CN110008645A - A kind of transformer loss calculation method - Google Patents
A kind of transformer loss calculation method Download PDFInfo
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- CN110008645A CN110008645A CN201910363556.XA CN201910363556A CN110008645A CN 110008645 A CN110008645 A CN 110008645A CN 201910363556 A CN201910363556 A CN 201910363556A CN 110008645 A CN110008645 A CN 110008645A
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Abstract
The present invention relates to a kind of transformer loss calculation methods, comprising: S1: the no-load test before being put into operation by transformer obtains transformer BH curve under practical power frequency operation state；S2: establishing J-A dynamic model, is optimized using BH curve to J-A dynamic model parameters, obtains the J-A dynamic model for being used to emulate the transformer core hysteresis loop under actual motion state；S3: establishing transformer winding model under harmonic wave, calculates primary side impedance and Excitation Impedance of Power Transformer；S4: non-sine input is handled by Fourier decomposition, obtains the winding current and exciting current under real time data using transformer circuit equivalent model；S5: transformer winding loss in real time is calculated to obtain by the relationship of a secondary side impedance in winding equivalent circuit and the winding current flowed through, calculates to obtain transformer core loss in real time by J-A model；The present invention has taken into account rapidity and the accuracy of transformer loss calculating to realize the real-time prediction of transformer loss.
Description
Technical field
The present invention relates to electric system, and prediction technique field is lost, more particularly, to a kind of transformer loss calculating side
Method.
Background technique
There are a large amount of exceeded harmonic currents and electricity as the nonlinear load in electric system gradually increases, in route
Pressure, so that the harmonic problem of electric system is on the rise；When transformer is run under harmonic environment for a long time, a large amount of damage can be generated
Consumption, fever reduce the service life of transformer, can cause to power grid security when serious to make transformer insulated horizontal decline
It influences.
Reducing transformer loss, improving for electric power energy efficiency of equipment is the basis for realizing that operation of power networks is high-quality and efficient；It is accurate fast
The model of fast ground calculating transformer real-time loss can provide important references in the scheduling switching of the operational process of transformer, also for
Electricity quality evaluation technique study provides emulation module.
Transformer loss computation model generally uses Steinmetz equation or using static state J-A model, change both at home and abroad at present
The non-linear of depressor field excitation branch line impedance is handled using segmented, is needed lot of experimental data, is not taken into account certain rapidity
Loss prediction in real time is realized with accuracy.
Summary of the invention
The present invention is that the calculating of transformer loss described in the above-mentioned prior art is overcome not take into account certain rapidity and essence
True property realizes defect that loss is predicted in real time, provides a kind of transformer loss calculation method.
It the described method comprises the following steps:
S1: the no-load test before being put into operation by transformer obtains transformer BH curve under practical power frequency operation state；
BH curve be characterize transformer core in magnetic history between magnetic induction B and magnetic field strength H relationship magnetization curve；
S2: establishing J-A dynamic model, is optimized using BH curve to J-A dynamic model parameters, obtains and is used to emulate
The J-A dynamic model of transformer core hysteresis loop under actual motion state；
S3: establishing transformer winding model under harmonic wave, according to transformer nameplate parameter calculating transformer primary side impedance；Benefit
With i-L function calculating transformer excitation impedance；
S4: one secondary voltage of transformer, current data are collected and recorded, according to one in data modification transformer winding model
Secondary voltage, current parameters；Non-sine input is handled by Fourier decomposition, obtains real time data using transformer winding model
Under winding current and exciting current；
S5: pass through the relationship calculating transformer winding of a secondary side impedance in winding equivalent circuit and the winding current flowed through
Loss calculates to obtain transformer core loss in real time by J-A model.
