CN108920731B - Method for calculating vibration acceleration of turn-to-turn short circuit of transformer winding - Google Patents
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Abstract
The invention discloses a method for calculating the vibration acceleration of turn-to-turn short circuit of a transformer winding, which is characterized by comprising the following steps of: and calculating a magnetic field model, a circuit model and the vibration acceleration of the winding. The method not only overcomes the limitation of a plurality of practical conditions for carrying out short-circuit tests and electrodynamic force measurement, but also fully considers the electromagnetic characteristics of the transformer during operation in the calculation, takes the short-circuit fault between the head end and the middle turn of the transformer as a calculation object, and accurately simulates the fault of the transformer winding; the method not only effectively simulates the internal magnetic field environment of the transformer winding during turn-to-turn short circuit by using the field coupling model, but also verifies the correctness of the field coupling model by comparing the simulation result with the experimental data, thereby providing a feasible method for identifying the turn-to-turn short circuit fault of the winding, and having the advantages of being scientific, reasonable, real, effective, high in practical value and the like.
Description
Technical Field
The invention discloses a method for calculating turn-to-turn short circuit vibration acceleration of a winding based on a three-dimensional field coupling model of a transformer, which is applied to vibration acceleration analysis and turn-to-turn short circuit fault identification of a power transformer winding.
Background
The power transformer is the heart of the power system, plays an irreplaceable role in the transmission process of electric energy, the stable operation of the power transformer is almost directly related to the operation reliability of the whole power system, and the transformer is easy to cause faults due to various reasons. The turn-to-turn short circuit of the transformer winding generally causes turn short circuit due to insulation damage, and has the characteristics of sudden change of fault phase short circuit current, severe electrodynamic force and vibration, and no obvious change of non-fault phase current. The traditional protection has higher difficulty in identifying the fault state of the winding when the turn-to-turn short circuit occurs to the transformer, and if the transformer runs under continuous load, the winding is deformed and even burnt, so that the safe and stable running of equipment and even a system is influenced. The turn-to-turn short circuit of the transformer winding belongs to an internal fault, and the problem of failure or refusal action exists when the differential protection is used for processing the fault. Therefore, the method has important research value and practical significance for calculating the vibration acceleration of the turn-to-turn short circuit of the transformer winding.
Disclosure of Invention
The invention aims to provide a method which is scientific, reasonable, real, effective and high in practical value, simulates the turn-to-turn short circuit fault of a winding by using a three-dimensional finite element magnetic field model of a transformer based on a field-circuit coupling principle, calculates the electromagnetic force of the winding, uses the electromagnetic force for harmonic response analysis, and calculates the vibration acceleration of the winding through numerical simulation.
The purpose of the invention is realized by the following technical scheme: a method for calculating the vibration acceleration of turn-to-turn short circuit of a transformer winding is characterized by comprising the following steps of:
1) magnetic field model
Aiming at the problem of transformer excitation nonlinearity, a magnetic field simulation method is adopted for analysis, hysteresis effect is not considered, a vector magnetic potential finite element method is adopted, and a transformer nonlinear magnetic field equation is obtained according to a Maxwell equation:
in the formula (1), mu is magnetic conductivity, A is vector magnetic potential, J is current density vector,
the overall interpolation function to solve the field is:
in the formula (2), M l For the sequence of basis functions, l is 1,2, …, l n Formed by corresponding superposition of related unit shape functions, n is a general item number of a basic function sequence, and l n The number of the total edges is the number of the edges,
and (3) applying the Green theorem to obtain a Galerkin weighted margin equation:
in formula (3), M m For the sequence of weight functions, Ω denotes the bounding volume integral,
if the winding current i is known in the magnetic field model, dispersing the weighted residual equation to form an algebraic equation set, solving to obtain A, and further calculating the magnetic field energy;
2) circuit model
Flux linkage equation of transformer
ψ＝LW(t,i a )i a (4)
In the formula (4), t is a time variable; psi is the flux linkage vector; l is W The static inductance matrix represents the relation between flux linkage and current; i.e. i a Is a vector of the current of the winding,
the differential equation of the transformer time domain circuit is as follows:
in the formula (5), u is voltage excitation; l is a radical of an alcohol D In the form of a dynamic inductor matrix, the inductor matrix,
