A New Controller for Variable Speed Wind Turbine Generator

Handan Nak Control Engineering Department

Istanbul Technical University Istanbul, Turkey nak@itu.edu.tr

Ali Fuat Ergenc Control Engineering Department

Istanbul Technical University Istanbul, Turkey

ergenca@itu.edu.tr

Abstract—In this paper, a new generator torque control algorithm is proposed for variable speed-variable pitch wind turbine to extract maximum energy from the wind. In this controller scheme double PI controllers are utilized where conventional wind turbine control systems incorporate single PI controller. The proposed controller structure uses double feedback both from speed and power of the generator to maximize the harvest of wind energy.

Keywords-component; Wind Turbine; Generator Control; PI Controller; Double Feedback

I. INTRODUCTION Electrical energy consumption is drastically growing

globally parallel to population growth and wide range of energy services. Although there are using nuclear or hydro power sources, power generation remains widely based on fossil fuels, it is the main and fastest-growing source of energy-related CO2 emissions. Increasing climate concerns and environmental pollution awareness have become an essential component of energy policy-making, thus countries are deviating more from the conventional electricity generation sources to renewable energy sources [1, 2].

In the last decade, wind energy has become a mainstream source of renewable electricity. According to the Global Wind Energy Council (GWEC)’s “Global Wind Statistics 2012” document; global cumulative installed wind capacity reached 282.430 MW by the end of 2012 [3]. GWEC 2012 market statistics show that the wind market expands continuously, with annual market growth of almost 10%, and cumulative capacity growth of about 19%.

Although there are several different types of wind turbine systems, variable speed wind turbine systems are becoming more popular due to the efficiency of energy harvesting. Variable speed generation provides better energy capture, less power fluctuation and less mechanical stress [4-6]. Since the electrical energy demand is growing continuously, maximization of the power, which is extracted from a wind turbine, presents an importance. Hence, development of advanced control techniques for harvesting maximum power out of wind energy at variable wind speeds plays critical role in wind turbine systems [7]. The variable speed techniques are

based on the fact that for any wind speed, there is an optimum turbine speed which produces the maximum power [8]. Therefore, it is very critical to make wind turbine output power to pursue the specific ideal power curve of the wind turbine.

There are many different maximum power point (MPP) tracking (MPPT) control strategies which have been developed in order to provide maximum aerodynamic power of the wind turbine in the literature [6-15]. These methods can be classified by three main categories. Among these, tip speed ratio (TSR) control is based on regulation of generator speed to provide the optimal TSR [6, 7]. Hill-climb searching (HSC) control is also known as perturb and observe (P&O) control continuously adjusts the turbine speed for the peak power of the wind turbine by regulating dc-side voltage [6, 9]. HSC control does not require any prior knowledge of the system and its implementation is quite easy; but speed–ef ciency trade-off and the wrong directionality under rapid wind change are main drawbacks [10, 11]. At last, power signal feedback (PSF) control targets shaft speed/power for the MPPT control of a wind turbine is determined from the wind turbine’s maximum power curve [6, 12]. The prerequisite of this method is that the maximum power curve has to be obtained via either simulations or tests for individual wind turbine model. Meanwhile, utilizing PSF control can reduce the fluctuation in generator power and it is relatively easy to execute in practice [7].

In this study, a new generator torque control method for variable speed variable pitch wind turbine system is presented. The generator of the turbine is doubly-fed induction generator (DFIG) for the advantages in utilization of these machines to maximize the produced power and independent control of active and reactive power. The control strategy is a type of optimal control structure which uses the power and the rotor speed points extracted from the wind turbine’s maximum power curve as control inputs to determine the reference torque signal for generator control system.

The paper is organized as follows. In Section II, the fundamental wind turbine principles are described. In Section III, the proposed control system is presented and discussed. Section IV includes the simulation results and, in Section V is the conclusion.

978-1-4799-1464-7/13/$31.00 ©2013 IEEE

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II. WIND TURBINE PRINCIPLES Fig. 1 illustrates the topology of a variable speed variable

pitch wind turbine system with DFIG. The aerodynamic power is transmitted to the generator over a gearbox to increase the rotational speed for power production. In this configuration, rotor of the DFIG is driven using a variable frequency converter to provide necessary magnetic field for the stator to synchronize with the grid. In Fig. 2 the block diagram of the wind turbine system is depicted. Here, ref , Tg,ref, Qg,ref are the reference pitch angle, the reference generator torque and the reference generator reactive power, respectively.