Preferably, the J-A dynamic model in S2 are as follows:
Wherein Man=Ms(coth(He/a)-(a/He))
B=μo(H+M)
In formula, magnetic field strength H is as input, and magnetic induction density B is as output, MsIt is irreversible for saturation magnetization, k
Coefficient, c are reversible coefficient, α is to characterize the parameter to interact between magnetic domain, the corrected parameter that a is anhysteretic curve shape,
ρ is the resistivity of material, and unit is Ω m；D is scantling when slice (is diameter when cylindrical body, be piece thickness), and unit is
M, general distribution transformer silicon steel sheet is with a thickness of 0.25-0.35mm；β is that (for 16 when cylindrical body, when slice is 6 to geometrical factor, ball
It is 20), β=6 to be taken for transformer when body；Wherein；W is slice width, unit m；HoFor parameter related with domain wall, value
0.0075；G is no guiding principle amount constant unrelated with size, value 0.1356；μ0For space permeability, t is the time, and M is that magnetization is strong
Degree, unit A/m, δ are the parameter for characterizing pinning effect inhibition in magnetic field, as dH/dt > 0, δ > 0；As dH/dt < 0, δ <
0；ManFor the lossless intensity of magnetization, unit A/m, HeFor effective magnetic field intensity, unit A/m, H are magnetic field strength, unit A/m.
Preferably, detailed process model parameter optimized using BH curve are as follows:
The silicon steel sheet BH curve obtained using particle swarm optimization algorithm fitting S1, obtains 5 of amendment J-A dynamic model
Parameter: saturation magnetization Ms, the cycle irreversibility parameter k, reversible coefficient c, characterization magnetic domain between interact parameter alpha, without magnetic hysteresis magnetic
Change the corrected parameter a of curve shape, remaining parameter is arranged with real transformer situation, obtains and is used to emulate actual motion state
Under transformer core hysteresis loop J-A dynamic model.
Preferably, transformer winding model includes: primary side power supply, primary side impedance, excitation impedance, secondary side electricity in S3
Source；
Primary side power supply and primary side impedance are connected in series；Primary side power supply and primary side impedance and excitation reluctance after series connection
Anti-, secondary side power supply three is connected in parallel.
Preferably, in S3 primary side impedance calculation formula are as follows:
Wherein, h is overtone order, and R is winding inductance, and X is winding reactance.
Preferably, in S3 excitation impedance calculating process are as follows:
S3.1: setting magnetic leakage free, and the magnetic field strength H on magnetic circuit l is equal everywhere；There is to obtain exciting current according to circuital law
imWith magnetic field strength H relationship:
?
In formula, l is that transformer be averaged iron circuit, and N is high order side number of winding turns；
S3.2: according to energy perturbation principle, the external magnetization energy increment provided, calculation formula are calculated are as follows:
ΔW1=Δ emΔim
That is Δ W1=LeqΔim 2
Wherein, Δ imTo be engraved in external power supply effect lower generation exciting current when circuit model coil, Δ λ is excitation
Magnetic linkage caused by electric current Δ i；ΔemFor excitation port voltage increment；LeqFor field excitation branch line equivalent inductance；
S3.3: energy increment caused by changes of magnetic field caused by exciting current, calculation formula in calculating magnetic field are as follows:
ΔW2=∫ Δ B Δ HdV
In formula, Δ B is magnetic induction intensity increment；Δ H is incremental magnetic field
S3.4: exciting current and field excitation branch line equivalent inductance are obtained in conjunction with S3.1-S3.3, and by the J-A model in S2
LeqRelationship；I-L function is obtained by Gaussian algorithm again；
I-L function are as follows:
Wherein aj、bj、cjFor different parameters, j=1,2,3,4,5,6,7,8；
S3.5: excitation impedance is calculated according to i-L function.
Preferably, S4 the following steps are included:
S4.1: one secondary voltage of transformer, current data are collected and recorded, according in data modification transformer winding model
One secondary voltage, current parameters；
Pass through Fourier spaceBy primary side non-sinusoidal voltage,
Secondary side non-sinusoidal current resolves into sinusoidal fundamental wave voltage and current, odd times multifrequency sinusoid voltage and current respectively.
S4.3: primary side voltage source voltage u of the input after S4.1 is decomposedp, secondary side current ource electric current iuser, and be arranged
One is less than 10% initial excitation electric current i of open-circuit excitation electric currentmInitial value be (one lesser exciting current of self-setting
Initial value im, to start calculation process, such as 0.05A), seek primary side current ip, calculation formula are as follows:
ip=iuser+im
S4.4: according to primary side current, counter electromotive force, calculation formula are calculated are as follows:
S4.5: excitation potential, calculation formula are asked are as follows:
S4.6: exciting current: calculation formula is calculated are as follows:
S4.7: judge whether exciting current restrains；If convergence, carries out S5；If not restraining, return step S4.3.
