Abstract — The stable operation of Doubly-fed induction generator (DFIG) is vital to wind power overall system reliability. The rotor winding inter-turn short circuit fault is one of the common electrical faults in DFIG, so it is necessary to research the fault features of DFIG with rotor winding inter-turn short circuit fault. The finite element model (FEM) of DFIG was presented and used to simulate the electromagnetic field distribution of DFIG under different degree of rotor inter-turn short circuit fault. The phase angle difference, the harmonic content of rotor currents and the harmonic content of air gap flux density were also explored. The approach presented in this paper will provide the basis for the protection of DFIG with rotor inter-turn short circuit fault.1 Index Terms—Doubly fed induction generators (DFIG), finite

element method (FEM), rotor inter-turn short circuit, flux density, rotor current

I. INTRODUCTION

Wind power as a clean energy has been widely used, the doubly-fed generator (DFIG) as one of the key equipment in the wind power system, its stable operation is vital for the overall reliability of wind power generation system. The rotor winding inter turn short circuit fault is one of the generator electrical faults, so it is necessary to study electromagnetic characteristics of DFIG in normal and rotor winding turn-to-turn short-circuit condition.

Usually, the electric machines’ fault detection parameters include voltage, current, speed, flux, temperature, vibration and so on [1-8]. The appropriate signal processing methods was taken to determine the operating status of the machine and to distinguish whether the machine was failure, fault type and severity. The main methods of signal analysis include unbalanced current law [1], flux assay [2], the coordinate transformation method, the negative sequence component method, the instantaneous power decomposition method and so on. [1] put forward unbalanced current law, in which the currents of three phases are asymmetrical when the three-phase windings are unbalanced. The principle of flux detection method is that the air-gap flux will change and generate the corresponding harmonic component when turn-to-turn short-circuit fault occurs in induction motor winding [2]. With coordinate transformation method, the signal is transformed into different coordinate system in order to extract the fault features easily. [3-5] found the mathematical model of DFIG

This work was supported by Natural Science Foundation of Hebei Province in China (E2010001705)

using the d-q transformation, and carried on the wavelet analysis of the current signal.

The finite element method (FEM) is widely used to engineering simulation technology [9-14]. The electromagnetic field distribution of permanent magnet motor with short-circuit winding was simulated using finite element analysis [9-10]. Reference [11] presented the finite element model for the study of the behavior of induction motors under inter-turn short circuit conditions. Reference [12,13] analyzed the working principle of DFIG, and the simulation method for mega watt level wind power generator based on FEM software was proposed．Comparison of simulation and experimental results proved that the method was both feasible and reliable．Reference [14] established finite element model of a synchronous generator with stator winding inter turn short circuit.

In this paper, the finite element model of DFIG was presented and used to simulate DFIG with rotor inter turn short circuit fault.

II. MODEL DESCRIPTION

The two-dimensional field-circuit coupled model of DFIG was built on the basis of the finite element simulation software Ansoft Maxwell 2D. In the proposed model, the eddy current loss and skin effect was ignored.

The finite element model of DFIG is given by (1).

0

:

:

Z ZZ

Z Z

A A Jx x y y

A A

ν ν

τ

Ω⎧ ⎛ ⎞∂ ∂∂ ∂⎛ ⎞ + = −⎪ ⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂⎝ ⎠⎨ ⎝ ⎠⎪ =⎩

(1)

Where, zA is the axial components of the magnetic vector potential; ZJ is the source current density; ν is material

reluctivity; 0ZA is the known values on the boundary τ, it is well known that the permeability of the ferromagnetic material is far greater than the air permeability, so the magnetic field lines are parallel to the boundary, 0Z ZA A= .

In this paper, the basic parameters of DFIG are as follows: rated power is 5.5kW; the pole number is 4; stator and rotor slot number are 36/24 and number of turns per slot is 74 / 24; the stator outer diameter is 210mm and inner one is 136mm; rotor winding is Y connection; the rotor outer diameter is 135.2mm, inner diameter is 48mm; air gap is 0.4mm. Fig.1 is geometric model of the generator. Fig.2 gives the circuit of rotor winding under turn-to-turn short circuit fault.

