A calculation method for the noise of a dry-type capacitor

Abstract

The present invention discloses a calculation method for the noise of a dry-type capacitor in the technical field of dry-type capacitor noise calculation, which includes the following steps: S1, establishing a noise calculation model for circular components; S2, establishing a capacitor noise calculation model based on S1; S3, establishing a dry-type capacitor noise calculation model based on S2. The present invention studies the influencing factors of the noise of the dry-type capacitor, and then establishes a calculation model and method for the noise of the dry-type capacitor.

Description

Technical Field

[0001] The present invention relates to the technical field of dry capacitor noise calculation, and specifically provides a method for calculating the noise of dry capacitors. Background Art

[0002] Noise has long been prominent and has always been a concern in capacitors for UHV DC power transmission. Especially in recent years, with the improvement of people's demand for a better life, the noise problem has become even more important. Regarding the noise problem of capacitors for UHV DC power transmission, previous studies have only focused on oil-immersed capacitors.

[0003] With the technological progress of dry self-healing capacitors, in recent years, some people have begun to pay attention to some problems of dry self-healing metallized film capacitors used in UHV capacitors, inevitably involving the noise problem of dry capacitors. Generally speaking, solids transmit pressure, liquids transmit pressure intensity, and solids are stronger in transmitting sound waves than liquids. Moreover, due to the tightness of dry capacitor components and the solidification of the insulation to the shell, the noise problem should be more prominent than that of oil-immersed capacitors. However, at room temperature, the noise of dry self-healing capacitors is much smaller than that of oil-immersed capacitors. It is necessary to study the influencing factors of dry capacitor noise and then establish a calculation model and method for dry capacitor noise. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating the noise of dry capacitors to solve the problem of the lack of a calculation model and method for dry capacitor noise proposed in the above background art.

[0005] To achieve the above purpose, the present invention provides the following technical solution: A method for calculating the noise of dry capacitors includes the following steps.

[0006] S1. Establish a noise calculation model for circular components;

[0007] The circular components are wound by a fully automatic constant-tension winding machine with a constant linear velocity, and the material is metallized polypropylene film; after winding, the pressure between the film layers satisfies: being proportional to the winding tension, proportional to the outer diameter of the component, and inversely proportional to the core rod diameter; the pressure between the polypropylene film layers in the circular component is calculated by the following formula:

[0008]

[0009] In formula (1): P n is the pressure on the nth layer of film, kPa; B is the correction coefficient of the pressure between the calculated value and the measured value of the film layer; k is the winding tension coefficient; D is the outer diameter of the circular component, mm; D n is the diameter of the component corresponding to the nth layer of film, mm.

[0010] S2. Establish a capacitor noise calculation model based on S1;

[0011] The plate pressure of the capacitor, that is, the electric force per unit area, is calculated according to the following formula:

[0012]

[0013] In formula (2): P1 is the electric force per unit area on the capacitor plate, that is, the pressure, Pa; ε0 = 8.85×10 -12 is the permittivity of free space, F / m; ε r is the relative permittivity of the dielectric between the capacitor plates; E is the electric field strength on the capacitor dielectric, MV / m;

[0014] Since the noise requirement of the capacitor for UHVDC transmission is the noise under a given current, considering E = U y / d = I / (ωCd), substituting into formula (2) we can get:

[0015]

[0016] In formula (3): ω is the angular frequency of the power supply, rad / s; d is the thickness of the dielectric between the component plates, μm; C is the capacitance of the capacitor component, μF;

[0017] The capacitance of the capacitor component can be calculated according to the following formula:

[0018]

[0019] In formula (4): S1 is the plate area of the component, and the others are the same as formula (3). Substituting formula (4) into formula (3) and simplifying, we can get:

[0020]

[0021] In formula (5): where V = S1d, approximately the volume of the polypropylene film of a single component; the relationship between the capacitance of the capacitor and temperature is as follows:

[0022] C = C0(1 - |α c |ΔT) (6)

