CN105301532A - Current transformer hysteresis loop observation method - Google Patents

Abstract

The invention relates to a current transformer hysteresis loop observation method. A hysteresis loop is obtained by utilizing hysteresis information included in primary current and secondary current of a current transformer so that current transformer hysteresis loop observation can be rapidly and simply and conveniently realized, the limit hysteresis loop under saturation of the current transformer can be conveniently observed and the hysteresis loop under unsaturation of the current transformer can also be conveniently observed, and thus the current transformer hysteresis loop observation method is particularly suitable for observation of the frequency characteristics of a current transformer iron core.

Description

A kind of current transformer magnetic hysteresis loop observation procedure

Technical field

The present invention relates to a kind of current transformer magnetic hysteresis loop observation procedure.

Background technology

Current transformer is the current transformation equipment be made up of iron cores such as siliconized plates, widespread use in electric system.Because current transformer core exists hysteresis, on the design of current transformer, manufacture and there is very large impact with operation.The magnetic hysteresis loop of Measurement accuracy iron core is current transformer design, manufactures the important evidence with operation.

Traditional magnetic hysteresis loop observation mainly contains Hall's technique and RC oscilloscope method, as follows

(1) Hall's technique is the size utilizing teslameter directly to observe the magnetic induction density B in iron core air gap.Hall's technique as shown in Figure 1, passes into electric current I in field copper, then the magnetization is,

$H=\frac{N_{1}I}{L}$

Wherein, L is ferromagnetic magnetic conduction length, N ₁for umber of turn on iron core.Hall probe is placed in iron core sample air gap, consistent with tested core interior average magnetic induction intensity in air gap uniform magnetic field region intrinsic inductance.And namely the corresponding relation of H and B constitutes magnetic hysteresis loop and the magnetization curve of this ferromagnetic material.Front also needs of this external experiment demagnetizes to iron core.

Hall's technique directly can measure the size of iron core intrinsic inductance B, but for the iron core profit closed in this way and be not suitable for.

(2) as shown in Figure 2, the parameter in figure is only illustratively to RC oscilloscope method observation magnetic hysteresis loop.

At winding N ₁in by magnetization current i ₁time, this electric current produces magnetic field in style, has according to Ampere circuit law:

HL＝N ₁i ₁-N ₂i ₂

Due to N ₂i ₂very littlely therefore to ignore, by measuring resistance R ₁on the voltage U at two ends ₁, H can be expressed as:

$H=\frac{N_1{U}_1}{{\mathrm{LR}}_1}$

For i ₂effective value, as 10 × 1/ ω c≤R ₂, i ₂can be approximately:

$I_2=\frac{E_2}{\sqrt{\[R_2^2+{\left(\frac{1}{\mathrm{\ω}c}\right)}^2\]}}\≈\frac{E_2}{R_2}$

The voltage u at electric capacity c two ends _ccan be expressed as:

$u_C=\frac{Q}{c}=\frac{1}{c}\∫i_{2}dt=\frac{1}{c}\∫\frac{E_2}{R_2}dt=\frac{1}{R_{2}c}\∫E_{2}dt=\frac{1}{R_{2}c}\∫N_{2}A\frac{dB}{dt}dt=\frac{N_{2}AB}{R_{2}c}$

Therefore B represents by electric capacity both end voltage.

$B=\frac{R_2{u}_{C}c}{N_{2}A}$

Just iron core magnetic hysteresis curves phenomenon can be shown intuitively with oscillographic X-axis display H, Y-axis display B.RC oscilloscope method has simple and convenient, and physical significance is advantage clearly.Owing to have ignored N ₂i ₂therefore cannot be applied to the observation of magnetic hysteresis loop inlet wire when current transformer runs, it is suitable that secondary resistance and electric capacity need to select, otherwise there will be wave form distortion phenomenon, also inconvenient to the magnetic hysteresis loop observing current transformer under different frequency responds.

These two kinds of methods all need independently to observe circuit, and are only suitable for the observation of the magnetic hysteresis loop a little sample being carried out to iron core.After current transformer is manufactured, the magnetic hysteresis loop in order to upper method observation iron core is very inconvenient.

Summary of the invention

The object of the present invention is to provide a kind of current transformer magnetic hysteresis loop observation procedure, to overcome the defect existed in prior art.

