A New Control Method of Permanent Magnet Generator for Maximum Power Tracking in Wind Turbine Application

8/3/2019 A New Control Method of Permanent Magnet Generator for Maximum Power Tracking in Wind Turbine Application

1/6

1

Abstract This paper discusses a new and simple control

method for maximum power tracking in a variable speed wind

turbine by using a step-up dc-dc converter. The output voltage of

permanent magnet generator is connected to a fixed dc-link

through a three-phase rectifier and the dc-dc converter. A

maximum power-tracking algorithm calculates the speed

command that corresponds to maximum power output of the

turbine. The dc-dc converter uses this speed command to control

the output power of the permanent magnet generator, such thatthe speed of generator tracks the command speed. A current

regulated PWM voltage source inverter maintains the output

voltage of dc-dc converter at a fixed value by balancing the input

and output power to the dc-link. In addition, the inverter can

improve power factor and inject a current with very low

harmonic distortion into the utility grid. The generating system

has potentials of high efficiency, good flexibility, and low cost.

Index Termsdc-dc converter, Maximum power tracking,

Permanent magnet generator, PWM inverter, Speed control,

Variable speed wind turbine.

I. INTRODUCTIONaximized electricity generation by wind turbines is aninteresting topic in electrical engineering and manytypes of variable speed generating systems have been

researched to achieve this goal. Use of a variable speedgenerating system in wind power application can increase thecaptured power from wind. In fact, the system based onpermanent magnet generator (PMG) is one of the mostfavorable and reliable methods of power generation.However, electricity generated directly by PMG has variableamplitude and frequency, requiring additional conditioning tomeet the amplitude and frequency requirements of the utilitygrid and/or conventional loads. Many types of power

electronic converters were introduced to find an appropriateand inexpensive solutions to the problems of electricityconditioning and the results are promising [1][2][5].

The use of the variable speed PMG in wind turbine

application can increase the energy capture from wind,

resolve other problems such as noise, and improve efficiency.

For example, in a wind turbine system if a gearbox is used,

noise, power losses, additional cost, and potential of

mechanical failure can cause problems. The use of a variable

speed PMG could solve these problems [8].

In a variable speed PMG system, a vector control approach is

often employed to achieve nearly decoupled active and

reactive power control on the supply side power converter,

which is a current regulated voltage source inverter. In this

way, the power converter maintains the dc-link voltage and

improves power factor of the system [4][5][9]. Different

control methods for maximum power tracking in variable

speed wind turbine generators have been discussed in

[5][6][7].

This study presents a new control approach and the related

power converter topology to track the maximum power

without measuring wind or generator speed, which is of great

importance for small size and low cost wind turbines. Using

PSIM software simulation, the circuit topology and control

method of the wind power generating system is investigated

with a PMG and a back-to-back ac-dc-ac power converter.

Also included in the investigation is the wind turbines

dynamics.

The paper is organized as follows: in section IIaerodynamic characteristics of turbine and principles of

maximum power tracking method are explained. Systemconfiguration, circuit topology, and power converters arediscussed in section III. In section IV simulation results arepresented to confirm that the control method for speed controland capturing maximum power from wind works properly.Section V summarizes the advantages of the overall systemand gives some final remarks.

II. WIND TURBINE

A. Wind Turbine Aerodynamic Characteristics

The amount of mechanical power captured from wind by awind turbine could be formulated as [3]:

3

Pm vAC21P = (1)

where, : air density (Kg/m3)

A : swept area (m2)

CP: power coefficient of the wind turbineV : wind speed (m/s)

Therefore, if the air density, swept area, and wind speed areconstant the output power of the turbine will be a function ofpower coefficient of the turbine. In addition, the wind turbineis normally characterized by its CP-TSR curve; where, TSR,tip-speed ratio, is given by:

A New Control Method of Permanent MagnetGenerator for Maximum Power Tracking in

Wind Turbine ApplicationR. Esmaili, Student Member, IEEE, and L. Xu, Fellow, IEEEand D. K. Nichols, Member, IEEE

M


2/6

2

v

RTSR = (2)

In (2), , R, and v are the turbine rotor speed in rad/s,

radius of the turbine blade in m, and wind speed in m/s,

respectively. Fig.1 shows a typical CP-TSR curve for a wind

turbine.

