CN103698586B - A kind of magnetic linkage analytic method determined containing double fed induction generators three short circuit current - Google Patents

Abstract

The present invention discloses a kind of magnetic linkage analytic method determined containing double fed induction generators three short circuit current, analyze the electrical-magnetic model of double fed induction generators (DFIG) and determine, the fault transient characteristic of rotor flux, after electric network fault, DFIG stator magnetic linkage DC component will induce the exchange magnetic linkage contrary with rotary speed direction at rotor windings, cannot go to describe in threephase stator reference axis (static coordinate axle), need to be by DFIG stator magnetic linkage forced component reduction to stator side, stator magnetic linkage DC component reduction forms Static Equivalent circuit to rotor-side, and then analyze rotor resistance on stator magnetic linkage DC component dynamic attenuation during fault and with rotor windings sensing process impact, derived electrical network three-phase shortcircuit time DFIG stator short circuit current analytical expression.

Description

A kind of magnetic linkage analytic method determined containing double fed induction generators three short circuit current

Technical field

The present invention relates to wind generator system technical field, particularly relate to one and determine that the three-phase containing double fed induction generators is short The magnetic linkage analytic method of road electric current.

Background technology

Wind-power electricity generation is as the new energy technology of the most most commercialized development prospect, in the whole world with per year over 30% Speed increment also becomes clean energy resource with fastest developing speed.The Devoting Major Efforts To Developing of wind energy resources has promoted developing rapidly of wind energy conversion system, double Feedback influence generator (DFIG) is to use relatively broad a kind of wind-force type in present stage wind-power electricity generation, and it has efficiency The plurality of advantages such as height, little, the power decoupled control of Converter Capacity, grid type double-feedback Wind turbines is at grid-connected voltage but then The transient characterisitics showed during bust are considerably complicated, and the power distribution network containing the distributed Wind turbines of high permeability is just protected by this Protect and propose challenge.

When after the large-scale access system of wind energy turbine set, the electrical equipment such as transformer, line impedance device and breaker dynamic, Heat endurance verification relies primarily on the calculation of short-circuit current of system, and one of them major issue is it should be understood that wind energy turbine set is in fault During short circuit current characteristic, decline including the amplitude of maximum impact electric current, the amplitude of fault component steady-state period, transient state component Subtracting time constant etc., therefore research DFIG short circuit current analytic expression is critically important.

The method of research DFIG short circuit current analytic expression mainly has frequency-domain calculations and two kinds of methods of the Physical Process Analyses at present, Owing to rotor frequency is different, it is impossible to go to describe in threephase stator reference axis (static coordinate axle).

Summary of the invention

For above-mentioned deficiency present in prior art, the invention provides one and determine containing double fed induction generators three-phase The magnetic linkage analytic method of short circuit current, utilizes the relation between Analysis of Equivalent Circuit stator and rotor magnetic linkage so that double-fed induction generates electricity Machine three short circuit current expression formula derivation is the easiest.

In order to solve above-mentioned technical problem, present invention employs following technical scheme:

A kind of magnetic linkage analytic method determined containing double fed induction generators three short circuit current, comprises the steps:

Step one: by double fed induction generators stator magnetic linkage forced component reduction to stator side, stator magnetic linkage DC component Reduction to rotor-side forms Static Equivalent circuit, thus it is straight with stator magnetic linkage to release rotor flux reverse rotation transient period component Damping time constant T of flow component_s, and rotor flux DC component damping time constant T_r；

Step 2: utilize Static Equivalent circuit, sets up the relation between stator and rotor electric current and magnetic linkage, derives electrical network three The analytic expression of double fed induction generators stator short circuit current during short circuit mutually；

Step 3: analyze the relation between stator and rotor flux coefficient correlation, stator and rotor magnetic linkage under checking stator coordinate The coefficient correlation of attenuating dc component can replace by the coefficient correlation of stator and rotor magnetic linkage attenuating dc component under rotor coordinate.

As a preferred embodiment of the present invention, concretely comprising the following steps of described step one:

By rotor equivalent circuit by frequency reduction to stator side, for stator magnetic linkage DC component, stator side electricity is pressed Frequency reduction to rotor-side, can obtain stator magnetic linkage DC component reduction to the equivalent circuit of rotor coordinate, hinder from stator side equivalence Anti-rotor flux of can trying to achieve reversely rotates damping time constant T of transient period component and stator magnetic linkage DC component_s:

$R_{sd}-{\mathrm{j\ω}}_r{L}_{sd}=R_e+R_s-{\mathrm{j\ω}}_r(L_e+L_{ls})+\frac{-{\mathrm{j\ω}}_r{L}_m(R_r-{\mathrm{j\ω}}_r{L}_{lr})}{R_r-{\mathrm{j\ω}}_r(L_{lr}+L_m)}---\left(1\right)$

$T_s=\frac{L_{sd}}{R_{sd}}=\frac{L_s{R}_r^2+{\mathrm{\ω}}_r^2{L}_r(L_s{L}_r-L_m^2)}{(R_s+R_e)R_r^2+{\mathrm{\ω}}_r^2{L}_m^2{R}_r+{\mathrm{\ω}}_r^2{L}_r^2(R_s+R_e)}---\left(2\right)$

