Influence of a Converter Control Malfunction on the Harmonic Behavior of Wind Turbines with

Permanent Magnet Generator

R. Melício CAST-UBI and CIEEE-IST

Portugal ruimelicio@gmail.com

V.M.F. Mendes CAST-UBI and ISEL

Portugal vfmendes@isel.pt

J.P.S. Catalão, Member, IEEE UBI and CIEEE-IST

Portugal catalao@ubi.pt

Abstract—This paper is on variable-speed wind turbines with permanent magnet generator. A three-mass drive train model and two different topologies for the power-electronic converters are considered. The two different topologies considered are respectively a matrix and a multilevel converter. A control strategy, based on fractional-order controllers, is proposed for the wind turbines. Previous papers were mainly focused on the transient stability of variable-speed wind turbines at external grid faults. Instead, this paper considers the possibility of an internal abnormal operating condition, namely a converter control malfunction. The influence of the converter control malfunction on the harmonic current emissions is studied. Comprehensive results are presented, and conclusions are duly drawn.

Keywords-wind turbines; permanent magnet generator; power-electronic converters; fractional-order control; malfunction

I. INTRODUCTION The study of harmonic current emissions associated with

renewable energy technologies is essential in order to analyze their effect on the electrical grids where they are connected [1]. Among the renewable energy technologies, wind turbine technology is now the world’s fastest growing energy source. Wind turbines achieve an excellent technical availability of about 98% on average, although they have to face a high number of malfunctions [2].

In Portugal, the wind power goal foreseen for 2012 was established by the government as 5100 MW. Hence, Portugal has one of the most ambitious goals in terms of wind power, and in 2006 was the second country in Europe with the highest wind power growth [3]-[4].

As the penetration level of wind power in power systems increases, the overall performance of the electrical grid will increasingly be affected by the characteristics of wind turbines. One of the major concerns related to the high penetration level of the wind turbines is the impact on power system stability [5]. Also, network operators have to ensure that consumer power quality is not compromised. Hence, the total harmonic distortion (THD) should be kept as low as possible, improving the quality of the energy injected into the electrical grid [6].

Power-electronic converters have been developed for integrating wind power with the electrical grid. The use of power-electronic converters allows for variable-speed operation of the wind turbine and enhanced power extraction [7]. Accurate modeling and control of wind turbines have high priority in the research activities all over the world [8]. At the moment, substantial documentation exists on modeling and control issues for the doubly fed induction generator wind turbine. But, this is not the case for wind turbines with permanent magnet generator.

Previous papers were mainly focused on the transient stability of variable-speed wind turbines at external grid faults [9]. However, little attention has been given to the possibility of internal abnormal operating conditions, such as a converter control malfunction.

Hence, this paper focuses on the harmonic behavior of wind turbines with permanent magnet generator, considering: (i) three-mass drive train model; (ii) two different topologies for the power-electronic converters: matrix and multilevel converters; (iii) a fractional-order control strategy; (iv) a converter control malfunction.

II. MODELING

A. Wind Speed The wind speed variation can be modeled as:

⎥⎦

⎤⎢⎣

⎡ω+= ∑

KKK tAuu )(sin10 , (1)

where 0u is the average wind speed and u is the wind speed value with disturbance [10].

B. Wind Turbine The mechanical power over the rotor of the wind turbine

has been modeled, using the mechanical eigenswings, as a set of harmonic terms multiplied by the power associated with the energy capture from the wind by the blades, given by [10]:

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+= ∑ ∑

= =

3

1

2

1

)()(1k

km

kmkmkttt thtgaAPP , (2)

The work of R. Melício was supported by the Fundação para a Ciência e a Tecnologia (FCT) under Post-Doctoral grant (SFRH/BPD/68585/2010).

2011 IEEE International Electric Machines & Drives Conference (IEMDC)

978-1-4577-0061-3/11/$26.00 ©2011 IEEE 783

⎟⎠⎞⎜

⎝⎛ ϕ+ω= ∫

t

kmkkm dttmg0

')'(sin , (3)

where KA is the magnitude of the eigenswing, Kmg is the distribution of the m-order harmonic in the eigenswing k, and

Kma is the normalized magnitude of Kmg .

C. Drive Train Model A three-mass drive train model is considered in this paper.

Fig. 1 shows the blade bending dynamics. Since the blade bending occurs at a significant distance from the joint between the blade and the hub, the blade can be split in two parts.

