05607690

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Abstract —This paper is on wind energy conversion systems

with full-power converter and permanent magnet synchronous

generator. Different topologies for the power-electronic

converters are considered, namely matrix and multilevel

converters. Also, a new fractional-order control strategy is

proposed for the variable-speed operation of the wind turbines.

Simulation studies are carried out in order to adequately assess

the quality of the energy injected into the electric grid.

Conclusions are duly drawn.

Index Terms —Wind energy, power electronics, converter

topologies, fractional controllers, simulation.

I. I NTRODUCTION HE general consciousness of finite and limited sources

of energy on earth, and international disputes over the

environment, global safety, and the quality of life, have

created an opportunity for new more efficient less polluting

wind and hydro power plants with advanced technologies of

control, robustness, and modularity [1].

Concerning renewable energies, wind power is a priority

for Portugal's energy strategy. The wind power goal foreseen

for 2010 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.An overview of the Portuguese technical approaches and

methodologies followed in order to plan and accommodate

the ambitious wind power goals to 2010/2013, preserving

the overall quality of the power system, is given in [2].

Power system stability describes the ability of a power

system to maintain synchronism and maintain voltage when

subjected to severe transient disturbances [3].

As wind energy is increasingly integrated into power

systems, the stability of already existing power systems is

becoming a concern of utmost importance [4].

Also, network operators have to ensure that consumer

power quality is not deteriorated. Hence, the total harmonicdistortion (THD) coefficient should be kept as low as

possible, improving the quality of the energy injected into

the electric grid [5].

The development of power electronics and their

applicability in wind energy extraction allowed for variable-

speed operation of the wind turbine [6].

The variable-speed wind turbines are implemented with

either doubly fed induction generator (DFIG) or full-power

converter.

In a variable-speed wind turbine with full-power

converter, the wind turbine is directly connected to the

R. Melício and J. P. S. Catalão are with the University of Beira Interior,Covilha, Portugal (e-mail: [email protected]).

V. M. F. Mendes is with the Instituto Superior de Engenharia de Lisboa,

Lisbon, Portugal (e-mail: [email protected]).

generator, which in this paper is a permanent magnet

synchronous generator (PMSG).

Harmonic emissions are recognized as a power quality

problem for modern variable-speed wind turbines.

Understanding the harmonic behavior of variable-speed

wind turbines is essential in order to analyze their effect on

the electric grids where they are connected [7].

In this paper, a variable-speed wind turbine is considered

with PMSG and different power-electronic converter

topologies: matrix and multilevel. Additionally, a new

fractional-order control strategy is proposed for the variable-

speed operation of wind turbines with PMSG/full-power

converter topology. Simulation studies are carried out inorder to adequately assess the quality of the energy injected

into the electric grid. Hence, the harmonic behavior of the

output current is computed by Discrete Fourier Transform

(DFT) and THD. A comparison with a classical integer-

order control strategy is also presented, illustrating the

improvements introduced by the proposed fractional-order

control strategy.

This paper is organized as follows. Section II presents the

modeling of the wind energy conversion system (WECS).

Section III presents the new fractional-order control strategy.

Section IV presents the power quality evaluation by DFT

and THD. Section V presents the simulation results. Finally,concluding remarks are given in Section VI.

II. MODELING

A. Wind Turbine

The mechanical power t P of the wind turbine is given by

pt c Au P 3

2

1ρ= (1)

where ρ is the air density, A is the area covered by the

rotor blades, u is the wind speed upstream of the rotor, and

pc is the power coefficient. The power coefficient is a

function of the pitch angle θ of rotor blades and of the tip

speed ratio λ , which is the ratio between blade tip speed and

wind speed value upstream of the rotor.

