阅读说明：本技术 电磁式pt误差的计算方法 (Electromagnetic PT error calculation method ) 是由 穆小星 鲍进 段梅梅 田正其 欧阳曾恺 周超 夏国芳 龚丹 于 2020-11-16 设计创作，主要内容包括：电磁式PT误差的计算方法,建立PT电路模型,利用PT电路模型建立PT绝对误差矢量及相对误差复数的数学模型；利用绝对误差矢量及相对误差复数的数学模型计算PT复误差；利用PT复误差,对其进行极坐标到直角坐标转换运算,使PT复误差分解为相应实部、虚部；确立PT比差与PT复误差的实部之间的对应关系,以及PT角差与PT复误差的虚部之间的对应关系；进行电压特性、负载特性、负载阻抗角特性影响量分析。本发明电磁式PT误差的计算方法的误差建模简单、严谨,逻辑性强,对电磁式PT误差的认知会更加清晰。(The electromagnetic PT error calculating method includes establishing a PT circuit model, and establishing a mathematical model of PT absolute error vectors and relative error complex numbers by utilizing the PT circuit model; calculating a PT complex error by using a mathematical model of the absolute error vector and the relative error complex number; utilizing the PT complex error to perform polar coordinate to rectangular coordinate conversion operation on the PT complex error, so that the PT complex error is decomposed into a corresponding real part and an imaginary part; establishing a corresponding relation between the PT ratio difference and the real part of the PT complex error, and a corresponding relation between the PT angle difference and the imaginary part of the PT complex error; and analyzing the influence quantity of the voltage characteristic, the load characteristic and the load impedance angle characteristic. The method for calculating the electromagnetic PT error has the advantages of simple and rigorous error modeling, strong logic and clearer cognition on the electromagnetic PT error.)

1. The method for calculating the electromagnetic PT error is characterized in that the vector algebraic analysis method comprises the following steps:

step 1, establishing a T-shaped equivalent circuit model of PT;

step 2, establishing a mathematical model of an absolute error vector and a relative error complex by using the T-shaped equivalent circuit model of the PT in the step 1;

step 3, calculating a PT complex error by using the mathematical model of the absolute error vector and the relative error complex number in the step 2;

4, performing polar coordinate to rectangular coordinate conversion operation on the PT complex error by using the PT complex error in the step 3, so that the PT complex error is decomposed into a corresponding real part and an imaginary part;

step 5, establishing a corresponding relation between the PT ratio difference and the real part of the PT complex error, and a corresponding relation between the PT angle difference and the imaginary part of the PT complex error;

step 6, analyzing the influence quantity of the voltage characteristic, the load characteristic and the load impedance angle characteristic according to the expression in the step 5,

wherein PT is a voltage transformer.

2. The method of calculating an electromagnetic PT error of claim 1, further comprising:

in the step 1, a PT circuit model is expressed in the following formula,

Z₁＝R₁+jX₁、Z′₁＝Z₁/K_n ²，Z₂＝R₂+jX₂、Z′₂＝K_n ²Z₂

wherein Z is₁Is primary coil impedance, R₁Is the real part of the impedance of the primary coil, X₁Is the imaginary part of the impedance of the primary coil, Z₂Is secondary coil impedance, R₂Is the real part of the impedance of the secondary coil, X₂Is the imaginary part, Z ', of the secondary coil impedance'₁Is Z₁Equivalent coil impedance, Z ', converted to secondary'₂Is Z₂Equivalent coil impedance, K, converted to one time_nIs the rated voltage ratio.

3. The method of calculating an electromagnetic PT error of claim 1, further comprising:

in step 1, the secondary load admittance is converted to the primary admittance, which is expressed by the following formula,

Y′＝Y/K_n ²

wherein Y is the secondary load admittance, Y' is the conversion of Y to the primary admittance, K_nIs the rated voltage ratio.

4. The method of calculating an electromagnetic PT error of claim 1, further comprising:

in said step 2, the absolute error is calculated, expressed in the following formula,

wherein the content of the first and second substances,a voltage difference phasor being a primary voltage phasor and a secondary voltage phasor, Z₁Is primary coil impedance, Z'₂Is Z₂The equivalent coil impedance is converted to one time,in order to excite the current phasor, the current phasor is excited,to convert to the secondary current phasor to the primary side.

5. The method of calculating electromagnetic PT errors of claim 1 or 5, further comprising:

in said step 3, the PT complex error is expressed by the following equation,

wherein the content of the first and second substances,is the relative error of the phasor of the PT voltage,in order to obtain the PT no-load complex error,in order to load the complex error for the PT,is a primary voltage phasor, Y_mFor excitation admittance, Y is secondary load admittance, Y' is Y converted to primary admittance, Z₁Is primary coil impedance, Z'₁Is Z₁Equivalent coil impedance, Z ', converted to secondary'₂Is Z₂Equivalent coil impedance converted to one time.

