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CN106250626B - A kind of extra-high voltage transformer zero load D.C. magnetic biasing quick calculation method based on L-I curve - Google Patents

A kind of extra-high voltage transformer zero load D.C. magnetic biasing quick calculation method based on L-I curve Download PDF

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CN106250626B
CN106250626B CN201610621444.6A CN201610621444A CN106250626B CN 106250626 B CN106250626 B CN 106250626B CN 201610621444 A CN201610621444 A CN 201610621444A CN 106250626 B CN106250626 B CN 106250626B
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current
transformer
inductance
bias
curve
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CN106250626A (en
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王泽忠
邓涛
谭瑞娟
杨箫箫
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North China Electric Power University
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Abstract

本发明公开了一种基于L‑I曲线的特高压变压器空载直流偏磁快速计算方法，其包括以下步骤：步骤1：根据变压器实际结构参数，构建变压器三维实体模型，采用棱边有限元法建立变压器直流偏磁计算磁场模型；步骤2：利用步骤1的磁场模型，根据能量扰动原理计算变压器绕组流过不同电流时的自感值和绕组间的互感值，绘制L‑I曲线；步骤3：根据变压器电气连接图，通过电压补偿搭建变压器直流偏磁等效电路计算模型；步骤4：利用修正电感参数的四阶龙格库塔法求解直流偏磁等效电路模型，适当加大直流电阻加快计算速度，其中的电感参数通过插值L‑I曲线获得；步骤5：计算特高压自耦变压器在不同直流偏置情况下的励磁电流，对各种偏置下的稳态励磁电流波形进行FFT变换，得到各偏置下的电流谐波变化情况。

The invention discloses a fast calculation method for no-load DC bias magnetization of an ultra-high voltage transformer based on an L-I curve, which comprises the following steps: Step 1: According to the actual structural parameters of the transformer, construct a three-dimensional solid model of the transformer, and adopt the edge finite element method Establish a magnetic field model for calculating the DC bias of the transformer; Step 2: Using the magnetic field model in Step 1, according to the principle of energy disturbance, calculate the self-inductance value and the mutual inductance value between the windings of the transformer when different currents flow, and draw the L‑I curve; Step 3 : According to the electrical connection diagram of the transformer, build the DC bias equivalent circuit calculation model of the transformer through voltage compensation; Step 4: Use the fourth-order Runge-Kutta method to correct the inductance parameters to solve the DC bias equivalent circuit model, and appropriately increase the DC resistance To speed up the calculation, the inductance parameters are obtained by interpolating the L‑I curve; Step 5: Calculate the excitation current of the UHV autotransformer under different DC bias conditions, and perform FFT on the steady-state excitation current waveform under various biases Transform to get the current harmonic changes under each bias.

Description

A kind of extra-high voltage transformer zero load D.C. magnetic biasing based on L-I curve quickly calculates Method
Technical field
The invention belongs to extra-high voltage grid equipment and safety and stability safeguard fields, in particular to a kind of bent based on L-I The extra-high voltage transformer zero load D.C. magnetic biasing quick calculation method of line.
Background technique
With super, extra-high voltage direct-current transmission technology rapid development, China realizes remote, large capacity, low energy consumption, height The power Transmission of efficiency.Core element one of of the extra-high voltage auto-transformer as extra-high voltage grid is improving power quality, is increasing Forceful electric power Force system operation stability, reduce system operation cost, meet society's electricity consumption demand etc. play it is extremely important Effect.But the operation of extra-high voltage transformer is influenced problem by DC power transmission line and is also become increasingly conspicuous, when direct current biasing interferes When being mixed into the sinusoidal power frequency excitation for being applied to extra-high voltage transformer winding overhang, transformer magnetizing current goes out in positive and negative half period Now obvious asymmetry, i.e., so-called DC magnetic bias phenomena, exciting current generate a large amount of harmonic wave, increase the idle of transformer Consumption causes transformer vibration enhancing, hardware and fuel tank hot-spot, brings greatly to the stable operation of electric system It influences.Structure is complicated for extra-high voltage transformer, and cost is high, it is difficult to directly study transformer DC magnetic bias by test method Response mechanism provides the evaluation of extra-high voltage transformer D.C. magnetic biasing and refers to verify extra-high voltage transformer D.C. magnetic biasing physical effect Mark establishes theory and technology foundation for the anti-bias transformation of extra-high voltage transformer, it is necessary within limited time and resource, find A kind of quickly accurate extra-high voltage transformer D.C. magnetic biasing calculation method, this has research extra-high voltage transformer D.C. magnetic biasing Significance.The method calculated currently used for transformer DC magnetic bias has circuit-Magnetic Circuit Method, harmonic balance finite element and time domain field Road coupled method.The D.C. magnetic biasing that circuit-Magnetic Circuit Method carries out transformer calculates, and analyzes winding current under different D.C. magnetic biasing operating conditions Situation of change, but magnetic circuit model does not fully consider the influence of leakage field, it is difficult to meet project analysis needs.Had based on harmonic balance The method for limiting member solves each harmonic of magnetic vector potential in unit simultaneously and is superimposed again, as a result by magnetic field coupling external circuit Accuracy with higher；But when transformer model number of nodes and more overtone order, solution equation is bigger, to lead It causes occupancy resource more, it is long to calculate the time.Transformer DC magnetic bias based on time domain coupled field-circuit method calculates, and discusses based on step The problem of long and runge kutta method is to the accuracy and stability of calculated result, this method accuracy with higher and stabilization Property, detailed Analysis of Electromagnetic Character under Direct Current Bias can be carried out, but this method has certain defect in computational efficiency. On the basis of pertinent literature road coupling calculation on the scene, a kind of adaptive optimization algorithm is introduced, is improved by variable step Computational efficiency, but this method and the D.C. magnetic biasing calculating for being not used for high-power transformer.