In formula: R_sdFor the equiva lent impedance in terms of stator side, j for plural number mark, ω_rFor rotor angular rate, L_sdFor from The equivalent inductance that stator side is seen, R_eFor transformer between double fed induction generators to access point and line equivalent resistance, R_sFor stator electricity Resistance, L_eFor transformer between double fed induction generators to access point and line equivalent inductance, L_mFor magnetizing inductance, L_lsLeak electricity for stator Sense, L_lrFor rotor leakage inductance, R_rFor rotor resistance, L_s=L_ls+L_e+L_m, L_r=L_lr+L_m；

For constant speed influence generator rotor resistance R_rThe least (differing more than 100 times with magnetizing inductance), then stator magnetic linkage DC component damping time constant T_s=(L_s-L_m ²/L_r)/(R_s+R_e)；

From rotor-side equiva lent impedance it is:

$R_{rd}+{\mathrm{j\ω}}_r{L}_{rd}=R_r+{\mathrm{j\ω}}_r{L}_{lr}+\frac{{\mathrm{j\ω}}_r{L}_m\[(R_s+R_e)+{\mathrm{j\ω}}_r(L_{ls}+L_e)\]}{R_s+R_e+{\mathrm{j\ω}}_r(L_{ls}+L_e+L_m)}---\left(3\right)$

In formula: R_rdFor the equiva lent impedance in terms of rotor-side, L_rdFor the equivalent inductance in terms of rotor-side, due to stator resistance With access transformer, the equivalent resistance R of circuit_s+R_e< ＜ ω_r(L_ls+L_e) and L_s=L_ls+L_e+L_m> ＞ L_e, now rotor flux is straight Flow component damping time constant T_rCan be approximately:

$T_r=\frac{L_{rd}}{R_{rd}}\&ap;\frac{L_s{L}_r-L_m^2}{L_s{R}_r}---\left(4\right).$

As the another kind of preferred version of the present invention, concretely comprising the following steps of described step 2:

The generator voltage sense of current presses Motor convention, and after using means of space vector representation can obtain three phase short circuit fault, stator is sat The lower double fed induction generators stator voltage equation of mark system is:

$u_s^{\&prime;}\left(t\right)={\stackrel{\&CenterDot;}{U}}_s^{\&prime;}{e}^{j\mathrm{\&omega;}t}=R_s{i}_s^{\&prime;}\left(t\right)+\frac{d}{dt}{\mathrm{\&psi;}}_s^{\&prime;}\left(t\right)---\left(5\right)$

In formula: u'_sT () is stator voltage after fault, i'_sT () is stator short circuit current, ψ '_sT () is stator magnet after fault The space vector of chain forced component,For stator voltage phasor, e is nature exponential symbol, and t is the operation time, and ω is for synchronizing electricity Angular speed, R_sFor stator resistance；

Ignore stator resistance R_s, formula (5) stator magnetic linkage forced component after fault can be obtained If double fed induction generators terminal voltage is time properly functioningElectric network fault rear end voltage step is changed toVoltage before and after fault is substituted into formula (5) and obtains double fed induction generators stator magnetic linkage ψ after three-phase shortcircuit_s(t) For:

${\mathrm{\&psi;}}_s\left(t\right)=\frac{{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{j\mathrm{\&omega;}t}+\frac{{\stackrel{\&CenterDot;}{U}}_s-{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{-t/T_s}---\left(6\right)$

Further according to the rotor current of stator side in Static Equivalent circuitRotor current reversal periods componentWith stator The stator current of sideStator current DC componentRelation is:

${\stackrel{\&CenterDot;}{I}}_{rf}=\frac{-{\mathrm{j\&omega;L}}_m{\stackrel{\&CenterDot;}{I}}_{sf}}{R_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})+{\mathrm{j\&omega;L}}_r},{\stackrel{\&CenterDot;}{I}}_{rd}=\frac{{\mathrm{j\&omega;}}_r{L}_m{\stackrel{\&CenterDot;}{I}}_{sd}}{R_r-{\mathrm{j\&omega;}}_r{L}_r}---\left(7\right)$

In conjunction with ψ_s(t)=L_si_s(t)+L_mi_r(t) and ψ_r(t)=L_mi_s(t)+L_ri_rT () obtains rotor flux forced component ψ_rf (t) and rotor flux reversal periods component ψ_rd(t) be,

$\begin{array}{c}{\mathrm{\&psi;}}_{rf}\left(t\right)=\frac{L_m{R}_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})\&CenterDot;{\mathrm{\&psi;}}_{sf}\left(t\right)}{L_s{R}_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})+j\mathrm{\&omega;}(L_s{L}_r-L_m^2)}={\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_r\right){\mathrm{\&psi;}}_{sf}\left(t\right)\\ {\mathrm{\&psi;}}_{rd}\left(t\right)=\frac{L_m{R}_r\&CenterDot;{\mathrm{\&psi;}}_{sd}\left(t\right)}{L_s{R}_r+{\mathrm{j\&omega;}}_r(L_m^2-L_s{L}_r)}={\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right){\mathrm{\&psi;}}_{sd}\left(t\right)\end{array}---\left(8\right)$

