CN105550496B - A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods - Google Patents
A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods Download PDFInfo
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Abstract
The invention discloses a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods：Initially set up voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion of doubly-fed wind turbine under normal circumstances, then failure mechanism when stator winding inter-turn short circuit is analyzed, the variation of voltage, electric current, magnetic linkage, resistance and inductance equal matrix when stator winding inter-turn short circuit is obtained, and then obtains voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion of the doubly-fed wind turbine in stator winding inter-turn short circuit.It establishes mathematical model when normal and stator winding inter-turn short circuit respectively in MATLAB/Simulink, different degree of short circuit is emulated.Simulation results show, double-fed aerogenerator stator winding interturn short-circuit modeling method proposed by the present invention can effectively simulate different degrees of stator winding inter-turn short circuit failure.
Description
Technical field：
The invention belongs to doubly-fed wind turbine fault simulation models to establish field, and in particular to a kind of double-fed wind generating
Machine stator winding interturn short-circuit Mathematical Modeling Methods.
Background technology：
Doubly-fed wind turbine running environment is more severe, and operating condition is complicated and changeable, therefore its failure rate is higher.It is common
Electric fault mostly occur in master section, fault type is mainly the internal fault of motor, and most electric fault is more
Betide stator, rotor, air gap etc..Stator winding inter-turn short circuit be due in winding bar adjacent two circle or a few circle coils
Between insulation by destroy so that cause short circuit.After winding interturn short-circuit failure occurs, not noticeable when slight, the time is grown,
Insulation at failure coil can be destroyed, and larger range of failure is likely to result in, and cause phase fault or ground short circuit
Failure etc..
Both at home and abroad focus mostly on the correlative study of double-fed wind power generator group failure in gear-box, transmission system and main shaft
The Study on Fault of bearing, and correlative study for doubly-fed wind turbine winding internal fault and few, although slight turn-to-turn
Short trouble can't cause big influence to the operation of generator, but as larger short circuit current is generated heat, cause short
Point temperature anomaly, and gradually influence the insulating materials around abort situation further occurs short between a greater degree of multiturn coil
Road failure, or even phase fault can occur, the catastrophe failures such as single-phase earthing.
In order to study the diagnostic method of double-fed aerogenerator stator winding interturn short-circuit failure, can be built in laboratory
Test platform simulates true stator winding inter-turn short circuit failure, but this method period is long, it is big to expend, and is easily made to motor
At permanent damage.It can be for so emulation mode is used to establish double-fed aerogenerator stator winding interturn short-circuit fault model
Its provide a preferred solution, can not only simulate various faults, but also can test repeatedly, and spend less, at
Effect is high, is the first choice of researcher.
It is wind-driven generator that the method for mathematical modeling, which has solid reliable Fundamentals of Mathematics, this mathematical model, in the present invention
The mechanism study of interturn in stator windings short trouble problem provides strong foundation；Simultaneously this modeling method also effectively instead of
Field experiment, it is more economical convenient.
Invention content：
It is an object of the invention in view of the above shortcomings of the prior art, provide a kind of double-fed aerogenerator stator around
Group turn-to-turn short circuit Mathematical Modeling Methods.
In order to achieve the above objectives, the present invention is achieved by the following scheme：
A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods, include the following steps：
1) according to the mathematical model of doubly-fed wind turbine, 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 the analysis doubly-fed wind turbine in stator winding inter-turn short circuit, and according to each mutually electricity of motor
Resistance, inductance calculation formula, calculate double-fed aerogenerator stator winding interturn short-circuit failure when each phase resistance, inductance it is big
Small, row write resistance, inductance matrix；
3) resistance, inductance matrix when by motor stator winding shorted-turn fault substitute into, and obtain motor stator winding circle
Between short trouble when voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion；
4) doubly-fed wind turbine is established in MATLAB/Simulink in normal and stator winding inter-turn short circuit failure feelings
Mathematic simulated mode under condition, and the time domain waveform of stator and rotor current and electromagnetic torque is obtained, the variation tendency of waveform is compared, is tested
Demonstrate,prove the correctness of modeling method.
