CN111880050B - Oil paper sleeve damp positioning method based on polarity reversal time domain dielectric response - Google Patents
Oil paper sleeve damp positioning method based on polarity reversal time domain dielectric response Download PDFInfo
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- G01R31/1245—Testing dielectric strength or breakdown voltage ; Testing or monitoring effectiveness or level of insulation, e.g. of a cable or of an apparatus, for example using partial discharge measurements; Electrostatic testing of components, parts or materials of line insulators or spacers, e.g. ceramic overhead line cap insulators; of insulators in HV bushings
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Abstract
The application discloses a polar inversion time domain dielectric response-based oiled paper sleeve damp positioning method, which comprises the following steps: 1) carrying out PDC test based on polarity reversal time domain dielectric response on the oiled paper casing, and adopting a comparison test of two wiring modes; 2) drawing a polarization current/depolarization current-time curve of the two connection modes, or drawing a polarization current/depolarization current difference-time curve of the two connection modes; 3) and judging the moist location of the oilpaper casing according to the difference of the polarization current/depolarization current-time curves of the two connection modes or the shape of the polarization current/depolarization current difference-time curve of the two connection modes. The method is not easily influenced by external interference, test excitation voltage amplitude, impurity ions and the like, and the damp positioning result is accurate; the specific damp part of the oiled paper sleeve can be obtained; the oil paper sleeve to be tested is not damaged, and the field test of the oil paper sleeve is more favorably realized.
Description
Technical Field
The application relates to a polarity inversion time domain dielectric response-based oiled paper sleeve damp positioning method, and belongs to the technical field of electrical equipment performance evaluation.
Background
With the rapid development of the power industry in China, a large number of power equipment such as transformers, reactors and the like with high voltage grade and large capacity are put into operation, and higher requirements are put forward on the maintenance level of field equipment. As an important component of the external insulation of a large oil paper insulation transformer, the high-voltage oil paper insulation sleeve has the characteristics of large usage amount, high price, excellent insulation performance and the like, and the insulation performance of the high-voltage oil paper insulation sleeve directly influences the stable operation of the transformer. Therefore, the safety and stability of the high-voltage power grid are determined by scientifically and effectively diagnosing and evaluating the insulation state of the high-voltage power grid.
The bushing can be classified into a wall bushing, a multi-oil circuit breaker bushing, a transformer bushing, and the like according to purposes. The ceramic sleeve comprises a pure ceramic sleeve and a ceramic and composite medium sleeve according to the structure. The bushing can be divided into a capacitive bushing and a non-capacitive bushing, wherein the capacitive bushing is mainly used in power equipment such as transformers and reactors with the voltage level of 100kV or above. The capacitive bushings may be classified into Resin-Bonded Paper (RBP), Resin-Impregnated Paper (RIP), and Oil-Impregnated Paper (OIP) capacitive bushings, which are classified by an internal insulating material.
The oil-immersed paper capacitive bushing is one of the main accessories of a high-voltage grade transformer, the external insulation of the oil-immersed paper capacitive bushing is generally a porcelain bushing with an umbrella skirt, and the internal insulation of the oil-immersed paper capacitive bushing is an oil-immersed insulating paper capacitor core which is coaxially connected in series. The capacitive bushing has the function of leading out a winding tap and is also an important supporting component.
The sleeve is affected with damp and is one of the main causes of insulation faults, partial discharge is obviously increased due to the accumulation of moisture in the oil-immersed insulation paper, the breakdown field intensity is greatly reduced, and further, electric power accidents are caused. Compared with the research on the diagnosis of the wetting of the oil-immersed insulation paper, the research on the distinguishing between the aging and the wetting of the oil-immersed insulation paper by scholars at home and abroad is less. Aging and moisture are generally considered to have a relatively similar effect on the dielectric properties of the paper-impregnated insulation. More weak polar small molecular acids such as formic acid, acetic acid and levulinic acid are generated due to aging. These small molecular acids have properties similar to moisture and have a good affinity with moisture and cellulose constituting the insulating paper. The frequency domain dielectric spectrum test standard indicates that a single aging factor and a single moisture factor can enable curves of the frequency domain dielectric spectrum to have the same amplitude and curve trend, so that the identification of induction factors of the two curves has certain difficulty.
In oil-paper composite insulation, the hydrophilic capacity of the insulating paper is 104 times that of the insulating oil. Therefore, 97% of moisture was concentrated in the insulating paper. And because the crystalline region of the cellulose is compact, moisture is not easy to enter, and the cellulose is mainly stored in the amorphous region of the insulating paper. In the amorphous regions of cellulose, there are more hydrophilic hydroxyl groups (-OH) which become attachment points for primary water molecules. Further, more moisture is attached to the primary water molecules in the form of hydrogen bonds. The moisture in the amorphous region accelerates the thermal stress melting process of the cellulose, so that the cellulose in the amorphous region is looser. The local high moisture generates bubbles at high temperature or high field strength, thereby enhancing the local discharge and reducing the insulation strength of the oilpaper bushing.
Therefore, it is necessary to develop a research on the local moisture-affected position of the oilpaper casing and provide a reasonable and effective evaluation method. Meanwhile, the radial damp distribution in the oil paper sleeve is important information in insulation evaluation of the oil paper sleeve, so that the oil paper sleeve can guide on-site maintenance, maintenance and diagnosis of oil paper sleeve equipment, and further can provide optimized and improved feedback information for manufacturers.
Disclosure of Invention
In order to solve the problems, the application provides a polar inversion time domain dielectric response-based oiled paper sleeve wetting positioning method which is not easily influenced by external interference, test excitation voltage amplitude, impurity ions and the like, and has accurate wetting positioning result; the specific damped part of the oilpaper sleeve can be obtained by the damping positioning method, and is damped close to the guide rod or the tail screen, or is uniformly damped or symmetrically damped; the damp positioning method is simple to operate, does not damage the oiled paper casing to be tested, and is more beneficial to realizing the field test of the oiled paper casing.
