CN109884564B - Method and device for measuring magnetic characteristics of transformer magnetic core - Google Patents
Method and device for measuring magnetic characteristics of transformer magnetic core Download PDFInfo
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Abstract
The invention discloses a method and a device for measuring the magnetic property of a magnetic core of a transformer, comprising the following steps: actually measuring a magnetic hysteresis loop H-B of the annular magnetic core in the process of reaching deep saturation; determining the optimal value of the characteristic parameters of the J-A model based on the actually measured hysteresis loop H-B to obtain a hysteresis loop H-B' based on the J-A model; correcting the magnetic flux density of the magnetic core approaching the saturation section to obtain a transition magnetic hysteresis loop H-B'; correcting the approaching saturation section of the hysteresis loop H-B 'based on the J-A model by utilizing the approaching saturation section of the transition hysteresis loop H-B'; and measuring the magnetic field intensity of the magnetic core of the transformer in the running state, and determining the magnetic flux density in the current state according to the corrected magnetic hysteresis loop. The magnetic characteristic measuring method provided by the invention corrects the magnetic flux density of the magnetic core approaching saturation section, so that the error of the J-A model in describing the magnetic core approaching saturation is greatly reduced, the defects of the J-A model are overcome, the accuracy of the J-A model in describing the magnetic characteristic of the magnetic core is improved, the calculation process is simple, and the operability is strong.
Description
Technical Field
The invention belongs to the technical field of transformer cores, and particularly relates to a method and a device for measuring magnetic characteristics of a transformer core.
Background
In the power system, a plurality of ferromagnetic elements such as power transformers and mutual inductors are contained, and in order to describe the operating characteristics of the ferromagnetic elements more accurately, an equivalent model of the ferromagnetic elements needs to be accurately expressed, so that the safety and the reliability of the operation of the power system are ensured. The magnetic core is a core component of a ferromagnetic element, and the key of the equivalent model expression lies in the description of the physical and mathematical aspects of the magnetization process of the magnetic core.
The magnetic hysteresis loop of the magnetic core is an important representation of the magnetic characteristics of the magnetic core, and important magnetic parameters such as the magnetic permeability, the residual magnetization intensity, the coercive force and the like of the magnetic core can be obtained through the magnetic hysteresis loop. There are many models for describing magnetic properties of magnetic cores, which can be classified into macroscopic magnetization models, semi-macroscopic magnetization models, and microscopic magnetization models. Although the fitting effect of the macroscopic magnetization model to the hysteresis loop is good, the macroscopic magnetization model lacks description of a physical mechanism; the microscopic magnetization model fully considers the physical mechanism of the magnetization process, but the calculation is too complex to be suitable for engineering practice. The J-A model is based on the domain wall theory of ferromagnetic materials, comprehensively considers the microscopic change and macroscopic expression in the magnetization process, has physical explanation more conforming to the magnetization process of the magnetic core, has simpler mathematical expression form, has the advantages of clear physical significance and simple and convenient calculation process, and is widely applied to the field of magnetic core magnetization modeling.
Because the J-A model only considers the physical process in the range of the middle-low magnetic field, namely the domain wall replacement process and the domain wall bending process, and does not consider the rotation process of the magnetic moment in the magnetic domain in the approaching saturation section of the magnetic core, and a larger error can be generated when the approaching saturation section of the magnetic hysteresis loop is described, the change of the magnetic property of the magnetic core of the transformer cannot be accurately described when the J-A model is applied to describe the magnetic property of the magnetic core of the transformer, so that the analysis of the running state of the transformer is deviated, the safe running of the transformer is influenced, and even the transformer is damaged.
Disclosure of Invention
The invention aims to provide a method and a device for measuring magnetic characteristics of a transformer core, aiming at solving the problem of low accuracy when a magnetic core approaches a saturation section when J-A model is applied to describe the magnetic characteristics of the transformer core.