[0023] In formula (6): C is the capacitance at temperature T; C0 is the component capacitance at the reference temperature. The reference temperature of the capacitor for UHVDC transmission projects is 25°C; α c is the capacitance temperature coefficient. For all-film capacitors, α c is approximately -4×10 -4 / K; for dry self-healing capacitors, α c = -2×10 -4 / K, ΔT is the temperature rise relative to the reference temperature, ΔT = T - 25,

[0024] Substituting Equation (6) into Equation (5) gives:

[0025]

[0026] In Equation (7): P1 is the electric field force or pressure per unit area between the plates of the element, Pa; is the electric field force pressure at the reference temperature, Pa; β T is the temperature coefficient of the electric field force pressure;

[0027] S3. Establish a dry capacitor noise calculation model based on S2;

[0028] The main feature of the circular element of the dry capacitor is that the compaction coefficient of the element is large and close to 1; according to the noise calculation model of the circular element defined in S1, the pressure between the film layers of the circular element is as shown in Equation (1). In Equation (1), since D = d0 + 4Nd, D n = d0 + 4nd, substituting into Equation (1) gives:

[0029]

[0030] For the pressure F2 between the plates brought by the winding tension of the circular element, it can be calculated by multiplying the pressure of Equation (8) by the area of the plate, that is:

[0031]

[0032] Considering S 1n = πD n b, substituting into Equation (9) gives:

[0033]

[0034] Since Substituting into Equation (10) gives:

[0035] F2 = 20BπdbN(N + 1) = 20BπT d N(N + 1) (11)

[0036] The average pressure between the plates generated by F2 is:

[0037]

[0038] According to the noise theory of the capacitor, the propagation direction of its noise is the same as the vibration direction and belongs to the longitudinal wave; for the circular element, the electric field force acts along the radial direction; according to the generalized Hooke's law, the stress on the nth layer of film can be calculated by the following formula:

[0039] σn = E r (T)ε n (13)

[0040] In formula (13): σ n is the stress on the nth layer of film, MPa; E r (T) is the elastic modulus of the polypropylene film, MPa; ε n is the deformation of the nth layer of film;

[0041] Comparing formula (12) and formula (13), it can be seen that P2 and E r (T) are both the pressures in the thickness direction of the polypropylene film and should be equal, that is:

[0042]

[0043] Formula (14) shows that the pressure between the film layers of the circular element generated by the winding factor is the equivalent elastic modulus.

[0044] Compared with the prior art, the beneficial effects of the present invention are: by studying the influencing factors of the noise of dry capacitors, and then establishing a calculation model and method for the noise of dry capacitors. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a schematic diagram of the noise calculation model of the circular element of the present invention;

[0046] Figure 2 is a schematic diagram of the noise calculation model of the capacitor element of the present invention;

[0047] Figure 3 is the relationship between the elastic modulus of the polypropylene material and the temperature in the present invention;

[0048] Figure 4 is a data table of the noise test of the dry self-healing capacitor at four temperature points of -25°C, 25°C, 55°C, and 80°C;

[0049] Figure 5 is a curve of the relationship between noise and temperature. DETAILED DESCRIPTION OF THE INVENTION

[0050] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0051] This invention studies the noise of dry self-healing capacitors. Based on circular components, starting from the pressure inside the circular components, it analyzes the influence of the pressure between the film layers inside the circular components on their noise and the variation law of the noise caused by temperature changes. First, the root cause of the capacitor generating noise is the action of the electric field force between the electrodes of the component; second, there is pressure between the film layers inside the circular component, which is the key difference between dry capacitors and oil-immersed capacitors; third, the influence of temperature on the pressure between the film layers of the circular component of the dry capacitor is definitely increasing, but whether it strengthens or weakens the influence on the noise requires the introduction of new concepts and new ideas.

[0052] The circular component studied in this invention is made of metallized polypropylene film material and wound by a fully automatic winding machine with constant tension and constant linear speed. The research takes the circular component as the fulcrum and verifies through the noise test of the capacitor unit, and finally obtains the correct noise calculation model and method for the circular component.

[0053] For the circular component of the dry capacitor, its noise calculation model uses cylindrical coordinates. The length direction of the component (corresponding to the width direction of the film) is defined as the z direction or the axial direction, and the radial direction of the component is the thickness direction of the film. The winding tension direction is the tangential direction in the radial direction. As Figure 1 shown.