According to one aspect of the application, a method for positioning a oiled paper casing pipe under the action of moisture based on polarity reversal time domain dielectric response is provided, and comprises the following steps:
1) carrying out PDC testing based on polarity reversal time domain dielectric response on the oiled paper bushing, wherein the testing mode is a comparison test adopting two wiring modes, wherein the first wiring mode is that a high-voltage end of a tester is connected with a tail screen lead of the oiled paper bushing and a conducting rod of the oiled paper bushing is measured and connected, the second wiring mode is that the high-voltage end of the tester is connected with the conducting rod of the oiled paper bushing and the tail screen lead of the oiled paper bushing is measured and connected;
2) according to the PDC test result obtained in the step 1), drawing a polarization current/depolarization current-time curve of the first connection mode and the second connection mode, or drawing a polarization current/depolarization current difference value-time curve of the first connection mode and the second connection mode;
3) and judging the moist location of the oilpaper sleeve according to the difference of the polarization current/depolarization current-time curves of the first connection mode and the second connection mode obtained in the step 2) or the shape of the polarization current/depolarization current difference-time curve of the first connection mode and the second connection mode obtained in the step 2).
Judging the specific operation mode of the oil paper sleeve to be affected with damp and positioned according to the difference of the polarization current/depolarization current-time curves of the first connection mode and the second connection mode obtained in the step 2): if the amplitude of the polarization current/depolarization current-time curve of the first connection mode is larger than that of the polarization current/depolarization current-time curve of the second connection mode, judging that the position close to the conducting rod is affected with damp; if the amplitude of the polarization current/depolarization current-time curve of the second connection mode is larger than that of the polarization current/depolarization current-time curve of the first connection mode, judging that the position close to the end screen is affected with damp; and if the polarization current/depolarization current-time curve of the first wiring mode is basically overlapped with the polarization current/depolarization current-time curve of the second wiring mode, judging that the oilpaper bushing is uniformly or symmetrically damped.
The specific operation mode for judging the wetting and positioning of the oilpaper bushing according to the shape of the polarization current/depolarization current difference-time curve of the first connection mode and the second connection mode obtained in the step 2) is as follows: if the polarization current/depolarization current difference value of the polarization current/depolarization current difference value-time curve is gradually reduced along with the increase of time and is a positive value, judging that the part close to the conducting rod is affected with damp; if the polarization current/depolarization current difference value of the polarization current/depolarization current difference value-time curve is gradually reduced along with the increase of time and is a negative value, judging that the position close to the end screen is affected with damp; and if the difference value of the polarization current/depolarization current difference value-time curve is basically 0, judging that the oilpaper casing pipe is uniformly or symmetrically affected with damp.
The electric field intensity of the PDC test in the step 1) is more than 7V/mm, and preferably, the electric field intensity is 15V/mm, 30V/mm, 45V/mm, 60V/mm, 75V/mm, 90V/mm, 105V/mm, 130V/mm, 145V/mm and 160V/mm. With the increase of the testing electric field intensity, the absolute value of the difference value of the polarization current/the depolarization current of the first connection mode and the second connection mode tends to increase and then decrease, and when the testing electric field intensity is 110V/mm, the absolute value of the difference value of the polarization current/the depolarization current reaches the maximum value.
The testing temperature of the PDC testing in the step 1) is more than 30 ℃, and the preferred testing temperature is 40 ℃, 50 ℃ and 60 ℃. The test temperature increase has the following effects on the ions of the medium: firstly, due to the fact that the temperature is increased, the dissociation balance of water molecules moves towards the right, the dissociation potential barrier of the water molecules is reduced, dissociated ions are increased, and therefore more ions participate in the movement under the electric field; secondly, the temperature is increased to enhance the ionic thermal motion, and the time for the ionic concentration to transit from the equilibrium state of the non-equilibrium state paper is reduced after the external electric field is removed. The increase in temperature increases the number of ions participating in the movement under the electric field, and a relatively low excitation voltage is required in the region near the electrodes to achieve a relatively stable concentration gradient. The increase in temperature reduces the viscosity of the oil and the difference in mobility of the positive and negative ions, and thus the difference in depolarizing current is reduced relative to lower temperatures. The region near the electrode accumulates a greater concentration of ions for the same polarization time as the excitation voltage amplitude is greater. During depolarization, ions diffuse from a region with high concentration to a region with low concentration under the action of thermal motion and a built-in electric field. The diffusion rate increases due to the increase in temperature. After the depolarization current difference value is consistent for the first time, the ion concentration difference is large, and the ion motion has a hysteresis effect relative to the change of the built-in electric field, so that the ion concentration difference gradually reaches an equilibrium state after undergoing a reverse overshoot.
To more accurately locate the location of the paper sleeve where it is wet, the paper sleeve is tested for non-uniformity prior to PDC testing. Before the step 1), the method further comprises the following steps: step 0), evaluating the wetting nonuniformity of the oiled paper sleeve, and testing the curve characteristic according to tan delta-f of the oiled paper sleeve and the complex capacitance C of the oiled paper sleeve*-f-curve characteristics or depolarization current difference relaxation time constant-test voltage curve characteristics determine whether the oiled paper bushing is unevenly wetted.
The specific steps for evaluating the wetting nonuniformity of the oiled paper sleeve according to the tan delta-f test curve characteristic of the oiled paper sleeve are as follows:
011) establishing tan delta-f standard curves of the oiled paper sleeves with different moisture degrees;
012) carrying out PDC test on the oiled paper casing;
013) judging the wetting nonuniformity of the oil paper sleeve, drawing a tan delta-f test curve aiming at the PDC test result in the step 012), comparing the tan delta-f test curve with the tan delta-f standard curve in the step 011), judging that the oil paper sleeve is not uniformly wetted if the tan delta-f test curve and the tan delta-f standard curve have intersection points in the middle and low frequency bands, and otherwise, judging that the oil paper sleeve is uniformly wetted.
According to the complex capacitance C of the oiled paper sleeve*The specific steps for evaluating the wetting nonuniformity of the oilpaper casing by the f curve characteristics are as follows:
021) establishing the complex capacitance C of the oiled paper casing pipe with different moisture degrees*-f a standard curve;
022) carrying out PDC test on the oiled paper casing;
023) judging the wetting nonuniformity of the oilpaper casing, and drawing a complex capacitance C according to the PDC test result in the step 022)*F test curve and comparison with complex capacitance C described in step 021)*And comparing f standard curves, if the complex capacitance real part C '-f test curve and the complex capacitance real part C' -f standard curve are upwarped in a low frequency band and the complex capacitance imaginary part C '-f test curve and the complex capacitance imaginary part C' -f standard curve have an intersection point in the low frequency band, judging that the oiled paper sleeve is not uniformly damped, otherwise, judging that the oiled paper sleeve is uniformly damped.