In order to achieve the above object, an aspect of the present invention provides a method for measuring magnetic properties of a magnetic core of a transformer, including:
(1) measuring the magnetic field intensity H and the magnetic flux density B of the annular magnetic core in the process of reaching deep saturation;
(2) root of herbaceous plantAccording to the measured magnetic field intensity H and magnetic flux density B, the optimal value of the characteristic parameter of the J-A model is obtained; the characteristic parameters comprise: saturation magnetization MsHysteresis loss coefficient k, magnetic domain coupling coefficient α, reversibility factor c and shape parameter a;
(3) obtaining a predicted magnetic flux density B' according to the optimal value of the characteristic parameter of the J-A model and the actually measured magnetic field intensity H;
(4) correcting the predicted magnetic flux density B 'in the approaching saturation section of the annular magnetic core to obtain a compensation magnetic flux density B';
(5) measuring the magnetic field intensity of the magnetic core of the transformer in the running state, and determining the magnetic flux density in the current running state according to the relation between the predicted magnetic flux density B' and the actually measured magnetic field intensity H in the non-approaching saturation section of the magnetic core; and in the magnetic core approaching saturation section, determining the magnetic flux density in the current operation state according to the relationship between the compensation magnetic flux density B' and the actually measured magnetic field intensity H.
Further, in the step (3), the method for obtaining the predicted magnetic flux density B' includes:
(31) obtaining a hysteresis-free magnetization Man：
(32) According to the magnetization M without hysteresisanObtaining a predicted magnetization M:
wherein, delta is a direction coefficient when dH/dt>When 0, δ is 1; when dH/dt<At 0, δ is-1, δMTo correct the factor, when delta (M)anwhen-M) < 0, δ M0; when delta (M)anwhen-M) > 0, δM＝1；
(33) Obtaining a predicted magnetic flux density B' from the predicted magnetization M and the actually measured magnetic field strength H:
B′＝μ0(H+M)
wherein，μ0Is a vacuum permeability, mu0＝4π×10-7N/A2。
Further, in the step (4), the method of correcting the predicted magnetic flux density B' to obtain the compensation magnetic flux density B ″ includes:
considering the rotation process of magnetic moment in magnetic domain in the magnetic core approaching saturation section, the predicted magnetization M in the magnetic core approaching saturation section is smaller than the actual value, and the non-hysteresis magnetization M is utilizedanAnd the weighted value of the predicted magnetization M characterizes the actual magnetization, the compensation flux density B' is expressed as:
B″＝μ0(H+p1Man+p2M)
wherein p is1、p2And the undetermined coefficient is obtained, so that the error between the compensation magnetic flux density B' and the actually measured magnetic flux density B in the magnetic core approaching saturation section is minimum.
Preferably, p is1Is 0.32, p2Is 0.60.
Further, the ring-shaped magnetic core approaches a saturation section: the magnetic flux density is a magnetic field intensity interval corresponding to 0.3 to 0.95 times of the maximum value of the actually measured magnetic flux density B;
further, the magnetic core non-approaching saturation section is as follows: the magnetic core approaches the interval outside the saturation section.
Further, the transformer core is the same material as the toroidal core.
In another aspect, the present invention provides a device for measuring magnetic properties of a magnetic core of a transformer, including: the system comprises a J-A model calibration module, a magnetic flux density prediction module, a magnetic flux density correction module and a transformer magnetic core magnetic characteristic acquisition module;
the J-A model calibration module is used for measuring the magnetic field intensity H and the magnetic flux density B of the annular magnetic core and obtaining the optimal value of the characteristic parameter of the J-A model according to the relation between the measured magnetic field intensity and the measured magnetic flux density;
the magnetic flux density prediction module is used for obtaining predicted magnetic flux density B' according to the optimal value of the characteristic parameter of the J-A model and the actually measured magnetic field intensity H;
the magnetic flux density correction module is used for correcting the predicted magnetic flux density B 'in the approaching saturation section of the annular magnetic core to obtain a compensated magnetic flux density B';
the magnetic property acquisition module of the transformer core is used for measuring the magnetic field intensity of the transformer core in the operating state, and determining the magnetic flux density in the current operating state according to the relation between the predicted magnetic flux density B' and the actually measured magnetic field intensity H in the non-approaching saturation section of the magnetic core; and in the magnetic core approaching saturation section, determining the magnetic flux density in the current operation state according to the relationship between the compensation magnetic flux density B' and the actually measured magnetic field intensity H.