[0054] The noise calculation model of the circular component adopts the following basic assumptions:

[0055] The circular component is wound by a fully automatic winding machine with constant tension and constant linear speed, and the material is metallized polypropylene film. The pressure between the film layers satisfies the following conditions: proportional to the winding tension, proportional to the outer diameter of the component, and inversely proportional to the core rod diameter. The pressure between the polypropylene film layers in the circular component is related to the number of turns it is in and will change with the change of the outer diameter of the component. At the same time, a correction coefficient is considered. As shown in the following formula:

[0056]

[0057] In formula (1): P n is the pressure on the nth layer of film, kPa; B is the correction coefficient of the pressure between the calculated value and the measured value of the film layer; k is the winding tension coefficient; D is the outer diameter of the circular component, mm; D n is the component diameter corresponding to the nth layer of film, mm.

[0058] The electric field force density of the component electrode plate The deformation generated on the dielectric between the electrodes is within the elastic change range of the material, proportional to the vibration generated by the capacitor, and positively correlated with the size of the capacitor noise;

[0059] The elastic modulus of the polypropylene film plays an inhibitory role in the electric field force vibration caused by the charging of the circular component, and is characterized by the deformation of the material;

[0060] The internal mechanical force generated by the winding tension of the circular component suppresses the vibration generated inside the circular component, which is also characterized by the material deformation amount, and this part of the pressure is equivalent to the additional elastic modulus.

[0061] The expansion of the polypropylene film due to the circular component being heated suppresses the vibration of the electrode plate, and the generated pressure is equivalent to the additional elastic modulus.

[0062] The elastic modulus of the polypropylene material changes with temperature. After superimposing the pressure between the film layers and the additional pressure generated by heating, its deformation amount is still within the elastic change range, and the change rule satisfies the temperature characteristics of the polypropylene material.

[0063] Analysis of the influence of temperature on capacitor noise;

[0064] The electric field force is the root cause of capacitor noise. The pressure on the electrode plate of the capacitor, that is, the electric field force per unit area, can be calculated by the following formula:

[0065]

[0066] In formula (2): P1 is the electric field force per unit area on the capacitor electrode plate, that is, the pressure, Pa; ε0 = 8.85 * 10 -12 is the permittivity of free space, F / m; ε r is the relative permittivity of the dielectric between the capacitor electrodes; E is the electric field strength on the capacitor dielectric, MV / m.

[0067] It can be seen from formula (2) that the larger the relative permittivity of the dielectric between the electrodes, the greater the electric field force on the electrode plate, and the greater the vibration amplitude of the electrode plate; the higher the electric field strength of the dielectric, the greater the electric field force pressure on the electrode plate.

[0068] Since the noise requirement of the capacitor for UHV DC transmission is the noise under a given current, considering E = U y / d = I / (ωCd), substituting it into formula (2) can obtain:

[0069]

[0070] In formula (3): ω is the angular frequency of the power supply, rad / s; d is the thickness of the dielectric between the component electrodes, μm; C is the capacitance of the capacitor component, μF. The rest is the same as formula (2).

[0071] 3.2 Influence of temperature on electric field force

[0072] The capacitance of the capacitor component can be calculated by the following formula:

[0073]

[0074] In Equation (4): S1 is the plate area of the component. The rest is the same as in Equation (3). Substituting Equation (4) into Equation (3) and simplifying gives:

[0075]

[0076] In Equation (5): where V = S1d, approximately the volume of the polypropylene film of a single component. Obviously, for a specific capacitor, A is a constant. In addition, the current - frequency ratio I / f is independent of temperature, so is also a constant independent of temperature. It can be considered that the change in the unit electric field force on the component plate with temperature is only inversely proportional to the capacitance.

