CN104215928B - Analytical model method for current conversion ratio and phase difference of open-type current transformer - Google Patents

Abstract

The invention relates to an analytical model method for the current conversion ratio and the phase difference of an open-type current transformer. The analytical model method comprises the following steps of: (1) establishing the principle model of the open-type current transformer; (2) deriving the magnetic path time-domain equation of the open-type current transformer according to an ohm law for magnetic path, calculating a circuit time-domain equation considering a secondary side load according to a Faraday law of electromagnetic induction and the ohm law, obtaining the actual current conversion ratio and phase difference calculation formulas of the primary side and the secondary side of the open-type current transformer by the magnetic path and circuit time-domain equations, so as to complete an analytical model for the current conversion ratio and the phase difference of the open-type current transformer. The analytical model established by the method disclosed by the invention has an important theoretical direction value on realization for compatibility between the current transformer for measurement and a current transformer for protection, and is capable of providing a theoretical basis for the error compensation of a split core type current transformer used for online calibration for an electric energy meter.

Description

Open type current transformer electric current no-load voltage ratio and the analytical model method of phase contrast

Technical field

The invention belongs to technical field of electromagnetic measurement, especially a kind of open type current transformer electric current no-load voltage ratio and phase contrast Analytical model method.

Background technology

Current transformer is widely used in power plant, transformer station and power distribution network, is power system electric energy metrical, shape One of state detection, the key equipment of Fault diagnosing and protecting, are also the base realized under intelligent grid for electricity consumption real-time information management One of plinth sensor device.Traditional current transformer typically adopts closed magnetic circuit to design, and that is, the iron core of current transformer is set It is calculated as the magnet ring of a closure, first winding and Secondary Winding are all wound on the annulus iron core of this closure.

Closed magnetic circuit designs it is ensured that magnetic circuit has less magnetoimpedance so that the energy of primary side is more efficiently delivered to two Secondary side.But there is an obvious shortcoming, that is, when there is DC component in primary side current, due to magnetic circuit in closed magnetic circuit design Magnetic resistance very little (close to short-circuit condition), its can produce very high DC magnetic flux in closed magnetic circuit, make iron core BH operating point Enter saturation region.For Verification of Measuring Current Transformer, saturation unshakable in one's determination can lead to current transformer very big measurement error； And for protective current transformer, saturation unshakable in one's determination can make the ratio that the ratio of primary side and secondary side current is higher than rated current Example, the electric current being perceived by current transformer will be significantly less than actual current, thus easily causing protective relaying device malfunction Make, cause power system accident to occur and brings unnecessary economic loss.

For solving this problem, 20 century 70s, the former Soviet Union proposes the design of open type current transformer, and by its Apply in the protection of power system., in iron circuit, there is the electric current of air-gap in the current transformer of so-called open type Sensor, its ultimate principle is to seal in the magnetic resistance of an air-gap in magnetic circuit, thus effectively reducing straight by primary side current The magnetic flux that flow component produces in iron core.Because air permeability is much smaller than pcrmeability unshakable in one's determination, even if therefore air-gap very little, Sufficiently large magnetic resistance can be produced, be in linear zone with the BH operating point ensureing current transformer iron core.

Open type current transformer is successfully applied to power system relay protection device, but not mutual with electric current in measurement It is widely used in sensor.This is because, the change of air-gap, can relatively significantly change magnetic circuit impedance so that current transformer Accuracy also change therewith, cause measurement error.Therefore, in actual electric network, Verification of Measuring Current Transformer with protection electricity consumption Current transformer is two kinds of independent equipment, each other can not be compatible.Obviously, such design increased current transformer volume and Functional redundancy, causes larger waste.

The analytical model of research open type current transformer, can obtain open type electricity from basic electromagnetic energy superposition principle The phase contrast of actual current ratio, primary current and secondary current of current transformer and actual parameter are (as pcrmeability unshakable in one's determination, air-gap Size, secondary load etc.) functional relationship, and then set up for measurement open type current transformer compensation model, be Finally realize open type current transformer measurement and the compatibility of defencive function is laid a solid foundation.

In addition, the progress with intelligent electric energy meter on-line testing technology and development, to a kind of hook type current transformer (opening Formula current transformer) accuracy it is also proposed higher requirement.The analytical model of research open type current transformer, to raising The measurement accuracy of hook type current transformer also has important references and is worth.