Summary of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a kind of extra-high voltage transformers based on L-I curve Unloaded D.C. magnetic biasing quick calculation method obtains L-I curve by extra-high voltage auto-transformer magnetic field model, using amendment inductance The Fourth order Runge-Kutta of parameter is completed extra-high voltage transformer zero load D.C. magnetic biasing and is quickly calculated.
In order to achieve the above-mentioned object of the invention, the present invention adopts the following technical scheme that:
A kind of extra-high voltage transformer zero load D.C. magnetic biasing quick calculation method based on L-I curve, the method includes with Lower step:
Step 1: according to transformer actual structure parameters, transformer three-dimensional entity model is constructed, using Edge Finite Element Method Establish transformer DC magnetic bias calculating magnetic field model；
Step 2: using the magnetic field model of step 1, different electric currents being flowed through according to energy perturbation principle calculating transformer winding When the mutual inductance value between inductance value and winding, draw L-I curve；
Step 3: according to transformer electrical connection diagram, transformer DC magnetic bias equivalent circuit being built by voltage compensation and is calculated Model；
Step 4: D.C. magnetic biasing equivalent-circuit model is solved using the Fourth order Runge-Kutta of amendment inductance parameters, it is appropriate to add Big D.C. resistance accelerates calculating speed, and inductance parameters therein are obtained by interpolation L-I curve；
Step 5: exciting current of the extra-high voltage auto-transformer in different DC biased is calculated, under various biasings Stable state excitation current waveform carry out FFT transform, obtain the current harmonics situation of change under each biasing.
Further, in the step 1, Edge Finite Element Method is using magnetic vector A as state variable, it is assumed that magnetic conductive media is respectively to same Property, the nonlinear magnetism field equation of inside transformer is obtained according to Maxwell equation group:
Wherein, ν is magnetic reluctance, m/H；A is vector magnetic potential, Wb/m2；J is excitation current density, A/m2。
The freedom degree of Lacrimal gland tumors is ring A of the field vector along seamed edge ll, the shape vector function N of usel, individual unit Interpolating function are as follows:
Wherein: nedgeFor element edges number
The interpolating function of whole field domain are as follows:
Wherein: { Mn, n=1,2 ..., nnIt is basic function sequence, by correlation unit shape function NiCorrespondence is formed by stacking, n For basic function sequence general term number；nnFor total seamed edge number；AnFor unit scalar magnetic potential.
Green's theorem is applied to formula (1), obtains the golden Weighted Residual equation of gal the Liao Dynasty:
Wherein, MmM=1,2 ..., nnIt is sequence of weighting function；
The weight function of Lacrimal gland tumors is substituted into equation (4) respectively, it is for whole weight functions, Weighted Residual equation is discrete Algebraic Equation set is formed, solving the magnetic vector on all seamed edges is A.
Further, in the step 2, the electromotive force equation of transformer winding:
Wherein, E is winding electromotive force；ψ is coil flux linkage vector；LDIt (I) is dynamic inductance matrix, I is transformer winding Current matrix, t are time variable.
