CN105550496A - Doubly-fed wind power generator stator winding interturnshort circuit mathematical modeling method - Google Patents

Abstract

The invention discloses a doubly-fed wind power generator stator winding interturn short circuit mathematical modeling method. The doubly-fed wind power generator stator winding interturn short circuit mathematical modeling method comprises the steps of: firstly, establishing a voltage equation, a flux linkage equation, an electromagnetic torque equation and a motion equation of a doubly-fed wind power generator under the normal condition; and then analyzing a failure mechanism when a stator winding interturn short circuit occurs to obtain changes of matrixes of a voltage, a current, a flux linkage, the resistance, the inductance and the like when the stator winding interturn short circuit occurs so as to obtain a voltage equation, a flux linkage equation, an electromagnetic torque equation and a motion equation of the doubly-fed wind power generator when the stator winding interturn short circuit occurs. Mathematical models under the normal condition and when a stator winding interturn short circuit occurs are respectively established in MATLAB/Simulink so as to carry out simulation of different short circuit degrees. Simulation results prove that the doubly-fed wind power generator stator winding interturn short circuit mathematical modeling method disclosed by the invention can effectively simulate different degrees of stator winding interturn short circuit faults.

Description

A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods

Technical field:

The invention belongs to double-fed wind power generator fault simulation model and set up field, be specifically related to a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods.

Background technology:

Double-fed wind power generator running environment is comparatively severe, and operating condition is complicated and changeable, and therefore its failure rate is higher.Common electric fault mostly occurs at master section, and the internal fault of fault type mainly motor, most electric fault is multiple is born in the places such as stator, rotor, air gap.Stator winding inter-turn short circuit is because adjacent two circles in winding bar or the insulation between a few circle coil are damaged and then cause short circuit.After winding interturn short-circuit fault occurs, not easily discover time slight, the time has been grown, and the insulation at fault coil place can be destroyed, and may cause wider fault, causes phase fault or ground short circuit fault etc.

Correlative study both at home and abroad for double-fed wind power generator group fault focuses mostly in gear case, the Study on Fault of kinematic train and main shaft bearing, and it is also few for the correlative study of double-fed wind power generator winding internal fault, although slight shorted-turn fault can't cause large impact to the operation of generator, but along with larger short-circuit current heating, cause short-circuiting percentage temperature anomaly, and the insulating material affected gradually around abort situation, further generation is short trouble between multiturn coil greatly, even phase fault can be there is, the catastrophic failures such as single-phase earthing.

In order to study the diagnostic method of double-fed aerogenerator stator winding interturn short-circuit fault, test platform stator winding inter-turn short circuit failure that is virtually reality like reality can be built in laboratory, but the method cycle is grown, it is large to expend, and easily causes permanent damage to motor.So adopt emulation mode to set up double-fed aerogenerator stator winding interturn short-circuit fault model can provide a better solution for it, not only various faults can be simulated, and can repeatedly test, and cost less, effect is high, is the first-selection of researcher.

In the present invention, the method for mathematical modeling has solid reliable Fundamentals of Mathematics, and this mathematical model is that the study mechanism of aerogenerator stator shorted-turn fault problem provides strong foundation; This modeling method also effectively instead of field experiment simultaneously, facilitates more economically.

Summary of the invention:

The object of the invention is to for above-mentioned the deficiencies in the prior art, provide a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods.

For achieving the above object, the present invention is achieved by the following technical solutions:

A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods, comprises the following steps:

1) according to the mathematical model of double-fed wind power generator, row write its voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion, and provide resistance, inductance matrix under normal circumstances;

2) failure mechanism of double-fed wind power generator when stator winding inter-turn short circuit is analyzed, and according to the computing formula of each phase resistance of motor, inductance, each phase resistance during calculating double-fed aerogenerator stator winding interturn short-circuit fault, the size of inductance, row write resistance, inductance matrix;

3) resistance during motor stator winding shorted-turn fault, inductance matrix are substituted into, obtain voltage equation, flux linkage equations, electromagnetic torque equation and equation of motion during motor stator winding shorted-turn fault;

4) in MATLAB/Simulink, double-fed wind power generator is set up at the mathematic simulated mode normally and in stator winding inter-turn short circuit failure situation, and obtain the time domain waveform of stator and rotor current and electromagnetic torque, the variation tendency of contrast waveform, the correctness of checking modeling method.

