CN111104743A - Method for determining distribution of direct-current magnetic bias transient magnetic field and eddy current loss of transformer - Google Patents
Method for determining distribution of direct-current magnetic bias transient magnetic field and eddy current loss of transformer Download PDFInfo
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Abstract
The invention discloses a method for determining distribution of a transient magnetic field and eddy current loss of a direct current magnetic bias of a transformer, which adopts the technical scheme that: establishing a transient circuit model and a magnetic circuit model of the transformer under the direct current magnetic biasing, wherein in the circuit model, a direct current voltage source is added on a primary side winding of the transformer, and a circuit equation containing direct current voltage is listed; in the magnetic circuit model, different topological structures of a transformer core and the magnetic saturation characteristics of ferromagnetic materials are considered, magnetomotive force generated by eddy current is introduced into the model, and a magnetic circuit equation is listed; and coupling the magnetic circuit equation with the circuit equation to obtain a nonlinear differential-algebraic equation set, solving the equation set by using a Newton-Raphson method, and determining the transient eddy current loss and the magnetic field distribution of the transformer with different topological structures under the direct-current magnetic bias. The calculation process of the invention has fast convergence speed, and the error of the calculation result is smaller and more accurate, and the problems of local overheating, vibration, noise and the like of the transformer caused by direct current magnetic biasing can be further accurately analyzed by using the calculation result of the invention.
Description
Technical Field
The invention relates to the technical field of transformers in the professional directions of motors and electric appliances, in particular to a method for determining distribution of direct-current magnetic bias transient magnetic field and eddy current loss of a transformer.
Background
Dc magnetic biasing is an abnormal phenomenon in which dc current is generated in a winding of a transformer to generate dc magnetic flux in an iron core. The reason for the dc magnetic bias phenomenon is two: firstly, the solar magnetic storm generates an induced potential difference on the earth surface, so that a Geomagnetic Induction Current (GIC) is entered into a transformer winding with a grounded neutral point. The frequency of the geomagnetic induction current is very low, about 0.001-1 Hz, and can be approximated to a DC current. And secondly, the influence of direct current transmission engineering. When the high-voltage direct-current transmission project adopts a single-pole-earth return line operation mode or a double-pole unbalanced operation mode, larger direct current flows into the earth through the grounding electrode, so that direct current potential difference is generated on the surface of the earth, and direct current components enter a transformer winding with a grounded neutral point through the earth.
The dc bias causes the core of the transformer to quickly reach a saturated state, and the exciting current is distorted, thereby generating a series of electromagnetic effects, as shown in fig. 1. In addition, the dc magnetic bias may cause malfunction of a relay protection device of the power system, harmonic amplification of a capacitor, and unstable system voltage, which may affect normal operation of the power system and power equipment, and may even cause accidents such as capacitor explosion, system voltage breakdown, and blackout. Therefore, the dc magnetic bias phenomenon is not negligible, and is a hot point of research particularly for transient magnetic field and loss distribution of the transformer core.
A hysteresis model method is mostly adopted for calculating transient magnetic fields and losses of transformer cores at home and abroad, and the method utilizes hysteresis characteristic models such as a Preisach model or a Jiles-Atherton model and the like to estimate hysteresis loops of ferromagnetic materials during alternating current dynamic magnetization, expresses the relation between magnetic flux density B or magnetization M and magnetic field intensity H through a mathematical formula, is coupled with finite element numerical calculation to analyze the magnetic field distribution of the cores, and finally calculates the core losses through numerical integration of B and H by utilizing the Pongting theorem. The method relates to complex finite element numerical derivation, the programming calculation workload is large, the calculation result has larger error, and the engineering practicability is poor.
Disclosure of Invention
In order to overcome the defects of the existing method, the invention provides a method for determining the distribution of the transient magnetic field and the eddy current loss of the direct current magnetic bias of the transformer. And establishing a circuit-magnetic circuit coupling model of the transformer under the DC magnetic biasing and a relational expression of magnetic flux and iron core eddy current loss, and performing simulation calculation on the transient magnetic field and the eddy current loss distribution of the iron core by using a Newton-Raphson method. The method converts the solving process of the nonlinear equation into iterative solving of the corresponding linear equation, has the advantages of simple and practical calculating process, high convergence rate, more accurate calculating result and smaller error, and can be widely applied to the engineering field.
