CN103698586A

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

Info

Publication number: CN103698586A
Application number: CN201410020446.0A
Authority: CN
Inventors: 周念成; 谢光莉; 王强钢; 罗艾青; 周川
Original assignee: Chongqing University
Current assignee: Chongqing University
Priority date: 2014-01-15
Filing date: 2014-01-15
Publication date: 2014-04-02
Anticipated expiration: 2034-01-15
Also published as: CN103698586B

Abstract

The invention discloses a flux linkage analysis method for determining the three-phase short-circuit current of a doubly-fed induction generator, which analyzes the electromagnetic transient model of the doubly-fed induction generator (DFIG) and the fault transient characteristics of the flux linkage of the stator and rotor. After the fault, the DC component of the DFIG stator flux linkage will induce an AC flux linkage in the opposite direction to the rotational speed in the rotor winding, which cannot be described in the three-phase stator coordinate axis (stationary coordinate axis), and the forced component of the DFIG stator flux linkage needs to be attributed to On the stator side, the DC component of the stator flux linkage is reduced to the rotor side to form a static equivalent circuit, and then the influence of the rotor resistance on the dynamic attenuation of the DC component of the stator flux linkage and the induction process with the rotor winding during a fault is analyzed. Analytical expression of DFIG stator short-circuit current.

Description

A Flux Linkage Analysis Method for Determining Three-phase Short-Circuit Current of Double-fed Induction Generator

技术领域technical field

本发明涉及风力发电系统技术领域，尤其涉及一种确定含双馈感应发电机三相短路电流的磁链解析方法。The invention relates to the technical field of wind power generation systems, in particular to a flux linkage analysis method for determining the three-phase short-circuit current of a doubly-fed induction generator.

背景技术Background technique

风力发电作为目前最具商业化发展前景的新能源技术，在全球以每年超过30%的速度增长并成为发展最快的清洁能源。风能资源的大力开发推动了风力机的迅速发展，双馈感应发电机（DFIG）便是现阶段风力发电中运用较为广泛的一种风力机型，它具有效率高、变流器容量小、功率解耦控制等诸多优点，但另一方面并网型双馈风电机组在并网电压突降时所表现出来的暂态特性相当复杂，这就对含有高渗透率分布式风电机组的配电网保护提出了挑战。As the new energy technology with the most commercial development prospects, wind power has grown at a rate of more than 30% per year globally and has become the fastest-growing clean energy. The vigorous development of wind energy resources has promoted the rapid development of wind turbines. The double-fed induction generator (DFIG) is a wind turbine model widely used in wind power generation at the present stage. It has high efficiency, small converter capacity, and high power. decoupling control and many other advantages, but on the other hand, the transient characteristics of the grid-connected doubly-fed wind turbines are quite complex when the grid-connected voltage drops suddenly, which is very difficult for the distribution network with high-permeability distributed wind turbines. Conservation presents challenges.

当风电场大规模的接入系统后，变压器、线路阻抗器以及断路器等电气设备的动、热稳定性校验主要依靠系统的短路电流计算，其中一个重要问题是需要了解风电场在故障过程中的短路电流特性，包括最大冲击电流的幅值、故障稳态周期分量的幅值、暂态分量衰减时间常数等，因此研究DFIG短路电流解析式很重要。When the wind farm is connected to the system on a large scale, the dynamic and thermal stability verification of electrical equipment such as transformers, line impedances, and circuit breakers mainly depends on the calculation of the short-circuit current of the system. One of the important issues is to understand the fault process of the wind farm. The short-circuit current characteristics in DFIG include the amplitude of the maximum inrush current, the amplitude of the fault steady-state periodic component, the decay time constant of the transient component, etc. Therefore, it is very important to study the analytical formula of DFIG short-circuit current.

目前研究DFIG短路电流解析式的方法主要有频域计算和物理过程分析两种方法，由于定转子频率不同，无法在三相定子坐标轴（静止坐标轴）中去描述。At present, the research methods of DFIG short-circuit current analysis mainly include frequency domain calculation and physical process analysis. Due to the difference in stator and rotor frequency, it cannot be described in the three-phase stator coordinate axis (stationary coordinate axis).

发明内容Contents of the invention

针对现有技术中存在的上述不足，本发明提供了一种确定含双馈感应发电机三相短路电流的磁链解析方法，利用等效电路分析定、转子磁链之间的关系，使得双馈感应发电机三相短路电流表达式推导过程更为简便。Aiming at the above-mentioned deficiencies in the prior art, the present invention provides a flux analysis method for determining the three-phase short-circuit current of a doubly-fed induction generator, which uses an equivalent circuit to analyze the relationship between the stator and rotor flux, so that the double The derivation process of three-phase short-circuit current expression of fed induction generator is more convenient.

为了解决上述技术问题，本发明采用了如下技术方案：In order to solve the above technical problems, the present invention adopts the following technical solutions:

一种确定含双馈感应发电机三相短路电流的磁链解析方法，包括如下步骤：A flux linkage analysis method for determining the three-phase short-circuit current of a doubly-fed induction generator comprises the following steps:

步骤一：将双馈感应发电机定子磁链强制分量归算至定子侧、定子磁链直流分量归算至转子侧形成静态等值电路，从而推出转子磁链反向旋转暂态周期分量与定子磁链直流分量的衰减时间常数T_s，以及转子磁链直流分量衰减时间常数T_r；Step 1: The forced component of the stator flux linkage of the doubly-fed induction generator is reduced to the stator side, and the DC component of the stator flux linkage is reduced to the rotor side to form a static equivalent circuit, thereby deducing the reverse rotation transient period component of the rotor flux linkage and the stator The decay time constant T _s of the DC component of the flux linkage, and the decay time constant T _r of the DC component of the rotor flux linkage;

步骤二：利用静态等值电路，建立定、转子电流及磁链之间的关系，推导出电网三相短路时双馈感应发电机定子短路电流解析式的；Step 2: use the static equivalent circuit to establish the relationship between the stator and rotor currents and flux linkage, and deduce the analytical formula for the short-circuit current of the stator of the doubly-fed induction generator when the three-phase short circuit of the power grid;

步骤三：分析定子与转子磁链相关系数之间的关系，验证定子坐标下定、转子磁链衰减直流分量的相关系数可以用转子坐标下定、转子磁链衰减直流分量的相关系数代替。Step 3: Analyze the relationship between the correlation coefficients of stator and rotor flux linkages, and verify that the correlation coefficients of stator coordinates and rotor flux attenuation DC components can be replaced by the correlation coefficients of rotor coordinates and rotor flux attenuation DC components.

