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Contribution to the Fault Diagnosis of a Doubly Fed Induction Generator for a Closed-loop Controlled Wind Turbine System Associated with a Two-level Energy Storage System

Issam Attoui^ab & Amar Omeiri^bc

a Welding and NDT Research Centre, Cheraga, Algeria

b Department of Electrical Engineering, Badji Mokhtar-Annaba University, Annaba, Algeria

c Laboratory of Electrical Engineering Annaba (Laboratoire d’électrotechnique LEA), Badji Mokhtar-Annaba University, Annaba, Algeria

Published online: 20 Oct 2014.

To cite this article: Issam Attoui & Amar Omeiri (2014) Contribution to the Fault Diagnosis of a Doubly Fed Induction Generator for a Closed-loop Controlled Wind Turbine System Associated with a Two-level Energy Storage System, Electric Power Components and Systems, 42:15, 1727-1742, DOI: 10.1080/15325008.2014.950361

To link to this article: http://dx.doi.org/10.1080/15325008.2014.950361

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Issam Attoui

^1,2

and Amar Omeiri

^2,3

1Welding and NDT Research Centre, Cheraga, Algeria

2Department of Electrical Engineering, Badji Mokhtar-Annaba University, Annaba, Algeria

3Laboratory of Electrical Engineering Annaba (Laboratoire d’´electrotechnique LEA), Badji Mokhtar-Annaba University, Annaba, Algeria

CONTENTS 1. Introduction

2. Description of the Proposed System

3. Control Strategy of the Wind Energy System 4. FOC

5. Illustrative Examples for FO-PI and FO-I Design Methods and Advantages

6. Proposed Diagnosis Technique 7. Results and Interpretation 8. Conclusion

References

Keywords: wind energy conversion systems, adaptive Fast Fourier transform, doubly fed induction generator, fault detection and diagnosis, fractional-order control, two-level energy storage system

Received 12 November 2013; accepted 22 June 2014

Address correspondence to Dr. Issam Attoui, Recherche Unit on Industrial Technology, Welding and NDT Research Centre (CSC), Cheraga, BP 64, Algeria. E-mail: iatoui@cscdz, atoui [email protected]

Abstract—In this article, a contribution to the fault diagnosis of a doubly fed induction generator for a closed-loop controlled wind turbine system associated with a two-level energy storage system using an on-line fault diagnostic technique is proposed. This technique is proposed to detect the rotor fault in the doubly fed induction generator under non-stationary conditions based on the spectral analysis of stator currents of the doubly fed induction generator by an adaptive fast Fourier transform algorithm. Furthermore, to prevent system deterioration, a fractional-order controller with a simple design method is used for the control of the whole wind turbine system. The fractional- order controller ensures that the system is stable in both healthy and faulty conditions. Additionally, to improve the production capacity under wind speed fluctuations and grid demand changes, a two-level energy storage system consisting of a supercapacitor bank and lead- acid batteries is proposed. The obtained simulation results show that the objectives of the fault diagnosis procedure and control strategy are reached.

1. INTRODUCTION

The wind energy conversion system (WECS) is considered to be a renewable energy source that has a great potential, and it is developing increasingly fast compared to its renewable-energy counterparts. The major technological developments of this system focus on maintenance strategies optimization [1–3], production capacity improvement [4], dynamic and control stability improvement [5, 6], and fault-tolerant control robustness [7]. Therefore, the design of an improved wind turbine system (WTS) often leads to the design of more robust control and an advanced fault diagnosis procedure.

The greater part of variable-speed wind turbines (WSWTs) is equipped with a doubly fed induction generator (DFIG).

Therefore, the control and the fault diagnosis of this machine 1727

Downloaded by [ATTOUI Issam] at 13:55 22 October 2014

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have regained importance. Based on experiences done by in- dustrials and experts, the rotor fault (short circuit or increasing resistance) that gives rise to rotor phase dissymmetry can be a serious problem in variable-speed induction machines [8]. In closed-loop operation of WTSs, this fault can easily be am- plified and consequently develop into a failure of the whole controlled WTS if the progress of the fault is not detected.

Therefore, it is necessary to detect this fault as soon as pos- sible to minimize maintenance cost and prevent unscheduled downtimes through advanced on-line diagnostic techniques.

In this perspective, several diagnostic techniques can be found in the literature for rotor fault diagnosis using the steady-state spectral components of the current variables [9–11]. Presently, these techniques are being applied to wind generators; however, the operation of wind generators is predominantly transient, which gives rise to the development of non-stationary techniques for fault detection and diagnosis [12]. A variety of recent non-stationary techniques have been proposed in the literature, including the adaptive short-time Fourier transform (STFT) [13], adaptive S-transformer [14], and adap- tive smoothed pseudo Wigner-Ville distribution (WVD) [15].

However, the main disadvantage of these approaches is the very high computational complexity [16]. In this article, depending on the rate of change of the instantaneous frequency (IF), an optimal window length can be deduced for the spectro- gram [17]. Based on this hypothesis, an adaptive fast tourier Transform (FFT) with optimal window length is proposed.

