CN114564858B - Lightning arrester potential distribution calculation method considering dielectric constant change of resistor disc - Google Patents
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Abstract
The invention provides a lightning arrester potential distribution calculation method considering the dielectric constant change of a resistor disc, which comprises the steps of measuring the current flowing through the resistor disc under different voltages by using a test loop, carrying out Fourier decomposition on the measured voltage waveform and current waveform of the resistor disc to obtain voltage components and current components under different voltages, and obtaining the equivalent capacitance of the resistor disc; calculating the relative dielectric constant of the resistor disc; setting the corresponding relation of the relative dielectric constants of the resistor disc as a global difference function, and referencing the global difference function in the material property of the resistor disc as a relative dielectric constant parameter of the resistor disc; and setting boundary conditions according to the established lightning arrester model and an air domain, solving relative dielectric constant parameters of the resistor disc in an electrostatic field, and calculating to obtain potential distribution of the lightning arrester. The calculation method of the potential distribution of the lightning arrester provided by the invention can be used for more accurately calculating the potential distribution of the lightning arrester under the continuous operation voltage, and providing a basis for the voltage equalizing design of the lightning arrester.
Description
Technical Field
The invention belongs to the technical field of lightning arrester potential distribution calculation, and particularly relates to a lightning arrester potential distribution calculation method considering dielectric constant change of a resistor disc
Background
Along with the continuous rising of the alternating current transmission capacity, the transmission voltage of the power system is higher and higher, and the reliability requirement of the power system is also improved. The principle of the arrester is that the arrester is used as main protection equipment for safe operation of a power system, and the arrester is in a high-resistance state non-conduction under low voltage by utilizing the nonlinear characteristic of a resistor sheet, and is changed into a low-resistance state under overvoltage to release energy. The improvement of the voltage level enables the number of the resistor discs in the lightning arrester to be continuously increased, the volume to be increased, the structure to be complex, and the operation safety of the lightning arrester to be threatened. Under the continuous running voltage of alternating current, the potential distribution of the lightning arrester along the axial direction of the resistor sheets can generate uneven phenomenon due to the existence of stray capacitance, and the ratio of the voltage born by each resistor sheet to the average voltage born by all resistor sheets of the whole lightning arrester is called an uneven coefficient.
The lightning arrester of power stations such as 750kV and 1000kV has a height of 9 meters or more and even more than 10 meters, and the phenomenon of uneven potential distribution caused by stray capacitance is more serious. Under the condition of no voltage equalizing measure, the non-uniformity coefficient of some resistance sheets can reach 50% -70%. This accelerates the ageing speed of the local resistor disc, eventually leading to premature failure of the whole arrester. In order to reduce the non-uniformity coefficient of the potential distribution of the lightning arrester, corresponding voltage equalizing measures are needed. The non-uniformity coefficient of the potential distribution of the lightning arrester can be obtained through a test or a simulation calculation method, electrodes are buried in the middle of each resistor sheet in advance in the test, the voltage born by each resistor sheet under the continuous operation voltage is measured through a voltage divider or other sensors, the test is complex, the workload is high, and therefore the simulation calculation method is widely adopted at present. At present, the potential distribution of the lightning arrester is calculated through simulation, the relative dielectric constant of a resistor disc is generally regarded as a constant, and the potential distribution is calculated by utilizing the principle of capacitive voltage division under an electrostatic field. However, in practice, the relative dielectric constant of the resistor is related to the charging rate thereof, which may make the potential distribution obtained by the simulation calculation by the method inaccurate, and affect the design and safe operation of the lightning arrester, especially for the lightning arrester with a higher height, the body capacitance determined by the relative dielectric constant of the resistor has a larger influence. Therefore, for high voltage class arresters, a more accurate simulation calculation method is needed.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a lightning arrester potential distribution calculating method considering the dielectric constant change of a resistor disc, which aims to more accurately calculate the potential distribution of the lightning arrester under the continuous operation voltage and provides a basis for the voltage equalizing design of the lightning arrester.