According to energy perturbation principle, when coil current increases δ IkWhen (δ=0~1), magnetic linkage changes δ ψk, port voltage need to apply Add increment δ uk=d (δ ψk)/dt, external energy increment dWk=δ ukδIkDt=ψkδIkD δ, and then the gross energy that power supply provides:
Wherein, δ IkFor coil current increment
The external power supply energy variation as caused by curent change is associated with dynamic inductance and exciting current:
Wherein, LDkpFor winding inductance matrix, k, p be around group #,
The magnetic field energy of field system:
Wherein, B is magnetic flux density, and H is magnetic field strength,
The internal magnetic field energy variation as caused by curent change are as follows:
Wherein, Δ B is change in magnetic flux density amount, and Δ H is change of magnetic field strength amount,
By conservation of energy principle, the energy variation in formula (7) and (9) is equal, can obtain dynamic inductance matrix LD (I)。
By applying a series of electric current discrete values to transformer coil, the corresponding inductance matrix of each electric current is recorded, is obtained To self-induction of loop value and mutual inductance value with the change curve of electric current, L-I curve is drawn.
Further, in the step 3, under D.C. magnetic biasing state, to accelerate calculating speed, it is possible to increase D.C. resistance, to make The close practical biasing circuit of counting circuit, transformer DC magnetic bias Equivalent circuit equations:
Wherein, u is alternating voltage source vector；UDCFor interference voltages source；I be previous calculating cycle in electric current from Dissipate value；idcFor the mean value of electric current in previous calculating cycle；LD(I) indicate that inductance matrix changes with curent change；R is meter Calculate D.C. resistance.
Further, in the step 4, above-mentioned transformer dc is solved using the Fourth order Runge-Kutta of amendment inductance parameters Bias Equivalent circuit equations, by k moment electric current ikCalculate k+1 moment electric current ik+1, detailed process is as follows:
1) by k moment electric current ikValue, substitutes into cubic spline functions, and interpolation L-I curve obtains ikCorresponding coil Self-induction L (ik) and mutual inductance M (ik)；By ik、L(ik) and M (ik) numerical value calculate i (t) in tkThe slope d at moment1；
2) from first (ik,tk) point sets out, advance half of step-length h/2, obtains unknown quantity at second point ik+h/2Discreet valueIt willCubic spline functions are substituted into, interpolation L-I curve obtainsCorresponding coil is certainly SenseAnd mutual inductanceByAndNumerical value calculate i (t) in ik+h/2The slope at moment d2；
3) with d2For slope, again from first point, advance half of step-length h/2, calculates second point Locate the discreet value of unknown quantityIt willCubic spline functions are substituted into, interpolation L-I curve obtainsCorresponding line Enclose self-inductionAnd mutual inductanceByAndNumerical value calculate i (t) in ik+h/2Moment it is oblique Rate d3, and with (d2+d3)/2 are as the derivative average value at second point；
4) with d3For slope, advance a step-length h, calculates the discreet value i of unknown quantity at third pointk+h；By ik+h Cubic spline functions are substituted into, interpolation L-I curve obtains ik+1Corresponding self-induction of loop L (ik+h) and mutual inductance M (ik+h)；By ik、L(ik+h) and M (ik+h) numerical value calculate i (t) in tk+1The slope d at moment4
5) last tk+1The electric current i at momentk+1Are as follows:
6) after a cycle having been calculated, the electric current discrete value I in the period is recorded, finds out the electric current mean value i in the perioddc, generation Enter the transformer DC magnetic bias Equivalent circuit equations (10) in step 3, carry out the calculating of next cycle electric current, is calculated until meeting Into stablizing Rule of judgment:
Wherein inT,kFor k-th of moment current value in n-th of period；i(n+1)T,kFor k-th of moment electricity in (n+1)th period Flow valuve；P is the total calculating current number of a cycle；ε is to sentence steady limit value, is the number of a very little.
Further, in the step 5, the exciting current in the case of different DC biased, the stabilization that will be calculated are calculated Current waveform is stored in corresponding document, works out FFT transform program, carries out frequency analysis, increase of the research with direct current biasing, harmonic wave Curent change situation.
Compared with the immediate prior art, technical solution provided by the invention is had the advantages that
1) proposed by the present invention that transformer magnetic field model is established based on Edge Finite Element Method, it is calculated according to energy perturbation principle Winding flows through the mutual inductance value between inductance value and winding when different electric currents, and the L-I curve of drafting is calculated for D.C. magnetic biasing, effectively It solves the problems, such as that dynamic inductance acquisition is difficult, time-consuming and inductance computes repeatedly, and saves amount of calculation, realizes very short Time in complete bias calculate.
2) proposed by the present invention that extra-high buckling is efficiently solved based on the quadravalence Long Gekutafa with amendment inductance parameters Depressor iron core magnetic conductivity realizes that extra-high voltage transformer bias accurately solves with the violent problem of curent change.