This method provides much better performance than the con- ventional FFT algorithm previously used [18, 19] and presents a low computational complexity.

Another way to prevent system deterioration is to develop a controller having some capabilities to remain robust in faulty conditions. The task to be tackled in achieving robust control is the design of a controller with a suitable structure to guarantee satisfactory performance, not only when the system is in healthy conditions but also in the case when the system is operating under a faulty mode. In this context, in the applied vector control strategy to the DFIG, two fractional- order controllers (FOCs)—the fractional-order proportional- integral (FO-PI) and the fractional-order-integral (FO-I)—are proposed and designed for the control of the whole wind energy system according to the imposed three tuning constraints to guarantee control performance and robustness to static gain variations. In comparison with the classical-order controllers used previously [4, 20, 21], the FOC has a potential to improve the control performance [22] and increase system robustness because of its additional parameters [23]. For these reasons, the application of fractional calculus in the control area has been recently been used more frequently [24–28]. The contribution in this article to WTS control is that the used analytical

parameters tuning methods for the FO-PI and FO-I controllers are practical, are simple to apply, and can achieve favorable dynamic performance and robustness in both healthy and faulty conditions.

To improve the production performance of the WECS, a two-level energy storage system (ESS) consisting of a supercapacitor bank and lead-acid batteries is proposed. Through the proposed energy management system, the power flow between the multiple energy sources (battery and supercapacitor) and the DC bus is controlled in a parallel mode.

The deviations between the available wind energy input and desired active power output are compensated by all energy sources simultaneously with different contributions depending on the characteristics of the energy source and also the defined energy control rules. The ESS is connected to the DC-link rather than to the grid for the reason that, in this topology, the ESS can reinforce the DC bus of the DFIG converters during transients, thereby enhancing the low-voltage ride through capability of the WTS [29, 30].

This article is organized as follows. Section 2 presents a description of the wind energy system. Section 3 describes the control strategy. In Sections 4 and 5, the proposed fractional- order control strategy with the FO-PI and FO-I FOCs is presented and compared with integer-order proportional-integral (IO-PI) controllers. Section 6 gives a description of the proposed fault detection and diagnosis procedure. Simulation results are presented in Section 8. Finally, concluding remarks are given in Section 8.

2. DESCRIPTION OF THE PROPOSED SYSTEM The wind energy system proposed in this study is depicted in Figure 1. This system consists of a VSWT driving a DFIG through a gearbox. The stator of the DFIG is directly connected to the electric network, and the rotor is connected through two multi-level converters, a DC-link, a two-level ESS, and an RL filter. The topology of the multi-level converters used in this system is three-level, neutral point clamped (NPC). The two-level ESS consisting of a supercapacitor bank, lead-acid batteries, and two-quadrant DC/DC converters is connected to the DC link of the DFIG converters. The use of converters between the rotor, two-level ESS, and electric network allows the power transfer control between the stator and the grid, the rotor and the grid, and also the two-level ESS and the grid.

Regarding the operation of the proposed system in power flow transfer, it is assumed that dispatched powerPgfrom the wind energy system to the mains grid is kept constant. The mismatch between wind powerPwandPgis compensated by the power of the two-level ESSPESS, wherePESS(t)=Pg(t) –Pw(t).

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FIGURE 1.Proposed wind power system.

3. CONTROL STRATEGY OF THE WIND ENERGY SYSTEM

The scheme of the system control (grid-side control, rotor-side control, and two-level ESS control) is shown in Figure 2. The grid-side control is dedicated to control the active and reactive power exchanged between the grid and wind energy system.

The rotor-side converter (RSC) is dedicated to control the stator reactive power exchange with the grid and also the rotor speed of the DFIG (mec) to extract maximum power from the wind. The two-level ESS control is dedicated to control the DC-link voltage with bi-directional DC-DC converters. These blocs can be controlled independently.

FIGURE 2.Scheme of system control.

To design the FO-PI controller, it is assumed that the controlled system is healthy. Next, the robustness of the control law is tested by using the faulty system (Rra=Rr+Rd), where Rdis the inserted additional resistance to phaseAof the rotor.

3.1. RSC Controller

When we apply vector control strategy to the DFIG, the Park reference frame is oriented as

⎧⎪

⎪⎪

⎪⎨

⎪⎪

⎩

Vqs =Vs =ωsφs

Vds =0 φds =φs

φqs =0

, (1)

whereVds,Vqs,φds, andφqsare the direct and quadrate stator voltages and magnetic fluxes, respectively. And because the d-axis lags theq-axis 90^◦ in phase, when ignoring stator resistance, the active and reactive stator power (Ps,Qs) and the electromagnetic torque (Tem-DFIG) can be described as follows:

⎧⎪

⎪⎪

⎨

⎪⎪

⎪⎩

Ps = −Vs

Lm

Ls

iqr

Qs= Vsφs

Ls

− VsLm

Ls

idr

Tem−D F I G = −(P.Lm.φs/Ls).iqr

, (2)

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wherePis the number of generator pole pairs,LmandLsare the magnetizing and total cyclic stator inductances, andidrand iqrare the two-phase rotor currents.

