143 tan aupec01paper revised

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Mechanical Sensorless Robust Control of Wind Turbine

Driven Permanent Magnet Synchronous Generator

For Maximum Power Operation

Kelvin Tan Syed Islam

Australian Cooperative Research Centre for Renewable Energy LtdCentre of Renewable Energy and Sustainable Technologies Australia (CRESTA)

Curtin University of Technology, WA

Abstract: This paper proposes a prototype version of the control strategy of a permanent magnet synchronousgenerator for maximum power operation without mechanical sensors. This approach is based on the calculated

maximum rotor power vs. alternator frequency curve, and calculated maximum rotor power vs. rectified DC

voltage curve to obtain a maximum power output at a certain wind speed. This control allowed the permanentmagnet gener ator to operate at an optimal speed for a given wind speed. To show the feasibility of this

mechanical sensorless control strategy for maximum power estimation, a simple mathematical model of a

variable speed wind energy conversion system – permanent magnet generator was developed. The mathematicalmodel was used to calculate the response of the wind energy conversion and to determine the maximum power

operating point. This paper also describes a theoretical aspect of this method. Digital simulation of the system

was performed to illustrate the advantages of this control strategy.

1. INTRODUCTION

Optimum wind energy extraction is achieved byrunning the wind turbine generator (WTG) invariable-speed variable-frequency mode. The rotor

speed is allowed to vary in sympathy with the wind

speed, by maintaining the tip speed ratio to thevalue that maximizes aerodynamic efficiency. In

order to achieve this, the permanent magnet

synchronous generator (PMSG) load line should bematched very closely to the maximum power line

of the wind turbine generator. In such a case, agood matching exists between the generator and the

load for the best performance of the system and

maximum utilization of the wind driven PMSG.However, the recent advancements in power

electronics and control strategies have made it

possible to regulate the voltage of the PMSG in

many different ways. When the generator torqueline can be controlled; the generator loading of the

turbine can be made to follow the desired locussuch as the optimum shaft power locus. In the

existing controller for the maximum power

extraction, most designed controllers use ananemometer to measure wind speed for deriving the

demand shaft speed [1]. In most cases, one

anemometer reading could not provide adequate

information. The required information would needto be provided through a number of anemometers at

some distance away from and surrounding the windturbine. Sensors measurement of mechanical

quantities such as shaft torque and rotation speed

may be required. These sensors increase the cost

and reduce the reliability of the overall system. To

achieve optimal power output, a sensorless schemewill be proposed for extracting desired output power from the permanent magnet generator over a

wide range of wind speeds. The proposed system

will increase the overall output of the generationsystem with a minimal increase in controller

complexity.

2.MATHEMATICAL MODELING OF THE

ELEMENTS OF THE WIND ENERGY

CONVERSION SYSTEM

Fig. 1 Wind Energy Conversion System

The proposed scheme consists of a PMSG driven by a fixed pitch wind turbine, a diode rectifier and aPWM feeding a local load as shown in Fig. 1. A

brief description of each element of the wind



energy conversion system is shown in this section.

These models are expressed in the d-q rotor

reference frame. This eliminates all time-varyinginductances by referring the stator and rotor

variables to a frame of references, which rotateswith rotor

2.1 Power from wind turbine

Fig. 2 Power Coefficient vs. Tip Speed Ratio

with β=0

The output mechanical power of the wind turbine

may be calculated from the following equation[1]:

Watts3

wAUC2

1mP ρρ= (1)

CP is the power coefficient, which is a function of

tip speed ratio λ and blade angle β. Thisrelationship is usually provided by the

manufacturer in the form of a set of non-dimensional curves. The power coefficient curve CP for the wind turbine used in this study is shown inFig. 2. The tip speed ratio is given by:

wU

r r ωλ = (2)

Where

r = radius of the rotor [m]

ρ = air density [Kgm-3

]

A = wind turbine rotor swept area [m2]

Uw = wind speed [m/s]

ωr = mechanical angular velocity of thegenerator

For a variable speed wind turbine with a pitch

control mechanism that alters the effective rotor

dynamic efficiency, optimum power can easily beobtained using appropriate control. However, fixed

pitch wind turbine has been used in this prototype

wind energy conversion scheme (WECS).

