CN106991263A - A kind of modeling method of mesolow distribution transformer winding thunder and lightning wideband model - Google Patents

Abstract

A kind of modeling method of mesolow distribution transformer winding thunder and lightning wideband model proposed by the present invention, belongs to mesolow distribution transformer lightning protection research field.This method builds the MTLs model of distribution transformer winding first, obtains the π type equivalent circuits of MTLs model；The lumped parameter model of distribution transformer winding is built, the π type equivalent circuits of lumped parameter model are obtained；Then two models of foundation are compared, obtain the low-frequency approximation that lumped parameter model is MTLs model, obtain final lumped parameter model.The present invention proposes a kind of modeling method of new lumped parameter model, the model set up using this method, solve former lumped parameter model and be applicable frequency range confinement problems, available for the research of distribution transformer winding wideband response in 4MHz frequency ranges, there is practical significance for the Insulation monitoring and lightning protection of distribution transformer winding.

Description

A kind of modeling method of mesolow distribution transformer winding thunder and lightning wideband model

Technical field

The invention belongs to mesolow distribution transformer lightning protection research field, and in particular to a kind of mesolow distribution transformer The modeling method of device winding thunder and lightning wideband model.

Background technology

Vast territory and abundant resources for China, and maldistribution of the resources is even, and distribution line is complicated extensively, and the insulation of distribution line and equipment is prevented Shield Disposing rate is low, and Lightning Over-voltage is to cause one of major reason of distribution transformer insulation fault.Set up distribution transformer Winding model, the wave process and voltage's distribiuting of analysis lightning wave in the windings, to the Insulation monitoring and thunder of distribution transformer winding Electricity is protected and its important.The frequency range that actual lightning wave is included in power frequency between several megahertzs, 100kHz or so energy Distribution is higher, but China currently for distribution transformer winding model research primary limitation at middle low-frequency range (1MHz), covering Scope is narrower, it is impossible to fully comprehensively react actual conditions.

The modeling method of existing distribution transformer winding model is broadly divided into externally measured method and circuit modeling method.It is outside Mensuration is " block box approach ", and Transformer Winding port identity is measured, then equivalent model is obtained through over-fitting, modeled Journey is simple, but can only analyze the characteristic of whole Transformer Winding, it is impossible to which the voltage for analyzing each wire turn of inside transformer winding rings Should.Circuit modeling method is the equivalent-circuit model with the elements such as electric capacity, inductance, resistance and conductance formation transformer coil, is used for Impedance operator and the voltage responsive of Transformer Winding are analyzed, current widely used circuit modeling approach is broadly divided into distributed constant Modeling and lumped parameter modeling.

Transformer Winding distributed parameter model is MTLs model, and the model regards Transformer Winding wire turn as straight Line transmission line, is connected according to the first relation of coil winding, according to wire turn first and last end current-voltage correlation, may finally solve section Point voltage responsive.The frequency domain telegraph equation of MTLs model is as follows：

L, C, R and G are respectively unit length inductance parameters matrix, capacitance parameter matrix, resistance parameter matrix and electricity in formula Parameter matrix is led, s represents complex frequency,The row that the voltage-to-ground phasor on each wire turn, electric current phasor are constituted are represented respectively Vector, x represents to point to the position of end along wire turn head end.MTLs model is used for high frequency (4~10MHz) scope Interior, response of the analysis Coefficients of Large Power Transformer Winding to very fast transient overvoltage, the highest energy of lightning voltage is distributed in a 100kHz left sides The right side, distributed constant is unable to Accurate Analysis distribution transformer winding and responded in the thunder and lightning of low-frequency range.

Transformer Winding lumped parameter modeling, by winding coil, (coil refers to the coil of whole winding, and wire turn refers to a circle line Circle) divide some units, the equivalent circuit into the formation of inductance, resistance, electric capacity and inductance element of each unit, the collection of each unit Total parameter equivalent circuit is as shown in figure 1, whereinWithRespectively wire turn first and last end electric current phasor,WithRespectively wire turn First and last terminal voltage phasor, L and R represent inductance parameters and resistance parameter respectively, and C and G represent capacitance parameter and conductance parameter, electric current Wire turn end is flowed to from wire turn head end, each wire turn is joined end to end according to winding technique relation, and current wave is transferred into whole winding. The accuracy of lumped parameter model is limited by division unit size, middle low frequency (below 1MHz) is mainly used in, by unit etc. Value circuit cascades the Type Equivalent Circuit Model that can obtain Transformer Winding according to coil annexation, is rung for solution node voltage Should.Transformer species is more, and loop construction is complicated, to simplify calculating, and division unit when setting up transformer lumped parameter model is not Together, in division unit, such as set up be entangled with the winding model of winding type transformer when, can using single line cake as unit very To using several line cakes as unit, it is assumed that the electric current for flowing through wire turn in unit is all equal, the inductance parameters in unit equivalent circuit are single The inductance series connection sum of wire turn, with the rise of frequency, the propagation time of electromagnetic wave all wire turns along along unit are included in member It can not ignore, error occurs in the parameter of lumped parameter model, cause final voltage response analysis to produce larger error.For with Piezoelectric transformer thunder and lightning response investigations, the lumped parameter model of Chinese scholar research is confined in the range of 1MHz, it is impossible to meet actual Need, the research suitable for mesolow distribution transformer thunder and lightning wideband model is extremely short of.