The computation of the power coefficient requires the use

of blade element theory and the knowledge of blade

geometry. In this paper, the numerical approximation

developed in [8] is followed, where the power coefficient is

given by

i

i

p ecλ

−

⎟⎟

⎠

⎞⎜⎜

⎝

⎛ −θ−θ−

λ

=

4.18

14.2 2.13002.058.0151

73.0 (2)

T

Simulation of Wind Power Generation with

Fractional Controllers: Harmonics AnalysisR. Melício, V. M. F. Mendes and J. P. S. Catalão, Member, IEEE

XIX International Conference on Electrical Machines - ICEM 2010, Rome

978-1-4244-4175-4/10/$25.00 ©2010 IEEE

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)1(

003.0

)02.0(

1

1

3 +θ−

θ−λ

=λ i (3)

B. Mechanical Drive Train Model

The mechanical drive train considered in this paper is a

two-mass model, consisting of a large mass and a small

mass, corresponding to the wind turbine rotor inertia andgenerator rotor inertia, respectively. The model for the

dynamics of the mechanical drive train for the WECS used

in this paper was reported by the authors in [9].

C. Generator

The generator considered in this paper is a PMSG. The

equations for modeling a PMSG can be found in the

literature [10]. In order to avoid demagnetization of

permanent magnet in the PMSG, a null stator current is

imposed [11].

D. Matrix Converter

The matrix converter is an AC-AC converter, with nine

bidirectional commanded insulated gate bipolar transistors

(IGBTs) ijS . It is connected between a first order filter and a

second order filter. The first order filter is connected to a

PMSG, while the second order filter is connected to an

electric network. A switching strategy can be chosen so that

the output voltages have nearly sinusoidal waveforms at the

desired frequency, magnitude and phase angle, and the input

currents are nearly sinusoidal at the desired displacement

power factor [12]. A three-phase active symmetrical circuit

in series models the electric network. The model for the

matrix converter used in this paper was reported by the

authors in [9]. The configuration of the simulated WECS

with matrix converter is shown in Fig. 1.

E. Multilevel Converter

The multilevel converter is an AC-DC-AC converter, with

twelve unidirectional commanded IGBTs ik S used as a

rectifier, and with the same number of unidirectional

commanded IGBTs used as an inverter. The rectifier is

connected between the PMSG and a capacitor bank. The

inverter is connected between this capacitor bank and a

second order filter, which in turn is connected to an electric

network. The groups of four IGBTs linked to the same phase

constitute a leg k of the converter. A three-phase active

symmetrical circuit in series models the electric network.

The model for the multilevel converter used in this paper

was reported by the authors in [9]. The configuration of the

simulated WECS with multilevel converter is shown in

Fig. 2.

III. CONTROL STRATEGY

A. Fractional-Order Controllers

A new control strategy based on fractional-order μ PI

controllers is proposed for the variable-speed operation of

wind turbines with PMSG/full-power converter topology.

A maximum power point tracking (MPPT) is used in

determining the optimal rotor speed at the wind turbine for

each wind speed to obtain maximum rotor power [6].

Fractional-order controllers are based on fractional

calculus theory, which is a generalization of ordinary

differentiation and integration to arbitrary (non-integer)

order [13]. Recently, applications of fractional calculus

theory in practical control field have increased significantly

[14].The fractional-order differentiator can be denoted by a

general operator μt a D [15], given by

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

<μℜ

=μℜ

>μℜ

τ

=

∫ μ−

μ

μ

μ

0)(

0)(

0)(

,)(

,1

,

t

a

t a

d

dt

d

D (4)

where μ is the order of derivative or integral, and ℜ(μ) is the

real part of the μ .

The mathematical definition of fractional derivatives and

integrals has been the subject of several approaches.