Preferably, in step S5 winding total losses calculation formula are as follows:
Wherein, iphFor primary side current ipElectric current caused by middle h subharmonic.
Preferably, in step S5 core loss calculating process are as follows:
S5.1: by the exciting current i under the different overtone orders for passing through iteration in S4mIt is added, substitutes into following equation and acquire
Input magnetic field H:
S5.2: pass through J-A model calculated magnetic induction intensity B；
S5.3: the core loss of calculating transformer, calculation formula are as follows:
PFe=Pec+PA+Ph
Ph=∫ BdH
Wherein, PFeFor core loss, PecFor eddy-current loss, PATo add damage as caused by local eddy currents between device structure
Consumption, PhFor magnetic hystersis loss.
Compared with prior art, the beneficial effect of technical solution of the present invention is: the present invention has taken into account transformer loss calculating
Rapidity and accuracy realize the real-time prediction of transformer loss, the present invention only needs measuring transformer iron core actual motion
BH curve forms corresponding J-A model to obtain the excitation impedance and BH loop line under corresponding input, embodies transformer core
It is non-linear；Frequency influences with embodying harmonic environment drag well dynamic to J-A model simultaneously, to the transformation of different model
As long as device, which changes parameter, can be carried out loss assessment.
Detailed description of the invention
Fig. 1 is the present embodiment transformer loss calculation method flow chart.
Fig. 2 is transformer equivalent circuit figure.
Fig. 3 is that nonlinear inductance parameter obtains flow chart.
Specific embodiment
The attached figures are only used for illustrative purposes and cannot be understood as limitating the patent；
In order to better illustrate this embodiment, the certain components of attached drawing have omission, zoom in or out, and do not represent actual product
Size；
To those skilled in the art, it is to be understood that certain known features and its explanation, which may be omitted, in attached drawing
's.
The following further describes the technical solution of the present invention with reference to the accompanying drawings and examples.
The present embodiment provides a kind of transformer loss calculation methods, as shown in Figure 1, the described method comprises the following steps:
S1: the no-load test before being put into operation by transformer obtains transformer BH curve under practical power frequency operation state.
S2: transformer core model is established by matlab/Simulink, J-A dynamic mathematical models such as formula (1) is shown:
B=μo(H+M) (2)
Man=Ms(coth(He/a)-(a/He)) (3)
In formula (1) (2), magnetic field strength H is as input, and magnetic induction density B is as output, MsIt is for saturation magnetization, k
The cycle irreversibility parameter, c are reversible coefficient, α is the parameter that interacts between characterizing magnetic domain, a is repairing for anhysteretic curve shape
Positive parameter, ρ are the resistivity of material, and unit is Ω m；D is scantling when slice (is diameter when cylindrical body, be piece thickness)
Unit is m, and general distribution transformer silicon steel sheet is with a thickness of 0.25-0.35mm；β is geometrical factor (for 16 when cylindrical body, when slice
It is 6,20), β=6 is taken for transformer when sphere；Wherein；W is slice width, unit m；HoFor ginseng related with domain wall
Number, value 0.0075；G is no guiding principle amount constant unrelated with size, value 0.1356.μ0For space permeability, t is the time, and M is
The intensity of magnetization, unit A/m, δ are the parameter for characterizing pinning effect inhibition in magnetic field, as dH/dt > 0, δ > 0；Work as dH/dt
< 0, δ < 0；ManFor the lossless intensity of magnetization, unit A/m, HeFor effective magnetic field intensity, unit A/m, H are magnetic field strength, unit A/
m。
The silicon steel sheet BH curve obtained using particle swarm optimization algorithm fit procedure 1 obtains amendment J-A dynamic model 5
Parameter: saturation magnetization Ms, the cycle irreversibility parameter k, reversible coefficient c, characterization magnetic domain between interact parameter alpha, without magnetic hysteresis magnetic
Change the corrected parameter a of curve shape, remaining parameter is arranged with real transformer situation, and acquisition can emulate under actual motion state
Transformer core hysteresis loop dynamic model.