The content of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art, proposes a kind of mesolow distribution transformer winding thunder and lightning wideband The modeling method of model.The present invention considers non-linear transformer core, skin effect of line, kindred effect, eddy-current loss etc. Influence, proposes a kind of modeling method of new lumped parameter model；The model set up using this method, solves former collection Headquarters of the General Staff Exponential model is applicable frequency range confinement problems, is ground available for distribution transformer winding wideband response in 4MHz frequency ranges Study carefully.

A kind of modeling method of mesolow distribution transformer winding thunder and lightning wideband model proposed by the present invention, its feature exists In comprising the following steps：

1) MTLs model of distribution transformer winding is built, the π types for obtaining MTLs model are equivalent Circuit；Comprise the following steps that

1-1) set up the telegraph equation of MTLs model；

Regard every circle coil of Transformer Winding as linear transmission line, according to transmission line theory, obtain in units of wire turn MTLs model frequency domain telegraph equation it is as follows：

In formula, L, C, R and G are respectively wire turn inductance parameters matrix, capacitance parameter matrix, resistance parameter matrix and conductance ginseng Matrix number, s represents complex frequency,Voltage-to-ground phasor, the column vector of electric current phasor composition on each wire turn are represented respectively, X represents to point to the position of end along wire turn head end；

1-2) telegraph equation of formula (1) is solved, the current-voltage correlation for obtaining wire turn first and last end is as follows：

In formula,WithThe respectively column vector of wire turn first and last end electric current phasor,WithRespectively wire turn first and last end is electric The column vector of phasor is pressed, P and T are respectively column voltage vector and the phase mould transition matrix of electric current column vector, and Λ is parameter matrix Characteristic value diagonal matrix, meets P^-1ZT=T^-1YP=Λ, obtain the π type equivalent circuits of MTLs model；In many conductors In transmission line model π type equivalent circuits, Y₁=Ttanh (Λ/2) P^-1, Y₂=Tcsch (Λ) P^-1, Y₁Node admittance over the ground is represented, Y₂Represent admittance between node；

2) lumped parameter model of distribution transformer winding is built, the π type equivalent circuits of lumped parameter model are obtained；

Using the every circle coil of identical Transformer Winding as unit, the π type equivalent circuits of lumped parameter model are set up；In collection Headquarters of the General Staff In the π type equivalent circuits of exponential model, Y₁=Y=C+sG, Y₂=Z=R+sL；

3) by step 1) and step 2) two models setting up are compared, by analysis, to obtain lumped parameter model be many The low-frequency approximation of conductor propagation line model；

According to step 1) set up MTLs model and step 2) set up lumped parameter model it is all equivalent into π Type equivalent circuit, the hyperbolic functions tanh (x/2) in formula (2), csch (x), coth (x) is deployed, x is unknown number, k₁、k₂For Parameter before unknown number；|x|<<When 1, hyperbolic functions are expressed as approximate equation, wherein k₁=1, k₂=0,0.5k₁+k₂= 0.5：

In middle low-frequency range, the element in the characteristic value diagonal matrix Λ of parameter matrix | Λ |<<1, obtain following formula：

4) k is updated₁、k₂Value, obtain final lumped parameter model as mesolow distribution transformer winding thunder and lightning wideband Model；

Using coth (x)=1/x+0.5x as standard, k is updated₁、k₂Value to reduce the error of formula (3), k₁、k₂Meet as follows Constraints：

As formula errcsch=| (csch (x)-x^-1-k₂x)²| when error is 0, k₁=1.41, k₂=-0.205；

In final lumped parameter model, Y₁And Y₂Expression formula is as follows：

Final lumped parameter model builds and finished.