2.2 Permanent magnet synchronous generator

model

Model for the power producing capabilities of awind turbine has been previously developed [2, 3].The outer-rotor PMSG described in the paper[4] isused in this WECS mathematical model. The

PMSG dynamic equations are expressed in the d-q

reference frame, which eliminate all time-varyinginductances by referring the stator and rotor

variables to a frame of references, which rotateswith the rotor. The model of electrical dynamics in

terms of voltages and current can be given as[3]:

mr di

dLr q)iqL(R qv λωωρ +−+−= (3)

qiqLr d)i

dL(R

dv ωρ ++−= (4)

Where

R, L= Machine resistance and inductance per phasevd, vq = 2-axis machine voltages

id, iq = 2-axis machine currents

The above equations are derived assuming that the

q-axis is aligned with the stator terminal voltage phasor (i.e.Vd=0). The expression for theelectromagnetic torque in the rotor is written as:

( )[ ]qmdqqde iiiLL2

P

2

3T λ−−

= (5)

Where

P = number of poles of the PMSGT e = electrical torque from the generator

λm =amplitude of the flux linkages established a

permanent magnet

The relationship between the angular frequency of

the stator voltage (ωr ) and the mechanical angular

velocity of the rotor (ωm) may be expressed as:

m2

pr ωω = (6)

The mathematical prediction of voltage variationwith the load current from the PMSG at six

different rotational speeds is calculated and shown

in Fig. 3. It seems that there is a good agreement between the predicted and experimental results.[4]



0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0 2 0 4 0 6 0 80 100 120Frequency (Hz)

D C P o w e r ( W

Fig. 3 calculated voltage regulationof the PMSG

2.3 Uncontrolled Rectifier

As the wind speed is constantly varying, the PMSG

produces variable-voltage and variable-frequencyoutput, which cannot be fed directly to load. A 3-

phase diode rectifier, which is used to convert thevariable magnitude, variable frequency voltage at

the PMSG terminal to dc. Under the assumption

that the both commutating angle & commutatinginductance are negligible, the rectifier outputvoltages (VR ) and current (IR ) expression may be

simplified and expressed in term of the peak phase

voltage and current (fundamental component) ofthe generator [5, 6]:

dv

p

33

R V = (7)

qi

32

p

R I = (8)

The dc power available at the rectifier output is

converted to ac power using a PWM inverter. The

output of the wind turbine generator is controlled by adjusting the modulation index M of the

reference sinusoidal signal of the PWM inverter,and it ranges from 0 to 1. In order to make the

inverter of the AC-DC-AC link to track the

maximum power output from the WTG, thesensorless controller is designed to determine the

operating dc voltage of the inverter at various

speeds. This will control the pulse width of the

PWM inverter and the power transferred to the

local load indirectly by controlling the powerextracted from the WTG.

3. WIND DRIVEN PMSG CHARACTERISTICS

In the proposed sensorless scheme, the inverterinput operating voltage is determined by a

“mapping-power” technique. In this technique, the

controller does not require a mathematical model of

the system/process being controlled. However, it is

important to understand the voltage, current and power characteristics generated by the system at

various constant wind speeds. Fig. 1 shows thecomponents of a typical stand-alone wind energy

conversion system. Wind energy conversion systemis simulated using Matlab Simulink to calculate thegenerator stator frequency, dc current and voltageat the dc link at various wind speeds.

The dc power output characteristics at the dc linkare then calculated following a step change in

different operating dc voltages. The results of thecalculations are for wind speed range 3-11m/sec.

The results are shown in Fig. 4 and Fig. 5. These

form the output power curves of the PMSG atvarious constant wind speeds, the generatormaximum power curves show the different

operating dc voltages and stator frequencies over a

range of wind speeds. In order to extract the p eak power from the WTG at a given wind speed, the

WECS has to operate at the target maximum powercurve. The operating dc voltage and stator

frequency have to match closely to the maximum

power curve, as shown in Fig. 4 (maximum powervs. stator frequency) and Fig. 5 (maximum power

vs. dc voltage).