solving the formula (5) in the circuit model by adopting a fourth-order Runge Kutta method, wherein t is h Coil current i at time h Calculating t h+1 I of the moment h+1 ：
In the formula (6), s 1 Is the step size, x 1 ～x 4 The slope is calculated for the segment within the step size,
based on the principle of energy disturbance, the dynamic inductance is calculated according to the time-varying system energy, and when the coil current increases by delta i, the total energy of the power supply is associated with the dynamic inductance and the current:
in the formula (7), p and q are winding numbers, and Δ W 1 The increment of energy supplied for the external power source,
on the other hand, in the time domain calculation process, the nonlinear magnetic field at each moment is solved according to a steady-state field, and the magnetic field energy increment calculation adopts a local linearization calculation method; if the current increment is delta i, the increment of the magnetic field energy of the internal system of the transformer is as follows:
in the formula (8), Δ W 2 Is the increment of magnetic field energy, B is the magnetic induction intensity, H is the magnetic field intensity,
based on the energy balance principle, the dynamic inductance L can be calculated when the energy of the formula (7) is equal to that of the formula (8) D ；
3) Calculation of winding vibration acceleration
The transformer winding is used as a multi-degree-of-freedom mechanical system, the winding vibration is forced vibration under the excitation of electromagnetic force, and the electromagnetic force of the transformer winding is calculated by using a virtual displacement method:
in the formula (9), F r For electromagnetic forces acting in the r direction, W m For storing energy in the magnetic field of the winding leakage field, i b For winding currents calculated on the basis of field coupling, L D The dynamic inductance of the winding is calculated based on field circuit coupling;
the electromagnetic force of the winding changing along with the time is obtained through transient electromagnetic field analysis, Fourier transformation is carried out on the electromagnetic force to obtain each harmonic component, the harmonic component is used as a simple harmonic excitation source to carry out steady-state structure harmonic response vibration analysis, the material rigidity and the frequency of the simple harmonic excitation are considered, and the stress harmonic response analysis principle is as follows:
in the formula (10), M is a mass matrix, C is a damping matrix, K is a stiffness matrix, F is a load matrix,
omega is the angular frequency of the simple harmonic excitation; s represents a displacement;
the vibration acceleration g can be calculated according to the vibration displacement:
the invention relates to a method for calculating electrodynamic force based on a three-dimensional finite element model of a transformer, which is used for carrying out magnetic field modeling and solving according to actual power transformer parameters. The magnetic field model applies boundary conditions with parallel magnetic lines at the outer boundary, excites sinusoidal voltage applied by the outer circuit model, adopts an edge finite element method based on vector magnetic potential, takes electromagnetic force under the condition of turn-to-turn short circuit of the transformer winding as load, solves and calculates the vibration acceleration of the winding, and verifies the obtained conclusion in a mode of combining numerical simulation and physical experiment. The invention not only overcomes the limitation of a plurality of practical conditions for carrying out short-circuit test and electrodynamic force measurement, but also fully considers the electromagnetic characteristic of the transformer during operation in the calculation, takes the short-circuit fault between the head end and the middle turn of the transformer as a calculation object, and accurately simulates the fault of the transformer winding. The method not only utilizes the field-circuit coupling model to effectively simulate the internal magnetic field environment when the turn-to-turn short circuit occurs in the transformer winding, but also verifies the correctness of the field-circuit coupling model by comparing the simulation result with the experimental data, thereby providing a feasible method for identifying the turn-to-turn short circuit fault of the winding, and having the advantages of science, reasonability, reality, effectiveness, high practical value and the like.
Drawings
FIG. 1 is a schematic diagram of a field-coupling model of a transformer;
FIG. 2 is a schematic diagram of a winding vibration acceleration calculation based on the field-circuit coupling principle;
FIG. 3 is a schematic diagram of the stress distribution of the head end coil of the winding;
FIG. 4 is a schematic diagram of a vibration acceleration distribution of a head end coil of a winding;
FIG. 5 is a schematic diagram of the distribution of the force applied to the wire cake in the middle of the winding;
FIG. 6 is a schematic diagram of the vibration acceleration distribution of the wire cake in the middle of the winding;
FIG. 7 is a schematic diagram of vibration acceleration of a short-circuited winding at the head end of a transformer under excitation of 50V;
FIG. 8 is a schematic diagram of vibration acceleration of a short-circuited winding at the head end of a transformer when excited at 125V;
FIG. 9 is a schematic diagram of the vibration acceleration of the short-circuited winding at the head end of the transformer when excited at 220V.
