CN109446707A - A kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method - Google Patents
A kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method Download PDFInfo
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Abstract
The present invention is a kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method, its main feature is that, including the following steps: state equation, magnetic field model, circuit model and basket vibration calculate under transformer turn-to-turn short circuit operating condition；Shorted-turn fault is occurred as object using transformer A phase head end, middle part, end respectively in calculating, it is saturated the corresponding relationship of excitation and basket vibration when having fully considered different location turn-to-turn short circuit, and effectively simulates the distribution situation of internal magnetic field environment when transformer winding turn-to-turn short circuit and basket vibration acceleration；Contrast simulation result and experimental data demonstrate the accuracy and validity of model foundation, provide possible ways for winding interturn short-circuit fault identification and the identification of winding construction stability.It is authentic and valid with scientific and reasonable, the advantages that practical value is high.
Description
Technical field
The present invention is to be related to transformer technology field, is a kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculating
Method.
Background technique
Transformer is the key equipment in electric system, and hinge work is played in different brackets Power System Interconnection and Power Exchange
With operation conditions not only influences equipment inherently safe, but also influences the stability and reliability of entire electric system.According to data
It has been shown that, transformer winding shorted-turn fault account for the 50%~60% of power transformer interior fault.Turn-to-turn short circuit is generally by inner wire
Caused by insulation ag(e)ing or breakage between circle, have the characteristics that electric current increases, iron core and basket vibration aggravate.If transformer is held
Reforwarding row can then cause the short circuit of (layer) stock and phase fault in this state, in turn result in equipment burnout or even power grid paralysis.At present
Numerous studies are done to transformer shorted-turn fault and transformer winding vibration respectively both at home and abroad, but rare document is to transformation
It is saturated excitation when device winding interturn short-circuit and the corresponding relationship of vibration characteristics is studied.Therefore, carry out to transformer winding circle
Between short-circuit vibration calculating there is highly important researching value and engineering significance.
Summary of the invention
The object of the present invention is to overcome the deficiencies of the prior art and provide a kind of scientific and reasonable, highly effective, it is accurate to calculate
Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method, this method be based on electromagnetic coupling principle construct Y/ Δ transformation
Device winding interturn short-circuit three-dimensional finite element model simultaneously solves, and calculates electromagnetic force suffered by winding, and carry out harmonic responding analysis, obtains
Basket vibration acceleration.
The purpose of the present invention is what is realized by following technical scheme: a kind of Y/ Δ transformer winding turn-to-turn short circuit vibration plus
Speed calculation method, characterized in that it the following steps are included:
1) transformer electromagnetic coupling state equation calculates
Electromagnetic coupling state equation is established to three-phase three-limb Y/ Δ transformer:
In formula: X (t) is system state variables, includes current matrix i and inductance matrix L；U (t) is system input variable,
Including alternating voltage and control parameter matrix, wherein voltage vector is sinusoidal excitation, and control parameter includes short-circuit mode and the number of turns
Than；Y (t) is output variable, is mainly measured comprising circuit parameter and magnetic field；B (t), C (t), D (t), E (t) are coefficient matrix, institute
Stating electromagnetic coupling state equation includes two parts in magnetic field and circuit, and solution procedure passes through magnetic field-circuit INDIRECT COUPLING side
Method is realized；
2) magnetic field model
Transformer magnetic field model is established using vector magnetic potential finite element:
In formula,Indicate curl of vector operation, A is vector magnetic potential；μ is magnetic conductivity, JsFor winding interturn short-circuit excitation
Current density；I is winding current, can be obtained by circuit model；
The golden Weighted Residual form of its gal the Liao Dynasty is obtained with Green's theorem to formula (2):