The invention is realized by the following technical scheme:
a lightning arrester potential distribution calculation method taking into consideration the dielectric constant change of a resistor disc is characterized by comprising the following steps of,
step 1, building a resistance sheet measurement test loop;
step 2, measuring the current flowing through the resistor disc under different voltages by using the test loop in the step 1, and recording the voltage waveform and the current waveform of the resistor disc;
step 3, carrying out Fourier decomposition on the voltage waveform and the current waveform of the resistor disc obtained by measurement in the step 2 to obtain voltage components and current components of the resistor disc under 50Hz under different voltages, and obtaining equivalent capacitances of the resistor disc under different voltages;
step 4, calculating the relative dielectric constants of the resistor sheets under different voltages according to the equivalent capacitances of the resistor sheets under different voltages obtained in the step 3;
step 5, setting the corresponding relation of the relative dielectric constants of the resistor sheets under different voltages obtained in the step 4 as a global difference function, and referencing the global difference function in the material properties of the resistor sheets as relative dielectric constant parameters of the resistor sheets under different voltages;
step 6, establishing a lightning arrester model and an air domain;
step 7, setting boundary conditions according to the lightning arrester model and the air domain established in the step 6;
and 8, solving in an electrostatic field according to the boundary conditions in the step 7 and the relative dielectric constant parameters of the resistor disc under different voltages in the step 5, and calculating to obtain the potential distribution of the lightning arrester.
Preferably, the resistance sheet measurement test loop built in the step 1 comprises 220V mains supply, an adjustable transformer, a single-phase transformer, water resistance, a resistance sheet, a sampling resistor and an oscilloscope; the 220V commercial power is sequentially connected with the adjustable transformer, the single-phase transformer, the water resistor and the oscilloscope in series, and the resistor disc and the sampling resistor are connected in parallel on a circuit for connecting the water resistor and the oscilloscope.
Preferably, in step 2, the current flowing through the resistor disc under different voltages is measured, and the specific method is as follows:
and (3) adjusting the adjustable transformer to change the voltage on the resistor disc, measuring and recording the voltages at two ends of the resistor disc and the sampling resistor r by using an oscilloscope, and calculating the current flowing through the resistor disc.
Preferably, in the step 3, the equivalent capacitance of the resistor disc under different voltages is calculated, and the specific method is as follows:
wherein: c (C) x Is equivalent capacitance of a resistor, alpha is phase difference between a voltage component and a current component, U m For the amplitude of the voltage, I m Is the current amplitude.
Preferably, the specific calculation method of the relative dielectric constants of the resistor disc under different voltages in the step 4 is as follows:
wherein: epsilon r The relative dielectric constant of the resistor sheet, d is the thickness of the resistor sheet, s is the upper surface area of the resistor sheet, ε 0 The dielectric constant of vacuum.
Preferably, in step 6, a lightning arrester model and an air domain are established, and the specific method comprises the following steps:
the method comprises the steps of taking the axis of the lightning arrester as a central line, taking the bottom surface of a lightning arrester support as an initial surface, establishing a three-dimensional model of the lightning arrester in Solidworks, and taking a cylinder drawn according to the three-dimensional model of the lightning arrester as an air domain.
Preferably, in the step 7, a boundary condition is set, and the specific method is as follows:
setting the lower bottom surface and the side surface of the cylinder of the air domain to be grounded; and setting the top end of the lightning arrester and the equalizing ring as a terminal.
Preferably, the radius of the cylinder is the minimum ground distance of the lightning arrester, and the height of the cylinder is 1.5 times the height of the lightning arrester.
Preferably, the specific method for potential distribution of the lightning arrester is as follows:
according to a steady-state physical equation of an electrostatic field, taking a lightning arrester and an air domain as boundary conditions, taking relative dielectric constant parameters of a resistor disc under different voltages as parameters in a solving equation, establishing a sparse matrix to be solved, adopting a MUMPS solver to solve matrix values, and calculating to obtain potential distribution of the lightning arrester.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a lightning arrester potential distribution calculation method considering the dielectric constant change of a resistor disc. Various types of lightning arresters can be calculated by utilizing the advantages of finite element simulation software. Compared with the traditional test measurement mode and simulation calculation mode, the method takes the influence factors of the bearing voltage of the resistor on the relative dielectric constant of the resistor into consideration, has the advantages of low cost, strong flexibility, high calculation accuracy and the like, and can reduce the economic loss caused by the damage of the lightning arrester to a certain extent.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for calculating the potential distribution of the lightning arrester of the present invention;
FIG. 2 is a schematic diagram of a test loop in an embodiment;
fig. 3 is a boundary condition setting of the lightning arrester in the embodiment;
fig. 4 is a three-dimensional model diagram of a 750kV lightning arrester provided by an embodiment of the invention;
fig. 5 is a schematic diagram of a 750kV lightning arrester model and an air domain according to an embodiment of the present invention;
FIG. 6 is a graph showing the relative permittivity of a resistor disc of an arrester and the relationship between the relative permittivity and the bearing voltage of the resistor disc of the present invention;
fig. 7 is a schematic diagram of potential distribution of a lightning arrester according to an embodiment of the present invention.