Content of the invention

The invention aims to overcoming the deficiencies in the prior art, provide open type current transformer electric current no-load voltage ratio and phase The analytical model method of potential difference.

The present invention solves its technical problem and takes technical scheme below to realize：

A kind of open type current transformer electric current no-load voltage ratio and the analytical model method of phase contrast are as follows including step：

(1) set up the principle model of open type current transformer, setting δ is the width of air-gap, l is the flat of yoke unshakable in one's determination All length, I₁It is primary side current, I₂It is secondary side current, Z is the total impedance of secondary coil loop and load it is assumed that edge unshakable in one's determination The cross-sectional area S of the length of magnetic path is constant, and the number of turn of primary winding is 1 circle, and the number of turn of secondary coil is N circle；

(2) derived according to ohm's law for magnetic circuit open type current transformer magnetic circuit when domain equation, according to faraday electricity Domain equation when law of magnetic induction and Ohm's law calculate the circuit considering secondary lateral load, by time domain magnetic circuit and circuit equation, will During the magnetic circuit obtaining domain equation and during circuit domain equation merge into an One-terminal, when solving directly by once differentiation Item is changed into the form that j ω is multiplied with electric current phasor, by solving the biography of the open type current transformer considering secondary lateral load The amplitude-frequency characteristic of delivery function and phase-frequency characteristic, obtain open type current transformer primary side and secondary side actual current no-load voltage ratio and phase Potential difference computing formula, completes the analytical model of open type current transformer electric current no-load voltage ratio and phase contrast.

And, described step (2) obtains open type current transformer primary side and secondary side actual current no-load voltage ratio and phase place Differ from comprising the following steps that of computing formula：

The principle model that A, combination are set up, sets up equation according to the Ohm's law of magnetic circuit, is considering secondary coil and electricity Impedance sum Z ≠ 0 of flow table itself, the equation listed is：

Wherein, Φ (t) is the magnetic flux in current transformer iron core；μ represents the pcrmeability of current transformer iron core material；μ₀ It is permeability of vacuum, here it is considered that it is equal to air permeability；

B, to secondary side circuit, make R and L be respectively resistive component and inductive component in secondary side total impedance Z, by farad The law of electromagnetic induction and Ohm's law set up equation, and equation is：

C, simultaneous formula (2) and formula (3), obtaining equation is：

D, formula (4) is used instead phasor approach it is expressed as：

Wherein,WithIt is primary side and secondary side current phasor respectively；

E, obtained by formula (5) open type current transformer transmission function characterize；

F, by the transmission function delivery amount shown in formula (6), obtain the ratio of the actual current value of open type current transformer, I.e.：

Secondary side can be solved by formula (6) with the phase contrast of primary side current is：

Thus complete the analytical model of open type current transformer electric current no-load voltage ratio and phase contrast.

Advantages of the present invention and good effect are：

The present invention proposes the analytical model when considering secondary lateral load for the open type current transformer, by simultaneous time domain Dynamic magnetic circuit equation and circuit equation, have obtained open type current transformer primary side and secondary side actual current no-load voltage ratio and phase The computing formula of position change.The analytical model set up, to realizing Verification of Measuring Current Transformer and protective current transformer, Compatibility has more important theoretical direction and is worth, and meanwhile, is alternatively used for the split core type current transformer of electric energy meter on-line calibration Error compensation provides theoretical foundation.

Brief description

Fig. 1 is the principle model schematic diagram of open type current transformer, and wherein, δ is the width of air-gap, and l is magnetic unshakable in one's determination The average length of yoke, I₁It is primary side current, I₂Secondary side current, Z be secondary coil loop and load total impedance it is assumed that Unshakable in one's determination constant along the cross-sectional area S of the length of magnetic path, the number of turn of primary winding is 1 circle, and the number of turn of secondary coil is N circle；

Fig. 2 is ε (N, result of calculation f)；

Fig. 3 is β (N, result of calculation f)；

Fig. 4 is the result of calculation of ε (R, L)；

Fig. 5 is the result of calculation of β (R, L)；

Fig. 6 is the result of calculation of ε (δ, μ r)；

Fig. 7 is the result of calculation of β (δ, μ r).

Specific embodiment

Below to the present invention implement be further described, following examples are descriptive, be not determinate it is impossible to Protection scope of the present invention is limited with this.