Through the technical scheme, compared with the prior art, the invention has the following beneficial effects:
(1) the method for measuring the magnetic properties of the transformer core provided by the invention considers the rotation process of magnetic moments in magnetic domains when the magnetic core approaches saturation, and corrects the magnetic flux density of the magnetic core approaching saturation section, so that the error of a J-A model when describing the magnetic core approaching saturation is greatly reduced, the defects of the J-A model are overcome, and the accuracy of the J-A model when describing the magnetic properties of the magnetic core is improved.
(2) The invention adopts a first-order linear equation to correct the magnetic flux density, and has simple calculation process and strong operability.
Drawings
Fig. 1 is a flowchart of a method for measuring magnetic properties of a magnetic core of a transformer according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an actually measured hysteresis loop H-B, a hysteresis loop H-B 'obtained based on a J-A model, and a transition hysteresis loop H-B';
FIG. 3 is a schematic diagram of an actually measured hysteresis loop H-B, a hysteresis loop H-B' obtained based on the J-A model, and a hysteresis loop obtained after correction.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, an embodiment of the present invention provides a method for measuring magnetic properties of a magnetic core of a transformer, including:
step 1: measuring the magnetic field intensity H and the magnetic flux density B of the annular magnetic core in the process of reaching deep saturation to obtain an actually measured magnetic hysteresis loop H-B;
specifically, a ferrite material annular magnetic core is adopted, windings with the turn ratio of 5:5 are wound on two sides of the magnetic core, a sinusoidal voltage with the frequency of 1kHz is applied to a primary side, the voltage amplitude is adjusted, the magnetic core is enabled to reach deep saturation, and the current of the primary side is measured through a current probe; and (3) opening the secondary side, measuring the open-circuit voltage of the secondary side through a voltage probe, and calculating to obtain an actually measured hysteresis loop based on the ampere loop theorem and the Faraday electromagnetic induction law, wherein the actually measured hysteresis loop is shown by a dotted line in figure 2.
Wherein, for the annular magnetic core, based on the ampere loop theorem, the calculation formula of the magnetic field intensity H is as follows:
wherein N is1Is the number of primary winding turns, i (t) is the primary current, d0Is the outer diameter of the magnetic core, diIs the inner diameter of the magnetic core;
based on Faraday's law of electromagnetic induction, the calculation formula of magnetic flux density B is:
wherein u (t) is the secondary side voltage, N2The number of secondary winding turns, h the core height, and η the lamination factor of the core.
Step 2: determining an optimal value of the characteristic parameters of the J-A model, so that the error between a hysteresis loop obtained by applying the J-A model and a hysteresis loop obtained by measurement is minimum; the characteristic parameters comprise: saturation magnetization MsHysteresis loss coefficient k, domain coupling coefficient α, reversibility factor c and shape parameter a.
Specifically, the characteristic parameters of the J-A model are determined by utilizing a particle swarm optimization algorithm, and the particle swarm optimization algorithm comprises the following steps: randomly initializing the position of each particle in the particle swarm; calculating and comparing the fitness of each current particle, and taking the position of the individual with the optimal fitness as the best position of the particle swarm, wherein the best position of the current particle swarm provides a direction for updating the position of each particle; updating the position of each particle; and repeating the steps until the iteration number reaches a set value.
In this embodiment, the number of iterations is set to 1000, and the optimal values of the J-a model characteristic parameters obtained according to the particle swarm optimization algorithm are respectively: ms＝6.92×105A/m，k＝2.03A/m，c＝0.40，a＝3.86A/m，α＝9.03×10-6。
And step 3: obtaining a predicted magnetic flux density B 'based on the optimal value of the characteristic parameter of the J-A model and the actually measured magnetic field intensity H to obtain a hysteresis loop H-B' based on the J-A model;
specifically, the hysteresis-free magnetization M is calculated by the formula (1)anAnd the hysteresis-free magnetization intensity is characterized in that under an ideal condition, the magnetization process of the magnetic core is used for assisting in solving and predicting the magnetization intensity when hysteresis loss does not exist.