In the practice, the mechanical power extracted from wind by rotor is generally expressed as,

( )2 3a w pP =0.5 R v C , . (1)

where is the air density, R is the rotor radius, vw is the wind speed, and Cp is the wind turbine power coefficient, and denotes the blade pitch angle. The term defined as the tip speed ratio, which is described as

r

w

R= .

v (2)

where r is the rotor rotational speed.

Figure 1. The topology of a wind turbine system with doubly-fed induction

generator.

aT

β

refβ

rω

gωgT

,g refQ,g refT

wv

Figure 2. Block diagram of the wind turbine system.

The turbine manufacturers provide the variation of the power coefficient or directly turbine power to wind speed, rotor speed, and pitch angle as a lookup table. This case leaves no need for an analytical formulation of power coefficient.

The produced aerodynamic torque (Ta) is derived using

a a rT =P / . (3)

The mathematical model of the mechanical system, which consists of the turbine rotor, the gearbox and the generator, is,

ra g t t r

dT -nT =J +B .dt

(4)

g r=n . (5)

where

2t r gJ =J +n J . (6)

2t r gB =B +n B . (7)

Here, Jr, Jg and Jt are rotor, generator and total turbine moments of inertia, respectively and Br, Bg and Bt denote rotor, generator and total turbine damping ratios, respectively. n represents the gear ratio, and g is the generator rotational speed.

The main task of the wind turbine control system is to make wind turbine operating curve follow the ideal power curve. Fig. 3 illustrates a typical ideal power curve of a variable speed variable pitch wind turbine system. The curve is segmented into three regions.

In Region 1, below the cut in wind speed, there is not enough aerodynamic power, thus the turbine is not operating.

In Region 2, between the cut in and rated wind speed, it is desired to harvest as much power as possible from the wind. In this region, only generator torque control methods are performed while blade pitch angle is kept constant at the point, which provides maximum power coefficient (Cp). Desired rotor speed is achieved by regulating the electrical torque, which ensures the maximum power efficiency.

cut inν − ratedν cut outν −

ratedP

( )m/s

( )P Aerodynamic power - W

Figure 3. Ideal power curve of a variable speed variable pitch wind turbine.

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In Region 3, above the rated wind speed, aerodynamic power is more than intended maximum turbine power, so rotor speed and generator torque are fixed at their rated operating points. Therefore, the extracted power needs to be limited to provide rated power and protect the turbine. Pitching the blades, excess power is shaded. In this region, generator torque control and blade pitch control are utilized together.

Each wind turbine model has its own specific power curve. In Region 2, there is an optimum rotor speed which gives maximum power for every wind speed. For maximum power generation, it is required that the wind turbine operates at the optimum rotor speed. Thus, variable speed control scheme is recommended in this region. In Region 3, for every wind condition, rated rotor speed and generator torque are achieved by an optimum pitch angle that limits the aerodynamic power to its rated value. Hence, the control system of a variable speed variable pitch wind turbine is responsible to provide that turbine operates with the optimum generator torque, rotor speed and blade pitch angle at the turbine ideal power curve. In this study, the generator torque control in Region 2 (fixed pitch angles are for maximum power generation) and in Region 3 (variable pitch angles to reduce the potential aerodynamic power to rated power) is the main focus.

III. PROPOSED CONTROL SYSTEM In proposed generator torque control scheme, the control

system is divided into two sections. First section, main turbine control system is responsible for determination of the reference generator torque, and second part, converter control system assures that generator produces that the reference torque.

The proposed control system utilizes two separate control loops to generate torque references so that the turbine follows its ideal power curve. Principle scheme of the proposed control algorithm is depicted in Fig. 4.

Note that, the aerodynamic power and so the torque depends strictly on the rotor speed as it is indicated in (1) and (3). If the turbine is not operated at its optimum speed, maximum power cannot be extracted from the wind. In this case, it is not reasonable to expect that generator produces maximum power. Therefore, it is obvious that one of the main tasks of the control system is to provide control signal that depends on the rotor speed, which has a critical effect on reference generator torque.