In formula: i_sT () is stator side electric current, i_rT () is rotor-side electric current, ψ_rThe rotor flux of (t), ψ_sfT () is stator magnet Chain forced component (frequency reduction is to stator synchronous coordinate), ψ_sdT () is stator magnetic linkage DC component (reduction is to rotor coordinate), if During fault, double fed induction generators initial speed is ω_r0, according to rotor flux conservation, lower turn of stator coordinate after three-phase shortcircuit can be obtained Sub-magnetic linkage ψ_r(t) be,

$\begin{array}{c}{\mathrm{\&psi;}}_r\left(t\right)={\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_r\right)\frac{{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{j\mathrm{\&omega;}t}+{\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right)\frac{{\stackrel{\&CenterDot;}{U}}_s-{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{-t/T_s}\\ +\&lsqb;{\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_{r0}\right)-{\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_{r0}\right)\&rsqb;\frac{{\stackrel{\&CenterDot;}{U}}_s-{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{-t/T_r}{e}^{{\mathrm{j\&omega;}}_{r}t}\end{array}---\left(9\right)$

In formula: η_fFor the coefficient correlation of stator coordinate lower rotor part magnetic linkage forced component Yu stator magnetic linkage forced component, η_dFor turning Subcoordinate lower rotor part magnetic linkage DC component and the coefficient correlation of stator magnetic linkage DC component；

I is had with current relationship again by double fed induction generators stator magnetic linkage, rotor flux_s(t)=[L_rψ_s(t)-L_mψ_r (t)]/(L_sL_r-L_m ²), formula (6) and formula (9) are substituted into the stator short circuit current i that can obtain double fed induction generators_s(t) expression formula For,

In formula: A₁For the amplitude of synchronizing frequency periodic component, A₂For the amplitude of rotor frequency periodic component, A₃Divide for direct current The amplitude of amount,For the phase place of synchronizing frequency periodic component,For the phase place of rotor frequency periodic component,For DC component Phase place.

As another preferred version of the present invention, concretely comprising the following steps of described step 3:

The attenuating dc component of stator magnetic linkage resolves into several frequencies omega_dClose to the low frequency component of 0,0 < ω_d< ＜ ω, Then for stator magnetic linkage ω_dFrequency component reduction is returned to stator side equivalent circuit with stator magnetic linkage forced component in described step one Calculate to the Static Equivalent circuit of stator side similar, the Static Equivalent circuit that stator magnetic linkage DC component reduction to rotor-side is formed Middle ω replaces with ω_d, slip s replaces with 1-ω_r/ω_d, can obtain accordingly, the rotor current reversal periods component of reduction to stator sideWith stator current DC componentRelation is:

${\stackrel{\&CenterDot;}{I}}_{rd}=\frac{-{\mathrm{j\&omega;}}_d{L}_m-{\stackrel{\&CenterDot;}{I}}_{sd}}{R_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)+{\mathrm{j\&omega;}}_d{L}_r}---\left(11\right)$

Again by ψ_s(t)=L_si_s(t)+L_mi_r(t) and ψ_r(t)=L_mi_s(t)+L_ri_rT () can obtain, stator magnet under stator coordinate Chain DC component with the coefficient correlation of rotor flux reversal periods component is:

$\frac{{\mathrm{\&psi;}}_{rd}\left(t\right)}{{\mathrm{\&psi;}}_{sd}\left(t\right)}=\frac{L_m{R}_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)}{L_s{R}_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)+{\mathrm{j\&omega;}}_d(L_s{L}_r-L_m^2)}=\frac{L_m{R}_r}{L_m{R}_r+j({\mathrm{\&omega;}}_d-{\mathrm{\&omega;}}_r)(L_s{L}_r-L_m^2)}---\left(12\right)$

In formula: ψ_rdT () is rotor flux reversal periods component, ψ_sdT () is stator magnetic linkage DC component；

Work as ω_dLevel off to 0 time stator coordinate under in both coefficient correlation, with formula (8) its under rotor coordinate Situation is equal to be:

$\frac{{\mathrm{\&psi;}}_{rd}\left(t\right)}{{\mathrm{\&psi;}}_{sd}\left(t\right)}=\frac{L_m{R}_r}{L_m{R}_r+{\mathrm{j\&omega;}}_r(L_m^2-L_s{L}_r)}={\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right)---\left(13\right)$

Owing to low frequency amount each in stator magnetic linkage attenuating dc component meets 0 < ω_d< ＜ ω, it is believed that stator and rotor coordinate Both ratio approximately equals down.

Advantages of the present invention: the present invention uses magnetic linkage analytic approach derivation DFIG three short circuit current, DFIG after electric network fault Stator magnetic linkage DC component will induce the exchange magnetic linkage contrary with rotary speed direction at rotor windings, due to stator and rotor frequency not With, it is impossible to go to describe, therefore for stator magnetic linkage DC component, by stator side in threephase stator reference axis (static coordinate axle) After electricity is by frequency reduction to rotor-side, directly can go out short circuit current expression formula with stator and rotor magnetic linkage relation derivation, thus simplify The derivation of DFIG three short circuit current expression formula.

