Accepted Manuscript

Title: Comparison of maximum peak power trackingalgorithms for a small wind turbine

Author: R. Kot M. Rolak M. Malinowski

PII: S0378-4754(13)00065-7DOI: http://dx.doi.org/doi:10.1016/j.matcom.2013.03.010Reference: MATCOM 3922

To appear in: Mathematics and Computers in Simulation

Received date: 1-11-2011Revised date: 30-1-2013Accepted date: 7-3-2013

Please cite this article as: R. Kot, M. Rolak, Comparison of maximum peak powertracking algorithms for a small wind turbine, Mathematics and Computers in Simulation(2013), http://dx.doi.org/10.1016/j.matcom.2013.03.010

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

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Comparison of maximum peak power tracking algorithms for a small wind turbine

R. Kot, M. Rolak, M. Malinowski

Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland.

e-mail: radoslaw.kot@ee.pw.edu.pl, michal.rolak@ee.pw.edu.pl, malin@isep.pw.edu.pl

Abstract – This paper reviews Maximum Power Point Tracking (MPPT) algorithms dedicated for

Small Wind Turbines (SWT). Many control strategies with different features are available and it is

very important to select proper one in order to achieve best performance and low cost. Three most

widely used algorithms are discussed. Two are based on turbine static parameters such as power

versus rotational speed characteristic Pm(ω) and optimum tip-speed ratio λopt. Third one, which

seems to be most promising, iteratively searches for optimum operating point and it doesn’t

require prior knowledge of the turbine. This work attempts to summarize and compare these

algorithms. Detailed description of each one is made with most significant qualities emphasized.

Discussion is supported by the simulation studies using Synopsys Saber software. Results for

5 kW SWT with diode rectifier and DC/DC boost converter are shown and commented.

Keywords – Maximum Power Point Tracking (MPPT), Small Wind Turbine (SWT), PMSG.

1. Introduction

Wind turbines are one of the most important and promising Renewable Energy Sources (RES), largely

contributing in world’s energy production. European wind power industry has formulated generation targets of

180GW, and 300GW in 2020 and 2030 respectively [10,16]. Due to huge improvement in power converter

control and technology wind energy, especially in the form of Small Wind Turbines (SWT), becomes more and

more available for individual customers. SWT is defined as a wind turbine with a rotor swept area less than

200m2 and rated power range of 1-15kW (residential) and 15-100kW (light commercial) [1]. Such turbines are

able to supply households or small companies as well as to support electrical grids on the low voltage side.

Poland with its 1 GW capacity and current 53% growth rate predicts 8,6 GW to be installed by 2020 [17].

However, considering SWTs, only 6 MW capacity is installed and 550 MW is expected to be deployed by the

same time. Hence, a significant development is assumed in the next few years. This work paper covers the 5 kW

wind energy system currently being developed (Fig. 1), [14]. It consist of three blade horizontal axis wind

turbine (HAWT), low-speed permanent magnet synchronous generator (PMSG), AC/DC/AC converter and the

energy storage module with Dual Active Bridge (DAB) DC/DC converter. AC/DC converter is controlled by

Maximum Power Point Tracking (MPPT) algorithm in order to ensure efficient energy conversion for various

atmospheric conditions. Paper focuses on different MPPT methods implemented for a particular AC/DC

converter configuration (diode bridge rectifier with DC/DC boost converter).

Fig. 1.Considered wind energy system

Manuscript

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2. Wind power basics

Power generated by the wind turbine is proportional to the area swept by its blades and the third power of the

wind velocity,

pm CVRP 32

2

1 (1)

where:

R: turbine rotor radius (m)

ρ: air density (kg/m3)

Cp: turbine power coefficient (-)

V: wind speed (m/s)

Power coefficient Cp is defined as the ratio between mechanical power Pm and power available from the wind Pw

:

w

m

P

PpC

(2)

Theoretically, value of Cp cannot exceed the limit expressed by Betz’ Law as follows[2,11]:

593.027

16max pC (3)

Power coefficient itself is not constant and strongly depends on the linear speed of the turbine blade tip and wind

speed. Ratio between these two quantities is called the tip-speed ratio and used as the important parameter in

wind turbine design:

V

R (4)

where:

ω: turbine rotational speed

Power coefficient changes also with turbine rotor blade pitch angle. Thus, it can be written that:

),( pp CC (5)

However, small wind turbines usually have fixed pitch mainly due to reduced cost and simplified maintenance.