The present invention further improves and is: described step 1) specifically comprise the following steps:

A) double-fed wind power generator voltage equation under normal circumstances:

v＝Ri+pψ

In formula, v=[v _as, v _bs, v _cs, v _ar, v _br, v _cr] ^tfor each phase voltage instantaneous value of motor;

R=diag (r) is resistor matrix under normal circumstances, r=[r _s, r _s, r _s, r _r, r _r, r _r], wherein r _s, r _rbe respectively the resistance of every phase winding of stators and rotators;

I=[i _as, i _bs, i _cs, i _ar, i _br, i _cr] ^tfor rotor phase current matrix under normal circumstances;

P is differentiating operator;

ψ=[ψ _as, ψ _bs, ψ _cs, ψ _ar, ψ _br, ψ _cr] ^tfor the total flux linkage matrix of each phase winding of rotor under normal circumstances;

B) double-fed wind power generator flux linkage equations under normal circumstances:

ψ＝Li

Wherein, $L=\left[\begin{array}{cc}{L}_{\mathrm{SS}}& L_{\mathrm{SR}}\\ L_{\mathrm{RS}}& L_{\mathrm{RR}}\end{array}\right]$ For the inductance matrix of motor, L _sS, L _rR, L _sRand L _rSfor the partitioned matrix of the inductance matrix L of motor;

C) double-fed wind power generator electromagnetic torque equation under normal circumstances:

$T_e=\frac{1}{2}{n}_p\[i_{abcr}^T\frac{\∂L_{RS}}{\∂{\mathrm{\θ}}_r}{i}_{abcs}+i_{abcs}^T\frac{\∂L_{SR}}{\∂{\mathrm{\θ}}_r}{i}_{abcr}\]$

Wherein, T _efor the electromagnetic torque of double-fed wind power generator;

N _pfor the number of pole-pairs of double-fed wind power generator;

D) the double-fed wind power generator equation of motion under normal circumstances:

$T_e-T_L=\frac{J}{n_p}\frac{{\mathrm{d\ω}}_r}{dt}+\frac{{\mathrm{D\ω}}_r}{n_p}$

In formula, T _lfor the driving torque that wind energy conversion system provides;

J is the moment of inertia of Wind turbines;

ω _rfor the angular rate of generator;

D is the resistive torque ratio of damping be directly proportional to rotating speed.

The present invention further improves and is: described step 1) specifically comprise the following steps:

Partitioned matrix in the inductance matrix L of motor can expand into:

$L_{SS}=\left[\begin{array}{ccc}{L}_s& -\frac{1}{2}{L}_{ms}& -\frac{1}{2}{L}_{ms}\\ -\frac{1}{2}{L}_{ms}& L_s& -\frac{1}{2}{L}_{ms}\\ -\frac{1}{2}{L}_{ms}& -\frac{1}{2}{L}_{ms}& L_s\end{array}\right]$

$L_{SR}={L_{RS}}^T=L_{sr}\left[\begin{array}{ccc}{\mathrm{cos\θ}}_r& \cos ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})& \cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})\\ \cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})& {\mathrm{cos\θ}}_r& \cos ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})\\ \cos (\mathrm{\θ}+\frac{2}{3}\mathrm{\π})& \cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})& {\mathrm{cos\θ}}_r\end{array}\right]$

$L_{RR}=\left[\begin{array}{ccc}{L}_r& -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& L_r& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}& L_r\end{array}\right]$

In formula, L _lsfor the every phase leakage inductance of stator winding, L _msfor the every phase main inductance of stator, L _s=L _ms+ L _lsfor the every phase self-induction of stator winding, L _lrfor the every phase leakage inductance of rotor windings, L _mrfor the every phase main inductance of rotor, L _r=L _mr+ L _lrfor the every phase self-induction of rotor windings, θ _rfor stator and rotor winding axis electrical angle.

The present invention further improves and is: described step 2) specifically comprise the following steps:

201) failure mechanism of double-fed wind power generator when stator winding inter-turn short circuit is analyzed:

When turn-to-turn short circuit occurs stator winding A phase, between short circuit circle, define a new loop, the impedance in this loop is very little, assuming that increase newly one is D phase mutually; Interturn in stator windings fault severity level failure coefficient μ represents, it is defined as the ratio of every phase short-circuited winding number of turn and every phase winding total number of turns; After stator winding inter-turn short circuit, the voltage of motor, electric current, magnetic linkage and resistance, inductance matrix all there occurs change;

202) resistor matrix during motor stator winding shorted-turn fault:

$R^{\′}=\left[\begin{array}{ccccccc}(1-\mathrm{\μ})r_s& 0& 0& 0& 0& 0& 0\\ 0& r_s& 0& 0& 0& 0& 0\\ 0& 0& r_s& 0& 0& 0& 0\\ 0& 0& 0& {\mathrm{\μr}}_s& 0& 0& 0\\ 0& 0& 0& 0& r_r& 0& 0\\ 0& 0& 0& 0& 0& r_r& 0\\ 0& 0& 0& 0& 0& 0& r_r\end{array}\right]$

Wherein R ' is the resistor matrix under failure condition.