Detailed Description
The invention will now be described in further detail with reference to specific examples, which are intended to illustrate, but not to limit, the invention.
As shown in fig. 1, a lightning arrester potential distribution calculation method taking into account a change in dielectric constant of a resistive sheet, is characterized by comprising,
step 1, building a resistance sheet measurement test loop; a test loop as shown in fig. 2 was constructed. The test loop is powered by 220V mains supply and an adjustable transformer T 1 Single-phase transformer T 2 The water resistance R, the test sample resistor disc, the sampling resistor R and the oscilloscope. The 220V commercial power is sequentially connected with the adjustable transformer, the single-phase transformer, the water resistor and the oscilloscope in series, and the resistor disc and the sampling resistor are connected in parallel on a circuit for connecting the water resistor and the oscilloscope.
Step 2, measuring the current flowing through the resistor disc under different voltages by using the test loop in the step 1, and recording the voltage waveform and the current waveform of the resistor disc; the test loop in step 1 was used to measure the current flowing through the resistor at different voltages. The specific measurement method comprises the following steps: adjusting knob of adjustable transformer to make voltage on resistor sheet be 0U in turn r 、10％U r 、20％U r 、30％U r ……150％U r (U r Representing a 1mA rated reference voltage for a metal oxide resistor pad). Measuring and recording the voltage of the two ends of the resistor disc and the sampling resistor r by using an oscilloscope, and calculating the flowing resistorSheet current.
Step 3, carrying out Fourier decomposition on the voltage waveform and the current waveform of the resistor disc obtained by measurement in the step 2 to obtain voltage components and current components of the resistor disc under 50Hz under different voltages, and obtaining equivalent capacitances of the resistor disc under different voltages; in the step 3, calculating the equivalent capacitance of the resistor disc under different voltages, wherein the specific method comprises the following steps:
carrying out Fourier decomposition on the voltage and current waveforms of the resistor disc measured by using an oscilloscope to obtain voltage components and current components with the frequency of 50Hz under different voltages, and calculating the phase difference alpha and the respective amplitude U of the voltage components and the current components m 、I m Thereby calculating the equivalent capacitance of the resistor disc:
regarding the resistor as a parallel capacitor plate model, the relative dielectric constant of the dielectric medium between the resistor and the capacitor plate model is calculated by the following formula:
wherein: d is the thickness of the resistor sheet, s is the upper surface area of the resistor sheet, ε 0 The dielectric constant of vacuum.
Thus, the corresponding relation of the relative dielectric constants of the resistor sheets under different voltages is obtained.
Step 4, calculating the relative dielectric constants of the resistor sheets under different voltages according to the equivalent capacitances of the resistor sheets under different voltages obtained in the step 3;
step 5, setting the corresponding relation of the relative dielectric constants of the resistor sheets under different voltages obtained in the step 4 as a global difference function, and referencing the global difference function in the material properties of the resistor sheets as relative dielectric constant parameters of the resistor sheets under different voltages; the relationship between the relative dielectric constant of the resistor and the different bearing voltages is set as a global difference function in COMSOL Mutiphysics, and the function is cited in the material properties of the resistor as the relative dielectric constant parameter of the resistor, and the relative dielectric constant of the rest of the material of the lightning arrester is set according to the respective properties.
Step 6, establishing a lightning arrester model and an air domain; in the step 6, a lightning arrester model and an air domain are established, and the specific method comprises the following steps: establishing a complete three-dimensional model of the lightning arrester in Solidworks, and importing the model into COMSOL Mutiphysic software; the method comprises the steps of taking the axis of the lightning arrester as a central line, taking the bottom surface of a lightning arrester support as an initial surface, establishing a three-dimensional model of the lightning arrester in Solidworks, and taking a cylinder drawn according to the three-dimensional model of the lightning arrester as an air domain.
Step 7, as shown in fig. 3, setting boundary conditions according to the lightning arrester model and the air domain established in step 6; in the step 7, boundary conditions are set, and the specific method is as follows: setting the lower bottom surface and the side surface of the cylinder of the air domain to be grounded; and setting the top end of the lightning arrester and the equalizing ring as a terminal. The radius of the cylinder is the minimum ground distance of the lightning arrester, and the height of the cylinder is 1.5 times of the height of the lightning arrester.
And 8, solving in an electrostatic field according to the set boundary conditions in the step 6 and the relative dielectric constant parameters of the resistor disc under different voltages in the step 5, and calculating to obtain the potential distribution of the lightning arrester.