The predicted magnetization M is calculated using equation (2) to assist in solving for the predicted magnetic flux density. Formula (2) is a magnetization expression representing the rate of change of magnetization with magnetic field strength:
wherein, delta is a direction coefficient when dH/dt>When 0, δ is 1; when dH/dt<At 0, δ is-1, δMTo correct the factor, when delta (M)anwhen-M) < 0, δ M0; when delta (M)anwhen-M) > 0, δM＝1；
Calculating the predicted magnetic flux density B 'by equation (3) to obtain a hysteresis loop H-B' based on the J-a model, as shown by a solid line in fig. 2;
B′＝μ0(H+M) (3)
wherein, mu0Is a vacuum permeability, mu0＝4π×10-7N/A2。
And 4, step 4: correcting the predicted magnetic flux density B ' in the approaching saturation section of the annular magnetic core to obtain a compensation magnetic flux density B ' and a transition magnetic hysteresis loop H-B ';
specifically, the rotation process of the magnetic moment in the magnetic domain in the approaching saturation section of the magnetic core is not considered based on the J-A model, and the rotation process of the magnetic moment in the magnetic domain is approximately a reversible process, so that the predicted magnetization M is smaller than the actual value in the approaching saturation sectionanAnd the weighted value of the predicted magnetization M characterizes the actual magnetization, the compensated flux density B' is expressed as:
B″＝μ0(H+p1Man+p2M) (4)
wherein p is1、p2In order to determine the coefficient, the value of the coefficient should be such that the error between the compensation magnetic flux density B' and the actually measured magnetic flux density B is the minimum when the magnetic core approaches the saturation section, in this embodiment, p1＝0.32，p2M calculated in step (3) is added to 0.60anM is substituted for formula (4) to obtain a transition hysteresis loop H-B' as shown by the dotted line in FIG. 2.
And 5: selecting a starting point A and an end point D of an approaching saturation section of a magnetic hysteresis loop H-B 'based on a J-A model in the part of magnetic field intensity greater than 0, selecting a starting point B and an end point C of an approaching saturation section of a transition magnetic hysteresis loop H-B', connecting A, B points, and connecting C, D points to finish the correction of the magnetic hysteresis loop of the part of magnetic field intensity greater than 0;
specifically, the error of the approaching saturation section of the hysteresis loop H-B 'based on the J-a model is larger and the error of the approaching saturation section of the transition hysteresis loop H-B "is smaller than that of the actually measured hysteresis loop H-B, so that the non-approaching saturation section of the hysteresis loop H-B' based on the J-a model needs to be connected with the approaching saturation section of the transition hysteresis loop H-B". Selecting a part of magnetic field intensity on a magnetic hysteresis loop H-B 'based on a J-A model, which is greater than 0 and approaches to a starting point A and an end point D of a saturation section, selecting a part of magnetic field intensity on a transition magnetic hysteresis loop H-B' which is greater than 0 and approaches to a starting point B and an end point C of the saturation section, connecting points A, B and connecting points C, D to obtain a corrected magnetic hysteresis loop; wherein, the magnetic field intensity is larger than 0 part, and the approaching saturation section on the hysteresis loop H-B' of the J-A model is as follows: the magnetic flux density B' is an interval of 0.3 to 0.95 times of the maximum magnetic flux density in the actually measured hysteresis loop H-B; the approach to the saturation section on the transition hysteresis loop H-B' means that: the magnetic flux density B' is in the interval of 0.5 times to 0.9 times of the maximum magnetic flux density in the actually measured hysteresis loop H-B.
Step 6: selecting a starting point E and an end point K of an approaching saturation section of a magnetic hysteresis loop H-B 'based on a J-A model in the part of magnetic field intensity less than 0, selecting a starting point F and an end point G of an approaching saturation section of a transition magnetic hysteresis loop H-B', connecting E, F points and G, H points, and finishing the correction of the magnetic hysteresis loop of the part of magnetic field intensity less than 0;
specifically, in the part where the magnetic field intensity is less than 0, a start point E and an end point K which are close to a saturation section on a hysteresis loop H-B 'based on a J-A model are selected, a start point F and an end point G which are close to the saturation section on a transition hysteresis loop H-B' are selected, E, F points are connected, G, H points are connected, and a corrected hysteresis loop is obtained.