Fig. 1. Power coefficient versus tip-speed ratio.

As can be seen from Fig.1, at TSRopt CP has its maximumvalue which results in the optimum efficiency; therefore,maximum power is captured from wind by the wind turbine.

Fig. 2 illustrates the output power of a wind turbine versusrotor speed while speed of wind is changed from v1 to v3(v3>v2>v1). As can be seen from Fig. 2, for example, if thespeed of wind is v1 the maximum power could be captured

when the rotor speed is 1; in other words, the operating pointof the system is Point A which corresponds to the maximumoutput power. If wind speed changes from v1 to v2 while the

rotor speed is fixed at 1, the operating point of system isPoint B which does not correspond to maximum power

tracking. The rotor speed should be increased from 1 to2which results in the maximum power at operating point C.

Fig. 2. Output power versus rotor speed for three different wind speeds.

Based on (2) and Fig.1, the optimum speed of rotor can beestimated as follows:

opt

optopt

optTSRRv

RTSRv == (3)

Unfortunately, measuring the wind speed in the rotor ofturbine is very difficult; so, to avoid using wind speed, (1)needs to be revised. By substituting the wind speed equivalentfrom (3) into (1), the output power of the turbine is given asfollows:

3

opt

opt

PmTSR

RAC

2

1P

= (4)

Finally, the target torque can be written as follows:2

optopttarget kT = (5)

where:

3

opt

PMaxoptTSR

RAC

2

1k

=

B. Maximum Power Tracking Algorithm

This algorithm includes several steps, which are:

1. Choose the initial reference rotor speed and measured theoutput power of the generator;

2. Increase or decrease the reference rotor speed by one stepand measure the output power again;

3. Calculate Sign(P) and Sign();4.ref(n)= ref(n-1)+ Sign(P) Sign() step ;5. Repeat from step 3 to reach to optimum operating point.

Fig. 3 is used to make this algorithm clearer. Let us assumethe speed of wind is v1 and operating point of the turbine ispoint A, represented as (A, PA) in P- characteristic curve.Also, let us assume that the turbine speed is increased by step,which results in a new speed B.The new operating point willbe (B, PB) which gives:

stepBref

AB

AB

sign

PsignPPP

+=

=>=

=>=

1)(0

1)(0

After the first iteration, the new operating point becomes (C,PC). The iterative process will continue till the operating pointof the system is found at (1, P1), corresponding to themaximum power for the wind speed of v1. If the wind speedchanges to v3, the new operating point will be searchedstarting at (D, PD) which results in:

steprefD

D

sign

PsignPPP

+=

===

=>=1

1

1

1)(0

1)(0

The next point will be (E, PE) and similarly this process willcontinue in the same manner as explained, till the finaloperating point is found at (3, P3), corresponding to themaximum power capture for the wind speed of v3. Now, if thewind velocity changes to v2, the operating point will move to(F, PF) that result in:

stepBref

F

F

sign

PsignPPP

=

===

=


3/6

3

Fig. 3. Adjustment of turbine operating point for maximum power tracking.

III. POWER ELECTRONICS AND CONTROL STRATEGY

A. Circuit Topology

Fig. 4 shows the proposed circuit topology for wind powergeneration system, which is used, to realize the aboveprinciples of maximum winding power capture. This systemincludes a wind turbine (WT), a permanent magnet generator(PMG), a three-phase diode rectifier bridge, a step-up dc-dc

converter, and a current regulated PWM voltage sourceinverter (CRPWM).

Fig. 4. Topology of wind power generation system.

The system has the following features: a). PMG has highperformance, higher efficiency, no exciting current, smaller insize, and less in weight in comparison to other types ofgenerators; b). The generated ac power from PMG is

converted to dc power through a diode bridge which is simple,robust, cheap and requires no control circuit; and c). Only onepower switching device is used in dc-dc converter, resulting inlow cost and simple control. In the following sections powerconverters and their control methods are discussed.