3) proposed by the present invention effectively to be solved based on the D.C. magnetic biasing circuit model for increasing direct current calculating resistance band voltage compensation Having determined, actual circuit D.C. resistance is small, time constant is big, the low problem of computational efficiency, realizes extra-high voltage transformer D.C. magnetic biasing Fast and accurate solution.
Detailed description of the invention
Fig. 1 is the 3-D geometric model (a) for the extra-high voltage transformer D.C. magnetic biasing calculating that the present invention establishes and is based on seamed edge The magnetic field model (b) that FInite Element is built.
Fig. 2 is the present invention by magnetic field model, and according to energy perturbation principle, the transformer self-induction of drafting and mutual inductance are with electric current Change curve, wherein (a) is high-voltage winding self-induction with current curve；It (b) is middle pressure winding self-induction with curent change song Line；It (c) is high pressure mutual inductance with current curve；It (d) is equivalent inductance in circuit with current curve.
Fig. 3 is that the D.C. magnetic biasing Equivalent circuit equations in step 3 of the present invention solve process.
Fig. 4 is the solution process of the Fourth order Runge-Kutta with amendment inductance parameters in step 4 of the present invention.
Fig. 5 is excitation current waveform situation in the case of the different bias that the present invention calculates.
Fig. 6 is the situation of change that harmonic component of the present invention occurs with direct current biasing increase.
Specific embodiment
With reference to the accompanying drawing, the present invention is described in more detail.
The present invention provides a kind of extra-high voltage transformer zero load D.C. magnetic biasing quick calculation method based on L-I curve, below In conjunction with attached drawing, specific embodiments of the present invention is described in detail.
Step 1, according to transformer actual structure parameters, transformer three-dimensional entity model is constructed, using Edge Finite Element Method Establish transformer DC magnetic bias calculating magnetic field model.
Edge Finite Element Method is using magnetic vector A as state variable, it is assumed that magnetic conductive media isotropism, according to Maxwell equation Group obtains the nonlinear magnetism field equation of inside transformer:
Wherein, ν is magnetic reluctance, m/H；A is vector magnetic potential, Wb/m2；J is excitation current density, A/m2。
The freedom degree of Lacrimal gland tumors is ring A of the field vector along seamed edge ll, the shape vector function N of usel, individual unit Interpolating function are as follows:
Wherein: nedgeFor element edges number
The interpolating function of whole field domain are as follows:
Wherein: { Mn, n=1,2 ..., nnIt is basic function sequence, by correlation unit shape function NiCorrespondence is formed by stacking, n For basic function sequence general term number；nnFor total seamed edge number；AnFor unit scalar magnetic potential.
Green's theorem is applied to formula (1), obtains the golden Weighted Residual equation of gal the Liao Dynasty:
Wherein, MmM=1,2 ..., nnIt is sequence of weighting function；
The weight function of Lacrimal gland tumors is substituted into equation (4) respectively, it is for whole weight functions, Weighted Residual equation is discrete Algebraic Equation set is formed, solving the magnetic vector on all seamed edges is A.
According to extra-high voltage auto-transformer actual size, obtain include transformer high-voltage winding and middle pressure winding internal diameter and Outer diameter, the radius of iron core, the height of iron core, the length of upper yoke and window width including parameter, according to transformer symmetry, Construct 1/8 3-D geometric model of extra-high voltage transformer.During geometrical model constructs, iron core is configured to entirety, by winding Consider as current-carrying block conductor, establishes cylinder barrel shaped, ignore the seam between iron yoke and main iron prop, the portion except iron core and winding Divide and is considered transformer oil or air；Regular cutting is carried out to model, convenient for obtaining hexahedral element, reduces cell node Number；The material properties parameter for obtaining each section component constructs transformer three-dimensional finite element magnetic field model using Edge Finite Element Method.
Step 2: using the magnetic field model of step 1, different electric currents being flowed through according to energy perturbation principle calculating transformer winding When the mutual inductance value between inductance value and winding, draw L-I curve；
Transformer winding electromotive force equation:
Wherein, E is winding electromotive force；ψ is coil flux linkage vector；LDIt (I) is dynamic inductance matrix, I is transformer winding Current matrix, t are time variable.