In formula, Mn、MmRespectively basic function, sequence of weighting function；M, n is sequence general term number；
If electric current in magnetic field model it is known that Weighted Residual equation is discretely formed Algebraic Equation set, solves to obtain A, in turn
Calculate other amounts, such as magnetic flux density B, the field magnetic field strength H amount；
At a time high low pressure winding current variation is diα、diβ, electromagnetic system gross energy and inductance and electric current are closed
Connection, obtains:
In formula: dW1、dW2Respectively circuit and magnetic field energy increment；
It, can simultaneous formula (4) equation calculation time domain inductance by electromagnetic energy conservation according to principle of energy balance；
3) circuit model
Ignore winding itself leakage inductance, derive the Y/ Δ high voltage side of transformer time domain circuit differential equation:
The inductance parameters that magnetic field is solved substitute into formula (5), using improved Euler method, by tkThe coil current at moment
ikCalculate tk+1The electric current i at momentk+1:
In formula: h is step-length, and s is that the segmentation in step-length calculates slope column vector；
Based on the dynamic inductance of energy balance Finite element arithmetic magnetic field model, and feedback circuit model, calculating are lower for the moment
Carve electric current；The input variable that the temporal current that circuit model is calculated is solved next time as magnetic field model carries out magnetic field
It solves, loop iteration solves field-road model；
4) basket vibration Harmony response
By solve interturn short-circuit state equation, can any winding element of calculating transformer magnetic field model electromagnetic force:
Fe=∫ Js×B dV
(7)
Fourier transformation is carried out to electromagnetic force suffered by winding, each harmonic component of electromagnetic force can be obtained, as
Harmonic excitation source carries out the vibration analysis of stable structure Harmony response, considers the frequency of material stiffness and harmonic excitation, stress Harmony response
Analysis principle are as follows:
F1+jF2=(- ω2m+jωC+K)(l1+jl2) (8)
In formula, ω is the angular frequency of harmonic excitation, and m is quality, and K is stiffness coefficient, and C is damped coefficient, and l is vibration position
It moves；
Vibration acceleration g can be calculated according to vibration displacement:
A kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method of the invention, according to practical power transformer
Device parameter establishes moulded dimension and actual ratio as the transformer three-dimensional finite element model of 1:1；It is established based on electromagnetic coupling principle
State equation under transformer turn-to-turn short circuit operating condition, loop iteration solves magnetic field model and circuit model realizes electromagnetic coupling；Herein
On the basis of building basket vibration harmonic responding analysis model obtain the Transient Electromagnetic power of winding, and FFT transform is carried out to it, by result
As driving source, harmonic responding analysis is carried out to basket vibration.The present invention is in calculating with transformer A phase head end, middle part, end point
Not Fa Sheng shorted-turn fault be object, saturation excitation is corresponding with basket vibration when having fully considered different location turn-to-turn short circuit
Relationship, and effectively simulate the distribution feelings of internal magnetic field environment when transformer winding turn-to-turn short circuit and basket vibration acceleration
Condition.Contrast simulation result and experimental data demonstrate the accuracy and validity of model foundation, distinguish for winding interturn short-circuit failure
Know and the identification of winding construction stability provides possible ways, there is scientific and reasonable, authentic and valid, the advantages that practical value is high.
Detailed description of the invention
Fig. 1 transformer high-voltage winding interturn short-circuit simulation model；
Basket vibration schematic diagram calculation of the Fig. 2 based on electromagnetic coupling principle；
Fig. 3 transformer winding head end line cake distribution of force schematic diagram；
Fig. 4 transformer winding head end line cake vibration acceleration distribution schematic diagram；
Line cake distribution of force schematic diagram in the middle part of Fig. 5 transformer winding；
Line cake vibration acceleration distribution schematic diagram in the middle part of Fig. 6 transformer winding；
Basket vibration acceleration spectrogram when different location failure when Fig. 7 110V is motivated；
Basket vibration acceleration spectrogram when different location failure when Fig. 8 220V is motivated；
Basket vibration acceleration spectrogram when different location failure when Fig. 9 380V is motivated.