B. DC-DC converter and control algorithm

The basic structure and control topology of the boostconverter is shown in Fig. 5. This converter divides the dc-link into two levels: dc-link voltage at the output terminals ofthe diode rectifier, which is a variable dc voltage, and the dc-link voltage at the input terminals of the voltage sourceinverter, which is fed from a fixed dc voltage. By varying theswitch duty cycle of the DC-DC converter the output voltageof the generator-rectifier system can be controlled. Thepurpose of this circuit is to control the shaft speed of thePMG so that the maximum power can be captured from windby the turbine.

iL

idc

ref

L

+

-

Sdc+

-

-+PI

-+

PI

iC

C

m

Vdc

Fig. 5. Power circuit and control topology of the dc-dc converter.

The state equation that describes the DC-DC boostconverter is given by (6), where Sdc is the switch status thattakes the value of 1 or 0.

+

=

dc

in

dc

L

dc

dc

dc

L

i

V

C

L

V

i

C

S

L

S

dt

dV

dt

di

10

01

01

10

(6)

C. Active and Reactive Power in Rotating Reference Frame

Fig.6 shows the vector representation of a balanced three-phase system and their equivalent vectors in a rotating d-qreference frame.

Fig. 6. Definition of rotating reference frame.

The variables in ABC system can be transformed to arotating d-q reference frame by using a time-varyingtransformation given in

( )

( )

2

1

2

1

2

1

3

2sin

3

2sinsin

3

2cos

3

2coscos

3

2

+

=

T (7)

f

f

f

T

f

f

f

C

B

A

o

q

d

=

(8)

=

=

o

q

d

C

B

A

T-

ff

f

Tff

f

TT

11

2

3(9)

where the variables f can be define as a set of voltages orcurrents in the system. Also, in a balanced three-phasesystem always fo, called zero sequence component, is equal tozero. The instantaneous power in a three-phase system isgiven by:

[ ]

=++=

C

B

A

CBACCBBAA

i

i

i

VVViViViVP(t) (10)


4/6

4

Using the transformation matrix and substituting the voltageand current vectors from (9) into (10) results in:

( )qqdd iViVP +=2

3 (11)

From Fig. 6, the rotating reference frame is chosen in sucha way that: Vq=0 and Vd=|V|, so the equation of active powercan be simplified in the rotating reference frame as

diVP

2

3= (12)

In a similar way, the equation of reactive power in therotating reference frame can be calculated as

qiVQ2

3= (13)

D. Supply Side Converter Control Strategy

Fig.7 shows a simplified representation of the supply side

converter which includes a dc-side capacitor, a 3-phase PWM

inverter, and series impedances which interface the output of

the inverter to the utility grid.

Fig. 7. Supply-side converter arrangement.

The voltage equations in Fig.7 can be written by using

KVL law as:

+

=

CC

BB

AA

S

C

B

A

S

S

C

B

A

Ve

Ve

Ve

Li

i

i

L

R

i

i

i

p1

100

010

001

(14)

where: p=d/dt

Transforming the voltage equations into the synchronous

reference frame by using the transformation matrix results in:

+

=

q

d

q

d

S

S

S

S

q

d

e

Ve

Li

i

L

R-

L

R

i

ip

1 (15)

To provide decoupled control of active power, or id,and

reactive power, or iq, base on (15), the output voltage from the

inverter in the synchronous reference frame should beV)i(xLe qSd += 1 (16)

)i(xLe dSq += 2 (17)

By substituting (16) & (17) into (15), the decoupled equations

of the system can be rewritten as follows:

+

=

2

1

0

0

x

x

i

i

L

R

L

R

i

ip

q

d

S

S

S

S

q

d (18)

As can be seen from (12) and (13) the active and reactive

power could be controlled through id and iq, respectively.

Therefore, the control rules of (16) and (17) can be completed

through defining the current feedback loops as follows:

( )d*d iis

kkx

+= 211 (19)

( )q*q iisk

kx

+= 212 (20)

Fig.8 shows the control block diagram of supply side

inverter based on the vector-control algorithm.

Fig. 8. Schematic of control strategy for supply side inverter.

IV. SIMULATION RESULTS

To check the proposed algorithm in Section III for speed

control of PMG, a dynamic simulation is implemented using

PSIM software when the wind speed was changed. There are

two sets of simulation results which are to be explained in the

following sections. Table I shows the parameters of the PMG

used in simulation.