Therefore:

.0 const (6)

Typical CP(λ) curve is presented in Fig. 2. For certain tip-speed ratio value, Cp is maximized. Based on this

curve, the actual turbine output power can be calculated as a function of its rotational speed for different wind

speeds. As a result the power versus rotational speed characteristic Pm(ω) is created as shown in Fig. 3. It can be

noticed that for every wind speed exist single point for which the amount of generated power is the highest. The

red curve connecting these points sets the range of desirable operating points. It is convenient to control the

turbine rotational speed to maintain the operation point as close as possible to the peak power curve. At very

high wind speeds, when the generated power exceeds the nominal power of the plant, the surplus of captured

energy has to be either stored or dissipated. Above the critical wind speed the turbine has to be stopped to avoid

damaging the system. On the other hand, for very light breeze turbine operation is not justified economically.

Referring to Fig. 2 and Fig. 3 it is worth mentioning that the efficiency of the wind turbine system has to be

taken into account. The product of wind turbine power coefficient, generator efficiency and power converter

efficiency gives the total efficiency of the system. Note that usually value of Cp contains also the aerodynamic

efficiency of the rotor.

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0 2 4 6 8 10 12 140

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Cp

Fig. 2. Power coefficient versus tip-speed ratio

Power delivered to the load Pe is then equal to:

cgpe CVRP 32

2

1 (7)

where:

ηg: generator efficiency

ηc: converter efficiency

In general, efficiency of the gearbox interconnecting the turbine and the generator should be included in (7).

However, discussed system consist of 5 kW multi-pole, low speed generator. Thus, gearbox is not required.

During the design process one of the most important factor is the energy yield in long time scale, that is, how

much energy can potentially be captured for a given turbine design and location. Fig. 4 presents the predicted

energy yield for 5 kW SWT as a function of wind speed. System efficiency, i.e. effective energy capture, is also

presented. The plot is based on the Rayleigh distribution of wind speed. It shows that for lighter and more

frequent winds, energy capture is smaller but the efficiency of the system is much higher than in the case of

stronger but very rare winds. It means that designing the turbine for lower wind speed is actually much more

reasonable in terms of energy gain. Long-term average wind speed in Poland varies from 5.5 to 7 m/s at 50 m

height and 3.5÷4.5 m/s at 30 m. The blue field in Fig. 4 represents the region of interest being the trade off

between the amount of captured energy per year and efficiency.

0 5 10 15 20 25 30 35 400

2000

4000

6000

8000

10000

12000

14000

16000

[rad/s]

Pm

[W

]

v = 5 m/s

v = 10 m/s

v = 9 m/s

v = 11 m/s

v = 4 m/s

v = 6 m/s

v = 7 m/s

v = 8 m/s

Typical Designed

Fig. 3. Mechanical power versus turbine rotational speed characteristic (typical: red dashed line, especially

designed for low wind speeds: red solid line)

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

ŚREDNIA DŁUGOTERMINOWA PRĘDKOŚĆ WIATRU V[m/s]

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

WY

DA

JN

OŚ

Ć E

NE

RG

ET

YC

ZN

A [

kW

h/r

ok]

20

30

40

SP

RA

WN

OŚ

Ć E

NE

RG

ET

YC

ZN

A [%

]

region of interest

en

erg

y y

ield

[kW

h/y

ea

r]

eff

icie

ncy [%

]

high powerfrequent winds

long-term mean wind speed [m/s] Fig. 4. SWT energy yield and system efficiency versus long-term average wind speed

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3. MPPT algorithms

Power produced by a wind turbine strongly depends on wind speed and rotor rotational speed, as was shown

in Section 2. In order to extract maximum energy, the generator rotational speed has to be controlled accordingly

by means of AC/DC converter with MPPT algorithm. There are many different MPPT types, but two basic

groups are most common. First of them requires prior knowledge of turbine parameters to calculate the operating

point. Algorithms from second group iteratively search the optimum with the use of power and rotational speed

increments. Fig. 5 presents more detailed subdivision of these methods, which differ in implementation and type

of required sensors. However, principle of operation remains the same.