S3: transformer winding model is established by matlab/Simulink；As shown in Fig. 2, winding model is by primary side electricity
Source, primary side impedance, excitation impedance, secondary side power supply composition.
When overtone order is relatively low, kindred effect is smaller to the influence for exchanging winding with kelvin effect.For electric power
Transformer in net, Main Analysis number are lower than 23 harmonic waves, calculate to simplify, and the present invention uses conventional transformer winding
Model, formula (2), the primary side equivalent impedance under transformer winding 50Hz are calculated by transformer nameplate parameter:
H is overtone order, and winding impedance changes with overtone order and changed, and R is winding inductance, and X is winding reactance.
As shown in figure 3, nonlinear inductance parameter acquisition procedure is as follows:
According to circuital law
In formula (5), l is that transformer be averaged iron circuit, and N is high order side number of winding turns；Leakage field does not consider (depending on single frame iron core
For no branch's magnetic circuit), and think that the magnetic field strength H on magnetic circuit l is equal everywhere, there is to obtain excitation electricity thus according to circuital law
Flow imWith magnetic field strength H relationship:
According to energy perturbation principle, it is engraved in when circuit model coil that external power supply effect is lower to generate exciting current Δ i
Magnetic linkage Δ λ is generated, excitation port voltage increment is thus obtainedWith the induced electromotive force in bucking coil.It is then external to mention
For magnetization energy increment be Δ W1=Δ emΔim, it may be assumed that
ΔW1=LeqΔim 2 (7)
Wherein, LeqFor field excitation branch line equivalent inductance.
And exciting current Δ i causes to obtain field amount changes delta B, Δ H in magnetic field, correspondence generates to obtain magnetic field energy increment
Are as follows:
ΔW2=∫ Δ B Δ HdV (8)
Joint type (4) (5) (6) can obtain exciting current i by the J-A model in step 2mWith field excitation branch line equivalent inductance
LeqRelationship, by matlab Fitting Toolbox using Gaussian algorithm obtain i-L function, i.e. excitation impedance ZeqParameter by
Exciting current imVariation and change；
Wherein, i-L function are as follows:
Wherein aj、bj、cjFor different parameters, j=1,2,3,4,5,6,7,8；
Excitation impedance is calculated further according to i-L function.
One secondary voltage of transformer, current data are collected and recorded, according to one or two in data modification transformer winding model
Secondary voltage, current parameters；Pass through Fourier spacePrimary side is non-just
String voltage, secondary side non-sinusoidal current resolve into sinusoidal fundamental wave voltage and current, odd times multifrequency sinusoid voltage and current respectively.
Input the primary side voltage source voltage u after S4.1 is decomposedp, secondary side current ource electric current iuser, and be arranged one small
In 10% initial excitation electric current i of open-circuit excitation electric currentmInitial value (the initial value of one lesser exciting current of self-setting
im, to start calculation process, such as 0.05A), primary side current i is asked by iterative circuit model such as (9) (10) (11) (12)p:
ip=iuser+im (9)
It obtains under different overtone orders after obtaining iteration convergence for calculating the primary side current i of winding losspWith for calculating
The exciting current i of core lossm。
S5: pass through the relationship calculating transformer winding of a secondary side impedance in winding equivalent circuit and the winding current flowed through
Loss calculates to obtain transformer core loss in real time by J-A model.
Calculate winding loss:
Transformer winding harmonic loss based on formula (3) can be obtained by formula (13):
H is overtone order, iphFor primary side current ipElectric current caused by middle h subharmonic.
The primary side current i under different overtone orders will be obtained by iterationpBy formula (13) can calculate winding always damages
Consumption.
Calculate core loss:
Exciting current i under different overtone orders will be obtained by iterationmIt being added, magnetic field strength H must be inputted by substituting into formula (5) (6),
The magnetic induction density B of core loss needs must be calculated by formula (1) (2) (3).