The present invention, which further improves, to be：The step 1) specifically includes following steps：
A) voltage equation of doubly-fed wind turbine under normal circumstances：
V=Ri+p ψ
In formula, v=[vas,vbs,vcs,var,vbr,vcr]TFor each phase voltage instantaneous value of motor；
R=diag (r) is resistor matrix under normal circumstances, r=[rs,rs,rs,rr,rr,rr], wherein rs, rrIt is respectively fixed
The resistance of every phase winding of son and rotor；
I=[ias,ibs,ics,iar,ibr,icr]TFor rotor phase current matrix under normal circumstances；
P is differential operator；
ψ=[ψas,ψbs,ψcs,ψar,ψbr,ψcr]TFor the total flux linkage matrix of each phase winding of rotor under normal circumstances；
B) flux linkage equations of doubly-fed wind turbine under normal circumstances：
ψ=Li
C) the electromagnetic torque equation of doubly-fed wind turbine under normal circumstances：
Wherein, TeFor the electromagnetic torque of doubly-fed wind turbine；
npFor the number of pole-pairs of doubly-fed wind turbine；
D) equation of motion of doubly-fed wind turbine under normal circumstances：
In formula, TLThe driving torque provided for wind energy conversion system；
J is the rotary inertia of Wind turbines；
ωrFor the angular rate of generator；
D is the resistive torque damped coefficient directly proportional to rotating speed.
The present invention, which further improves, to be：The step 1) specifically includes following steps：
Matrix in block form in the inductance matrix L of motor can expand into：
In formula, LlsIt is the every phase leakage inductance of stator winding, LmsIt is the every phase main inductance of stator, Ls=Lms+LlsIt is the every phase of stator winding
Self-induction, LlrIt is the every phase leakage inductance of rotor windings, LmrIt is the every phase main inductance of rotor, Lr=Lmr+LlrIt is the every phase self-induction of rotor windings, θr
For stator and rotor winding axis electrical angle.
The present invention, which further improves, to be：The step 2) specifically includes following steps：
201) failure mechanism of the analysis doubly-fed wind turbine in stator winding inter-turn short circuit：
When turn-to-turn short circuit occurs for stator winding A phases, a new circuit, the resistance in the circuit are formd between short-circuit circle
Anti- very little, it is assumed that a newly-increased phase is D phases；Interturn in stator windings fault severity level indicates that it is defined as every mutually short with failure coefficient μ
The ratio between road umber of turn and every phase winding total number of turns；After stator winding inter-turn short circuit, voltage, electric current, magnetic linkage and the electricity of motor
Resistance, inductance matrix are all changed；
202) resistor matrix when motor stator winding shorted-turn fault：
Wherein R ' is the resistor matrix under fault condition.
203) inductance matrix when motor stator winding shorted-turn fault：
(1) stator self inductance matrix is：
(2) rotor self-induction matrix is：
(3) rotor mutual inductance matrix is：
Wherein L 'SSFor stator self inductance matrix, L ' under fault conditionRRFor fault condition lower rotor part self-induction matrix, L 'SRAnd L 'RS
For rotor mutual inductance matrix under fault condition.
The present invention, which further improves, to be：The step 3) specifically includes following steps：
301) resistance, inductance matrix and flux linkage equations when by double-fed generator stator winding inter-turn short circuit failure substitute into electricity
It presses in equation, obtains voltage equation when double-fed aerogenerator stator winding interturn short-circuit：
Wherein v 'as,v’bs,v’cs,v’ds,v’ar,v’br,v’crRespectively in the case of expression stator winding inter-turn short circuit failure
Each phase voltage.
302) resistance, inductance matrix when by double-fed generator stator winding inter-turn short circuit failure substitute into electromagnetic torque equation
In, obtain electromagnetic torque equation when double-fed aerogenerator stator winding interturn short-circuit：
Wherein T 'eFor the electromagnetic torque in the case of stator winding inter-turn short circuit failure.