TABLE I

PERMANENT MAGNET GENERATOR PARAMETERS

Rated Power Output 20kW

Rated Speed 211r/min

Stator Connection winding Star

Number of Rotor poles 36

Stator Phase Resistor 0.1764

Synchronous Inductance 4.24mH

Rated Phase Current 35A

Rated Phase Voltage 205V

A. Speed Control of PMG

In this case the reference turbine speed of the generator is

the command signal to prepare a switching pattern for the

DC-DC boost converter. Fig.9-d shows speed-tracking

characteristic of the generator when the reference command

turbine signal increases linearly from 80 to 120 r/min and

again from 120 to 200 r/min and finally decreases linearly

from 200 to 160 r/min, assuming the wind speed has changed.

As can be seen from Fig. 9-a and b, by controlling the input

current to the DC/DC boost converter the output voltage of

generator-rectifier system could be controlled so that

generators shaft follows the speed command.


5/6

5

As shown in Fig.4 a current regulated PWM voltage

source inverter is used to interface the dc-link bus to utility

grid. This inverter can maintain the voltage of dc-link at a

constant voltage. As shown in Fig.9-c the dc-link voltage is

adjusted at 810 volts in this system. Furthermore, it can

improve power factor and reduce current harmonic distortion.

As can be seen from Fig.10, power factor of the system is

adjusted to almost unity power factor and total harmonic

distortion of injected current is less than 3%.

Fig. 9. Turbine speed tracking.

B. Maximum Power Tracking

The simulation program uses the typical wind turbine

characteristics that are shown in Fig. 11. As revealed by the

graphs, the optimum operating points of the turbine are(175r/min, 10kW), (188r/min, 15kW), and (203r/min, 20kW)

for three different wind speeds.

In this simulation the algorithm iteration period and step are

chosen 1 second and 2 r/min, respectively. As can be seen

from Fig. 12 the generator speed starts from zero and reaches

to 1752 r/min, related to the maximum output power of

10kW for the turbine at the wind speed of v1. In 20 seconds it

is assumed that the wind speed increases to v3; therefore, the

control system changes the required turbine speed by using

the maximum power tracking algorithm to capture the

maximum power from wind in this speed. As can be seen

from Fig. 12 the speed of PMG (or turbine shaft) is adjusted

to 2032 r/min that generates 20kW power. After 42 seconds

from the beginning the wind speed decreases to v2 from v3.

Consequently, the reference turbine speed will be decreased

by the control system. Fig.12 shows speed of the PMG is

adjusted to 1882 r/min in 10 seconds. As a result, the output

power of turbine is 15kW.

Fig. 10. Grid phase voltage and Phase current of PWM inverter

Fig. 11. Turbine characteristics used for simulation.

FIG. 12. OUT PUT POWER AND ROTOR SPEED OF PMG.


6/6

6

Fig.13 Simulation results showing maximum power

tracking.

Fig. 13. Tracking the maximum power by wind turbine.

V. CONCLUSION

This paper presents a power electronic converter structureand related simple speed control method that can be used to

implement maximum power tracking in wind turbine

application. The proposed system and control algorithm

reduces the cost of the system, because there is just one

switching device in the dc-dc converter. Also no copper loss

in rotor circuit in PMG ensures higher efficiency.

Additionally, independent control of active and reactive

power on the power grid side is possible. Simulation results

confirm that control algorithm works well to track the

maximum power for different wind speeds.

At present, a prototype system including a 10kW Bergey

wind turbine, a three-phase 40kW Powerx inverter, a 10 kWstep-up dc-dc converter and digital controller to be

implemented on TMS320F2812-DSP platform are planned at

Dolan Technology Center. The preparation of prototype and

laboratory testing of PMG based wind turbine is in progress

and the final testing results are to be reported.

VI. REFERENCES

[1] Z. Chen and E. Spooner,Wind turbine power converters: a comparative

study, in Proc. 1998 IEE Power Electronics and Variable Speed Drives,

Seventh International Conference, pp. 471 476.

[2] Z. Chen and E. Spooner, A modular, permanent magnet generator for

variable speed wind turbines, in Proc. 1995 IEE Electrical Machines

and Drives, Seventh International Conference, pp. 453 457.