作为本发明的一种优选方案，所述步骤一的具体步骤为：As a preferred solution of the present invention, the specific steps of said step one are:

将转子等效电路按频率归算至定子侧，对于定子磁链直流分量，将定子侧电量按频率归算至转子侧，可得定子磁链直流分量归算至转子坐标的等值电路，从定子侧等效阻抗可求得转子磁链反向旋转暂态周期分量与定子磁链直流分量的衰减时间常数T_s：The equivalent circuit of the rotor is reduced to the stator side according to the frequency, and for the DC component of the stator flux linkage, the electric quantity of the stator side is reduced to the rotor side according to the frequency, and the equivalent circuit of the DC component of the stator flux linkage to the rotor coordinates can be obtained, from The equivalent impedance on the stator side can be obtained from the decay time constant T _s of the transient periodic component of the rotor flux reverse rotation and the DC component of the stator flux:

${R R}_{sd sd} - - j j {ω ω}_{r r} {L L}_{sd sd} = = {R R}_{e e} + + {R R}_{s the s} - - j j {ω ω}_{r r} (({L L}_{e e} + + {L L}_{ls ls})) + + \frac{- - j j {ω ω}_{r r} {L L}_{m m} (({R R}_{r r} - - j j {ω ω}_{r r} {L L}_{lr lr}))}{{R R}_{r r} - - j j {ω ω}_{r r} (({L L}_{lr lr} + + {L L}_{m m}))} - - - - - - ((11))$

${T T}_{s the s} = = \frac{{L L}_{sd sd}}{{R R}_{sd sd}} = = \frac{{L L}_{s the s} {R R}_{r r}^{22} + + {ω ω}_{r r}^{22} {L L}_{r r} (({L L}_{s the s} {L L}_{r r} - - {L L}_{m m}^{22}))}{(({R R}_{s the s} + + {R R}_{e e})) {R R}_{r r}^{22} + + {ω ω}_{r r}^{22} {L L}_{m m}^{22} {R R}_{r r} + + {ω ω}_{r r}^{22} {L L}_{r r}^{22} (({R R}_{s the s} + + {R R}_{e e}))} - - - - - - ((22))$

式中：R_sd为从定子侧看的等效阻抗，j的为复数标志，ω_r为转子电角速度，L_sd为从定子侧看的等效电感，R_e为双馈感应发电机至接入点间变压器及线路等效电阻，R_s为定子电阻，L_e为双馈感应发电机至接入点间变压器及线路等效电感，L_m为励磁电感，L_ls为定子漏电感，L_lr为转子漏电感，R_r为转子电阻，L_s=L_ls+L_e+L_m，L_r=L_lr+L_m；In the formula: R _sd is the equivalent impedance seen from the stator side, j is the complex number sign, ω _r is the rotor electrical angular velocity, L _sd is the equivalent inductance seen from the stator side, Re _is the doubly-fed induction generator to the ground Transformer and line equivalent resistance between the input point, R _s is the stator resistance, L _e is the equivalent inductance of the transformer and line between the double-fed induction generator and the access point, L _m is the excitation inductance, L _ls is the stator leakage inductance, L _lr is the rotor leakage inductance, R _r is the rotor resistance, L _s =L _ls +L _e +L _m , L _r =L _lr +L _m ;

对于定速感应发电机转子电阻R_r很小（与励磁电感相差100倍以上），则定子磁链直流分量衰减时间常数T_s=(L_s-L_m ²/L_r)/(R_s+R_e)；For the rotor resistance R _r of the fixed speed induction generator is very small (more than 100 times the difference from the excitation inductance), then the decay time constant of the DC component of the stator flux linkage T _s =(L _s -L _m ² /L _r )/(R _s + R _e );

从转子侧等效阻抗为：The equivalent impedance from the rotor side is:

${R R}_{rd rd} + + j j {ω ω}_{r r} {L L}_{rd rd} = = {R R}_{r r} + + j j {ω ω}_{r r} {L L}_{lr lr} + + \frac{j j {ω ω}_{r r} {L L}_{m m} [[(({R R}_{s the s} + + {R R}_{e e})) + + j j {ω ω}_{r r} (({L L}_{ls ls} + + {L L}_{e e}))]]}{{R R}_{s the s} + + {R R}_{e e} + + j j {ω ω}_{r r} (({L L}_{ls ls} + + {L L}_{e e} + + {L L}_{m m}))} - - - - - - ((33))$

式中：R_rd为从转子侧看的等效阻抗，L_rd为从转子侧看的等效电感，由于定子电阻和接入变压器、线路的等效电阻R_s+R_e<<ω_r(L_ls+L_e)且L_s=L_ls+L_e+L_m>>L_e，此时转子磁链直流分量衰减时间常数T_r可近似为：In the formula: R _rd is the equivalent impedance seen from the rotor side, L _rd is the equivalent inductance seen from the rotor side, due to the stator resistance and the equivalent resistance of the connected transformer and line R _s +R _e <<ω _r ( L _ls +L _e ) and L _s =L _ls +L _e +L _m >>L _e , at this time the rotor flux DC component decay time constant T _r can be approximated as:

${T T}_{r r} = = \frac{{L L}_{rd rd}}{{R R}_{rd rd}} \approx \approx \frac{{L L}_{s the s} {L L}_{r r} - - {L L}_{m m}^{22}}{{L L}_{s the s} {R R}_{r r}} - - - - - - ((44)) . .$

作为本发明的另一种优选方案，所述步骤二的具体步骤为：As another preferred solution of the present invention, the specific steps of said step 2 are:

发电机电压电流方向按电动机惯例，采用空间矢量法可得三相短路故障后定子坐标系下双馈感应发电机定子电压方程为：The direction of voltage and current of the generator is in accordance with the motor convention, and the stator voltage equation of the doubly-fed induction generator in the stator coordinate system after the three-phase short-circuit fault can be obtained by using the space vector method:

${u u}_{s the s}^{' '} ((t t)) = = {\overset{\cdot \cdot}{U u}}_{s the s}^{' '} {e e}^{jωt jωt} = = {R R}_{s the s} {i i}_{s the s}^{' '} ((t t)) + + \frac{d d}{dt dt} {ψ ψ}_{s the s}^{' '} ((t t)) - - - - - - ((55))$

式中：u'_s(t)为故障后定子电压，i'_s(t)为故障后定子电流，ψ'_s(t)为故障后定子磁链强制分量的空间矢量，

为定子电压相量，e为自然幂数符号，t为运行时间，ω为同步电角速度，R_s为定子电阻；In the formula: u' _s (t) is the stator voltage after the fault, i' _s (t) is the stator current after the fault, ψ' _s (t) is the space vector of the forced component of the stator flux linkage after the fault,

is the stator voltage phasor, e is the natural power symbol, t is the running time, ω is the synchronous electrical angular velocity, R _s is the stator resistance;

忽略定子电阻R_s，由式（5）可得故障后定子磁链强制分量

设正常运行时双馈感应发电机端电压为

电网故障后端电压阶跃变化至

将故障前后电压代入式（5）得三相短路后双馈感应发电机定子磁链ψ_s(t)为：Neglecting the stator resistance R _s , the forced component of the stator flux linkage after the fault can be obtained from formula (5):

Assuming that the terminal voltage of the doubly-fed induction generator is

After the power grid fault, the terminal voltage changes step by step to

Substituting the voltage before and after the fault into formula (5), the stator flux linkage ψ _s (t) of the doubly-fed induction generator after the three-phase short circuit is:

${ψ ψ}_{s the s} ((t t)) = = \frac{{\overset{\cdot \cdot}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{jωt jωt} + + \frac{{\overset{\cdot \cdot}{U u}}_{s the s} - - {\overset{\cdot \cdot}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{- - t t / / {T T}_{s the s}} - - - - - - ((66))$

再根据静态等值电路中定子侧的转子电流

转子侧的转子电流反向周期分量

与定子侧的定子电流

转子侧的定子电流反向周期分量

关系为：Then according to the rotor current on the stator side in the static equivalent circuit

The reverse periodic component of the rotor current on the rotor side

Stator current with stator side

The reverse periodic component of the stator current on the rotor side

The relationship is:

${\overset{\cdot &Center Dot;}{I I}}_{rf rf} = = \frac{- - jω jω {L L}_{m m} {\overset{\cdot \cdot}{I I}}_{sf sf}}{{R R}_{r r} / / ((11 - - {ω ω}_{r r} / / ω ω)) + + jω jω {L L}_{r r}},, {\overset{\cdot \cdot}{I I}}_{rd rd} = = \frac{j j {ω ω}_{r r} {L L}_{m m} {\overset{\cdot \cdot}{I I}}_{sd sd}}{{R R}_{r r} - - j j {ω ω}_{r r} {L L}_{r r}} - - - - - - ((77))$

结合ψ_s(t)=L_si_s(t)+L_mi_r(t)和ψ_r(t)=L_mi_s(t)+L_ri_r(t)得转子磁链强制分量ψ_rf(t)和暂态反向周期分量ψ_rd(t)为，Combining ψ _s (t)=L _s i _s (t)+L _m i _r (t) and ψ _r (t)=L _m i _s (t)+L _r i _r (t) to get the forced component of rotor flux linkage ψ _rf (t) and the transient reverse periodic component ψ _rd (t) are,

$\begin{matrix} {ψ ψ}_{rf rf} ((t t)) = = \frac{{L L}_{m m} {R R}_{r r} / / ((11 - - {ω ω}_{r r} / / ω ω)) \cdot \cdot {ψ ψ}_{sf sf} ((t t))}{{L L}_{s the s} {R R}_{r r} / / ((11 - - {ω ω}_{r r} / / ω ω)) + + jω jω (({L L}_{s the s} {L L}_{r r} {L L}_{m m}^{22}))} = = {η η}_{f f} (({ω ω}_{r r})) {ψ ψ}_{sf sf} ((t t)) \\ {ψ ψ}_{rd rd} ((t t)) = = \frac{{L L}_{m m} {R R}_{r r} \cdot \cdot {ψ ψ}_{sd sd} ((t t))}{{L L}_{s the s} {R R}_{r r} + + j j {ω ω}_{r r} (({L L}_{m m}^{22} - - {L L}_{s the s} {L L}_{r r}))} = = {η η}_{d d} (({ω ω}_{r r})) {ψ ψ}_{sd sd} ((t t)) \end{matrix} - - - - - - ((88))$