Accompanying drawing explanation

Fig. 1 is that stator magnetic linkage forced component reduction is to stator side equivalent circuit；

Fig. 2 is that stator magnetic linkage DC component reduction is to rotor-side equivalent circuit.

Detailed description of the invention

With detailed description of the invention, the present invention is described in further detail below in conjunction with the accompanying drawings.

A kind of magnetic linkage analytic method determined containing double fed induction generators three short circuit current, the method utilizes double-fed induction The Static Equivalent that generator unit stator magnetic linkage forced component reduction is formed to stator side, stator magnetic linkage DC component reduction to rotor-side Circuit, analysis rotor resistance senses the shadow of process to stator magnetic linkage DC component dynamic attenuation during fault and with rotor windings Ring, thus the analytical expression of double fed induction generators stator short circuit current when deriving electrical network three-phase shortcircuit.Concrete steps are such as Under:

Step one: by double fed induction generators stator magnetic linkage forced component reduction to stator side, stator magnetic linkage DC component Reduction to rotor-side forms Static Equivalent circuit, thus it is straight with stator magnetic linkage to release rotor flux reverse rotation transient period component Damping time constant T of flow component_s, and rotor flux DC component damping time constant T_r；

Step 2: utilize Static Equivalent circuit, sets up the relation between stator and rotor electric current and magnetic linkage, derives electrical network three Double fed induction generators stator short circuit current analytic expression during short circuit mutually；

Step 3: analyze the relation between stator and rotor flux coefficient correlation, stator and rotor magnetic linkage under checking stator coordinate The coefficient correlation of attenuating dc component can replace by the coefficient correlation of stator and rotor magnetic linkage attenuating dc component under rotor coordinate.

Wherein, the concretely comprising the following steps of step one:

Fig. 1 is stator magnetic linkage forced component reduction to the equivalent circuit of stator synchronously rotating reference frame, due to rotor frequency Difference, must be the most right by rotor equivalent circuit by frequency reduction to stator side (without winding reduction during impedance employing perunit value) In stator magnetic linkage DC component, by stator side electricity by frequency reduction to rotor-side, Fig. 2 stator magnetic linkage DC component reduction can be obtained Equivalent circuit to rotor coordinate.In Fig. 1For the stator current of reduction to stator side,Rotor for reduction to stator side Electric current, in Fig. 2For the stator current DC component of reduction to rotor-side,Rotor current for reduction to rotor-side is reverse Periodic component, L_mFor magnetizing inductance, L_lsFor stator leakage inductance, L_lrFor rotor leakage inductance, R_rFor rotor resistance, ω_rFor rotor electricity Angular speed, slip s=1-ω_r/ ω, R_eFor transformer between DFIG to access point and line equivalent resistance, L_eFor DFIG to access point Between transformer and line equivalent inductance.In terms of stator side equiva lent impedance can try to achieve rotor flux reversely rotate transient period component with Damping time constant T of stator magnetic linkage DC component_s:

$R_{sd}-{\mathrm{j\&omega;}}_r{L}_{sd}=R_e+R_s-{\mathrm{j\&omega;}}_r(L_e+L_{ls})+\frac{-{\mathrm{j\&omega;}}_r{L}_m(R_r-{\mathrm{j\&omega;}}_r{L}_{lr})}{R_r-{\mathrm{j\&omega;}}_r(L_{lr}+L_m)}---\left(1\right)$

$T_s=\frac{L_{sd}}{R_{sd}}=\frac{L_s{R}_r^2+{\mathrm{\&omega;}}_r^2{L}_r(L_s{L}_r-L_m^2)}{(R_s+R_e)R_r^2+{\mathrm{\&omega;}}_r^2{L}_m^2{R}_r+{\mathrm{\&omega;}}_r^2{L}_r^2(R_s+R_e)}---\left(2\right)$

In formula: R_sdFor the equiva lent impedance in terms of stator side, j for plural number mark, ω_rFor rotor angular rate, L_sdFor from The equivalent inductance that stator side is seen, R_eFor transformer between double fed induction generators to access point and line equivalent resistance, R_sFor stator electricity Resistance, L_eFor transformer between double fed induction generators to access point and line equivalent inductance, L_mFor magnetizing inductance, L_lsLeak electricity for stator Sense, L_lrFor rotor leakage inductance, R_rFor rotor resistance, L_s=L_ls+L_e+L_m, L_r=L_lr+L_m；

For constant speed influence generator rotor resistance R_rThe least (differing more than 100 times with magnetizing inductance), then stator magnetic linkage DC component damping time constant T_s=(L_s-L_m ²/L_r)/(R_s+R_e)。

In terms of rotor-side, equiva lent impedance is:

$R_{rd}+{\mathrm{j\&omega;}}_r{L}_{rd}=R_r+{\mathrm{j\&omega;}}_r{L}_{lr}+\frac{{\mathrm{j\&omega;}}_r{L}_m\&lsqb;(R_s+R_e)+{\mathrm{j\&omega;}}_r(L_{ls}+L_e)\&rsqb;}{R_s+R_e+{\mathrm{j\&omega;}}_r(L_{ls}+L_e+L_m)}---\left(3\right)$