The specific steps for evaluating the wetting nonuniformity of the oilpaper casing according to the depolarization current difference relaxation time constant-test voltage curve characteristic of the oilpaper casing are as follows:
031) testing the depolarization current difference value of the first wiring mode and the second wiring mode of the oilpaper casing pipe under different testing voltages, and extracting relaxation time constants under different testing voltages by means of a Debye model;
032) drawing a curve of the depolarization current difference relaxation time constant and the voltage in the step 031);
033) judging the wetting nonuniformity of the oilpaper sleeves according to the shape of the depolarization current difference relaxation time constant-voltage curve in the step 032), judging the oilpaper sleeves to be wetted unevenly if the depolarization current difference relaxation time constant-voltage curve has a peak value in a high test voltage section, and otherwise judging the oilpaper sleeves to be wetted evenly or symmetrically wetted.
Further, the larger the peak value of the depolarization current difference relaxation time constant-voltage curve appearing in a high test voltage section is, the larger the degree of unevenness of the oil paper sleeve due to moisture is determined to be.
The expression of the depolarization current difference relaxation time constant is as follows:
wherein k isbBoltzmann constant, 1.380649 × 10-23(ii) a T-absolute temperature/K; epsilonr-the relative dielectric constant of the liquid; n is±-the concentration of positive and negative ions; mu.s±-mobility of positive and negative ions.
Benefits of the present application include, but are not limited to:
1. according to the polarity reversal time domain dielectric response-based oiled paper casing pipe wetting positioning method, the positioning method is simple to operate, the PDC testing wiring mode is only needed to be changed, the wetting position of the oiled paper casing pipe can be positioned by comparing the difference of polarization current/depolarization current-time curves of the two wiring modes or according to the shape of the polarization current/depolarization current difference-time curves of the two wiring modes, and the PDC testing is carried out in the same environment only after the wiring mode is changed, so that the testing result cannot be adversely affected due to the change of the environment.
2. According to the polarity inversion time domain dielectric response-based oiled paper sleeve wetting positioning method, the oiled paper sleeve to be tested is not damaged, and the field test of the oiled paper sleeve is more favorably realized.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a drawing of two radial nonuniform-wetted casing models of the present application.
FIG. 2 is a model of the present application for a bushing with different radial moisture distributions.
Fig. 3 shows the effect of different connection modes on the polarization current/depolarization current-time curve of the casing model according to the present application, wherein (a) is a model # 1 and (b) is a model # 4.
Fig. 4 is a polarization current/depolarization current-time curve of a model No. 1 oiled paper casing with different wiring modes at different test voltages according to the present application, wherein (a) is 50V, (b) is 200V, (c) is 500V, (d) is 700V, (e) is 900V, and (f) is 1000V.
Fig. 5 is a polarization current/depolarization current-time curve of the oiled paper bushing model of different wiring modes at different test voltages at different temperatures according to the present application, wherein (a) is 50 ℃ and (b) is 60 ℃.
Fig. 6 is a plot of polarization current/depolarization current versus time for two connection modes at different test pressures for the same test temperature of the present application, wherein (a) the difference between the polarization currents for model # 1 and (b) the difference between the depolarization currents for model # 1.
FIG. 7 is a basic operation flowchart of the positioning method for wetting the oiled paper bushing based on the polarity-reversal time-domain dielectric response.
FIG. 8 is a flowchart illustrating the detailed operation of the add-on oilpaper casing non-uniformity evaluation step of the present application.
FIG. 9 is a flowchart illustrating the specific operation of the present application for evaluating the moisture non-uniformity of the oilpaper bushing according to the tan delta-f test curve characteristic of the oilpaper bushing.
FIG. 10 shows the complex capacitance C of the oiled paper bushing according to the present application*F, specific operation flow chart of evaluating the wetting nonuniformity of the oilpaper casing pipe by the curve characteristic.
Fig. 11 is a specific operation flowchart for evaluating the wetting nonuniformity of the oilpaper casing according to the depolarization current difference relaxation time constant-test voltage curve characteristic of the oilpaper casing.
Fig. 12 is a tan delta-f curve for a liner of varying average moisture content for the subject application, wherein (a) the average moisture content is 2%, (b) the average moisture content is 3%, (c) the average moisture content is 4%.
Fig. 13 is a graph of C x-f curves for different average moisture content oilpaper sleeves of the present application, wherein (a) average moisture content 2%, (b) average moisture content 3%, (C) average moisture content 4%.
Figure 14 is a plot of depolarization current difference relaxation time constant versus test voltage for oiled paper bushings of different tidal models of the present application.
Detailed Description
The present application will be described in detail with reference to examples, but the present application is not limited to these examples.
The radial thickness of the oiled paper sleeve suitable for the method for positioning the oiled paper sleeve under the damp condition is 2-15mm, preferably 4-10mm, and more preferably 5-8 mm.
For the actual oiled paper casing and the casing experimental model, when the casing is unevenly wetted, the internal moisture content increases or decreases along the radial direction, so that a moisture gradient is formed, as shown in fig. 1.
In order to facilitate explanation of the mechanism of the positioning method of the present application, models of the oiled paper casings at different positions affected with moisture were constructed, the radial water content distribution of the oiled paper casings is shown in table 1, and the casing model is shown in fig. 2, wherein the thickness of each layer of oiled paper is 1.6mm, and the radial thickness of the oiled paper casing is 6.4 mm. And carrying out PDC test by using the PDC test platform. Measurement frequency range: 1 mHz-5 kHz, the temperature is above 30 ℃, and the peak value of the test voltage is 50V-1000V. The test process does not adopt multi-frequency superposition test, and only collects and analyzes the voltage and current waveforms in one period when the frequency of the excitation source is lower than 1 Hz. To avoid interaction between the tests, the time between the tests was 10 minutes. Adopting two wiring modes for comparison test, wherein the first wiring mode is a tail screen lead of a high-voltage end connection sleeve model of a tester, and measuring a conducting rod of the end connection sleeve model; and the second wiring mode is that the high voltage of the tester is connected with the conducting rod of the bushing model, and the end screen lead of the bushing model is measured and connected.