203) inductance matrix during motor stator winding shorted-turn fault:

(1) stator self inductance matrix is:

$L_{SS}^{\′}=\left[\begin{array}{cccc}{(1-\mathrm{\μ})}^2{L}_s& -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& (1-\mathrm{\μ}){\mathrm{\μL}}_{ms}\\ -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& L_s& -\frac{1}{2}{L}_{ms}& -\frac{1}{2}{\mathrm{\μL}}_{ms}\\ -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& -\frac{1}{2}{L}_{ms}& L_s& -\frac{1}{2}{\mathrm{\μL}}_{ms}\\ (1-\mathrm{\μ}){\mathrm{\μL}}_{ms}& -\frac{1}{2}{\mathrm{\μL}}_{ms}& -\frac{1}{2}{\mathrm{\μL}}_{ms}& {\mathrm{\μ}}^2{L}_s\end{array}\right]$

(2) rotor self-induction matrix is:

$L_{RR}^{\′}=\left[\begin{array}{ccc}{L}_r& -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& L_r& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}& L_r\end{array}\right]$

(3) rotor mutual inductance matrix is:

$L_{SR}^{\′}={L_{RS}^{\′}}^T=L_{sr}\left[\begin{array}{ccc}(1-\mathrm{\μ}){\mathrm{cos\θ}}_r& (1-\mathrm{\μ})\cos ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})& (1-\mathrm{\μ})\cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})\\ \cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})& {\mathrm{cos\θ}}_r& \cos ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})\\ \cos ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})& \cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})& {\mathrm{cos\θ}}_r\\ {\mathrm{\μcos\θ}}_r& \mathrm{\μ}\cos ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})& \mathrm{\μ}\cos ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})\end{array}\right]$

Wherein L ' _sSfor stator self inductance matrix under failure condition, L ' _rRfor failure condition lower rotor part self-induction matrix, L ' _sRand L ' _rSfor rotor mutual inductance matrix under failure condition.

The present invention further improves and is: described step 3) specifically comprise the following steps:

301) resistance, inductance matrix and flux linkage equations during double-fed generator stator winding inter-turn short circuit failure is substituted in voltage equation, obtains voltage equation during double-fed aerogenerator stator winding interturn short-circuit:

$\begin{array}{c}{v}_{as}^{\′}=(1-\mathrm{\μ})r_s{i}_{as}+{(1-\mathrm{\μ})}^2{L}_s\frac{{\mathrm{di}}_{as}}{dt}-(1-\mathrm{\μ})\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{bs}}{dt}-(1-\mathrm{\μ})\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{cs}}{dt}+(1-\mathrm{\μ})\left(\mathrm{\μ}\right)L_{ms}\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[(1-\mathrm{\μ})i_{ar}{\mathrm{cos\μ}}_r+(1-\mathrm{\μ})i_{br}\cos ({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})+(1-\mathrm{\μ})i_{ci}\cos ({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})\]\end{array}$

$\begin{array}{c}{v}_{bs}^{\′}=r_s{i}_{bs}-(1-\mathrm{\μ})\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{as}}{dt}+L_s\frac{{\mathrm{di}}_{bs}}{dt}-\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{cs}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{ar}\cos ({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})+i_{br}{\mathrm{cos\θ}}_r+i_{cr}\cos ({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})\]\end{array}$

$\begin{array}{c}{v}_{cs}^{\′}=r_s{i}_{cs}-(1-\mathrm{\μ})\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{as}}{dt}-\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{bs}}{dt}+L_s\frac{{\mathrm{di}}_{cs}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{ar}\cos ({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})+i_{br}\cos ({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})+i_{cr}{\mathrm{cos\θ}}_r\]\end{array}$

$\begin{array}{c}{v}_{ds}^{\′}=\left(\mathrm{\μ}\right)r_s{i}_{ds}+\mathrm{\μ}(1-\mathrm{\μ})L_{ms}\frac{{\mathrm{di}}_{as}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{bs}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{cs}}{dt}+{\left(\mathrm{\μ}\right)}^2{L}_s\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[\left(\mathrm{\μ}\right)i_{ar}{\mathrm{cos\θ}}_r+\left(\mathrm{\μ}\right)i_{br}\cos ({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})+\left(\mathrm{\μ}\right)i_{cr}\cos ({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})\]\end{array}$