A kind of open type current transformer electric current no-load voltage ratio and the analytical model method of phase contrast are as follows including step：

(1) set up the principle model of open type current transformer, as shown in figure 1, wherein, δ is the width of air-gap, and l is The average length of yoke unshakable in one's determination, I₁It is primary side current, I₂It is secondary side current, Z is total resistance of secondary coil loop and load Anti- it is assumed that iron core is constant along the cross-sectional area S of the length of magnetic path, the number of turn of primary winding is 1 circle, and the number of turn of secondary coil is N circle；

(2) derived according to ohm's law for magnetic circuit open type current transformer magnetic circuit when domain equation, according to faraday electricity Domain equation, the time domain magnetic circuit write by row and circuit side when law of magnetic induction and Ohm's law calculate the circuit considering secondary lateral load Journey, domain equation when domain equation during the magnetic circuit obtaining and circuit is merged into an One-terminal, when solving directly by one Subdifferential item is changed into the form that j ω is multiplied with electric current phasor, by solving the open type Current Mutual Inductance considering secondary lateral load The amplitude-frequency characteristic of the transmission function of device and phase-frequency characteristic, obtain its primary side and secondary side actual current no-load voltage ratio and phase difference calculating Formula：Comprise the following steps that：

A, the principle model set up with reference to step (1), under ideal conditions it is believed that the total load of Current Transformer Secondary side Impedance Z=0, the primary side of transformer main magnetic circuit is equal with the electric current number of ampere turns of secondary side, therefore primary side is full with secondary side current The following relation of foot：

I₁=NI₂(1)

And under actual current transformer ruuning situation, due to secondary coil and ammeter itself impedance sum Z ≠ 0, therefore the ratio of actual primary side and the electric current of secondary side be unsatisfactory for formula (1), and also can there is phase contrast between the two.

Here from when domain equation, solve actual primary side and secondary side current when both phase contrasts respectively, right The main magnetic circuit of current transformer, sets up equation according to the Ohm's law of magnetic circuit, and the equation listed is：

Wherein, Φ (t) is the magnetic flux in current transformer iron core；μ represents the pcrmeability of current transformer iron core material；μ₀ It is permeability of vacuum, here it is considered that it is equal to air permeability；

B, to secondary side circuit, make R and L be respectively resistive component and inductive component in secondary side total impedance Z, by farad The law of electromagnetic induction and Ohm's law set up equation, and equation is：

C, simultaneous formula (2) and formula (3), obtaining equation is：

Formula (4) shows, if not considering secondary lateral load, that is, thinks Z=0 (R=0, L=0), then can substantially obtain formula (1) conclusion.Now consider secondary lateral load, that is, think Z ≠ 0, solve respectively the proportionality coefficient α of primary side and secondary side current= I₂/I₁And phase difference beta.

D, formula (4) is used instead phasor approach it is expressed as：

Wherein,WithIt is primary side and secondary side current phasor respectively.

E, obtained by formula (5) open type current transformer transmission function characterize；

F, by the transmission function delivery amount shown in formula (6), obtain the ratio of the actual current value of open type current transformer, I.e.：

Similarly, can solve secondary side by formula (6) with the phase contrast of primary side current is：

Example

For quantifying and more intuitively showing the parsing of open type current transformer that present patent application is set up further Model, in conjunction with a specific embodiment, discusses the groundwork feature of the open type current transformer considering secondary load.Definition The relative difference of the actual current ratio of open type current transformer and ideal current transformer current ratio is：

During calculating, the typical set value of each parameter is：N=200 circle；R=5Ohm；L=1mH；L=100mm；δ= 0.5mm；μ=5000*4 π * 1e-7H/m；F=50Hz；S=0.01*0.01mm².For the sake of convenient, open type electric current will be affected mutual The parameter of the relative difference ε of sensor current ratio and phase difference beta is divided into three groups to discuss, be specifically respectively (N, f), (R, ) and (μ, δ) L.

Calculate actual current no-load voltage ratio change and phase contrast relatively first (i.e. secondary, primary winding with secondary coil number of turn N Turn ratio) and operating frequency f of this open type current transformer between two-dimensional function relation ε (N, f), β (N, f).Calculate When, N and f is set to variable, other specification all takes standard value.ε (N, f) and β (N, result of calculation f), respectively as Fig. 2 and Fig. 3 Shown.

Can obtain as drawn a conclusion from the result of calculation of Fig. 2 and Fig. 3：

1) number of turn of open type current transformer secondary coil is more, actual current no-load voltage ratio closer to preferable no-load voltage ratio, and one Secondary side is also less with the phase contrast of secondary side current.This is because, with the increase of the secondary coil number of turn, secondary side current is corresponding Diminish, the shared ratio in total load of the active loss being caused by secondary lateral load will reduce, the changing of actual current no-load voltage ratio Become and phase offset also will accordingly reduce.

