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Parameter Identification of Wind Turbinefor Maximum Power-point TrackingControlAbdul Motin Howlader a , Naomitsu Urasaki a , Kousuke Uchida a ,Atsushi Yona a , Tomonobu Senjyu a , Chul-Hwan Kim b & A. Y. Saber ca Department of Electrical and Electronics Engineering , Universityof the Ryukyus , Okinawa, Japanb Department of Electrical and Electronics Engineering ,Sungkyunkwan University , Koreac Department of Electrical and Computer Engineering , MissouriUniversity of Science and Technology , Rolla, Missouri, USAPublished online: 22 Mar 2010.

To cite this article: Abdul Motin Howlader , Naomitsu Urasaki , Kousuke Uchida , Atsushi Yona ,Tomonobu Senjyu , Chul-Hwan Kim & A. Y. Saber (2010) Parameter Identification of Wind Turbine forMaximum Power-point Tracking Control, Electric Power Components and Systems, 38:5, 603-614, DOI:10.1080/15325000903376974

To link to this article: http://dx.doi.org/10.1080/15325000903376974

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Electric Power Components and Systems, 38:603–614, 2010

Copyright © Taylor & Francis Group, LLC

ISSN: 1532-5008 print/1532-5016 online

DOI: 10.1080/15325000903376974

Parameter Identification of Wind Turbine

for Maximum Power-point Tracking Control

ABDUL MOTIN HOWLADER,1 NAOMITSU URASAKI,1

KOUSUKE UCHIDA,1 ATSUSHI YONA,1

TOMONOBU SENJYU,1 CHUL-HWAN KIM,2 and

A. Y. SABER3

1Department of Electrical and Electronics Engineering, University of the

Ryukyus, Okinawa, Japan2Department of Electrical and Electronics Engineering, Sungkyunkwan

University, Korea3Department of Electrical and Computer Engineering, Missouri University

of Science and Technology, Rolla, Missouri, USA

Abstract In this article, a technique is proposed for maximum power-point trackingcontrol of a wind generation system. The optimal operation speed to which the

wind turbine output power maximizes is determined with parameters identified byan iterative least squares technique. The effectiveness of the maximum point tracking

control with identified parameters of wind turbine is verified by computer simulation.In addition, the article discusses how to address rotational speed and output power

in the case when the wind turbine parameters used for determining the optimumrotational speed have errors.

Keywords wind turbine generation system, maximum power-point tracking, onlineparameter identification

1. Introduction

Electric power generation using non-conventional sources is receiving considerable at-

tention throughout the world. Wind energy is a significant and powerful resource. It

is safe, clean, and abundant. Unlike conventional fuels, wind energy is a massive in-

digenous power source permanently available in virtually every nation in the world. It

delivers energy security benefits by avoiding fuel costs, long-term fuel price risk, and

the economic and supply risks that come with reliance on imported fuels and political

dependence on other countries [1]. However, wind energy has a drawback of having

only 1/800 density and irregularity as compared to that of water energy. How it can

be utilized as a highly efficient electric power energy source is important. Because

Received 17 February 2009; accepted 30 September 2009.Address correspondence to Mr. Abdul Motin Howlader, Department of Electrical and

Electronics Engineering, University of the Ryukyus, 1 Senbaru, Nishihara-cho, Okinawa, 903-0213,Japan. E-mail: k088477@eve.u-ryukyu.ac.jp

603

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604 A. M. Howlader et al.

of this problem, various high-efficiency control schemes have been reported in recent

years [2–5].