In this paper a DC/DC boost converter supplied by three phase diode rectifier is used to control the

turbine/generator rotational speed. Converter plays the role of an apparent load for the generator. It can be shown

that the equivalent resistance Req seen from the input terminal of a boost converter with load resistance R is given

as:

2)1( DRReq (8)

It means that changing duty cycle of the boost converter results in change of generator load and therefore its

rotational speed.

3.1. MPPT algorithms based on Pm(ω)

Algorithms based on knowledge of Pm(ω) characteristics are well known and widely used [3,9,15]. Block

diagram of this method is presented in Fig. 6. Peak power curve for desired power range (Fig. 3) is stored in a

microcontroller memory or approximated by a polynomial function. To calculate the optimum operation point

measurement of either the power or rotational speed is required.

MPPT

algorithms

· knowledge of

Pm(ω)

characteristic

· power and

rotational speed

measurement

with rotational

speed control

with power

control

· knowldge of λopt

· wind speed and

generator

rotational speed

measurement

based on

iterative search

With outer generator

rotaional speed

control loop:

· power and

rotational speed

measurement

With duty cycle as

direct refernce:

· power

measurement

based on

knowledge of

turbine

parameters

data required

[8-9]

[11-12][10]

[13-16] [10]

Fig. 5. Classification of MPPT algorithms

PMSG

iL

UdcUd

io

PI

pd = ud∙iL

-

udiL

iL*ω* D*ωPI

-

++

-

+

Fig. 6 Control scheme for Pm(ω) characteristic based MPPT.

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Based on the measurement and stored data the reference value (power or rotational speed) is determined. Main

advantage of this method is its simplicity and fast response. Assuming precise data, algorithm immediately finds

optimum operation point. Unfortunately, accurate determination of optimum Pm(ω) curve is unavoidably

connected with aerodynamic tests using wind tunnel, which in practice is omitted due to the high cost. Moreover,

it may vary significantly with time and atmospheric conditions. Factors like icing, dirt and aging are the cause of

decrease in turbine rotor efficiency and cannot be compensated by the control algorithm.

In this paper PMSG rotational speed has been chosen as a control variable. The optimum power curve was

generated by taking a vector of maximum power points existing in assumed wind speed range. It was then

approximated by the third order polynomial with the help of Matlab/Simulnik curve fitting functions. Actual

values of the polynomial result only from particular wind turbine model parameters.

01

2

2

3

3

* aPaPaPa eee (9)

where:

a0 - a3: polynomial coefficients

ω*: reference speed of the generator

Based on the power measurement the reference speed is calculated and compared to actual generator speed.

Resulting error is then used to calculate the reference value for inductor current iL*. Hence, current controller

determines the adequate duty cycle D* for boost converter.

3.2. MPPT algorithms based on λopt

Similar method, based on wind speed measurement, is shown in Fig. 7, [5,12]. In this case, according to

Fig.2, knowledge of optimum tip-speed ratio λopt is required in order to calculate the reference generator

rotational speed:

R

Vopt *

(10)

PMSG

V

ω

iL

UdcUd

io

PI

-iL*ω* D*

PI-

++-

+

iL

Fig. 7 Control scheme for λopt based MPPT

Despite the determination of ω*, algorithm remains unchanged comparing to one described in Section 3.1.

