A method for calculating the voltage steepness that a DC support capacitor can withstand

Abstract

The present invention discloses a method for calculating the voltage steepness that a DC support capacitor can withstand in the technical field of capacitor withstand performance calculation, comprising the following steps: step one: establishing a capacitor withstand voltage steepness calculation model; step two: obtaining a limit voltage steepness calculation model that a lossless capacitor can withstand according to the capacitor withstand voltage steepness calculation model in step one; step three: deducing a limit voltage steepness calculation model that an actual lossy capacitor can withstand according to the limit voltage steepness calculation model that a lossless capacitor can withstand in step two; step four: obtaining a further voltage steepness calculation model that a DC support capacitor can withstand through step two and step three; the present invention can calculate the voltage steepness in a capacitor test by analyzing the voltage steepness of an RLC basic circuit, and clarify the harm of the voltage steepness to the capacitor from a mechanism perspective.

Description

Technical Field

[0001] The present invention relates to the technical field of capacitor tolerance performance calculation, and in particular to a method for calculating the voltage steepness that a DC support capacitor can tolerate. Background Art

[0002] Voltage steepness refers to the voltage change rate du / dt in a very short time. For capacitors, voltage tolerance is crucial; because the main body of the capacitor is the dielectric, the capacitor fails after the dielectric breakdown, so the design of the capacitor is based on voltage, and its core parameter is the design field strength. In the standard, the main performance indicators of capacitors are also based on voltage. Operating experience shows that capacitors themselves are rarely damaged by overcurrent. In contrast to capacitors, the voltage of the reactor in the circuit is determined by the current change rate. The turn-to-turn insulation test uses the turn-to-turn voltage generated by the current change rate to assess the turn-to-turn insulation of the reactor. Under normal operating voltage, the turn-to-turn voltage is very small.

[0003] Voltage steepness is covered in capacitor-related standards and is hidden in certain tests. For example, the polarity reversal test in DC filter capacitors for high-voltage DC transmission is an assessment of the capacitor's ability to withstand voltage change rates. However, in reality, due to limitations in test conditions, it is difficult to achieve the purpose of the polarity reversal test to assess the capacitor's ability to withstand voltage steepness. There is also an impulse current discharge test in the DC support capacitor test, which is actually an assessment of the capacitor's ability to withstand voltage change rates. Other capacitors, including parallel capacitors, series capacitors, and AC filter capacitors for DC transmission, all have short-circuit discharge tests, which also involve the assessment of voltage steepness.

[0004] However, the prior art has not analyzed the voltage steepness of the basic RLC circuit, calculated the voltage steepness in the capacitor test, and clarified the harm of the voltage steepness to the capacitor from the mechanism. Summary of the invention

[0005] The object of the present invention is to provide a method for calculating the voltage steepness that a DC support capacitor can withstand, so as to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a method for calculating the voltage steepness that a DC support capacitor can withstand, characterized in that it comprises the following steps:

[0007] Step 1: Establish a capacitor withstand voltage calculation model;

[0008] Step 2: According to the capacitor withstand voltage calculation model in step 1, a limit voltage steepness calculation model that the lossless capacitor can withstand is obtained;

[0009] Step 3: Based on the calculation model of the limit voltage steepness that the lossless capacitor can withstand in step 2, deduce the calculation model of the limit voltage steepness that the actual lossy capacitor can withstand;

[0010] Step 4: A voltage steepness calculation model that the DC support capacitor can withstand is further obtained through steps 2 and 3.

[0011] As a further solution of the present invention, the capacitor withstand voltage calculation model is established based on the RLC circuit, and its discharge current waveform is expressed by formula (1):

[0012]

[0013] In formula (1), i is the discharge current, kA; U0 is the discharge voltage, kV; ω is the angular frequency of the discharge current, rad / s; L is the inductance of the discharge circuit, H; is the limiting discharge current of the discharge circuit, kA; δ=R / 2L is the damping coefficient of the circuit. Where R is the equivalent series resistance of the discharge circuit;

[0014] Where the capacitor current is:

[0015] From formula (2), we can get:

[0016] As a further solution of the present invention, the calculation model of the extreme voltage steepness that the lossless capacitor can withstand is obtained based on the capacitor withstand voltage calculation model; the steepness that the lossless capacitor can withstand is the extreme voltage steepness, that is:

[0017]

[0018] Considering the natural frequency of the capacitor For an ideal capacitor, the equivalent series resistance is very small, and the influence of the damping coefficient δ, ω0≈ω, can be obtained by substituting it into formula (4):

[0019]

[0020] The maximum voltage steepness that a lossless capacitor can withstand is related to its stray inductance as follows:

[0021]

[0022] In formula (6):

[0023] As a further solution of the present invention, the calculation model of the limit voltage steepness that the actual lossy capacitor can withstand is obtained based on the calculation model of the limit voltage steepness that the lossless capacitor can withstand; the limit current I0 in formula (4) is replaced by the maximum peak current Im1 ; So we have:

[0024]

[0025] In formula (7): I is the maximum voltage steepness that the capacitor can withstand; m1 is the maximum peak current of the discharge current (the first peak in the waveform), kA;

[0026] In addition, δ=lnα / T, considering T=2π / ω, we can get:

[0027]

[0028] Formulas (7) to (8): T is the period of the discharge current waveform, s; α is the ratio of adjacent peak values ​​on the same side of the discharge current, and α>1;

[0029] The natural angular frequency of the discharge circuit is Substituting formula (8) into the equation, we can obtain:

[0030]

[0031] From formula (9), we can see that for capacitors, generally is very small, so ω0≈ω; the first peak of the discharge current appears at t1=T / 4; thus:

[0032]

[0033] Considering Substituting formula (10) into formula (7), we can obtain:

[0034]

[0035] As a further solution of the present invention, the discharge current is adjusted to: I by reducing the charging voltage and / or increasing the impedance of the discharge circuit. test =1.1I s ;due:

[0036]

[0037]

[0038] In formulas (12) to (13): is the maximum allowable voltage gradient of the capacitor, MV / s; C is the capacitance, μF; U N is the rated voltage of the capacitor, kV; I z1 is the first peak current in the discharge current waveform, kA; ω 0zis the natural angular frequency of the DC support capacitor, rad / s; α z I is the ratio of two adjacent peaks on the same side of the discharge current deformation; s is the maximum inrush current of the DC support capacitor, kA;

[0039] If the value of formula (12) is required to be greater than the value of formula (13), then: The natural angular frequency of the capacitor is obtained by solving:

[0040]

[0041] In formula (14): q z =C z U N is the amount of charge that the capacitor can store, mC; t z For capacitors at I s Equivalent charge and discharge time under , s;

[0042] From formula (14), the requirement of impulse discharge current on capacitor stray inductance can be obtained as follows:

[0043]

[0044] From formula (15), we can get:

[0045]

[0046] In formula (16): is the energy storage of the capacitor, J; The energy stored in stray inductance.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The present invention can calculate the voltage steepness in a capacitor test by analyzing the voltage steepness of a basic RLC circuit, and clarify the harm of the voltage steepness to the capacitor from a mechanism perspective. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a typical RLC circuit diagram;

[0050] Figure 2 It is a typical discharge current waveform of the RLC circuit;

[0051] Figure 3 This is a graph showing the relationship between the voltage steepness that a capacitor can withstand and its stray inductance;

[0052] Figure 4 This is the relationship between the maximum voltage steepness that a capacitor can withstand and its discharge current attenuation coefficient;

[0053] Figure 5 is the stray inductance L z With the maximum surge current I s relationship diagram. DETAILED DESCRIPTION

[0054] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0055] The present invention provides a method for calculating the voltage steepness that a DC support capacitor can withstand, as follows:

[0056] Firstly, a model for calculating the steepness of capacitor withstand voltage is established;

[0057] Among the basic circuits, the RLC circuit is the most typical, which includes the basic components in the circuit; a typical RLC circuit is as follows Figure 1 As shown, the typical discharge current waveform is as follows Figure 2 shown.

[0058] Figure 2 The discharge current waveform shown can be expressed by equation (1):

[0059]

[0060] In formula (1), i is the discharge current, kA; U0 is the discharge voltage, kV; ω is the angular frequency of the discharge current, rad / s; L is the inductance of the discharge circuit, H; is the limiting discharge current of the discharge circuit, kA; δ=R / 2L is the damping coefficient of the circuit. R is the equivalent series resistance of the discharge circuit.

