CN103698586A - Flux linkage analysis method for determining doubly fed induction generator-containing three-phase short circuit current - Google Patents

Abstract

The invention discloses a flux linkage analysis method for determining doubly fed induction generator-containing three-phase short circuit current. According to the method, an electromagnetic transient model of a doubly fed induction generator (DFIG) and fault transient characteristics of stator and rotor flux linkage are analyzed, after a grid is failed, the DFIG stator flux linkage direct current component induces alternating current flux linkage in reverse direction of the revolving speed direction at a rotor winding, the alternating current flux linkage cannot be described in three-phase stator coordinate axis (static coordinate axis), the DFIG stator flux linkage forced component needs to be treated by reduction to a stator side and stator flux linkage direct current component needs to be treated by reduction to a rotor side so as to form a static equivalent circuit, thus, in the case of fault, influence of rotor resistance on dynamic attenuation of the stator flux linkage direct current component and induction process of the stator flux linkage direct current component and the rotor winding is analyzed, and an analytical expression of DFIG stator short circuit current in the case of grid three-phase short circuit is deduced.

Description

A kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current

Technical field

The present invention relates to wind generator system technical field, relate in particular to a kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current.

Background technology

Wind-power electricity generation is as the current new energy technology of tool commercialized development prospect, in the whole world to surpass every year 30% speed increment and to become 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 fed induction generators (DFIG) is in present stage wind-power electricity generation, to use a kind of wind-force type comparatively widely; it has the plurality of advantages such as efficiency is high, Converter Capacity is little, power decoupled control; the transient characterisitics that grid type double-feedback wind-powered electricity generation unit shows when grid-connected voltage die are but then quite complicated, and this has just proposed challenge to the distribution protection that contains the distributed wind-powered electricity generation unit of high permeability.

After the large-scale connecting system of wind energy turbine set, moving, the thermal stability verification of the electrical equipments such as transformer, line impedance device and isolating switch mainly relies on the calculation of short-circuit current of system, one of them major issue is to understand the short-circuit current characteristic of wind energy turbine set in failure process, comprise the amplitude of maximum impact electric current, therefore the amplitude of fault component steady-state period, transient state component damping time constant etc. study DFIG short-circuit current analytic expression very important.

The method of research DFIG short-circuit current analytic expression mainly contains frequency-domain calculations and two kinds of methods of the Physical Process Analyses at present, because rotor frequency is different, cannot in threephase stator coordinate axis (static coordinate axle), go to describe.

Summary of the invention

For above shortcomings in prior art, the invention provides a kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current, utilize the relation between Analysis of Equivalent Circuit stator and rotor magnetic linkage, make double fed induction generators three-phase shortcircuit current expression derivation more easy.

In order to solve the problems of the technologies described above, the present invention has adopted following technical scheme:

Determine the magnetic linkage analytic method containing double fed induction generators three-phase shortcircuit electric current, comprise the steps:

Step 1: double fed induction generators stator magnetic linkage forced component reduction to stator side, stator magnetic linkage DC component reduction to rotor-side formed to Static Equivalent circuit, thereby release the damping time constant T of rotor flux reverse rotation transient state periodic component and stator magnetic linkage DC component _s, and rotor flux DC component damping time constant T _r;

Step 2: utilize Static Equivalent circuit, set up the relation between stator and rotor electric current and magnetic linkage, double fed induction generators stator short-circuit current analytic expression while deriving electrical network three-phase shortcircuit;

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

As a preferred embodiment of the present invention, the concrete steps of described step 1 are:

Rotor equivalent circuit is pressed to frequency reduction to stator side, for stator magnetic linkage DC component, stator side electric weight is pressed to frequency reduction to rotor-side, can obtain the reduction of stator magnetic linkage DC component to the equivalent circuit of rotor coordinate, from stator side equiva lent impedance, can try to achieve the damping time constant T of rotor flux reverse rotation transient state periodic component and stator magnetic linkage DC component _s:

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

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

In formula: R _sdfor the equiva lent impedance of seeing from stator side, j's is plural number sign, ω _rfor rotor electric angle speed, L _sdfor the equivalent inductance of seeing from stator side, R _efor double fed induction generators is to transformer between access point and circuit equivalent resistance, R _sfor stator resistance, L _efor double fed induction generators is to transformer between access point and circuit equivalent inductance, L _mfor magnetizing inductance, L _lsfor stator leakage inductance, 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 inductor generator rotor resistance R _rvery little (differing more than 100 times with magnetizing inductance), 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, be:

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

In formula: R _rdfor the equiva lent impedance of seeing from rotor-side, L _rdfor the equivalent inductance of seeing from rotor-side, due to the equivalent resistance R of stator resistance with access transformer, circuit _s+ R _e<< ω _r(L _ls+ L _e) and L _s=L _ls+ L _e+ L _m>>L _e, rotor flux DC component damping time constant T now _rcan be approximately:

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

As another kind of preferred version of the present invention, the concrete steps of described step 2 are:

Generator voltage direction of current is pressed Motor convention, adopts means of space vector representation can obtain after three phase short circuit fault double fed induction generators stator voltage equation under stator coordinate to be:

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

In formula: u' _s(t) be stator voltage after fault, i' _s(t) be stator current after fault, ψ ' _s(t) be the space vector of stator magnetic linkage forced component after fault,

for stator voltage phasor, e is nature exponential symbol, and t is working time, and ω is synchronous electric angular velocity, R _sfor stator resistance;

Ignore stator resistance R _s, by formula (5), can obtain stator magnetic linkage forced component after fault

if double fed induction generators terminal voltage is while normally moving

electric network fault rear end voltage step is changed to

by voltage substitution formulas (5) before and after fault double fed induction generators stator magnetic linkage ψ after three-phase shortcircuit _s(t) be:

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

Again according to the rotor current of stator side in Static Equivalent circuit

the rotor current reversal periods component of rotor-side

stator current with stator side

the stator current reversal periods component of rotor-side

pass is:

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

In conjunction with ψ _s(t)=L _si _s(t)+L _mi _rand ψ (t) _r(t)=L _mi _s(t)+L _ri _r(t) obtain rotor flux forced component ψ _rfand transient state reversal periods component ψ (t) _rd(t) be,

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

In formula: i _s(t) be stator side electric current, i _r(t) be rotor-side electric current, ψ _r(t) rotor flux, ψ _sf(t) be stator magnetic linkage forced component (frequency reduction is to stator synchronous coordinate), ψ _sd(t) be stator magnetic linkage DC component (reduction is to rotor coordinate), while establishing fault, double fed induction generators initial speed is ω _r0, according to rotor flux conservation, can obtain stator coordinate lower rotor part magnetic linkage ψ after three-phase shortcircuit _r(t) be,

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

In formula: η _ffor the related coefficient of stator coordinate lower rotor part magnetic linkage forced component and stator magnetic linkage forced component, η _drelated coefficient for rotor coordinate lower rotor part magnetic linkage DC component and stator magnetic linkage DC component;

By double fed induction generators stator magnetic linkage, rotor flux and current relationship, there is i again _s(t)=[L _rψ _s(t)-L _mψ _r(t)]/(L _sl _r-L _m ²), formula (6) and formula (9) substitution can be obtained to double fed induction generators three-phase shortcircuit current space vector i _s(t) expression formula is,

In formula: A ₁for the amplitude of synchronizing frequency periodic component, A ₂for the amplitude of rotor frequency periodic component, A ₃for the amplitude of DC component,

for the phase place of synchronizing frequency periodic component,

for the phase place of rotor frequency periodic component,

phase place for DC component.