[0077] It can be seen from Equation (5) that the pressure on the capacitor plate is proportional to the current - frequency ratio (the ratio of current to frequency); and inversely proportional to the capacitance of the capacitor. As the temperature rises, the capacitance becomes smaller and the noise of the capacitor becomes larger. The relationship between the capacitance of the capacitor and temperature is as follows:

[0078] C = C0(1 - |α c |ΔT) (6)

[0079] In Equation (6): C is the capacitance at temperature T; C0 is the component capacitance at the reference temperature. The reference temperature for the capacitor used in the UHVDC transmission project is 25°C; α c is the capacitance temperature coefficient. For all - film capacitors, α c is about - 4×10 -4 / K; for dry self - healing capacitors, α c = - 2×10 -4 / K. ΔT is the temperature rise relative to the reference temperature, ΔT = T - 25.

[0080] Substituting Equation (6) into Equation (5) gives:

[0081]

[0082] In Equation (7): P1 is the electric field force or pressure per unit area between the component plates, Pa; is the electric field force pressure at the reference temperature, Pa; β T is the temperature coefficient of the electric field force pressure. The rest is the same as before.

[0083] It can be seen from Equation (7) that the plate pressure characterizing the capacitor noise increases with the increase of temperature.

[0084] Analysis of the influence of temperature on the noise of dry capacitors:

[0085] The main feature of the dry-type capacitor circular element is that the compaction coefficient of the element is large and close to 1; according to the noise calculation model of the circular element defined above, the pressure between the film layers of the circular element is as shown in Equation (1). In Equation (1), since D = d0 + 4Nd, D n = d0 + 4nd, substituting it into Equation (1) we can get:

[0086]

[0087] For the pressure F2 between the electrodes brought by the winding tension of the circular element, it can be calculated by multiplying the pressure of Equation (8) by the area of the electrode plate. That is:

[0088]

[0089] Considering S 1n = πD n b, substituting it into Equation (9) we can get:

[0090]

[0091] Since Substituting it into Equation (10) we can get:

[0092] F2 = 20BπdbN(N + 1) = 20BπT d N(N + 1) (11)

[0093] The average pressure between the electrodes generated by F2 is:

[0094]

[0095] According to the noise theory of the capacitor, the propagation direction of its noise is consistent with the vibration direction and belongs to the longitudinal wave; for the circular element, referring to Figure 1 , the electric field force acts along the radial direction; according to the generalized Hooke's law, the stress on the nth layer of film can be calculated by the following formula:

[0096] σ n = E r (T)ε n (13)

[0097] In Equation (13): σ n is the stress on the nth layer of film, MPa; E r (T) is the elastic modulus of the polypropylene film, MPa; ε n is the deformation of the nth layer of film.

[0098] Comparing Equation (12) and Equation (13), it can be seen that both P2 and E r (T) are the pressures in the thickness direction of the polypropylene film and should be equal, that is:

[0099]

[0100] Equation (14) shows that the pressure between the film layers of the circular element caused by factors such as winding is the equivalent elastic modulus.

[0101] The influence of temperature on polypropylene materials:

[0102] The elastic modulus of polypropylene materials has a great correlation with temperature. At high temperatures, the elastic modulus of polypropylene materials is much smaller than at room temperature. The elastic modulus of polypropylene materials changes with temperature. After fitting with the least squares method, the relationship between the elastic modulus of polypropylene materials and temperature change is a straight line, as Figure 3 shown. Figure 3 In, the unit of the elastic modulus is MPa. Generally, the elastic modulus of polypropylene materials is in the range of (1700 - 2500) MPa.

[0103] According to Figure 3 , the change of the elastic modulus of polypropylene materials with temperature can be expressed by the following formula:

[0104] E r (T) = -13.9T + 1353.8 (15)

[0105] In Equation (15): T - the temperature of the polypropylene material, °C; E r (T) - the elastic modulus of the polypropylene material at temperature T, MPa.

[0106] The pressure between the film layers of the circular element due to temperature:

[0107] In the circular element, as the temperature increases, the volume of the circular element expands, which is equivalent to stretching the polypropylene film, and stretching will increase the pressure between the film layers. Assuming that the thickness expansion coefficient of the polypropylene film is α, for the nth turn of the circular element, at temperature T n below, the increase in its circumference is:

[0108] ΔL n / L0 = (L n -L0) / L0 = ΔTα (16)

[0109] In Equation (16): ΔT n = T n -T0, where T n ——the temperature of the circular element; T0——the reference temperature of the circular element, synchronized with Equation (2), and T0 = 25 °C can be taken; ΔL n = L n -L0——the increase in the circumference of the circular element at temperature T n ; L n ——at temperature T nThe circumference of the nth turn of the lower circular element; L0——The circumference of the nth turn of the circular element at temperature T0; D n ——The diameter of the nth turn of the circular element; α——The thickness expansion coefficient of the polypropylene film.

