A method for calculating the air gap length of an anti-dc current transformer

Abstract

The application relates to a method for calculating the air gap length of an anti-DC current transformer, comprising the following steps: calculating the maximum magnetic density and the maximum magnetic field strength that the current transformer needs to bear in theory under AC-DC working conditions; calculating the equivalent permeability of the air gap core according to the maximum magnetic density and the maximum magnetic field strength; and solving the air gap length according to the relationship between the air gap length and the core permeability of the air gap core and the equivalent permeability. Through the method, the optimal air gap length can be calculated, so that the current transformer meets the anti-DC index of design and reaches the optimal AC measurement accuracy.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of current transformers, in particular to a method for calculating the air gap length of a direct current-resistant current transformer. BACKGROUND

[0002] With the construction of extra-high voltage direct current transmission projects, the Chinese power grid assumes the form of an AC / DC hybrid power grid. When direct current transmission is operated in a monopole ground return or bipolar unbalanced operation mode, direct current with a magnitude of several thousand amperes flows into the ground, part of which flows through a neutral point grounded power transformer to form a loop in the AC system, thereby generating direct current bias magnetization in the transformer and the current transformer.

[0003] When operating normally, the current transformer operates in the linear region, and the excitation current i0 is very small, so the ratio of the primary side current to the secondary side current is equal to the turn ratio, and the information of the primary side current can be obtained by measuring the small current on the secondary side. However, when the current transformer has a direct current component, the direct current component generates a bias magnetic flux, which causes the operating point of the current transformer to deviate, easily causing the operating region of the current transformer to shift from the linear region to the saturation region, and causing the secondary side current to be distorted. At this time, if the primary side current is still calculated according to the turn ratio relationship, the measurement error will be large, which does not meet the original measurement accuracy requirement.

[0004] In order to enable the current transformer to still have good measurement accuracy under direct current bias magnetization, there are mainly two kinds of mainstream ideas at present: one is to process the core by opening an air gap, so that the current transformer still operates in the linear region under the condition that the primary side contains direct current; and the other is to increase compensation on the secondary side of the current transformer, and compensate for the direct current bias magnetization by connecting an external circuit or correct the output secondary current by using an algorithm.

[0005] For the core material of the current transformer, the saturation point is determined by the saturation magnetic induction B max and the saturation magnetic field strength H max Two parameters, and the linear region permeability μ of the core material is the ratio of the two, that is, B max / H max . High measurement accuracy requires the material to have a high permeability, and the anti-saturation requires the material to have a long linear region range, that is, H max is a large value. These two requirements are actually contradictory.

[0006] Processing the core by opening an air gap is essentially to obtain a larger H max to achieve the purpose of anti-saturation, but this also reduces the material permeability, thereby reducing the measurement accuracy, which is manifested as an increase in the ratio difference and the angle difference. Moreover, in terms of the performance of the material, the H maxIt can not meet the requirement of once side containing larger DC, and compared with the core opening air gap can obtain higher anti-saturation capacity.

[0007] For adding compensation on the secondary side of the current transformer, compensation DC bias needs to extract the secondary current characteristic reaction of the size of the primary DC, needs to connect the external circuit including filter, negative feedback circuit and so on, the structure is complex and the cost is high; Using algorithm correction needs a large number of sample data as the basis, physical algorithm needs to establish magnetic field model to solve complex differential equation, artificial intelligence algorithm has robustness and generalization problem, and it is difficult to adapt to the changing DC component in actual power system. SUMMARY

[0008] The purpose of the present application is to provide a method for calculating the air gap length of a DC-resistant current transformer, so that the current transformer meets the design DC resistance index and achieves the best AC measurement accuracy.