As another preferred version of the present invention, the concrete steps of described step 3 are:

The attenuating dc component of stator magnetic linkage resolves into several frequencies omega _dlow frequency component close to 0,0< ω _d<< ω, for stator magnetic linkage ω _dfrequency component reduction is similar to the Static Equivalent circuit of stator side to stator side equivalent circuit and the reduction of stator magnetic linkage forced component, and in the Static Equivalent circuit that stator magnetic linkage DC component reduction to rotor-side is formed, ω replaces with ω _d, slip s replaces with 1-ω _r/ ω _d, can obtain accordingly, reduction is to stator side rotor current

with stator current

pass is:

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

Again by ψ _s(t)=L _si _s(t)+L _mi _rand ψ (t) _r(t)=L _mi _s(t)+L _ri _r(t) can obtain, under stator coordinate, the related coefficient of rotor magnetic linkage attenuating dc component is:

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

In formula: ψ _rd(t) be rotor flux DC component, ψ _sd(t) be stator magnetic linkage DC component;

Work as ω _dlevel off under 0 o'clock stator coordinate both related coefficient, with in formula (8), it equates to be in the situation under rotor coordinate:

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

Because each low frequency amount in stator magnetic linkage attenuating dc component meets 0< ω _d<< ω, can think under stator and rotor coordinate both ratio approximately equal.

Advantage of the present invention: the present invention adopts magnetic linkage analytic approach derivation DFIG three-phase shortcircuit electric current, after electric network fault, DFIG stator magnetic linkage DC component will induce the interchange magnetic linkage contrary with rotary speed direction at rotor winding, because stator and rotor frequency is different, cannot in threephase stator coordinate axis (static coordinate axle), go to describe, therefore for stator magnetic linkage DC component, stator side electric weight is pressed to frequency reduction to rotor-side, can directly with stator and rotor magnetic linkage relation derivation, go out short-circuit current expression formula, thereby simplify the derivation of DFIG three-phase shortcircuit current expression.

Accompanying drawing explanation

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

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

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

A kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current, the Static Equivalent circuit that the method utilizes the reduction of double fed induction generators stator magnetic linkage forced component to form to rotor-side to stator side, the reduction of stator magnetic linkage DC component, while analyzing rotor resistance on fault stator magnetic linkage DC component dynamic attenuation and with the impact of rotor winding induction process, thereby the analytical expression of double fed induction generators stator short-circuit current while deriving electrical network three-phase shortcircuit.Concrete steps are as follows:

Step 1: double fed induction generators stator magnetic linkage forced component reduction to stator side, stator magnetic linkage DC component reduction to rotor-side formed to Static Equivalent circuit, thereby release the damping time constant T of rotor flux reverse rotation transient state periodic component and stator magnetic linkage DC component _s, and rotor flux DC component damping time constant T _r;

Step 2: utilize Static Equivalent circuit, set up the relation between stator and rotor electric current and magnetic linkage, double fed induction generators stator short-circuit current analytic expression while deriving electrical network three-phase shortcircuit;

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

Wherein, the concrete steps of step 1 are:

Fig. 1 is that the reduction of stator magnetic linkage forced component is to the equivalent circuit of stator synchronously rotating reference frame, because rotor frequency is different, must be by rotor equivalent circuit by frequency reduction to stator side (when impedance adopts perunit value need not winding reduction), in like manner for stator magnetic linkage DC component, stator side electric weight is pressed to frequency reduction to rotor-side, can obtain the reduction of Fig. 2 stator magnetic linkage DC component to the equivalent circuit of rotor coordinate.In Fig. 1

for the stator current of reduction to stator side,

for the rotor current of reduction to stator side, in Fig. 2

for the stator current reversal periods component of reduction to rotor-side,

for the rotor current reversal periods component of reduction to rotor-side, L _mfor magnetizing inductance, L _lsfor stator leakage inductance, L _lrfor rotor leakage inductance, R _rfor rotor resistance, ω _rfor rotor electric angle speed, slip s=1-ω _r/ ω, R _efor DFIG is to transformer between access point and circuit equivalent resistance, L _efor DFIG is to transformer between access point and circuit equivalent inductance.From stator side, see that equiva lent impedance can try to achieve the damping time constant T of rotor flux reverse rotation transient state periodic component and stator magnetic linkage DC component _s:

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

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

In formula: R _sdfor the equiva lent impedance of seeing from stator side, j's is plural number sign, ω _rfor rotor electric angle speed, L _sdfor the equivalent inductance of seeing from stator side, R _efor double fed induction generators is to transformer between access point and circuit equivalent resistance, R _sfor stator resistance, L _efor double fed induction generators is to transformer between access point and circuit equivalent inductance, L _mfor magnetizing inductance, L _lsfor stator leakage inductance, 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 inductor generator rotor resistance R _rvery little (differing more than 100 times with magnetizing inductance), stator magnetic linkage DC component damping time constant T _s=(L _s-L _m ²/ L _r)/(R _s+ R _e).