In formula: R_rdFor the equiva lent impedance in terms of rotor-side, L_rdFor the equivalent inductance in terms of rotor-side, due to stator resistance With access transformer, the equivalent resistance R of circuit_s+R_e< ＜ ω_r(L_ls+L_e) (both compare perunit value differ 20 times with On) and L_s=L_ls+L_e+L_m> ＞ L_e(perunit value differs more than 20 times), now rotor flux DC component damping time constant T_r Can be approximately:

$T_r=\frac{L_{rd}}{R_{rd}}\&ap;\frac{L_s{L}_r-L_m^2}{L_s{R}_r}---\left(4\right).$

And the concretely comprising the following steps of step 2:

Utilize rotor Static Equivalent circuit, set up the relation between stator and rotor current and magnetic linkage, derive electrical network three-phase DFIG stator short circuit current analytic expression during short circuit.The generator voltage sense of current presses Motor convention, uses means of space vector representation After can obtaining three phase short circuit fault, under stator coordinate, double fed induction generators stator voltage equation is:

$u_s^{\&prime;}\left(t\right)={\stackrel{\&CenterDot;}{U}}_s^{\&prime;}{e}^{j\mathrm{\&omega;}t}=R_s{i}_s^{\&prime;}\left(t\right)+\frac{d}{dt}{\mathrm{\&psi;}}_s^{\&prime;}\left(t\right)---\left(5\right)$

In formula: u '_sT () is stator voltage after fault, i '_sT () is stator short circuit current, ψ '_sT () is stator magnet after fault The space vector of chain forced component,For stator voltage phasor, e is nature exponential symbol, and t is the operation time, and ω is for synchronizing electricity Angular speed, R_sFor stator resistance.

Ignore stator resistance R_s, formula (5) stator magnetic linkage forced component after fault can be obtainedIf Time properly functioning, double fed induction generators terminal voltage isElectric network fault rear end voltage step is changed toVoltage before and after fault is substituted into formula (5) and obtains double fed induction generators stator magnetic linkage ψ after three-phase shortcircuit_s(t) For:

${\mathrm{\&psi;}}_s\left(t\right)=\frac{{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{j\mathrm{\&omega;}t}+\frac{{\stackrel{\&CenterDot;}{U}}_s-{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{-t/T_s}---\left(6\right)$

Further according to the rotor current of stator side in Fig. 1 and Fig. 2 Static Equivalent circuitRotor current reversal periods componentStator current with stator sideStator current DC componentRelation is:

${\stackrel{\&CenterDot;}{I}}_{rf}=\frac{-{\mathrm{j\&omega;L}}_m{\stackrel{\&CenterDot;}{I}}_{sf}}{R_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})+{\mathrm{j\&omega;L}}_r},{\stackrel{\&CenterDot;}{I}}_{rd}=\frac{{\mathrm{j\&omega;}}_r{L}_m{\stackrel{\&CenterDot;}{I}}_{sd}}{R_r-{\mathrm{j\&omega;}}_r{L}_r}---\left(7\right)$

In conjunction with ψ_s(t)=L_si_s(t)+L_mi_r(t) and ψ_r(t)=L_mi_s(t)+L_ri_rT () obtains rotor flux forced component ψ_rf (t) and rotor flux reversal periods component ψ_rd(t) be,

$\begin{array}{c}{\mathrm{\&psi;}}_{rf}\left(t\right)=\frac{L_m{R}_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})\&CenterDot;{\mathrm{\&psi;}}_{sf}\left(t\right)}{L_s{R}_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})+j\mathrm{\&omega;}(L_s{L}_r-L_m^2)}={\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_r\right){\mathrm{\&psi;}}_{sf}\left(t\right)\\ {\mathrm{\&psi;}}_{rd}\left(t\right)=\frac{L_m{R}_r\&CenterDot;{\mathrm{\&psi;}}_{sd}\left(t\right)}{L_s{R}_r+{\mathrm{j\&omega;}}_r(L_m^2-L_s{L}_r)}={\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right){\mathrm{\&psi;}}_{sd}\left(t\right)\end{array}---\left(8\right)$

In formula: i_sT () is stator side electric current, i_rT () is rotor-side electric current, ψ_rThe rotor flux of (t), ψ_sfT () is stator magnet Chain forced component (frequency reduction is to stator synchronous coordinate), ψ_sdT () is stator magnetic linkage DC component (reduction is to rotor coordinate).If During fault, double fed induction generators initial speed is ω_r0, according to rotor flux conservation, lower turn of stator coordinate after three-phase shortcircuit can be obtained Sub-magnetic linkage ψ_r(t) be,

$\begin{array}{c}{\mathrm{\&psi;}}_r\left(t\right)={\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_r\right)\frac{{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{j\mathrm{\&omega;}t}+{\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right)\frac{{\stackrel{\&CenterDot;}{U}}_s-{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{-t/T_s}\\ +\&lsqb;{\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_{r0}\right)-{\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_{r0}\right)\&rsqb;\frac{{\stackrel{\&CenterDot;}{U}}_s-{\stackrel{\&CenterDot;}{U}}_s^{\&prime;}}{j\mathrm{\&omega;}}{e}^{-t/T_r}{e}^{{\mathrm{j\&omega;}}_{r}t}\end{array}---\left(9\right)$