[0061] Figure 1 The current in the capacitor is: In formula (2): i c is the current flowing through the capacitor, kA; C is the loop capacitance, mF; u c is the voltage on the capacitor, kV; is the voltage steepness on the capacitor, MV / s.

[0062] Usually, the voltage on the capacitor cannot change suddenly, which actually means that the capacitor current shown in equation (2) cannot be infinite, which also means that the voltage waveform cannot be interrupted. The interruption of the voltage waveform on the capacitor means that the capacitor is broken down.

[0063] From formula (2), we can get:

[0064]

[0065] It can be seen from equation (3) that the voltage steepness of the capacitor is proportional to the current flowing through the capacitor and inversely proportional to the capacitance of the capacitor.

[0066] About lossless capacitors:

[0067] A lossless capacitor is an ideal capacitor with no loss and no need to consider the attenuation factor of the capacitor's discharge current. The steepness that can be tolerated at this time is the limit voltage steepness, that is:

[0068]

[0069] It can be seen from equation (4) that the extreme voltage steepness that the capacitor can withstand is proportional to the voltage, and inversely proportional to the discharge current angular frequency and the capacitance and stray inductance of the capacitor.

[0070] Considering the natural frequency of the capacitor For an ideal capacitor, the equivalent series resistance is very small, and the influence of the damping coefficient δ, ω0≈ω, can be obtained by substituting it into formula (4):

[0071]

[0072] From formula (5), it can be seen that the maximum voltage steepness that a capacitor can withstand is equal to the product of the capacitor voltage and its natural frequency. In other words, when the voltage is constant, the natural frequency of the capacitor determines the maximum voltage steepness that the capacitor can withstand. Since the capacitance of the capacitor is fixed, how to reduce the stray inductance of the capacitor is the only way to increase the voltage steepness that the capacitor can withstand. The relationship between the maximum voltage steepness that a capacitor can withstand and its stray inductance is as follows:

[0073]

[0074] In formula (6): The rest is the same as before; from formula (6), it can be seen that the typical curve of formula (6) is as follows Figure 3 shown.

[0075] from Figure 3 It can be seen that, when the capacitance remains unchanged, as the stray inductance of the capacitor increases, the voltage steepness that the capacitor can withstand decreases.

[0076] For actual lossy capacitors;

[0077] The previous analysis did not consider the attenuation of the discharge current. If the current attenuation factor is taken into account, the limiting current I0 in equation (4) is replaced by the maximum peak current I m1 . So we have:

[0078]

[0079] In formula (7): I is the maximum voltage steepness that the capacitor can withstand; m1 is the maximum peak current of the discharge current (the first peak in the waveform), kA; the rest are the same as before.

[0080] In addition, δ=lnα / T, considering T=2π / ω, we can get:

[0081]

[0082] Formulas (7) to (8): T is the period of the discharge current waveform, s; α is the ratio of adjacent peak values ​​on the same side of the discharge current, and α>1; the rest is the same as before.

[0083] The natural angular frequency of the discharge circuit is Substituting formula (8) into the equation, we can obtain:

[0084]

[0085] From formula (9), we can see that for capacitors, generally is very small, so ω0≈ω; according to Figure 2 , the first peak of the discharge current appears at t1 = T / 4. So:

[0086]

[0087] Considering Substituting formula (10) into formula (7), we can obtain:

[0088]

[0089] Comparing equation (5) with equation (11), it can be seen that after considering the attenuation factor of the circuit, the limit voltage steepness that the capacitor can withstand is reduced to 1 / α without considering the circuit discharge attenuation factor. 1 / 4 Typical curves are as follows: Figure 4 shown.

[0090] from Figure 4 It can be seen that as the ratio of two adjacent peaks in the same direction increases, the steepness of the maximum withstand voltage of the capacitor decreases slowly as the peak ratio increases.