式中：i_s(t)为定子侧电流，i_r(t)为转子侧电流，ψ_r(t)的转子磁链，ψ_sf(t)为定子磁链强制分量(频率归算至定子同步坐标)，ψ_sd(t)为定子磁链直流分量(归算至转子坐标)，设故障时双馈感应发电机初始转速为ω_r0，根据转子磁链守恒，可得三相短路后定子坐标下转子磁链ψ_r(t)为，In the formula: i _s (t) is the stator side current, i _r (t) is the rotor side current, ψ _r (t) is the rotor flux, ψ _sf (t) is the forced component of the stator flux (the frequency is reduced to the stator Synchronous coordinates), ψ _sd (t) is the DC component of the stator flux (reduced to the rotor coordinates), and the initial speed of the doubly-fed induction generator is ω _r0 when the fault occurs. According to the conservation of the rotor flux linkage, the stator after a three-phase short circuit The rotor flux linkage ψ _r (t) in coordinates is,

$\begin{matrix} {ψ ψ}_{r r} ((t t)) = = {η η}_{f f} (({ω ω}_{r r})) \frac{{\overset{\cdot &Center Dot;}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{jωt jωt} + + {η η}_{d d} (({ω ω}_{r r})) \frac{{\overset{\cdot \cdot}{U u}}_{s the s} - - {\overset{\cdot \cdot}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{- - t t / / {T T}_{s the s}} \\ + + [[{η η}_{f f} (({ω ω}_{r r 00})) - - {η η}_{d d} (({ω ω}_{r r 00}))]] \frac{{\overset{\cdot &Center Dot;}{U u}}_{s the s} - - {\overset{\cdot &Center Dot;}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{- - t t / / {T T}_{s the s}} {e e}^{j j {ω ω}_{r r} t t} \end{matrix} - - - - - - ((99))$

式中：η_f为定子坐标下转子磁链强制分量与定子磁链强制分量的相关系数，η_d为转子坐标下转子磁链直流分量与定子磁链直流分量的相关系数；In the formula: η _f is the correlation coefficient between the forced component of the rotor flux linkage and the forced component of the stator flux linkage under the stator coordinates, and η _d is the correlation coefficient between the DC component of the rotor flux linkage and the DC component of the stator flux linkage under the rotor coordinates;

再由双馈感应发电机定子磁链、转子磁链与电流关系有i_s(t)=[L_rψ_s(t)-L_mψ_r(t)]/(L_sL_r-L_m ²)，将式（6）和式（9）代入可得双馈感应发电机三相短路电流空间矢量i_s(t)表达式为，Then, the relationship between stator flux linkage, rotor flux linkage and current of doubly-fed induction generator is i _s (t)=[L _r ψ _s (t)-L _m ψ _r (t)]/(L _s L _r -L _m ² ), substituting formula (6) and formula (9) into the three-phase short-circuit current space vector i _s (t) of doubly-fed induction generator can be expressed as,

式中：A₁为同步频率周期分量的幅值，A₂为转子频率周期分量的幅值，A₃为直流分量的幅值，

为同步频率周期分量的相位，

为转子频率周期分量的相位，

为直流分量的相位。In the formula: A ₁ is the amplitude of the periodic component of the synchronous frequency, A ₂ is the amplitude of the periodic component of the rotor frequency, A ₃ is the amplitude of the DC component,

is the phase of the periodic component of the synchronous frequency,

is the phase of the periodic component of the rotor frequency,

is the phase of the DC component.

作为本发明的又一种优选方案，所述步骤三的具体步骤为：As another preferred solution of the present invention, the specific steps of the third step are:

定子磁链的衰减直流分量分解成若干个频率ω_d接近于0的低频分量，0<ω_d<<ω，则对于定子磁链ω_d频率分量归算至定子侧等值电路与定子磁链强制分量归算至定子侧的静态等值电路类似，将定子磁链直流分量归算至转子侧形成的静态等值电路中ω替换为ω_d，转差s替换为1-ω_r/ω_d，据此可得，归算至定子侧转子电流

与定子电流

关系为：The attenuated DC component of the stator flux linkage is decomposed into several low-frequency components whose frequency ω _d is close to 0, 0<ω _d <<ω, then the frequency component of the stator flux ω _d is reduced to the equivalent circuit on the stator side and the stator flux linkage The static equivalent circuit where the forced component is reduced to the stator side is similar. In the static equivalent circuit formed by reducing the stator flux DC component to the rotor side, ω is replaced by ω _d , and the slip s is replaced by 1-ω _r /ω _d , according to which it can be obtained that the rotor current reduced to the stator side

vs stator current

The relationship is:

${\overset{\cdot &Center Dot;}{I I}}_{rd rd} = = \frac{- - j j {ω ω}_{d d} {L L}_{m m} {\overset{\cdot &Center Dot;}{I I}}_{sd sd}}{{R R}_{r r} / / ((11 - - {ω ω}_{r r} / / {ω ω}_{d d})) + + j j {ω ω}_{d d} {L L}_{r r}} - - - - - - ((1111))$

再由ψ_s(t)=L_si_s(t)+L_mi_r(t)和ψ_r(t)=L_mi_s(t)+L_ri_r(t)可得，定子坐标下定转子磁链衰减直流分量的相关系数为：From ψ _s (t)=L _s i _s (t)+L _m i _r (t) and ψ _r (t)=L _m i _s (t)+L _r i _r (t), the stator coordinates The correlation coefficient of the attenuation DC component of the stator and rotor flux linkage is:

$\frac{{ψ ψ}_{rd rd} ((t t))}{{ψ ψ}_{sd sd} ((t t))} = = \frac{{L L}_{m m} {R R}_{r r} / / ((11 - - {ω ω}_{r r} / / {ω ω}_{d d}))}{{L L}_{s the s} {R R}_{r r} / / ((11 - - {ω ω}_{r r} / / {ω ω}_{d d})) + + j j {ω ω}_{d d} (({L L}_{s the s} {L L}_{r r} - - {L L}_{m m}^{22}))} = = \frac{{L L}_{m m} {R R}_{r r}}{{L L}_{m m} {R R}_{r r} + + j j (({ω ω}_{d d} - - {ω ω}_{r r})) (({L L}_{s the s} {L L}_{r r} - - {L L}_{m m}^{22}))} - - - - - - ((1212))$