Specific embodiment
The invention will be further described in the following with reference to the drawings and specific embodiments:
Referring to Fig.1, a kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method of the invention, including it is following
Step:
1) transformer electromagnetic coupling state equation calculates
Using three-phase three-limb Y/ Δ transformer as research object, electromagnetic coupling state equation is established:
In formula: X (t) is system state variables, includes current matrix i and inductance matrix L；U (t) is system input variable,
Including alternating voltage and control parameter matrix, wherein voltage vector is sinusoidal excitation, and control parameter includes short-circuit mode and the number of turns
Than；Y (t) is output variable, is mainly measured comprising circuit parameter and magnetic field；B (t), C (t), D (t), E (t) are coefficient matrix.It should
State equation includes two parts in magnetic field and circuit, and solution procedure is realized by magnetic field-circuit INDIRECT COUPLING method.
2) magnetic field model
Transformer magnetic field model is established using vector magnetic potential finite element:
In formula,Indicate curl of vector operation, A is vector magnetic potential；μ is magnetic conductivity, JsFor winding interturn short-circuit excitation
Current density；I is winding current, can be obtained by circuit model.
The golden Weighted Residual form of its gal the Liao Dynasty is obtained with Green's theorem to formula (2):
In formula, Mn、MmRespectively basic function, sequence of weighting function；M, n is sequence general term number.
If the electric current in magnetic field model is it is known that be discretely formed Algebraic Equation set for Weighted Residual equation, solution can obtain A, into
And other amounts are calculated, such as magnetic flux density B, the field magnetic field strength H amount.
At a time high low pressure winding current variation is diα、diβ, electromagnetic system gross energy and inductance and electric current are closed
Connection, obtains:
In formula: dW1、dW2Respectively circuit and magnetic field energy increment.
It, can equation calculation time domain inductance in simultaneous (4) by electromagnetic energy conservation according to principle of energy balance.
3) circuit model
Ignore winding itself leakage inductance, derive the Y/ Δ high voltage side of transformer time domain circuit differential equation:
In formula: η=Α, B, C；iA、iB、iCFor high-voltage winding electric current；iA、iB、iCFor high-voltage winding resistance；uA、uB、uCFor
High-pressure side winding voltage；L is self-induction, and M is mutual inductance；idηFor each stem winding difference stream after reduction.
The inductance parameters that magnetic field is solved substitute into formula (5), using improved Euler method, by tkThe coil current at moment
ikCalculate tk+1The electric current i at momentk+1:
In formula: h is step-length, and s is that the segmentation in step-length calculates slope column vector.
Based on the dynamic inductance of energy balance Finite element arithmetic magnetic field model, and feedback circuit model, calculating are lower for the moment
Carve electric current；The input variable that the temporal current that circuit model is calculated is solved next time as magnetic field model carries out magnetic field
It solves, loop iteration solves field-road model.
4) basket vibration Harmony response
By solve interturn short-circuit state equation, can any winding element of calculating transformer magnetic field model electromagnetic force:
Fe=∫ Js×B dV (7)
Fourier transformation is carried out to electromagnetic force suffered by winding, each harmonic component of electromagnetic force can be obtained, as
Harmonic excitation source carries out the vibration analysis of stable structure Harmony response.Consider the frequency of material stiffness and harmonic excitation, stress Harmony response
Analysis principle are as follows:
F1+jF2=(- ω2m+jωC+K)(l1+jl2) (8)
In formula, ω is the angular frequency of harmonic excitation, and m is quality, and K is stiffness coefficient, and C is damped coefficient, and l is vibration position
It moves.
Vibration acceleration g can be calculated according to vibration displacement:
5) transformer winding vibration acceleration analysis
(1) A phase high-voltage winding head end turn-to-turn short circuit electromagnetic force calculates analysis
When transformer full-load run, it is (short that turn-to-turn short circuit occurs for setting A phase high-voltage winding head end (No. 1 in Fig. 1, No. 2 line cakes)
3%) road turn ratio is that electromagnetic force suffered by winding wire cake is as shown in Figure 3.As calculated result it is found that electromagnetism suffered by short-circuit line cake
Power is much larger than non-shorting line cake, wherein No. 2 line cake stress are maximum.The axial force that non-shorting winding is born is greater than radial force, short circuit
The radial electromagnetic force that winding is born is greater than axial electromagnetic force.