According to loss separation theory, transformer core loss can be divided into three parts, eddy-current loss, magnetic hystersis loss and by equipment
Added losses caused by local eddy currents between structure:
PFe=Pec+PA+Ph (14)
Wherein, PFeFor core loss, PecFor eddy-current loss, PATo add damage as caused by local eddy currents between device structure
Consumption, PhFor magnetic hystersis loss.
Under conditions of field homogeneity penetrates, classical eddy-current loss can be obtained by solving Maxwell equation, express
Are as follows:
Can occur microcosmic local eddy currents near neticdomain wall during magnetic domain wall moving, cause eddy-current loss, table
Up to formula are as follows:
The area that the size of each cycle magnetic hystersis loss, that is, magnetic hysteresis BH curve is surrounded.The magnetic hystersis loss of unit volume iron core
It can be calculated by calculating the area of hysteresis loop:
Ph=∫ BdH (17)
Three loss additions can obtain the total core loss data of transformer.
The terms describing the positional relationship in the drawings are only for illustration, should not be understood as the limitation to this patent；
Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair
The restriction of embodiments of the present invention.For those of ordinary skill in the art, may be used also on the basis of the above description
To make other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.It is all this
Made any modifications, equivalent replacements, and improvements etc., should be included in the claims in the present invention within the spirit and principle of invention
Protection scope within.
Claims (9)
1. a kind of transformer loss calculation method, which is characterized in that the described method comprises the following steps:
S1: the no-load test before being put into operation by transformer obtains transformer BH curve under practical power frequency operation state；
S2: establishing J-A dynamic model, is optimized using BH curve to J-A dynamic model parameters, obtains and is used to emulate reality
The J-A dynamic model of transformer core hysteresis loop under operating status；
S3: transformer winding model under harmonic wave, the impedance of calculating transformer primary side and Excitation Impedance of Power Transformer are established；
S4: collecting and recording one secondary voltage of transformer, current data, according to one or two times in data modification transformer winding model
Voltage, current parameters；Non-sine input is handled by Fourier decomposition, is obtained under real time data using transformer winding model
Winding current and exciting current；
S5: it is damaged by a secondary side impedance in winding equivalent circuit and the relationship calculating transformer winding of the winding current flowed through
Consumption calculates to obtain transformer core loss in real time by J-A model.
2. transformer loss calculation method according to claim 1, which is characterized in that the J-A dynamic model in S2 are as follows:
Man=Ms(coth(He/a)-(a/He))
B=μo(H+M)
In formula, magnetic field strength H is as input, and magnetic induction density B is as output, MsFor saturation magnetization, k be the cycle irreversibility parameter,
C is reversible coefficient, α is to characterize the parameter to interact between magnetic domain, the corrected parameter that a is anhysteretic curve shape, and ρ is material
The resistivity of material, unit are Ω m；D is scantling, unit m；β is geometrical factor；Wherein；W is slice width, unit
For m；HoIt is no guiding principle amount constant unrelated with size for parameter G related with domain wall；μ0For space permeability, t is the time, and M is magnetic
Change intensity, unit A/m, δ are the parameter for characterizing pinning effect inhibition in magnetic field, as dH/dt > 0, δ > 0；As dH/dt <
0, δ < 0；ManFor the lossless intensity of magnetization, unit A/m, HeFor effective magnetic field intensity, unit A/m, H are magnetic field strength, unit A/m.
3. transformer loss calculation method according to claim 2, which is characterized in that using BH curve to model parameter
The detailed process optimized are as follows:
The silicon steel sheet BH curve obtained using particle swarm optimization algorithm fitting S1, obtains 5 parameters of amendment J-A dynamic model:
Saturation magnetization Ms, the cycle irreversibility parameter k, reversible coefficient c, characterization magnetic domain between interact parameter alpha, anhysteretic curve
The corrected parameter a of shape, remaining parameter are arranged with real transformer situation, obtain and are used to emulate the change under actual motion state
The J-A dynamic model of depressor iron core hysteresis loop.
4. transformer loss calculation method according to claim 1, which is characterized in that transformer winding model packet in S3
It includes: primary side power supply, primary side impedance, excitation impedance, secondary side power supply；
Primary side power supply and primary side impedance are connected in series；Primary side power supply and primary side impedance after series connection and excitation impedance,
Secondary side power supply three is connected in parallel.