The features of the present invention and beneficial effect：

1) frequency characteristic of thunder and lightning is directed to, the problem of former lumped parameter model is applicable frequency range limitation is solved, will The applicable frequency range of lumped parameter model brings up to 4MHz, meets the research of distribution transformer winding thunder and lightning wideband response.

2) dependence of the model parameter to frequency caused by the factors such as the non-linear of transformer core, skin effect of line is considered Property, and consider parameter is lost, improve the modeling degree of accuracy of distribution transformer thunder and lightning wideband model；Carried using generalized eigenvalue method High model calculating speed.

3) thunder and lightning wideband model proposed by the present invention is using easy and effective, it is not necessary to set up lumped parameter model and distribution is joined The mixed model of exponential model carries out wideband emulation, has important directive significance to the lightning protection research of distribution transformer.

Brief description of the drawings

Fig. 1 is conventional single wire turn lumped parameter model equivalent circuit diagram.

Fig. 2 is the FB(flow block) of the inventive method.

Fig. 3 is the lumped parameter model and MTLs model π type equivalent circuit diagrams of the present invention.

Fig. 4 is unit wire turn equivalent circuit diagram in the final lumped parameter model that the inventive method is obtained.

Embodiment

The modeling method of a kind of mesolow distribution transformer winding thunder and lightning wideband model proposed by the present invention, with reference to attached Figure and specific embodiment are further described as follows.

A kind of modeling method of mesolow distribution transformer winding thunder and lightning wideband model proposed by the present invention, the mesolow Scope be 0.4~30kV, this method flow chart is as shown in Fig. 2 comprise the following steps：

1) MTLs model of distribution transformer winding is built, the π types for obtaining MTLs model are equivalent Circuit；Comprise the following steps that

1-1) set up the telegraph equation of MTLs model；Regard every circle coil of Transformer Winding as linear transmission Line, according to transmission line theory, the frequency domain telegraph equation for obtaining MTLs model in units of wire turn is as follows：

In formula, L, C, R and G are respectively wire turn inductance parameters matrix, capacitance parameter matrix, resistance parameter matrix and conductance ginseng Matrix number, s represents complex frequency,Voltage-to-ground phasor, the column vector of electric current phasor composition on each wire turn are represented respectively, X represents to point to the position of end along wire turn head end.

1-2) telegraph equation of formula (1) is solved, the current-voltage correlation for obtaining wire turn first and last end is as follows：

In formula,WithThe respectively column vector of wire turn first and last end electric current phasor,WithRespectively wire turn first and last end is electric The column vector of phasor is pressed, P and T are respectively column voltage vector and the phase mould transition matrix of electric current column vector, and Λ is parameter matrix Characteristic value diagonal matrix, meets P^-1ZT=T^-1YP=Λ.Then MTLs model can be with equivalent into π types as shown in Figure 3 In equivalent circuit, Fig. 3,WithThe respectively column vector of wire turn first and last end electric current phasor,WithRespectively wire turn first and last end The column vector of voltage phasor, Y₁=Ttanh (Λ/2) P^-1, Y₂=Tcsch (Λ) P^-1, Y₁Represent node admittance over the ground, Y₂Represent section Admittance between point, electric current flows to wire turn end from wire turn head end, and each wire turn joins end to end according to winding technique relation, passes through electromagnetism Current wave is quickly transferred to whole winding by induction effect, if the frequency of electric current component is overlapped with wire turn resonant frequency, may Cause resonance overcurrent, overvoltage.

2) lumped parameter model of distribution transformer winding is built, the π type equivalent circuits of lumped parameter model are obtained；

Using the every circle coil of identical Transformer Winding as unit, the π type equivalent circuits of lumped parameter model are set up, it is same as schemed Shown in 3, whereinWithThe respectively column vector of wire turn first and last end electric current phasor,WithRespectively wire turn first and last terminal voltage The column vector of phasor, in the π type equivalent circuits of lumped parameter model, Y₁=Y=C+sG, Y₂=Z=R+sL；Electric current is from wire turn Head end flows to wire turn end, and each wire turn joins end to end according to winding technique relation, acts on quick by current wave by electromagnetic induction It is transferred to whole around rent, if the frequency of electric current component is overlapped with wire turn resonant frequency, resonance overcurrent may be caused, excessively electric Pressure；

3) by step 1) and step 2) set up two models be compared, lumped parameter model is obtained by comparative analysis It is the low-frequency approximation of MTLs model；