For achieving the above object, technical scheme of the present invention is: a kind of current transformer magnetic hysteresis loop observation procedure, realizes in accordance with the following steps:

Step S1: utilize digital oscilloscope current probe directly to gather the primary current of primary side; After utilizing described digital oscilloscope voltage probe to measure secondary resistive voltage, then be converted into secondary current;

Step S2: gathered described primary current, described secondary current and time are carried out data processing by Matlab;

Step S3: primary current i ₁by producing magnetic field during first side winding, according to Ampere circuit law:

$H=\frac{N_1{i}_1-N_2{i}_2}{L}$

Wherein, N ₁be the number of turn of a winding, N ₂for the number of turn of Secondary Winding, L are the effective magnetic conduction length of iron core, i ₂for secondary current;

Step S4: for the secondary side of current transformer, according to the law of electromagnetic induction:

$e=N_{2}A\frac{dB}{dt}=R_2{i}_2+L_2\frac{{\mathrm{di}}_2}{dt}$

Trapezoidal Bei Ruilong integral method is adopted to above formula, in adjacent spaces time Δ t, magnetic flux and secondary current i ₂relation be shown below:

$\mathrm{\Δ}B\left(t\right)=\frac{R_2\mathrm{\Δ}t}{N_{2}A}(\frac{{\mathrm{\Δi}}_2\left(t\right)}{2}+i_2(t-\mathrm{\Δ}t\left)\right)+\frac{L_2}{N_{2}A}{\mathrm{\Δi}}_2\left(t\right)$

Wherein, A is magnetic conduction cross-sectional area, the R of iron core ₂for all-in resistance, the L of Secondary Winding and secondary load ₂for the total inductance of Secondary Winding and secondary load;

Step S5: because secondary current value is known, obtains the size of Δ B in adjacent spaces time Δ t by the relational expression of magnetic flux and secondary current in described step S4; Remember that first moment magnetic induction density is arbitrary value B ₍₁₎, then second moment induction level is:

B ₍₂₎＝B ₍₁₎+ΔB ₍₁₎

After this magnetic induction density in each moment all adds the difference DELTA B of magnetic induction on the magnetic induction density of previous moment _(n-1), as follows:

B _(n)＝B _(n-1)+ΔB _(n-1)

Namely the magnetic induction density B in the n-th moment is obtained _(n), by using H as X-axis, using B as Y-axis, obtain magnetic hysteresis loop.

In an embodiment of the present invention, can be obtained by the relational expression of magnetic flux and secondary current in described step S4, in described step S5, for arbitrary neighborhood interval time, Δ B is and initial value B ₍₁₎irrelevant amount, for normally stable situation, actual initial value is B ' ₍₁₎:

$B_{\left(1\right)}^{\′}=B_{\left(1\right)}-\frac{B_{max}+B_{min}}{2}$

Wherein, B _maxfor maximum magnetic induction in one-period, B _minfor magnetic induction density minimum in one-period, utilize initial value B ' ₍₁₎act on behalf of B ₍₁₎bring formula B into _(n)=B _(n-1)+ Δ B _(n-1)recalculate, obtain the B value that each moment H is corresponding.

In an embodiment of the present invention, in described step S1, described digital oscilloscope bandwidth is more than or equal to 100MHz; In described digital oscilloscope use procedure, described primary current and described secondary current are the waveform about time shaft t symmetry, and storage format is csv form.

Compared to prior art, the present invention has following beneficial effect: a kind of current transformer magnetic hysteresis loop observation procedure proposed by the invention, the magnetic hysteresis information utilizing current transformer first and second electric current to comprise obtains magnetic hysteresis loop, the current transformer magnetic hysteresis loop that realizes that can be fast and convenient is observed, the magnetic hysteresis loop under the limit magnetic hysteresis loop under CT saturation can be observed easily also can to observe current transformer unsaturation easily.Avoid, for observation magnetic hysteresis loop is separately tested, to observe making shaping current transformer magnetic hysteresis loop easily, being particularly suitable for the observation of current transformer core magnetic hysteresis loop frequency characteristic.

Accompanying drawing explanation

Fig. 1 is Hall's technique measuring principle figure.

Fig. 2 is RC oscilloscope method schematic diagram.

Fig. 3 is the low-voltage current mutual inductor connection diagram of 5/50 circle adopted in the embodiment of the present invention.