From rotor-side, see that equiva lent impedance is:

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

In formula: R _rdfor the equiva lent impedance of seeing from rotor-side, L _rdfor the equivalent inductance of seeing from rotor-side, due to the equivalent resistance R of stator resistance with access transformer, circuit _s+ R _e<< ω _r(L _ls+ L _e) (both compare perunit value differ more than 20 times) 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 _rcan be approximately:

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

And the concrete steps of step 2 are:

Utilize rotor Static Equivalent circuit, set up the relation between stator and rotor current and magnetic linkage, DFIG stator short-circuit current analytic expression while deriving electrical network three-phase shortcircuit.Generator voltage direction of current is pressed Motor convention, adopts means of space vector representation can obtain after three phase short circuit fault double fed induction generators stator voltage equation under stator coordinate to be:

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

In formula: u ' _s(t) be stator voltage after fault, i ' _s(t) be stator current after fault, ψ ' _s(t) be the space vector of stator magnetic linkage forced component after fault,

for stator voltage phasor, e is nature exponential symbol, and t is working time, and ω is synchronous electric angular velocity, R _sfor stator resistance.

Ignore stator resistance R _s, by formula (5), can obtain stator magnetic linkage forced component after fault

if double fed induction generators terminal voltage is while normally moving

electric network fault rear end voltage step is changed to

by voltage substitution formulas (5) before and after fault double fed induction generators stator magnetic linkage ψ after three-phase shortcircuit _s(t) be:

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

Again according to the rotor current of stator side in Fig. 1 and Fig. 2 Static Equivalent circuit

the rotor current reversal periods component of rotor-side stator current with stator side

the stator current reversal periods component of rotor-side

pass is:

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

In conjunction with ψ _s(t)=L _si _s(t)+L _mi _rand ψ (t) _r(t)=L _mi _s(t)+L _ri _r(t) obtain rotor flux forced component ψ _rfand transient state reversal periods component ψ (t) _rd(t) be,

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

In formula: i _s(t) be stator side electric current, i _r(t) be rotor-side electric current, ψ _r(t) rotor flux, ψ _sf(t) be stator magnetic linkage forced component (frequency reduction is to stator synchronous coordinate), ψ _sd(t) be stator magnetic linkage DC component (reduction is to rotor coordinate).If double fed induction generators initial speed is ω during fault _r0, according to rotor flux conservation, can obtain stator coordinate lower rotor part magnetic linkage ψ after three-phase shortcircuit _r(t) be,

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

In formula: η _ffor the related coefficient of stator coordinate lower rotor part magnetic linkage forced component and stator magnetic linkage forced component, η _drelated coefficient for rotor coordinate lower rotor part magnetic linkage DC component and stator magnetic linkage DC component;

By double fed induction generators stator magnetic linkage, rotor flux and current relationship, there is i again _s(t)=[L _rψ _s(t)-L _mψ _r(t)]/(L _sl _r-L _m ²), formula (6) and formula (9) substitution can be obtained to rear double fed induction generators three-phase shortcircuit current space vector i _s(t) expression formula is,

In formula: A ₁for the amplitude of synchronizing frequency periodic component, A ₂for the amplitude of rotor frequency periodic component, A ₃for the amplitude of DC component,

for the phase place of synchronizing frequency periodic component, for the phase place of rotor frequency periodic component, phase place for DC component.