Due to step 1) set up MTLs model and step 2) set up lumped parameter model all can be equivalent into π Type equivalent circuit, by hyperbolic functions tanh (x/2) related in formula (2), csch (x), (x deploys coth, and x is unknown number, k₁、k₂ For parameter before unknown number.|x|<<When 1, hyperbolic functions can be expressed as to approximate equation, wherein k₁=1, k₂=0,0.5k₁+ k₂=0.5；

In middle low-frequency range (within 1MHz), the element in the characteristic value diagonal matrix Λ of parameter matrix | Λ |<<1, can Following formula is obtained to analyze：

Now, the Y in two models₁And Y₂Approximately equal, it is believed that two kinds of models have identical accuracy, therefore can To think that lumped parameter model is the low-frequency approximation of MTLs model.

4) k is updated₁、k₂Value, obtain final lumped parameter model as mesolow distribution transformer winding thunder and lightning wideband Model；

Using coth (x)=1/x+0.5x as standard, k is updated₁、k₂Value to reduce the mistake of hyperbolic functions approximate equation (3) Difference, k₁、k₂Meet following constraints：

As formula errcsch=| (csch (x)-x^-1-k₂x)²| when error is 0, k₁=1.41, k₂=-0.205；

In final lumped parameter model, Y₁And Y₂Expression formula is as follows：

Final lumped parameter model builds and finished.

The unit wire turn equivalent circuit of final lumped parameter model as shown in figure 4, in Fig. 4,WithRespectively wire turn First and last end electric current phasor,WithRespectively wire turn first and last terminal voltage phasor, L and R represent inductance parameters and resistance ginseng respectively Number, C and G represent capacitance parameter and conductance parameter, and admittance is changed into inductive branch between 0.705 (G+sC), node and increased newly node over the ground Negative capacitance branch road -0.205 (G+sC) in parallel, each wire turn joins end to end according to winding technique relation, in high band, increases parallel connection newly Capacitive branch flows to wire turn end beneficial to energy from wire turn head end, and current wave is transferred into whole winding.

New lumped parameter model constructed by the present invention is determined by longitudinal inductive branch electric capacity conductance in parallel, with frequency Rate increases, and admittance will not simply reduce, and the receiving of the increased shunt capacitance branch road of institute can increase, and makes circle transmission, phase along energy When in adding capacitance compensation in longitudinal branch road.

According to transformer coil structure, the Transformer Winding Type Equivalent Circuit Model being made up of new π types equivalent circuit is formulated, by The relation of network interior joint and wire turn head end obtains incidence matrix A₁, incidence matrix is obtained by the relation of node Yu wire turn end A₂, so as to obtain the bus admittance matrix of winding modelFurther according to Node current source column vector, you can obtain nodal voltage equation, is computed that input impedance and node voltage response can be obtained.Calculate wide Node voltage response in each sampled point to admittance matrix, it is necessary to invert in the range of frequency, because transformer wire turn is more, matrix dimensionality Height, calculates complicated, therefore proposition is calculated with generalized eigenvalue method, accelerates the solving speed of equation.

In the specific embodiment of the present invention, S13-30/10 model distribution transformer impedance characteristics are measured, in matlab The emulation of middle programming realization model of the present invention, compares the simulation result and measurement result of input impedance, verifies model of the present invention Applicable frequency range reaches 4MHz, and with high accuracy.

Claims (1)

1. a kind of modeling method of mesolow distribution transformer winding thunder and lightning wideband model, it is characterised in that comprise the following steps：

1) MTLs model of distribution transformer winding is built, the π type equivalent circuits of MTLs model are obtained； Comprise the following steps that

1-1) set up the telegraph equation of MTLs model；

Regard every circle coil of Transformer Winding as linear transmission line, according to transmission line theory, obtain many in units of wire turn The frequency domain telegraph equation of conductor propagation line model is as follows：

$\left\{\begin{array}{c}\frac{d\stackrel{\&CenterDot;}{U}}{dx}=-(R+sL)\stackrel{\&CenterDot;}{I}\\ \frac{d\stackrel{\&CenterDot;}{I}}{dx}=-(G+sC)\stackrel{\&CenterDot;}{U}\end{array}\right.---\left(1\right)$

In formula, L, C, R and G are respectively wire turn inductance parameters matrix, capacitance parameter matrix, resistance parameter matrix and conductance parameter square Battle array, s represents complex frequency,Voltage-to-ground phasor, the column vector of electric current phasor composition on each wire turn are represented respectively, and x is represented The position of end is pointed to along wire turn head end；