The invention adopts the following technical scheme:
a method for determining distribution of transient magnetic field and eddy current loss of direct current magnetic biasing of a transformer comprises the following steps:
establishing a transient circuit model and a magnetic circuit model of the transformer under the direct current magnetic biasing, wherein in the circuit model, a direct current voltage source is added on a primary side winding of the transformer, and a circuit equation containing direct current voltage is listed; in the magnetic circuit model, different topological structures of a transformer core and the magnetic saturation characteristics of ferromagnetic materials are considered, magnetomotive force generated by eddy current is introduced into the model, and a magnetic circuit equation is listed;
and coupling the magnetic circuit equation with the circuit equation to obtain a nonlinear differential-algebraic equation set, solving the equation set by using a Newton-Raphson method, and determining the transient magnetic field and eddy current loss distribution of the transformer with different topological structures under the direct-current magnetic bias.
Further, a no-load equivalent circuit model of the transformer under the direct-current magnetic biasing is established, and a corresponding circuit equation is obtained:
wherein u isjRepresenting an alternating voltage, U0Representing a direct voltage, rjpDenotes the winding resistance, LjpRepresenting the equivalent leakage inductance of the winding, ijpRepresents the current, ejpRepresenting induced electromotive force,. phijDenotes a magnetic flux, and p denotes a primary-side three-phase winding.
Further, in the magnetic circuit model, a magnetic circuit equation obtained based on the three-phase five-column transformer is as follows:
wherein j is 1 to 7, Fa、FbAnd FcMagnetomotive force, R, generated for primary side three-phase winding currentjIs the magnetic resistance of the iron core column, the magnet yoke and the side column, phijIs the magnetic flux of the core limb, the magnet yoke and the side limb, R8For magnetic leakage resistance,. phi8For leakage flux, FejMagnetomotive force generated by eddy currents;
for a three-phase three-column or single-phase three-column transformer, j is 1-5, R6For magnetic leakage resistance,. phi6Is the leakage flux.
Further, the magnetic saturation characteristic of the ferromagnetic material of the transformer core under the direct current magnetic bias is expressed by a B-H nonlinear equation:
B＝f(H)
where B is the magnetic flux density and H is the magnetic field strength.
Further, the nonlinear reluctance in the magnetic circuit is:
where A is the core cross-sectional area and l is the magnetic path length.
Further, R isjSubstituting into a magnetic circuit equation, then combining with the circuit equation to obtain a nonlinear differential-algebraic equation system, and performing iterative solution on the nonlinear differential-algebraic equation system by using a Newton-Raphson method to obtain instantaneous values of B, H phi.
Further, determining transient eddy current loss P of transformer coreeAnd Φ as:
pe＝f(Φ)；
solving to obtain the transient eddy current loss P of the iron coreeDistribution of (2).
Compared with the prior art, the invention has the beneficial effects that:
(1) the invention fully considers the different topological structures of the transformer iron core and the magnetic saturation characteristics of the ferromagnetic material, introduces the magnetomotive force generated by the eddy current into the magnetic circuit model, and then couples the magnetomotive force with the circuit model; the distribution of the transient magnetic field of the transformer under the direct current magnetic bias can be accurately and quickly obtained through the circuit-magnetic circuit model; and then the relation expression of the eddy current loss and the magnetic flux is utilized to quickly obtain the transient eddy current loss distribution of the iron core.
(2) Compared with the existing calculation method, the method is simple and clear, the calculation process is fast in convergence, the calculation result is more accurate, the error is smaller, and the method is suitable for transformers with different topological structures.
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The accompanying drawings, which form a part of the specification, are included to provide a further understanding of the application, and are incorporated in and constitute a part of this specification, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application.