The rotor voltages can be described as follows:

⎧⎪

⎪⎪

⎪⎨

⎪⎪

⎩

Vdr =Rr didr+Rdqriqr

+

Lr− ^L_L²^m_sdidr

dt −sωs

Lr−L²_m Ls

iqr

s =ωs−ωr/ωs

Vqr =Rr qiqr+Rqdridr

+

Lr− L²_m Ls

di_qr dt −sωs

Lr−^L_L²^m_s

idr+s^L_L^m

sVs

,

(3) where ωr =P mec is the electrical speed,s is the generator slip. Rrd,Rrq,Rqdr, andRdqr are thedqrotor resistances, given by

Rdr Rr dq

Rr qd Rqr

=PR.RRPR−1, RR =

⎡

⎢⎢

⎣

Rr a 0 0 0 Rr a 0 0 0 Rr a

⎤

⎥⎥

⎦,

PR= 2

3

sin (θ) sin θ−²₃^π

sin θ+²₃^π cos (θ) cos

θ−²₃^π cos

θ+²₃^π

, (4) whereRris a 3-by-3 rotor resistance matrix, andPris the Park transformation for rotor variables.

The control strategy applied to the to control the rotor speed of the DFIG and the stator reactive power exchange with the grid is depicted in Figure 3.

The measured rotor speed is compared with the reference rotor speed (mec-ref), and the difference is sent to an FO- PI controller to get the electromagnetic torque reference. The electromagnetic torque reference is compared with the actual measurement. The error between these signals is used in FO-PI controllers to defineVdr-ref. Furthermore, the measured stator reactive power is compared with its reference (Qs-ref) to define Vqr-ref.

To extract maximum power from the wind, tip speed ratio λis tuned toλopt over different wind speedsυw by adapting

FIGURE 3.Control diagram of RSC.

the wind turbine (WT) speedtrtotr-ref: tr−r e f = λoptυw

R ; (5)

Cpis maintained atCp-max, and the maximal power is achieved by trackingtr-refin Eq. (5).

3.2. Grid-side Converter (GSC) Controller

The active and reactive powers (PGSC,QGSC) at the GSC are defined as

PG SC =Vdsid f +Vqsiq f QG SC =Vqsid f −Vdsiq f. (6) In Eq. (7), the relation betweenVDC(the DC-link capacitor voltage),PGSC(GSC output power,PESS(two-level ESS output power), andPr(RSC input power) is presented:

Pr −PG SC −PE S S= 1 2Cd

V_DC²

dt . (7)

For a constant DC-link voltage, the relation betweenPESS, PGSC, andPrdefined as

PG SC =Pr−PESS. (8) For a constant DC-link voltage, the active power at the grid is defined as

Pg=PG SC+Ps =Pr−PE S S+Ps. (9) The block diagram of the GSC with its controllers is presented in Figure 4.

The GSC active power reference (PGSC-ref) is determined from the difference between the stator active power of the DFIG and the desired grid active power output. The active and reactive powers of the GSC are compared with the actual measurement. The error between these signals is used in FO-PI controllers to defineVqf-refandVdf-ref.

The GSC and RSC are derived by voltage reference pulse- width modulation (VRPWM). Once the reference voltages are determined, the actual voltages can be generated using a voltage sourced converter operated with VRPWM.

3.3. Two-level ESS and Control Strategy

Lead-acid batteries are suitable for storing energy for long periods of time [31]; they have a high energy density but a

FIGURE 4.Control diagram of GSC.

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FIGURE 5.Two-level ESS and its associated proposed control.

relatively slow charging and discharging speed. Furthermore, such batteries have limited lifespan [32, 33]. On the other hand, the lifetime of supercapacitors is long; their power density is higher than that of other batteries, while their energy density is generally lower [34–36]. Based on these characteristics of a battery and a supercapacitor, a two-level energy storage control scheme is proposed and shown in Figure 5. In the proposed energy control scheme, the DC bus voltage is controlled in a parallel mode by all energy sources simultaneously with a different contribution depending on the characteristics of energy sources and also the defined energy control rules. To optimize the lifespan of batteries, it is recommended that the battery’s current slope must be limited within a safety range to reduce peak power transient stresses toward it. The implemented current slope limitation is modeled as a first-order feedback system with magnitude saturation in the forward path. In this case, the peak power response could come from the supercapacitors.

The size of the two-level ESS depends on the maximum mismatch power between the available wind energy input and desired grid power output. Both the wind power and grid power are variable. Then the size of the two-level ESS requires an estimate of the maximum variation of the wind power and also the maximum variation of the desired grid power.

In Figure 5,d1andd2are the duty ratios of switchesST3and ST1, respectively; SOC is the state of charge; andibandisare the currents of the battery and the supercapacitor, respectively.