6. The method of calculating an electromagnetic PT error of claim 6, further comprising:

in said step 4, the PT no-load complex error is decomposed into corresponding real and imaginary parts, which are expressed by the following formula,

f₀＝-|Y_m|·|Z₁|sin(ψ+φ₁)

δ₀＝|Y_m|·|Z₁|cos(ψ+φ₁)

wherein the content of the first and second substances,is PT no-load complex error, f₀Is PT no load ratio difference, Y_mFor excitation admittance, delta₀Is PT no-load angle difference, Z₁Is the primary coil impedance, phi₁Is the primary winding impedance angle and psi is the excitation impedance angle.

7. The method of calculating an electromagnetic PT error of claim 6, further comprising:

in said step 4, the PT load complex error is decomposed into corresponding real and imaginary parts, expressed by the following formula,

f_f＝-|Y|·|Z′₁+Z₂|cos(φ-φ₂)

δ_f＝|Y|·|Z′₁+Z₂|sin(φ-φ₂)

wherein the content of the first and second substances,for PT loading complex error, f_fIs PT load ratio difference, delta_fIs PT load angle difference, Z'₁Is Z₁Equivalent coil impedance, Z, converted to the second order₂Is the secondary coil impedance, Y is the secondary load admittance, phi₂The winding impedance angle is converted for the secondary side, and phi is the secondary load impedance angle.

8. The method of calculating an electromagnetic PT error of claim 1, further comprising:

in the step 5, the PT ratio difference f ═ f₀+f_f

Wherein f is₀Is PT no load ratio difference, f_fPT duty ratio difference.

9. The method of calculating an electromagnetic PT error of claim 1, further comprising:

in the step 5, the PT angle difference δ is δ₀+δ_f

Wherein, delta₀Is PT no-load angle difference, delta_fIs the PT load angle difference.

Technical Field

The invention belongs to the technical field of mutual inductor error analysis, and relates to a method for calculating electromagnetic PT errors.

Background

Electromagnetic PT (voltage transformer) has its classical circuit model and error mathematical model, and all documents are modeled and analyzed by geometric analysis method based on vector diagram of model parameters. The vector diagram geometric analysis method has certain defects in theory, the error modeling is unclear, the derivation of a calculation formula is very strong, the rigor and the logicality are not strong, and the graph and the derivation process are complex. This is because the geometric analysis method is difficult to deal with the arithmetic problems of algebraic signs and mathematics, and cannot form logical reasoning and deduction, which is very difficult to understand.

The current modeling method:

as shown in FIGS. 1 and 2, the ratio difference f is converted to the primary secondary voltage U'₂(i.e. K)_nU₂) And the actual primary voltage U₁By the difference between U₁Is expressed in percent, i.e.

Wherein, K_nIs the rated voltage ratio.

When K is_nU₂＞U₁When f is positive; otherwise, f is a negative value.

The phase difference delta is the secondary voltage phasor after 180 DEG rotationAnd the actual primary voltageThe angle between the phasors is expressed in minutes. When in useAhead ofWhen, δ is a positive value; otherwise, δ is negative.

The calculation formula for the ratio difference f and the phase angle difference δ can be derived from the phasor diagram as follows:

wherein, I₀Is an excitation current, I'₂To convert to a secondary current on the primary side, r₁Is the primary winding resistance, x₁Is primary winding leakage reactance r'₂Is converted into secondary winding resistance, x 'to the primary side'₂For conversion to leakage reactance of the secondary winding on the primary side, theta₀Is a magnetic hysteresis angle of an iron core,is the primary load impedance angle of the transformer,the secondary load impedance angle of the transformer is shown, and delta is the phase difference.

The electromagnetic voltage transformer (PT) has a classical circuit model and an error mathematical model, and all documents at present are modeled and analyzed by a geometric analysis method by means of a vector diagram of model parameters. The vector diagram geometric analysis method has certain defects in theory, the error modeling is unclear, the derivation of a calculation formula is very strong, the rigor and the logicality are not strong, and the graph and the derivation process are complex. This is because the geometric analysis method is difficult to deal with the arithmetic problems of algebraic signs and mathematics, and cannot form logical reasoning and deduction, which is very difficult to understand.

Disclosure of Invention

In order to solve the problems in the prior art, the invention aims to provide a method for calculating an electromagnetic PT error. According to the invention, the electromagnetic PT error mathematical model is established through a vector mathematical analysis method, compared with the current theory, the error modeling is simple and rigorous, the logic is strong, and the cognition of the electromagnetic PT error is clearer. It is a perfect and innovative theory for electromagnetic PT error.