$v_{ar}^{\′}=r_r{i}_{ar}+L_r\frac{{\mathrm{di}}_{ar}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{br}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{cr}}{dt}$

$+L_{sr}\frac{d}{dt}\[i_{as}(1-\mathrm{\μ}){\mathrm{cos\θ}}_r+i_{bs}cos({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})+i_{cs}cos({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})+i_{ds}{\mathrm{\μcos\θ}}_r\]$

$v_{br}^{\′}=r_r{i}_{br}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{ar}}{dt}+L_r\frac{{\mathrm{di}}_{br}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{cr}}{dt}$

$+L_{sr}\frac{d}{dt}\[i_{as}(1-\mathrm{\μ})cos({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})+i_{bs}{\mathrm{cos\θ}}_r+i_{cs}cos({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})+i_{ds}\mathrm{\μ}cos({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})\]$

$v_{cr}^{\′}=r_r{i}_{cr}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{ar}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{br}}{dt}+L_r\frac{{\mathrm{di}}_{cr}}{dt}$

$+L_{sr}\frac{d}{dt}\[i_{as}(1-\mathrm{\μ})cos({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})+i_{bs}cos({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3})+i_{cs}{\mathrm{cos\θ}}_r+i_{ds}\mathrm{\μ}cos({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3})\]$

Wherein v ' _as, v ' _bs, v ' _cs, v ' _ds, v ' _ar, v ' _br, v ' _crrepresent each phase voltage in stator winding inter-turn short circuit failure situation respectively.

302) resistance during double-fed generator stator winding inter-turn short circuit failure, inductance matrix are substituted in electromagnetic torque equation, obtain electromagnetic torque equation during double-fed aerogenerator stator winding interturn short-circuit:

$T_e^{\′}=-n_p{L}_{sr}\left\{\begin{array}{c}\[(1-\mathrm{\μ})i_{as}{i}_{ar}+i_{bs}{i}_{br}+i_{cs}{i}_{cr}+{\mathrm{\μi}}_{ds}{i}_{ar}\]{\mathrm{sin\θ}}_r+\[(1-\mathrm{\μ})i_{as}{i}_{br}+i_{bs}{i}_{cr}+i_{cs}{i}_{ar}+{\mathrm{\μi}}_{ds}{i}_{bs}\]\sin ({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π})+\\ \[(1-\mathrm{\μ})i_{as}{i}_{cr}+i_{bs}{i}_{ar}+i_{cs}{i}_{br}+{\mathrm{\μi}}_{ds}{i}_{cr}\]\sin ({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π})\end{array}\right\}$

Wherein T ' _efor the electromagnetic torque in stator winding inter-turn short circuit failure situation.

303) electromagnetic torque equation during double-fed generator stator winding inter-turn short circuit failure is substituted in the equation of motion, obtains equation of motion during double-fed aerogenerator stator winding interturn short-circuit:

$T_e^{\′}-T_L=\frac{J}{n_p}\frac{{\mathrm{d\ω}}_r}{dt}+\frac{{\mathrm{D\ω}}_r}{n_p}.$

Relative to prior art, beneficial effect of the present invention is embodied in:

The present invention is on the basis of the motor mathematical model of maturation, by calculating, deriving the stator winding inter-turn short circuit failure model of the double-fed wind power generator obtained, and in current the most popular, most widely used software for calculation MATLAB in the world, this model is emulated.The simulation result of normal model and fault model is contrasted, demonstrates the correctness of modeling method.The Changing Pattern research of the stator and rotor current that the stator winding inter-turn short circuit failure model that this modeling method obtains occurs when being interturn in stator windings short trouble and electromagnetic torque provides model, in on-line monitoring system, the extraction of characteristic parameter provides foundation.

Accompanying drawing illustrates:

Fig. 1 is double-fed wind power generator of the present invention stator three-phase current time domain beamformer under normal circumstances;

Fig. 2 is double-fed wind power generator of the present invention rotor three-phase electric current time domain beamformer under normal circumstances;

Fig. 3 is double-fed wind power generator of the present invention electromagnetic torque time domain beamformer under normal circumstances;

Fig. 4 (a) ~ (h) be respectively double-fed aerogenerator stator winding A phase of the present invention 0.09%, 0.9%, 1%, 3%, 5%, 7%, 9%, 11% turn-to-turn short circuit time stator current time domain beamformer;

Fig. 5 (a) ~ (h) be respectively double-fed aerogenerator stator winding A phase of the present invention 0.09%, 0.9%, 1%, 3%, 5%, 7%, 9%, 11% turn-to-turn short circuit time rotor current time domain beamformer;

Fig. 6 (a) ~ (h) be respectively double-fed aerogenerator stator winding A phase of the present invention 0.09%, 0.9%, 1%, 3%, 5%, 7%, 9%, 11% turn-to-turn short circuit time electromagnetic torque time domain beamformer.