Fig. 4 Predicted characteristic

(dc power-stator frequency ) of the WECS

Fig. 5 Predicted characteristic

(dc power-dc voltage ) of the WECS

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

22000

0 100 200 300 400 500 600 700

DC Voltage ( V)

D C P o w e r



By combining the characteristics of the PMSG

which determine, dc power output at different wind

speeds, operating limit of the WECS system could be drawn in the power- frequency or power-Vdc

plane. Such system limitation is shown in Fig. 6.

Fig. 6 System limitation in the powervoltage plane

From Fig. 6, it is seen that the limitation on the left

is bounded by the minimum dc link voltage

required by the inverter. This line is due to thevoltage-current characteristic of the PMSG. At aconstant given wind speed, the PMSG is under

increasing load as the dc voltage decreases. When

the dc voltage is less then the minimum dc linkrequirement, the operating of PMSG wind turbine

is in stalled region of operation. Any decrease in

the tip speed ratio will cause a further decrease untilthe turbine stops. The upper limitation is bounded

by the rated wind speed (11m/s) and maximum power capability of the PMSG. If the maximum

power limitation of the inverter is lower than the

maximum power capability of the PMSG. Theupper limitation is bounded by inverter power

limitation. The right limitation represents the

maximum speed of the wind turbine PMSG. The

system controller is constrained to operate withinthe power limitations shown in Fig. 6. This is an

important consideration for the design of thesystem controllers.

4. DESCRIPTION OF THE CONTROLLEDWECS STRUCTURE

The block diagram shown in Fig. 7 is the

preliminary design of the sensorless WECScontrolled system. In the preliminary design stage,

the system does not include the minimum dc link

limitation, cut-in and cutout wind speed control

features. To show the feasibility of this mechanical

sensorless control strategy for maximum power

estimation, a simple mathematical model of the

proposed control system is developed. The controlsystem consists of two signal-tracking loops,

namely the “power-mapping" loop and alternatorfrequency derivative loop. The tracking signals

required for both loops are the output power fromthe WECS that is transferred to the dc link andPMSG stator frequency.

It is recognized that the inverter has the flexibility

to operate over a wide range of dc input voltages.At a given wind speed, the output dc link power is

used to estimate the optimal dc operating voltagefrom the "power-mapping" maximum power vs. dc

voltage curve shown in Fig. 5. Due to the

sensitivity of Pdc to the changes in Vdc for thePMSG, the Pdc and Vdc will continue to increase ordecrease till the intersection of Pdc and Vdc at the

maximum power for the given wind speed. The

stator frequency will also be changing (increasingor decreasing) during the change of the operating

dc voltage. In the alternator frequency derivativeloop, the derivative control action provides a means

of obtaining the controller with higher sensitivity.

This derivative control responds to the rate ofchanges of the stator frequency and can produce a

significant correction to the operating dc voltage.

The gain value from frequency derivative loop will become zero when the operating dc voltage is

optimal one which leads to the maximum power

point. Using the results determined by both loops,

the controller allows the dc bus voltage to vary tothe maximum power operating point.

Fig.7 Block diagram of the sensorless WECS

controlled system

5. SIMULATION RESULTS

A mathematical simulation model of the proposed

WECS is developed. The WECS has beensimulated on a PC using Matlab Simulink software



Fig. 8 Simulation results depicting variation of system variables with step changes in wind velocity

and its toolbox packages. With the simulation

results, we are able to study most of the system

characteristics such as its tracking performance andits ability to recover from large disturbances. Two

case studies are considered and described as

follows:-

5.1 Case 1: Step model of wind speed

The simulation result is shown in Fig. 8. The wind

speed is shown in the form of fast step variation

(from 5 to 11m/s). It seems that with increase inwind speed, the sensorless controller increases the

operating dc voltage, which directly controls the

modulation index of the PWM inverter. This

increases the power output of the inverter and the power transferred over the dc link. Also, the power

output of the rectifier drawn from the wind drivenPMSG increases, thereby ensuring the complete

utilization of available wind energy. As shown in

Fig. 8, the change in the peak power in the dc linkfollows the wind speed profile. The peak power

shown in the Fig. 8(iii) is the actual maximum

power for each given wind speed. It is also observedthat the peaks in the error are recorded only in the

points of sudden change in the wind speed.