Figure 1. Blade bending dynamics for the three-mass drive train model.

D. Generator The model for the permanent magnet generator is the usual

one, which can be found in the literature [11]. In order to avoid demagnetization of permanent magnet, a null stator current is imposed [12].

E. Power-Electronic Converters Matrix and multilevel power-electronic converters are

comparatively studied in this paper.

The matrix converter is an AC-AC converter, with nine bidirectional commanded insulated gate bipolar transistors (IGBTs). It is connected between a first order filter and a second order filter. The first order filter is connected to the permanent magnet generator, while the second order filter is connected to the grid. The configuration of the simulated wind energy system with matrix converter is shown in Fig. 2.

The multilevel converter is an AC-DC-AC converter, with twelve unidirectional commanded IGBTs used as a rectifier, and with the same number of unidirectional commanded IGBTs used as an inverter. The rectifier is connected between the permanent magnet generator and a capacitor bank. The inverter is connected between this capacitor bank and a second order filter, which in turn is connected to the grid. The configuration of the simulated wind energy system with multilevel converter is shown in Fig. 3.

Figure 2. Wind energy system with matrix converter.

Figure 3. Wind energy system with multilevel converter.

III. CONTROL STRATEGY

A control strategy based on fractional-order μPI controllers is considered for the variable-speed operation of wind turbines with permanent magnet generator. Fractional-order calculus used in mathematical models of the systems can improve the design, properties and controlling abilities in dynamical systems [13].

A. Fractional-Order Controller The fractional-order differentiator can be denoted by a

general operator μta D [14], given by:

⎪⎪

⎩

⎪⎪

⎨

⎧

<μℜ

=μℜ

>μℜ

τ

=

∫ μ−

μ

μ

μ

0)(

0)(

0)(

,)(

,1

,

t

a

ta

d

dtd

D , (4)

where μ is the order of derivative or integrals, )(μℜ is the real part of the μ . In this paper, μ is assumed as a real number that satisfies the restrictions 10 <μ< .

The influence of fractional-order controllers is due to their ability for memory. An important property is that while integer-order operators imply finite series, the fractional-order counterparts are defined by infinite series [14]. This means that integer operators are local operators in opposition with the fractional operators that have, implicitly, a memory of all past events.

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The differential equation of the fractional-order μPI controller, 10 <μ< , in time domain, is given by:

)()()( teDKteKtf tipμ−+= , (5)

where pK is a proportional constant and iK is an integration constant. Taking 1=μ in (5), a classical PI controller is obtained.

B. Converters Control Power converters are variable structure systems, because

of the on/off switching of their IGBTs. Pulse width modulation (PWM) by space vector modulation (SVM) associated with sliding mode is used for controlling the converters. The sliding mode control strategy presents attractive features such as robustness to parametric uncertainties of the wind turbine and the generator as well as to electrical grid disturbances [15]. Sliding mode controllers are particularly interesting in systems with variable structure, such as switching power converters, guaranteeing the choice of the most appropriate space vectors.

IV. HARMONIC BEHAVIOR The harmonic behavior computed by the Discrete Fourier

Transform (DFT) is given by:

∑−

=

π−=1

0

2 )()(N

n

Nnkj nxekX for 1,...,0 −= Nk , (6)

where )(nx is the input signal and )(kX is the amplitude and phase of the different sinusoidal components of )(nx . The harmonic behaviour computed by the THD is given by:

FX

X HH

2

2100(%)THD∑

== , (7)

where HX is the root mean square (RMS) value of the individual harmonic components of the signal, and FX is the RMS value of the fundamental component.

Standards such as IEEE-519 [16] impose limits for different order harmonics and the THD. Hence, IEEE-519 standard is used in this paper as a guideline for comparison purposes.

V. RESULTS The wind energy system considered has a rated electrical

power of 900 kW, and the time horizon considered in the simulation is 4 s. The mathematical models for the wind energy system with the matrix and multilevel converters were implemented in Matlab/Simulink. The switching frequency used in the simulation results is 5 kHz. The average wind speed considered is a ramp wind speed starting at 10 m/s and stabilizing after 1.5 s at 20 m/s. Fig. 4 shows the wind speed profile.