[0091] Further, the voltage steepness that the DC support capacitor can withstand is calculated;

[0092] For DC support capacitors, the standard GB / T 17702-2021 stipulates the impulse discharge test as follows: "The unit should be charged with a DC power supply and then discharged through a short-circuit device as close to the capacitor as possible. The unit should be discharged five times within 10 minutes. For capacitors without specified impulse current limits (anti-short-circuit capacitors), the test voltage of the impulse discharge test should be equal to 1.1U N For test voltages higher than 1.1U N , should be determined by negotiation between the manufacturer and the user. If the maximum impulse current is specified, the discharge current should be adjusted to: I test =1.1I s ". According to the previous analysis, there should be:

[0093]

[0094] In formulas (12) to (13): is the maximum allowable voltage gradient of the capacitor, MV / s; C is the capacitance, μF; U N is the rated voltage of the capacitor, kV; I z1 is the first peak current in the discharge current waveform, kA; ω 0z is the natural angular frequency of the DC support capacitor, rad / s; α z I is the ratio of two adjacent peaks on the same side of the discharge current deformation; s is the maximum inrush current of the DC support capacitor, kA.

[0095] It can be seen from formula (12) that the maximum voltage steepness that the DC support capacitor can withstand is proportional to the voltage and natural angular frequency of the impulse discharge test, and inversely proportional to the 1 / 4 power of the same-direction peak ratio. The technical specification requires that the equivalent series inductance of the DC support capacitor be in the nanohenry level, which is also to improve the capacitor's ability to withstand voltage steepness so as to match the performance of the IGBT. The maximum discharge current given in the DC support capacitor technical specification is also based on the du / dt of the IGBT. The technical specification's requirements for the equivalent series resistance of the capacitor are also to reduce the peak ratio and maximize the capacitor's ability to withstand voltage steepness.

[0096] In the standards GB / T 17702 and IEC 61071, the impulse discharge test requires that the maximum peak current should reach 1.1 times the rated voltage. If the peak current cannot be reached, the voltage cannot be increased. If the specified current cannot be reached at the specified voltage, it means that the capacitor's withstand voltage steepness does not meet the requirements. If the value of formula (12) is required to be greater than the value of formula (13), then: The natural angular frequency of the capacitor is obtained by solving:

[0097]

[0098] In formula (14): q z =C z U N is the amount of charge that the capacitor can store, mC; t z For capacitors at I s The equivalent charge and discharge time under , s; the rest is the same as before.

[0099] It can be seen from formula (14) that if the capacitor is required to withstand the output impulse discharge current, its natural angular frequency must be no less than the ratio of the impulse discharge current to the amount of charge that the capacitor can store.

[0100] From formula (14), the requirement of impulse discharge current on capacitor stray inductance can be calculated.

[0101]

[0102] Put C z =9000μF, U N =2.8kV, I s =800kA, α z =1.56 Substituting into formula (15) we can get: L z ≤88.3nH. That is to say, the stray inductance of the capacitor is not greater than 88.3nH. N Short circuit discharge, impulse discharge current I s Can reach 1.1*800kA. Stray inductance L z With the maximum surge current I s The relationship is as Figure 5 As shown;

[0103] from Figure 5 It can be seen that as the maximum impact current of the capacitor increases, the stray inductance of the capacitor decreases rapidly. It can be seen that the stray inductance of the capacitor with the maximum impact current has a great influence.

[0104] From formula (15), we can get:

[0105]

[0106] In formula (16): is the energy storage of the capacitor, J; is the energy storage of stray inductance, and the rest is the same as before.

[0107] From equation (16), it can be seen that the ratio of the energy storage of the capacitor to the energy storage of the equivalent stray inductance is Actually that is Figure 2 The inverse peak ratio of the current waveform.

[0108] For the kilo-impulse test of DC support capacitors, according to the standard, the voltage can be reduced or the reactance can be increased. The former requires the voltage to be adjusted to several hundred volts, but the discharge current frequency will be relatively high, which can test the skin absorption effect of the component at high frequency. The latter mainly considers the DC voltage effect of the component. It is more meaningful to test the skin absorption effect of the component. The DC withstand voltage of the component has been tested in the durability test, and the amplitude is higher than 1.1U N High, and at a temperature of 70°C.

[0109] It should be noted that the voltage steepness of the capacitor is accompanied by the current. If it exceeds the capacitor's tolerance, the first part to be damaged is the conductor part, such as the internal fuse and the weak points of soldering.