In formula: η_fFor the coefficient correlation of stator coordinate lower rotor part magnetic linkage forced component Yu stator magnetic linkage forced component, η_dFor turning Subcoordinate lower rotor part magnetic linkage DC component and the coefficient correlation of stator magnetic linkage DC component；

Is (t)=[Lr ψ s (t)-Lm ψ r is had with current relationship again by double fed induction generators stator magnetic linkage, rotor flux (t)]/(LsLr-Lm2), formula (6) and formula (9) are substituted into stator short circuit current is (t) expression formula that can obtain double fed induction generators For,

In formula: A₁For the amplitude of synchronizing frequency periodic component, A₂For the amplitude of rotor frequency periodic component, A₃Divide for direct current The amplitude of amount,For the phase place of synchronizing frequency periodic component,For the phase place of rotor frequency periodic component,For DC component Phase place.

Concretely comprising the following steps of step 3:

The attenuating dc component of stator magnetic linkage resolves into several frequencies omega_dClose to the low frequency component of 0,0 < ω_d< ＜ ω, Then for stator magnetic linkage ω_dFrequency component reduction is returned to stator side equivalent circuit with stator magnetic linkage forced component in described step one Calculate to the Static Equivalent circuit of stator side similar, the Static Equivalent circuit that stator magnetic linkage DC component reduction to rotor-side is formed Middle ω replaces with ω_d, slip s replaces with 1-ω_r/ω_d, can obtain accordingly, the rotor current reversal periods component of reduction to stator sideWith stator current DC componentRelation is:

${\stackrel{\&CenterDot;}{I}}_{rd}=\frac{-{\mathrm{j\&omega;}}_d{L}_m-{\stackrel{\&CenterDot;}{I}}_{sd}}{R_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)+{\mathrm{j\&omega;}}_d{L}_r}---\left(11\right)$

Again by ψ_s(t)=L_si_s(t)+L_mi_r(t) and ψ_r(t)=L_mi_s(t)+L_ri_rT () can obtain, stator magnet under stator coordinate Chain DC component with the coefficient correlation of rotor flux reversal periods component is:

$\frac{{\mathrm{\&psi;}}_{rd}\left(t\right)}{{\mathrm{\&psi;}}_{sd}\left(t\right)}=\frac{L_m{R}_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)}{L_s{R}_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)+{\mathrm{j\&omega;}}_d(L_s{L}_r-L_m^2)}=\frac{L_m{R}_r}{L_m{R}_r+j({\mathrm{\&omega;}}_d-{\mathrm{\&omega;}}_r)(L_s{L}_r-L_m^2)}---\left(12\right)$

In formula: ψ_rdT () is rotor flux reversal periods component, ψ_sdT () is stator magnetic linkage DC component；

Work as ω_dLevel off to 0 time stator coordinate under in both coefficient correlation, with formula (8) its under rotor coordinate Situation is equal to be:

$\frac{{\mathrm{\&psi;}}_{rd}\left(t\right)}{{\mathrm{\&psi;}}_{sd}\left(t\right)}=\frac{L_m{R}_r}{L_m{R}_r+{\mathrm{j\&omega;}}_r(L_m^2-L_s{L}_r)}={\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right)---\left(13\right)$

Owing to low frequency amount each in stator magnetic linkage attenuating dc component meets 0 < ω_d< ＜ ω, it is believed that stator and rotor coordinate Both ratio approximately equals down, it can thus be appreciated that the rotor magnetic linkage attenuating dc component derived under rotor coordinate is relevant Coefficient can substitute the coefficient correlation of rotor magnetic linkage attenuating dc component under stator coordinate so that rotor is relevant to stator magnetic linkage Coefficient η_fAnd η_dEven if computing can not carried out under same coordinate yet, thus simplify pushing away of DFIG three short circuit current expression formula Lead process.

Finally illustrating, above example is only in order to illustrate technical scheme and unrestricted, although with reference to relatively The present invention has been described in detail by good embodiment, it will be understood by those within the art that, can be to the skill of the present invention Art scheme is modified or equivalent, and without deviating from objective and the scope of technical solution of the present invention, it all should be contained at this In the middle of the right of invention.

Claims (1)

1. the magnetic linkage analytic method determined containing double fed induction generators three short circuit current, it is characterised in that include as follows Step:

Step one: by double fed induction generators stator magnetic linkage forced component reduction to stator side, stator magnetic linkage DC component reduction Form Static Equivalent circuit to rotor-side, thus release rotor flux reverse rotation transient period component and divide with stator magnetic linkage direct current Damping time constant T of amount_s, and rotor flux DC component damping time constant T_r；

Step 2: utilize Static Equivalent circuit, sets up the relation between stator and rotor electric current and magnetic linkage, derives electrical network three-phase short The analytic expression of double fed induction generators stator short circuit current during road；

Step 3: analyze the relation between stator and rotor flux coefficient correlation, stator and rotor magnetic linkage decay under checking stator coordinate The coefficient correlation of DC component can replace by the coefficient correlation of stator and rotor magnetic linkage attenuating dc component under rotor coordinate；

Wherein, the concretely comprising the following steps of described step one:

By rotor equivalent circuit by frequency reduction to stator side, for stator magnetic linkage DC component, by stator side electricity by frequency Reduction to rotor-side, can obtain stator magnetic linkage DC component reduction to the Static Equivalent circuit of rotor coordinate, hinder from stator side equivalence Anti-rotor flux of can trying to achieve reversely rotates damping time constant T of transient period component and stator magnetic linkage DC component_s:

$R_{sd}-{\mathrm{j\&omega;}}_r{L}_{sd}=R_e+R_s-{\mathrm{j\&omega;}}_r(L_e+L_{ls})+\frac{-{\mathrm{j\&omega;}}_r{L}_m(R_r-{\mathrm{j\&omega;}}_r{L}_{lr})}{R_r-{\mathrm{j\&omega;}}_r(L_{lr}+L_m)}---\left(1\right)$

$T_s=\frac{L_{sd}}{R_{sd}}=\frac{L_s{R}_r^2+{\mathrm{\&omega;}}_r^2{L}_r(L_s{L}_r-L_m^2)}{(R_s+R_e)R_r^2+{\mathrm{\&omega;}}_r^2{L}_m^2{R}_r+{\mathrm{\&omega;}}_r^2{L}_r^2(R_s+R_e)}---\left(2\right)$

In formula: R_sdFor the equiva lent impedance in terms of stator side, j is complex symbol, ω_rFor rotor angular rate, L_sdFor from stator side The equivalent inductance seen, R_eFor transformer between double fed induction generators to access point and line equivalent resistance, R_sFor stator resistance, L_e For transformer between double fed induction generators to access point and line equivalent inductance, L_mFor magnetizing inductance, L_lsFor stator leakage inductance, L_lr For rotor leakage inductance, R_rFor rotor resistance, L_s=L_ls+L_e+L_m, L_r=L_lr+L_m；

Relative to constant speed influence generator, double fed induction generators rotor resistance R_rThe least, i.e. differ with magnetizing inductance 100 times with On, then stator magnetic linkage DC component damping time constant T_s=(L_s-L_m ²/L_r)/(R_s+R_e)；

From rotor-side equiva lent impedance it is:

$R_{rd}+{\mathrm{j\&omega;}}_r{L}_{rd}=R_r+{\mathrm{j\&omega;}}_r{L}_{lr}+\frac{{\mathrm{j\&omega;}}_r{L}_m\&lsqb;(R_s+R_e)+{\mathrm{j\&omega;}}_r(L_{ls}+L_e)\&rsqb;}{R_s+R_e+{\mathrm{j\&omega;}}_r(L_{ls}+L_e+L_m)}---\left(3\right)$

In formula: R_rdFor the equiva lent impedance in terms of rotor-side, L_rdFor the equivalent inductance in terms of rotor-side, due under normal circumstances, fixed Sub-resistance and access transformer, the equivalent resistance R of circuit_s+R_e<<ω_r(L_ls+L_e) and L_s=L_ls+L_e+L_m>>L_e, now rotor magnetic Chain DC component damping time constant T_rCan be approximately:

$T_r=\frac{L_{rd}}{R_{rd}}\&ap;\frac{L_s{L}_r-L_m^2}{L_s{R}_r}---\left(4\right);$

Concretely comprising the following steps of described step 2:

The generator voltage sense of current presses Motor convention, uses means of space vector representation can obtain stator coordinate after three phase short circuit fault Lower double fed induction generators stator voltage equation is:

$u_s^{\&prime;}\left(t\right)={\stackrel{\&CenterDot;}{U}}_s^{\&prime;}{e}^{j\mathrm{\&omega;}t}=R_s{i}_s^{\&prime;}\left(t\right)+\frac{d}{dt}{\mathrm{\&psi;}}_s^{\&prime;}\left(t\right)---\left(5\right)$

In formula: u'_sT () is stator voltage after fault, i'_sT () is stator current after fault, ψ '_sT () is stator magnetic linkage after fault The space vector of forced component,For stator voltage phasor after fault, e is nature exponential symbol, and t is the operation time, and ω is same Step angular rate, R_sFor stator resistance；

Ignore stator resistance R_s, formula (5) space vector of stator magnetic linkage forced component after fault can be obtained If double fed induction generators terminal voltage is time properly functioningElectric network fault rear end voltage step It is changed toVoltage before and after fault is substituted into formula (5) and obtains double fed induction generators stator magnetic linkage after three-phase shortcircuit ψ_{S is short}(t) be:

Further according to the rotor current of stator side in Static Equivalent circuitRotor current reversal periods componentWith determining of stator side Electron currentStator current DC componentRelation is:

${\stackrel{\&CenterDot;}{I}}_{rf}=\frac{-{\mathrm{j\&omega;L}}_m{\stackrel{\&CenterDot;}{I}}_{sf}}{R_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})+{\mathrm{j\&omega;L}}_r},{\stackrel{\&CenterDot;}{I}}_{rd}=\frac{{\mathrm{j\&omega;}}_r{L}_m{\stackrel{\&CenterDot;}{I}}_{sd}}{R_r-{\mathrm{j\&omega;}}_r{L}_r}---\left(7\right)$