式中：ψ_rd(t)为转子磁链直流分量，ψ_sd(t)为定子磁链直流分量；In the formula: ψ _rd (t) is the DC component of the rotor flux linkage, and ψ _sd (t) is the DC component of the stator flux linkage;

当ω_d趋近于0时定子坐标系下两者的相关系数，与式（8）中其在转子坐标系下的情况相等即为：When ω _d approaches 0, the correlation coefficient between the two in the stator coordinate system is equal to the situation in the rotor coordinate system in formula (8):

$\frac{{ψ ψ}_{rd rd} ((t t))}{{ψ ψ}_{sd sd} ((t t))} = = \frac{{L L}_{m m} {R R}_{r r}}{{L L}_{m m} {R R}_{r r} + + j j {ω ω}_{r r} (({L L}_{m m}^{22} - - {L L}_{s the s} {L L}_{r r}))} = = {η η}_{d d} (({ω ω}_{r r})) - - - - - - ((1313))$

由于定子磁链衰减直流分量中各低频量满足0<ω_d<<ω，可认为定子和转子坐标下两者的比例近似相等。Since the low-frequency quantities in the attenuation DC component of the stator flux linkage satisfy 0<ω _d <<ω, it can be considered that the proportions of the stator and rotor coordinates are approximately equal.

本发明的优点：本发明采用磁链分析法推导DFIG三相短路电流，电网故障后DFIG定子磁链直流分量将在转子绕组感应出与转速方向相反的交流磁链，由于定、转子频率不同，无法在三相定子坐标轴(静止坐标轴)中去描述，因此对于定子磁链直流分量，将定子侧电量按频率归算至转子侧后，可直接用定、转子磁链关系推导出短路电流表达式，从而简化了DFIG三相短路电流表达式的推导过程。Advantages of the present invention: the present invention adopts the flux linkage analysis method to deduce the DFIG three-phase short-circuit current. After the power grid fails, the DC component of the DFIG stator flux linkage will induce an AC flux linkage opposite to the direction of the rotating speed in the rotor winding. Because the stator and rotor frequencies are different, It cannot be described in the three-phase stator coordinate axis (stationary coordinate axis). Therefore, for the DC component of the stator flux linkage, the short-circuit current can be directly derived from the relationship between the stator and rotor flux linkage after the stator side power is transferred to the rotor side according to the frequency. The expression thus simplifies the derivation process of the DFIG three-phase short-circuit current expression.

附图说明Description of drawings

图1为定子磁链强制分量归算至定子侧等值电路；Figure 1 is the equivalent circuit for the calculation of the forced component of the stator flux linkage to the stator side;

图2为定子磁链直流分量归算至转子侧等值电路。Figure 2 is the equivalent circuit for the calculation of the DC component of the stator flux linkage to the rotor side.

具体实施方式Detailed ways

下面结合附图和具体实施方式对本发明作进一步详细地描述。The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

一种确定含双馈感应发电机三相短路电流的磁链解析方法，该方法利用双馈感应发电机定子磁链强制分量归算至定子侧、定子磁链直流分量归算至转子侧形成的静态等值电路，分析转子电阻对故障时定子磁链直流分量动态衰减及其与转子绕组感应过程的影响，从而推导出电网三相短路时双馈感应发电机定子短路电流的解析表达式。具体步骤如下：A flux linkage analysis method for determining the three-phase short-circuit current of a doubly-fed induction generator. This method uses the force component of the stator flux of the doubly-fed induction generator to be reduced to the stator side, and the DC component of the stator flux to be reduced to the rotor side. The static equivalent circuit analyzes the influence of the rotor resistance on the dynamic attenuation of the DC component of the stator flux linkage and the induction process with the rotor winding during a fault, and then deduces the analytical expression of the stator short-circuit current of the doubly-fed induction generator when the three-phase short-circuit of the grid is short-circuited. Specific steps are as follows:

步骤二：利用静态等值电路，建立定、转子电流及磁链之间的关系，推导出电网三相短路时双馈感应发电机定子短路电流解析式的；Step 2: Using the static equivalent circuit to establish the relationship between the stator and rotor currents and the flux linkage, deduce the analytical formula of the short-circuit current of the stator of the doubly-fed induction generator when the three-phase short circuit of the power grid;

步骤三：分析定子与转子磁链相关系数之间的关系，验证定子坐标下定、转子磁链衰减直流分量的相关系数可以用转子坐标下定、转子磁链衰减直流分量的相关系数代替。Step 3: Analyze the relationship between the stator and rotor flux correlation coefficients, and verify that the correlation coefficients of the stator coordinates and the rotor flux attenuation DC component can be replaced by the rotor coordinates and the rotor flux attenuation DC component correlation coefficient.

其中，步骤一的具体步骤为：Among them, the specific steps of step 1 are:

图1为定子磁链强制分量归算至定子同步旋转坐标的等值电路，由于定转子频率不同，须将转子等效电路按频率归算至定子侧（阻抗采用标幺值时无须绕组归算），同理对于定子磁链直流分量，将定子侧电量按频率归算至转子侧，可得图2定子磁链直流分量归算至转子坐标的等值电路。图1中