The DC bus voltage is coordinately controlled by the battery and supercapacitor. First, the measured DC bus voltage is compared with the reference DC bus voltage (VDC-ref), and the difference is sent to a fractional-order integration controller to get the current references. The current references are compared with the actual measurements. The error between these

signals is used in FO-PI controllers to define the duty of the two-quadrant DC/DC converters.

4. FOC

A novel control strategy based on FOCs is proposed for the variable-speed operation of the WTs. Fractional calculus gives a generalization of ordinary differentiation and integration to arbitrary (non-integer) order [37].

The fractional-order differentiator can be denoted by a gen- eral operatoraD^λt[38], given by

aD^λ_t =

⎧⎪

⎪⎪

⎪⎨

⎪⎪

⎩ d^λ

dt^λ, R(λ)>0

1, R(λ)=0

t a

(dτ)^−λ, R(λ)<0

, (10)

whereλis the order of derivative or integrals, andR(λ) is the real part ofλ.

The called Riemann–Liouville definition of fractional derivatives and integrals is

aD_t^−λf (t)= 1 (λ)

t a

(t−τ)^λ−¹f (τ)dτ, (11)

aD^λ_t f (t)= 1 (n−λ)

dⁿ dtⁿ

⎡

⎣ t a

f (τ)dτ (t−τ)^λ−ⁿ⁺¹dτ

⎤

⎦, (12)

where

(x)= ∞

0

y^x⁻¹e⁻^yd y (13)

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is the Euler’s Gamma function,a andt are the limits of the operation, andλis the number identifying the fractional order.

In this article,λis assumed to be a real number that satisfies the restriction 0< λ≤1. Also, it is assumed thata=0. The following assumption is used:0D^−λt≡D^−λt.

In this work, Oustaloup’s approximation method [39] is used. Assuming the frequency range to fit is selected as (ωb, ωh), the Oustaloup algorithm is based on the approximation of a function of the form:

H(p)= p^λ, λ∈ ⁺ (14) by a rational function

H∧(p)=C N k=−N

p+ω_k p+ωk

, (15)

where the zeros, poles, and the gain can be evaluated from ωk=ωb

ωh

ωb

k+N+1 2(1−λ)

2N+1 , ωk=ωb

ωh

ωb

k+N+1 2(1+λ)

2N+1 ,

C = ωh

ωb

−^λ2 N k=−N

ωk

,

where [ωb,ωh] is the selected frequency band for the approximation of the fractional order.

4.1. FO-PI^λController

The differential equation of the FO-PI^λcontroller, 0< λ<2, in the time domain, is given by

u(t)=Kp

e(t)+KiD_t^−λe(t)

, (16)

whereKpis a proportional gain, andKiis an integration constant. Takingλ=1 in Eq. (16), a classical proportional-integral (PI) controller is obtained. Hence, using Laplace transforms, the transfer function of the FO-PI^λ and PI controllers are, respectively, given by

C (p)=Kp

1+Ki

p^λ , (17)

G (p)=Kp

1+Ki

p , (18)

wherepis the usual Laplace transform variable.

The FO-PI^λcontroller is more flexible than the classical PI controller because it has one more adjustable parameter, which reflects the intensity of integration.

Evidently, Eq. (17) is a specific form of the common PI^λD^μ controller mentioned in [40].

Design Specifications of the FO-PI

Assuming that the gain crossover frequency is ωc and the phase margin isϕm, for system stability and robustness, three

specifications concerned with the phase and the gain of the open-loop transfer function are proposed [41, 42]:

(i) phase margin specification:

Ar g[G(jωc)]=Ar g[C(jωc)P(jω|c)]= −π+ϕm; (ii) gain specification at the crossover frequency:

|G(jωc)|dB = |C(jωc)P(jωc)|dB =0;

(iii) robustness to variations in the gain of the plant imposes that the phase derivative with respect to (w.r.t.) the frequency is zero;i.e., Bode’s phase plot is flat at the gain crossover frequency; this means that the system is more robust to gain changes and that the overshoots of the response are almost the same:

d(Arg|G (jω)|)

dω _ω=ω_c =0.

4.2. FO-I Controller

In this study on the design of feedback amplifiers, Bode [38]

suggested an ideal shape of the open-loop transfer function of the form:

F(p)= ωc

p

λ, λ∈R. (19)

This choice of F(p) gives a closed-loop system with the desirable property of being insensitive to gain changes. If the gain changes, crossover frequencyωcwill vary, but the phase margin of the system remainsφm=π (1 –λ/2) rad indepen- dently of the value of the gain.

5. ILLUSTRATIVE EXAMPLES FOR FO-PI AND FO-I DESIGN METHODS AND ADVANTAGES This section presents illustrative examples to verify the FO- PI and FO-I designs. A comparative study of the robustness performances obtained with the FO-PI/FO-I controllers and a classical type PI controller is presented.