TABLE 1 radial damp distribution of oiled paper insulation bushing model
| Model serial number | Water content of |
Water content of |
Water content of |
Water content of |
Type of wetting |
| 1# | 4% | 4% | 1% | 1% | Near the guide rod, is affected with |
| 2# | 1% | 1% | 4% | 4% | Near the end screen and affected with damp |
| 3# | 1% | 4% | 4% | 1% | The intermediate laminate is wetted |
| 4# | 1% | 1% | 1% | 1% | Is evenly wetted |
Corresponding polarization current/depolarization current tests were performed for the first four casing models, and fig. 3 shows polarization current/depolarization current-time curves for model # 1 and model # 4. As can be seen from fig. 3(a) and (b), the wetting non-uniformity of the casing model has different effects on the polarization/depolarization currents of the two wiring modes. Under the condition that the sleeve model is uniformly affected with damp, the polarization/depolarization current values measured by adopting the first connection mode and the second connection mode are basically consistent, and the polarization current/depolarization current-time curves of the two connection modes are basically coincident, as shown in fig. 3 (b), in addition, the polarization current/depolarization current-time curves of the two connection modes of the 3# model which are symmetrical to the damp are also basically coincident and are similar to the polarization current/depolarization current-time curves of the 4# model, therefore, if the polarization current/depolarization current-time curves of the oil-paper sleeves of the two connection modes are basically coincident, the oil-paper sleeves can be judged to be uniformly or symmetrically affected with the damp. Under the condition that the sleeve model is not uniformly damped, polarization/depolarization current values measured by adopting a first wiring mode and a second wiring mode are different, and for a model 1# close to a guide rod to be damped, as shown in fig. 3(a), the amplitude of a polarization current/depolarization current-time curve of the first wiring mode is larger than that of the second wiring mode, namely the amplitude of the polarization current/depolarization current-time curve is smaller when the positive half of voltage is firstly added in an area with higher water content; compared with the model No. 1, the amplitude of the polarization current/depolarization current-time curve of the connection mode II of the model No. 2 close to the end screen affected with damp is larger than that of the connection mode I, namely the amplitude of the polarization current/depolarization current-time curve is smaller when the positive half of the voltage is firstly added in an area with higher water content. Therefore, the wetting position of the oilpaper sleeve can be judged by comparing the amplitudes of the polarization current/depolarization current of the first wiring mode and the second wiring mode on the polarization current/depolarization current-time curve, if the amplitude of the polarization/depolarization current of the first wiring mode is larger than that of the polarization/depolarization current of the second wiring mode, the wetting position of the oilpaper sleeve can be judged to be near the guide rod, otherwise, the wetting position of the oilpaper sleeve is near the end screen.
If only the influence of moisture is considered, a large amount of OH-ions and H + ions are accumulated in the region with a large water content in the model No. 1. In the first half cycle (negative polarity) of the excitation voltage in the first wiring scheme, H + ions are first collected in the region near the conductive rod. After a half cycle the polarity is reversed, the H + ions gradually decrease and the OH "ions gradually accumulate after a time delay. In the first half-cycle (positive polarity) of the second connection method, OH ions are first concentrated in a large amount in the vicinity of the conductive rod. Since the mobility of the OH "ions is much smaller than that of the H + ions, the ion concentration in the first half period in the first wiring scheme is relatively greater. And because the ion concentration has a certain hysteresis effect relative to the change of the electric field, the concentration distribution in the first half period basically determines the concentration distribution amplitude in the whole period. Overall, when the positive voltage is applied first in a region with a high water content, the resulting conduction losses are relatively small.
In order to more clearly illustrate the influence of the test electric field strength on the moisture localization method, the electric field strength of the PDC test described in the present application is 7V/mm or more, and preferably, the electric field strengths are 15Vmm, 30V/mm, 45V/mm, 60V/mm, 75V/mm, 90V/mm, 105V/mm, 130V/mm, 145V/mm and 160V/mm. The test electric field strength is equal to the test voltage divided by the radial thickness of the oiled paper sleeve. On the premise of meeting the test electric field intensity, test voltages of 50V, 200V, 500V, 700V, 900V and 1000V are selected, a damp positioning experiment is carried out on the No. 1 oiled paper casing model, and fig. 4 shows polarization current/depolarization current-time curves of the No. 1 oiled paper casing model in different wiring modes at different test voltages. Under the same test voltage, the polarization and depolarization current values of the second connection mode are far smaller than those of the first connection mode, the polarization/depolarization current values of the second connection mode are smaller than those of the first connection mode within 0-1000 s, the absolute value of the difference between the polarization/depolarization current values of the first connection mode is gradually reduced, and finally a certain difference is kept and cannot be coincided. Similarly, experiments are carried out on the No. 2 sleeve model, and experimental results show that under the same test voltage, the polarization and depolarization current values of the second connection mode are far larger than those of the first connection mode, the polarization/depolarization current values of the second connection mode are larger than those of the first connection mode within 0-1000 s, the absolute value of the difference between the polarization/depolarization current values is gradually reduced, and finally a certain difference value is kept to be incapable of being coincided.
As can be seen from fig. 4 (a), when the test voltage is 50V, the polarity inversion of the voltage has less influence on the polarization and depolarization currents, but it can still be determined that the polarization and depolarization currents under the second connection method are smaller than those under the first connection method. With the increase of the test voltage, it can be seen from fig. 4 (b) that the difference between the polarization current and the depolarization current in the two connection modes is significantly increased, and the polarization current in the second connection mode is smaller than that in the first connection mode within 0-1000 s. The depolarization currents of the two wiring modes in fig. 4 (b) gradually tend to be the same as the test time increases, and finally reach a stable value. When the test voltage is increased to 700V, it can be seen from fig. 4 (d) that the polarization and depolarization currents in the second connection mode are much smaller than those in the first connection mode. And the polarized current of the second wiring mode is smaller than that of the first wiring mode within 0-1000 s, but the difference between the polarized current and the first wiring mode is gradually reduced, and finally a certain difference is kept and cannot be superposed. The depolarization currents of the two wiring modes in fig. 4 (d) gradually tend to be the same as the test time increases, and finally reach a stable value. As the test voltage was further increased to 1000V, in fig. 4 (f), the polarity reversal of the voltage had an initial smaller effect on the polarization and depolarization currents, and the difference between the depolarization currents remained and exhibited a trend of decreasing and approaching unity.
