InternalFaultDiagnosisof.doc

精品論文internal fault diagnosis ofpermanent magnet synchronous generatorfang hongwei(school of electrical engineering and automation,tianjin university,tianjin, 300072) abstract: a coupled field-circuit method by taking into account the saturation is proposed in this paper. the stator winding inter-turn short circuit and the rotor eccentricity hybrid fault of permanent magnet10synchronous generators (pmsg) is analyzed. the harmonic currents were used in order to investigate this kind of fault in a 7.5 kva pmsg suitable for low-power wind generation applications. simulation results have shown that the sideband frequency currents at 25 hz and 75 hz, and the 17th and 19th order components of terminal currents can be used as fault detection criteria.key words: permanent magnet synchronous generator; inter-turn short circuit fault; rotor eccentricity;15coupled fieldcircuit0introductionalong with the development of renewable energy and electrical power industry, diagnostics and monitoring of the internal faults of wind generators has attracted greater research attention 1,2. permanent magnetic synchronous generator (pmsg) and doubly-fed induction generators20(dfig) are the most widely used in variable-speed wind turbines at present. pmsg is increasingly finding its applications in wind power generation because of its outstanding advantages such as simple structure, high efficiency, small size and easy control 3-6. in addition, there is a clear tendency to use this kind of generators with a full-rate converter. however, stator winding faults of pmsg, which occur due to a combination of thermal, electrical, mechanical and environmental25stresses that act on the stator, are found to be one of the major causes of machine failure. accurate diagnosis and protection for this kind of fault can play a vital role in reducing the unnecessary production downtime and enhancing the reliability of wind power system, which leads to a cost effective generator operation. in the meantime, rotor eccentricities detection and fault severity assessment in electrical machines have regained increased interests for many researchers 7-12. if30the air gap eccentricity is large, then the resulting unbalanced radial forces can cause rotor to stator rub. this can result in the damage of the stator core and stator winding. notice that the inter-turn short circuit probably leads to a vibration or eccentricity in generator too. in order to overcome these problems, this paper aims to study the hybrid fault, namely the inter-turn short circuit and the rotor eccentricity. furthermore, it is our worth to enhance the detection accuracy for this kind35hybrid fault in pmsg, proper harmonic currents, such as the sideband frequency current at 25 hz and 75 hz, the 17th and 19th order currents, are selected to be the fault detection criteria. the finite element (fe) model for pmsg was presented. the common methods employed to model and detect the inter-turn short circuit and eccentricity fault are described. the hybrid fault is analyzedby the coupled field-circuit method and fft technique.foundations: ph.d. programs foundation of ministry of education of china (no. 20090032120078).brief author introduction:fang hongwei(1977-), male, associate professor, main research: electrical machine and its control. e-mail: hongwei_- 6 -401modeling of inter-turn short circuit and eccentricity with couple field-circuitmany references have addressed the principles of how a wind turbine works 13-15. although, there are many models that have been derived for the pmsg wind turbine, all of them have slightly differences. based on these papers, the wind turbine power can be expressed as45p = c( ,) av3 = c( ,) r 2 v3(1)p2 wp2 wwhere cp is the performance coefficient, is the tip speed ratio, is the blade pitch angle, a is the effective air volume flow in the rotor area, is the air density, and vw is the wind speed.the typical cp- characteristics can be shown in fig. 1.taking the saturation and other nonlinear effects into account, the coupled field-circuit method 1650is used to model the stator winding inter-turn short circuit fault and air-gap eccentricity in pmsgs.neglecting the displacement current, then the electromagnetic governing equation for a pmsg canbe represented as az v + a vz = j+ az(2)x x y y z twhere az is the magnetic vector potential, jz is the current density, and v and are the material55reluctivity and conductivity respectively.using galerkin discretization method, equation (2) can be rewritten ast pa + k a = c b i b(3)where a is the magnetic vector potential to be solved; ib is a z-dimension current vector, in which zrepresents the number of equivalent windings; p is the differential operator; t is the eddy current60coefficient matrix; k is the element stiffness matrix; and cb is the node incidence matrix for ib.fig. 2 shows a typical multi-loop model of the stator winding for the generator with an inter-turnshort circuit fault in different branch at the same phase. using this model (ns loops) with nd damping loops (nd is the number of damper bars), the voltage equation of all the n loops (n= ns+nd) can be written as65u = p + r i (4)where r is a nn matrix,u , and i represents the n1 column vector of voltage, flux andcurrent respectively. the loop current i and ib will satisfyib = g i where g is the incidence matrix between the branch and loop circuits.l70notice