5.1. Electromagnetic Torque FO-PI Controller (RSC Control)

The simplified bloc diagram of theTem-DFIG control for the FO-PI design (Figure 6) is given by

F(p)= −PφsLm/(LsRr) 1+p

Lr−^L_L²^m_s /Rr

= −P VsLm/(LsRrωs) 1+p

Lr−^L_L²^m_s /Rr

= K

1+pT. (20)

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G(p)=C(p)F(p)=Kp

1+Ki

p^λ

K

1+pT . (21) According to specification (i), the phase of G(jω) can be expressed as

Arg|G(jωc)| = −arctan Kiωc^−λsin (λπ/2) 1+Kiω^−λc sin (λπ/2)

−arctan (ωcT)= −π+φm. (22) From Eq. (22), the relationship between Ki andλ can be established as follows:

Ki = −tan [arctan (ωcT)+φm]

ω^−λc sin (λπ/2)+ω^−λc cos (λπ/2) tan [arctan (ωcT)+φm]. (23) According to specification (iii) about the robustness to gain variations in the plant,

d(Arg|G(jω)|)

dω _ω=ω_c = Kiλωc^λ−¹sin (λπ/2) ω²c^λ+2Kiω^λccos (λπ/2)+K_i²

− T

1+(Tωc)² =0. (24) From Eq. (24), another equation aboutKican be established in the following form:

Cω⁻c²^λK_i²+D Ki+C =0; (25) that is,

Ki = −D±

D²−4C²ω⁻c²^λ

2Cω⁻c²^λ

, (26)

where

C= T

1+(Tωc)² and

D=2Cω^−λc cos (λπ/2)−λωc^−λ−¹sin (λπ/2). (27) According to specification (ii), an equation aboutKpandK can be established:

KpK

1+Kiωc^−λcos (λπ/2)2

+

Kiω^−λc sin (λπ/2)2

1+(ωcT)²

=1.

(28)

Clearly, Eqs. (24), (26), and (28) can be solved to getλ,Ki, andKp.

FO-PI Robust Controller Design Procedure

Using a graphical method [43], the procedure of the FO-PI controller design is summarized as:

(1) givenωc=900 (rad/sec), the gain crossover frequency;

(2) givenϕm=70^◦, the desired phase margin;

(3) plot curve 1,Kiw.r.t.λ, according to Eq. (24), and plot curve 2,Ki w.r.t.λ, according to Eq. (26); Figure 7 shows the two curves;

(4) Obtain the values ofλandKifrom the intersection point on the above two curvesλ=0.407 andKi=28.14;

(5) calculateKpfrom Eq. (28);Kp=0.0172.

The open-loop frequency response can then be fixed with the FO-PI controller. For the first-order velocity servo plant, the proposed FO-PI controller is

C(p)=0.0172

1+28.14

p⁰^.⁴⁰⁷ . (29) The Bode diagrams of open-loop transfer function G(p) (Eq. (21)) is plotted in Figure 8, where it can be seen that all three specifications are satisfied with the FO-PI controller.

However, with the IO-PI, specification (iii) is not satisfied (phase>–110 rad/sec). This means that the FO-PI controller realizes better robustness against system parameter variation compared to the IO-PI controller (Kp = 0.0415 and Ki = 392.290).

5.2. DC-link Voltage Control with FO-I Controller The simplified bloc diagram of the DC-link voltage control of DFIG is given by Figure 9. Substitutingωc=90 (rad/sec) andϕm=70^◦in Eq. (19) givesλvdc=0.222 (λ=1.222) and Kivdc=7.3317.

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10 10 10 10 10 10 10

−100 0 100 200

M a g n i t u d e ( d B )

10 10 10 10 10 10 10

−150

−100

−50 0

P h a s e ( d e g )

F r e q u e n c y ( r a d / s e c )

FO−PI IO−PI

FO−PI IO−PI X : 9 0 0

Y: 0 0

X : 9 0 0 Y : − 1 1 0

FIGURE 8.Bode plot of open-loop transfer functionG(p) with FO-I and IO-PI controllers.

The Bode diagrams of open-loop DC-link voltage control are plotted in Figure 10.

It can be seen in Figure 10 that the FO-I controller realizes better robustness against plant parameter variation compared to the IO-PI controller (Kp=1.268 andKi=32.757).

5.3. Comparison Example with IO-PI Controller in Time Domain

This section compares the performance of the FO-PI controller with the IO-PI controller in the time domain with the parameter variations of theTem-DFIGcontrol loop.

In applying the IO-PI controller (Figure 11(a)) and the FO- PI controller (Figure 11(b)), the unit step responses are plotted with a closed-loop gain (k) varying from 0.3 to 4. From Figures 11(a) and 11(b), it is obvious that with the fractional controller, good unit step responses are achieved, and the overshoots remain almost constant under gain variations over that with the IO-PI controller, demonstrating that the controlled system using the FO-PI controller is more robust to gain changes in the loop.

6. PROPOSED DIAGNOSIS TECHNIQUE

Simulations of the proposed WTS in a closed loop operating under faulty and healthy conditions have been performed to test the diagnosis technique. The diagnosis technique is based on frequency component analysis of the stator current signal that are related to rotor fault. In variable-speed operation of

FIGURE 9.DC-link voltage loop control.