In conjunction with ψ_s(t)=L_si_s(t)+L_mi_r(t) and ψ_r(t)=L_mi_s(t)+L_ri_rT () obtains rotor flux forced component ψ_rf(t) and Rotor flux reversal periods component ψ_rd(t) be,

$\begin{array}{c}{\mathrm{\&psi;}}_{rf}\left(t\right)=\frac{L_m{R}_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})\&CenterDot;{\mathrm{\&psi;}}_{sf}\left(t\right)}{L_s{R}_r/(1-{\mathrm{\&omega;}}_r/\mathrm{\&omega;})+j\mathrm{\&omega;}(L_s{L}_r-L_m^2)}={\mathrm{\&eta;}}_f\left({\mathrm{\&omega;}}_r\right){\mathrm{\&psi;}}_{sf}\left(t\right)\\ {\mathrm{\&psi;}}_{rd}\left(t\right)=\frac{L_m{R}_r\&CenterDot;{\mathrm{\&psi;}}_{sd}\left(t\right)}{L_s{R}_r+{\mathrm{j\&omega;}}_r(L_m^2-L_s{L}_r)}={\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right){\mathrm{\&psi;}}_{sd}\left(t\right)\end{array}---\left(8\right)$

In formula: i_sT () is stator side electric current, i_rT () is rotor-side electric current, ψ_rT () is rotor flux, ψ_sT () is stator magnetic linkage, ψ_sfT () is stator magnetic linkage forced component, ψ_sdT () is stator magnetic linkage DC component, if double fed induction generators initially turns during fault Speed is ω_r0, according to rotor flux conservation, stator coordinate lower rotor part magnetic linkage ψ after three-phase shortcircuit can be obtained_{R is short}(t) be,

In formula: η_fFor the coefficient correlation of stator coordinate lower rotor part magnetic linkage forced component Yu stator magnetic linkage forced component, η_dSit for rotor Mark lower rotor part magnetic linkage reversal periods component and the coefficient correlation of stator magnetic linkage DC component；

I is had with current relationship again by double fed induction generators stator magnetic linkage, rotor flux_s(t)=[L_rψ_s(t)-L_mψ_r(t)]/ (L_sL_r-L_m ²), formula (6) and formula (9) are substituted into the stator short circuit current i that can obtain double fed induction generators_{S is short}T () expression formula is,

In formula: A₁For the amplitude of synchronizing frequency periodic component, A₂For the amplitude of rotor frequency periodic component, A₃For DC component Amplitude,For the phase place of synchronizing frequency periodic component,For the phase place of rotor frequency periodic component,Phase for DC component Position；

Concretely comprising the following steps of described step 3:

The attenuating dc component of stator magnetic linkage resolves into several frequencies omega_dClose to the low frequency component of 0,0 < ω_d< < ω, the most right In stator magnetic linkage frequency component ω_dReduction is to stator side equivalent circuit with stator magnetic linkage forced component reduction in described step one extremely The Static Equivalent circuit of stator side is similar to, ω in the Static Equivalent circuit formed stator magnetic linkage DC component reduction to stator side Replace with ω_d, slip s replaces with 1-ω_r/ω_d, can obtain accordingly, the rotor current reversal periods component of reduction to stator sideWith Stator current DC componentRelation is:

${\stackrel{\&CenterDot;}{I}}_{rd}=\frac{-{\mathrm{j\&omega;}}_d{L}_m-{\stackrel{\&CenterDot;}{I}}_{sd}}{R_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)+{\mathrm{j\&omega;}}_d{L}_r}---\left(11\right)$

Again by ψ_s(t)=L_si_s(t)+L_mi_r(t) and ψ_r(t)=L_mi_s(t)+L_ri_rT () can obtain, stator magnetic linkage direct current under stator coordinate Component with the coefficient correlation of rotor flux reversal periods component is:

$\frac{{\mathrm{\&psi;}}_{rd}\left(t\right)}{{\mathrm{\&psi;}}_{sd}\left(t\right)}=\frac{L_m{R}_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)}{L_s{R}_r/(1-{\mathrm{\&omega;}}_r/{\mathrm{\&omega;}}_d)+{\mathrm{j\&omega;}}_d(L_s{L}_r-L_m^2)}=\frac{L_m{R}_r}{L_s{R}_r+j({\mathrm{\&omega;}}_d-{\mathrm{\&omega;}}_r)(L_s{L}_r-L_m^2)}---\left(12\right)$

In formula: ψ_rdT () is rotor flux reversal periods component, ψ_sdT () is stator magnetic linkage DC component；

Work as ω_dLevel off to 0 time stator coordinate under both coefficient correlation, with its situation phase under rotor coordinate in formula (8) Etc. being:

$\frac{{\mathrm{\&psi;}}_{rd}\left(t\right)}{{\mathrm{\&psi;}}_{sd}\left(t\right)}=\frac{L_m{R}_r}{L_s{R}_r+{\mathrm{j\&omega;}}_r(L_m^2-L_s{L}_r)}={\mathrm{\&eta;}}_d\left({\mathrm{\&omega;}}_r\right)---\left(13\right)$

Owing to low frequency amount each in stator magnetic linkage attenuating dc component meets 0 < ω_d< < ω, it is believed that both under stator and rotor coordinate Ratio approximately equal.