2) operating frequency of open type current transformer is higher, and actual current no-load voltage ratio and phase place are also mutual closer to ideal current The situation of sensor.Therefore, use if open type current transformer is made measurement, the accuracy of its measurement high frequency electric is better than surveying The accuracy of amount low-frequency current.

Secondly, calculate the relative change of actual current no-load voltage ratio and function of ε (R, L) that phase contrast changes, β with secondary lateral load (R,L).During calculating, using similar Variable Control method, obtain result of calculation as shown in Figure 4 and Figure 5.

Fig. 4 and Fig. 5 result of calculation shows, the relative change of the actual no-load voltage ratio of open type current transformer and preferable no-load voltage ratio ε, can increase with the increase of secondary resistance or inductance；Phase difference beta between first and second side electric current, determines in inductance Under the conditions of, can increase with the increase of resistance, but in the case that resistance is fixing, the increase with inductance can reduce on the contrary.

Finally, the relative change calculating actual current no-load voltage ratio is relative with the width of air-gap and core material with phase contrast Function of ε (δ, the μ of pcrmeability change_r)、β(δ,μ_r).During concrete calculating, by the relative permeability of air-gap width δ and core material μ_rIt is set to variable, other specification takes standard value, result of calculation is as shown in Figure 6 and Figure 7.

Fig. 6 and Fig. 7 result of calculation shows, the relative change ε of the actual no-load voltage ratio of open type current transformer and preferable no-load voltage ratio And phase difference beta, with the change of air-gap width, acute variation can occur；And the change to core material relative permeability for ε and β Very insensitive, this is mainly determined by the relative change of current transformer main magnetic circuit magnetic resistance.Closed magnetic circuit iron core Magnetic resistance is

And increasing after opening is air-gap, the magnetic resistance change rate of main magnetic circuit is

Work as δ<<l/μ_rWhen, the major part of magnetic circuit reluctance based on magnetoimpedance component unshakable in one's determination, by secondary in formula (8) and formula (9) The component that side resistance and inductance cause mainly is determined by the relative permeability of core material, but its value is much smaller than 1, i.e. now ε With the value of β all close to 0.But the increase with δ, gap reluctance becomes the principal component of main magnetic circuit magnetic resistance, l/ μ_rδ relatively is changed into In a small amount, therefore main magnetic circuit magnetic resistance is to μ_rChange insensitive, and δ>>l/μ_r, lead to the value of ε and β to change with the width of opening air-gap Change can occur violent change.

Define the diamagnetic saturation coefficient of open type current transformerFor

Reflect open type current transformer with respect to the diamagnetic saturability of closed magnetic circuit current transformer change times Number.It is not difficult to find out it is only necessary to increase less air-gap from formula (12), just can obviously improve the diamagnetic saturability of current transformer Energy.

It should be noted that during setting up above-mentioned analytical model, not considering open type current transformer itself Eddy-current loss.The introducing of open type current transformer air-gap, can significantly increase the magnetic resistance of main magnetic circuit, thus reducing main magnetic circuit Magnetic flux change.Therefore, the eddy-current loss of open type current transformer itself is mutual significantly lower than the electric current of closing magnetic path structure Sensor.

In addition, during the foundation of above-mentioned analytical model, for simplicity, the pcrmeability of core material is approximately considered It is a constant.And it is true that the pcrmeability of ferromagnetic material should be the nonlinear function of magnetic field intensity in iron core.But analysis is sent out Existing, the analytical model set up itself changes and inconspicuous to pcrmeability unshakable in one's determination, therefore, because not considering saturation of magnetic material And the error causing, should be an a small amount of in theory.