5.2 Case 2 : Random variation of wind speed

On achieving the goal of efficiently tracking the

maximum output power from the wind, the designedcontroller should respond to the wide variation of

wind speed. The variation of wind profile is shown

in Fig. 9(i). In the case when the wind is fluctuating

with a non-uniform distribution, the output powerfrom the inverter will not be smooth. From Fig.

9(iv), it is clear that that the two profiles, operating

dc voltage and required operating voltage for

maximum power, are close to each other withinalmost the whole wind variation. Therefore, the peak

power shown in Fig. 9(iii) is close to the actualmaximum power for each variation of wind speed.

On the other hand, comparing the error signal obtain

from operating dc voltage and required operatingvoltage for maximum power, there is a high value of

error signal at starting of each sudden change of

wind speed. This is due to high gain in the alternator

frequency derivative loop and slow response of thesystem. A more intelligent controller may be

required for higher tracking performance with fastresponse and robust control.

6. CONCLUSION

The paper presents modeling and simulation resultof a prototype variable speed sensorless WECS. The

variable amplitude, variable frequency voltage at the

PMSG terminals is first rectified in a diode rectifierand the dc power is transferred over the dc link to aPWM inverter feeding to a local load. A sensorless

controller is used to determine the optimal operating

dc voltage which is then used to control the ofmodulation index of the PWM inverter to utilize



Fig. 9 Simulation results depicting variation of system variables with random changes in wind velocity

completely the available wind energy. The proposedcontrol system consists of two loops, namely the

“mapping-power" loop and differentiation of

alternator frequency loop. Using the results

determined by both loops, the controller allows thedc bus voltage to vary to the maximum power

operating point. Two case studies are considered,namely the (a) Step model of wind speed, and (b)

random variation of wind speed. Both have proved

the feasibility and maximum power trackingcapabilities of the designed sensorless controller.

But due to slow response of the prototype controller,

an alternative controller based on the fuzzy set

theory or PID controller will be proposed in a future publication.

7. ACKNOWLEDGEMENTS

"The work described in this paper has beensupported by the Australian Cooperative Research

Centre for Renewable Energy Ltd (ACRE). ACRE'sactivities are funded by the Australian

Commonwealth's Cooperative Research Centres

Program.” Mr. Kelvin Tan has been supported by an

ACRE Postgraduate Research Scholarship. Allauthors wish to thank CRESTA, School of Electrical

Engineering at Curtin University of Technology forsupporting the research work.

8. REFERENCES

[1] L. L. Freris, Wind energy conversion system :

Prentice Hall, 1990.

[2] A. J. G. Westlake, J. R. Bumby and E.Spooner, "Damping the power-angle

oscillations of a permanent-magnetsynchronous generator with particular

reference to wind applications," IEE Proc.-

Electr. Power Appl , vol. 143, no. 3, May 1996, pp.269-280.

[3] B. S. Borowy and Z. M. Salameh, "Dynamic

response of a stand-alone wind energy

conversion system with battery energy storageto a wind gust," IEEE Transactions on Energy

Conversion, vol. 12, no. 1, March 1997, pp.73-78.

[4] J. Y. Chen and C. V. Nayar, "A low speed,

high touque, direct coupled permanent magnetgenerator for wind turbine application.,"

presented at Proceedings of Solar'97 -

Australian and New Zealand Solar EnergySociety, 1997.

[5] P. C. Krause, O. Wasynczuk and S. D.

Sudhoff, Analysis of electric machinery: IEEEPress, 1994.

[6] N. Mohan, T. M. Undeland and W. P. Robbins,

Power Electronic: Converter, application and

design: John Wiley & Sons, Inc. , 1995 .

143 tan aupec01paper revised

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