Nevertheless, there are some important features, which need to be addressed. First, using wind speed as input

variable allows for fast operating point determination and dynamic response. On the other hand, data acquisition

from anemometer has to be insensitive to rapid wind gusts to eliminate unwanted changes in operating point. It

should be pointed that inertia of the turbine is generally one order of magnitude higher that the one of the

generator. Thus, even with strong gust of wind turbine power variation is slow . Sudden change in operating

point, set by control algorithm, may cause high torque difference resulting in mechanical stress on the turbine

rotor blades. Moreover, the use of anemometer increases overall cost and complexity of the system. As in the

case of previous MPPT algorithm λopt cannot be determined with high degree of accuracy and varies with time

and atmospheric conditions . However, λopt is a single parameter and it can be adjusted much more easily than

polynomial coefficients in optimum power curve approximation.

3.3. Incremental MPPT algorithms

Output power can be maximized without any information of turbine parameters by iteratively changing the

control variable which results in generator rotational speed adjustment [4,6-7,9,13]. Although the steepest ascent

method is generally used for this purpose, all algorithms of this type are based on the assumption that for a given

wind velocity maximum power is produced when:

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0

eP

(11)

It can be proven that for a boost converter condition (11) is also satisfied by [9]:

0

D

Pe (12)

Thus, this particular method requires only power measurement. Flowchart the algorithm is presented in Fig. 8.

Power is continuously sampled and increment ΔP is calculated after each cycle. In order to reach condition (12),

the actual derivative sign has to be evaluated. Therefore individual signs of the power SP and duty cycle SD

increments are determined to get information about power change and the last search direction, respectively

(Table I, Fig. 9). Step size K is often constant, although variable step size can be used for tracking performance

improvement. It should be mentioned that algorithm operates constantly and as a result, oscillations around the

optimum are unavoidable. To minimize the unwanted changes due to small power variations, hysteresis was

introduced.

This class of algorithms allows to minimize the number of sensors. There is no dependency on specific type

of turbine or its rated power. A key role in implementation plays proper selection of the step size K. Higher value

of K accelerates the tracking process but results also in larger oscillations about the optimum operating point.

.

PMSG

iL

UdcUd

io

pd = ud∙iLiL

D*

-

+

ud

ΔP(k)=P(k)-P(k-1)

Sd = Sign(ΔD(k-1))

D*(k) = D*(k-1)

D*(k) = D*(k-1) + ΔD(k)

D*(k-1) = D*(k)

ΔD(k-1) = ΔD(k)

P(k-1) = P(k)

Yes

ΔD(k) = K∙Sd∙Sp

Sp = Sign(ΔP(k))

ΔP(k)≤ Hist

No

fT

Fig. 8. Control scheme for incremental MPPT algorithm

Table I. Operation principle of the incremental MPPT algorithm

calculated condition result from previous change required action

SD SP eq. (11) eq. (12) D ω

-1 1 0

eP

0

D

Pe ↑ ↓

1 -1

-1 -1 0

eP

0

D

Pe ↓ ↑

1 1

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0

P0

P

0

D

P0

D

P

Fig. 9. Possible conditions for incremental MPPT algorithm

Another important issue is the proper selection of sampling frequency fT. Too high may effect in false selection

of tracking direction. Wind turbine with its rotor inertia represents the dominant time constant of the system and

creates a low-pass filtering action for rapid wind speed changes. This results in relatively low MPPT sampling

frequency fT required for stable power tracking. Obviously, with too low frequency algorithm will not be able to

track the wind changes with adequate precision, decreasing the efficiency of the system. For the purpose of this

study fT of 10 Hz was chosen.

4. Model description

In order to verify and compare presented algorithms the simulation studies were provided using Synopsys

Saber software. Full model configuration is presented in Fig. 10. MPPT algorithms were implemented using

MAST language with its syntax and instruction set very similar to C.

4.1. Wind turbine

Wind turbine model was based on the real three-blade, HAWT design. It converts the wind speed to a

mechanical torque as follows:

32 )(2

1VCR

PT

pm

m (13)

here: ρ = 1.225 kg/m3, R = 3.75 m

The power coefficient as a function of tip-speed ratio can be generally represented by the exponential function

with coefficients selected to fit given turbine parameters. For the purpose of this scope, Matlab wind turbine

model was selected and adjusted accordingly. It was assumed that λopt= 8

4.2. Generator

The 5 kW axial flux PMSG model was created. With 20 pole pairs the nominal rotational speed is 150 rpm.