FEM Analysis on Interturn Fault of Rotor Wingding in DFIG

Li Jun-qing, Wang Xi-mei School of Electrical and Electronic Engineering, North China Electric Power University, Baoding, China

e-mail:junqing03@163.com

797

2013 International Conference on Electrical Machines and Systems, Oct. 26-29, 2013, Busan, Korea

978-1-4799-1447-0/13/$31.00 ©2013 IEEE

Fig.1 The geometric model of the generator

Fig.2 The circuit which set rotor winding turn-to-turn short-circuit fault

The excitation source is applied on the rotor, the rotor

winding inter-turn short circuit fault is simulated by connecting the transition resistance with the normal winding resistance in parallel, and the transition resistance is 10moh, shown as Fig.2.

III. SIMULATION RESULTS AND ANALYSIS DFIG is also known as variable speed constant frequency

(VSCF) generating set. The relationship between the frequency and rotor speed is shown as (2).

1 260pn f f= ± (2)

Where, 1f is current frequency of generator stator and grid; 2f is the frequency of the rotor current; p is number of pole pairs; n is the rotor speed. In (2), the sign "-" is taken when the DFIG operates on the state of sub-synchronous speed, and the sign "+" is taken when DFIG operates on the state of super-synchronous speed.

The grid frequency is 50HZ and the synchronous speed of the generator is 1500rpm. In this paper, we analyzed the sub-synchronous condition where the rotor speed is 1200rpm, so the frequency of the rotor current is 2 1 =10f sf Hz= . The excitation source is applied on the rotor side, and the stator current is zero. The magnetic field, air-gap magnetic flux density and rotor current are analyzed when the generator operates healthy and rotor interturn fault state respectively.

A. The simulation of DFIG in normal operation state Fig.3 to Fig.7 describes rotor current, magnetic flux

density, magnetic field line, 3D distribution of air-gap magnetic flux density and the relationship between air-gap magnetic flux density and air-gap spatial distance respectively

when DFIG operates in healthy state. In this paper, 2D map of magnetic field distribution and air-gap magnetic flux density is given at 0.7 seconds moment.

Fig.3 gives the current waveform of rotor side in normal operation of DFIG. It can be seen that the current of three phases is symmetrical. Fig.4 and Fig.5 give the distribution of the magnetic flux density and the magnetic field lines respectively. From Fig.4 and Fig.5, the magnetic field is symmetrical distribution because the three phase windings are symmetrical.

The air-gap flux can be obtained by defining a certain path between stator and rotor of the generator, shown as Fig.6 and Fig.7. Fig.6 gives 3D map of the radial air-gap magnetic flux density when healthy generator operates in normal state. In Fig.6, green ordinate represents space distance of air gap in unit millimeter, red ordinate represents magnetic flux density in unit Tesla and blue ordinate represents time in unit millisecond. Fig.7 gives the relationship between air-gap magnetic flux density and air-gap spatial distance when healthy generator operates on 0.7 second point. In Fig.7, horizontal ordinate represents spatial distance of air gap in unit millimeter and vertical ordinate represents magnetic flux density in unit Tesla.

From Fig.6 and Fig.7，the air-gap magnetic flux density is rotating with the period of time. The air-gap magnetic flux density is a two-pair of pole symmetrical distribution at any moment. The magnetic field speed is synchronous speed, and therefore the magnetic field is movement relative to the stator. The axis of magnetic field acts on the stator teeth, may also act on the stator slot at different moments. Since cogging effect, the waveform and maximum value of the air-gap magnetic flux density change slightly in different time. In addition, the position of the fixed rotor notch is changing with the time, and it also impact on the waveform and maximum value of the air-gap magnetic flux density.