(2) A phase high-voltage winding head end turn-to-turn short circuit calculation analysis on vibration
As shown in Figure 4, basket vibration acceleration is corresponding with suffered electromagnetic force, and more violent vibration occurs for short-circuited winding,
Wherein the amplitude of No. 2 line cakes is the most serious.The vibration acceleration frequency spectrum of winding is concentrated mainly on preceding ten subharmonic, at 100Hz
It vibrates most violent.
(3) turn-to-turn short circuit electromagnetic force calculates analysis in the middle part of A phase high-voltage winding
3% turn-to-turn short circuit is set in the middle part of A phase high-voltage winding, as shown in Figure 1, short-circuit line cake is No. 35, No. 36.Winding wire
Electromagnetic force suffered by cake is as shown in Figure 5.As calculated result it is found that electromagnetic force suffered by short-circuit line cake is much larger than non-shorting line cake, and
Electromagnetic force suffered by intermediate two circle short-circuit line cakes is of substantially equal；The axial force that non-shorting winding is born is greater than radial force, short circuit around
The radial electromagnetic force that group is born is greater than axial electromagnetic force.
(4) turn-to-turn short circuit electromagnetic force calculates analysis in the middle part of A phase high-voltage winding
It will be appreciated from fig. 6 that basket vibration acceleration is corresponding with suffered electromagnetic force, and vibration is most violent at 100Hz.Short-circuit line
The more non-shorting line cake of the vibration amplitude of cake significantly increases, and the vibration amplitude of two circle short-circuit line cakes is of substantially equal.
Since the electromagnetism rule of end turn-to-turn short circuit is almost the same with head end, details are not described herein.
(5) simulation result and experimental data compare
The Vibration Condition of winding when measuring different location turn-to-turn short circuit in transformer boost process, as shown in Fig. 7,8,9,
Occur that vibration when turn-to-turn short circuit is most violent in the middle part of winding, extent of vibration when turn-to-turn short circuit occurs for head end and end is of substantially equal.
Basket vibration is concentrated mainly on preceding 10 subharmonic, wherein variation is most violent at 100Hz, and containing relatively high in rumble spectrum
High fdrequency component.Experiment and emulation gained rule are almost the same.
A kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method of the invention by simulation calculation and is divided
Analysis the result shows that, can effectively analogue transformer core interior magnetic field, vibration acceleration distribution situation, realize mesh of the present invention
Sum achieved the effect that it is described.
Design conditions, legend in the embodiment of the present invention etc. are only used for that the present invention is further illustrated, not exhaustive,
Do not constitute the restriction to claims, the enlightenment that those skilled in the art obtain according to embodiments of the present invention, no
It would occur to other substantially equivalent substitutions by creative work, all fall in the scope of protection of the present invention.
