CN103823137A - Method for analyzing response characteristics of electric reactor winding under action of lightning waves - Google Patents

Abstract

The invention discloses a method for analyzing response characteristics of an electric reactor winding under the action of lightning waves. The distributed capacitance of an electric reactor is obtained in a computing mode through the structure of a cylindrical winding and an iron core winding. The distributed capacitance of the electric reactor comprises turn-to-turn capacitance, cake layer capacitance, the capacitance of the winding on an iron core and the capacitance of the winding on an electric reactor shell. The turn-to-turn capacitance and the cake layer capacitance are longitudinal capacitance. The capacitance of the winding on the iron core and the capacitance of the winding on the shell are ground capacitance. The distributed capacitance of the electric reactor can be obtained in the computing mode through the structure parameter of the electric reactor. Under the action of lightning high-frequency voltages, the skin effect of a conductor needs to be considered when resistance parameters in the conductor are computed. Then, a circuit model is built in Matlab software according to the distribution parameter of the winding, the voltage distributing conditions of all points of the winding are analyzed under the action of the lightning waves, the method is quite suitable for engineering design, and has important guide significance for electric reactor insulation design according to the voltage distributing conditions of the winding.

Description

The analytical approach of a kind of reactor winding response characteristic under lightning wave effect

Technical field

The invention belongs to power equipment analysis technical field, be specifically related to the analytical approach of a kind of reactor winding response characteristic under lightning wave effect.

Background technology

The high speed development of national economy and living standards of the people improve constantly the rapid growth that has brought electric load.In recent years, because electric load increases rapidly, and capacity of installed generator and power transmission and distribution scarce capacity cause nearly 20 the provinces and cities' power supply shortages in the whole nation, and drug in some provinces occurs rationing the power supply and operates a switch.Meanwhile, along with the opening of electricity market, power consumer is also improving the requirement of the quality of power supply; Electrical production and supply enterprise also all pay attention to the economy of Operation of Electric Systems than ever.

In electric system, reactor has a wide range of applications, and reactor can be done to following division by purposes: 1. current limiting reactor, is series in power circuit, with the numerical value of limiting short-circuit current; 2. shunt reactor, is generally connected between the end and ground of ultra high-tension transmission line, plays inactive power compensation; 3. communication reactor, claims again trap, is connected on and doubles as in the transmission line of electricity that communication line uses, and in order to stop carrier signal, makes it to enter receiving equipment; 4. arc, be connected between the neutral point and ground of three-phase transformer, in order to supply with inductive current when the phase ground connection of three phase network, cross the capacitive current of earth point with flow compensated, make electric arc be difficult for ignition, thereby eliminate due to the electric arc superpotential causing of repeatedly restriking; 5. filter reactor, reduces the amplitude of ripple on bamboo stream electric current for rectification circuit, also can form, to certain frequency, the circuit resonating can occur with capacitor, to eliminate voltage or the electric current of power circuit subharmonic; 6. electric furnace reactor, connects with furnace transformer, limits its short-circuit current; 7. starting reactor, with motor in series, limits its starting current.

Reactor winding technique is around iron core.Iron core forms by siliconized plate is stacking, forms the magnetic circuit part of reactor, between winding, insulate by insulators such as insulating oil or resins.Winding is around core of reactor coiling, and winding construction is divided into drum type brake winding and two kinds of structures of pie winding.Drum type brake winding generally turns to circle line and lenticular wire, wire around iron core vertically from top to bottom around under, axially form ground floor coil, same layer wire do bending process, endways, from bottom to up around, form second layer coil, can form successively lattice coil.Pie winding is made up of the line cake of some continuous coilings that distribute vertically, each line cake by some circle wires radially side by side lap wound get up.