[3] E. Muljadi, S. Drouilhet, R. Holz, and V. Gevorgian, Analysis of

permanent magnet generator for wind power battery charging, in Proc.

1996 IEEE Industry Applications Conference, pp. 541 548.

[4] Y. Tang and L. Xu, flexible active and reactive power control strategy for

a variable speed constant frequency generating system, in Proc. 1993

IEEE Power Electronics Specialists Conference , pp.568 573.

[5] S. Song, S. Kang, and N. Hahm, Implementation and control of grid

connected AC-DC-AC power converter for variable speed wind energy

conversion system, in Proc. 2003 IEEE Applied Power Electronics

Conference and Exposition, pp.154 - 158 vol.1

[6] F. Martinez Rodrigo, J. M. Ruiz Gonzalez, J. A. Dominguez Vazquez,

and L. C. Herrero de Lucas, Sensorless control of a squirrel cage

induction generator to track the peak power in a wind turbine, in Proc.

2002 IEEE Industrial Electronics Society Conference, pp.169 - 174 vol.1.

[7] 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 Conversion,vol.18, pp.163 168, Mar. 2003.

[8] Y. Higuchi,N. Yamamura, M. Ishida, and T. Hori, An improvement of

performance for small-scaled wind power generating system with

permanent magnet type synchronous generator, in Proc. 2000 IEEE

Industrial Electronics Society Conference , pp.1037-1043 vol.2.

[9] C. Schauder and H. Mehta, Vector analysis and control of advanced static

VAr compensators, in Proc. 1993 IEE Generation, Transmission and

Distribution Conference, pp.299-306, vol.140.

VII. BIOGRAPHIES

Reza Esmaili (S05) received his B.S. and M.S.

degrees from Isfahan University of Technology,

Isfahan, Iran, in 1993 and 1996 both are in Electrical

Engineering. He is currently pursuing the Ph.D.

degree in the Department of Electrical Engineering at

the Ohio State University, Columbus, OH. From 1997

to 2000, he was faculty member of school of

engineering at Isfahan University, Isfahan, Iran. Since

2001, he has been an Intern Engineer at Dolan

Technology Center of American Electric Power. His research interest includes

design and control of power converters for variable speed generating and drive

systems, wind turbine, and supercapacitor application. Mr. Esmaili is a student

member of IEEE.

Longya Xu (S89-M90-SM93-F04) receivedhis M.S. and Ph.D. degrees from the University of

Wisconsin, Madison, in 1986 and 1990 both are in

Electrical Engineering. He joined the Department of

Electrical Engineering at the Ohio State University in

1990, where he is presently a Professor. He has served

as a consultant to many industry companies including

Raytheon Co., US Wind Power Co., General Motor,

Ford and Unique Mobility Inc. for various industrial

concerns.

Dr. Xu received the 1990 First Prize Paper Award in the Industry Drive

Committee, IEEE/IAS. In 1991, Dr. Xu won a Research Initiation Award from

National Science Foundation. Dr. Xu is also a recipient of 1995 and 1999

Lumley ResearchAward for his understanding research accomplishments fromCollege of Engineering, The Ohio State University.

Dr. Xus research and teaching interests include dynamic modeling andoptimized design of electrical machines and power converters for variable speed

generating and drive system, application of advanced control theory and digital

signal processor for controlling of motion and distributed power systems in

super-high speed operation.

Dr. Xu is an IEEE fellow and served as the chairman of Electric Machine

Committee of IEEE/IAS and an Associate Editor of IEEE Transactions on

Power Electronics in the past several years.

David K. Nichols holds a BSEE degree from Akron

University. He began work at American Electric Power in

1972. He transferred to the Electrical Laboratory in 1976

and is currently manager of AEPs Technology Solutions

Management Section at the Dolan Technology Center in

Groveport, Ohio. A specialist in high-voltage electrical

and mechanical equipment, Nichols oversees research anddevelopment projects, including several distributed

resource and energy storage projects. Nichols is a member

of IEEE.

Documents

A New Control Method of Permanent Magnet Generator for Maximum Power Tracking in Wind Turbine Application