The most frequently encountered definition is called

Riemann–Liouville definition, in which the fractional-order

integrals are defined as

∫ τττ−μ

= −μμ−t

at a d f t t f D )()(

)(Γ

1)( 1 (5)

while the definition of fractional-order derivatives is

⎥⎦

⎤

⎢⎣

⎡

ττ−

τ

μ−= ∫ +−μ

μ t

a nn

n

t a d t

f

dt

d

nt f D 1)(

)(

)(Γ

1

)( (6)

where

∫ ∞ −−≡0

1)(Γ dye y x

y x(7)

is the Gamma function, a and t are the limits of the

operation, and μ is the fractional order which can be a

complex number. In this paper, μ is assumed as a real

number that satisfies the restrictions 10 <μ< . Also, a can

be taken as a null value. The following convention is used:

μ−μ− ≡ t t D D0 . The differential equation of the fractional-

order μ PI controller is given by

)()()( t e D K t e K t u t i pμ−+= (8)

where p K is the proportional constant and i K is the

integration constant. Taking 1=μ , a classical PI controller

is obtained. In this paper, it is assumed that 5.0=μ . Using

the Laplace transform of fractional calculus, the transfer

function of the fractional-order μ PI controller is obtained,

given by

5.0)( −+= s K K sG i p (9)

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Fig. 1. WECS with matrix converter.

Fig. 2. WECS with multilevel converter.

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 electric grid disturbances [16].

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.

Their aim is to let the system slide along a predefined

sliding surface by changing the system structure.

The power semiconductors present physical limitations,

since they cannot switch at infinite frequency. Also, for a

finite value of the switching frequency, an error αβe will

exist between the reference value and the control value.

In order to guarantee that the system slides along the

sliding surface ),( t eS αβ , it has been proven that it is

necessary to ensure that the state trajectory near the surfaces

verifies the stability conditions [17] given by

0),(

),( <αβ

αβdt

t edS t eS (10)

IV. HARMONIC BEHAVIOR

The harmonic behavior computed by the DFT is based on

Fourier analysis. If is )(ω X a continuous periodical signal

with period of T and satisfies Dirichlet condition, the

Fourier series is given by

∑=

ω −=ω N

n

n jen x X 1

)()( for π≤ω ≤ 20 (11)

In order to implement Fourier analysis in a computer, the

signal in both time and frequency domains is discrete andhas finite length with N points per cycle. Hence, Discrete

Fourier Transform (DFT) is introduced, given by

∑−

=

π−=1

0

2 )()( N

n

N nk j n xek X for 1,...,0 −= N k (12)

where )(n x is the input signal and )(k X is the amplitude

and phase of the different sinusoidal components of the

)(n x .

The harmonic behavior computed by the THD is given by

F X

X H

H

2

2100(%)THD

∑== (13)

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where H X is the root mean square (RMS) value of the

signal, and F X is the RMS value of the fundamental

component.

V. SIMULATION R ESULTS

The mathematical models for the WECS with the matrix

and multilevel power converter topologies were

implemented in Matlab/Simulink. The WECSs simulated inthis case study have a rated electric power of 900 kW.

Table I summarizes the WECS data.

TABLE IWECS DATA

Turbine moment of inertia 2500×10³ kgm²

Turbine rotor diameter 49 m

Tip speed 17.64-81.04 m/s

Rotor speed 6.9-31.6 rpm

Generator rated power 900 kW

Generator moment of inertia 100×10³ kgm²

The operational region of the WECS was simulated for

wind speed range from 5-25 m/s. The switching frequency

used in the simulation results is 5 kHz.

The first harmonic of the output current, computed by the

DFT, for the WECS with the matrix converter is shown in

Fig. 3. The THD of the output current for the WECS with

the matrix converter is shown in Fig. 4. The first harmonic

of the output current, computed by the DFT, for the WECS

with the multilevel converter is shown in Fig. 5. The THD of

the output current for the WECS with the multilevel

converter is shown in Fig. 6. Both classical and fractional PIcontrollers are considered.

The presence of the energy-storage elements allows the

proposed WECS with the multilevel converter to achieve the

best performance, in comparison with the matrix converter.

The new fractional-order control strategy provides better

results comparatively to a classical integer-order control

strategy, in what regards the harmonic behavior computed

by the DFT and the THD.

5 10 15 20 2586

87

88

89

90

91

92

93

94

Wind speed (m/s)

C u r r e n t f u n d a m e n t a l c o m p o n e n t ( % )

↑Classical PI controllers

↓ Fractional PI controllers

Fig. 3. First harmonic of the output current, matrix converter. The first

harmonic is expressed in percentage of the fundamental component.