FIG. 1 is a schematic diagram of the effect of DC magnetic bias on a transformer;
FIG. 2 is a flowchart of a first embodiment of the present invention;
fig. 3 is a no-load circuit model of a three-phase transformer under dc magnetic biasing according to a first embodiment of the present invention;
fig. 4 is a magnetic circuit model of a three-phase five-limb transformer under dc magnetic bias according to a first embodiment of the present invention;
5(a) -5(b) are transient magnetic field distributions in the iron core of the three-phase five-limb transformer of the second embodiment of the invention when no DC current is provided;
6(a) -6(b) are transient magnetic field distributions in the iron core when the three-phase five-column transformer of the second embodiment of the present invention has DC;
fig. 7(a) -7(b) are graphs showing the variation of the magnetic field amplitude of the three-phase five-limb transformer according to the second embodiment of the present invention with dc current;
fig. 8 shows the distribution of the transient eddy current loss in the core of the three-phase five-limb transformer according to the second embodiment of the present invention without dc;
fig. 9 shows the transient eddy current loss distribution in the core when the three-phase five-limb transformer of the second embodiment of the invention has dc;
fig. 10 shows the eddy current loss amplitude of the three-phase five-limb transformer according to the second embodiment of the present invention as a function of dc current.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an", and/or "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof;
the first embodiment is as follows:
the present invention will be described in detail with reference to fig. 3 to 10, and specifically, the structure is as follows:
the embodiment provides a method for determining distribution of a transient magnetic field and eddy current loss of a direct current magnetic bias of a transformer, which comprises the following steps: and establishing a transient circuit-magnetic circuit model of the transformer under the DC magnetic biasing. In the circuit model, a direct-current voltage source is added on a primary side winding of a transformer, and a circuit equation containing direct-current voltage is listed; in the magnetic circuit model, different topological structures of a transformer core and the magnetic saturation characteristics of ferromagnetic materials are considered, magnetomotive force generated by eddy current is introduced into the model, and a magnetic circuit equation is listed; and then coupling the magnetic circuit equation with the circuit equation to obtain a nonlinear differential-algebraic equation set, solving the equation set by using a Newton-Raphson method, and determining the transient magnetic field and eddy current loss distribution of the transformer with different topological structures under the direct current magnetic biasing. Specifically, the method comprises the following steps:
firstly, establishing a circuit model:
the no-load equivalent circuit model of the three-phase transformer under DC magnetic bias is shown in FIG. 3, U0Representing a direct voltage u1、u2And u3Is a three-phase alternating voltage, e1a、e2b、e3cInduced electromotive force of the primary side windings, respectively, e1A、e2B、e2CInduced electromotive force, i, of the secondary winding, respectively1a、i2bAnd i3Are respectively primary side winding current, r1a、r2b、r3cAre primary side winding resistances, r1A、r2B、r3CRespectively, secondary side winding resistance, L1a、L2bAnd L3cRespectively, equivalent leakage inductance, L, of only the interlinked primary windings1A、L2BAnd L3CThe equivalent leakage inductance of only the cross-linked secondary side winding is respectively, and a loop formed by three phases in the primary side winding and a neutral wire meets the following circuit equation:
wherein p represents a primary side three-phase winding (a, b, c), ΦjRepresents the three legs flux of the transformer, j is 1,2, 3.
If the transformer is a single-phase transformer, j is 1.
Secondly, establishing a magnetic circuit model:
the equivalent magnetic circuit model of the three-phase five-column transformer is shown in FIG. 4, Fa、FbAnd FcMagnetomotive force generated by primary side three-phase winding current (only F if single-phase three-pole transformer)a)，RjAnd phij(j 1-7) is the magnetic resistance and flux of the core limb, the magnetic yoke and the side limb, R8And phi8For leakage magnetic resistance and flux, Fej(j 1-7) is magnetomotive force generated by eddy current (if the transformer is a three-phase three-pole or single-phase three-pole transformer, j 1-5, R6And phi6Leakage magnetic resistance and leakage magnetic flux) and the magnetic path equation is:
the magnetic circuit model takes the influence of eddy current into consideration. On a section of magnetic circuit with the cross section area of A and the length of l, a winding with the number of turns of N is connected with current i, the magnetic flux in the magnetic circuit is phi, and the magnetomotive force generated by the eddy current can be expressed as:
in the formula, the coefficient keComprises the following steps:
where σ denotes an electric conductivity, d denotes a silicon steel sheet thickness, τ denotes a silicon steel sheet width, G-0.1356, H0Representing the internal magnetic potential generated by the magnetic domain.