Fig. 4 is embodiment of the present invention mesolow current transformer by first and second current waveform of the current transformer after digital oscilloscope record ripple when core sataration.

Magnetic hysteresis loop schematic diagram when Fig. 5 is core sataration in the embodiment of the present invention.

Iron-core magnetic induction intensity schematic diagram when Fig. 6 is core sataration in the embodiment of the present invention.

Iron core magnetization schematic diagram when Fig. 7 is core sataration in the embodiment of the present invention.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is specifically described.

The invention provides a kind of current transformer magnetic hysteresis loop observation procedure.Current transformer primary current obtains secondary current through magnetic hysteresis loop conversion.When magnetic hysteresis loop unsaturation, secondary current is actual is an approximate sinusoidal waveform, and when magnetic hysteresis loop is saturated, secondary current is being not near sinusoidal waveform.No matter saturated or unsaturation, first and second current transformer all contains the information of iron core magnetic hysteresis curves.The object of current transformer magnetic hysteresis loop numerical method utilizes the time dependent waveform of current transformer first and second electric current, shows iron core magnetic hysteresis curves phenomenon intuitively.In order to form magnetic hysteresis loop in lower experimental voltage, in the present embodiment, be the low-voltage current mutual inductor of 5/50 circle as shown in Figure 3, secondary load is 10 Ω, and supply frequency is 50Hz, and iron core is siliconized plate, iron core internal diameter d ₁=38mm, iron core outside diameter d ₂=53mm, iron core width d ₃=23mm, lamination thickness d ₄=0.23mm.Utilize digital oscilloscope current probe directly to gather primary side current, after utilizing voltage probe to measure secondary resistive voltage, be converted into secondary current again.

By digital oscilloscope sampling current transformer primary current, secondary current simultaneously, first and second electric current of oscillograph recording and time are imported the data processing softwares such as Matlab.

Primary current i ₁by producing magnetic field during first side winding, according to Ampere circuit law:

$H=\frac{N_1{i}_1-N_2{i}_2}{L}$

Wherein, N ₁be the number of turn of a winding, N ₂for the number of turn of Secondary Winding, L are the effective magnetic conduction length of iron core, i ₂for secondary current;

For the secondary side of current transformer, according to the law of electromagnetic induction:

$e=N_{2}A\frac{dB}{dt}=R_2{i}_2+L_2\frac{{\mathrm{di}}_2}{dt}$

Trapezoidal Bei Ruilong integral method is adopted to above formula, in adjacent spaces time Δ t, magnetic flux and secondary current i ₂relation be shown below:

$\mathrm{\Δ}B\left(t\right)=\frac{R_2\mathrm{\Δ}t}{N_{2}A}(\frac{{\mathrm{\Δi}}_2\left(t\right)}{2}+i_2(t-\mathrm{\Δ}t\left)\right)+\frac{L_2}{N_{2}A}{\mathrm{\Δi}}_2\left(t\right)$

Wherein, A is magnetic conduction cross-sectional area, the R of iron core ₂for all-in resistance, the L of Secondary Winding and secondary load ₂for the total inductance of Secondary Winding and secondary load;

Because secondary current value is known, obtained the size of Δ B in adjacent spaces time Δ t by the relational expression of magnetic flux in above formula and secondary current; Remember that first moment magnetic induction density is arbitrary value B ₍₁₎, then second moment induction level is:

B ₍₂₎＝B ₍₁₎+ΔB ₍₁₎

After this magnetic induction density in each moment all adds the difference DELTA B of magnetic induction on the magnetic induction density of previous moment _(n-1), as follows:

B _(n)＝B _(n-1)+ΔB _(n-1)

Namely the magnetic induction density B in the n-th moment is obtained _(n), by using H as X-axis, using B as Y-axis, obtain magnetic hysteresis loop.

For arbitrary neighborhood interval time, Δ B is initial value B ₍₁₎irrelevant amount, for normally stable situation, actual initial value is B ' ₍₁₎:

$B_{\left(1\right)}^{\′}=B_{\left(1\right)}-\frac{B_{max}+B_{min}}{2}$

Wherein, B _maxfor maximum magnetic induction in one-period, B _minfor magnetic induction density minimum in one-period, utilize initial value B ' ₍₁₎act on behalf of B ₍₁₎bring formula B into _(n)=B _(n-1)+ Δ B _(n-1)recalculate, obtain the B value that each moment H is corresponding.