Fig.3 Rotor current in Healthy DFIG

Fig.4 Magnetic flux density distribution in Healthy DFIG

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Fig.5 Magnetic field lines distribution in Healthy DFIG

Fig.6 3D map of air-gap magnetic flux density on normal operation

Mag

netic

flux

den

sity

(T)

Fig.7 Air-gap magnetic flux density on normal operation

B. The simulate of DFIG in rotor turn-to-turn short circuit fault

The FEM model of the generator is established when the rotor winding exists inter turn short circuit fault based on Fig.1 and Fig.2. In order to analyze the characteristic of rotor inter turn short-circuit fault, three fault degrees are simulated, in which the turn number of inter-turn short circuit fault is respectively 2, 5 and 12 turns. The inter turn short circuit fault occurs in a-phase of rotor winding, and the generator is operating on sub-synchronous state where the rotor speed is 1200rpm. The rotor current, the magnetic flux density and the spatial distribution of the air-gap flux density are shown in Fig. 8, Fig. 9 and Fig. 10 respectively.

(a) 2 turns inter-turn short circuit fault

(b) 5 turns inter-turn short circuit fault

(c) 12 turns inter-turn short circuit fault

Fig.8 The rotor current under 2, 5 and 12 turns interturn fault

(a) 2 turns inter-turn short circuit fault

(b) 5 turns inter-turn short circuit fault

(c) 12 turns inter-turn short circuit fault

Fig. 9 Magnetic flux density distribution under 2, 5 and 12 turns interturn fault

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-1.25

-0.63

0.00

0.63

1.25

0.00 100.00 200.00 300.00 400.00Distance (mm)

(a) 2 turns inter-turn short circuit fault

0.00 100.00 200.00 300.00 400.00Distance (mm)

-1.25

-0.63

0.00

0.63

1.25

Mag

netic

flux

den

sity

(T)

(b) 5 turns inter-turn short circuit fault

(c) 12 turns inter-turn short circuit fault

Fig.10 Air-gap magnetic flux density under 2, 5 and 12 turns interturn fault

C. Analysis of the magnetic field From Fig.4 and Fig.9, comparing with healthy generator,

the magnetic field is asymmetrical for fault one. From Fig.9 (a), the symmetrical distribution of the magnetic field is not obviously damaged when rotor winding occurs 2 turns short circuit, only the magnetic flux density near the fault winding has a slight change, the rest region of the generator has not significant change. From Fig.9 (b) and Fig.9 (c), compared to the healthy generator, the magnetic flux density near the fault winding has a larger change with the increase of the fault degree, where the fault winding slot corresponding to the air gap have a great change, and the magnetic flux density of the stator and rotor core has a small change. In addition, the rest region of the generator occur change when 5 and 12 turns short circuit fault occurs.

By comparing the distribution of the generator magnetic flux density under different fault conditions, the following features can be obtained. When the rotor winding occurs minor interturn short-circuit fault, the magnetic flux density near the fault winding has a minor change, and the air gap flux density corresponding to the fault winding slot has a obvious change, the field in remaining positions of the generator does not change significantly. With the increase of the number of interturn short circuit, the magnetic flux density in the other parts of the generator would change. And the short-circuit

turns is more, the greater the change.

D. Analysis of the air-gap magnetic flux density From Fig.7 and Fig.10, the air-gap magnetic flux density

near the fault winding has a larger changing compared to the healthy generator. Air-gap magnetic flux density is the hub of generator energy conversion, so the in-depth study is necessary.

Spectral analysis of the air-gap magnetic flux density is an effect method in generator. Fig.11 gives the spectrum diagram of the air gap magnetic flux density, in which (a) represents healthy generator, (b), (c) and (d) respectively represent 2 turns, 5turns and 12 turns short circuit fault of rotor winding.