[0110] According to Standard GB / T 13542.2, it can be obtained that: That is:

[0111] P nr =E r (T)e T =E r (T)ΔTα (17)

[0112] In formula (17): P nr ——The additional pressure caused by heating the circular element, MPa; e T ——The elongation rate of the polypropylene film caused by heating the circular element. The rest is the same as before.

[0113] Calculation and test cases of the noise of dry-type capacitors;

[0114] Analysis of material strain caused by temperature:

[0115] According to the noise calculation model of the circular element, the pressure between the film layers of the circular element should include the pressure between the film layers caused by the winding tension of the element in formula (1) and the pressure caused by heating the element in formula (17). That is:

[0116] P nT =P2+P nr (18)

[0117] Substituting formula (14) and formula (17) into formula (18), it can be obtained that:

[0118]

[0119] According to the previous model, the calculation result of formula (19) is the additional elastic modulus, which inhibits the vibration between the electrodes. Considering the elastic modulus of the polypropylene film itself, the total equivalent elastic modulus of the circular element is:

[0120] E rz (T)=E r (T)+P nT =(1+ΔTα)E r (T)+E r2 (20)

[0121] The vibration deformation amount generated by the plate pressure of the circular element can be calculated according to the following formula:

[0122]

[0123] According to the circular element noise calculation model, the noise of the circular element can be calculated by the following formula:

[0124] L w = 10log(ε d ) (22)

[0125] The noise of the capacitor unit can be calculated by the following formula:

[0126] L wd = L w + log(N) (23)

[0127] The typical calculated values of formulas (22) to (23) are shown in Figure 4 , and the curve of the relationship between noise and temperature is as shown in Figure 5 .

[0128] Measurement results and analysis of the noise of dry-type capacitors at different temperatures;

[0129] According to the previous analysis, the noise of the dry-type self-healing capacitor was tested at four temperature points of -25°C, 25°C, 55°C, and 80°C, and the results are as shown in Figure 4 .

[0130] According to Figure 4 the data plotted curve is as shown in Figure 5 .

[0131] From Figure 4 and Figure 5 it can be seen that the measured values of the capacitor noise are consistent with the theoretical calculated values and basically coincide. It shows that the circular element noise calculation model assumed in this paper is basically correct and can be used for qualitatively calculating the noise of circular elements and their capacitor units, but there is still a gap for quantitative calculation.

