CN104991994A - Transformer field current simulation method based on J-A magnetic hysteresis model - Google Patents

Abstract

The invention relates to a transformer field current simulation method based on a J-A magnetic hysteresis model, wherein the technical characteristic comprises following steps: a classical four-order Runge-Kutta method or an Euler method is utilized to solve a J-A magnetic hysteresis model to obtain a B-H curve; and according to the obtained B-H curve, a magnetic field intensity H value corresponding to each magnetic flux density B point is calculated to obtain the relationship between voltage and field current, thus the whole simulation process is completed. According to the utility model, a Jiles-Atherton magnetic hysteresis model is utilized; the simulation processing of the field current to a transformer at different amplitude power frequency over-voltages is performed through a Matlab software; and saturation and magnetic hysteresis effect of a transformer iron core are fully considered, thus the field current waveform of the transformer at different power frequency over-voltage levels can be obtained accurately; the simulation result is more accurate and reliable; and a reference can be provided for an operating worker.

Description

A kind of transformer magnetizing current emulation mode based on J-A hysteresis model

Technical field

The invention belongs to transformer technology field, be specifically related to a kind of transformer magnetizing current emulation mode based on J-A hysteresis model.

Background technology

Power transformer is the visual plant in electric system, and the iron core due to power transformer has saturated and hysteresis effect, and its BH curve is not linear single valued relation.Although general transformer is operated in linearity range, but when carrying out simulation calculation, sometimes need to consider the nonlinear characteristic of transformer and the impact of magnetic hysteresis, such as power-frequency overvoltage etc., therefore, in the urgent need to a kind of effective ways, simulation process is carried out to transformer magnetizing current.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, provide a kind of reasonable in design, fast and accurately based on the transformer magnetizing current emulation mode of J-A hysteresis model.

The present invention solves its technical matters and takes following technical scheme to realize:

Based on a transformer magnetizing current emulation mode for J-A hysteresis model, comprise the following steps:

Step 1, use classical method of Runge-Kutta or Euler's method to solve J-A hysteresis model, obtain BH curve;

Step 2, calculate each magnetic field intensity H value corresponding to magnetic density B point according to obtaining BH curve, thus obtain the relation of voltage and exciting current, complete whole simulation process.

And described J-A hysteresis model is:

$\left\{\begin{array}{c}{M}_{an}=M_{s}L\left(\frac{H+\mathrm{\α}M}{a}\right)\\ \frac{{\mathrm{dM}}_{irr}}{dH}=\frac{\mathrm{\θ}(M_{an}-M_{irr})}{\mathrm{\δ}k-\mathrm{\α}(M_{an}-M_{irr})}\\ M_{rev}=c(M_{an}-M_{irr})\\ M=M_{irr}+M_{rev}\end{array}\right.$

Wherein:

$\mathrm{\&delta;}=\left\{\begin{array}{cc}1,& \frac{dH}{dt}>0\\ -1,& \frac{dH}{dt}<0\end{array}\right.$

L (x) is Langevin function, and its expression is:

$L\left(x\right)=\frac{e^x+e^{-x}}{e^x-e^{-x}}-\frac{1}{x}$

M _anfor the anhysteretic magnetization, H is magnetic field intensity, and B is magnetic induction density, and M is the magnetization, M _irrfor irreversible magnetization intensity, M _revfor reversible magnetization intensity, e is the natural logarithm truth of a matter, M _sfor saturation magnetization, a is the parameter showing anhysteretic magnetization curve shape, and c is reversible magnetization coefficient, and k is the parameter of magnetic domain to motion inhibition, and α is the parameter of the interaction situation between magnetic domain.

And, the parameter that described J-A hysteresis model has following five needs to determine:

M _s: saturation magnetization;

A: the parameter showing anhysteretic magnetization curve shape;

C: reversible magnetization coefficient, value is 0 to 1;

K: magnetic domain is to the parameter of motion inhibition;

α: the parameter characterizing the interaction situation between magnetic domain;

Above parameter can be determined by the method for test.

And, described in solve J-A hysteresis model method comprise the following steps:

The parameter that step (1), five needs inputting J-A hysteresis model are determined: saturation magnetization M _s, parameter a, the reversible magnetization coefficient c of delayed magnetization curve shape, magnetic domain is to the parameter alpha of the interaction situation between the parameter k of motion inhibition, magnetic domain;

Step (2), input computing time and institute's making alive;

Step (3), Initial values of Differential Equations is set;

Step (4), calculating anhysteretic magnetization M _an;

Step (5), determine this slope;

Step (6), calculate any value lower, and judge whether the time, if do not return step to the time

(4) continue process, otherwise terminate.