Detailed Description
The method for calculating the vibration acceleration of the turn-to-turn short circuit of the transformer winding according to the present invention is further described with reference to the accompanying drawings and the specific embodiments:
the method for calculating the vibration acceleration of the turn-to-turn short circuit of the transformer winding comprises the following steps of:
referring to fig. 1, a method for calculating vibration acceleration of turn-to-turn short circuit of a transformer winding includes the following steps:
1) magnetic field model
Aiming at the problem of transformer excitation nonlinearity, a magnetic field simulation method is adopted for analysis, hysteresis effect is not considered, a vector magnetic potential finite element method is adopted, and a transformer nonlinear magnetic field equation is obtained according to a Maxwell equation:
in the formula (1), mu is magnetic conductivity, A is vector magnetic potential, J is current density vector,
the overall interpolation function to solve the field is:
in the formula (2), M l Is a sequence of basis functions, l is 1,2, …, l n Formed by corresponding superposition of related unit shape functions, n is a base function sequenceItem number,/ n The number of the total edges is the number of the total edges,
and (3) applying the Green theorem to obtain a Galerkin weighted margin equation:
in formula (3), M m For the series of weight functions, Ω denotes the bounding volume component,
if the winding current i is known in the magnetic field model, discretizing the weighted residual equation to form an algebraic equation set, solving to obtain A, and further calculating the magnetic field energy;
2) circuit model
Flux linkage equation of transformer
ψ＝LW(t,i a )i a (4)
In the formula (4), t is a time variable; psi is the flux linkage vector; l is W The static inductance matrix represents the relation between flux linkage and current; i.e. i a Is a vector of the current of the winding,
the differential equation of the transformer time domain circuit is as follows:
in the formula (5), u is voltage excitation; l is D In the form of a dynamic inductor matrix,
solving the formula (5) in the circuit model by adopting a fourth-order Runge Kutta method, wherein t is h Coil current i at time h Calculating t h+1 I of the moment h+1 ：
In the formula (6), s 1 Is the step size, x 1 ～x 4 The slope is calculated for the segment within the step size,
based on the principle of energy disturbance, the dynamic inductance is calculated according to the time-varying system energy, and when the coil current increases by delta i, the total energy of the power supply is related to the dynamic inductance and the current:
in the formula (7), p and q are winding numbers, and Δ W 1 The increment of energy provided for the external power source,
on the other hand, in the time domain calculation process, the nonlinear magnetic field at each moment is solved according to a steady-state field, and the magnetic field energy increment calculation adopts a local linearization calculation method; if the current increment is delta i, the increment of the magnetic field energy of the internal system of the transformer is as follows:
in the formula (8), Δ W 2 Is the increment of magnetic field energy, B is the magnetic induction intensity, H is the magnetic field intensity,
based on the energy balance principle, the dynamic inductance L can be calculated when the energy of the formula (7) is equal to that of the formula (8) D ；
3) Calculation of the vibration acceleration of the winding
The transformer winding is used as a multi-degree-of-freedom mechanical system, the winding vibration is forced vibration under the excitation of electromagnetic force, and the electromagnetic force of the transformer winding is calculated by using a virtual displacement method:
in the formula (9), F r For electromagnetic forces acting in the r direction, W m For storing energy in the magnetic field of the winding leakage field i b For winding currents calculated on the basis of field coupling, L D The dynamic inductance of the winding is calculated based on field circuit coupling;
the electromagnetic force of the winding changing along with the time is obtained through transient electromagnetic field analysis, Fourier transformation is carried out on the electromagnetic force to obtain each harmonic component, the harmonic component is used as a simple harmonic excitation source to carry out steady-state structure harmonic response vibration analysis, the material rigidity and the frequency of the simple harmonic excitation are considered, and the stress harmonic response analysis principle is as follows:
in the formula (10), M is a mass matrix, C is a damping matrix, K is a stiffness matrix, F is a load matrix,
omega is the angular frequency of the simple harmonic excitation; s represents a displacement;
the vibration acceleration g can be calculated according to the vibration displacement:
4) transformer winding turn-to-turn short circuit vibration acceleration analysis
(1) Calculation analysis of high-voltage winding head end turn-to-turn short circuit electrodynamic force
The transformer operates in no-load mode, the head end of the high-voltage winding is provided with 10% turn-to-turn short-circuit faults, the short-circuit line cake is the line cake No. 1-7 in the figure 1, the obtained winding short-circuit electromagnetic force is shown in the figure 3, and the calculation result shows that the short-circuit winding is small in radial stress, and the stress value of the non-short-circuit winding in the radial direction is higher than that of the short-circuit winding. The short-circuit winding and the non-short-circuit winding are mainly subjected to axial electromagnetic force, the stress of the non-short-circuit winding along the axial direction is smaller than that of the short-circuit winding, and the resultant force of the No. 7 line cake is the largest.