[0009] To achieve the above purpose, the air gap length calculation method of the DC-resistant current transformer provided by the embodiments of the present application comprises:

[0010] Calculate the maximum magnetic flux density and the maximum magnetic field strength that the current transformer theoretically needs to bear under AC and DC working conditions;

[0011] According to the maximum magnetic flux density and the maximum magnetic field strength, the equivalent permeability of the air gap core is calculated;

[0012] According to the relationship between the air gap length of the air gap core and the core permeability and the equivalent permeability, the air gap length is solved.

[0013] Further, the maximum magnetic field strength is calculated according to the following formula:

[0014]

[0015] Where, H max is the maximum magnetic field strength, I D is the DC current, N1 is the primary turns of the current transformer, and l is the average magnetic path length of the air gap core.

[0016] Further, the maximum magnetic flux density is calculated according to the following formula:

[0017] B max = B acm + B dc

[0018]

[0019]

[0020] a = H maxl / (N2B acm )

[0021] b=H c l / N2

[0022] c=1 / (B acm ) 2

[0023] Wherein, B max is the maximum magnetic flux density, B acm is the alternating current maximum magnetic flux density, B dc is the direct current bias magnetic flux density, I 2max is the maximum value of the current transformer secondary current modulus respectively, Z2 is the current transformer secondary circuit impedance modulus, ω is the angular frequency, N2 is the current transformer secondary turns respectively, S is the core cross-sectional area, I dc is the direct current component, K n is the current transformer transformation ratio coefficient, a, b, c is the coefficient, H c is the core coercivity, σ is the direction coefficient.

[0024] Further, the equivalent permeability of the air gap core is calculated according to the following formula:

[0025]

[0026] Wherein, μ equ is the equivalent permeability of the air gap core.

[0027] Further, the air gap length is calculated according to the following formula:

[0028]

[0029]

[0030] Wherein, l a is the air gap length, λ is the ratio of the air gap length to the total magnetic circuit length, μ r is the relative permeability of the air gap core, μ i is the core permeability, μ0 is the vacuum permeability, l i is the average magnetic circuit length of the core material.

[0031] The implementation of the present application has the following beneficial effects:

[0032] The present application is aimed at the current transformer for measurement, by calculating the maximum magnetic flux density B max and the maximum magnetic field strength H max which the current transformer theoretically needs to undertake.The application determines the limit working point of the current transformer, and in combination with the magnetic characteristics of the selected core material, determines the optimal air gap length of the current transformer core, so that the current transformer meets the design DC resistance index and achieves the optimal AC measurement accuracy.

[0033] More features and advantages of the embodiments of the application are embodied in the following. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the drawings needed in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0035] Figure 1 The flowchart of the air gap length calculation method of the DC resistance current transformer in the embodiments of the application.

[0036] Figure 2 The schematic diagram of the limit working point of the current transformer in the embodiments of the application.

[0037] Figure 3 The structural schematic diagram of the air gap core in the embodiments of the application. DETAILED DESCRIPTION

[0038] Reference Figure 1 The embodiments of the application provide an air gap length calculation method of a DC resistance current transformer, comprising the following steps:

[0039] Step S10, calculating the maximum magnetic flux density and the maximum magnetic field strength that the current transformer theoretically needs to bear under AC and DC working conditions;

[0040] Step S20, calculating the equivalent permeability of the air gap core according to the maximum magnetic flux density and the maximum magnetic field strength;

[0041] Step S30, solving the air gap length according to the relationship between the air gap length and the core permeability of the air gap core and the equivalent permeability.

[0042] The maximum magnetic flux density B max and the maximum magnetic field strength H max of the current transformer theoretically need to bear are combined as the limit working point (B max , H max ) on the B-H diagram of the core material, as shown in Figure 2shown. When designing the current transformer, it is necessary to ensure that the turning point of the linear region and the saturation region of the core of the current transformer is located at the right upper feasible region of the limit working point, so that the current transformer works in the linear region, ensures its linear transfer characteristics, and determines the limit working point of the current transformer, i.e. determines the value of B max and H max .

[0043] H max can be calculated by the full current law.