Claims

1. A method for calculating the noise of a dry capacitor, characterized in that: The following steps are included: S1. Establish a noise calculation model for circular elements; The round element is wound by a fully automatic winding machine with constant tension and constant linear speed, and the material is a metallized polypropylene film; the pressure between film layers after winding satisfies: proportional to the winding tension, proportional to the outer diameter of the element, and inversely proportional to the diameter of the mandrel; the pressure between film layers of the polypropylene film in the round element is calculated by the following formula: （1） In formula (1): P n For the n Pressure on the membrane, kPa; B is the correction factor of the calculated and measured inter-membrane pressure; k is the winding tension coefficient; D is the outer diameter of the circular element, mm; D n For the n Component diameter corresponding to the layer film, mm; S2, establish a capacitor noise calculation model based on S1; The plate pressure of the capacitor, that is, the electric field force per unit area, is calculated as follows: （2） In formula (2): P 1 is the electric field force per unit area on the capacitor plate, that is, the pressure, Pa; is the dielectric constant in vacuum, F / m; is the relative dielectric constant of the capacitor interelectrode medium; E is the field strength on the capacitor dielectric, MV / m; Since the noise requirement of capacitors for UHV DC transmission is the noise at a given current, E = I / (ω Cd) , substituting into formula (2) we can get: （3） In formula (3): ω is the angular frequency of the power supply, rad / s; d is the thickness of the dielectric between the electrodes of the element, µ m; C is the capacitance of the capacitor element, µ F; The capacitance of a capacitor element can be calculated as follows: （4） In formula (4): S 1 is the plate area of ​​the element, and the rest is the same as formula (3). Substituting formula (4) into formula (3) and simplifying it, we can get: （5） In formula (5): in V=S 1 d , which is approximately the volume of the polypropylene film of a single element; the relationship between the capacitance and temperature of the capacitor is as follows: （6） In formula (6): C For the temperature T The capacitance below; C 0 is the component capacitance at the reference temperature. The reference temperature of capacitors used in UHV DC transmission projects is 25°C. is the capacitance temperature coefficient, for full film capacitors, Approximately -4*10 -4 / K; For dry self-healing capacitors, , is the temperature rise relative to the reference temperature, , Substituting formula (6) into formula (5) we can obtain: （7） In formula (7): P 1 is the electric field force or pressure per unit area between the component plates, Pa; is the electric field pressure at reference temperature, Pa; is the temperature coefficient of the electric field pressure; S3, establish a dry capacitor noise calculation model based on S2; The main feature of the circular element of the dry capacitor is that the element has a large compression coefficient, which is close to 1. According to the noise calculation model of the circular element defined by S1, the pressure between the film layers of the circular element is shown in formula (1). In formula (1), due to , substituting into formula (1) we can get: （8） The pressure between the plates caused by the winding tension of the round element F 2, we can multiply the pressure in formula (8) by the area of ​​the plate To calculate, that is: （9） Considering , substituting into formula (9) we can get: （10） because , substituting into formula (10) we can get: （11） Depend on F 2 The average pressure between the plates generated is: （12） According to the noise theory of capacitors, the propagation direction of the noise is consistent with the vibration direction, which belongs to the longitudinal wave; for circular elements, the electric field force acts in the radial direction; according to the generalized Hooke's law, for the n The stress on the film can be calculated as follows: （13） In formula (13): σ n For the n Stress of the film, MPa; E r (T) is the elastic modulus of polypropylene film, MPa; ε n For the n Deformation of the membrane; Comparing formula (12) and formula (13), we can see that P 2 and E r (T) The pressure on the polypropylene film in the thickness direction should be equal, that is: （14） Formula (14) shows that the pressure between the circular element membrane layers caused by the winding factor is the equivalent elastic modulus; The change of elastic modulus of polypropylene material with temperature can be expressed by the following formula: （15） In formula (15): T ——Temperature of polypropylene material, °C; ——Polypropylene material at temperature T Elastic modulus under, MPa; The pressure between the membrane layers of the circular element due to temperature: In the round element, as the temperature rises, the volume of the round element expands, which is equivalent to stretching the polypropylene film. Stretching will increase the pressure between the film layers. Assuming that the thickness expansion coefficient of the polypropylene film is α , for the circular element n Circle, at temperature The increase in its perimeter is: （16） In formula (16): ,in - temperature of the circular element; ——The reference temperature of the circular element, synchronized with equation (6), ; ——At temperature Increase in the circumference of the lower circular element; ——At temperature Lower round element n the circumference of the circle; ——At temperature Lower round element n the circumference of the circle; According to the standard GB / T 13542.2, we can get: ,Right now: （17） In formula (17): P nr ——Additional pressure caused by heating of round element, MPa; - elongation of the polypropylene film due to heating of the round element; Calculation of dry capacitor noise: Analysis of material strain due to temperature: According to the circular element noise calculation model, the pressure between the membrane layers of the circular element should include the pressure between the membrane layers caused by the winding tension of the element in equation (14) and the pressure caused by the heating of the element in equation (17), that is: （18） Substituting equation (14) and equation (17) into equation (18), we can obtain: （19） According to the previous model, the calculation result of formula (19) is the additional elastic modulus, which has a suppressive effect on the vibration between the plates. Considering the elastic modulus of the polypropylene film itself, the total equivalent elastic modulus of the circular element is: （20） The vibration deformation caused by the plate pressure of the circular element can be calculated as follows: （21） According to the circular element noise calculation model, the noise of the circular element can be calculated using the following formula: （22） The noise of a capacitor unit can be calculated as follows: （23）。

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