(2) Calculation analysis of high-voltage winding head end turn-to-turn short circuit vibration acceleration
According to the principle of fig. 2, the short-circuit electromagnetic force is used as the load to obtain the short-circuit vibration acceleration of the winding, as shown in fig. 4, the calculation result shows that the short-circuit winding generates severe vibration, the vibration acceleration corresponds to the stress of the winding, the main frequency of the vibration is 100Hz, the vibration harmonic response is mainly concentrated on the first 6 harmonics, and the larger the stress of the winding is, the higher the amplitude is.
(3) Calculation and analysis of high-voltage winding middle turn-to-turn short circuit electrodynamic force
When the transformer runs in no-load mode, the middle of the high-voltage winding is provided with 10% of turn-to-turn short circuit faults, the short-circuit line cake is a No. 30-36 line cake in the figure 1, the short-circuit electromagnetic force of the obtained winding is shown in the figure 5, according to the calculation result, the stress borne by the non-short-circuit winding in the y direction is higher than that of the short-circuit winding, and the stress situation in the x direction is opposite. The short-circuit winding and the non-short-circuit winding are mainly subjected to axial electromagnetic force, the axial electromagnetic force of the short-circuit winding is higher than that of the non-short-circuit winding, and the maximum value of resultant force is distributed at two ends of a short-circuit turn.
(4) Calculation analysis of vibration acceleration of turn-to-turn short circuit in middle of high-voltage winding
According to the principle of fig. 2, the short-circuit electromagnetic force is used as the load to obtain the short-circuit vibration acceleration of the winding, as shown in fig. 6, the calculation result shows that the short-circuit winding generates severe vibration, the vibration acceleration corresponds to the stress of the winding, the main frequency of the vibration is 100Hz, the vibration harmonic response is mainly concentrated on the first 6 harmonics, and the larger the stress of the winding is, the higher the amplitude is.
(5) Comparison verification of numerical simulation and physical experiment
Fig. 7, fig. 8 and fig. 9 are schematic diagrams showing the vibration acceleration of the faulty winding at the head end of the transformer when the excitation is 50V, 125V and 220V, respectively, and the higher harmonic distribution of the vibration acceleration of the winding is complicated due to the vibration of the electromagnetic force of the iron core and the vibration effect of magnetostrictive vibration and other components. The results show that the vibration acceleration frequency spectrum of the short-circuit winding is mainly concentrated on the first 10 harmonics, wherein the 2 harmonics have the most severe component change, and the rule obtained by simulation and experiment is basically consistent.
According to the method for calculating the vibration acceleration of the turn-to-turn short circuit of the transformer winding, the results of simulation calculation and experimental comparison show that the method can effectively simulate the distribution situation of the winding electromagnetic force and the vibration acceleration when the transformer has no-load turn-to-turn faults, so that the purpose of the invention is achieved and the effect is achieved.
The embodiments of the present invention have been described in order to explain the present invention rather than to limit the scope of the claims, and it is intended that all such modifications and variations that fall within the true spirit and scope of the invention are possible and within the scope of the invention.