[0044] According to the full current law:

[0045] N1i1-N2i2=Hl (1)

[0046] In the formula, N1 and N2 are the number of turns of the primary and secondary, i1 and i2 are the primary and secondary currents, H is the magnetic field strength, and l is the average magnetic path length of the air gap core.

[0047] When the primary side contains a DC component, since the DC component cannot be transmitted to the secondary side when passing through the primary winding, it is all used for excitation, and when the DC content is greater than 3%, there is:

[0048] I D N1>>I e N1 (2)

[0049] In the formula, I D is the DC current, and Ie is the excitation current.

[0050] Therefore, H max can be considered as:

[0051]

[0052] In the environment of alternating current and direct current, the maximum magnetic flux density B max that the current transformer theoretically needs to bear should be the sum of the maximum alternating current magnetic flux density B acm and the direct current bias magnetic flux density B dc , i.e.:

[0053] B max =B acm +B dc (4)

[0054] The maximum alternating current magnetic flux density B acm can be derived from the secondary potential balance equation.

[0055] The secondary potential balance equation of the current transformer is:

[0056]

[0057] Where φ is the magnetic flux of the core, N2 is the number of turns of the secondary winding, R2 and L2 are the resistance and inductance of the secondary circuit respectively, and i2 is the secondary current.

[0058] The magnetic flux and the magnetic flux density satisfy:

[0059] φ = BS (6)

[0060] Where S is the cross-sectional area of the core.

[0061] By combining equations (5) and (6) and converting them into phasor form, we get:

[0062] ωN2BS = I2Z2 (7)

[0063] Where ω is the angular frequency, Z2 is the impedance modulus of the secondary circuit, and I2 is the modulus of the secondary current.

[0064] Therefore, the maximum magnetic flux density B acm is:

[0065]

[0066] The DC bias magnetic flux can be derived by combining the J-A model of the core.

[0067] The secondary current of the current transformer can be represented as an algebraic sum of each harmonic:

[0068]

[0069] Where n is the harmonic number, I 2n and β n are the amplitude and phase angle of the nth harmonic current respectively.

[0070] According to the basic current equation of the current transformer, the harmonic expression of the excitation current (converted to the secondary side) is:

[0071]

[0072] Where i e (t) is the error current, i1(t) is the instantaneous value of the primary current, i2(t) is the instantaneous value of the secondary current, K n is the transformation ratio coefficient of the current transformer, I dc is the DC current component, and I ac is the DC current component.

[0073] According to the electromagnetic induction relationship and the secondary circuit equation (5), the excitation magnetic flux density of the current transformer can be obtained as:

[0074]

[0075] Where Z bnγ is the nth harmonic impedance on the secondary side of the current transformer. n Let be the load impedance angle of the nth harmonic, as shown in equations (12) and (13) respectively.

[0076]

[0077]

[0078] The JA model describes the excitation characteristics of the iron core as follows:

[0079]

[0080] In the formula, H c For the coercivity of the iron core, H M The maximum magnetic field strength of the iron core is H. max B M The maximum alternating magnetic flux density, i.e., B acm σ is the direction coefficient.

[0081] By combining equations (11) and (14), we can obtain:

[0082]

[0083] In the formula, a = H M l / (N2B M b = Hcl / N2

[0084] Combining equations (11) and (15), in B = B dc Expanding this into a Taylor series, we get:

[0085]

[0086] According to the harmonic balance method, by comparing the corresponding terms of equations (10) and (16), we can obtain:

[0087]

[0088] Equation (17) is a quadratic equation in one variable concerning DC magnetic flux density. Solving it yields B. dc .