The specific method for calculating the potential distribution of the lightning arrester comprises the following steps:
according to a steady-state physical equation of an electrostatic field, taking a lightning arrester and an air domain as boundary conditions, taking relative dielectric constant parameters of a resistor disc under different voltages as parameters in a solving equation, establishing a sparse matrix to be solved, adopting a MUMPS solver to solve matrix values, and calculating to obtain potential distribution of the lightning arrester.
In order to make the above objects, features and advantages of the present invention more comprehensible, preferred embodiments accompanied with figures are described in detail below.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The specific implementation flow of the lightning arrester potential distribution calculation method considering the dielectric constant change of the resistor disc is shown in fig. 3, and the specific implementation method is as follows:
(1) Building up test 220V mains supply, adjustable transformer T 1 Single-phase transformer T 2 And a test loop consisting of a water resistor R, a test sample resistor, a sampling resistor R and an oscilloscope. The resistance of the water resistor R is 1MΩ, and the resistance of the sampling resistor R is 2 Ω. The resistor disc specification is phi 100 x 22mm, and the 1MA reference voltage is 5kV.220V voltage is connected to the adjustable transformer T 1 Preliminary boost, T 1 Is connected to the output of the single-phase transformer T 2 Is provided. T (T) 2 The output end of the test sample resistor is connected to the surface electrode of the test sample resistor disc after passing through a water resistor, and then a loop is formed through a sampling resistor r. The two high-voltage measuring probes are connected to two channels of the oscilloscope, and the grounding end is connected to the ground wire.
(2) The voltage at the two ends of the resistor disc +r and the resistor r is measured through the high-voltage probe in the two channels of the oscilloscope, and the knob of the adjustable transformer is adjusted, so that the voltage peak value on the resistor disc is 0.5kV, 1kV, 1.5kV, 2kV … … kV, 6.5kV, 7kV and 7.5kV in sequence. The voltage data of the two channels are recorded by an oscilloscope, and the voltage at the two ends of the sampling resistor r is divided by the resistance value 2 omega, namely the current waveform flowing through the resistor disc.
(3) Taking voltage and current waveform data measured under the condition that the resistor disc bears 3.5kV voltage as an example, carrying out Fourier analysis on the voltage and current waveform data to obtain the voltage waveform 50Hz component with the amplitude of 3.5kV and the current waveform 50Hz component with the amplitude of 1.533mA, wherein the phase difference between the voltage and the current waveform 50Hz component is 79.9 degrees, so that the equivalent capacitance of the resistor disc is calculated:
(4) Regarding the resistor as a parallel capacitor plate model, the thickness d of the resistor is 22mm, and the upper surface of the resistor is provided withProduct s is 7850mm 2 Dielectric constant ε of vacuum 0 ＝8.854187817×10 -12 F/m. Taking the equivalent capacitance calculated in the step (3) as an example, the relative dielectric constant of the resistor disc dielectric is calculated as follows:
thus, the correspondence of the relative dielectric constants of the resistive sheets at different voltages is obtained, as shown in fig. 6.
(5) A complete three-dimensional model of the arrester was built in Solidworks as shown in fig. 4 and imported into COMSOL Mutiphysic software. The axis of the lightning arrester is taken as a central line, the bottom surface of the lightning arrester support is taken as an initial surface, and a cylinder is drawn to be taken as an air domain. The radius of the cylinder is the minimum ground distance of the arrester, i.e. 6.4m, and the height is 1.5 times the height of the arrester, i.e. 19.33m.
(6) The relative permittivity of the resistor disc and the relationship of the different bearing voltages are set as a global difference function in COMSOL Mutiphysics and this function is referenced in the material properties of the resistor disc as a relative permittivity parameter of the resistor disc. The relative dielectric constant of the air domain was set to 1.00053, and the relative dielectric constant of the metal was set to 10 10 The relative dielectric constant of the insulating material was set to 3.5.
(7) Setting boundary conditions, namely setting the lower bottom surface and the side surface of the air domain cylinder to be grounded; the top end of the lightning arrester and the grading ring are set as terminals, and the voltage is 704.172kV of continuous operation voltage of the lightning arrester.
(8) The lightning arrester and the air domain model were split as shown in fig. 5, and free tetrahedral ultrafine splitting was adopted. The physical field is an electrostatic field, the research content is a steady state, and the potential distribution of the lightning arrester can be obtained by adopting a MUMPS direct solver to calculate, as shown in figure 7.