The concrete steps of step 3 are:

The attenuating dc component of stator magnetic linkage resolves into several frequencies omega _dlow frequency component close to 0,0< ω _d<< ω (close to 0), for stator magnetic linkage ω _dfrequency component reduction is similar to the Static Equivalent circuit of stator side to stator side equivalent circuit and the reduction of Fig. 1 stator magnetic linkage forced component, and in the Static Equivalent circuit that only stator magnetic linkage DC component reduction to rotor-side must be formed, ω replaces with ω _d, slip s replaces with 1-ω _r/ ω _d, can obtain accordingly, reduction is to stator side rotor current

with stator current

pass is:

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

Again by ψ _s(t)=L _si _s(t)+L _mi _rand ψ (t) _r(t)=L _mi _s(t)+L _ri _r(t) can obtain, under stator coordinate, the related coefficient of rotor magnetic linkage attenuating dc component is:

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

In formula: ψ _rd(t) be rotor flux DC component, ψ _sd(t) be stator magnetic linkage DC component;

Work as ω _dlevel off under 0 o'clock stator coordinate both related coefficient, with in formula (8), it equates to be in the situation under rotor coordinate:

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

Because each low frequency amount in stator magnetic linkage attenuating dc component meets 0< ω _d<< ω, can think under stator and rotor coordinate both ratio approximately equal, the related coefficient of the rotor magnetic linkage attenuating dc component that hence one can see that derives under rotor coordinate can substitute the related coefficient of rotor magnetic linkage attenuating dc component under stator coordinate, makes rotor and stator magnetic linkage related coefficient η _fand η _deven if also can not carry out computing under same coordinate, thereby simplified the derivation of DFIG three-phase shortcircuit current expression.

Finally explanation is, above embodiment is only unrestricted in order to technical scheme of the present invention to be described, although the present invention is had been described in detail with reference to preferred embodiment, those of ordinary skill in the art is to be understood that, can modify or be equal to replacement technical scheme of the present invention, and not departing from aim and the scope of technical solution of the present invention, it all should be encompassed in the middle of claim scope of the present invention.

Claims (4)

1. determine the magnetic linkage analytic method containing double fed induction generators three-phase shortcircuit electric current, it is characterized in that, comprise the steps:

Step 1: by the reduction of double fed induction generators stator magnetic linkage forced component to stator side, stator magnetic linkage DC component reduction to rotor-side forms Static Equivalent circuit, thereby releases the damping time constant T of rotor flux reverse rotation transient state periodic component and stator magnetic linkage DC component _s, and rotor flux DC component damping time constant T _r;

Step 2: utilize Static Equivalent circuit, set up the relation between stator and rotor electric current and magnetic linkage, double fed induction generators stator short-circuit current analytic expression while deriving electrical network three-phase shortcircuit;

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

2. a kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current according to claim 1, is characterized in that, the concrete steps of described step 1 are:

Rotor equivalent circuit is pressed to frequency reduction to stator side, for stator magnetic linkage DC component, stator side electric weight is pressed to frequency reduction to rotor-side, can obtain the reduction of stator magnetic linkage DC component to the equivalent circuit of rotor coordinate, from stator side equiva lent impedance, can try to achieve the damping time constant T of rotor flux reverse rotation transient state periodic component and stator magnetic linkage DC component _s:

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

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

In formula: R _sdfor the equiva lent impedance of seeing from stator side, j's is complex symbol, ω _rfor rotor electric angle speed, L _sdfor the equivalent inductance of seeing from stator side, R _efor double fed induction generators is to transformer between access point and circuit equivalent resistance, R _sfor stator resistance, L _efor double fed induction generators is to transformer between access point and circuit equivalent inductance, L _mfor magnetizing inductance, L _lsfor stator leakage inductance, 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 inductor generator rotor resistance R _rvery little, 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, be:

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

In formula: R _rdfor the equiva lent impedance of seeing from rotor-side, L _rdfor the equivalent inductance of seeing from rotor-side, due to generally, the equivalent resistance R of stator resistance and access transformer, circuit _s+ R _e<< ω _r(L _ls+ L _e) and L _s=L _ls+ L _e+ L _m>>L _e, rotor flux DC component damping time constant T now _rcan be approximately:

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

3. a kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current according to claim 1, is characterized in that, the concrete steps of described step 2 are:

Generator voltage direction of current is pressed Motor convention, adopts means of space vector representation can obtain after three phase short circuit fault double fed induction generators stator voltage equation under stator coordinate to be:

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

In formula: u' _s(t) be stator voltage after fault, i' _s(t) be stator current after fault, ψ ' _s(t) be the space vector of stator magnetic linkage forced component after fault,

for stator voltage phasor, e is nature exponential symbol, and t is working time, and ω is synchronous electric angular velocity, R _sfor stator resistance;

Ignore stator resistance R _s, by formula (5), can obtain stator magnetic linkage forced component after fault

if double fed induction generators terminal voltage is while normally moving electric network fault rear end voltage step is changed to

by voltage substitution formulas (5) before and after fault double fed induction generators stator magnetic linkage ψ after three-phase shortcircuit _s(t) be:

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

Again according to the rotor current of stator side in Static Equivalent circuit

the rotor current reversal periods component of rotor-side

stator current with stator side the stator current reversal periods component of rotor-side

pass is:

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

In conjunction with ψ _s(t)=L _si _s(t)+L _mi _rand ψ (t) _r(t)=L _mi _s(t)+L _ri _r(t) obtain rotor flux forced component ψ _rfand transient state reversal periods component ψ (t) _rd(t) be,

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

In formula: i _s(t) be stator side electric current, i _r(t) be rotor-side electric current, ψ _r(t) rotor flux, ψ _sf(t) be stator magnetic linkage forced component, ψ _sd(t) be stator magnetic linkage DC component, while establishing fault, double fed induction generators initial speed is ω _r0, according to rotor flux conservation, can obtain stator coordinate lower rotor part magnetic linkage ψ after three-phase shortcircuit _r(t) be,

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

In formula: η _ffor the related coefficient of stator coordinate lower rotor part magnetic linkage forced component and stator magnetic linkage forced component, η _drelated coefficient for rotor coordinate lower rotor part magnetic linkage DC component and stator magnetic linkage DC component;

By double fed induction generators stator magnetic linkage, rotor flux and current relationship, there is i again _s(t)=[L _rψ _s(t)-L _mψ _r(t)]/(L _sl _r-L _m ²), formula (6) and formula (9) substitution can be obtained to double fed induction generators three-phase shortcircuit current space vector i _s(t) expression formula is,

In formula: A ₁for the amplitude of synchronizing frequency periodic component, A ₂for the amplitude of rotor frequency periodic component, A ₃for the amplitude of DC component, for the phase place of synchronizing frequency periodic component,

for the phase place of rotor frequency periodic component, phase place for DC component.

4. a kind of magnetic linkage analytic method of determining containing double fed induction generators three-phase shortcircuit electric current according to claim 1, is characterized in that, the concrete steps of described step 3 are:

The attenuating dc component of stator magnetic linkage resolves into several frequencies omega _dlow frequency component close to 0,0< ω _d<< ω, for stator magnetic linkage ω _dfrequency component reduction is similar to the Static Equivalent circuit of stator side to stator side equivalent circuit and the reduction of stator magnetic linkage forced component, and in the Static Equivalent circuit that stator magnetic linkage DC component reduction to rotor-side is formed, ω replaces with ω _d, slip s replaces with 1-ω _r/ ω _d, can obtain accordingly, reduction is to stator side rotor current

with stator current

pass is:

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

Again by ψ _s(t)=L _si _s(t)+L _mi _rand ψ (t) _r(t)=L _mi _s(t)+L _ri _r(t) can obtain, under stator coordinate, the related coefficient of rotor magnetic linkage attenuating dc component is:

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

In formula: ψ _rd(t) be rotor flux DC component, ψ _sd(t) be stator magnetic linkage DC component;

Work as ω _dlevel off under 0 o'clock stator coordinate both related coefficient, with in formula (8), it equates to be in the situation under rotor coordinate:

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

Because each low frequency amount in stator magnetic linkage attenuating dc component meets 0< ω _d<< ω, can think under stator and rotor coordinate both ratio approximately equal.

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