303) electromagnetic torque equation when by double-fed generator stator winding inter-turn short circuit failure substitutes into the equation of motion, obtains
Equation of motion when to double-fed aerogenerator stator winding interturn short-circuit：
Compared with the existing technology, beneficial effects of the present invention are embodied in：
The present invention is to pass through the double-fed wind generating for calculating, being derived by the basis of ripe motor mathematical model
The stator winding inter-turn short circuit failure model of machine, and in most popular, most widely used software for calculation in the world at present
The model is emulated in MATLAB.The simulation result of normal model and fault model is compared, modeling is demonstrated
The correctness of method.The stator winding inter-turn short circuit failure model that this modeling method obtains goes out when being interturn in stator windings short trouble
The changing rule research of existing stator and rotor current and electromagnetic torque provides model, is carried for characteristic parameter in on-line monitoring system
It takes and provides foundation.
Description of the drawings：
Fig. 1 is the stator three-phase current time domain waveform of doubly-fed wind turbine of the present invention under normal circumstances；
Fig. 2 is the rotor three-phase electric current time domain waveform of doubly-fed wind turbine of the present invention under normal circumstances；
Fig. 3 is the electromagnetic torque time domain waveform of doubly-fed wind turbine of the present invention under normal circumstances；
Fig. 4 (a)~(h) be respectively double-fed aerogenerator stator winding A phases of the present invention 0.09%, 0.9%, 1%, 3%,
5%, 7%, 9%, stator current time domain waveform when 11% turn-to-turn short circuit；
Fig. 5 (a)~(h) be respectively double-fed aerogenerator stator winding A phases of the present invention 0.09%, 0.9%, 1%, 3%,
5%, 7%, 9%, rotor current time domain waveform when 11% turn-to-turn short circuit；
Fig. 6 (a)~(h) be respectively double-fed aerogenerator stator winding A phases of the present invention 0.09%, 0.9%, 1%, 3%,
5%, 7%, 9%, electromagnetic torque time domain waveform when 11% turn-to-turn short circuit.
Specific implementation mode：
Technical scheme of the present invention is described in further detail with reference to the accompanying drawings and examples.
A kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods of the present invention include mainly following
Step：
1) according to the mathematical model of doubly-fed wind turbine, row write its voltage equation, flux linkage equations, electromagnetic torque equation and
The equation of motion, and provide resistance, inductance matrix under normal circumstances；Double-fed wind generating is established in MATLAB/Simulink
The mathematic simulated mode of machine under normal circumstances, and obtain the time domain waveform of stator and rotor current and electromagnetic torque；
2) reason of changes of doubly-fed wind turbine winding parameter in stator winding inter-turn short circuit is analyzed, and according to motor
Each phase resistance, the calculation formula of inductance, calculate double-fed aerogenerator stator winding interturn short-circuit failure when each phase resistance, electricity
The size of sense, row write resistance, inductance matrix；
3) resistance, inductance matrix when by motor stator winding shorted-turn fault substitute into, and obtain motor stator winding circle
Between short trouble when voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion；It is built in MATLAB/Simulink
Vertical doubly-fed wind turbine is in stator A phase windings 0.09%, 0.9%, 1%, 3%, 5%, 7%, 9% and 11% turn-to-turn short circuit event
Mathematic simulated mode in the case of barrier, and obtain the time domain waveform of stator and rotor current and electromagnetic torque；
4) compare the time domain waveform of stator and rotor current and electromagnetic torque in the case of normal condition and different faults, compare waveform
Variation tendency, verify the correctness of modeling method.
Embodiment：
The present invention emulation parameter of electric machine used is as shown in table 1：
Table 1 emulates the parameter of electric machine
When doubly-fed wind turbine is in normal operating conditions, normal model is carried out in MATLAB/Simulink
Emulation, obtains stator current as shown in Figure 1, rotor current is as shown in Fig. 2, electromagnetic torque is as shown in Figure 3.