10 10 10 10 10 10 10

−100 0 100 200 300

M a g n i t u d e ( d B )

10 10 10 10 10 10 10

−200

−150

−100

P h a s e ( d e g )

F r e q u e n c y ( r a d / s e c )

IO−PI FO−I

IO−PI FO−I X : 9 0

Y : 0 0

X : 9 0 Y : − 1 1 0

FIGURE 10.Bode plot of open-loop DC-link voltage control with FO-I and IO-PI controllers.

WTs under faulty conditions, this fault’s component frequency included in the stator current signal are variable over time according to the machine slip. Then, in these conditions, the stator current signal is not stationary. However, it is well known that classical FFT supposes a stationary signal during the signal analysis. If this is not guaranteed, classical FFT techniques are not sufficient to represent correctly this signal.

Depending on the rate of change of the IF of the fault’s component due to the rotor fault, it is suggested to adaptively

0 0.005 0.01 0.015 0.02 0.025 0.03

0 0.2 0.4 0.6 0.8 1 1.2 1.4

T i m e ( s )

S t e p R e s p o n s e

k=1 k=0.6 k=0.3 k=4

0 0.005 0.01 0.015 0.02 0.025 0.03

0 0.2 0.4 0.6 0.8 1 1.2 1.4

T i m e ( s )

S t e p R e s p o n s e

k=1 K=0.6 k=0.3 k=4

( b ) ( a )

FIGURE 11.Step torque responses: (a) with IO-PI controller (b) with FO-PI controller.

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Figure 12. First, optimal window durationToptimalis calculated using Eq. (34), stator voltage frequency, and measured rotor speed. Second, the stator current that has total durationToptimal

is analyzed by the FFT algorithm, which gives a frequency representation of the temporal signal. The spectrum generated by this transformation includes only the magnitude information about each frequency component. Third, using the theoretical fault harmonics (Eq. (31)), only the components that are of particular interest are kept, because they specify char- acteristic frequencies in the stator current spectrum that are known to be coupled to a particular DFIG fault (rotor fault).

The classification of failure types is based on differences in spectra signatures on the stator current of the DFIG and theoretical fault spectra signatures (theoretical fault harmonics [Eq. (31)]). When the rotor fault is detected and diagnosed, the alarm/warning system will be active and can cause the shutdown of the equipment.

6.1. Instantaneous Fault Frequency Evolution (IFFE) As far as the rotor fault is concerned, rotor unbalance produced by additional resistance of the same value of one phase resistance is considered. This asymmetry produces an inverse sequence component at frequency–sf in the rotor, which, in turn, generates a chain of fault components in the stator wind- ings. The first one is the well-known harmonic component at frequency:

fsa =(1−2s) fs, (30) wheresis the slip, andfsis the stator voltage frequency.

The corresponding IFFE of fault component is (1−2s)fs, which was computed in time domain as [44]:

fsa(t)=(1−2s(t))fs. (31) 6.2. Optimal Window Length of FFT for Rotor

Fault Detection

For a mono-component signal, the optimal window duration is inversely related to the rate of change of the IF. More precisely, if the window has total durationT, the following value can be

FIGURE 12.Flowchart of proposed diagnosis procedure.

shown [45, 46]:

Topti mal =√ 2

d fi(t) dt

⁻¹^/². (32)

It is evident from Eq. (31) that the frequency of the fault component is a function of the machine slip.

The only solution, therefore, is to adapt the duration of the window to FFT at each time location to optimize frequency

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resolution of the fault components:

Topti mal(t)=√ 2

d fsa(t) dt

⁻¹^/²=√ 2

d((1−2s) fs) dt

⁻¹^/²

=√ 2

(1−2s)d fs

dt −2fs

ds dt

⁻¹^/². (33)

For a constant stator voltage frequency, the expression in Eq. (33) can be simplified as follows:

Topti mal(t)= fs

ds dt

⁻¹^/². (34)

7. RESULTS AND INTERPRETATION

To verify the efficiencies of the control strategy and diagnosis procedure, three simulation cases are presented for the WECS in Figure 1 with the specified parameters given in Table 1, where the nominal power of the generator is 1.5 MW, the rated wind speed is 10 m/s, and the rated rotational speed of the DFIG is 1755 rpm.

The first case is the simulation of the WT in healthy conditions with reference reactive powersQs-ref=0 andQGSC-ref

=0 and reference active powerPg-ref=–1.5 MW. The second case presents the same problem, but the WT is in faulty conditions with the rotor fault under wind speed fluctuations and

WT mechanical model

R = 47 m Number of blades = 3 G = 90 λcp-max=8.1

Jt=50 Kg.m² ft=7.1e^–2Nm

DFIG

Pn=1.5 MW Us=690 V fs=50 Hz P=2 Rs=0.012 ohm

Ls=13.732 mH Lm=13.528 mH Rr=0.021 ohm Lr=13.703 mH

Back-to-back VSC and filters

VDC=1800 V C=30,000e–6 F Rf=0.0015 ohm Lf=2 mH

Medium-term storage (lead–acid battery)