According to energy perturbation principle, when coil current increases δ IkWhen (δ=0~1), magnetic linkage changes δ ψk, port voltage need to apply Add increment δ uk=d (δ ψk)/dt, external energy increment dWk=δ ukδIkDt=ψkδIkD δ, and then the gross energy that power supply provides:
Wherein, δ IkFor coil current increment
The external power supply energy variation as caused by curent change is associated with dynamic inductance and exciting current:
LDkpFor winding inductance matrix, k, p be around group #,
The magnetic field energy of field system:
Wherein, B is magnetic flux density, and H is magnetic field strength,
The internal magnetic field energy variation as caused by curent change are as follows:
Wherein, Δ B is change in magnetic flux density amount, and Δ H is change of magnetic field strength amount,
By conservation of energy principle, the energy variation in formula (7) and (9) is equal, can obtain dynamic inductance matrix LD (I)。
According to the number of turns and sectional area of high-voltage winding and middle pressure winding, applied to transformer high-voltage winding and middle pressure winding coil Add a series of electric current discrete values, cylindrical-coordinate system is set to winding, balanced current distribution is on winding cross section, high pressure winding Current direction is identical, and magnetic line of force parallel condition is arranged at 1:2 relationship, in the outer surface of model in size.When electric current discrete value is set, In view of extra-high voltage transformer core material field performance is fine, the exciting current of very little can make iron core reach saturation state, because , when electric current is smaller, the very little of current intervals setting when electric current is larger, can amplify current intervals, to reduce reversal meter for this The inductance error of calculation is become opposite number, carries out corresponding negative value electric current when each positive value electric current discrete value has been calculated It calculates, records each corresponding inductance matrix of electric current discrete value, self-induction of loop and mutual inductance can be obtained with the variation of electric current Curve draws L respectively1- I curve, L2- I curve, M12- I or M21Equivalent inductive current curve L- in-I curve and biasing circuit I curve.
Step 3, equivalent to the progress of practical extra-high voltage transformer D.C. magnetic biasing circuit model, high-voltage winding uses 4 windings simultaneously Connection mode, middle pressure winding use 2 winding parallel modes, and series system, therefore circuit direct resistance are used between high pressure winding For the sum of high-voltage winding resistance and middle pressure winding resistance, circuit equivalent inductance is the mutual inductance that the sum of self-induction adds 2 times, is indicated Are as follows:
RAlways=R1+R2 (9-1)
LD(I)=L1(I)+L2(I)+2M12(I) (9-2)
Wherein, RAlwaysFor equivalent d.c. resistance；R1For high-voltage winding resistance；R2For middle pressure winding resistance；L1It (I) is high voltage winding Group self-induction；L2It (I) is middle pressure winding self-induction；M12It (I) is high pressure winding mutual inductance.
Under D.C. magnetic biasing state, to accelerate calculating speed, D.C. resistance can be increased when calculating, reduce time constant, subtract Transient process is calculated less.In view of in actual circuit, extra-high voltage transformer winding uses Multiple coil parallel way, winding cross-section Product is bigger relative to common transformer, and the number of turns is more, D.C. resistance very little, and the pressure drop generated on resistance can relative to alternating voltage To ignore, to make the close practical biasing circuit of counting circuit, transformer DC magnetic bias Equivalent circuit equations:
Wherein, u is alternating voltage source vector；UDCFor interference voltages source；I is that the electric current in a calculating cycle is discrete Value；idcFor the mean value of electric current in a calculating cycle；LD(I) indicate that equivalent inductance matrix changes with curent change；R is meter Calculate D.C. resistance.
The D.C. magnetic biasing circuit model can guarantee that the voltage at coil inductance both ends during calculating is essentially alternating current Pressure, close to the corresponding biasing circuit model of D.C. resistance of very little.
Step 4, above-mentioned transformer DC magnetic bias equivalent circuit is solved using the Fourth order Runge-Kutta of amendment inductance parameters Equation, by k moment electric current ikCalculate k+1 moment electric current ik+1Detailed process is as follows:
1) by k moment electric current ikValue, substitutes into cubic spline functions, and interpolation L-I curve obtains ikCorresponding coil Self-induction L (ik) and mutual inductance M (ik)；By ik、L(ik) and M (ik) numerical value calculate i (t) in tkThe slope d at moment1
2) from first (ik,tk) point sets out, advance half of step-length h/2, obtains unknown quantity at second point ik+h/2Discreet valueIt willCubic spline functions are substituted into, interpolation L-I curve obtainsCorresponding coil is certainly SenseAnd mutual inductanceByAndNumerical value calculate i (t) in ik+h/2The slope d at moment2
3) with d2For slope, again from first point, advance half of step-length h/2, calculates second point Locate the discreet value of unknown quantityIt willCubic spline functions are substituted into, interpolation L-I curve obtainsCorresponding line Enclose self-inductionAnd mutual inductanceByAndNumerical value calculate i (t) in ik+h/2Moment Slope d3, and with (d2+d3)/2 are as the derivative average value at second point；
4) with d3For slope, advance a step-length h, calculates the discreet value i of unknown quantity at third pointk+h；By ik+h Cubic spline functions are substituted into, interpolation L-I curve obtains ik+1Corresponding self-induction of loop L (ik+h) and mutual inductance M (ik+h)；By ik、L(ik+h) and M (ik+h) numerical value calculate i (t) in tk+1The slope d at moment4
5) last tk+1The electric current i at momentk+1Are as follows:
6) after a cycle having been calculated, the electric current discrete value I in the period is recorded, finds out the electric current mean value i in the perioddc, generation Enter the transformer DC magnetic bias Equivalent circuit equations (10) in step 3, carry out the calculating of next cycle electric current, is calculated until meeting Into stablizing Rule of judgment:
Wherein inT,kFor k-th of moment current value in n-th of period；i(n+1)T,kFor k-th of moment electricity in (n+1)th period Flow valuve；P is a period total calculating current number；ε is to sentence steady limit value, is the number of a very little, is taken as 10 in calculating process-3。
Step 5, the exciting current in the case of different DC biased is calculated, I is enabledDC=2A, IDC=10A, IDC=20A, IDC= 60A,IDC=100A carries out the calculating of extra-high voltage auto-transformer D.C. magnetic biasing respectively, the stabling current waveform being calculated is deposited Enter corresponding document, work out FFT transform program, carries out frequency analysis, increase of the research with direct current biasing, harmonic current variation feelings Condition.The result shows that exciting current and low-order harmonic all increase with it with the increase of direct current biasing.