Wherein, the magnetic field intensity is less than 0 part, and the approaching saturation section on the hysteresis loop H-B' of the J-A model is as follows: the magnetic flux density B' is an interval of 0.3 to 0.95 times of the negative maximum magnetic flux density in the actually measured hysteresis loop H-B; the approach to the saturation section on the transition hysteresis loop H-B' means that: the magnetic flux density B' is the interval of 0.5 to 0.9 times of the negative maximum magnetic flux density in the actually measured hysteresis loop H-B.
As can be seen from FIG. 3, the J-A model generates a large error when describing that the hysteresis loop approaches the saturation section, and after being corrected, the error of the J-A model when describing that the hysteresis loop approaches the saturation section is greatly reduced.
And 7: measuring the magnetic field intensity of the magnetic core of the transformer in the running state, and determining the magnetic flux density in the current running state according to the relation between the predicted magnetic flux density B' and the actually measured magnetic field intensity H in the non-approaching saturation section of the magnetic core; and in the magnetic core approaching saturation section, determining the magnetic flux density in the current operation state according to the relationship between the compensation magnetic flux density B' and the actually measured magnetic field intensity H.
Another aspect of the embodiments of the present invention provides a device for measuring magnetic properties of a magnetic core of a transformer, including: the system comprises a J-A model calibration module, a magnetic flux density prediction module, a magnetic flux density correction module and a transformer magnetic core magnetic characteristic acquisition module;
the J-A model calibration module is used for measuring the magnetic field intensity H and the magnetic flux density B of the annular magnetic core and obtaining the optimal value of the characteristic parameter of the J-A model according to the relation between the measured magnetic field intensity and the measured magnetic flux density;
the magnetic flux density prediction module is used for obtaining predicted magnetic flux density B' according to the optimal value of the characteristic parameter of the J-A model and the actually measured magnetic field intensity H;
the magnetic flux density correction module is used for correcting the predicted magnetic flux density B 'in the approaching saturation section of the annular magnetic core to obtain a compensated magnetic flux density B';
the magnetic characteristic acquisition module of the transformer core is used for measuring the magnetic field intensity of the transformer core in the operating state, and determining the magnetic flux density in the current operating state according to the relation between the predicted magnetic flux density B' and the actually measured magnetic field intensity H in the non-approaching saturation section of the magnetic core; and in the magnetic core approaching saturation section, determining the magnetic flux density in the current operation state according to the relationship between the compensation magnetic flux density B' and the actually measured magnetic field intensity H.
In the embodiment of the present invention, the specific implementation manner of each module may refer to the description in the corresponding method embodiment, and the embodiment of the present invention will not be repeated.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A method for measuring magnetic characteristics of a magnetic core of a transformer, comprising:
step 1: measuring the magnetic field intensity H and the magnetic flux density B of the annular magnetic core in the process of reaching deep saturation;
step 2: obtaining an optimal value of the characteristic parameter of the J-A model according to the actually measured magnetic field intensity H and the magnetic flux density B; the characteristic parameters comprise: saturation magnetization MsHysteresis loss coefficient k, magnetic domain coupling coefficient α, reversibility factor c and shape parameter a;
and step 3: obtaining a predicted magnetic flux density B' according to the optimal value of the characteristic parameter of the J-A model and the actually measured magnetic field intensity H; the method for obtaining the predicted magnetic flux density B' is:
obtaining a hysteresis-free magnetization Man；
According to the magnetization M without hysteresisanObtaining a predicted magnetization M;
obtaining a predicted magnetic flux density B' according to the predicted magnetization M and the actually measured magnetic field intensity H;
and 4, step 4: correcting the predicted magnetic flux density B 'in the approaching saturation section of the annular magnetic core to obtain a compensation magnetic flux density B'; the method for correcting the predicted magnetic flux density B 'to obtain the compensated magnetic flux density B' comprises the following steps:
considering the rotation process of the magnetic moment in the magnetic domain of the annular magnetic core approaching the saturation section, the hysteresis-free magnetization M is utilizedanAnd the weighted value of the predicted magnetization M characterizes the actual magnetization, the compensation flux density B' is expressed as:
B″＝μ0(H+p1Man+p2M)
wherein p is1、p2The undetermined coefficient is obtained by the value of the compensation magnetic flux density B 'and the actually measured magnetic flux density B, the error of the compensation magnetic flux density B' and the actually measured magnetic flux density B is minimum when the annular magnetic core approaches to a saturation section, and mu is0Is a vacuum magnetic conductivity;
and 5: measuring the magnetic field intensity of the magnetic core of the transformer in the running state, and determining the magnetic flux density in the current running state according to the relation between the predicted magnetic flux density B' and the actually measured magnetic field intensity H in the non-approaching saturation section of the magnetic core of the transformer; and determining the magnetic flux density under the current operation state according to the relation between the compensation magnetic flux density B' and the actually measured magnetic field intensity H in the approaching saturation section of the magnetic core of the transformer.