In the wind turbine generation system, the squirrel-cage induction generator (IG) is

introduced because it is robust and has low cost. Power generation using wind energy

is possible in two ways, viz., constant-speed operation and variable-speed operation

using power electronic converters. Variable-speed power generation for a wind turbine

is attractive, because maximum efficiency can be achieved at all wind velocities. Some

works proposed determining the optimum operating speed based on the hill-climbing

method [6, 7]. However, the hill-climbing method takes a long time to arrive at a solution

and is, therefore, disadvantageous for maximum power-point tracking. The optimal wind

turbine rotor speed method obtains the maximum power point swiftly. The parameters

of the optimal wind turbine rotor speed method are sensitive. In case of the chage

in parameters, the output power is affected significantly. In this article, a technique is

proposed to identify the parameters of the wind turbine. Moreover, a wind power system

has to operate at the maximum power point by using the above-identified wind turbine

parameters to optimize operation speed. The rest of the article is organized as follows.

The modeling of the wind generation system is presented in Section 2. The optimization

of operating points is presented in Section 3. Section 4 shows how to control the IG. The

wind turbine parameter identification method is presented in Section 5. The proposed

method has been tested by simulation as described in Section 6, and Section 7 provides

the conclusion.

2. Wind Turbine Generation System

The configuration of the maximum power-point tracking wind power generation system

is shown in Figure 1. The wind energy obtained from the wind turbine is sent to the

squirrel-cage IG through a gear. The IG is controlled by the pulse width modulation

(PWM) converter with a wind turbine parameter identifier. If all the wind power is

converted to mechanical power by the turbine the input power for the wind turbine, Pwind

Figure 1. Wind turbine generation system configuration.

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Parameter Identification of Wind Turbine Generation System 605

is expressed as

Pwind D1

2��R2

oV 3w ; (1)

where Ro is wind turbine blade radius, � is the air density, and Vw is the wind speed.

The wind turbine input torque Twind can be described as

Twind D�

!w

Pwind;

D1

2��R3

oV 2w ; (2)

where !w is the rotor speed of the wind turbine, and � is the tip speed ratio, which

can be defined as � D Ro!w

Vw. The wind turbine converts wind power into mechanical

power Pw:

Pw D1

2��R2

oV 3wCp: (3)

The power coefficient Cp is defined as Cp D ��3 C ��2 C �, where � , �, and are

coefficients that are determined by size, form of blade, number of blades, and pitch angle

of the wind tubine blade. Wind turbine output torque is defined by

Tw D1

2��R3

oV2

wCt ; (4)

where Ct is the torque coefficient, defined as Ct DCp

�. The wind turbine loss torque Tf

serves as a convex function according to wind velocity and the angular velocity of wind

turbine; it can be expressed as an approximation equation [4]

Tf D Twind � Tw ;

D K0V 2w C K1Vw!w C K2!2

w: (5)

Here, the wind turbine loss coefficients K0, K1, and K2 are expressed as

K0 D1

2�SRo.1 � /; (6)

K1 D �1

2�SR2

o�; (7)

K2 D �1

2�SR3

o�; (8)

where S is the blade rotation area. The motion equation of the wind turbine output torque

that can actually be extracted from a wind turbine can be expressed as

Tw D Jw

d!w

dtC Tlw ; (9)

where J! is the wind turbine inertia, and Tlw is the load torque. The relationship of

the rotor speed and torque between the wind turbine and the generator is expressed

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606 A. M. Howlader et al.

as the following equations by using the gear ratio Rn:

!m D Rn!w ; (10)

Tlm D �1

Rn

Tlw ; (11)

where !m is the generator rotor speed, and Tlm is the generator input torque. Input power

to the generator Pin is expressed as

Pin D �Tlm!m: (12)

The motion equation of the generator is expressed as

Jm

d!m

dtC Dm!m C Tlm D Tm; (13)

where Jm is the generator inertia, Dm is the damping coefficient, and Tm is the generator

electric torque. The output power of generator Pout is expressed as

Pout D Tm!m: (14)

3. Optimization of Operating Points

Maximum efficiency can be achieved at all wind velocities, as shown in Figure 2. Since

the wind turbine output Pw in a steady state is Pw D Tw!w , a wind turbine output serves

as the cubic function of wind turbine rotor speed !w, which is described as

Pw D .Twind � Tf /!w ;

D

�1

2��R3

o � K0

�V 2

! !w � K1V!!2w � K2!3

w: (15)

Figure 2. Performance curve of wind turbine.