To more clearly illustrate the influence of the test temperature on the moisture localization method, moisture localization experiments were performed at the test temperature of 50 ℃ and 60 ℃, and fig. 5 shows polarization current/depolarization current-time curves of a model No. 1 oilpaper casing model in different wiring modes at different temperatures. According to the change law of the polarization current/depolarization current-time curve shown in fig. 5, the number of ions participating in the movement of the electric field is increased due to the increase of the temperature, and a relatively low excitation voltage is only needed in the region near the electrode to achieve a relatively stable concentration gradient. The increase in temperature reduces the viscosity of the oil and the difference in mobility of the positive and negative ions, and thus the difference in depolarizing current is reduced relative to lower temperatures. The region near the electrode accumulates a greater concentration of ions for the same polarization time as the excitation voltage amplitude is greater. During depolarization, ions diffuse from a region with high concentration to a region with low concentration under the action of thermal motion and a built-in electric field. The diffusion rate increases due to the increase in temperature. After the depolarization current difference value is consistent for the first time, the ion concentration difference is large, and the ion motion has a hysteresis effect relative to the change of the built-in electric field, so that the ion concentration difference gradually reaches an equilibrium state after undergoing a reverse overshoot.
To further illustrate the change rule of the polarization current/depolarization current difference-time curves of different wiring modes, PDC tests of different voltages are respectively performed on the model # 1 at a test temperature of 50 ℃ according to the wiring mode one and the wiring mode two, the polarization current/depolarization current difference-time curves of the wiring mode one and the wiring mode two are drawn, and fig. 6 shows the polarization current/depolarization current difference-time curves of the two wiring modes of different test voltages at the same test temperature of the model # 1. The difference value-time curves of the polarization current/depolarization current of different damping models are obviously different, and for a No. 1 model with damping conducting rods, the difference value-time curves of the polarization current/depolarization current of the first connection mode and the second connection mode show a gradually reduced trend along with the increase and decrease of the test time in a first quadrant, and the difference value of the polarization current/depolarization current tends to be 0; for the model 2 with damp end screen, the difference value-time curve of the polarized current/depolarized current of the first connection mode and the second connection mode shows a gradually increasing trend along with the increase and decrease of the test time in the fourth quadrant, and the difference value of the polarized current/depolarized current tends to 0; for the 3# model with symmetric damping and the 4# model with uniform damping, the difference between the polarized current/depolarized current of the first connection mode and the second connection mode tends to 0 within the time range of the test. Conversely, according to the shapes of the polarized current/depolarization current difference-time curves of the two wiring modes of the oilpaper sleeve, the affected position of the oilpaper sleeve can be judged, and if the polarized current/depolarization current difference-time curves of the first wiring mode and the second wiring mode show a gradually reduced trend along with the increase and decrease of the test time in the first quadrant and the polarized current/depolarization current difference tends to be 0, the affected position of the oilpaper sleeve is judged to be close to the guide rod; if the polarized current/depolarization current difference-time curves of the first connection mode and the second connection mode show a gradually increasing trend along with the increase and decrease of the test time in the fourth quadrant and the polarized current/depolarization current difference tends to 0, the fact that the affected position of the oilpaper casing is close to the end screen can be judged; if the difference value of the polarization current/depolarization current of the first connection mode and the second connection mode in the test time range tends to 0, the oil paper sleeve can be judged to be uniformly damped or symmetrically damped. The initial polarization current/depolarization current difference value of the polarization current/depolarization current difference-time curve shows a tendency to increase and then decrease as the test voltage increases, and reaches a maximum value at 700V, as the test pressure increases.
FIG. 7 shows the basic operation flow of the positioning method for wetting the oiled paper casing based on the polarity-reversed time-domain dielectric response. A polarity reversal time domain dielectric response-based oiled paper casing wetting positioning method comprises the following steps:
1) carrying out PDC testing based on polarity reversal time domain dielectric response on the oiled paper bushing, wherein the testing mode is a comparison test adopting two wiring modes, wherein the first wiring mode is that a high-voltage end of a tester is connected with a tail screen lead of the oiled paper bushing and a conducting rod of a measuring end of the oiled paper bushing, the second wiring mode is that a high-voltage end of the tester is connected with a conducting rod of a bushing model, and a tail screen lead of the measuring end of the bushing model;
2) according to the PDC test result obtained in the step 1), drawing a polarization current/depolarization current-time curve of the first connection mode and the second connection mode, or drawing a polarization current/depolarization current difference value-time curve of the first connection mode and the second connection mode;
3) and judging the moist location of the oilpaper sleeve according to the difference of the polarization current/depolarization current-time curves of the first connection mode and the second connection mode obtained in the step 2) or the shape of the polarization current/depolarization current difference-time curve of the first connection mode and the second connection mode obtained in the step 2).
Judging the specific operation mode of the oil paper sleeve to be affected with damp and positioned according to the difference of the polarization current/depolarization current-time curves of the first connection mode and the second connection mode obtained in the step 2): if the amplitude of the polarization current/depolarization current-time curve of the first connection mode is larger than that of the polarization current/depolarization current-time curve of the second connection mode, judging that the position close to the conducting rod is affected with damp; if the amplitude of the polarization current/depolarization current-time curve of the second connection mode is larger than that of the polarization current/depolarization current-time curve of the first connection mode, judging that the position close to the end screen is affected with damp; and if the polarization current/depolarization current-time curve of the first wiring mode is basically overlapped with the polarization current/depolarization current-time curve of the second wiring mode, judging that the oilpaper bushing is uniformly or symmetrically damped.
The specific operation mode for judging the wetting and positioning of the oilpaper bushing according to the shape of the polarization current/depolarization current difference-time curve of the first connection mode and the second connection mode obtained in the step 2) is as follows: if the polarization current/depolarization current difference value of the polarization current/depolarization current difference value-time curve is gradually reduced along with the increase of time and is a positive value, judging that the part close to the conducting rod is affected with damp; if the polarization current/depolarization current difference value of the polarization current/depolarization current difference value-time curve is gradually reduced along with the increase of time and is a negative value, judging that the position close to the end screen is affected with damp; and if the difference value of the polarization current/depolarization current difference value-time curve is basically 0, judging that the oilpaper casing pipe is uniformly or symmetrically affected with damp.