Detailed parameters are shown in Table II.

Table II. PMSG simulation model parameters

Parameter Value

Rated power 5 kW

Moment of inertia 6 kgm2

d-axis inductance 10 mH

q-axis inductance 10 mH

Damping constant 0.002 kgm2/ s

Rated speed 150 rpm (15.7 rad/s)

Number of pole pairs 20

PM flux linkage 1.07 Wb

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4.3. Converter

The AC/DC converter consists of six-pulse diode bridge rectifier and DC/DC boost converter Considering

maximum ripple in inductor current and capacitor voltages the inductance and capacitances for the converter

were selected using eq. (15-17) accordingly [8]:

Fig. 10. Simulation model (Synopsys Saber)

s

IonIL

Lf

DV

L

tVI (14)

1

16 Cf

IV

g

LC

(15)

s

OonOC

fC

DI

C

tIV

22

2 (16)

where:

C1: boost converter input capacitor value

C2: boost converter output capacitor value

fg: frequency of the generator phase voltage

IL: inductor current

IO: output current

L: boost converter inductor value

VI: boost converter input voltage

Converter parameters are summarized in Table III. The value of inductor, which is the most expensive part of the

converter, can be easily adjusted with respect to nominal generator voltage and switching frequency as shown in

Fig. 11.

5. Simulation results and comparative study

All three MPPT algorithms have been implemented in Saber software and tested for the same wind speed and

load conditions. Results are presented in Fig. 12. It can be seen that every MPPT algorithm works properly, i.e.

successfully tracks the optimum power point. Dynamic response for algorithms based on Pm(ω) and λopt is

similar. In comparison, the incremental algorithm is slower but it is not too important due to high inertia of the

turbine.

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VI [V] fs [Hz]

Δi

[%]

L=10 mH

L=5 mH

Fig. 11. Inductor current ripples ΔiL as a function of switching frequency fs and input voltage VI for different

values of inductance: 5 mH, 10 mH.

Table III. Boost converter simulation model parameters

Parameter Value

L 12 mH

C1 400 uF

C2 400 uF

fs 10 kHz

Fig. 12. Comparison of discussed MPPT algorithms: based on Pm(ω) (orange), based on λopt (black), incremental

(blue); from the top: reference wind speed, turbine rotational speed, turbine power

6. Conclusion

In this paper a description and comparison of Maximum Power Point Tracking (MPPT) algorithms has been

presented. All most important features are summarized in Table IV. Control schemes requiring turbine

parameters are fast and simple in implementation, but their application is limited to specific turbine designs.

Algorithm based on incremental search of optimum operating point seems to be most promising due to

elimination of wind and rotational speed measurements which ensures low cost and flexibility. Computational

effort is comparable for all methods. There are, however, slight differences in signal filtering and algorithm

tuning requirements.

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Table IV. Summary and comparison of described MPPT algorithms

Feature based on Pm(ω)

characteristic

based on λopt and wind

speed measurement incremental

Efficiency depends on accurate

approximation of Pm(ω)

depends on accurate

determination of λopt

depends on proper

adjustment of K and fT

Flexibility

very low: unique for a single

turbine / periodic adjustments

required

low: unique for a single

turbine / periodic

adjustments required

high: self-adjusting /

continuous oscillations

around operating point

Complexity very high: approximation of

Pm(ω) required

high: knowledge of λopt

required

low: no prior knowledge of

turbine parameters required

Dynamics very fast very fast slow

Price

high: PMSG rotational speed

and power measurement

required

very high: wind speed and

PMSG rotational speed

measurement required

low: only power

measurement required

Computation

complexity

low: PMSG rotational speed

and ud filtering required (for

power calculation)

low: PMSG rotational speed

and wind speed filtering

required

very low: only ud filtering

required (for power

calculation); no PI controllers

Acknowledgment

Described problems are part of the research project No. N R01 0015 06/2009 “Complex solution for low speed

small wind turbine with energy storage module for distributed generation systems”, sponsored by The National

Centre for Research and Development.

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