Pn=840 kW Vb=675V imax-nom=1700 A imin-nom=–1700 A

Vb-max=735 V Rb=0.0039 ohm Lb=4.1 mH SOCmax/SOCmin%=

90/20%

Short-term storage (supercapacitor)

Esc=7 MJ Pn=800 kW V(0)=675 V Csc=48 F SOCmax/SOCmin%=

95/15%

Lsc=4.1 mH Rsc=0.019 ohm imax-nom=1700 A imin-nom=–1700 A Ns=250 Np=4 Main parameters of FO-PI and FO-I controllers

Kp Ki λ

Eelectromagnetic torque (RSC control)

0.9333 0.407 –0.1556e^–4

0.0504 0.2282

— 0.0172

6389

336.5 77.95

7.3317 442 28.14

28.14

0.222

0.226 0.24 0.222 0.225 0.407

0.407 Rotor speed rotor speed (RSC control)

Stator reactive power (RSC control)

Grid active and reactive powers (GSC control) Battery current (two-level ESS control) Supercapacitor current (two-level ESS control) DC-link voltage (two-level ESS control)

TABLE 1.Main parameters of complete WECS model

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Case 1: Simulation Results of the WECS in Healthy Conditions

Simulations of the wind energy system connected directly to the grid through the DFIG were carried out in a MATLAB environment (The MathWorks, Natick, Massachusetts, USA).

Simulation results are obtained for reactive powersQs-ref=0 andQGSC-ref=0 and active powerPg-ref=–1.5 MW.

Figures 13(a) and 13(b) show, respectively, the wind speed profile and slip of the DFIG. Figure 13(c) presents some differences between the rotational speed of the turbine and the imposed optimal speed corresponding to the wind speed evolution. The turbine’s rotational speed components follow their references perfectly. Electromagnetic torque Tem-DFIG

is then independently controlled to track reference torque Tem-DFIG-ref. The torque controller achieves good performance, whileTem-DFIGandTem-DFIG-refexhibit almost the same behav- ior (Figure 14(a)).

The rotor current waveform is also shown in Figure 15(b), the frequency of which varies according to slips. Figures 14(c) and 14(d) show, respectively, the wind generator power and stator active power of the DFIG. The responses of grid active power and stator reactive power are shown in Figure 15(a). It is noted that the wind generator power can also be maintained

0 10 20 30

8 10 12

W i n d ( m / s )

T i m e ( s ) −0.20 10 20 30 0

0.2

s

T i m e ( s )

0 5 10 15 20 25 30

140 160 180

Ω ( r e d / s )

T i m e ( s ) 5.7 5.8 5.9

187 187.2

( b )

( c ) ( a )

Ω

FIGURE 13.(a) Wind speed profile, (b) DFIG slips, and (c) rotational speed of turbine.

FIGURE 14.(a) DFIG electromagnetic torque, (b) rotor voltage and current of DFIG, (c) wind generator powerPmec, and (d) stator active powerPs.

as constant at the desired level of transmission system under the proposed control strategy.

The responses of GSC active and reactive powers are shown in Figure 15(b); these components follow their references perfectly. The nearly constant DC voltage of the DC link between two three-level converters and two-level ESSs, the active power injected into the two-level ESS, and the total current of the two-level ESS are shown in Figures 15(c), 15(d), and 15(e), respectively.

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FIGURE 15.(a) Grid active and stator reactive powers, (b) GSC active and reactive powers, (c) DC voltage waveform of DC link between two three-level converters, (d) power injected into two-level ESS, and (e) total current of two-level ESS.

Case 2: Simulation Results of the WECS in Faulty Conditions with Rotor Fault

In this part, simulations of the WTS in closed-loop operating conditions under faulty conditions with reactive powers (Qs-ref =0, QGSC-ref =0) and variable reference grid active power (Pg ref) have been performed to test the diagnosis method and control strategy. It is considered that the failure of a rotor phase starts at instantt1=15 sec. Rotor unbalance is produced by an additional resistance of the rotor phase.

FIGURE 16.(a) Grid active and stator reactive powers, (b) GSC active and reactive powers, (c) DC voltage waveform of DC link between two three-level converters, (d) power injected into two-level ESS, and (e) total current of two-level ESS.

The grid active power and stator reactive power, GSC active and reactive powers, nearly constant DC voltage, active power injected into the two-level ESS, and total current of the two-level ESS are shown in Figures 16(a), 16(b), 16(c), and 16(d), respectively. These components follow their references perfectly in both healthy and faulty conditions. The small oscillations of the dynamic characteristics of different parameters of the WTS start from time instantt1=15 sec and justify the presence of a rotor phase defect in the DFIG.

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FIGURE 17. Case 2 with classical PI controllers: (a) grid active and stator reactive powers, (b) GSC active and reactive powers, (c) DC voltage waveform of DC link between two three-level converters, (d) power injected into two-level ESS, and (e) total current of two-level ESS.

grid demand (Pg ref) have been performed to test ESS ability and control strategy robustness. It is considered that the failure of a rotor phase starts at instantt1=15 sec. The grid active

FIGURE 18.(a) Grid active and stator reactive powers, (b) GSC active and reactive powers, (c) DC-link voltage, and (d) power injected into two-level ESS.