0 0.5 1 1.5 2 2.5 3 3.5 45

10

15

20

25

Time (s)

Win

d sp

eed

(m/s

)

Figure 4. Wind speed profile.

A converter control malfunction is considered to occur between 2 s and 2.02 s, modeled by a random selection of the voltage vectors for the matrix converter and for the inverter of the multilevel converter.

Fig. 5 shows what happens to the vectors selection on the converter before and after the converter control malfunction, for the matrix converter and a three-mass model. Fig. 6 shows the output RMS current.

1.99 2 2.01 2.02 2.03−10

−5

0

5

10

Time (s)

Vec

tor

Malfunction

Figure 5. Vectors selection for the matrix converter and a three-mass model.

Fig. 7 shows what happens to the vectors selection on the inverter before and after the converter control malfunction, for the multilevel converter and a three-mass model. Fig. 8 shows the voltage dcv for the multilevel converter and a three-mass model. Fig. 9 shows the output RMS current.

The harmonic behaviour of the current injected into the electrical grid, computed by the DFT, is shown in Figs. 10 and 11 for the matrix and multilevel converters, respectively.

The THD of the current injected into the electrical grid is shown in Figs. 12 and 13 for the matrix and multilevel converters, respectively.

785

1.95 1.975 2 2.025 2.05 2.0750

100

200

300

400

500

600

700

Time (s)

Cur

rent

(A

)

Figure 6. Output RMS current for the matrix converter and a three-mass

model.

1.99 2 2.01 2.02 2.03−5

0

5

10

15

20

25

30

Time (s)

Vec

tor

Malfunction

Figure 7. Vectors selection for the multilevel converter and three-mass

model.

1.5 1.75 2 2.25 2.52450

2475

2500

2525

2550

Time (s)

Vol

tage

(V

) ↓ Converter control malfunction

Figure 8. Voltage dcv for the multilevel converter and a three-mass

model.

1.95 1.975 2 2.025 2.05 2.0750

100

200

300

400

500

600

700

Time (s)

Cur

rent

(A

)

Figure 9. Output RMS current for the multilevel converter and a three-mass

model.

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

100

Frequency (Hz)

Cur

rent

(%

)

Figure 10. DFT of the current injected into the electrical grid for the

matrix converter and a three-mass model.

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

100

Frequency (Hz)

Cur

rent

(%

)

Figure 11. DFT of the current injected into the electrical grid for the

multilevel converter and a three-mass model.

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1 1.5 2 2.5 3 3.5 40

1

2

3

4

5

6

Time (s)

TH

D ← Converter control malfunction

Figure 12. THD of the current injected into the electrical grid for the

matrix converter and a three-mass model.

1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

Time (s)

TH

D (

%)

← Converter control malfunction

Figure 13. THD of the current injected into the electrical grid for the

multilevel converter and a three-mass model.

The harmonics are related to the power electronic conversion system and their control. The presence of the energy-storage elements, in comparison with the matrix converter, allows the wind energy system with the multilevel converter to achieve the best performance.

Nevertheless, for both power-electronic converter topologies, the average THD of the current injected into the electrical grid is lower than the 5% limit imposed by the IEEE-519 standard.

Table I summarizes an overall comparison between the conventional PI controller and fractional-order 5.0PI and

7.0PI controllers, for the three-mass drive train model and both matrix and multilevel converters, concerning the average THD of the current injected into the electrical grid. As can been seen, the best results are achieved by considering

7.0=μ .

TABLE I. AVERAGE THD OF THE CURRENT INJECTED INTO THE ELECTRICAL GRID

Wind energy system

THD (%) considering PI controller

THD (%) considering

5.0PI controller

THD (%) considering

7.0PI controller Matrix

converter 3.32 2.93 2.80

Multilevel converter 0.76 0.64 0.61

VI. CONCLUSIONS This paper focuses on the harmonic behavior of wind

turbines with permanent magnet generator, considering: (i) three-mass drive train model; (ii) matrix and multilevel power-electronic converters; (iii) a fractional-order control strategy; (iv) a converter control malfunction. The three-mass model may be more appropriate for the precise harmonic assessment of variable-speed wind turbines. Blades flexibility can indeed influence wind turbine response during internal abnormal operating conditions. Also, the fractional-order controller can effectively decrease total harmonic distortion for the variable-speed operation of wind turbines with permanent magnet generator.

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