2. The method as claimed in claim 1, wherein the undetermined coefficient p is determined by a predetermined factor p1Is 0.32, p2Is 0.60.
3. The method according to claim 1, wherein the step 5 is that the transformer core approaches a saturation section: the magnetic flux density is a magnetic field intensity interval corresponding to 0.3 to 0.95 times of the maximum value of the actually measured magnetic flux density B; the non-approaching saturation section of the magnetic core of the transformer is as follows: the magnetic core of the transformer approaches the interval outside the saturation section.
4. A method for measuring the magnetic characteristics of a magnetic core of a transformer according to any one of claims 1 to 3, wherein the magnetic core of the transformer is made of the same material as the toroidal core.
5. A magnetic characteristic measuring apparatus for a magnetic core of a transformer, comprising: the system comprises a J-A model calibration module, a magnetic flux density prediction module, a magnetic flux density correction module and a transformer magnetic core magnetic characteristic acquisition module;
the J-A model calibration module is used for measuring the magnetic field intensity H and the magnetic flux density B of the annular magnetic core and obtaining the optimal value of the characteristic parameter of the J-A model according to the relation between the measured magnetic field intensity and the measured magnetic flux density;
the magnetic flux density prediction module is used for obtaining predicted magnetic flux density B' according to the optimal value of the characteristic parameter of the J-A model and the actually measured magnetic field intensity H; the method for obtaining the predicted magnetic flux density B' is: obtaining a hysteresis-free magnetization Man(ii) a According to the magnetization M without hysteresisanObtaining a predicted magnetization M; obtaining a predicted magnetic flux density B' according to the predicted magnetization M and the actually measured magnetic field intensity H;
the magnetic flux density correction module is used for correcting the predicted magnetic flux density B 'in the approaching saturation section of the annular magnetic core to obtain a compensated magnetic flux density B'; the method for correcting the predicted magnetic flux density B 'to obtain the compensated magnetic flux density B' comprises the following steps:
considering the rotation process of the magnetic moment in the magnetic domain of the annular magnetic core approaching the saturation section, the hysteresis-free magnetization M is utilizedanAnd the weighted value of the predicted magnetization M characterizes the actual magnetization, the compensation flux density B' is expressed as:
B″＝μ0(H+p1Man+p2M)
wherein p is1、p2The undetermined coefficient is obtained by the value of the compensation magnetic flux density B 'and the actually measured magnetic flux density B, the error of the compensation magnetic flux density B' and the actually measured magnetic flux density B is minimum when the annular magnetic core approaches to a saturation section, and mu is0Is a vacuum magnetic conductivity;
the magnetic property acquisition module of the transformer core is used for measuring the magnetic field intensity of the transformer core in the operating state, and determining the magnetic flux density in the current operating state according to the relation between the predicted magnetic flux density B' and the actually measured magnetic field intensity H in the non-approaching saturation section of the transformer core; and determining the magnetic flux density under the current operation state according to the relation between the compensation magnetic flux density B' and the actually measured magnetic field intensity H in the approaching saturation section of the magnetic core of the transformer.
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