Furthermore, in order to improve the positioning accuracy of the oiled paper sleeve pipe when being affected with dampBefore the PDC test of the oilpaper bushing, the judgment of the wetting uniformity of the oilpaper bushing is carried out, a specific operation flow of the step of evaluating the non-uniformity of the oilpaper bushing is added is shown in figure 8, step 0) is carried out, the wetting non-uniformity of the oilpaper bushing is evaluated, and the wetting uniformity of the oilpaper bushing is judged according to the tan delta-f test curve characteristic of the oilpaper bushing and the complex capacitance C of the oilpaper bushing*-f-curve characteristics or depolarization current difference relaxation time constant-test voltage curve characteristics determine whether the oiled paper bushing is unevenly wetted.
Fig. 9 shows a specific operation flow for evaluating the moisture nonuniformity of the oiled paper bushing according to the tan delta-f test curve characteristic of the oiled paper bushing, which comprises the following specific steps: 011) establishing tan delta-f standard curves of the oiled paper sleeves with different moisture degrees; 012) carrying out PDC test on the oiled paper casing; 013) judging the wetting nonuniformity of the oil paper sleeve, drawing a tan delta-f test curve aiming at the PDC test result in the step 012), comparing the tan delta-f test curve with the tan delta-f standard curve in the step 011), judging that the oil paper sleeve is not uniformly wetted if the tan delta-f test curve and the tan delta-f standard curve have intersection points in the middle and low frequency bands, and otherwise, judging that the oil paper sleeve is uniformly wetted.
FIG. 10 shows the complex capacitance C according to the oiled paper bushing*The specific operation flow of evaluating the wetting nonuniformity of the oilpaper casing by the f curve characteristics comprises the following specific steps: 021) establishing the complex capacitance C of the oiled paper casing pipe with different moisture degrees*-f a standard curve; 022) carrying out PDC test on the oiled paper casing; 023) judging the wetting nonuniformity of the oilpaper casing, and drawing a complex capacitance C according to the PDC test result in the step 022)*F test curve and comparison with complex capacitance C described in step 021)*And comparing f standard curves, if the complex capacitance real part C '-f test curve and the complex capacitance real part C' -f standard curve are upwarped in a low frequency band and the complex capacitance imaginary part C '-f test curve and the complex capacitance imaginary part C' -f standard curve have an intersection point in the low frequency band, judging that the oiled paper sleeve is not uniformly damped, otherwise, judging that the oiled paper sleeve is uniformly damped.
Fig. 11 shows a specific operation flow for evaluating the wetting nonuniformity of the oilpaper casing according to the depolarization current difference relaxation time constant-test voltage curve characteristic of the oilpaper casing, which comprises the following specific steps: 031) testing the depolarization current difference value of the first wiring mode and the second wiring mode of the oilpaper casing pipe under different testing voltages, and extracting relaxation time constants under different testing voltages by means of a Debye model; 032) drawing a curve of the depolarization current difference relaxation time constant and the voltage in the step 031); 033) judging the wetting nonuniformity of the oilpaper sleeves according to the shape of the depolarization current difference relaxation time constant-voltage curve in the step 032), judging the oilpaper sleeves to be wetted unevenly if the depolarization current difference relaxation time constant-voltage curve has a peak value in a high test voltage section, and otherwise judging the oilpaper sleeves to be wetted evenly or symmetrically wetted.
The relaxation time constant is expressed as follows:
wherein k isbBoltzmann constant, 1.380649 × 10-23(ii) a T-absolute temperature/K; epsilonr-the relative dielectric constant of the liquid; n is±-the concentration of positive and negative ions; mu.s±-mobility of positive and negative ions.
The dielectric constant of the macroscopic space charge polarization caused by ion accumulation can evolve into the Debye relaxation equation, meaning that the macroscopic space charge polarization conforms to the Debye single polarization model. Thereby providing a basis with clear physical significance for depolarization current analysis of radial tidal unevenness. However, since the depolarization current contains a plurality of depolarization components, it is still difficult to directly extract a macroscopic space charge depolarization current component from the depolarization current. By changing the way of applying the voltage, a direct relation with the macroscopic space charge polarization can be directly established. Meanwhile, the depolarization current difference has high relevance to the test temperature, the excitation voltage and the radial water content distribution, and the depolarization current difference has low relevance to dipole polarization, interface polarization and the like. The essential reason of the depolarization current difference in the two connection modes is the difference of positive and negative ion mobility, which is represented by the depolarization process of space charge polarization with different polarization degrees in the two connection modes.
According to experimental phenomena, the current difference can be defined as the difference between two macroscopic space charge polarizations of different intensities. The Debye model has higher accuracy in describing a single medium or a single polarization process. Therefore, the characteristic time constant of the depolarization current difference relaxation process can be indirectly used to reflect the relaxation process of concentration polarization. And modeling aiming at the depolarization current difference value only related to the macroscopic space charge polarization by means of a Debye model, and extracting time constants reflecting relaxation polarization characteristics under different voltages so as to indirectly reflect the macroscopic space charge polarization and the initial water content distribution.
Fig. 12 shows the tan delta-f curves of the oiled paper bushings with different average water contents, and compares the tan delta-f curves of the oiled paper bushings with uneven moisture with the tan delta-f curve variation trend of the oiled paper bushings with even moisture, so that the tan delta-f curve variation trend of the oiled paper bushings with uneven moisture can be clearly seen to be obviously different from the tan delta-f curve variation trend of the oiled paper bushings with even moisture, and the non-uniformity of the oiled paper bushings with moisture can be judged according to the difference of the tan delta-f curve variation trends.
FIG. 12 (a) shows the tan delta-f curve for an average moisture content of 2%. The larger the non-uniformity coefficient, the larger the fluctuation of tan delta-f curve around the uniform combination. Compared with a sample which is uniformly damped, the dielectric loss of the medium-high frequency band of the tan delta-f curve of the non-uniform sample is increased, and the low frequency band of the tan delta-f curve of the non-uniform sample is reduced. Both combinations of uneven moisture exposure had significant dielectric loss peaks relative to the uniformly wetted samples, with the loss peak for the 1.10% +2.84% sample combination between 0.01Hz and 0.1Hz and the high band curve trend similar to the 2.84% curve. The loss peak for the sample combination of 0.41+3.91% was between 0.01Hz and 0.1Hz, which was significantly higher than the 2.84% curve. The sample combination of 0.41+3.91% has a greater non-uniformity coefficient than the sample combination of 1.10% +2.84% and the tan delta f curve has a greater frequency of onset of loss peaks. The interfacial polarization time constant for the sample combination of 0.41+3.91% decreased. A common curve intersection point exists between the two combinations with uneven moisture and the sample with even moisture, and the frequency corresponding to the intersection point is approximately 0.0046 Hz.