为归算至定子侧的定子电流，

为归算至定子侧的转子电流，图2中

为归算至转子侧的定子电流反向周期分量，

为归算至转子侧的转子电流反向周期分量，L_m为励磁电感，L_ls为定子漏电感，L_lr为转子漏电感，R_r为转子电阻，ω_r为转子电角速度，转差s=1-ω_r/ω，R_e为DFIG至接入点间变压器及线路等效电阻，L_e为DFIG至接入点间变压器及线路等效电感。从定子侧看等效阻抗可求得转子磁链反向旋转暂态周期分量与定子磁链直流分量的衰减时间常数T_s：Figure 1 is the equivalent circuit for the calculation of the forced component of the stator flux linkage to the synchronous rotation coordinates of the stator. Since the frequency of the stator and the rotor are different, the equivalent circuit of the rotor must be calculated to the stator side according to the frequency (when the impedance adopts the per unit value, the winding calculation is not required ), similarly, for the DC component of the stator flux linkage, the electricity on the stator side is reduced to the rotor side according to the frequency, and the equivalent circuit of the DC component of the stator flux linkage to the rotor coordinates in Figure 2 can be obtained. Figure 1

is the stator current attributed to the stator side,

is the rotor current attributed to the stator side, in Figure 2

is the reverse periodic component of the stator current attributed to the rotor side,

is the reverse periodic component of the rotor current attributed to the rotor side, L _m is the excitation inductance, L _ls is the stator leakage inductance, L _lr is the rotor leakage inductance, R _r is the rotor resistance, ω _r is the rotor electrical angular velocity, slip s =1-ω _r /ω, Re _is the transformer and line equivalent resistance between DFIG and access point, L _e is the transformer and line equivalent inductance between DFIG and access point. Looking at the equivalent impedance from the stator side, the decay time constant T _s of the transient periodic component of the rotor flux reverse rotation and the DC component of the stator flux can be obtained:

对于定速感应发电机转子电阻R_r很小（与励磁电感相差100倍以上），则定子磁链直流分量衰减时间常数T_s=(L_s-L_m ²/L_r)/(R_s+R_e)。For the rotor resistance R _r of the fixed speed induction generator is very small (more than 100 times the difference from the excitation inductance), then the decay time constant of the DC component of the stator flux linkage T _s =(L _s -L _m ² /L _r )/(R _s + R _e ).

从转子侧看等效阻抗为：The equivalent impedance seen from the rotor side is:

式中：R_rd为从转子侧看的等效阻抗，L_rd为从转子侧看的等效电感，由于定子电阻和接入变压器、线路的等效电阻R_s+R_e<<ω_r(L_ls+L_e)（两者相比较而言标幺值相差20倍以上）且L_s=L_ls+L_e+L_m>>L_e（标幺值相差20倍以上），此时转子磁链直流分量衰减时间常数T_r可近似为：In the formula: R _rd is the equivalent impedance seen from the rotor side, L _rd is the equivalent inductance seen from the rotor side, due to the stator resistance and the equivalent resistance of the connected transformer and line R _s +R _e <<ω _r ( L _ls + L _e ) (compared with the difference of more than 20 times per unit value) and L _s = L _ls + L _e + L _m >>L _e (the difference of more than 20 times per unit value), at this time the rotor The decay time constant T _r of the DC component of flux linkage can be approximated as:

而步骤二的具体步骤为：The specific steps of step two are:

利用定转子静态等值电路，建立定转子电流及磁链之间的关系，推导出电网三相短路时DFIG定子短路电流解析式的。发电机电压电流方向按电动机惯例，采用空间矢量法可得三相短路故障后定子坐标系下双馈感应发电机定子电压方程为：Using the static equivalent circuit of the stator and rotor, the relationship between the stator and rotor current and the flux linkage is established, and the analytic formula of the DFIG stator short-circuit current is deduced when the three-phase short circuit of the power grid occurs. The direction of voltage and current of the generator is in accordance with the motor practice, and the stator voltage equation of the doubly-fed induction generator in the stator coordinate system after the three-phase short-circuit fault can be obtained by using the space vector method:

${u u}_{s the s}^{' '} ((t t)) = = {\overset{\cdot &Center Dot;}{U u}}_{s the s}^{' '} {e e}^{jωt jωt} = = {R R}_{s the s} {i i}_{s the s}^{' '} ((t t)) + + \frac{d d}{dt dt} {ψ ψ}_{s the s}^{' '} ((t t)) - - - - - - ((55))$

式中：u’_s(t)为故障后定子电压，i’_s(t)为故障后定子电流，ψ’_s(t)为故障后定子磁链强制分量的空间矢量，

为定子电压相量，e为自然幂数符号，t为运行时间，ω为同步电角速度，R_s为定子电阻。In the formula: u' _s (t) is the stator voltage after the fault, i' _s (t) is the stator current after the fault, ψ' _s (t) is the space vector of the forced component of the stator flux linkage after the fault,

is the stator voltage phasor, e is the natural power symbol, t is the running time, ω is the synchronous electrical angular velocity, and R _s is the stator resistance.

忽略定子电阻R_s，由式（5）可得故障后定子磁链强制分量

设正常运行时双馈感应发电机端电压为

电网故障后端电压阶跃变化至

Assuming that the terminal voltage of the doubly-fed induction generator is

After the power grid fault, the terminal voltage changes step by step to

${ψ ψ}_{s the s} ((t t)) = = \frac{{\overset{\cdot &Center Dot;}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{jωt jωt} + + \frac{{\overset{\cdot &Center Dot;}{U u}}_{s the s} - - {\overset{\cdot &Center Dot;}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{- - t t / / {T T}_{s the s}} - - - - - - ((66))$

再根据图1和图2静态等值电路中定子侧的转子电流

转子侧的转子电流反向周期分量与定子侧的定子电流

转子侧的定子电流反向周期分量

关系为：Then according to the rotor current on the stator side in the static equivalent circuit in Figure 1 and Figure 2

The reverse periodic component of the rotor current on the rotor side Stator current with stator side

The reverse periodic component of the stator current on the rotor side

The relationship is:

${\overset{\cdot \cdot}{I I}}_{rf rf} = = \frac{- - jω jω {L L}_{m m} {\overset{\cdot \cdot}{I I}}_{sf sf}}{{R R}_{r r} / / ((11 - - {ω ω}_{r r} / / ω ω)) + + jω jω {L L}_{r r}},, {\overset{\cdot &Center Dot;}{I I}}_{rd rd} = = \frac{j j {ω ω}_{r r} {L L}_{m m} {\overset{\cdot \cdot}{I I}}_{sd sd}}{{R R}_{r r} - - j j {ω ω}_{r r} {L L}_{r r}} - - - - - - ((77))$

$\begin{matrix} {ψ ψ}_{rf rf} ((t t)) = = \frac{{L L}_{m m} {R R}_{r r} / / ((11 - - {ω ω}_{r r} / / ω ω)) \cdot &Center Dot; {ψ ψ}_{sf sf} ((t t))}{{L L}_{s the s} {R R}_{r r} / / ((11 - - {ω ω}_{r r} / / ω ω)) + + jω jω (({L L}_{s the s} {L L}_{r r} {L L}_{m m}^{22}))} = = {η η}_{f f} (({ω ω}_{r r})) {ψ ψ}_{sf sf} ((t t)) \\ {ψ ψ}_{rd rd} ((t t)) = = \frac{{L L}_{m m} {R R}_{r r} \cdot \cdot {ψ ψ}_{sd sd} ((t t))}{{L L}_{s the s} {R R}_{r r} + + j j {ω ω}_{r r} (({L L}_{m m}^{22} - - {L L}_{s the s} {L L}_{r r}))} = = {η η}_{d d} (({ω ω}_{r r})) {ψ ψ}_{sd sd} ((t t)) \end{matrix} - - - - - - ((88))$

式中：i_s(t)为定子侧电流，i_r(t)为转子侧电流，ψ_r(t)的转子磁链，ψ_sf(t)为定子磁链强制分量（频率归算至定子同步坐标），ψ_sd(t)为定子磁链直流分量（归算至转子坐标）。设故障时双馈感应发电机初始转速为ω_r0，根据转子磁链守恒，可得三相短路后定子坐标下转子磁链ψ_r(t)为，In the formula: i _s (t) is the stator side current, i _r (t) is the rotor side current, ψ _r (t) is the rotor flux linkage, ψ _sf (t) is the forced component of the stator flux linkage (the frequency is reduced to the stator Synchronous coordinates), ψ _sd (t) is the DC component of the stator flux linkage (reduced to the rotor coordinates). Assuming that the initial speed of the doubly-fed induction generator is ω _r0 when the fault occurs, according to the conservation of the rotor flux linkage, the rotor flux linkage ψ _r (t) in the stator coordinates after the three-phase short circuit can be obtained as,

$\begin{matrix} {ψ ψ}_{r r} ((t t)) = = {η η}_{f f} (({ω ω}_{r r})) \frac{{\overset{\cdot \cdot}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{jωt jωt} + + {η η}_{d d} (({ω ω}_{r r})) \frac{{\overset{\cdot \cdot}{U u}}_{s the s} - - {\overset{\cdot \cdot}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{- - t t / / {T T}_{s the s}} \\ + + [[{η η}_{f f} (({ω ω}_{r r 00})) - - {η η}_{d d} (({ω ω}_{r r 00}))]] \frac{{\overset{\cdot &Center Dot;}{U u}}_{s the s} - - {\overset{\cdot &Center Dot;}{U u}}_{s the s}^{' '}}{jω jω} {e e}^{- - t t / / {T T}_{s the s}} {e e}^{j j {ω ω}_{r r} t t} \end{matrix} - - - - - - ((99))$

再由双馈感应发电机定子磁链、转子磁链与电流关系有i_s(t)=[L_rψ_s(t)-L_mψ_r(t)]/(L_sL_r-L_m ²)，将式（6）和式（9）代入可得后双馈感应发电机三相短路电流空间矢量i_s(t)表达式为，Then, the relationship between stator flux linkage, rotor flux linkage and current of doubly-fed induction generator is i _s (t)=[L _r ψ _s (t)-L _m ψ _r (t)]/(L _s L _r -L _m ² ), substituting Equation (6) and Equation (9) into the three-phase short-circuit current space vector i _s (t) of the doubly-fed induction generator can be expressed as,

为同步频率周期分量的相位，为转子频率周期分量的相位，为直流分量的相位。In the formula: A ₁ is the amplitude of the periodic component of the synchronous frequency, A ₂ is the amplitude of the periodic component of the rotor frequency, A ₃ is the amplitude of the DC component,

is the phase of the periodic component of the synchronous frequency, is the phase of the periodic component of the rotor frequency, is the phase of the DC component.

步骤三的具体步骤为：The specific steps of step three are:

定子磁链的衰减直流分量分解成若干个频率ω_d接近于0的低频分量，0<ω_d<<ω（接近于0），则对于定子磁链ω_d频率分量归算至定子侧等值电路与图1定子磁链强制分量归算至定子侧的静态等值电路类似，仅须将定子磁链直流分量归算至转子侧形成的静态等值电路中ω替换为ω_d，转差s替换为1-ω_r/ω_d，据此可得，归算至定子侧转子电流

与定子电流

关系为：The attenuated DC component of the stator flux linkage is decomposed into several low-frequency components whose frequency ω _d is close to 0, 0<ω _d <<ω (close to 0), then the frequency component of the stator flux ω _d is reduced to the equivalent value on the stator side The circuit is similar to the static equivalent circuit in Figure 1 where the forced component of the stator flux linkage is reduced to the stator side, only the DC component of the stator flux linkage is reduced to the static equivalent circuit formed by the rotor side, and ω is replaced by ω _d , and the slip s Replaced by 1-ω _r /ω _d , according to which, it can be calculated to the stator side rotor current

vs stator current

The relationship is:

由于定子磁链衰减直流分量中各低频量满足0<ω_d<<ω，可认为定子和转子坐标下两者的比例近似相等，由此可知在转子坐标下推导出的定转子磁链衰减直流分量的相关系数可以替代定子坐标下定转子磁链衰减直流分量的相关系数，使得转子与定子磁链相关系数η_f和η_d即使不在同一坐标下也能进行运算，从而简化了DFIG三相短路电流表达式的推导过程。Since the low-frequency quantities in the DC component of the stator flux attenuation satisfy 0<ω _d <<ω, it can be considered that the proportions of the two in the stator and rotor coordinates are approximately equal, so it can be known that the stator-rotor flux attenuation DC derived in the rotor coordinates The correlation coefficient of the component can replace the correlation coefficient of the stator-rotor flux attenuation DC component in the stator coordinates, so that the rotor-stator flux correlation coefficients η _f and η _d can be calculated even if they are not in the same coordinates, thus simplifying the DFIG three-phase short-circuit current The derivation process of the expression.

最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本发明技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。Finally, it is noted that the above embodiments are only used to illustrate the technical solutions of the present invention without limitation. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be carried out Modifications or equivalent replacements without departing from the spirit and scope of the technical solution of the present invention shall be covered by the claims of the present invention.

Claims

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_{sd} - j ω_{r} L_{sd} = R_{e} + R_{s} - j ω_{r} (L_{e} + L_{ls}) + \frac{- j ω_{r} L_{m} (R_{r} - j ω_{r} L_{lr})}{R_{r} - j ω_{r} (L_{lr} + L_{m})} - - - (1)

T_{s} = \frac{L_{sd}}{R_{sd}} = \frac{L_{s} R_{r}^{2} + ω_{r}^{2} L_{r} (L_{s} L_{r} - L_{m}^{2})}{(R_{s} + R_{e}) R_{r}^{2} + ω_{r}^{2} L_{m}^{2} R_{r} + ω_{r}^{2} L_{r}^{2} (R_{s} + R_{e})} - - - (2)

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_{rd} + j ω_{r} L_{rd} = R_{r} + j ω_{r} L_{lr} + \frac{j ω_{r} L_{m} [(R_{s} + R_{e}) + j ω_{r} (L_{ls} + L_{e})]}{R_{s} + R_{e} + j ω_{r} (L_{ls} + L_{e} + L_{m})} - - - (3)

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_{rd}}{R_{rd}} \approx \frac{L_{s} L_{r} - L_{m}^{2}}{L_{s} R_{r}} - - - (4) .

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}^{'} (t) = {\overset{\cdot}{U}}_{s}^{'} e^{jωt} = R_{s} i_{s}^{'} (t) + \frac{d}{dt} ψ_{s}^{'} (t) - - - (5)

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:

ψ_{s} (t) = \frac{{\overset{\cdot}{U}}_{s}^{'}}{jω} e^{jωt} + \frac{{\overset{\cdot}{U}}_{s} - {\overset{\cdot}{U}}_{s}^{'}}{jω} e^{- t / T_{s}} - - - (6)

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:

{\overset{\cdot}{I}}_{rf} = \frac{- jω L_{m} {\overset{\cdot}{I}}_{sf}}{R_{r} / (1 - ω_{r} / ω) + jω L_{r}}, {\overset{\cdot}{I}}_{rd} = \frac{j ω_{r} L_{m} {\overset{\cdot}{I}}_{sd}}{R_{r} - j ω_{r} L_{r}} - - - (7)

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{matrix} ψ_{rf} (t) = \frac{L_{m} R_{r} / (1 - ω_{r} / ω) \cdot ψ_{sf} (t)}{L_{s} R_{r} / (1 - ω_{r} / ω) + jω (L_{s} L_{r} L_{m}^{2})} = η_{f} (ω_{r}) ψ_{sf} (t) \\ ψ_{rd} (t) = \frac{L_{m} R_{r} \cdot ψ_{sd} (t)}{L_{s} R_{r} + j ω_{r} (L_{m}^{2} - L_{s} L_{r})} = η_{d} (ω_{r}) ψ_{sd} (t) \end{matrix} - - - (8)

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{matrix} ψ_{r} (t) = η_{f} (ω_{r}) \frac{{\overset{\cdot}{U}}_{s}^{'}}{jω} e^{jωt} + η_{d} (ω_{r}) \frac{{\overset{\cdot}{U}}_{s} - {\overset{\cdot}{U}}_{s}^{'}}{jω} e^{- t / T_{s}} \\ + [η_{f} (ω_{r 0}) - η_{d} (ω_{r 0})] \frac{{\overset{\cdot}{U}}_{s} - {\overset{\cdot}{U}}_{s}^{'}}{jω} e^{- t / T_{s}} e^{j ω_{r} t} \end{matrix} - - - (9)

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:

{\overset{\cdot}{I}}_{rd} = \frac{- j ω_{d} L_{m} {\overset{\cdot}{I}}_{sd}}{R_{r} / (1 - ω_{r} / ω_{d}) + j ω_{d} L_{r}} - - - (11)

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{ψ_{rd} (t)}{ψ_{sd} (t)} = \frac{L_{m} R_{r} / (1 - ω_{r} / ω_{d})}{L_{s} R_{r} / (1 - ω_{r} / ω_{d}) + j ω_{d} (L_{s} L_{r} - L_{m}^{2})} = \frac{L_{m} R_{r}}{L_{m} R_{r} + j (ω_{d} - ω_{r}) (L_{s} L_{r} - L_{m}^{2})} - - - (12)

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{ψ_{rd} (t)}{ψ_{sd} (t)} = \frac{L_{m} R_{r}}{L_{m} R_{r} + j ω_{r} (L_{m}^{2} - L_{s} L_{r})} = η_{d} (ω_{r}) - - - (13)

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.