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0 5 10 15 20 25 30

−10

−8

−6

−4

−2 0 2 4 6

x 10⁵

P B a t t e r i e s a n d P S u p e r c a p a c i t o r s ( W )

T i m e ( s ) P S u p e r c a p a c i t o r s

P B a t t e r i e s

FIGURE 19.Active powers of batteries and supercapacitors.

power and stator reactive power, GSC active and reactive powers, nearly constant DC voltage, and total active power injected into the two-level ESS are shown in Figures 18(a), 18(b), and 18(c), respectively. These components follow their references

T i m e ( s ) T o p t i m a l ( s )

F r e q u e n c y ( H z )

A m p l i t u d e ( d B )

Spectrum of stator current in healthy condition

Spectrum of stator current in faulty condition with classical FFT

Spectrum of stator current in faulty condition

( b )

T o p t i m a l − m a x = 0 . 9 s ( a )

( c )

( d )

(1 + 2 s ) f

s

t = 1 6 . 8 s e c T o p t i m a l = 0 . 6 se c

S l i p = 0 . 1 t = 1 6 . 8 s e c T = 2 s e c S l i p = 0 . 1 t = 1 6 . 8 s e c T o p t i m a l = 0 . 6 se c

S l i p = 0 . 1

FIGURE 20.(a) Optimal window length of FFT, (b) proposed FFT of stator current in healthy conditions, (c) classical FFT of stator current in faulty conditions, (d) proposed FFT of stator current in faulty conditions.

perfectly with small oscillations starting from time instant t1 = 15 sec. Figure 19 shows the active power of the batteries and supercapacitors. When the battery’s current slope is limited within a safety range to reduce peak power transient stresses toward it, the peak power response could come from the supercapacitors.

The result obtained with the proposed algorithm (Eq. (34)) is shown in Figure 20(a). This result gives the optimal window length (Toptimal) as a function of the time of the FFT algorithm to optimize frequency resolution of the fault components (Eq. (31)) at each time location. In the present work,Toptimal-max

(maximal value of the window length) equal to 0.9 sec is cho- sen. In a healthy period, harmonic components (1±2s)fsare negligible. Consequently, the stator current signal is stationary. However, the use of the adaptive FFT algorithm in this case can confirm that the harmonic components (1 ±2s)fs

are negligible. In a faulty period, harmonic components (1± 2s)fsare not negligible; consequently, the stator current signal is not stationary. The use of the adaptive FFT algorithm in this case improves the frequency resolution of the harmonic components (1±2s)fs. Figure 20(b) shows the stator currents’

adaptive FFT in healthy conditions, and the harmonic component (1 – 2s)fsis negligible, while Figures 20(c) and 20(d) show the classical and adaptive FFT algorithms of the stator current in the case of rotor unbalance. The presence of the fault components at frequencies (1±2s)fsis clear using the adaptive FFT algorithm (Figure 20(d)), but with the classical FFT algorithm, the presence of the fault components at frequencies (1±2s)fsis not clear (Figure 20(c)).

8. CONCLUSION

In this article, a contribution to the fault diagnosis of a variable- speed DFIG-based WTS using a fault diagnosis technique is proposed. The proposed adaptive FFT can be used for diagnosis purposes, providing interesting possibilities for the detection of rotor faults in variable-speed induction generators. In fact, the window length is optimized at each time location to improve frequency resolution of the stator current using only the measured rotor speed. This method may be also applied to diagnosis faults in other types of electrical machines.

To prevent system deterioration under faulty conditions, a control strategy based on an FOC with a simple design method is proposed to control the whole wind energy system. Simu- lation results show that the closed-loop wind energy system achieves favorable dynamic performance and robustness in healthy and faulty conditions.

The two-level ESS can maintain the power balance between WT generation and the demands, and thus improves the stability of the whole system, because the bi-directional DC/DC

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BIOGRAPHIES

Issam Attouiwas born in Annaba, Algeria, in 1985. He received his engineer degree and magister degree in electrical engineering from Badji Mokhtar-Annaba University, Algeria, in 2007 and 2009, respectively. In 2011, he joined the Weld- ing and NDT Research Centre/Industrial Technologies Re- search Unit (URTI/CSC) in Annaba, Algeria. He is currently a Ph.D. student in Department of Electrical Engineering, Badji Mokhtar-Annaba University, Annaba, Algeria. His research interests include system modeling and control, process fault diagnosis, signal processing, renewable energy, vibration mon- itoring, fractional-order control, and neural networks.

Amar Omeiriwas born in Skikda, Algeria, in 1958. He received his engineer degree from Annaba University in 1983;

his master degree of science by research from Strathclyde University, United Kingdom, in 1986; and his Ph.D. in 2007 from Annaba University, Algeria. Since 1987, he has been a lecturer at Annaba University in the Electrical Engineering Department. His current research field includes active power filters, renewable energies, power electronics, and AC and DC drives.