1-2) telegraph equation of formula (1) is solved, the current-voltage correlation for obtaining wire turn first and last end is as follows：

$\left\{\begin{array}{c}{\stackrel{\&CenterDot;}{I}}_S=T\coth \left(\mathrm{\&Lambda;}\right)P^{-1}{\stackrel{\&CenterDot;}{U}}_S-T\csc h\left(\mathrm{\&Lambda;}\right)P^{-1}{\stackrel{\&CenterDot;}{U}}_R\\ {\stackrel{\&CenterDot;}{I}}_R=-T\csc h\left(\mathrm{\&Lambda;}\right)P^{-1}{\stackrel{\&CenterDot;}{U}}_S+T\coth \left(\mathrm{\&Lambda;}\right)P^{-1}{\stackrel{\&CenterDot;}{U}}_R\end{array}\right.---\left(2\right)$

In formula,WithThe respectively column vector of wire turn first and last end electric current phasor,WithRespectively wire turn first and last terminal voltage phase The column vector of amount, P and T are respectively column voltage vector and the phase mould transition matrix of electric current column vector, and Λ is the feature of parameter matrix It is worth diagonal matrix, meets P^-1ZT=T^-1YP=Λ, obtain the π type equivalent circuits of MTLs model；In many conductor propagations In line model π type equivalent circuits, Y₁=Ttanh (Λ/2) P^-1, Y₂=Tcsch (Λ) P^-1, Y₁Represent node admittance over the ground, Y₂Table Show admittance between node；

2) lumped parameter model of distribution transformer winding is built, the π type equivalent circuits of lumped parameter model are obtained；

Using the every circle coil of identical Transformer Winding as unit, the π type equivalent circuits of lumped parameter model are set up；In lumped parameter mould In the π type equivalent circuits of type, Y₁=Y=C+sG, Y₂=Z=R+sL；

3) by step 1) and step 2) two models setting up are compared, by analysis, to obtain lumped parameter model be many conductors The low-frequency approximation of transmission line model；

According to step 1) set up MTLs model and step 2) set up lumped parameter model it is all equivalent into π types etc. It is worth circuit, the hyperbolic functions tanh (x/2) in formula (2), csch (x), coth (x) is deployed, x is unknown number, k₁、k₂To be unknown Parameter before number；|x|<<When 1, hyperbolic functions are expressed as approximate equation, wherein k₁=1, k₂=0,0.5k₁+k₂= 0.5：

$\left\{\begin{array}{c}\tanh \left(\frac{x}{2}\right)\&ap;\frac{k_1}{2}x\\ \csc h\left(x\right)\&ap;x^{-1}+k_{2}x\\ \coth \left(x\right)=\tanh \left(\frac{x}{2}\right)+\csc h\left(x\right)\&ap;x^{-1}+(\frac{k_1}{2}+k_2)x\end{array}\right.---\left(3\right)$

In middle low-frequency range, the element in the characteristic value diagonal matrix Λ of parameter matrix | Λ |<<1, obtain following formula：

$\left\{\begin{array}{c}{Y}_1=T\tanh \left(\frac{\mathrm{\&Lambda;}}{2}\right)P^{-1}\&ap;\frac{1}{2}\left({\mathrm{T\&Lambda;P}}^{-1}\right)=\frac{1}{2}Y\\ Y_2=T\csc h\left(\mathrm{\&Lambda;}\right)P^{-1}\&ap;{\left(P\mathrm{\&Lambda;}T\right)}^{-1}=Z^{-1}\end{array}\right.---\left(4\right)$

4) k is updated₁、k₂Value, obtain final lumped parameter model as mesolow distribution transformer winding thunder and lightning wideband mould Type；

Using coth (x)=1/x+0.5x as standard, k is updated₁、k₂Value to reduce the error of formula (3), k₁、k₂Meet following constraint Condition：

$\left\{\begin{array}{c}\frac{k_1}{2}+k_2=\frac{1}{2}\\ k_1>1\\ k_2<-\frac{1}{6}\end{array}\right.---\left(5\right)$

As formula errcsch=| (csch (x)-x^-1-k₂x)²| when error is 0, k₁=1.41, k₂=-0.205；

In final lumped parameter model, Y₁And Y₂Expression formula is as follows：

$\left\{\begin{array}{c}{Y}_1=\frac{k_1}{2}Y=0.705\left(G+sC\right)\\ Y_2=Z^{-1}+k_{2}Y={\left(R+sL\right)}^{-1}-0.205\left(G+sC\right)\end{array}\right.---\left(6\right)$

Final lumped parameter model builds and finished.