Table 1 is the exciting current harmonic component amplitude under the different bias calculated
Table 1
As described above, being explained in detail to the present invention, it is clear that as long as essentially without invention of the invention is detached from Point and effect, obvious variations to those skilled in the art, be also all contained in protection scope of the present invention it It is interior.

Claims (4)

1.一种基于L-I曲线的特高压变压器空载直流偏磁快速计算方法，其特征在于，所述方法包括以下步骤：1. a UHV transformer no-load DC bias magnetization fast calculation method based on L-I curve, is characterized in that, described method comprises the following steps: 步骤1：根据变压器实际结构参数，构建变压器三维实体模型，采用棱边有限元法建立变压器直流偏磁计算磁场模型；Step 1: According to the actual structural parameters of the transformer, build a three-dimensional solid model of the transformer, and use the edge finite element method to establish the DC bias magnetic field model of the transformer; 步骤2：利用步骤1的磁场模型，根据能量扰动原理计算变压器绕组流过不同电流时的自感值和绕组间的互感值，绘制L-I曲线；Step 2: Using the magnetic field model of Step 1, according to the principle of energy disturbance, calculate the self-inductance value and the mutual inductance value between the windings when the transformer winding flows through different currents, and draw the L-I curve; 步骤3：根据变压器电气连接图，通过电压补偿搭建变压器直流偏磁等效电路计算模型；Step 3: According to the electrical connection diagram of the transformer, build the DC bias equivalent circuit calculation model of the transformer through voltage compensation; 步骤4：利用修正电感参数的四阶龙格库塔法求解直流偏磁等效电路模型，适当加大直流电阻加快计算速度，其中的电感参数通过插值L-I曲线获得；Step 4: Use the fourth-order Runge-Kutta method to correct the inductance parameters to solve the DC bias equivalent circuit model, appropriately increase the DC resistance to speed up the calculation speed, and the inductance parameters are obtained by interpolating the L-I curve; 步骤5：计算特高压自耦变压器在不同直流偏置情况下的励磁电流，对各种偏置下的稳态励磁电流波形进行FFT变换，得到各偏置下的电流谐波变化情况；Step 5: Calculate the excitation current of the UHV autotransformer under different DC bias conditions, perform FFT transformation on the steady-state excitation current waveform under various biases, and obtain the current harmonic changes under each bias; 所述步骤3中，直流偏磁状态下，为加快计算速度，可增大直流电阻，为使计算电路接近实际偏磁电路，变压器直流偏磁等效电路方程：In the step 3, in the DC bias state, in order to speed up the calculation, the DC resistance can be increased. In order to make the calculation circuit close to the actual bias circuit, the equivalent circuit equation of the DC bias of the transformer is: 其中，u为交流电压源向量；UDC为直流干扰电压源；I为前一个计算周期内的电流离散值；idc为前一个计算周期内电流的均值；LD(I)表示电感矩阵随着电流变化而变化；R为计算直流电阻；Among them, u is the AC voltage source vector; U DC is the DC interference voltage source; I is the current discrete value in the previous calculation cycle; i dc is the average value of the current in the previous calculation cycle; change with the current change; R is the calculated DC resistance; 所述步骤4中，利用修正电感参数的四阶龙格库塔法求解上述变压器直流偏磁等效电路方程，由k时刻电流ik计算k+1时刻电流ik+1，具体过程如下：In the step 4, the fourth-order Runge-Kutta method for correcting the inductance parameters is used to solve the above-mentioned transformer DC bias equivalent circuit equation, and the current i k+1 at time k+1 is calculated from the current i k at time k . The specific process is as follows: 1)将k时刻电流ik值，代入三次样条插值函数，插值L-I曲线，获得ik所对应的线圈自感L(ik)和互感M(ik)；由ik、L(ik)及M(ik)的数值计算i(t)在tk时刻的斜率d1；1) Substitute the value of the current i k at time k into the cubic spline interpolation function, and interpolate the LI curve to obtain the coil self-inductance L( ik ) and mutual inductance