Embodiment:

Below in conjunction with drawings and Examples, technical scheme of the present invention is described in further detail.

A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods of the present invention, mainly comprises the following steps:

1) according to the mathematical model of double-fed wind power generator, row write its voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion, and provide resistance, inductance matrix under normal circumstances; In MATLAB/Simulink, set up double-fed wind power generator mathematic simulated mode under normal circumstances, and obtain the time domain waveform of stator and rotor current and electromagnetic torque;

2) reason of changes of double-fed wind power generator winding parameter when stator winding inter-turn short circuit is analyzed, and according to the computing formula of each phase resistance of motor, inductance, each phase resistance during calculating double-fed aerogenerator stator winding interturn short-circuit fault, the size of inductance, row write resistance, inductance matrix;

3) resistance during motor stator winding shorted-turn fault, inductance matrix are substituted into, obtain voltage equation, flux linkage equations, electromagnetic torque equation and equation of motion during motor stator winding shorted-turn fault; In MATLAB/Simulink, set up the mathematic simulated mode of double-fed wind power generator in stator A phase winding 0.09%, 0.9%, 1%, 3%, 5%, 7%, 9% and 11% shorted-turn fault situation, and obtain the time domain waveform of stator and rotor current and electromagnetic torque;

4) time domain waveform of stator and rotor current and electromagnetic torque in normal condition and different faults situation is compared, the variation tendency of contrast waveform, the correctness of checking modeling method.

Embodiment:

It is as shown in table 1 that the present invention emulates the parameter of electric machine used:

Table 1 emulates the parameter of electric machine

When double-fed wind power generator is in normal operating conditions, emulate in MATLAB/Simulink to normal model, obtain stator current as shown in Figure 1, as shown in Figure 2, electromagnetic torque as shown in Figure 3 for rotor current.

Make μ=0.0009 respectively, 0.009,0.01,0.03,0.05,0.07,0.09, the turn-to-turn short circuit of 0.11 model stator A phase 0.09%, 0.9%, 1%, 3%, 5%, 7%, 9% and 11%.Emulate double-fed aerogenerator stator winding interturn short-circuit fault model in MATLAB/Simulink, obtain stator three-phase current as shown in Figure 4, as shown in Figure 5, electromagnetic torque as shown in Figure 6 for rotor three-phase electric current.

Comparison diagram 1 and Fig. 4 known, double-fed wind power generator is when non-fault, and stator three-phase current is symmetrical; When stator winding inter-turn short circuit, stator three-phase current is no longer symmetrical, and with the intensification of fault degree, the degree of unbalancedness of three-phase current increases, and show as fault phase amplitude increasing, healthy phases amplitude is more and more less.

Comparison diagram 2 and Fig. 5 known, double-fed wind power generator when non-fault, rotor three-phase current-symmetrical and image smoothing; When stator winding inter-turn short circuit, rotor three-phase current image is no longer level and smooth, and harmonic wave increases.

Comparison diagram 3 and Fig. 6 known, double-fed wind power generator when non-fault, electromagnetic torque reach stable after be constant; When stator winding inter-turn short circuit, electromagnetic torque reach stable after there will be fluctuation, and with the intensification of fault degree, electromagnetic torque reach stable after fluctuation more and more obvious.

Comprehensive above-mentioned explanation and analysis, can by introducing failure coefficient μ and setting up double-fed aerogenerator stator winding interturn short-circuit fault time resistor matrix and inductance matrix, thus voltage equation, flux linkage equations, electromagnetic torque equation and equation of motion when setting up double-fed aerogenerator stator winding interturn short-circuit fault, obtain realistic model during double-fed aerogenerator stator winding interturn short-circuit fault.

Above content is the further description done the present invention in conjunction with concrete embodiment, can not assert that specific embodiment of the invention is confined to these explanations.For general technical staff of the technical field of the invention, without departing from the inventive concept of the premise, some simple deductions can also be made or substitute, all should be considered as belonging to protection scope of the present invention.

