计算是相互独立的，所以当客车与输电线路的相对位置发生改变时不需要进行重复计算。As mentioned above, the calculation of this step is independent of the calculation of the electric field of the AC high-voltage transmission line, so there is no need to repeat the calculation when the relative position of the passenger car and the transmission line changes.
图2客车表面网格剖分；仿真得到客车的电容Cc＝2182pF，以及客车表面所有三角形单元的节点电荷密度。输电线路在进地处的电场可近似为垂直于地面的均匀电场。本文以居民区允许的最大电场强度E＝4000V/m为例计算输电线路在客车表面单元节点上产生的电位，节点位置及编号与求解电荷密度时完全一致。由式(4)的数值积分可计算出客车的开路电压Uoc＝2.81kV。Fig. 2 Meshing of the surface of the passenger car; the simulation obtains the capacitance C c =2182pF of the passenger car, and the nodal charge density of all triangular elements on the surface of the passenger car. The electric field of the transmission line at the entrance can be approximated as a uniform electric field perpendicular to the ground. This paper takes the maximum allowable electric field intensity E=4000V/m in residential area as an example to calculate the potential generated by the transmission line on the surface unit nodes of the passenger car. The node position and number are exactly the same as when the charge density is calculated. The open-circuit voltage U oc =2.81kV of the passenger car can be calculated from the numerical integration of formula (4).
通过ANSYS建立客车处于均匀电场中的有限元模型可仿真得到汽车表面的电压为2990kV，数值计算结果与仿真结果的相对误差为6.1％。The finite element model of the passenger car in a uniform electric field is established by ANSYS, and the voltage on the surface of the car is 2990kV. The relative error between the numerical calculation results and the simulation results is 6.1%.
本文取轮胎的对地电容Ct＝670pF；接触电阻Rg＝1kΩ；人体电容Cb＝35pF；人体电阻Rb＝1kΩ。将Cc＝2182pF、Uoc＝2.81kV以及上述经验取值带入图1所示的电路中计算得到稳态接触电流的大小为306.23μA。In this paper, the ground capacitance of the tire is C t =670pF; the contact resistance R g =1kΩ; the body capacitance C b =35pF; the body resistance R b =1kΩ. Taking C c =2182pF, U oc =2.81kV and the above empirical values into the circuit shown in Figure 1, the steady-state contact current is calculated to be 306.23μA.
以上所述仅是对本发明的较佳实施例而已，并非对本发明作任何形式上的限制，凡是依据本发明的技术实质对以上实施例所做的任何简单修改，等同变化与修饰，均属于本发明技术方案的范围内。The above is only the preferred embodiments of the present invention, and does not limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention belong to the present invention. within the scope of the technical solution of the invention.
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