In recent years, Lightning Disaster has become the main source that current power failure produces, the circuit that is for example struck by lightning, thunderbolt shaft tower, lightning surge intrusion transformer station etc.The cost of shunt reactor is high, and maintenance is inconvenient, and maintenance cycle is long, and the Lightning Disaster of reactor brings great inconvenience and economic loss to the operation of electrical network.According to statistics, Reactor Fault is the winding failure of reactor greatly, and reactor winding breaks down and is mostly that the insulation system due to itself is reasonable not, so that under extreme ruuning situation, as while being struck by lightning, winding insulation damages and causes.Most reactor is all protected by devices such as lightning arresters, but under lightning impulse, lightning arrester itself easily damages, or malfunction, can not play effective lightning protection to transformer.To the lightning protection of the transformer lightning arrester that can not place one's entire reliance upon, should try to explore the method for the lightning protection optimal design of transformer own.Therefore, understand and study under lightning current impact, the wave process of Transformer Winding inside, in transformer lightning protection research, transformer body design and Lightning Warning system have great significance.

The research of reactor is mainly divided into two kinds of the research based on electric field and the researchs based on circuit, the Wang Zanji of Tsing-Hua University how in its thesis, to have discussed in detail that the mode based on field is set up transformer (reactor) thereby the electromagnetic model of winding is analyzed its thunder and lightning response characteristic, but, the analytical approach of field is too complicated, various informative, for the shunt reactor of different structure, single model applicability and limited, does not possess versatility.

Circuit model highly versatile, applicability is wide, so need to build reactor thunder and lightning response model according to the thinking of circuit.The superpotential that the people such as Zhang Xile are Transformer Winding under VFTO effect at title is calculated (High-Voltage Technology, 2005.31 (8): 4-7 page) in document, proposed the winding of reactor and transformer to enter circuit modeling, adopt complete many conductors model, it has ignored the electromagnetic coupled relation between several line cakes of middle part, this model has been simplified calculated amount greatly, but has brought larger error.

Summary of the invention

For the existing above-mentioned technical matters of prior art, the invention provides the analytical approach of a kind of reactor winding response characteristic under lightning wave effect, there is stronger versatility, utilize less structural parameters just can calculate required data, and computing method are simple and effective.

An analytical approach for reactor winding response characteristic under lightning wave effect, comprises the steps:

(1), according to the structural parameters of reactor winding, calculate equivalent capacitance, substitutional resistance and the equivalent inductance of the adjacent cake interlayer of reactor winding;

(2), according to the characteristic of lightning wave, determine that the voltage of lightning wave is expressed;

(3) set up reactor winding about the equivalent electrical circuit under lightning wave effect, it comprises a voltage source, two direct earth capacitance C ₁～C ₂with n-1 RLC(RLC resistance-inductance-capacitance) unit, n is the cake layer number of reactor winding; Wherein n-1 RLC unit connect successively after one end and direct earth capacitance C ₁one end and the high-pressure side of voltage source be connected, the other end and direct earth capacitance C ₂one end be connected, direct earth capacitance C ₁the other end and direct earth capacitance C ₂the other end and the low pressure end of voltage source is connected and ground connection; The two ends that described RLC unit is connected into loop and capacitor C by resistance R, inductance L and capacitor C correspond to two series connection ports of RLC unit;

Wherein, in i RLC unit, the parameter value of resistance R, inductance L and capacitor C corresponds to equivalent capacitance, substitutional resistance and the equivalent inductance of reactor winding i cake layer and i+1 cake interlayer; Described voltage source voltage is corresponding lightning wave voltage, and i is natural number and 1≤i≤n-1;

(4) above-mentioned equivalent electrical circuit is carried out to emulation, to analyze the response characteristic of reactor winding under lightning wave effect.

In described step (1), calculate the equivalent capacitance C of the adjacent cake interlayer of reactor winding according to following formula _h:

$C_H=C_B+\frac{m-1}{{2m}^2}{C}_A$

Wherein: C _afor the turn-to-turn capacitance in the last cake layer of adjacent cake layer, C _bfor the cake layer capacitance of adjacent cake layer, m is the wire number of turn of each cake layer of reactor winding.