The invention adopts the following technical scheme:

the electromagnetic PT error calculation method and the vector algebraic analysis method comprise the following steps:

step 1, establishing a PT circuit model;

step 2, establishing a mathematical model of an absolute error vector and a relative error complex number by using the PT circuit model in the step 1;

step 3, calculating a PT complex error by using the mathematical model of the absolute error vector and the relative error complex number in the step 2;

4, performing polar coordinate to rectangular coordinate conversion operation on the PT complex error by using the PT complex error in the step 3, so that the PT complex error is decomposed into a corresponding real part and an imaginary part;

step 5, establishing a corresponding relation between the PT specific difference and the PT complex error real part and a corresponding relation between the PT angular difference and the PT complex error imaginary part;

step 6, analyzing the influence quantity of the voltage characteristic, the load characteristic and the load impedance angle characteristic according to the expression in the step 5,

wherein PT is a voltage transformer.

In the step 1, a PT circuit model is expressed in the following formula,

Z₁＝R₁+jX₁、Z′₁＝Z₁/K_n ²，Z₂＝R₂+jX₂、Z′₂＝K_n ²Z₂

wherein Z is₁Is primary coil impedance, R₁Is the real part of the impedance of the primary coil, X₁Is the imaginary part of the impedance of the primary coil, Z₂Is secondary coil impedance, R₂Is the real part of the impedance of the secondary coil, X₂Is the imaginary part, Z ', of the secondary coil impedance'₁Is Z₁Equivalent coil impedance, Z ', converted to secondary'₂Is Z₂Equivalent coil impedance, K, converted to one time_nIs the rated voltage ratio.

In step 1, the secondary load admittance is converted to the primary admittance, which is expressed by the following formula,

Y′＝Y/K_n ²

wherein Y is the secondary load admittance, Y' is the converted primary admittance, K_nIs the rated voltage ratio.

In the step 2, a voltage difference phasor of the primary voltage phasor and the secondary voltage phasor is calculated, expressed by the following formula,

wherein the content of the first and second substances,a voltage difference phasor being a primary voltage phasor and a secondary voltage phasor, Z₁Is primary coil impedance, Z'₂To convert to the equivalent coil impedance of one time,in order to excite the current phasor, the current phasor is excited,to convert to the secondary current phasor to the primary side.

In said step 3, the PT complex error is calculated, expressed by the following formula,

wherein the content of the first and second substances,is the relative error of the phasor of the PT voltage,in order to obtain the PT no-load complex error,in order to load the complex error for the PT,is a primary voltage phasor, Y_mFor excitation admittance, Y is secondary load admittance, Y' is Y converted to primary admittance, Z₁Is primary coil impedance, Z'₁Is Z₁Equivalent coil impedance, Z ', converted to secondary'₂Is Z₂Equivalent coil impedance converted to one time.

In said step 4, the PT no-load complex error is decomposed into corresponding real and imaginary parts, which are expressed by the following formula,

f₀＝-|Y_m|·|Z₁|sin(ψ+φ₁)

δ₀＝|Y_m|·|Z₁|cos(ψ+φ₁)

wherein f is₀Is PT no load ratio difference, Y_mFor excitation admittance, delta₀Is PT no-load angle difference, Z₁Is the primary coil impedance, phi₁Is the primary winding impedance angle and psi is the excitation impedance angle.

In said step 4, the PT load complex error is decomposed into corresponding real and imaginary parts, expressed by the following formula,

f_f＝-|Y|·|Z′₁+Z₂|cos(φ-φ₂)

δ_f＝|Y|·|Z′₁+Z₂|sin(φ-φ₂)

wherein the content of the first and second substances,for PT loading complex error, f_fIs PT load ratio difference, delta_fIs PT load angle difference, Z'₁For equivalent coil impedance converted to quadratic, Z₂Is the secondary coil impedance, Y is the secondary load admittance, phi₂The winding impedance angle is converted for the secondary side, and phi is the secondary load impedance angle.

In the step 5, the PT ratio difference f ═ f₀+f_f

Wherein f is₀Is PT no load ratio difference, f_fPT duty ratio difference.

In the step 5, the PT angle difference δ is δ₀+δ_f

Wherein, delta₀Is PT no-load angle difference, delta_fIs the PT load angle difference.

Compared with the prior art, the method for calculating the electromagnetic current transformer error has the advantages that the error modeling is simple and rigorous, the logic is strong, and the cognition on the electromagnetic PT error is clearer.

The two methods are compared:

1) the vector diagram geometric analysis method is a geometric method, is complex and strong in tension and has the specification property; the vector mathematical analysis method is a vector method, deductive reasoning and natural generation;

2) the vector diagram geometric analysis method error calculation model contains voltage and current excitation parameters and does not show the essence of errors, and the vector mathematical analysis method calculation model only has design (manufacturing) parameters of a mutual inductor and reflects internal factors of the errors.