that the flux contains two parts: the ending flux linkage (5).mand the remainder the latter one is related to the saturation, and can be calculated from the finite element model.ikl u abucau bc fig. 1. cp - curves.fig. 2. stator winding multi-loop model.75it is well known that there are two kinds of eccentricity in electrical machines, i.e., the static eccentricity (se) and the dynamic eccentricity (de). further, these two eccentricities can result in a nonuniform air gap between the stator and the pm rotor, which is shown in fig. 3. in fig. 3, os is the symmetry center of the stator, or is the rotor symmetry axis, and ow is the rotor rotation center. from fig. 3, it can be seen that the whirling angular velocity is the same as the mechanical angular velocity of80the rotor under dynamic eccentricity, and thus it will be zero under static eccentricity.hereinafter, the degree of dynamic eccentricity is defined ase = e 100%g(6)85where g is the average airgap length, ande = or owis the dynamic eccentricity vector in pmsg.notice that this dynamic eccetricity vector is fixed in all angular positions of the pm rotor, however its angle varies as can be seen in fig. 3(b). thus, in such a condition, the air gap around the pm rotor is time varying and nonuniform.here, the static and dynamic eccentricity is realized by placing the rotor in a new position with mesh90regeneration in the fem. fig. 4 shows the corresponding fem for the healthy pm generator that is used in this paper. the transient equations of the multi-loop circuits and the motion equations are combinedwith the magnetic field equations in the finite element modeling procedure. thus, we can obtain the corresponding stator terminal currents with different kinds of inter-turn short circuit faults and different degree of dynamic eccentricity.95fig. 3. schematic diagram of eccentricity for pmsg: (a) static eccentricity; (b) dynamic eccentricity.2hybrid fault analysisfig. 4. finite element model.100it has been pointed out in 17 that the de fault can be diagnosed by using a novel pattern frequency, which can be calculated as= 2k 1 f eccentricity1 f sp (7)105where p is the number of pole pairs, k is an integer number 1, 2, 3, and fs is the supply frequency.the reason to choose the 17th and 19th order harmonic currents as de fault indicators is that they have a considerable increase at such a case. thus, the sideband frequency currents at 25 hz and 75 hz,and the 17th and 19th order harmonic currents are chosen to be the fault indicators for the inter-turn shortcircuit and de hybrid fault.110115combined the fe model with the multi-loop method, the 17th and 19th order harmonic currents spectrum under inter-turn short circuit and dynamic eccentricity hybrid fault can be obtained. fig. 5 shows the stator winding taps diagram for a 7.5kva pmsg used in wind generation. fig. 6 presents the analysis results in the condition that the inter-turn short circuit fault occurs between the stator winding taps a11 and n. fig. 7 shows the corresponding results of the sideband frequency harmonic currents at25 hz and 75 hz with the same hybrid fault.fig. 5. diagram of winding distribution and eight short-circuit taps.120i/ai/a0.60.5eccentricity fault hybrid fault0.050. 045 e ccentri city faulthybrid fault0.040.40. 0350.30.030. 0250.20.020.10. 0150051015202530354045500.010 5 10 15 20 25 30 35 40 45 50125e (%)e (%) (a) (b)fig. 6. the terminal harmonic currents under eccentricity: (a) the 17th order; (b) the 19th order.i/a0.050.04525hz 75hz0.040.0350.030.0250.020.0150.010 5 10 15 20 25 30 35 40 45 50e (%)fig. 7. terminal sideband frequency harmonic currents under eccentricity.130135140145from fig. 6, we can see that the amplitude of the 17th and 19th harmonics (phase a) decreases when the inter-turn fault occurs. notice that the 17th harmonic is bigger than the 19th one. after the inter-turn faults appears, the 17th and 19th harmonics increase when increasing the percentage of dynamic eccentricity. in fig. 7, the sideband frequency harmonic currents at 25 hz and 75 hz also increase with the de severity. in addition, the 25 hz harmonic current is bigger than the 75 hz component. thus, these four quantities can be used to detect the hybrid fault.3conclusionin this paper, the stator winding inter-turn short circuit and dynamic eccentricity hybrid fault in pmsg was modelled by using the fem and the multi-loop circuit method, while taking the saturation phenomena into account.then, the sideband frequency currents at 25hz and 75hz, and the 17th and 19th order stator current components were introduced to analyze them by using fft technique. the main contribution of this paper is that the 17th and 19th order stator current components, and the sideband frequency currents at 25hz and 75hz, are used as fault characteristics for pmsg with stator winding inter-turn short circuit and dynami c eccentricit y hybrid fault.references1501551601651701751801851 r. m. brandao, j. b. carvalho, and f. m. barbosa. fault detection on wind generatorsc. universities powerengineering conference, padova, 2008. pp. 1- 5.2 iset. advanced maintenance and repair for offshore wind farms using fault prediction and condition monitoring techniques - final reportol. http:/ec.europa.eu/energy/res/sectors/doc/wind_energy/offshore_mr_final_public_report.pdf (online available). 3 j. y. dai; 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