Described turn-to-turn capacitance C _acalculation expression as follows:

$C_A=\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_0\mathrm{<figure-callout\; id="1"\; label="pl\; d"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">pl</figure-callout>}}{d_{}}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, the girth that p is conductor cross-section, the width that l is conductor cross-section, d ₁for the distance between adjacent two circle wires.

Described cake layer capacitance C _bcalculation expression as follows:

$C_B=\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_0\mathrm{ph}}{{3\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, the girth that p is wire, h is the wire turn length (the corresponding thickness of line cake, coil respective heights) of cake layer, d ₂for the distance between adjacent cake layer.

In described step (1), calculate the equivalent inductance L of the adjacent cake interlayer of reactor winding according to following formula _h:

$L_H=\frac{L_0}{n}$

Wherein: L ₀for the specified reactance value of reactor.

In described step (1), calculate the substitutional resistance R of the adjacent cake interlayer of reactor winding according to following formula _h:

$R_H=\frac{k}{2(l+d)}\sqrt{\frac{\mathrm{\&pi;fu}}{\mathrm{\&delta;}}}$

Wherein: l and d are respectively width and the height of conductor cross-section, and f is thunder and lightning wave frequency, and u and δ are respectively magnetic permeability and the conductivity of wire, and k is the half of adjacent two cake layer conductor total lengths.

In described step (2), determine the voltage expression of lightning wave according to following relational expression:

$U=U_0(e^{-{\mathrm{\&tau;}}_{1}t}-e^{-{\mathrm{\&tau;}}_{2}t})$

Wherein: U is lightning wave voltage, U ₀for lightning wave voltage magnitude, τ ₁=1.386 × 10 ⁴, τ ₂=2.5 × 10 ⁶, t is the time.

Described direct earth capacitance C ₁for the electric capacity of reactor winding to core of reactor, its capacitance is determined according to following relational expression:

${\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1=\frac{{2\mathrm{\&pi;\&epsiv;}}_0{\mathrm{\&epsiv;}}_{r}H}{\ln \frac{r_1}{r_i}}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, H is the whole height of reactor winding, r ₁for the inside radius of reactor winding, r _ifor the radius of core of reactor.

Described direct earth capacitance C ₂for the electric capacity of reactor winding to reactor shell, its capacitance is determined according to following relational expression:

${\mathrm{<figure-callout\; id="2"\; label="C"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_2=\frac{{2\mathrm{\&pi;\&epsiv;}}_0{\mathrm{\&epsiv;}}_{r}H}{\ln \frac{{\mathrm{<figure-callout\; id="2"\; label="r\; t\; r"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">r</figure-callout>}}_t}{r_{}}}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, H is the whole height of reactor winding, r ₂for the external radius of reactor winding, r _tfor the inside radius of reactor shell.

The present invention, according to the structure of drum type brake winding and iron core type winding, calculates the distributed capacitance of reactor.Reactor distributed capacitance comprises turn-to-turn capacitance, electric capacity and winding electric capacity and the winding electric capacity of reactor shell over the ground to iron core between cake (layer).Between turn-to-turn capacitance and cake (layer), electric capacity belongs to longitudinal electric capacity.Winding belongs to ground capacitance to the electric capacity between iron core and shell.Structural parameters by reactor can calculate its distributed capacitance.Distributed inductance comprises two parts, and a part is the main inductance of reactor winding, and a part is the leakage inductance producing due to leakage field in addition, and both sums are distributed inductance parameter.Under the effect of thunder and lightning HF voltage, in conductor, the calculating of resistance parameter need to be considered the skin effect of conductor.And then according to the above-mentioned distribution parameter of winding, in Matlab software, built circuit model, analyze under lightning wave effect the voltage distribution situation of winding each point.

Useful technique effect of the present invention is as follows:

(1) in the thunder and lightning response model of reactor winding of the present invention, consider the profile of reactor, analyzed two kinds of conventional pie windings of reactor and two kinds of structures of laminar winding, there is stronger versatility, be applicable to various dissimilar reactors.