Further, in the present embodiment, described digital oscilloscope bandwidth is more than or equal to 100MHz; In described digital oscilloscope use procedure, described primary current and described secondary current are the waveform about time shaft t symmetry, and storage format is csv form.

Further, in the present embodiment, Figure 4 shows that the low-voltage current mutual inductor of 5/50 circle is by first and second current waveform of current transformer when magnetic hysteresis loop is saturated after digital oscilloscope record ripple.During the core sataration obtained by method in technical solution of the present invention, magnetic hysteresis loop is as shown in Fig. 5 ~ 7.

Be more than preferred embodiment of the present invention, all changes done according to technical solution of the present invention, when the function produced does not exceed the scope of technical solution of the present invention, all belong to protection scope of the present invention.

Claims (3)

1. a current transformer magnetic hysteresis loop observation procedure, is characterized in that, realizes in accordance with the following steps:

Step S1: utilize digital oscilloscope current probe directly to gather the primary current of primary side; After utilizing described digital oscilloscope voltage probe to measure secondary resistive voltage, then be converted into secondary current;

Step S2: gathered described primary current, described secondary current and time are carried out data processing by Matlab;

Step S3: primary current i ₁by producing magnetic field during first side winding, according to Ampere circuit law:

$H=\frac{N_1{i}_1-N_2{i}_2}{L}$

Wherein, N ₁be the number of turn of a winding, N ₂for the number of turn of Secondary Winding, L are the effective magnetic conduction length of iron core, i ₂for secondary current;

Step S4: for the secondary side of current transformer, according to the law of electromagnetic induction:

$e=N_{2}A\frac{dB}{dt}=R_2{i}_2+L_2\frac{{\mathrm{di}}_2}{dt}$

Trapezoidal Bei Ruilong integral method is adopted to above formula, in adjacent spaces time Δ t, magnetic flux and secondary current i ₂relation be shown below:

$\mathrm{\Δ}B\left(t\right)=\frac{R_2\mathrm{\Δ}t}{N_{2}A}(\frac{{\mathrm{\Δi}}_2\left(t\right)}{2}+i_2(t-\mathrm{\Δ}t\left)\right)+\frac{L_2}{N_{2}A}{\mathrm{\Δi}}_2\left(t\right)$

Wherein, A is magnetic conduction cross-sectional area, the R of iron core ₂for all-in resistance, the L of Secondary Winding and secondary load ₂for the total inductance of Secondary Winding and secondary load;

Step S5: because secondary current value is known, obtains the size of Δ B in adjacent spaces time Δ t by the relational expression of magnetic flux and secondary current in described step S4; Remember that first moment magnetic induction density is arbitrary value B ₍₁₎, then second moment induction level is:

B ₍₂₎＝B ₍₁₎+ΔB ₍₁₎

After this magnetic induction density in each moment all adds the difference DELTA B of magnetic induction on the magnetic induction density of previous moment _(n-1), as follows:

B _(n)＝B _(n-1)+ΔB _(n-1)

Namely the magnetic induction density B in the n-th moment is obtained _(n), by using H as X-axis, using B as Y-axis, obtain magnetic hysteresis loop.

2. a kind of current transformer magnetic hysteresis loop observation procedure according to claim 1, is characterized in that, can be obtained by the relational expression of magnetic flux and secondary current in described step S4, and in described step S5, for arbitrary neighborhood interval time, Δ B is and initial value B ₍₁₎irrelevant amount, for normally stable situation, actual initial value is B ' ₍₁₎:

$B_{\left(1\right)}^{\′}=B_{\left(1\right)}-\frac{B_{max}+B_{min}}{2}$

Wherein, B _maxfor maximum magnetic induction in one-period, B _minfor magnetic induction density minimum in one-period, utilize initial value B ' ₍₁₎act on behalf of B ₍₁₎bring formula B into _(n)=B _(n-1)+ Δ B _(n-1)recalculate, obtain the B value that each moment H is corresponding.

3. a kind of current transformer magnetic hysteresis loop observation procedure according to claim 1, it is characterized in that, in described step S1, described digital oscilloscope bandwidth is more than or equal to 100MHz; In described digital oscilloscope use procedure, described primary current and described secondary current are the waveform about time shaft t symmetry, and storage format is csv form.