Claims (5)

1. a double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods, is characterized in that, comprises the following steps:

1) according to the mathematical model of double-fed wind power generator, row write its voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion, and provide resistance, inductance matrix under normal circumstances;

2) reason of double-fed wind power generator winding parameter change when stator winding inter-turn short circuit is analyzed, and according to the computing formula of each phase resistance of motor, inductance, each phase resistance during calculating double-fed aerogenerator stator winding interturn short-circuit fault, the size of inductance, row write resistance, inductance matrix;

3) resistance during motor stator winding shorted-turn fault, inductance matrix are substituted into, obtain voltage equation, flux linkage equations, electromagnetic torque equation and equation of motion during motor stator winding shorted-turn fault;

4) in MATLAB/Simulink, double-fed wind power generator is set up at the mathematic simulated mode normally and in stator winding inter-turn short circuit failure situation, and obtain the time domain waveform of stator and rotor current and electromagnetic torque, the variation tendency of contrast waveform, the correctness of checking modeling method.

2. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 1, is characterized in that, described step 1) specifically comprise:

A) double-fed wind power generator voltage equation under normal circumstances:

v＝Ri+pψ

In formula, v=[v _as, v _bs, v _cs, v _ar, v _br, v _cr] ^tfor each phase voltage instantaneous value of motor;

R=diag (r) is resistor matrix under normal circumstances, r=[r _s, r _s, r _s, r _r, r _r, r _r], wherein r _s, r _rbe respectively the resistance of every phase winding of stators and rotators;

I=[i _as, i _bs, i _cs, i _ar, i _br, i _cr] ^tfor rotor phase current matrix under normal circumstances;

P is differentiating operator;

ψ=[ψ _as, ψ _bs, ψ _cs, ψ _ar, ψ _br, ψ _cr] ^tfor the total flux linkage matrix of each phase winding of rotor under normal circumstances;

B) double-fed wind power generator flux linkage equations under normal circumstances:

ψ＝Li

Wherein, $L=\left[\begin{array}{cc}{L}_{SS}& L_{SR}\\ L_{RS}& L_{RR}\end{array}\right]$ For the inductance matrix of motor, L _sS, L _rR, L _sRand L _rSfor the partitioned matrix of the inductance matrix L of motor;

C) double-fed wind power generator electromagnetic torque equation under normal circumstances:

$T_e=\frac{1}{2}{n}_p\[i_{abcr}^T\frac{\∂L_{RS}}{\∂{\mathrm{\θ}}_r}{i}_{abcs}+i_{abcs}^T\frac{\∂L_{SR}}{\∂{\mathrm{\θ}}_r}{i}_{abcr}\]$

Wherein, T _efor the electromagnetic torque of double-fed wind power generator;

N _pfor the number of pole-pairs of double-fed wind power generator;

D) the double-fed wind power generator equation of motion under normal circumstances:

$T_e-T_L=\frac{J}{n_p}\frac{{\mathrm{d\ω}}_r}{dt}+\frac{{\mathrm{D\ω}}_r}{n_p}$

In formula, T _lfor the driving torque that wind energy conversion system provides;

J is the moment of inertia of Wind turbines;

ω _rfor the angular rate of generator;

D is the resistive torque ratio of damping be directly proportional to rotating speed.

3. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 2, it is characterized in that, the partitioned matrix in the inductance matrix L of motor can expand into:

$L_{SS}=\left[\begin{array}{ccc}{L}_s& -\frac{1}{2}{L}_{ms}& -\frac{1}{2}{L}_{ms}\\ -\frac{1}{2}{L}_{ms}& L_s& -\frac{1}{2}{L}_{ms}\\ -\frac{1}{2}{L}_{ms}& -\frac{1}{2}{L}_{ms}& L_s\end{array}\right]$

$L_{SR}={L_{RS}}^T=L_{sr}\left[\begin{array}{ccc}{\mathrm{cos\θ}}_r& \cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)& \cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)\\ \cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)& {\mathrm{cos\θ}}_r& \cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)\\ \cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)& \cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)& {\mathrm{cos\θ}}_r\end{array}\right]$

$L_{RR}=\left[\begin{array}{ccc}{L}_r& -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& L_r& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}& L_r\end{array}\right]$

In formula, L _lsfor the every phase leakage inductance of stator winding, L _msfor the every phase main inductance of stator, L _s=L _ms+ L _lsfor the every phase self-induction of stator winding, L _lrfor the every phase leakage inductance of rotor windings, L _mrfor the every phase main inductance of rotor, L _r=L _mr+ L _lrfor the every phase self-induction of rotor windings, θ _rfor stator and rotor winding axis electrical angle.

4. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 1, is characterized in that, described step 2) specifically comprise the following steps:

201) double-fed wind power generator winding parameter reason of changes when stator winding inter-turn short circuit is analyzed:

When turn-to-turn short circuit occurs stator winding A phase, between short circuit circle, define a new loop, the impedance in this loop is very little, assuming that increase newly one is D phase mutually; Interturn in stator windings fault severity level failure coefficient μ represents, it is defined as the ratio of every phase short-circuited winding number of turn and every phase winding total number of turns; After stator winding inter-turn short circuit, the voltage of motor, electric current, magnetic linkage and resistance, inductance matrix all there occurs change;

202) resistor matrix during motor stator winding shorted-turn fault:

$R^{\′}=\left[\begin{array}{ccccccc}(1-\mathrm{\μ})r_s& 0& 0& 0& 0& 0& 0\\ 0& r_s& 0& 0& 0& 0& 0\\ 0& 0& r_s& 0& 0& 0& 0\\ 0& 0& 0& {\mathrm{\μr}}_s& 0& 0& 0\\ 0& 0& 0& 0& r_r& 0& 0\\ 0& 0& 0& 0& 0& r_r& 0\\ 0& 0& 0& 0& 0& 0& r_r\end{array}\right]$

Wherein R ' is the resistor matrix under failure condition;

203) inductance matrix during motor stator winding shorted-turn fault:

(1) stator self inductance matrix is:

$L_{SS}^{\′}=\left[\begin{array}{cccc}{(1-\mathrm{\μ})}^2{L}_s& -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& (1-\mathrm{\μ}){\mathrm{\μL}}_{ms}\\ -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& L_s& -\frac{1}{2}{L}_{ms}& -\frac{1}{2}{\mathrm{\μL}}_{ms}\\ -\frac{1}{2}(1-\mathrm{\μ})L_{ms}& -\frac{1}{2}{L}_{ms}& L_s& -\frac{1}{2}{\mathrm{\μL}}_{ms}\\ (1-\mathrm{\μ}){\mathrm{\μL}}_{ms}& -\frac{1}{2}{\mathrm{\μL}}_{ms}& -\frac{1}{2}{\mathrm{\μL}}_{ms}& {\mathrm{\μ}}^2{L}_s\end{array}\right]$

(2) rotor self-induction matrix is:

$L_{RR}^{\′}=\left[\begin{array}{ccc}{L}_r& -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& L_r& -\frac{1}{2}{L}_{mr}\\ -\frac{1}{2}{L}_{mr}& -\frac{1}{2}{L}_{mr}& L_r\end{array}\right]$

(3) rotor mutual inductance matrix is:

$L_{SR}^{\′}={L_{RS}^{\′}}^T=L_{sr}\left[\begin{array}{ccc}\left(1-\mathrm{\μ}\right){\mathrm{cos\θ}}_r& \left(1-\mathrm{\μ}\right)\cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)& \left(1-\mathrm{\μ}\right)\cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)\\ \cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)& {\mathrm{cos\θ}}_r& \cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)\\ \cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)& \cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)& {\mathrm{cos\θ}}_r\\ {\mathrm{\μcos\θ}}_r& \mathrm{\μ}\cos \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)& \mathrm{\μ}\cos \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)\end{array}\right]$

Wherein L ' _sSfor stator self inductance matrix under failure condition, L ' _rRfor failure condition lower rotor part self-induction matrix, L ' _sRand L ' _rSfor rotor mutual inductance matrix under failure condition.

5. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 1, is characterized in that, described step 3) specifically comprise the following steps:

301) resistance, inductance matrix and flux linkage equations during double-fed generator stator winding inter-turn short circuit failure is substituted in voltage equation, obtains voltage equation during double-fed aerogenerator stator winding interturn short-circuit:

$\begin{array}{c}{v}_{as}^{\′}=\left(1-\mathrm{\μ}\right)r_s{i}_{as}+{\left(1-\mathrm{\μ}\right)}^2{L}_s\frac{{\mathrm{di}}_{as}}{dt}-\left(1-\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{bs}}{dt}-\left(1-\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{cs}}{dt}+\left(1-\mathrm{\μ}\right)\left(\mathrm{\μ}\right)L_{ms}\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[\left(1-\mathrm{\μ}\right)i_{ar}{\mathrm{cos\θ}}_r+\left(1-\mathrm{\μ}\right)i_{br}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)+\left(1-\mathrm{\μ}\right)i_{cr}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)\]\end{array}$

$\begin{array}{c}{v}_{bs}^{\′}=r_s{i}_{bs}-\left(1-\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{as}}{dt}+L_s\frac{{\mathrm{di}}_{bs}}{dt}-\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{cs}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{ar}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)+i_{br}{\mathrm{cos\θ}}_r+i_{cr}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)\]\end{array}$