Defining eddy currents i in branches of the magnetic circuiteThe expression is as follows:
the eddy current loss P in this magnetic circuit brancheComprises the following steps:
the total core eddy current loss P is determined for single-phase three-column and three-phase three-column transformerseCan be expressed as:
for three-phase five-column transformer, the total core eddy current loss PeCan be expressed as:
in addition, considering the magnetic saturation characteristics of the ferromagnetic material of the transformer under direct-current magnetic biasing, a B-H nonlinear equation adopts a single-value curve:
B＝f(H) (9)
the nonlinear reluctance in the magnetic circuit is then:
respectively substituting formula (7) or formula (8) and formula (10) into magnetic circuit equation (2) of transformers with different topological structures, then combining formula (1) and formula (2), and transforming and sorting the magnetic circuit equation to obtain a matrix form:
RΦj＝F(j＝1,2,3) (11)
and (4) iteratively solving the equation set by using a Newton-Raphson method. By selecting proper step length, the stability and the calculation precision of the solution can be ensured.
Example two:
in the present embodiment, a three-phase five-pole transformer is taken as an example, and the transient magnetic field and the eddy current loss under the presence and absence of dc bias are determined respectively, as shown in fig. 5 to 10.
In FIGS. 5 to 10, H represents the magnetic field intensity, B represents the magnetic induction intensity, and P representseRepresents the eddy current loss; subscripts 1,2,3 denote three core legs of a phase, b phase, c phase, 4, 5 denote yokes, 6, 7 denote side legs.
Fig. 5 and 6 show the transient magnetic field distribution without dc and with dc, respectively. As can be seen from fig. 5, when there is no dc intrusion, the magnetic field intensity in the core is a peak wave (same as the excitation current waveform), the magnetic flux density is a sine wave, and the positive and negative half axes are symmetrical. The magnetic field intensity and the magnetic flux density amplitude are the largest in the three iron core columns, the magnetic yoke is arranged next to the magnetic field intensity and the magnetic flux density amplitude is the smallest in the side columns. As can be seen from fig. 6, when there is dc intrusion, the magnetic field intensity and the magnetic flux density waveform are shifted, the positive and negative half-axes are no longer symmetrical, the amplitude of the positive half-axis is greater than that of the negative half-axis, and the positive amplitude of the waveform of the b-phase pillar is the largest.
Fig. 7 shows the variation of the magnetic field amplitude in the iron core of the three-phase five-limb transformer with the dc current. It can be seen that, as the dc current increases, the magnetic field strength and the magnetic flux density in the iron core increase in amplitude in a non-linear manner. The amplitude of the magnetic field intensity and the magnetic flux density of the phase b core column increases at the fastest speed, then the phase a and the phase c core columns, then the two side columns, and the yoke increases at the slowest speed. The magnetic field of the b-phase core column is influenced the most by the direct current, and the magnetic field of the magnetic yoke is influenced the least by the direct current.
Fig. 8 and 9 are distributions of transient eddy current losses in a three-phase five-limb transformer core without dc and with dc, respectively. As can be seen from FIG. 8, the eddy current loss (P) of the three legs is found in the absence of DCe1、Pe2、Pe3) Eddy current loss (P) from yokee4、Pe5) Equivalent, eddy current losses (P) of the two side legse6、Pe7) And, at a minimum, the amplitude in each half cycle is respectively equal. As shown in FIG. 9, when there is a DC intrusion, the slave Pe1～Pe7The amplitude of each half period is not equal any more, namely the amplitude of one half period is reduced, and the amplitude of the other half period is increased, which indicates that the DC current causes the offset of the eddy current loss.
Fig. 10 shows the eddy current loss amplitude in the iron core of the three-phase five-limb transformer as a function of the direct current. As can be seen, the eddy current loss amplitude is greatest in the yoke, followed by three legs, and the side legs are smallest. Because the length of the yoke is less than the length of the stem, the magnitude of the eddy current loss in the yoke is greater than the magnitude of the eddy current loss in the stem, although the magnitude of the magnetic field in the yoke is smaller. The eddy current loss in the iron core increases in amplitude in a nonlinear manner with the increase of the direct current. Wherein the eddy current loss amplitude in the side leg increases at the fastest rate, followed by the yoke, and the eddy current loss amplitude in the three legs increases the slowest. The direct current has the largest influence on the eddy current loss in the side column and the smallest influence on the eddy current loss in the center column.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.