Claims (1)
1. a kind of Y/ Δ transformer winding turn-to-turn short circuit vibration acceleration calculation method, characterized in that it the following steps are included:
1) transformer electromagnetic coupling state equation calculates
Electromagnetic coupling state equation is established to three-phase three-limb Y/ Δ transformer:
In formula: X (t) is system state variables, includes current matrix i and inductance matrix L；U (t) is system input variable, including
Alternating voltage and control parameter matrix, wherein voltage vector is sinusoidal excitation, and control parameter includes short-circuit mode and turn ratio；Y
(t) it is output variable, is mainly measured comprising circuit parameter and magnetic field；B (t), C (t), D (t), E (t) are coefficient matrix, the electricity
Magnetic coupling state equation includes two parts in magnetic field and circuit, and solution procedure is real by magnetic field-circuit INDIRECT COUPLING method
It is existing；
2) magnetic field model
Transformer magnetic field model is established using vector magnetic potential finite element:
In formula,Indicate curl of vector operation, A is vector magnetic potential；μ is magnetic conductivity, JsFor winding interturn short-circuit exciting current
Density；I is winding current, can be obtained by circuit model；
The golden Weighted Residual form of its gal the Liao Dynasty is obtained with Green's theorem to formula (2):
In formula, Mn、MmRespectively basic function, sequence of weighting function；M, n is sequence general term number；
If electric current in magnetic field model it is known that Weighted Residual equation is discretely formed Algebraic Equation set, solves to obtain A, and then calculate
Other amounts, such as magnetic flux density B, the field magnetic field strength H amount；
At a time high low pressure winding current variation is diα、diβ, electromagnetic system gross energy is associated with inductance and electric current, is obtained
It arrives:
In formula: dW1、dW2Respectively circuit and magnetic field energy increment；
It, can simultaneous formula (4) equation calculation time domain inductance by electromagnetic energy conservation according to principle of energy balance；
3) circuit model
Ignore winding itself leakage inductance, derive the Y/ Δ high voltage side of transformer time domain circuit differential equation:
In formula: η=Α, B, C；iA、iB、iCFor high-voltage winding electric current；iA、iB、iCFor high-voltage winding resistance；uA、uB、uCFor high pressure
Side winding voltage；L is self-induction, and M is mutual inductance；idηFor each stem winding difference stream after reduction.
The inductance parameters that magnetic field is solved substitute into formula (5), using improved Euler method, by tkThe coil current i at momentkMeter
Calculate tk+1The electric current i at momentk+1:
In formula: h is step-length, and s is that the segmentation in step-length calculates slope column vector；
Based on the dynamic inductance of energy balance Finite element arithmetic magnetic field model, and feedback circuit model, calculating subsequent time are electric
Stream；The input variable that the temporal current that circuit model is calculated is solved next time as magnetic field model carries out magnetic field solution,
Loop iteration solves field-road model；
4) basket vibration Harmony response
By solve interturn short-circuit state equation, can any winding element of calculating transformer magnetic field model electromagnetic force:
Fe=∫ Js×B dV (7)
Fourier transformation is carried out to electromagnetic force suffered by winding, each harmonic component of electromagnetic force can be obtained, as simple harmonic quantity
Driving source carries out the vibration analysis of stable structure Harmony response, considers the frequency of material stiffness and harmonic excitation, stress harmonic responding analysis
Principle are as follows:
F1+jF2=(- ω2m+jωC+K)(l1+jl2) (8)
In formula, ω is the angular frequency of harmonic excitation, and m is quality, and K is stiffness coefficient, and C is damped coefficient, and l is vibration displacement；
Vibration acceleration g can be calculated according to vibration displacement:
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN112798993A (en) * | 2021-04-08 | 2021-05-14 | 中国电子科技集团公司第九研究所 | Device and method for measuring temperature coefficient of permanent magnet material based on accelerometer |
| CN116029181A (en) * | 2023-03-30 | 2023-04-28 | 西安热工研究院有限公司 | Wave process simulation method and system for winding turn-to-ground short circuit under magnetic pulse |
-
2018
- 2018-11-10 CN CN201811335365.4A patent/CN109446707A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
| CN112798993A (en) * | 2021-04-08 | 2021-05-14 | 中国电子科技集团公司第九研究所 | Device and method for measuring temperature coefficient of permanent magnet material based on accelerometer |
| CN112798993B (en) * | 2021-04-08 | 2021-07-13 | 中国电子科技集团公司第九研究所 | Device and method for measuring temperature coefficient of permanent magnet material based on accelerometer |
| CN116029181A (en) * | 2023-03-30 | 2023-04-28 | 西安热工研究院有限公司 | Wave process simulation method and system for winding turn-to-ground short circuit under magnetic pulse |
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Application publication date: 20190308 |