$\begin{array}{c}{v}_{cs}^{\′}=r_s{i}_{cs}-\left(1-\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{as}}{dt}-\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{bs}}{dt}+L_s\frac{{\mathrm{di}}_{cs}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{ar}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)+i_{br}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)+i_{cr}{\mathrm{cos\θ}}_r\]\end{array}$

$\begin{array}{c}{v}_{ds}^{\′}=\left(\mathrm{\μ}\right)r_s{i}_{ds}+\mathrm{\μ}\left(1-\mathrm{\μ}\right)L_{ms}\frac{{\mathrm{di}}_{as}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{bs}}{dt}-\left(\mathrm{\μ}\right)\frac{L_{ms}}{2}\frac{{\mathrm{di}}_{cs}}{dt}+{\left(\mathrm{\μ}\right)}^2{L}_s\frac{{\mathrm{di}}_{ds}}{dt}\\ +L_{sr}\frac{d}{dt}\[\left(\mathrm{\μ}\right)i_{ar}{\mathrm{cos\θ}}_r+\left(\mathrm{\μ}\right)i_{br}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)+\left(\mathrm{\μ}\right)i_{cr}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)\]\end{array}$

$\begin{array}{c}{v}_{ar}^{\′}=r_r{i}_{ar}+L_r\frac{{\mathrm{di}}_{ar}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{br}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{cr}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{as}\left(1-\mathrm{\μ}\right){\mathrm{cos\θ}}_r+i_{bs}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)+i_{cs}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)+i_{ds}{\mathrm{\μcos\θ}}_r\]\end{array}$

$\begin{array}{c}{v}_{br}^{\′}=r_r{i}_{br}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{ar}}{dt}+L_r\frac{{\mathrm{di}}_{br}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{cr}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{as}\left(1-\mathrm{\μ}\right)\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)+i_{bs}{\mathrm{cos\θ}}_r+i_{cs}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)+i_{ds}\mathrm{\μ}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)\]\end{array}$

$\begin{array}{c}{v}_{cr}^{\′}=r_r{i}_{cr}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{ar}}{dt}-\frac{L_{mr}}{2}\frac{{\mathrm{di}}_{br}}{dt}+L_r\frac{{\mathrm{di}}_{cr}}{dt}\\ +L_{sr}\frac{d}{dt}\[i_{as}\left(1-\mathrm{\μ}\right)\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)+i_{bs}\cos \left({\mathrm{\θ}}_r+\frac{2\mathrm{\π}}{3}\right)+i_{cs}{\mathrm{cos\θ}}_r+i_{ds}\mathrm{\μ}\cos \left({\mathrm{\θ}}_r-\frac{2\mathrm{\π}}{3}\right)\]\end{array}$

Wherein v ' _as, v ' _bs, v ' _cs, v ' _ds, v ' _ar, v ' _br, v ' _crrepresent each phase voltage in stator winding inter-turn short circuit failure situation respectively;

302) resistance during double-fed generator stator winding inter-turn short circuit failure, inductance matrix are substituted in electromagnetic torque equation, obtain electromagnetic torque equation during double-fed aerogenerator stator winding interturn short-circuit:

$T_e^{\′}=-n_p{L}_{sr}\left\{\begin{array}{c}\[\left(1-\mathrm{\μ}\right)i_{as}{i}_{ar}+i_{bs}{i}_{br}+i_{cs}{i}_{cr}+{\mathrm{\μi}}_{ds}{i}_{ar}\]{\mathrm{sin\θ}}_r+\[\left(1-\mathrm{\μ}\right)i_{as}{i}_{br}+i_{bs}{i}_{cr}+i_{cs}{i}_{ar}+{\mathrm{\μi}}_{ds}{i}_{br}\]\sin \left({\mathrm{\θ}}_r+\frac{2}{3}\mathrm{\π}\right)+\\ \[\left(1-\mathrm{\μ}\right)i_{as}{i}_{cr}+i_{bs}{i}_{ar}+i_{cs}{i}_{br}+{\mathrm{\μi}}_{ds}{i}_{cr}\]\sin \left({\mathrm{\θ}}_r-\frac{2}{3}\mathrm{\π}\right)\end{array}\right\}$

Wherein T ' _efor the electromagnetic torque in stator winding inter-turn short circuit failure situation;

303) electromagnetic torque equation during double-fed generator stator winding inter-turn short circuit failure is substituted in the equation of motion, obtains equation of motion during double-fed aerogenerator stator winding interturn short-circuit:

$T_e^{\′}-T_L=\frac{J}{n_p}\frac{{\mathrm{d\ω}}_r}{dt}+\frac{{\mathrm{D\ω}}_r}{n_p}.$