Claims (7)
1. A method for determining distribution of transient magnetic field and eddy current loss of direct current magnetic biasing of a transformer is characterized by comprising the following steps:
establishing a transient circuit model and a magnetic circuit model of the transformer under the direct current magnetic biasing, wherein in the circuit model, a direct current voltage source is added on a primary side winding of the transformer, and a circuit equation containing direct current voltage is listed; in the magnetic circuit model, different topological structures of a transformer core and the magnetic saturation characteristics of ferromagnetic materials are considered, magnetomotive force generated by eddy current is introduced into the model, and a magnetic circuit equation is listed;
and coupling the magnetic circuit equation with the circuit equation to obtain a nonlinear differential-algebraic equation set, solving the equation set by using a Newton-Raphson method, and determining the transient magnetic field and eddy current loss distribution of the transformer with different topological structures under the direct-current magnetic bias.
2. The method for determining distribution of transient magnetic field and eddy current loss of DC magnetic bias of transformer according to claim 1, wherein an unloaded equivalent circuit model of the transformer under DC magnetic bias is established, and corresponding circuit equation is obtained:
wherein u isjRepresenting an alternating voltage, U0Representing a direct voltage, rjpDenotes the winding resistance, LjpRepresenting the equivalent leakage inductance of the winding, ijpRepresents the current, ejpRepresenting induced electromotive force,. phijDenotes a magnetic flux, and p denotes a primary-side three-phase winding.
3. The method for determining the distribution of the transient magnetic field and the eddy current loss of the direct current bias magnet of the transformer as claimed in claim 1, wherein in the magnetic circuit model, the magnetic circuit equation obtained based on the three-phase five-column transformer is as follows:
wherein j is 1 to 7, Fa、FbAnd FcMagnetomotive force, R, generated for primary side three-phase winding currentjIs the magnetic resistance of the iron core column, the magnet yoke and the side column, phijIs the magnetic flux of the core limb, the magnet yoke and the side limb, R8For magnetic leakage resistance,. phi8For leakage flux, FejMagnetomotive force generated by eddy currents;
for a three-phase three-column or single-phase three-column transformer, j is 1-5, R6For magnetic leakage resistance,. phi6Is the leakage flux.
4. The method for determining the distribution of the transient magnetic field and the eddy current loss of the DC bias of the transformer according to claim 3, wherein the magnetic saturation characteristics of the ferromagnetic material of the iron core of the transformer under the DC bias are expressed by a B-H nonlinear equation:
B＝f(H)
where B is the magnetic flux density and H is the magnetic field strength.
5. The method for determining the distribution of the transient magnetic field and the eddy current loss of the direct current bias magnet of the transformer as claimed in claim 4, wherein the nonlinear magnetic resistance in the magnetic circuit is as follows:
where A is the core cross-sectional area and l is the magnetic path length.
6. The method for determining the distribution of transient magnetic field and eddy current loss of DC bias of transformer according to claim 5, wherein R isjSubstituting into a magnetic circuit equation, then combining with the circuit equation to obtain a nonlinear differential-algebraic equation system, and performing iterative solution on the nonlinear differential-algebraic equation system by using a Newton-Raphson method to obtain instantaneous values of B, H phi.
7. The method of claim 6, wherein the transient eddy current loss P of the transformer core is determinedeAnd Φ as:
pe＝f(Φ)；
solving to obtain the transient eddy current loss P of the iron coreeDistribution of (2).
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| CN111931310A (en) * | 2020-08-28 | 2020-11-13 | 西南交通大学 | Method for evaluating eddy current loss of wound core interlayer short circuit in consideration of boundary conditions of different magnetic fields |
| CN112560301A (en) * | 2020-11-26 | 2021-03-26 | 东南大学 | Magnetic material eddy current loss calculation method based on magnetic induction principle |
| CN112560301B (en) * | 2020-11-26 | 2021-10-08 | 东南大学 | Magnetic material eddy current loss calculation method based on magnetic induction principle |
| WO2022110529A1 (en) * | 2020-11-26 | 2022-06-02 | 东南大学 | Magnetic material eddy-current loss calculation method based on magnetic induction principle |
| US11790132B2 (en) | 2020-11-26 | 2023-10-17 | Southeast University | Calculation method of eddy current loss in magnetic materials based on magnetic-inductance |
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