−+aT

gT

−+,r refω

rω

+

−,g refT

Figure 4. Block diagram of the proposed generator control system.

When the turbine operates at its optimum speed point, the aerodynamic torque is at its optimum point which results in maximum power. At this point, the generator torque is equal to aerodynamic torque and the acceleration or deceleration of the rotor is prevented. At other rotor speed points, it is desired to create a torque difference between aerodynamic torque and the generator torque (electrical torque) until the rotor speed reaches its optimum value. Ideally, in case of the turbine power coefficient or power curve is known, the aerodynamic torque is estimated for any wind speed. In reality, aerodynamic torque of the turbine is not precisely known so the speed loop is incorporated in our proposed control scheme. The parallel control structure is not conventional in wind turbine system which presents our approaches novelty.

The control principle is proposed as follows:

1) If the rotor speed is smaller than reference speed, then control system generates negative control signal to reduce the torque reference in order to accelerate the rotor according to (4) as seen from the Fig. 4.

2) If the rotor speed is greater than the reference speed, the control system increases the torque reference. As a result generator torque operates as the braking torque for the system, and rotor decelerates.

In combined control structure, the reference torque is taken

as the aerodynamic torque, and the uncertainties are compensated using the speed loop. Hence, the controller structure has double feedback both from speed and torque of the generator which are controlled by conventional PI controllers.

The control system equation is,

( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )g,ref a g 1 r,ref r 2T s = T s -nT s C s - s - s C s . (8)

where C1(s) and C2(s) are the transfer functions of the conventional PI controllers as given below,

( ) i11 p1

KC s =K + .

s (9)

( ) i22 p2

KC s =K + .

s (10)

The dynamics of the torque control loop of the generator is neglected due to its electrical time constant is considerably smaller than mechanical side. It is also assumed that the generator torque control system is unitary gain and the generator torque reference variable Tg,ref is used instead of the actual generator torque Tg without parting from reality.

The generator torque and the rotor speed are derived by algebraic manipulations on (4) and (8) and expressed as,

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( ) ( )( ) ( ) ( )

( )( ) ( ) ( )

2T p1 T i1 p1 p2 i1 i2

g a2T T p1 i1 p1 p2 i1

2p2 T i2 p2 i2

r,ref2T T p1 i1 p1 p2 i1

s J K +s J K +BK +K +BK +KT s = T s

s J +nJ K +s B+BnK +BnK +nK +nK

s JK +s J K +BK +BK - s .

s J +nJ K +s B+BnK +BnK +nK +nK

(11)

( ) ( ) ( ) ( )

( ) ( ) ( )

r a2T T p1 i1 p1 p2 i1

p2 i2r,ref2

T T p1 i1 p1 p2 i1

ss = T ss J +nJ K +s B+BnK +BnK +nK +nK

snK +nK + s .

s J +nJ K +s B+BnK +BnK +nK +nK

(12)

The characteristic polynomial of the system is,

( ) ( ) ( )2c T T p1 i1 p1 p2 i1p s =s J +nJ K +s B+BnK +BnK +nK +nK . (13)

The mathematical model of the wind turbine control system remains linear time invariant by utilizing double control structure on torque and speed loops. In many applications, there is a single loop on produced and consumed power where the control system exhibits nonlinear behavior. In linear time invariant systems, it is known that for stability of the system, the roots of the characteristic polynomial must lie on the open left half complex plane. Assigning appropriate controller parameters, both system stability and the performance are achieved. In the following section, the proposed control structure is demonstrated via an example case and numerical simulations.

IV. EXAMPLE CASE AND SIMULATION RESULTS The mathematical model of the control system of a variable

speed variable pitch wind turbine system with DFIG is constructed in MATLAB Simulink® R14 for the simulations. The wind turbine system is segmented in five different subsystems; aerodynamics, drive train, DFIG, generator control system, and blade pitch control system. The block diagram is presented in Fig. 5.