(2) the present invention utilizes analytical algorithm to calculate the distribution parameter of reactor winding, has listed concrete computing method and corresponding computing formula, utilizes less structural parameters just can calculate required data.Computing method are simple and effective, are highly suitable for engineering design.

(3) the present invention has built thunder wave generator in Matlab software, set up the circuit model of reactor winding, can comprehensively analyze the voltage distribution situation of each point in reactor winding, for its voltage distribution situation, can be to the very good directive significance of reactor insulating Design.

Accompanying drawing explanation

Fig. 1 is the structural representation of reactor.

Fig. 2 (a) is the structural representation of drum type brake winding.

Fig. 2 (b) is the potential difference (PD) schematic diagram of drum type brake winding adjacent two layers correspondence position.

The structural representation that Fig. 3 (a) is pie winding.

Fig. 3 (b) is the potential difference (PD) schematic diagram of pie winding adjacent two layers correspondence position.

The waveform schematic diagram that Fig. 4 (a) is lightning wave.

The voltage oscillogram that when Fig. 4 (b) acts on reactor for lightning wave, reactor bears.

Fig. 5 is the equivalent-circuit model figure of the reactor winding set up in Matlab.

Fig. 6 (a) is the voltage oscillogram of winding cake interlayer under lightning wave effect.

Fig. 6 (b) is the voltage oscillogram of winding cake interlayer between lightning wave action period.

Fig. 6 (c) is the lightning wave effect voltage oscillogram of winding cake interlayer later.

Embodiment

In order more specifically to describe the present invention, below in conjunction with the drawings and the specific embodiments, technical scheme of the present invention is elaborated.

As shown in Figure 1, reactor schematic diagram.Iron core and upper and lower yoke 1 adopt cold-reduced silicon sheet closed assembly, have less specific loss, less excitation capacity and higher magnetic flux density.Winding 2 is distributed in around each iron core, in the time passing through electric current in winding, can in iron core, induction produce corresponding magnetic field.In electric system, in electric system, reactor has a wide range of applications.

As shown in Fig. 2 (a), drum type brake winding construction schematic diagram.Drum type brake winding generally turns to circle line and lenticular wire, and wire turn is normally made up of the wire by axial array, and circle wire is around iron core, from top to bottom around under, axially form ground floor coil, Single-layer Windings comprises m circle.Same circle wire does bending and processes, endways, from bottom to up around, form second layer coil.Can form successively lattice coil.

As shown in Fig. 2 (b), the potential difference (PD) schematic diagram of cartridge type winding adjacent two layers correspondence position.Under lightning wave effect, the distributed capacitance C of electric capacity two interlayers _xneed to consider the turn-to-turn capacitance C between winding same layer _aand layer capacitance C between different layers _b.Two-layer winding endways junction potential difference (PD) is 0, and on top, potential difference (PD) is U to the maximum _d.Get wherein a bit of winding d _xthe point potential difference at place is U _x.The electric field energy of this place's storage is as shown in Equation 1:

${\mathrm{dW}}_x=\frac{1}{2}{C}_x{U_x}^2=\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_0{\mathrm{pd}}_x{U_x}^2}{{2\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}=\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_{0}p}{{2d}_2}{\left[U_d\frac{x}{h}\right]}^2{d}_x---\left(1\right)$

In formula 1, C _xfor the d calculating according to plate condenser formula _xplace's electric capacity, ε ₀represent the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of insulating medium.P represents the girth of wire, and d is the distance between two-layer winding.Formula 1 is done to integration from 0 to h, can obtain the electrostatic energy of interlayer storage as shown in Equation 2:

$W_c=\frac{1}{2}{C}_2{\mathrm{<figure-callout\; id="2"\; label="U\; d"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">U</figure-callout>}}_d^{}=\underset{0}{\overset{h}{\&Integral;}}\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_{0}p}{2d}{\left[U_d\frac{x}{h}\right]}^2{d}_x---\left(2\right)$