5. transformer loss calculation method according to claim 1, which is characterized in that the calculating of primary side impedance in S3 is public
Formula are as follows:
Wherein, h is overtone order, and R is winding inductance, and X is winding reactance.
6. transformer loss calculation method according to claim 1, which is characterized in that the calculating process of excitation impedance in S3
Are as follows:
S3.1: setting magnetic leakage free, and the magnetic field strength H on magnetic circuit l is equal everywhere；There is to obtain exciting current i according to circuital lawmWith
Magnetic field strength H relationship:
?
In formula, l is that transformer be averaged iron circuit, and N is high order side number of winding turns；
S3.2: according to energy perturbation principle, the external magnetization energy increment provided, calculation formula are calculated are as follows:
ΔW1=Δ emΔim
That is Δ W1=LeqΔim 2
Wherein, Δ imTo be engraved in external power supply effect lower generation exciting current when circuit model coil, Δ λ is exciting current
Magnetic linkage caused by Δ i；ΔemFor excitation port voltage increment；LeqFor field excitation branch line equivalent inductance；
S3.3: energy increment caused by changes of magnetic field caused by exciting current, calculation formula in calculating magnetic field are as follows:
ΔW2=∫ Δ B Δ HdV
In formula, Δ B is magnetic induction intensity increment；Δ H is incremental magnetic field；
S3.4: exciting current and field excitation branch line equivalent inductance L are obtained in conjunction with S3.1-S3.3, and by the J-A model in S2eq's
Relationship；I-L function is obtained by Gaussian algorithm again；
I-L function are as follows:
Wherein aj、bj、cjFor different parameters, j=1,2,3,4,5,6,7,8；
S3.5: excitation impedance is calculated according to i-L function.
7. transformer loss calculation method according to claim 1, which is characterized in that S4 the following steps are included:
S4.1: one secondary voltage of transformer, current data are collected and recorded, according to one or two in data modification transformer winding model
Secondary voltage, current parameters；
Pass through Fourier spaceBy primary side non-sinusoidal voltage, secondary side
Non-sinusoidal current resolves into sinusoidal fundamental wave voltage and current, odd times multifrequency sinusoid voltage and current respectively；
S4.2: primary side voltage source voltage u of the input after S4.1 is decomposedp, secondary side current ource electric current iuser, and it is arranged one
Less than 10% initial excitation electric current i of open-circuit excitation electric currentmInitial value seeks primary side current ip, calculation formula are as follows:
ip=iuser+im
S4.3: according to primary side current, counter electromotive force, calculation formula are calculated are as follows:
S4.4: excitation potential, calculation formula are asked are as follows:
S4.5: exciting current: calculation formula is calculated are as follows:
S4.7: judge whether exciting current restrains；If convergence, carries out S5；If not restraining, return step S4.2.
8. transformer loss calculation method according to claim 7, which is characterized in that the meter of winding total losses in step S5
Calculate formula are as follows:
Wherein, iphFor primary side current ipElectric current caused by middle h subharmonic.
9. transformer loss calculation method according to claim 8, which is characterized in that the calculating of core loss in step S5
Process are as follows:
S5.1: by the exciting current i under the different overtone orders for passing through iteration in S4mIt is added, substitutes into following equation and acquire input magnetic
Field H:
S5.2: pass through J-A model calculated magnetic induction intensity B；
S5.3: the core loss of calculating transformer, calculation formula are as follows:
PFe=Pec+PA+Ph
Ph=∫ BdH
Wherein, PFeFor core loss, PecFor eddy-current loss, PAFor the added losses as caused by local eddy currents between device structure, Ph
For magnetic hystersis loss.
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| CN113933597A (en) * | 2021-10-19 | 2022-01-14 | 北京智芯仿真科技有限公司 | Magnetic core loss determination method and device for integrated circuit current bidirectional distortion |
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| CN114297832B (en) * | 2021-12-14 | 2022-08-30 | 西南交通大学 | Traction transformer hysteresis loss solving method considering frequent vibration |
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