Claims (2)

1. a kind of analytical model method of open type current transformer electric current no-load voltage ratio and phase contrast is it is characterised in that include step such as Under：

(1) set up the principle model of open type current transformer, setting δ is the width of air-gap, and l is the average length of yoke unshakable in one's determination Degree, I₁It is primary side current, I₂It is secondary side current, Z is the total impedance of secondary coil loop and load it is assumed that iron core is along magnetic circuit The cross-sectional area S of length is constant, and the number of turn of primary winding is 1 circle, and the number of turn of secondary coil is N circle；

(2) derived according to ohm's law for magnetic circuit open type current transformer magnetic circuit when domain equation, according to faraday's electromagnetism sense Domain equation when answering law and Ohm's law to calculate the circuit considering secondary lateral load, by time domain magnetic circuit and circuit equation, will obtain Magnetic circuit when domain equation and during circuit domain equation merge into an One-terminal, directly once differentiation item is turned when solving It is changed into the form that j ω is multiplied with electric current phasor, by solving the transmission letter of the open type current transformer considering secondary lateral load The amplitude-frequency characteristic of number and phase-frequency characteristic, obtain open type current transformer primary side and secondary side actual current no-load voltage ratio and phase contrast Computing formula, completes the analytical model of open type current transformer electric current no-load voltage ratio and phase contrast.

2. the analytical model method of open type current transformer electric current no-load voltage ratio according to claim 1 and phase contrast, it is special Levy and be：Described step (2) obtains open type current transformer primary side and secondary side actual current no-load voltage ratio and phase difference calculating The comprising the following steps that of formula：

The principle model that A, combination are set up, sets up equation according to the Ohm's law of magnetic circuit, is considering secondary coil and ammeter Impedance sum Z ≠ 0 of itself, the equation listed is：

$(\frac{l}{\mathrm{\&mu;}S}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_{0}S})\mathrm{\&Phi;}\left(t\right)=I_1\left(t\right)-{\mathrm{NI}}_2\left(t\right)---\left(2\right);$

Wherein, Φ (t) is the magnetic flux in current transformer iron core；μ represents the pcrmeability of current transformer iron core material；μ₀It is true Empty pcrmeability, here it is considered that it is equal to air permeability；

B, to secondary side circuit, make R and L be respectively resistive component and inductive component in secondary side total impedance Z, by faraday's electricity Law of magnetic induction and Ohm's law set up equation, and equation is：

$N\frac{d\mathrm{\&Phi;}\left(t\right)}{dt}=L\frac{{\mathrm{dI}}_2\left(t\right)}{dt}+{\mathrm{RI}}_2\left(t\right)---\left(3\right);$

C, simultaneous formula (2) and formula (3), obtaining equation is：

$\frac{1}{NS}(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0})\&lsqb;L\frac{{\mathrm{dI}}_2\left(t\right)}{dt}+{\mathrm{RI}}_2\left(t\right)\&rsqb;=\frac{{\mathrm{dI}}_1\left(t\right)}{dt}-N\frac{{\mathrm{dI}}_2\left(t\right)}{dt}---\left(4\right);$

D, formula (4) is used instead phasor approach it is expressed as：

$\frac{1}{NS}(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0})(j\mathrm{\&omega;}L{\stackrel{\&CenterDot;}{I}}_2+R{\stackrel{\&CenterDot;}{I}}_2)=j\mathrm{\&omega;}{\stackrel{\&CenterDot;}{I}}_1-j\mathrm{\&omega;}NL{\stackrel{\&CenterDot;}{I}}_2---\left(5\right);$

Wherein,WithIt is primary side and secondary side current phasor respectively；

E, obtained by formula (5) open type current transformer transmission function characterize；

$\frac{{\stackrel{\&CenterDot;}{I}}_2}{{\stackrel{\&CenterDot;}{I}}_1}=\frac{j\mathrm{\&omega;}}{\left(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0}\right)\frac{R}{NS}+j\&lsqb;\mathrm{\&omega;}N+\left(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0}\right)\frac{\mathrm{\&omega;}L}{NS}\&rsqb;}---\left(6\right);$

F, by the transmission function delivery amount shown in formula (6), obtain the ratio of the actual current value of open type current transformer, that is,：

$\mathrm{\&alpha;}=\frac{1}{\sqrt{{\&lsqb;(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0})\frac{R}{\mathrm{\&omega;}NS}\&rsqb;}^2+{\&lsqb;N+(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0})\frac{L}{NS}\&rsqb;}^2}}---\left(7\right);$

Secondary side can be solved by formula (6) with the phase contrast of primary side current is：

$\mathrm{\&beta;}=\arctan \frac{(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0})\frac{R}{\mathrm{\&omega;}NS}}{N+(\frac{l}{\mathrm{\&mu;}}+\frac{\mathrm{\&delta;}}{{\mathrm{\&mu;}}_0})\frac{L}{NS}}---\left(8\right)$

Thus complete the analytical model of open type current transformer electric current no-load voltage ratio and phase contrast.