Enable μ=0.0009 respectively, 0.009,0.01,0.03,0.05,0.07,0.09,0.11 model stator A phases 0.09%,
0.9%, 1%, 3%, 5%, 7%, 9% and 11% turn-to-turn short circuit.To doubly-fed wind turbine in MATLAB/Simulink
Stator winding inter-turn short circuit failure model is emulated, and obtains stator three-phase current as shown in figure 4, rotor three-phase electric current such as Fig. 5
Shown, electromagnetic torque is as shown in Figure 6.
It is found that doubly-fed wind turbine is in fault-free, stator three-phase current is symmetrical by comparison diagram 1 and Fig. 4；Work as stator winding
When turn-to-turn short circuit, stator three-phase current is no longer symmetrical, and with the intensification of fault degree, and the degree of unbalancedness of three-phase current increases, table
It is now that failure phase amplitude is increasing, non-faulting phase amplitude is smaller and smaller.
Comparison diagram 2 and Fig. 5 it is found that doubly-fed wind turbine in fault-free, rotor three-phase current-symmetrical and image smoothing；
When stator winding inter-turn short circuit, rotor three-phase current image is no longer smooth, and harmonic wave increases.
Comparison diagram 3 and Fig. 6 it is found that doubly-fed wind turbine in fault-free, electromagnetic torque reach stablize after be constant；When
When stator winding inter-turn short circuit, electromagnetic torque will appear fluctuation after reaching stable, and with the intensification of fault degree, electromagnetic torque reaches
Fluctuation after to stabilization is more and more obvious.
In summary illustrate and analyze, double-fed aerogenerator stator winding can be established by introducing failure coefficient μ
Resistor matrix when shorted-turn fault and inductance matrix, to establish double-fed aerogenerator stator winding interturn short-circuit failure
When voltage equation, flux linkage equations, electromagnetic torque equation and the equation of motion, it is short to obtain double-fed aerogenerator stator winding inter-turn
The simulation model when failure of road.
The above content is combine specific embodiment to the further description of the invention done, and it cannot be said that this hair
Bright specific implementation is confined to these explanations.For those of ordinary skill in the art to which the present invention belongs, it is not taking off
Under the premise of from present inventive concept, several simple deductions or replacement can also be made, all shall be regarded as belonging to the protection of the present invention
Range.
Claims (4)
1. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods, which is characterized in that include the following steps：
1) according to the mathematical model of doubly-fed wind turbine, row write its voltage equation, flux linkage equations, electromagnetic torque equation and movement
Equation, and provide resistance, inductance matrix under normal circumstances；It specifically includes：
A) voltage equation of doubly-fed wind turbine under normal circumstances：
V=Ri+p ψ
In formula, v=[vas,vbs,vcs,var,vbr,vcr]TFor each phase voltage instantaneous value of motor；
R=diag (r) is resistor matrix under normal circumstances, r=[rs,rs,rs,rr,rr,rr], wherein rs, rrRespectively stator and
The resistance of every phase winding of rotor；
I=[ias,ibs,ics,iar,ibr,icr]TFor rotor phase current matrix under normal circumstances；
P is differential operator；
ψ=[ψas,ψbs,ψcs,ψar,ψbr,ψcr]TFor the total flux linkage matrix of each phase winding of rotor under normal circumstances；
B) flux linkage equations of doubly-fed wind turbine under normal circumstances：
ψ=Li
Wherein,For the inductance matrix of motor, LSS、LRR、LSRAnd LRSFor the piecemeal square of the inductance matrix L of motor
Battle array；
C) the electromagnetic torque equation of doubly-fed wind turbine under normal circumstances：
Wherein, TeFor the electromagnetic torque of doubly-fed wind turbine；
npFor the number of pole-pairs of doubly-fed wind turbine；
D) equation of motion of doubly-fed wind turbine under normal circumstances：
In formula, TLThe driving torque provided for wind energy conversion system；
J is the rotary inertia of Wind turbines；
ωrFor the angular rate of generator；
D is the resistive torque damped coefficient directly proportional to rotating speed；
2) doubly-fed wind turbine is analyzed in stator winding inter-turn short circuit the reason of winding parameter variation, and according to each phase of motor
The calculation formula of resistance, inductance, each phase resistance, inductance when calculating double-fed aerogenerator stator winding interturn short-circuit failure
Size, row write resistance, inductance matrix；
3) resistance, inductance matrix when by motor stator winding shorted-turn fault substitute into, and it is short to obtain motor stator winding turn-to-turn
Voltage equation, flux linkage equations, electromagnetic torque equation when the failure of road and the equation of motion；
4) doubly-fed wind turbine is established in MATLAB/Simulink in normal and stator winding inter-turn short circuit failure
Mathematic simulated mode, and obtain the time domain waveform of stator and rotor current and electromagnetic torque, compare the variation tendency of waveform, verification is built
The correctness of mould method.
2. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 1, special
Sign is that the matrix in block form in the inductance matrix L of motor can expand into：
In formula, LlsIt is the every phase leakage inductance of stator winding, LmsIt is the every phase main inductance of stator, Ls=Lms+LlsCertainly for the every phase of stator winding
Sense, LlrIt is the every phase leakage inductance of rotor windings, LmrIt is the every phase main inductance of rotor, Lr=Lmr+LlrIt is the every phase self-induction of rotor windings, θrFor
Stator and rotor winding axis electrical angle.
3. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 2, special
Sign is that the step 2) specifically includes following steps：
201) doubly-fed wind turbine winding parameter reason of changes in stator winding inter-turn short circuit is analyzed：
When turn-to-turn short circuit occurs for stator winding A phases, a new circuit is formd between short-circuit circle, the impedance in the circuit is very
It is small, it is assumed that a newly-increased phase is D phases；Interturn in stator windings fault severity level indicates with failure coefficient μ, it be defined as every phase short circuit around
The ratio between group the number of turns and every phase winding total number of turns；After stator winding inter-turn short circuit, voltage, electric current, magnetic linkage and resistance, the electricity of motor
Sense matrix is all changed；
202) resistor matrix when motor stator winding shorted-turn fault：
Wherein R ' is the resistor matrix under fault condition；
203) inductance matrix when motor stator winding shorted-turn fault：
(1) stator self inductance matrix is：
(2) rotor self-induction matrix is：
(3) rotor mutual inductance matrix is：
Wherein L 'SSFor stator self inductance matrix, L ' under fault conditionRRFor fault condition lower rotor part self-induction matrix, L 'SRAnd L 'RSFor event
Rotor mutual inductance matrix in the case of barrier.
4. a kind of double-fed aerogenerator stator winding interturn short-circuit Mathematical Modeling Methods according to claim 3, special
Sign is that the step 3) specifically includes following steps：
301) resistance, inductance matrix and flux linkage equations when by double-fed generator stator winding inter-turn short circuit failure substitute into voltage side
Cheng Zhong obtains voltage equation when double-fed aerogenerator stator winding interturn short-circuit：
Wherein v 'as,v’bs,v’cs,v’ds,v’ar,v’br,v’crEach phase in the case of stator winding inter-turn short circuit failure is indicated respectively
Voltage；
302) resistance, inductance matrix when by double-fed generator stator winding inter-turn short circuit failure substitute into electromagnetic torque equation,
Obtain electromagnetic torque equation when double-fed aerogenerator stator winding interturn short-circuit：
Wherein T 'eFor the electromagnetic torque in the case of stator winding inter-turn short circuit failure；
303) electromagnetic torque equation when by double-fed generator stator winding inter-turn short circuit failure substitutes into the equation of motion, obtains double
Present equation of motion when aerogenerator stator winding interturn short-circuit：
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| CN106124989B (en) * | 2016-06-29 | 2019-08-02 | 华北电力科学研究院有限责任公司 | Turbine generators machines under rotor winding faults diagnostic method and device based on diagnostic model |
| CN108733937B (en) * | 2018-05-28 | 2021-09-03 | 同济大学 | Electromagnetic noise simulation method of claw-pole generator under stator winding turn-to-turn short circuit |
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