The aerodynamic part generates the turbine power curve of which the inputs are wind speed, rotor speed, and pitch angle as seen in (1). The drive train consists of the mechanical system equations (4) – (7). DFIG is modeled using standard d-q model equations [2, 7]. In generator control system, the proposed control system (Fig. 4) is utilized for determination of the reference torque signal, and the reactive power reference is zero at all operational modes. To provide the desired torque and reactive power, a standard cascade control structure is used, which provides rotor voltages in d-q reference frame. Although we are interested in generator control system blade pitch control system is included for the simulations. This system regulates the reference pitch angle by using the turbine ideal power curve and a speed compensation loop which uses the reference rotor speed. A first order transfer function is used to represent the pitch angle actuator.

MPPs of the benchmark wind turbine in Region 2 for zero pitch angles are depicted in Fig. 6. Projection of the MPP curve is presented in Fig. 7 and the reference rotor speed is obtained from this curve which is a part of ideal power curve of the wind turbine. The basic turbine parameters are given in Table 1.

Figure 5. Block diagram of the variable speed variable pitch wind turbine with proposed generator torque control system.

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1015

2025

30

46

810

120

100

200

300

400

500

Rotor Speed [rpm]Wind Speed [m/s]

Aer

odyn

amic

Pow

er [K

W]

MPP

Figure 6. MPPs of the benchmark wind turbine in Region 2.

Figure 7. Ideal power curve of wind turbine used in the simulation.

TABLE I. TURBINE PARAMETERS

Parameters Value [Unit]

Turbine inertia (Jt) 67650 [kgm2]

Turbine damping coefficient (Bt) 0.5 [Nms/rad]

Gear ratio (n) 28.3

Cut in wind speed 4 [m/s]

Cut out wind speed 24.5 [m/s]

Rated wind speed 11.25 [m/s]

Rated generator power 500 [kW]

Rated rotor speed 30 [rpm]

In Fig.8, the variability of the wind-speed is exhibited. The wind speed varies between 5.5 m/s and 7.5 m/s for partial load (Region 2) operating region, and between 13 m/s and 19 m/s for full load operating region (Region 3).

Fig. 9 to Fig. 11 presents simulation results for partial load operation. Simulation results of the generator power tracking the aerodynamic power are presented in Fig. 9, while the rotor speed is compared with the reference speed in Fig. 10 for partial load operation. The generator torque, which is controlled using the proposed strategy to provide the maximum power coefficient at partial load, is depicted in Fig. 11.

0 10 20 30 40 50 605

10

15

20

Time [s]

Win

d sp

eed

[m/s

]

Full load wind speedPartial load wind speed

Figure 8. Wind speed profiles.

0 10 20 30 40 50 600

5

10

15x 104

Time [s]

Pow

er [W

]

Partial load generator powerPartial load aerodynamic power

Figure 9. Aerodynamic and generator power at partial load operation.

0 10 20 30 40 50 605

10

15

20

25

Time [s]

Rot

or s

peed

[rpm

]

Reference rotor speedActual rotor speed

Figure 10. Rotor speed at partial load operation.

0 10 20 30 40 50 600

1000

2000

3000

4000

5000

Time [s]

Gen

erat

or to

rque

[Nm

]

Figure 11. Generator torque at partial load operation.

Fig. 12 to Fig. 15 display simulation results for full load operation. As seen from Fig. 12 and Fig. 13, when rotor speed reaches its rated value (30 rpm), generator power is almost constant at the rated value 500 kW despite the variable wind speed. The controlled generator torque is given in Fig. 14 which provides the generator to produce the rated power. As illustrated in Fig. 15, pitch angle remains constant (0o) at partial load region (Region 2) for maximum power harvesting. At full load operation (Region 3), the pitch angle deviates to shade the excess power according to the turbine power curve given by the turbine manufacturer. Again, the power curve and pitch angle relation is not precisely known, thus double control structure compensates for the uncertainties.

0 10 20 30 40 50 600

1

2

3

4

5

x 105

Time [s]

Pow

er [W

]

Full load generator powerFull load aerodynamis power

Figure 12. Aerodynamic and generator power at full load operation.

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0 10 20 30 40 50 605

10

15

20

25

30

Time [s]

Rot

or s

peed

[rpm

]

Reference rotor speedActual rotor speed

Figure 13. Rotor speed at full load operation.