[0110] The voltage steepness that other capacitors, including DC filter capacitors and AC filter capacitors, can withstand can refer to the derivation in this article. Since the voltage selection takes into account a certain margin, especially for capacitors used in UHV DC transmission, the voltage is selected according to the arithmetic sum. Under actual operating conditions, the voltage is too low, which will reduce the capacitor's ability to withstand voltage steepness.

Claims

1. A method for calculating the voltage steepness that a DC support capacitor can withstand, characterized in that: The steps include: Step 1: Establish a calculation model for the capacitor withstand voltage steepness; Step 2: According to the capacitor withstand voltage steepness calculation model in step 1, a limit voltage steepness calculation model that the lossless capacitor can withstand is obtained; Step 3: Based on the calculation model of the limit voltage steepness that the lossless capacitor can withstand in step 2, deduce the calculation model of the limit voltage steepness that the actual lossy capacitor can withstand; Step 4: A voltage steepness calculation model that the DC support capacitor can withstand is further obtained through steps 2 and 3; The capacitor withstand voltage steepness calculation model is established based on the RLC circuit, and its discharge current waveform is expressed by formula (1): （1）； In formula (1), is the discharge current, kA; U 0 is the discharge voltage, kV; ω is the frequency of the discharge current, rad / s; L is the inductance of the discharge circuit, H; is the limiting discharge current of the discharge circuit, kA; δ = R / 2L is the damping coefficient of the loop, where R is the equivalent series resistance of the discharge circuit; Where the capacitor current is: (2); From formula (2), we can get: (3); The calculation model of the extreme voltage steepness that the lossless capacitor can withstand is obtained based on the calculation model of the capacitor withstand voltage steepness; the steepness that the lossless capacitor can withstand is the extreme voltage steepness, that is: （4）； Considering the natural frequency of the capacitor , for an ideal capacitor, the equivalent series resistance is very small and the damping coefficient δ The impact of ω 0 ≈ω , substituting into formula (4) we can get: （5）； The relationship between the extreme voltage steepness that a lossless capacitor can withstand and its stray inductance is as follows: （6）； In formula (6): ; The calculation model of the limit voltage steepness that the actual lossy capacitor can withstand is obtained according to the calculation model of the limit voltage steepness that the lossless capacitor can withstand; the limit current in formula (4) is Change to maximum peak current ; So we have: （7）； In formula (7): is the limit voltage steepness that the capacitor can withstand; is the maximum peak current of the discharge current, kA; in addition, , considering, we can get: , we can get: （8）； Formula (7)~(8): T is the period of the discharge current waveform, s; α is the ratio of adjacent peak values ​​on the same side of the discharge current, and α>1; The natural frequency of the discharge circuit is , substituting formula (8) into it, we can get: （9）； From formula (9), we can see that for a capacitor, Very small, so ω 0 ≈ω; The first peak of the discharge current occurs at t 1= T / 4; so there are: （10）； Considering , substituting formula (10) into formula (7) we can get: （11）。 2. The method for calculating the voltage steepness that a DC support capacitor can withstand according to claim 1 is characterized in that: By reducing the charging voltage and / or increasing the impedance of the discharge circuit, the discharge current is adjusted to: ;due: （12）； （13）； In formula (12)~(13): is the maximum allowable voltage steepness of the capacitor, MV / s; is the capacitance, µF; U N is the rated voltage of the capacitor, kV; is the first peak current in the discharge current waveform, kA; is the natural frequency of the DC support capacitor, rad / s; α z It is the ratio of two adjacent peaks on the same side of the discharge current deformation; I s is the maximum inrush current of the DC support capacitor, kA; If the value of formula (12) is required to be greater than the value of formula (13), then: , the natural frequency of the DC support capacitor is obtained as: （14）； In formula (14): is the amount of charge that a capacitor can store, mxD ; t z For capacitors in I s Equivalent charge and discharge time under , s; From formula (14), the requirement of impulse discharge current on capacitor stray inductance can be obtained as follows: （15）； From formula (15), we can get: （16）； In formula (16): is the energy storage of the capacitor, J; The energy stored in stray inductance.

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