Drawings

FIG. 1 is a diagram of an equivalent circuit of PT;

FIG. 2 is a phasor diagram of PT;

fig. 3 is a PT equivalent circuit diagram.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. The embodiments described herein are only some embodiments of the invention, and not all embodiments. All other embodiments obtained by a person skilled in the art without making any inventive step on the basis of the spirit of the present invention are within the scope of protection of the present invention.

According to the invention, the electromagnetic PT error mathematical model is established through a vector mathematical analysis method, compared with the current theory, the error modeling is simple and rigorous, the logic is strong, and the cognition of the electromagnetic PT error is clearer. It is a perfect and innovative theory for electromagnetic PT error.

The vector algebra analysis method comprises the following modeling steps:

step 1, establishing a PT circuit model;

step 2, establishing a mathematical model of an absolute error vector and a relative error complex number by using the PT circuit model in the step 1;

step 3, calculating a PT complex error by using a mathematical model of the absolute error vector and the relative error complex number;

4, performing polar coordinate to rectangular coordinate conversion operation on the PT complex error by using the PT complex error in the step 3, so that the PT complex error is decomposed into a corresponding real part and an imaginary part;

step 5, establishing a corresponding relation between the PT specific difference and the PT complex error real part and a corresponding relation between the PT angular difference and the PT complex error imaginary part;

step 6, analyzing the influence quantity of the voltage characteristic, the load characteristic and the load impedance angle characteristic according to the expression in the step 5,

wherein PT is a voltage transformer.

PT circuit model in step 1:

as shown in figure 3 of the drawings,

the PT circuit model is expressed by the following formula,

Z₁＝R₁+jX₁、Z′₁＝Z₁/K_n ²，Z₂＝R₂+jX₂、Z′₂＝K_n ²Z₂

wherein Z is₁Is primary coil impedance, R₁Is the real part of the impedance of the primary coil, X₁Is the imaginary part of the impedance of the primary coil, Z₂Is secondary coil impedance, R₂Is the real part of the impedance of the secondary coil, X₂Is the imaginary part, Z ', of the secondary coil impedance'₁Is Z₁Equivalent coil impedance, Z ', converted to secondary'₂Is Z₂Equivalent coil impedance, K, converted to one time_nIs the rated voltage ratio.

The secondary load admittance is converted to the primary admittance, expressed by the following formula,

Y′＝Y/K_n ²

wherein Y is the secondary load admittance, Y' is the converted primary admittance, K_nIs the rated voltage ratio.

PT error mathematical model:

according to the principle of polarity reduction, the reference directions of voltage and current are defined as shown in fig. 1, and according to the circuit theory and the vector mathematical expression method, the following steps are provided:

calculating a voltage difference phasor of the primary voltage phasor and the secondary voltage phasor, expressed by the following formula,

wherein the content of the first and second substances,a voltage difference phasor being a primary voltage phasor and a secondary voltage phasor, Z₁Is primary coil impedance, Z'₂To convert to the equivalent coil impedance of one time,in order to excite the current phasor, the current phasor is excited,to convert to the secondary current phasor to the primary side.

The PT complex error is calculated, expressed by the following equation,

wherein the content of the first and second substances,in order to obtain the PT no-load complex error,in order to load the complex error for the PT,is the primary voltage phasor.

The PT no-load complex error is decomposed into a corresponding real part and an imaginary part, which are expressed by the following formula,

f₀＝-|Y_m|·|Z₁|sin(ψ+φ₁)

＝-|Y_m|[R₁sinψ+x₁cosψ] (4)

δ₀＝|Y_m|·|Z₁|cos(ψ+φ₁)

＝|Y_m|[R₁cosψ-x₁sinψ] (5)

wherein f is₀Is PT no load ratio difference, Y_mFor excitation admittance, delta₀Is PT no-load angle difference, Z₁Is the primary coil impedance, phi₁Is the primary winding impedance angle and psi is the excitation impedance angle.

The PT load complex error is decomposed into corresponding real and imaginary parts, expressed by the following equation,

f_f＝-|Y|·|Z′₁+Z₂|cos(φ-φ₂)(7)

δ_f＝|Y|·|Z′₁+Z₂|sin(φ-φ₂) (8)

wherein the content of the first and second substances,for PT loading complex error, f_fIs PT load ratio difference, delta_fIs PT load angle difference, Z'₁For equivalent coil impedance converted to quadratic, Z₂Is the secondary coil impedance, Y is the secondary load admittance, phi₂The winding impedance angle is converted for the secondary side, and phi is the secondary load impedance angle.

PT ratio f ═ f₀+f_f, (9)

Wherein f is₀Is PT no load ratio difference, f_fPT duty ratio difference.

Angle difference of PT (delta)₀+δ_f (10)

Wherein, delta₀Is PT no-load angle difference, delta_fIs the PT load angle difference.

It should be noted later that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.