FIG. 12 (b) shows the tan. delta. -f curve for an average water content of 3%. The larger the non-uniformity coefficient, the larger the fluctuation of tan delta-f curve around the uniform combination, with the largest fluctuation of the sample combination curve being 0.41+ 6.11%. The high frequency portion of the tan delta-f curve for the 0.41+6.11% sample gradually approximates the tan delta-f curve for the 6.11% sample, while the low frequency portion gradually approximates the tan delta-f curve for the 0.41% sample. The tan delta-f curve trends for the 1.10% +5.08% sample combination and the dry +6.11% sample combination are similar. While the curves are less similar for the 2.03% +3.91% sample combination versus the dry +6.11% sample combination. The similarity of the three sets of curves indicates that the tan delta-f curve trends are similar for the combinations with closer non-uniformity coefficients. The initial frequency of the loss peak of each curve gradually increases along with the increase of the uneven coefficient, and the time constant of the corresponding interface polarization is reduced. A common curve intersection point exists between the three combinations with uneven moisture and the samples with even moisture, and the frequency corresponding to the intersection point is approximately 0.15 Hz.
FIG. 12 (c) shows the tan. delta. -f curve for an average water content of 4%. Similar to the curve law in fig. 12 (a) and 12 (b), the peak-to-peak loss frequency of the curves increases with the increase of the uneven coefficient, and the two groups of uneven moisture curves have obvious intersection points with the uniform moisture curves, and the intersection point frequency is 1 Hz.
Fig. 13 shows the C × f curves of the oilpaper casings with different average water contents, and compares the C × f curves of the oilpaper casings which are not uniformly wetted with water with the C × f curves of the oilpaper casings which are uniformly wetted with water, so that the C × f curve variation trend of the oilpaper casings which are not uniformly wetted with water is clearly different from the C × f curve variation trend of the oilpaper casings which are uniformly wetted with water, and the non-uniformity of the oilpaper casings which are wetted with water can be judged by combining the variation trends of the real complex capacitance part C' and the imaginary complex capacitance part C ″ along with the frequency.
Fig. 13(a) shows the C x-f curve for an average water content of 2%. The real part of the complex capacitance C' of the sample combination of 0.41+3.91% is larger than that of the sample combination of 1.10% +2.84%, 2% +2% and 1.10% +2.84% are nearly coincident in the high frequency band, and the latter is slightly increased in the low frequency band. The interfacial polarization of the sample combination of 0.41+3.91% corresponds to a greater additional capacitance. The imaginary part C' of the complex capacitance in FIG. 13(a) varies greatly, but substantially similarly to the tan delta-f curve.
Fig. 13 (b) shows the C x-f curve for an average water content of 3%. The larger the uneven coefficient of the sample combination is, the more obvious the low-frequency-band rising of the complex capacitance real part C' -f curve is, and the larger the corresponding interface polarization additional capacitance is. Wherein the uneven coefficient of 0.41+6.11% of the sample is the largest, and the low-frequency band rise of the C' -f curve is the most obvious. The curves of the real part of complex capacitance C' -f of 1.10% +5.08%, 2.03% +3.91% and 0.41+6.11% form a closed loop curve of a "spindle" shape in the low frequency part, and the frequency corresponding to the maximum diameter of the spindle-shaped curve is the same as the intersection frequency of the curve of fig. 12 (C).
Fig. 13 (C) shows the C x-f curve for an average water content of 4%. Similar to the curve law in fig. 13(a) and 13 (b), there are obvious intersections between the two sets of non-uniform complex capacitance imaginary part C "curves and the uniform complex capacitance imaginary part C" curves.
Fig. 14 shows the curves of depolarization current difference relaxation time constants and test voltages of the oilpaper bushings of different wetting models, and the wetting uniformity of the oilpaper bushings can be judged according to the shapes of the curves. The 2 layers in the 5# sleeve model are undried paper layers, the water content is about 5%, and the outer layer is completely dried insulating paper, and the water content is about 0.5%. The increase in radial wetting non-uniformity results in an overall decrease in the relaxation time constant of the depolarization current difference, meaning that the combination with the larger concentration difference tends to a steady state distribution more quickly under the action of thermal motion. Because the testing temperature is the same, the relative humidity unevenness is increased, the ion concentration accumulated near the electrode is larger, and in the depolarization process, the built-in electric field caused by the ion concentration difference is larger, and the ion distribution is easier to reach the steady state balance. This is consistent with the rules described in the relaxation time constant relation above.
By combining the experimental results and the oil paper sleeve wetting positioning method, the radial wetting position of the oil paper sleeve on site can be accurately and quickly judged, and guiding suggestions are provided for on-site maintenance, maintenance and diagnosis of the oil paper sleeve equipment.
The above description is only an example of the present application, and the protection scope of the present application is not limited by these specific examples, but is defined by the claims of the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the technical idea and principle of the present application should be included in the protection scope of the present application.
Claims (12)
1. A polarity reversal time domain dielectric response-based oiled paper casing wetting positioning method is characterized by comprising the following steps:
1) carrying out PDC testing based on polarity reversal time domain dielectric response on the oiled paper bushing, wherein the testing mode is a comparison test adopting two wiring modes, wherein the first wiring mode is that a high-voltage end of a tester is connected with a tail screen lead of the oiled paper bushing and a conducting rod of the oiled paper bushing is measured and connected, the second wiring mode is that the high-voltage end of the tester is connected with the conducting rod of the oiled paper bushing and the tail screen lead of the oiled paper bushing is measured and connected;
2) according to the PDC test result obtained in the step 1), drawing a polarization current/depolarization current-time curve of the first connection mode and the second connection mode, or drawing a polarization current/depolarization current difference value-time curve of the first connection mode and the second connection mode;
3) and judging the moist location of the oilpaper sleeve according to the difference of the polarization current/depolarization current-time curves of the first connection mode and the second connection mode obtained in the step 2) or the shape of the polarization current/depolarization current difference-time curve of the first connection mode and the second connection mode obtained in the step 2).