Claims (9)
1. A lightning arrester potential distribution calculation method taking into consideration the dielectric constant change of a resistor disc is characterized by comprising the following steps of,
step 1, building a resistance sheet measurement test loop;
step 2, measuring the current flowing through the resistor disc under different voltages by using the test loop in the step 1, and recording the voltage waveform and the current waveform of the resistor disc;
step 3, carrying out Fourier decomposition on the voltage waveform and the current waveform of the resistor disc obtained by measurement in the step 2 to obtain voltage components and current components of the resistor disc under 50Hz under different voltages, and obtaining equivalent capacitances of the resistor disc under different voltages;
step 4, calculating the relative dielectric constants of the resistor sheets under different voltages according to the equivalent capacitances of the resistor sheets under different voltages obtained in the step 3;
step 5, setting the corresponding relation of the relative dielectric constants of the resistor sheets under different voltages obtained in the step 4 as a global difference function, and referencing the global difference function in the material properties of the resistor sheets as relative dielectric constant parameters of the resistor sheets under different voltages;
step 6, establishing a lightning arrester model and an air domain;
step 7, setting boundary conditions according to the lightning arrester model and the air domain established in the step 6;
and 8, solving in an electrostatic field according to the boundary conditions in the step 6 and the relative dielectric constant parameters of the resistor disc under different voltages in the step 5, and calculating to obtain the potential distribution of the lightning arrester.
2. The lightning arrester potential distribution calculation method considering the change of the dielectric constant of the resistor disc according to claim 1, wherein the resistor disc measurement test loop set up in the step 1 comprises 220V mains supply, an adjustable transformer, a single-phase transformer, water resistor, a resistor disc, a sampling resistor and an oscilloscope; the 220V commercial power is sequentially connected with the adjustable transformer, the single-phase transformer, the water resistor and the oscilloscope in series, and the resistor disc and the sampling resistor are connected in parallel on a circuit for connecting the water resistor and the oscilloscope.
3. The method for calculating the potential distribution of the lightning arrester taking into consideration the change of the dielectric constant of the resistor disc according to claim 2, wherein the step 2 is to measure the current flowing through the resistor disc under different voltages, and the specific method is as follows:
and (3) adjusting the adjustable transformer to change the voltage on the resistor disc, measuring and recording the voltages at two ends of the resistor disc and the sampling resistor r by using an oscilloscope, and calculating the current flowing through the resistor disc.
4. The method for calculating the potential distribution of the lightning arrester with consideration of the dielectric constant change of the resistor disc according to claim 1, wherein the step 3 is characterized in that the equivalent capacitance of the resistor disc under different voltages is calculated by the following specific method:
wherein:is the equivalent capacitance of the resistive patch,αfor the phase difference of the voltage component and the current component, +.>For the magnitude of the voltage,is the current amplitude.
5. The method for calculating the potential distribution of the lightning arrester with consideration of the dielectric constant change of the resistor disc according to claim 1, wherein the specific calculation method for the relative dielectric constant of the resistor disc under different voltages in the step 4 is as follows:
wherein:is the relative dielectric constant of the resistive sheet,dfor the thickness of the resistive sheet,sis a resistorUpper surface area of the sheet->The dielectric constant of vacuum.
6. The method for calculating the potential distribution of the lightning arrester taking the dielectric constant change of the resistor disc into consideration as set forth in claim 1, wherein the lightning arrester model and the air domain are established in the step 6, and the specific method is as follows:
the method comprises the steps of taking the axis of the lightning arrester as a central line, taking the bottom surface of a lightning arrester support as an initial surface, establishing a three-dimensional model of the lightning arrester in Solidworks, and taking a cylinder drawn according to the three-dimensional model of the lightning arrester as an air domain.
7. The method for calculating the potential distribution of the lightning arrester taking into consideration the variation of the dielectric constant of the resistor disc according to claim 1, wherein the boundary condition is set in the step 7, specifically comprising the following steps:
setting the lower bottom surface and the side surface of the cylinder of the air domain to be grounded; and setting the top end of the lightning arrester and the equalizing ring as a terminal.
8. The method for calculating potential distribution of lightning arrester according to claim 7, wherein the radius of the cylinder is the minimum distance to ground of the lightning arrester, and the height of the cylinder is 1.5 times the height of the lightning arrester.
9. The lightning arrester potential distribution calculating method considering the change of the dielectric constant of the resistor disc according to claim 1, wherein the specific method for calculating the potential distribution of the lightning arrester is as follows:
according to a steady-state physical equation of an electrostatic field, taking a lightning arrester and an air domain as boundary conditions, taking relative dielectric constant parameters of a resistor disc under different voltages as parameters in a solving equation, establishing a sparse matrix to be solved, adopting a MUMPS solver to solve matrix values, and calculating to obtain potential distribution of the lightning arrester.
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