Can obtain layer capacitance the electric capacity that meanwhile, can calculate between adjacent two circle coils according to capacity plate antenna computing formula is

total electrostatic energy of storing in Single-layer Windings is

the energy that can obtain thus winding storage is always energy between two-layer winding and the energy sum of Single-layer Windings storage inside, and the equivalent capacity of establishing between 1 layer and 2 layers is C _h, obtain formula 3:

$\frac{1}{2}{C}_{\mathrm{<figure-callout\; id="2"\; label="H\; U\; d"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">H</figure-callout>}}{U_d}^{}{{}_{}}^2=W_c+2W---\left(3\right)$

Calculate the equivalent capacitance between two-layer winding

As shown in Fig. 3 (a), cake-type winding structure schematic diagram.Pie winding is made up of the line cake of the some continuous coilings that distribute vertically around iron core, each line cake by some circle wires radially side by side lap wound get up.

As shown in Fig. 3 (b), the potential difference (PD) schematic diagram of pie winding adjacent two layers correspondence position.With the similar mode of laminar winding, can calculate turn-to-turn capacitance C _aand capacitor C between cake _b.The umber of turn comprising in each line cake is m, and the turn-to-turn capacitance number between each line cake is m-1.Equivalent capacitance between two cakes can be expressed as shown in formula 4:

$C_H=C_B+\frac{m-1}{{2m}^2}{C}_A---\left(4\right)$

In lightning wave, comprise a large amount of radio-frequency components, under lightning wave effect, there is skin effect in conductor, and under this effect effect, the substitutional resistance of winding cake interlayer calculates by formula 5:

$R_H=\frac{k}{2(1+d)}\sqrt{\frac{\mathrm{\&pi;fu}}{\mathrm{\&delta;}}}---\left(5\right)$

Wherein: l and d are respectively width and the height of conductor cross-section, and f is thunder and lightning wave frequency, and u and δ are respectively magnetic permeability and the conductivity of wire, and k is the conductor length of the last cake layer of adjacent cake layer.

The equivalent inductance L of winding cake interlayer _hcalculate by formula 6:

$L_H=\frac{L_0}{n}---\left(6\right)$

Wherein: L ₀for the specified reactance value of reactor, n is the cake layer number of reactor winding.

The lightning wave generation module of setting up in Matlab software.Under lightning wave effect, reactor winding terminal voltage is equivalent to the lightning wave of a pulse shape of line voltage stack, and according to national standard, lightning wave can be expressed as:

$U=U_0(e^{-{\mathrm{\&tau;}}_{1}t}-e^{-{\mathrm{\&tau;}}_{2}t})---\left(7\right)$

Wherein: U is lightning wave voltage, U ₀for lightning wave voltage magnitude, τ ₁=1.386 × 10 ⁴, τ ₂=2.5 × 10 ⁶, t is the time.

In formula 7, τ ₁and τ ₂represent respectively wave-head time constant and wave rear time constant, the apparent wave head time T of the lightning wave obtaining ₁be 1.2 μ s, apparent wave rear time T ₂be 50 μ s.After obtaining, lightning wave waveform through time delay module time delay, can control lightning wave and act on the time of electrical network by adjusting the parameter of time delay module.After time delay, process is amplified, the amplitude that amplification coefficient is lightning wave.Sinusoidal module represents line voltage, and lightning wave waveform is added with line voltage through time delay with after amplifying processing, obtains reactor at the waveform suffering under lightning impulse.

Lightning wave oscillogram as shown in Fig. 4 (a), in emulation, sets thunder and lightning and in the time that line voltage reaches maximal value, acts on line voltage, obtains reactor voltage as shown in Fig. 4 (b).From Fig. 4 (b), very of short duration for the line voltage cycle action time at lightning wave.