5 10 15 20 250

0.5

1

1.5

2

2.5

Wind speed (m/s)

T H D

( % )

↓ Classical PI controllers

↑ Fractional PI controllers

Fig. 4. THD of the output current, matrix converter.

5 10 15 20 2591

92

93

94

95

96

Wind speed (m/s)

C u r r e n t f u n d a m e n t a l c o m p o n e n t ( % )

↑ Classical PI controllers

↓ Fractional PI controllers

Fig. 5. First harmonic of the output current, multilevel converter. The first

harmonic is expressed in percentage of the fundamental component.

5 10 15 20 250

0.5

1

1.5

2

Wind speed (m/s)

T H D ( % )

← Classical PI controllers

← Fractional PI controllers

Fig. 6. THD of the output current, multilevel converter.

The THD of the output current is lower than 5% limit

imposed by IEEE-519 standard [18], for both power

converter topologies considered. Although IEEE-519standard might not be applicable in such situation, it is used

as a guideline for comparison purposes [19].

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VI. CONCLUSIONS

The harmonic behavior of variable-speed wind turbines

with PMSG/full-power converter topology is studied in this

paper. As a new contribution to earlier studies, a new

fractional-order control strategy is proposed in this paper,

which achieves superior dynamic characteristics and output

power quality. Simulation studies revealed a better

performance of the proposed WECS with the multilevel

converter, in comparison with the matrix converter. Also, the

harmonic behavior computed by the DFT and the THD

revealed that the power quality injected in the electric grid is

enhanced using the new fractional-order control strategy, in

comparison with a classical integer-order control strategy,

for both power converter topologies considered.

VII. R EFERENCES

[1] T. Ahmed, K. Nishida, and M. Nakaoka, “Advanced control of PWM

converter with variable-speed induction generator,” IEEE Trans. Industry Applications , vol. 42, pp. 934-945, Jul.-Aug. 2006.

[2] A. Estanqueiro, R. Castro, P. Flores, J. Ricardo, M. Pinto,

R. Rodrigues, and J. Peças Lopes, “How to prepare a power system for

15% wind energy penetration: the Portuguese case study,” Wind Energy, vol. 11, pp. 75-84, Jan.-Feb. 2008.

[3] Y. Coughlan, P. Smith, A. Mullane, and M. O’Malley, “Wind turbinemodeling for power system stability analysis - A system operator

perspective,” IEEE Trans. Power Systems, vol. 22, pp. 929-936, Aug.

2007.[4] N. R. Ullah and T. Thiringer, “Variable speed wind turbines for power

system stability enhancement,” IEEE Trans. Energy Conversion,

vol. 22, pp. 52-60, Mar. 2007.[5] J. M. Carrasco, L. G. Franquelo, J. T. Bialasiewicz, E. Galvan, R. C.

P. Guisado, A. M. Prats, J. I. Leon, and N. Moreno-Alfonso, “Power-

electronic systems for the grid integration of renewable energy

sources: A survey,” IEEE Trans. Industrial Electronics, vol. 53, pp.

1002-1016, Aug. 2006.

[6] J. A. Baroudi, V. Dinavahi, and A. M. Knight, “A review of power converter topologies for wind generators,” Renewable Energy, vol. 32,

pp. 2369-2385, Nov. 2007.[7] S. T. Tentzrakis and S. A. Papathanassiou, “An investigation of the

harmonic emissions of wind turbines,” IEEE Trans. Energy

Conversion, vol. 22, pp. 150-158, Mar. 2007.

[8] J. G. Slootweg, S. W. H. de Haan, H. Polinder, and W. L. Kling,“General model for representing variable speed wind turbines in

power system dynamics simulations,” IEEE Trans. Power Syst., vol.18, pp. 144-151, Feb. 2003.