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Parameter Identification of Wind Turbine Generation System 607

The optimal wind turbine rotor speed !optw is obtained as the local maxima of the following

equation due to dPw=d!w D 0 [8]:

dP!

d!w

D

�1

2��R3

o � K0

�V 2

! � 2K1V!!w � 3K2!2w D 0; (16)

!optw D

�K1Vw C

s.K1Vw/2 � 3K2

�1

2��R3

o � K0

�V 2

w

3K2

: (17)

4. Parameter Identification

In this article, the parameter identification method deals with the wind turbine loss

coefficients K0, K1, and K2. Here is proposed least squares off-line technique based

on N units of the data to identify parameters. To implement identification the algorithm

in recursive form, the parameters estimate are updated when new data points become

available [9].

The system equation is

Tw.N / D zTN K N C e.N /; (18)

where zTN is the regressions vector that contains input–output data, KN is the wind

turbine parameters, and e.N / is the white noise. The zTN is given by

zTN � ŒTwind.N � 1/; Twind.N � 2/; : : : ; Twind.N � n/;

Tw.N /; Tw.N � 1/; : : : ; Tw.N � n/�: (19)

The wind turbine parameter is constant, expressed by K NC1 D K N : The white noise

e.N / is defined by

Efe.N /g D 0; (20)

where E denotes the exceptation of operator. The calculation of identification is ex-

pressed by

bK N D bK N�1 C C N .Tw.N / � zTN

bK N�1/; (21)

where C N is given by

C N D PN�1zN .1 C PN�1z2N /�1; (22)

and the factor .Tw.N / � zTN

bKN�1/ is the prediction error. To update P ,

PN D PN�1 � P2N�1z

2N .1 C z

TN PN�1zN /�1 : (23)

Initially, PN is a large positive number. The initial value of zN is expressed by

z1 � ŒTwind.0/; Twind.�1/; : : : ; Twind.1 � N /; Tw.1/; Tw.0/; : : : ; Tw.1 � n/�T : (24)

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608 A. M. Howlader et al.

Figure 3. Control system.

5. Control of Squirrel-cage IG

The system configuration of the proposed control system is shown in Figure 3. The

IG and wind turbine parameters are shown in Table 1. !opt is obtained from the speed

optimizer, which is discussed in Section 3, and it depends on the parameter identifier,

which is explained in Section 4. The vector control method is used to perform the speed

Table 1

IG and wind turbine parameters

Squirrel-cage IG parameters

Rated capacity P D 2:2 kW

Rated voltage 160 V

Rated current 15 A

Number of poles P D 2

Stator resistance Rs D 1:00 �

Rotor resistance Rr D 0:80 �

Core loss Ri D 1:00 k �

Exciter inductance Lm D 0:08 mH

Stator inductance Ls D 0:085 mH

Rotor inductance Lr D 0:085 mH

Inertia coefficient Jm D 2:25 � 10�3 kgm2

Damping coefficient D D 2:14 � 10�3 kgm2/s

Wind turbine parameters

Blade radius Ro D 0:95 m

Inertia coefficient Jw D 0:312 N�m�s2/rad

Air density � D 1:204 N�s2=m4

Gear ratio Rn D 3:0

Wind turbine loss coefficient K0 D 1:610319

K1 D �0:07617

K2 D 0:00997

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Parameter Identification of Wind Turbine Generation System 609

control of the IG. The torque current reference value is given as

i�

qs D1

KT

�Jm

d!�m

dtC D!�

m C bTlm C kP!e! C kI!