Shown in Fig. 5, the reactor winding circuit illustraton of model of setting up in Matlab.Wherein C ₁and C ₂expression winding is the electric capacity to shell to iron core and winding, and cake (layer) number of reactor is 6, comprises inductance capacitance and resistance between each layer.C _ij, R _ijrepresent respectively the distribution parameter between reactor layer (cake).L _ijinductance between presentation layer (cake), is made up of self-induction and the mutual inductance of layer (cake), considers that the mutual inductance between different layer (cake) is very little for self-induction, therefore ignore mutual inductance effect in the time of modeling.In the time of modeling, L _ijequal the self-induction of this layer (cake).Lightning wave is by controllable voltage source equivalence, and its waveform is as shown in Fig. 4 (a); Resistance R _ij, inductance L _ijand capacitor C _ijparameter value correspond to equivalent capacitance, substitutional resistance and the equivalent inductance of reactor winding i cake layer and i+1 cake interlayer; Capacitor C ₁and C ₂capacitance according to following relational expression determine:

$\begin{array}{cc}{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">C</figure-callout>}}_1=\frac{2{\mathrm{\&pi;\&epsiv;}}_0{\mathrm{\&epsiv;}}_{r}H}{\ln \frac{r_1}{{\mathrm{<figure-callout\; id="2"\; label="r\; i\; C"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">r</figure-callout>}}_i}}& C_{}{}_2=\frac{2{\mathrm{\&pi;\&epsiv;}}_0{\mathrm{\&epsiv;}}_{r}H}{\ln \frac{r_t}{{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000469538690000011.png,HDA0000469538690000012.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}}\end{array}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, H is the whole height of reactor winding, r ₁for the inside radius of reactor winding, r _ifor the radius of core of reactor, r ₂for the external radius of reactor winding, r _tfor the inside radius of reactor shell.

Shown in Fig. 6 (a), voltage oscillogram between winding layers under lightning wave effect (cake).In the time that lightning wave acts on reactor winding, between layer (cake), on winding, there is larger peak voltage, there is concussion in winding both end voltage thereafter, because lightning wave frequency is higher, so the follow-up concussion electric voltage frequency of winding is far longer than line voltage frequency.

Shown in Fig. 6 (b), it is voltage oscillogram between winding layers (cake) between lightning wave action period.Between lightning wave action period, between winding layers (cake), there is peak voltage.Compare with Fig. 4 (a), its peak voltage is similarly pulse waveform, but the wave rear time is elongated.

Shown in Fig. 6 (c), it is lightning wave effect later voltage oscillogram between winding layers (cake).After lightning wave effect, owing to there is LC loop in reactor, add lightning wave and comprise various radio-frequency components, in reactor, produced high-frequency resonant.Energy is constantly concussion between electric capacity and inductance, and concussion waveform is sinusoidal wave, and As time goes on, sinusoidal wave amplitude constantly reduces and finally decays to zero.

Claims (9)

1. an analytical approach for reactor winding response characteristic under lightning wave effect, comprises the steps:

(1), according to the structural parameters of reactor winding, calculate equivalent capacitance, substitutional resistance and the equivalent inductance of the adjacent cake interlayer of reactor winding;

(2), according to the characteristic of lightning wave, determine that the voltage of lightning wave is expressed;

(3) set up reactor winding about the equivalent electrical circuit under lightning wave effect, it comprises a voltage source, two direct earth capacitance C ₁～C ₂with n-1 RLC unit, n is the cake layer number of reactor winding; Wherein n-1 RLC unit connect successively after one end and direct earth capacitance C ₁one end and the high-pressure side of voltage source be connected, the other end and direct earth capacitance C ₂one end be connected; Direct earth capacitance C ₁the other end and direct earth capacitance C ₂the other end and the low pressure end of voltage source is connected and ground connection; The two ends that described RLC unit is connected into loop and capacitor C by resistance R, inductance L and capacitor C correspond to two series connection ports of RLC unit;

In i RLC unit, the parameter value of resistance R, inductance L and capacitor C corresponds to equivalent capacitance, substitutional resistance and the equivalent inductance of reactor winding i cake layer and i+1 cake interlayer; Described voltage source voltage is corresponding lightning wave voltage, and i is natural number and 1≤i≤n-1;

(4) above-mentioned equivalent electrical circuit is carried out to emulation, to analyze the response characteristic of reactor winding under lightning wave effect.