0 10 20 30 40 50 60

-4000

-2000

0

2000

4000

6000

8000

Time [s]

Gen

erat

or to

rque

[Nm

]

Figure 14. Generator torque at full load operation.

0 10 20 30 40 50 600

5

10

15

20

Time [s]

Pitc

h an

gle

[deg

ree]

Full load pitch anglePartial load pitch angle

Figure 15. Pitch angle for partial and full load.

V. CONCLUSION In this paper, a novel and simple generator torque control

strategy for variable speed variable pitch wind turbines is presented. A type of optimal control structure that uses the turbine speed and torque as inputs is used to obtain a reference generator torque signal. Simulation results present that it is possible to make wind turbine track the ideal power curve with this novel control scheme with minimum error. These numerical results provide substantial basis for us to pursue further into the expensive experimental studies.

ACKNOWLEDGMENT This research is supported by The Scientific and

Technological Research Council of Turkey (TUBITAK) in the framework of National Wind Turbine Project (MILRES).

REFERENCES [1] International Energy Agency, “Climate & Electricity Annual 2011: Data

and analyses,” France, 2011. [2] Billah, M. M., Hosseinzadeh, N., and Ektesabi, M. M., “Modelling of a

doubly fed induction generator (DFIG) to study its control system,” in Universities Power Engineering Conference, New Zealand, 2010, pp. 1–6.

[3] Global Wind Eenrgy Council, “Global Wind Statistics 2012,” Belgium, February 2013.

[4] S. M. Muyeen, Rion Takahashi, Toshiaki Murata, and Junji Tamura, “A variable speed wind turbine control strategy to meet wind farm grid code requirements,” IEEE Trans. Power Syst., vol. 25, no. 1, pp. 331–340, February 2010.

[5] E. Muljadi, and C. P. Butterfield, “Pitch-controlled variable-speed wind turbine generation,” IEEE Trans. Ind. Appl., vol. 37, no. 1, pp. 240–246, January/February 2001.

[6] W. Quincy, and C. Liuchen, “An intelligent maximum power extraction algorithm for inverter-based variable speed wind turbine systems,” IEEE Trans. Power Electron., vol. 19, no. 5, pp. 1242–1249, September 2004.

[7] Hua, G., and Geng, Y., “A Novel Control Strategy of MPPT Taking Dynamics of Wind Turbine into Account,” in Power Electronics Specialists Conference, Jeju, Korea (South), 2006, pp. 1–6.

[8] Leidhold, R., Garcia, G., and Valla, M.I., “Maximum efficiency control for variable speed wind driven generators with speed and power limits,” in Annual Conference of the IEEE Industrial Electronics Society, Sevilla, 2002, pp. 157–162.

[9] Y. Xia, K. H. Ahmed, and B. W. Williams, “Wind turbine power coefficient analysis of a new maximum power point tracking technique,” IEEE Trans. Ind. Electron., vol. 60, no. 3, pp. 1122–1132, March 2013.

[10] N. Femia, G. Petrone, G. Spagnuolo, and M. Vitelli, “Optimization of perturb and observe maximum power point tracking method,” IEEE Trans. Power Electron., vol. 20, no. 4, pp. 963–973, July 2005.

[11] S. M. R. Kazmi, H. Goto, G. Hai-Jiao, and O. Ichinokura, “A novel algorithm for fast and efficient speed-sensorless maximum power point tracking in wind energy conversion systems,” IEEE Trans. Ind. Electron.,vol. 58, no. 1, pp. 29–36, January 2011.

[12] Qiao, W., “ Intelligent mechanical sensorless MPPT control for wind energy systems, in Power and Energy Society General Meeting, San Diego, California USA, 2012, pp. 1–8.

[13] R. Datta, and V. T. Ranganathan, “A method of tracking the peak power points for a variable speed wind energy conversion system,” IEEE Trans. Energy Convers., vol. 18, no. 1, pp. 163–168, March 2003.

[14] E. Koutroulis, and K. Kalaitzakis, “Design of a maximum power tracking system for wind-energy-conversion applications,” IEEE Trans. Ind. Electron., vol. 53, no. 2, pp. 486–494, April 2006.

[15] M. Pucci, and M. Cirrincione, “Neural MPPT control of wind generators with induction machines without speed sensors,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 37–47, January 2011.

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