[0089] Once the limiting operating point is determined, the equivalent permeability of the air-gap core can be obtained:

[0090]

[0091] For example Figure 3 The open-gap current transformer core shown, from a magnetic circuit perspective, is essentially an air-gap reluctance coil connected in series with the core reluctance. According to Ohm's law of reluctance:

[0092]

[0093]

[0094] where R im is the core reluctance, R am is the air gap reluctance; l i is the average magnetic path length of the core material, l a is the air gap length; μ i is the core permeability, μ0 is the vacuum permeability, and S is the cross-sectional area.

[0095] The equivalent reluctance R m is:

[0096]

[0097] The equivalent permeability μ equ after opening the air gap satisfies:

[0098]

[0099] where l is the total magnetic path length.

[0100] It can be obtained that:

[0101]

[0102] where λ is the ratio of the air gap length to the total magnetic path length, μ r is the relative permeability of the core.

[0103] The simultaneous equations (18) and (23) can be used to solve the air gap length l a of the core.

[0104] The method of the embodiment calculates the maximum magnetic flux density B max and the maximum magnetic field strength H max that the current transformer theoretically needs to bear under AC and DC working conditions, calculates the equivalent permeability μ equ of the air gap core according to the calculated limit working point (B max , H max ), and simultaneously solves the air gap length according to the relationship between the air gap length and the core permeability of the air gap core. The air gap length is the minimum air gap length that the core needs to open to meet the DC resistance index. Since the larger the air gap length is, the lower the equivalent permeability of the core is, and the error of the current transformer also increases. Therefore, the calculated air gap length can be considered as the best air gap length that meets the DC resistance index, which provides a basis for the air gap design of the DC resistance current transformer.

[0105] Having described various embodiments of the application, it is to be understood that the above description is meant not to limit and not to encompass all of the possible embodiments. Many modifications and variations of this application can be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. It is intended that the scope of the application be defined by the scope of the patent and by the claims as allowed by the patent office, which can include adaptations based on the description, equivalents, and / or substitutions of elements individually or collectively to the entire disclosure.

Claims

1. A method of calculating the air gap length of an anti-DC current transformer, characterized by, The method comprises: calculating the maximum magnetic flux density and the maximum magnetic field strength that the current transformer theoretically needs to bear under AC / DC operation; calculating the equivalent permeability of the air gap core according to the maximum magnetic flux density and the maximum magnetic field strength; the equivalent permeability of the air gap core is calculated according to the following formula: wherein, μ equ is the equivalent permeability of the air gap core, B max is the maximum magnetic flux density, H max is the maximum magnetic field strength; solving the air gap length according to the relationship between the air gap length and the core permeability of the air gap core and the equivalent permeability; the air gap length is calculated according to the following formula: wherein, l a Lg is the air gap length, λ Lg / L is the ratio of air gap length to total magnetic circuit length, μ r μg is the relative permeability of the air gap core, μ i μc is the permeability of the core, μ 0 is the permeability of vacuum, l i Lc is the average magnetic circuit length of the core material, l Lg is the average magnetic circuit length of the air gap core, S Ac is the cross-sectional area of the core.

2. The air gap length calculation method according to claim 1, characterized by, the maximum magnetic field strength is calculated according to the following formula: wherein H max is the maximum magnetic field strength, I D is the direct current, N 1is the primary number of turns of the current transformer, l is the average magnetic path length of the air gap core.

3. The air gap length calculation method according to claim 2, characterized by, the maximum magnetic flux density is calculated according to the following formula: a = H max l / ( N 2 B acm ) b = H c l / N 2 c =1 / ( B acm ) 2 wherein, B max is the maximum magnetic flux density, B acm is the maximum alternating magnetic flux density, B dc is the direct current bias magnetic flux density ，I 2max are the maximum values of the current transformer secondary current modulus, respectively, Z 2 is the current transformer secondary circuit impedance modulus, ω is the angular frequency, N 2 are the current transformer secondary turns, respectively, S is the core cross-sectional area, I dc is the direct current component, K n is the current transformer transformation ratio coefficient, a , b , c is the coefficient, H c is the core coercivity, σ is the direction coefficient.

Images