Claims (1)
1. A method for calculating the vibration acceleration of turn-to-turn short circuit of a transformer winding is characterized by comprising the following steps of:
1) magnetic field model
Aiming at the problem of transformer excitation nonlinearity, a magnetic field simulation method is adopted for analysis, hysteresis effect is not considered, a vector magnetic potential finite element method is adopted, and a transformer nonlinear magnetic field equation is obtained according to a Maxwell equation:
in the formula (1), mu is magnetic conductivity, A is vector magnetic potential, J is current density vector,
the overall interpolation function to solve the field is:
in the formula (2), M l Is a sequence of basis functions, l is 1,2, …, l n Formed by corresponding superposition of related unit shape functions, n is a general item number of a basic function sequence, and l n The number of the total edges is the number of the total edges,
and (3) applying the Green theorem to obtain a Galerkin weighted margin equation:
in formula (3), M m For the series of weight functions, Ω denotes the bounding volume component,
if the winding current i is known in the magnetic field model, discretizing the weighted residual equation to form an algebraic equation set, solving to obtain A, and further calculating the magnetic field energy;
2) circuit model
Flux linkage equation of transformer
ψ＝L W (t,i a )i a (4)
In the formula (4), t is a time variable; psi is the flux linkage vector; l is W The static inductance matrix represents the relation between flux linkage and current; i all right angle a Is a vector of the current of the winding,
the differential equation of the transformer time domain circuit is as follows:
in the formula (5), u is voltage excitation; l is a radical of an alcohol D In the form of a dynamic inductor matrix, the inductor matrix,
solving the formula (5) in the circuit model by adopting a fourth-order Runge Kutta method, wherein t is h Coil current i at time h Calculating t h+1 I of time h+1 ：
In the formula (6), s 1 Is the step size, x 1 ～x 4 The slope is calculated for the segment within the step size,
based on the principle of energy disturbance, calculating dynamic inductance according to time-varying system energy, and when the coil current increases by delta i, associating the total energy of the power supply with the dynamic inductance and the current:
in the formula (7), p and q are winding numbers, and Δ W 1 The increment of energy supplied for the external power source,
on the other hand, in the time domain calculation process, the nonlinear magnetic field at each moment is solved according to a steady-state field, and the magnetic field energy increment calculation adopts a local linearization calculation method; if the current increment is Δ i, the increment of the magnetic field energy of the internal system of the transformer is as follows:
in formula (8), Δ W 2 Is the increment of magnetic field energy, B is the magnetic induction intensity, H is the magnetic field intensity,
according to the energy balance principle, the energy of the formula (7) is equal to that of the formula (8), and then the dynamic inductance matrix L can be calculated D ；
3) Calculation of winding vibration acceleration
The transformer winding is used as a multi-degree-of-freedom mechanical system, the winding vibration is forced vibration under the excitation of electromagnetic force, and the electromagnetic force of the transformer winding is calculated by using a virtual displacement method:
in the formula (9), F r For electromagnetic forces acting in the r direction, W m For storing energy in the magnetic field of the winding leakage field i b Calculating the obtained winding current based on field circuit coupling;
the electromagnetic force of the winding changing along with time is obtained through transient electromagnetic field analysis, Fourier transformation is carried out on the electromagnetic force to obtain each harmonic component, the harmonic component is used as a simple harmonic excitation source to carry out harmonic response vibration analysis on a stable structure, the material rigidity and the frequency of simple harmonic excitation are considered, and the stress harmonic response analysis principle is as follows:
in the formula (10), M is a mass matrix, C is a damping matrix, K is a stiffness matrix, F is a load matrix, and omega is the angular frequency of simple harmonic excitation; s represents a displacement;
the vibration acceleration g can be calculated according to the vibration displacement:
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| CN109800522B (en) * | 2019-01-28 | 2023-04-07 | 国网山东省电力公司电力科学研究院 | Method for evaluating stress influence of no-load closing excitation inrush current on transformer winding |
| CN109991508B (en) * | 2019-04-15 | 2021-01-12 | 中国计量大学 | Transformer winding state diagnosis method based on dynamic nonlinear characteristic sequence |
| CN111474496A (en) * | 2020-04-09 | 2020-07-31 | 国网山东省电力公司滨州供电公司 | Transformer turn-to-turn short circuit rapid diagnosis method based on vibration signal identification |
| CN112541290A (en) * | 2020-12-16 | 2021-03-23 | 河北工业大学 | Method for calculating continuous winding overvoltage of large power transformer |
| CN112834148A (en) * | 2021-03-11 | 2021-05-25 | 云南电网有限责任公司电力科学研究院 | Winding model beneficial to axial and radial vibration test |
| CN113405787B (en) * | 2021-05-28 | 2023-11-10 | 上海电机学院 | Motor stator system mechanical admittance testing method and device |
| CN117540539B (en) * | 2023-10-25 | 2024-08-27 | 湖南大学 | Transformer optimal design method and system based on vibration acceleration |
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