2. analytical approach according to claim 1, is characterized in that: the equivalent capacitance C that calculates the adjacent cake interlayer of reactor winding in described step (1) according to following formula _h:

$C_H=C_B+\frac{m-1}{{2m}^2}{C}_A$

Wherein: C _afor the turn-to-turn capacitance in the last cake layer of adjacent cake layer, C _bfor the cake layer capacitance of adjacent cake layer, m is the wire number of turn of each cake layer of reactor winding.

3. analytical approach according to claim 2, is characterized in that: described turn-to-turn capacitance C _acalculation expression as follows:

$C_A=\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_0\mathrm{pl}}{d_1}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, the girth that p is conductor cross-section, the width that l is conductor cross-section, d ₁for the distance between adjacent two circle wires.

4. analytical approach according to claim 2, is characterized in that: described cake layer capacitance C _bcalculation expression as follows:

$C_B=\frac{{\mathrm{\&epsiv;}}_r{\mathrm{\&epsiv;}}_0\mathrm{ph}}{{3d}_2}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, the girth that p is wire, h is the wire turn length of cake layer, d ₂for the distance between adjacent cake layer.

5. analytical approach according to claim 1, is characterized in that: the equivalent inductance L that calculates the adjacent cake interlayer of reactor winding in described step (1) according to following formula _h:

$L_H=\frac{L_0}{n}$

Wherein: L ₀for the specified reactance value of reactor.

6. analytical approach according to claim 1, is characterized in that: the substitutional resistance R that calculates the adjacent cake interlayer of reactor winding in described step (1) according to following formula _h:

$R_H=\frac{k}{2(l+d)}\sqrt{\frac{\mathrm{\&pi;fu}}{\mathrm{\&delta;}}}$

Wherein: l and d are respectively width and the height of conductor cross-section, and f is thunder and lightning wave frequency, and u and δ are respectively magnetic permeability and the conductivity of wire, and k is the half of adjacent two cake layer conductor total lengths.

7. analytical approach according to claim 1, is characterized in that: in described step (2), determine the voltage expression of lightning wave according to following relational expression:

$U=U_0(e^{-{\mathrm{\&tau;}}_{1}t}-e^{-{\mathrm{\&tau;}}_{2}t})$

Wherein: U is lightning wave voltage, U ₀for lightning wave voltage magnitude, τ ₁=1.386 × 10 ⁴, τ ₂=2.5 × 10 ⁶, t is the time.

8. analytical approach according to claim 1, is characterized in that: described direct earth capacitance C ₁for the electric capacity of reactor winding to core of reactor, its capacitance is determined according to following relational expression:

$C_1=\frac{{2\mathrm{\&pi;\&epsiv;}}_0{\mathrm{\&epsiv;}}_{r}H}{\ln \frac{r_1}{r_i}}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, H is the whole height of reactor winding, r ₁for the inside radius of reactor winding, r _ifor the radius of core of reactor.

9. analytical approach according to claim 1, is characterized in that: described direct earth capacitance C ₂for the electric capacity of reactor winding to reactor shell, its capacitance is determined according to following relational expression:

$C_2=\frac{{2\mathrm{\&pi;\&epsiv;}}_0{\mathrm{\&epsiv;}}_{r}H}{\ln \frac{r_t}{r_2}}$

Wherein: ε ₀for the specific inductive capacity in vacuum, ε _rfor the relative dielectric constant of turn-to-turn insulation medium, H is the whole height of reactor winding, r ₂for the external radius of reactor winding, r _tfor the inside radius of reactor shell.

Images