And the concrete treatment step of described step 2 comprises:

Step (1), provide the BH curve that obtains and the time dependent vector of magnetic density B;

Do you step (2), judge that dB/dt is greater than 0? if be greater than 0, then perform step (3), otherwise perform step (4);

Step (3) upwards finds and two points in the immediate BH curve of current magnetic density B; The magnetic field intensity H value of now corresponding magnetic density B is tried to achieve, jump procedure (5) in these two some Linear differences;

Step (4), to find and two points in the immediate BH curve of current magnetic density B downwards; The magnetic field intensity H value of now corresponding magnetic density B is tried to achieve in these two some Linear differences;

Step (5), judge whether the time, if not to the time, then go to step (2);

Step (6), tried to achieve the situation of change of Current versus time by magnetic field intensity H, process terminates.

Advantage of the present invention and good effect are:

The present invention utilizes Jiles-Atherton hysteresis model, the simulation process of transformer exciting current under different amplitude power-frequency overvoltage is carried out by Matlab software, it fully takes into account the saturated of transformer core and hysteresis effect, the excitation current waveform of transformer under different power-frequency overvoltage level can be obtained exactly, its simulation result more accurately and reliably, for operations staff provides reference.

Accompanying drawing explanation

Fig. 1 is that the present invention solves J-A hysteresis model process flow diagram;

Fig. 2 is that the present invention solves exciting current process flow diagram.

Embodiment

Below in conjunction with accompanying drawing, the embodiment of the present invention is further described:

Based on a transformer magnetizing current emulation mode for J-A hysteresis model, comprise the following steps:

Step 1, use classical method of Runge-Kutta or Euler's method to solve Jiles-Atherton hysteresis model (J-A hysteresis model), obtain BH curve (magnetization curve).

The present invention adopts following Jiles-Atherton hysteresis model:

$\left\{\begin{array}{c}{M}_{an}=M_{s}L\left(\frac{H+\mathrm{\&alpha;}M}{a}\right)\\ \frac{{\mathrm{dM}}_{irr}}{dH}=\frac{\mathrm{\&theta;}(M_{an}-M_{irr})}{\mathrm{\&delta;}k-\mathrm{\&alpha;}(M_{an}-M_{irr})}\\ M_{rev}=c(M_{an}-M_{irr})\\ M=M_{irr}+M_{rev}\end{array}\right.---\left(1\right)$

Wherein:

$\mathrm{\&delta;}=\left\{\begin{array}{cc}1,& \frac{dH}{dt}>0\\ -1,& \frac{dH}{dt}<0\end{array}\right.---\left(3\right)$

In formula (1), L (x) is Langevin function, and its expression is

$L\left(x\right)=\frac{e^x+e^{-x}}{e^x-e^{-x}}-\frac{1}{x}---\left(4\right)$

M in above-mentioned formula _anfor the anhysteretic magnetization, H is magnetic field intensity, and B is magnetic induction density, and M is the magnetization, M _irrfor irreversible magnetization intensity, M _revfor reversible magnetization intensity, e is the natural logarithm truth of a matter, M _sfor saturation magnetization, a is the parameter showing anhysteretic magnetization curve shape, and c is reversible magnetization coefficient, and k is the parameter of magnetic domain to motion inhibition, and α is the parameter of the interaction situation between magnetic domain.

The parameter that above-mentioned Jiles-Atherton hysteresis model has five needs to determine, they respectively:

M _s: saturation magnetization;

A: the parameter showing anhysteretic magnetization curve shape;

C: reversible magnetization coefficient, value is 0 to 1;

K: magnetic domain is to the parameter of motion inhibition;

α: the parameter characterizing the interaction situation between magnetic domain.

Above parameter can be determined by the method for test.

The concrete processing procedure solving Jiles-Atherton hysteresis model (J-A hysteresis model) as shown in Figure 1, comprises following treatment step:

The parameter that step (1), five needs inputting J-A hysteresis model are determined;

Step (2), input computing time and institute's making alive;

Step (3), Initial values of Differential Equations is set;

Step (4), calculating anhysteretic magnetization M _an;

Step (5), determine this slope;

Step (6), calculate any value lower, and judge whether the time, if do not return step to the time

(4) continue process, otherwise terminate.

Step 2, calculate each magnetic field intensity H value corresponding to magnetic density B point according to obtaining BH curve, thus obtain the relation of voltage and exciting current, complete whole simulation process.

Magnetic density B over time situation tries to achieve in advance, because no-load transformer is not when considering leakage impedance pressure drop:

$u=N_{1}S\frac{dB}{dt}---\left(5\right)$

Wherein S is area of core section, N ₁it is the former limit number of turn.

Therefore, the concrete processing procedure of this step, as shown in Figure 2, comprises following treatment step:

Step (1), provide the BH curve that obtains and the time dependent vector of B;

Do you step (2), judge that dB/dt is greater than 0? if be greater than 0, then perform step (3), otherwise perform step (4);

Step (3) upwards finds and two points in the immediate BH curve of current B; The H value of now corresponding B is tried to achieve, jump procedure (5) in these two some Linear differences

Step (4), to find and two points in the immediate BH curve of current B downwards; The H value of now corresponding B is tried to achieve in these two some Linear differences;

Step (5), judge whether the time, if not to the time, then go to step (2);

Step (6), tried to achieve the situation of change of Current versus time by H, process terminates.