2. The method for positioning the oiled paper bushing affected with damp based on the dielectric response of the polarity reversal time domain as claimed in claim 1,
judging the specific operation mode of the oil paper sleeve to be affected with damp and positioned according to the difference of the polarization current/depolarization current-time curves of the first connection mode and the second connection mode obtained in the step 2): if the amplitude of the polarization current/depolarization current-time curve of the first connection mode is larger than that of the polarization current/depolarization current-time curve of the second connection mode, judging that the position close to the conducting rod is affected with damp; if the amplitude of the polarization current/depolarization current-time curve of the second connection mode is larger than that of the polarization current/depolarization current-time curve of the first connection mode, judging that the position close to the end screen is affected with damp; and if the polarization current/depolarization current-time curve of the first wiring mode is basically overlapped with the polarization current/depolarization current-time curve of the second wiring mode, judging that the oilpaper bushing is uniformly or symmetrically damped.
3. The method for positioning the oiled paper bushing affected with damp based on the dielectric response of the polarity reversal time domain as claimed in claim 1,
the specific operation mode for judging the wetting and positioning of the oilpaper bushing according to the shape of the polarization current/depolarization current difference-time curve of the first connection mode and the second connection mode obtained in the step 2) is as follows: if the polarization current/depolarization current difference value of the polarization current/depolarization current difference value-time curve is gradually reduced along with the increase of time and is a positive value, judging that the part close to the conducting rod is affected with damp; if the polarization current/depolarization current difference value of the polarization current/depolarization current difference value-time curve is gradually reduced along with the increase of time and is a negative value, judging that the position close to the end screen is affected with damp; and if the difference value of the polarization current/depolarization current difference value-time curve is basically 0, judging that the oilpaper casing pipe is uniformly or symmetrically affected with damp.
4. The method for positioning the oiled paper bushing affected with damp based on the dielectric response of the polarity reversal time domain as claimed in claim 1,
the electric field intensity of the PDC test in the step 1) is more than 7V/mm.
5. The method for positioning oiled paper bushings affected with moisture based on polarity reversal time domain dielectric response as claimed in claim 4,
the electric field intensity of the PDC test in the step 1) is 15V/mm, 30V/mm, 45V/mm, 60V/mm, 75V/mm, 90V/mm, 105V/mm, 130V/mm, 145V/mm or 160V/mm.
6. The method for positioning the oiled paper bushing affected with damp based on the dielectric response of the polarity reversal time domain as claimed in claim 1,
the testing temperature of the PDC testing in the step 1) is more than 30 ℃.
7. The method for positioning oiled paper bushings affected with moisture based on polarity reversal time domain dielectric response as claimed in claim 6,
the PDC test of step 1) has a test temperature of 40 ℃, 50 ℃ or 60 ℃.
8. The method for positioning the oiled paper casing pipe under the damp based on the polarity reversal time domain dielectric response as claimed in claim 1), further comprising, before the step 1):
step 0) evaluating the wetting nonuniformity of the oiled paper sleeve, and testing the curve characteristic according to the tan delta-f of the oiled paper sleeve and the complex capacitance C of the oiled paper sleeve*-f-curve characteristics or depolarization current difference relaxation time constant-test voltage curve characteristics determine whether the oiled paper bushing is unevenly wetted.
9. The method for positioning oiled paper bushings in wet condition based on the dielectric response of polarity reversal time domain as claimed in claim 8,
the specific steps for evaluating the wetting nonuniformity of the oiled paper sleeve according to the tan delta-f test curve characteristic of the oiled paper sleeve are as follows:
011) establishing tan delta-f standard curves of the oiled paper sleeves with different moisture degrees;
012) carrying out PDC test on the oiled paper casing;
013) judging the wetting nonuniformity of the oil paper sleeve, drawing a tan delta-f test curve aiming at the PDC test result in the step 012), comparing the tan delta-f test curve with the tan delta-f standard curve in the step 011), judging that the oil paper sleeve is not uniformly wetted if the tan delta-f test curve and the tan delta-f standard curve have intersection points in the middle and low frequency bands, and otherwise, judging that the oil paper sleeve is uniformly wetted.
10. The method for positioning oiled paper bushings in wet condition based on the dielectric response of polarity reversal time domain as claimed in claim 8,
according to the complex capacitance C of the oiled paper sleeve*The specific steps for evaluating the wetting nonuniformity of the oilpaper casing by the f curve characteristics are as follows:
021) establishing the complex capacitance C of the oiled paper casing pipe with different moisture degrees*-f a standard curve;
022) carrying out PDC test on the oiled paper casing;
023) judging the wetting nonuniformity of the oilpaper casing, and drawing a complex capacitance C according to the PDC test result in the step 022)*F test curve and comparison with complex capacitance C described in step 021)*And comparing f standard curves, if the complex capacitance real part C '-f test curve and the complex capacitance real part C' -f standard curve are upwarped in a low frequency band and the complex capacitance imaginary part C '-f test curve and the complex capacitance imaginary part C' -f standard curve have an intersection point in the low frequency band, judging that the oiled paper sleeve is not uniformly damped, otherwise, judging that the oiled paper sleeve is uniformly damped.
11. The method for positioning oiled paper bushings in wet condition based on the dielectric response of polarity reversal time domain as claimed in claim 8,
the specific steps for evaluating the wetting nonuniformity of the oilpaper casing according to the depolarization current difference relaxation time constant-test voltage curve characteristic of the oilpaper casing are as follows:
031) testing the depolarization current difference value of the first wiring mode and the second wiring mode of the oilpaper casing pipe under different testing voltages, and extracting relaxation time constants under different testing voltages by means of a Debye model;
032) drawing a curve of the depolarization current difference relaxation time constant and the voltage in the step 031);
033) judging the wetting nonuniformity of the oilpaper sleeves according to the shape of the depolarization current difference relaxation time constant-voltage curve in the step 032), judging the oilpaper sleeves to be wetted unevenly if the depolarization current difference relaxation time constant-voltage curve has a peak value in a high test voltage section, and otherwise judging the oilpaper sleeves to be wetted evenly or symmetrically wetted.
12. The method for positioning oiled paper bushings in wet condition based on the dielectric response of polarity reversal time domain as claimed in claim 8,
the expression of the depolarization current difference relaxation time constant is as follows:
wherein k isbBoltzmann constant, 1.380649 × 10-23(ii) a T-absolute temperature/K; epsilonr-the relative dielectric constant of the liquid; n is±-the concentration of positive and negative ions; mu.s±-mobility of positive and negative ions; d-radial thickness of the oilpaper sleeve.
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