M( ik ) corresponding to ik ; k ) and M( ik ) numerically calculate the slope d 1 of i(t) at time t k ; 2)从第一个(ik,tk)积分点出发，前进半个步长h/2，得到第二个积分点处未知量的ik+h/2的预估值将代入三次样条插值函数，插值L-I曲线，获得所对应的线圈自感和互感由及的数值计算i(t)在ik+h/2时刻的斜率d2；2) Starting from the first (i k , t k ) integration point, advance half a step h/2 to obtain the estimated value of i k+h/2 of the unknown quantity at the second integration point Will Substitute the cubic spline interpolation function, interpolate the LI curve, and obtain The corresponding coil self-inductance and mutual inductance Depend on and The numerical calculation of the slope d 2 of i(t) at the moment i k+h/ 2; 3)以d2为斜率，重新从第一个积分点出发，前进半个步长h/2，计算第二个积分点处未知量的预估值将代入三次样条插值函数，插值L-I曲线，获得所对应的线圈自感和互感由及的数值计算i(t)在ik+h/2时刻的斜率d3，并以(d2+d3)/2作为第二个积分点处的导数平均值；3) Take d 2 as the slope, start from the first integration point again, advance half a step size h/2, and calculate the estimated value of the unknown quantity at the second integration point Will Substitute the cubic spline interpolation function, interpolate the LI curve, and obtain The corresponding coil self-inductance and mutual inductance Depend on and Calculate the slope d 3 of i(t) at the moment i k+h/2 with the value of , and take (d 2 +d 3 )/2 as the average value of the derivative at the second integration point; 4)以d3为斜率，前进一个步长h，计算第三个积分点处未知量的预估值ik+h；将ik+h代入三次样条插值函数，插值L-I曲线，获得ik+1所对应的线圈自感L(ik+h)和互感M(ik+h)；由ik、L(ik+h)及M(ik+h)的数值计算i(t)在tk+1时刻的斜率d4；4) take d 3 as the slope, advance a step h, calculate the estimated value i k+h of the unknown quantity at the third integration point; substitute i k+h into the cubic spline interpolation function, interpolate the LI curve, and obtain i Coil self-inductance L(i k + h ) and mutual inductance M(i k+h ) corresponding to k+1 ; calculate i( t) the slope d 4 at time t k+1 ; 5)最后tk+1时刻的电流ik+1为：5) The current i k+ 1 at the last moment t k +1 is: 6)计算完一个周期后，记录该周期的电流离散值I，求出该周期的电流均值idc，代入步骤3中的变压器直流偏磁等效电路方程(10)，进行下一个周期电流计算，直至满足计算进入稳定判断条件：6) After calculating a cycle, record the current discrete value I of the cycle, find the current average value i dc of the cycle, and substitute it into the transformer DC bias equivalent circuit equation (10) in step 3, and calculate the current in the next cycle. , until the calculation enters the stable judgment condition: 其中inT,k为第n个周期的第k个时刻电流值；i(n+1)T,k为第n+1个周期的第k个时刻电流值；p为一个周期总的计算电流数；ε为判稳限值，为一很小的数。where i nT,k is the current value at the kth moment of the nth cycle; i (n+1)T,k is the current value at the kth moment of the n+1th cycle; p is the total calculated current of a cycle number; ε is the judgment stability limit, which is a very small number. 2.根据权利要求1所述方法，其特征在于，所述步骤1中，棱边有限元法以磁矢量A为状态变量，假设导磁介质各向同性，根据Maxwell方程组得到变压器内部的非线性磁场方程：2. The method according to claim 1, characterized in that, in the step 1, the edge finite element method takes the magnetic vector A as a state variable, assuming that the magnetically permeable medium is isotropic, and obtains the non-transformer inside the transformer according to Maxwell equations. Linear magnetic field equation: 其中，ν为磁阻率，m/H；A为矢量磁位，Wb/m2；J为激磁电流密度，A/m2，Among them, ν is the magnetoresistance, m/H; A is the vector magnetic potential, Wb/m 2 ; J is the excitation current density, A/m 2 , 棱边有限元的自由度为场矢量沿棱边l的环Al，采用的矢量形状函数Nl，单个单元的插值函数为：The degree of freedom of the edge finite element is the ring A l of the field vector along the edge l, the vector shape function N l used, and the interpolation function of a single element is: 其中：nedge为单元棱边号Where: n edge is the unit edge number 整体场域的插值函数为：The