The present invention can pass through Matlab software, and two the flow chart programming designs provided according to Fig. 1 and Fig. 2 realize.

It is emphasized that; embodiment of the present invention is illustrative; instead of it is determinate; therefore the present invention includes the embodiment be not limited to described in embodiment; every other embodiments drawn by those skilled in the art's technical scheme according to the present invention, belong to the scope of protection of the invention equally.

Claims (5)

1., based on a transformer magnetizing current emulation mode for J-A hysteresis model, it is characterized in that comprising the following steps:

Step 1, use classical method of Runge-Kutta or Euler's method to solve J-A hysteresis model, obtain BH curve;

Step 2, calculate each magnetic field intensity H value corresponding to magnetic density B point according to obtaining BH curve, thus obtain the relation of voltage and exciting current, complete whole simulation process.

2. a kind of transformer magnetizing current emulation mode based on J-A hysteresis model according to claim 1, is characterized in that: described J-A hysteresis model is:

$\left\{\begin{array}{c}{M}_{an}=M_{s}L\left(\frac{H+\mathrm{\&alpha;}M}{a}\right)\\ \frac{{\mathrm{dM}}_{irr}}{dH}=\frac{\mathrm{\&theta;}(M_{an}-M_{irr})}{\mathrm{\&delta;}k-\mathrm{\&alpha;}(M_{an}-M_{irr})}\\ M_{rev}=c(M_{an}-M_{irr})\\ M=M_{irr}+M_{rev}\end{array}\right.$

Wherein:

$\mathrm{\&delta;}=\left|\begin{array}{cc}1,& \frac{dH}{dt}>0\\ -1,& \frac{dH}{dt}<0\end{array}\right.$

L (x) is Langevin function, and its expression is:

$L\left(x\right)=\frac{e^x+e^{-x}}{e^x-e^{-x}}-\frac{1}{x}$

M _anfor the anhysteretic magnetization, H is magnetic field intensity, and B is magnetic induction density, and M is the magnetization, M _irrfor irreversible magnetization intensity, M _revfor reversible magnetization intensity, e is the natural logarithm truth of a matter, M _sfor saturation magnetization, a is the parameter showing anhysteretic magnetization curve shape, and c is reversible magnetization coefficient, and k is the parameter of magnetic domain to motion inhibition, and α is the parameter of the interaction situation between magnetic domain.

3. a kind of transformer magnetizing current emulation mode based on J-A hysteresis model according to claim 2, is characterized in that: the parameter that described J-A hysteresis model has following five needs to determine: saturation magnetization M _s, the parameter a of anhysteretic magnetization curve shape, reversible magnetization coefficient c, magnetic domain, to the parameter k of motion inhibition, characterizes the parameter alpha of the interaction situation between magnetic domain, and above parameter is determined by the method for test.

4. a kind of transformer magnetizing current emulation mode based on J-A hysteresis model according to any one of claims 1 to 3, is characterized in that: described in solve J-A hysteresis model method comprise the following steps:

The parameter that step (1), five needs inputting J-A hysteresis model are determined: saturation magnetization M _s, parameter a, the reversible magnetization coefficient c of delayed magnetization curve shape, magnetic domain is to the parameter alpha of the interaction situation between the parameter k of motion inhibition, magnetic domain;

Step (2), input computing time and institute's making alive;

Step (3), Initial values of Differential Equations is set;

Step (4), calculating anhysteretic magnetization M _an;

Step (5), determine this slope;

Step (6), calculate any value lower, and judge whether the time, if do not return step (4) to the time to continue process, otherwise terminate.

5. a kind of transformer magnetizing current emulation mode based on J-A hysteresis model according to any one of claims 1 to 3, is characterized in that: the concrete treatment step of described step 2 comprises:

Step (1), provide the BH curve that obtains and the time dependent vector of magnetic density B;

Do you step (2), judge that dB/dt is greater than 0? if be greater than 0, then perform step (3), otherwise perform step (4);

Step (3) upwards finds and two points in the immediate BH curve of current magnetic density B; The magnetic field intensity H value of now corresponding magnetic density B is tried to achieve, jump procedure (5) in these two some Linear differences;

Step (4), to find and two points in the immediate BH curve of current magnetic density B downwards; The magnetic field intensity H value of now corresponding magnetic density B is tried to achieve in these two some Linear differences;

Step (5), judge whether the time, if not to the time, then go to step (2);

Step (6), tried to achieve the situation of change of Current versus time by magnetic field intensity H, process terminates.