Ze!dt

�; (25)

where bTlm is the estimated input torque of the generator, kP! is the propotional gain for

the speed controller, kI! is the integral gain for the speed controller, and the speed error

is e! D !�m � !m. In addition, the generator may minimize the electric power loss by

executing the motor operation for tracking to the reference value, and an over-current

may occur for motor operation. Hence, a restriction of �20 � i�qs � 0A is adapted in

the q-axis current reference value i�qs . Furthermore, the d -q-axis reference voltages are

determined by the following equations by a proportional-integral (PI) controller using

the current reference value [10]:

v�

ds D kP ieid C kI i

Zeid dt; (26)

v�

qs D kP ieiq C kI i

Zeiqdt; (27)

where kP i is the proportional gain for the current controller, kI i is integral gain for the

current controller, eid D i�

ds � ids is the d -axis current error, and eiq D i�

qs � iqs is

the q-axis current error.

6. Simulation Results

6.1. Sensitivity Analysis of Wind Turbine Parameter

The response of the system with a parameter error is evaluated for operation speed and

output power. In this simulation, wind turbine parameters K0, K1, and K2 have been

changed from 80 to 120% of their true values, respectively. Figure 4 shows the behavior

of the rotational speed. From Figures 4(a)–4(c), when the parameters K0, K1, and K2

have been changed from 80 to 120%, the deviation ratio from the optimum speed !w�!optw

!optw

is observed to be about 70, 40, and 40%, respectively. From Figures 5(a)–5(c), to obtain

90% output power, parameter K0 can be changed to about ˙5%. On the other hand, the

K1 and K2 can be changed up to ˙15%.

From these figures, parameter K0 is the most influential on rotation speed and output

power, which is why K0 is the most important parameter. The small errors are identified

in parameters K1 and K2 for maximum power-point tracking control.

6.2. Wind Turbine Parameter Identification

The effectiveness of the proposed method is demonstrated through simulation results. In

this simulation, given wind turbine parameters have errors at first, and the wind turbine

parameters identified are applied 5 sec after the wind power generation system was

started. Wind velocity Vw , wind turbine output torque Tw , parameter error, generator

operation speed !m, and generator output power Pout are shown in Figures 6(a)–6(e). It

can be confirmed from Figure 6(c) that the parameter is identified with a small error.

Since the errors are within ˙5%, the rotational speed and output power are similiar to the

optimum one, as shown in Figures 6(d) and 6(e). Controlling the generator with optimum

operation speed maximized the input power from the wind turbine.

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610 A. M. Howlader et al.

(a)

(b)

(c)

Figure 4. Effect of change of wind turbine parameter value on rotational speed: (a) K0, (b) K1,

and (c) K2.

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Parameter Identification of Wind Turbine Generation System 611

(a)

(b)

(c)

Figure 5. Effect of change of wind turbine parameter value on output power: (a) K0, (b) K1, and

(c) K2.

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612 A. M. Howlader et al.

(a)

(b)

(c)

Figure 6. Simulation results: (a) wind velocity, (b) wind turbine output torque, (c) error of

parameter for determining optimum operation speed, (d) rotational speed, and (e) output power.

(continued)

7. Conclusion

In this article, the method of an optimal control structure for variable-speed fixed-pitch

wind turbines is presented. An iterative least square technique has been used for wind

turbine parameter identification. The proposed method was tested by simulations. The

simulation results confirm that wind turbine parameters identified well by proposed

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Parameter Identification of Wind Turbine Generation System 613

(d)

(e)

Figure 6. (Continued).

techniques. The small error in identified parameters K1 and K2 are acceptable for

maximum power-point tracking control. In the case of parameter K0, the large error is

identified, and it is a sensitive parameter for the maximum power-point tracking control.

However, the operating point of maximum power-point tracking control oscillates

largely around the energetic maximum, which is harmful to the provided power quality

and to the mechanical reliability. The improvement of the optimization criterion is a point

to consider for mechanical stress in future research, as well as the design of a robust

identification strategy to take into account the parameter variations.

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