From Fig.11 (a), air gap the magnetic flux density in healthy generator only contain odd harmonic, not even and fractional one. In addition to the main fundamental component, there has been a small amount of 3rd, 5th and some higher odd harmonic components, such as 11th, 13th, 17th, 19th harmonic component. The higher odd harmonic component mentioned above is actually the tooth harmonic which is produced by the sharp of the stator and rotor slot. From Fig.11 (b, c, d), comparing with healthy generator, some small content of even harmonics and fractional harmonics are produced. With the degree increase of inter-turn short circuit fault, fundamental component gradually decrease and the even harmonics and fractional harmonics obviously increases.

Fig.11 Frequency spectrum diagram of air-gap magnetic flux density under

healthy, 2, 5 and 12 turns interturn fault

E. Analysis of the rotor current From Fig.3 and Fig.8, comparing with healthy generator,

the three-phase current of rotor windings is not symmetrical and their amplitude is no longer equal. From Fig.8 (a), the amplitude of three-phase has a slight change when 2 turns short circuit fault occurs, b-phase current is the largest, followed by a-phase and c-phase. From Fig.8 (b) and Fig.8 (c), the asymmetry of three-phase is more obviously with the increase of the fault degree. In addition, the phase angle of the rotor current has significant changes. TABLE I gives the values of the phase angle. Fig.12 gives the spectrum of the rotor current distribution.

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TABLE I THE CURRENT PHASE ANGLE OF THE ROTOR LATERAL LINE

Short-circuit turns abθ bcθ caθ0 120 120 120 2 124.4 119.2 116.4 5 133.9 113.7 112.4

12 144 100.8 115.2 From TABLE I, the phase angle difference of the rotor

phase current is no longer symmetrical when inter-turn short circuit fault occurs in the rotor windings. Phase angle difference abθ between rotor current a-phase and b-phase increases and more than 120 degree, phase angle difference

bcθ and caθ decreases and less than 120 degree when rotor a-phase winding occur 2 turns turn-to-turn short circuit fault. When the rotor winding occurs 5 and 12 turns short circuit fault, the phase angle difference abθ is being larger and more than 120 °, the phase angle difference bcθ and caθ are decreasing obviously.

Fig.12 gives the three phase current spectrum diagram of healthy and varying degree inter turn short circuit fault. In Fig.12, (a) represents healthy generator and (b), (c) and (d) respectively represent 2 turns, 5turns and 12 turns short circuit fault.

Current（A）

Current（

A）

Current（A）

Current（A）

Fig.12 Current spectrum on normal and different short-circuit turns failure

From Fig.12 (a), the amplitude of three-phase currents is

equal, and there is few other frequency harmonics. It can be seen that the fundamental component of a-phase and b-phase current increase and the b-phase current is slightly larger than the a-phase current, the fundamental one of c-phase current slightly decrease; a-phase, c-phase occurs a small amount of DC component and the 3rd harmonic component when rotor winding occurs 2 turns short circuit fault, shown as Fig.12 (b). When rotor winding occur 5 turns and 12 turns short circuit fault, the fundamental component of a-phase and b-phase current increase significantly, and b-phase is greater than a-phase, c-phase current increases a smaller value with respect to the a-phase and b-phase; all the three phases currents

contain a small amount of DC component and 5th harmonic components, and 3rd harmonic component significantly increase, shown as Fig.12 (c) and (d).

Generally speaking, there will appear a small amount of DC component and the 3rd harmonic component in the case of inter-turn short circuit. With the increase of fault degree, there will be 5th harmonic component, and the fundamental, DC, 3rd harmonic component will increase.

IV. CONCLUSION

In this paper, the finite element model of DFIG is established. The distribution of the electromagnetic field and rotor current are explored when DFIG is in healthy and rotor winding inter turn short-circuit fault state. With the increase of the fault degree, the magnetic flux density distribution is not symmetrical, especially at the air-gap between stator and rotor. Fractional harmonic components and even harmonic components of air-gap magnetic flux density will also increase. The phase angle and amplitude of the rotor current have a significant change and the third harmonic component increases in the case of inter turn short circuit fault. Research methods and analysis in this article will provide a theoretical reference and a basis to DFIG rotor winding inter turn short circuit fault protection mechanism.

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