interpolation function of the overall field is: 其中：{Mn,n＝1,2,…,nn}为基函数序列，由相关单元形状函数Ni对应叠加而成，n为基函数序列通项编号；nn为总棱边数；An为单元标量磁位；Among them: {M n ,n=1,2,…,n n } is the basis function sequence, which is formed by the corresponding superposition of the relevant unit shape functions Ni, n is the general item number of the basis function sequence; n n is the total number of edges ; An is the unit scalar magnetic potential; 对公式(1)应用格林定理，得伽辽金加权余量方程：Applying Green's theorem to formula (1), the Galerkin weighted remainder equation is obtained: 其中，Mm{m＝1,2,…,nn}为权函数序列；Among them, M m {m=1,2,...,n n } is the weight function sequence; 将棱边有限元的权函数分别代入方程(4)，针对全部权函数，将加权余量方程离散形成代数方程组，求解所有棱边上的磁矢量为A。Substitute the weight functions of the edge finite element into equation (4) respectively. For all the weight functions, the weighted residual equations are discretized to form an algebraic equation system, and the magnetic vector on all edges is solved as A. 3.根据权利要求1所述方法，其特征在于，所述步骤2中，变压器绕组的电动势方程：3. method according to claim 1, is characterized in that, in described step 2, the electromotive force equation of transformer winding: 其中，E为绕组电动势；ψ为线圈磁链矢量；LD(I)为动态电感矩阵，I为变压器绕组电流矩阵，t为时间变量；Among them, E is the winding electromotive force; ψ is the coil flux linkage vector; L D (I) is the dynamic inductance matrix, I is the transformer winding current matrix, and t is the time variable; 根据能量扰动原理，当线圈电流增加δIk(δ＝0～1)时，磁链变化δψk，端口电压需施加增量δuk＝d(δψk)/dt，外部能量增量dWk＝δukδIkdt＝ψkδIkdδ，进而电源提供的总能量：According to the principle of energy disturbance, when the coil current increases δI k (δ=0～1), the flux linkage changes δψ k , the port voltage needs to be applied with an increment δu k =d(δψ k )/dt, and the external energy increment dW k = δu k δI k dt=ψ k δI k dδ, and then the total energy provided by the power supply: 其中，δIk为线圈电流增量Among them, δI k is the coil current increment 由电流变化引起的外部电源能量变化与动态电感及励磁电流相关联：Changes in external power supply energy due to current changes are associated with dynamic inductance and excitation current: 其中LDkp为绕组电感矩阵，k,p为绕组编号，where L Dkp is the winding inductance matrix, k, p are the winding numbers, 磁场系统的磁场能量：Magnetic field energy of a magnetic system: 其中，B为磁通密度，H为磁场强度，where B is the magnetic flux density, H is the magnetic field strength, 由电流变化引起的内部磁场能量变化为：The internal magnetic field energy change caused by the current change is: 其中，ΔB为磁通密度变化量，ΔH为磁场强度变化量，Among them, ΔB is the change of magnetic flux density, ΔH is the change of magnetic field strength, 由能量守恒原理，式(7)和(9)中的能量变化相等，便可以得到动态电感矩阵LD(I)；According to the principle of energy conservation, the energy changes in equations (7) and (9) are equal, and the dynamic inductance matrix L D (I) can be obtained; 通过给变压器线圈施加一系列电流离散值，记录每一个电流对应的电感矩阵，得到线圈自感值及互感值随电流的变化曲线，绘制L-I曲线。By applying a series of current discrete values to the transformer coil, recording the inductance matrix corresponding to each current, obtaining the curve of the coil self-inductance and mutual inductance with the current, and drawing the L-I curve. 4.根据权利要求1所述方法，其特征在于，所述步骤5中，计算不同直流偏置情况下的励磁电流，将计算得到的稳定电流波形存入相应文件，编制FFT变换程序，进行谐波分析，研究随着直流偏置的增大，谐波电流变化情况。4. The method according to claim 1, characterized in that, in the step 5, the excitation current under different DC bias conditions is calculated, the calculated stable current waveform is stored in a corresponding file, an FFT transformation program is compiled, and the harmonics are performed. Wave analysis to study the change of harmonic current with the increase of DC bias.
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