[9] R. Melício, V. M. F. Mendes, and J. P. S. Catalão, “Simulation of wind power generation with matrix and multi-level converters: power quality analysis,” in: Proc. XVIII Int. Conf. on Electrical Machines ICEM’08, Vilamoura, Portugal, Sept. 2008.

[10] C.-M. Ong, Dynamic Simulation of Electric Machinery: Using

Matlab/Simulink . NJ: Prentice-Hall, 198, pp. 259-350.

[11] T. Senjyu, S. Tamaki, N. Urasaki, and K. Uezato, “Wind velocity and position sensorless operation for PMSG wind generator,” in: Proc. 5th

Int. Conf. on Power Electronics and Drive Systems, Singapore, pp.

787-792, Nov. 2003.[12] S. M. Barakati, J. D. Aplevich, and M. Kazerani, “Controller design

for a wind turbine system including a matrix converter,” in: Proc.

2007 IEEE Power Eng. Soc. Gen. Meeting , Tampa, FL, Jun. 2007.

[13] I. Podlubny, “Fractional-order systems and PI-lambda-D-mu-

controllers,” IEEE Trans. Automatic Control , vol. 44, pp. 208-214,

Jan. 1999.

[14] W. Li, and Y. Hori, “Vibration suppression using single neuron-basedPI fuzzy controller and fractional-order disturbance observer,” IEEE

Trans. Ind. Electron., vol. 54, pp. 117-126, Feb. 2007.[15] A. J. Calderón, B. M. Vinagre, and V. Feliu, “Fractional order control

strategies for power electronic buck converters,” Signal Processing ,

vol. 86, pp. 2803-2819, Mar. 2006.[16] B. Beltran, T. Ahmed-Ali, and M. E. H. Benbouzid, “Sliding mode

power control of variable-speed wind energy conversion systems,” IEEE Trans. Energy Conversion, vol. 23, pp. 551-558, Jun. 2008.

[17] J. F. Silva and S. F. Pinto, “Control methods for switching power

converters,” in: Power Electronics Handbook , 2nd ed., M. H. Rashid,

Ed. NY: Academic Press, 2007, pp. 935-998.[18] IEEE Guide for Harmonic Control and Reactive Compensation of

Static Power Converters, IEEE Standard 519-1992.

[19] T. M. H. Nick, K. Tan, and S. Islam, “Mitigation of harmonics in windturbine driven variable speed permanent magnet synchronous

generators,” in: Proc. 7th Int. Power Engineering Conf., pp. 1159-1164, Dec. 2005.

VIII. BIOGRAPHIES

R. Melício received the M.Sc. degree from the Instituto Superior Técnico,

Lisbon, Portugal, in 2004.

He is currently a Ph.D. student at the University of Beira Interior,Covilha, Portugal, in collaboration with the Instituto Superior de Engenharia

de Lisboa, Lisbon, Portugal. His research interests include power electronic

converters, power quality, and wind energy systems.

V. M. F. Mendes received the M.Sc. and Ph.D. degrees from the InstitutoSuperior Técnico, Lisbon, Portugal, in 1987 and 1994, respectively.

He is currently a Coordinator Professor with Aggregation at the InstitutoSuperior de Engenharia de Lisboa, Lisbon, Portugal. His research interests

include hydrothermal scheduling, optimization theory and its applications,

and renewable energies.

J. P. S. Catalão (M’04) received the M.Sc. degree from the InstitutoSuperior Técnico, Lisbon, Portugal, in 2003 and the Ph.D. degree from the

University of Beira Interior, Covilha, Portugal, in 2007.

He is currently an Assistant Professor at the University of Beira Interior.His research interests include hydro scheduling, unit commitment, price

forecasting, wind energy systems, and electricity markets. He has authored

or coauthored more than 110 technical papers.Dr. Catalão is an Associate Editor for the International Journal of Power

and Energy Systems, and a Member of the Editorial Board of Electric

Power Components & Systems. Also, he is a reviewer for IEEE

TRANSACTIONS ON E NERGY CONVERSION, and other IEEE and

International Journals .

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