Control of the stalling behaviour in Wave Power Generation Plants

Modesto Amundarain, Mikel Alberdi, Aitor Garrido, Izaskun Garrido

University of the Basque Country (Bilbao, Spain) molty.amundarain@ehu.es, mikel.alberdi@ehu.es, aitor.garrido@ehu.es, izaskun.garrido@ehu.es

Abstract- In this paper the performance of the Wells turbine

has been improved, studying its stalling behaviour when the flow coefficient (phy) reaches a specific characteristic value. For this purpose, a control scheme for the flow coefficient is derived based on the addition of external resistances in series with the rotor winding of the induction generator connected to the turbine. Due to the stalling behaviour, the generator increases its velocity as the flow coefficient of the turbine approaches the critical point at which the turbine losses power. The proposed control system does appropriately adapt the rotor resistance according to the entry pressure drop. To do so, the control implements a continuous resistance switching depending on the pressure drop and it will be demonstrated that the proposed control method used for this purpose clearly improves the performance of the system, maximizing the power generated by the turbine.

I. INTRODUCTION

In the last couple of years, there has been a worldwide resurgent interest for wave energy and especially in Europe. The developments in this sector are comparable to those of wind energy a few decades ago with similar economic potentials.

Worldwide, the estimated technically and economically energy production potential for ocean wave energy is estimated at about 1000 TWh/year [1].

Many governments are adopting new energy generation and energy renewable guidelines towards an ecologically sustainable society. As an example, the UK Government has risen the challenge of generating 10% of UK electricity demand from renewable sources by 2010 and 15% by 2015 with the intention of reaching the 20% by 2020 [2].

The Basque Government's energy strategy for 2010 has also set ambitious targets for energy development in the Basque Country, where renewables have a prominent role. Investments over 15 M€ for the development of installations for harnessing the energy of waves are planned, that will collectively achieve the 5 MW of installed power provided for in 2010 [3].

Technologies to convert ocean wave power into electricity are many. It remains unclear what the winning technical approach is. This is reflected by several different technical approaches and different methods and systems for converting this power into electrical power, such as Oscillating Water Columns (OWC), hinged contour devices as the Pelamis, overtopping devices as the Wave Dragon and the Archimedes wave [4].

At present day there exit several ways to obtain energy from the sea, in this sense our interest focuses on extracting energy from sea waves by using oscillating water columns

(OWCs) to translate the wave movement into pneumatic energy [5]. This can be converted into mechanical energy with the use of a turbine with in turn is used to move a generator, getting from its stator the electrical power that will be delivered to the grid [6].

II. BACKGROUND

As shown schematically in Fig. 1, the oscillating water column (OWC) is a device that converts the hydraulic energy of the waves into an oscillating air flow.

The upper part of the OWC chamber has the power take off system, consisting of the turbine and the generator, connected through a gear box.

The Wells turbine which was invented by Prof. A.A. Wells in the mid-1970s has been extensively researched over the last 30 years. This turbine converts the bi-directional air flow into mechanical energy, in the form of unidirectional shaft power used in turn to move the wound rotor induction machine.

The wound rotor machine controlled by rotor resistance has several advantages like high line power factor, absence of line current harmonics and smooth and wide range of speed control. As the external resistance is increased, the torque/slip curve becomes flatter, giving less speed until the speed becomes zero at high resistance [7].

III. STALLING BEHAVIOUR IN THE WELLS TURBINE

The performance of the Wells turbine is limited by the onset of stalling phenomenon on the turbine blades. It must be that

Breakwater

Waves

Turbine-generator

Air-flow

OWC chamber

Fig. 1. Scheme of OWC

POWER QUALITY, ALTERNATIVE ENERGY AND DISTRIBUTED SYSTEMS 117

978-1-4244-2856-4/09/$25.00 ©2009 IEEE

the input power to any wave energy induction is variable in considered both the short and a long term, since each wave cycle produces two power cycles giving a short-term variation, and a fluctuation in the medium and long-term wave environment that produces the corresponding change in the output of the induction generator[8].

Therefore subject to the local conditions a control strategy is

necessary to accommodate these fluctuations. Two basic control strategies or a combination of them can be considered:

• Variable Rotor Resistance • Inverter Drives

The equation for the system turbo-generator can be written

as:

gt TTt

J −=⎟⎠⎞

⎜⎝⎛

∂∂⋅ ω (1)

where:

J Moment of Inertia of the system (kg·m2). ω Angular velocity of rotor (rad/s)

tT Torque produced by turbine (N·m)

gT Torque imposed by generator (N·m)

As it is shown in Fig. 8 the input to the Wells turbine is the pulsating pressure drop across the turbine rotor which is generated due to the airflow from the OWC chamber.

The equations for the turbine are:

])()[/1( 22txa rVaKCdP ω+= (2)

])([ 22txtt rVKrCT ω+= (3)

raCdPCT att1−= (4)

1)( −= tx rVphy ω (5)

aVQ x= (6)

11 )()( −− == phyCCdPQT atttturbine ωη (7)

2ln/bK ρ= (8)

dPQPin = (9)

where:

dP Pressure drop across rotor (Pa) aC Power coefficient

K Constants (Kg/m) a Cross sectional area (m2)

xV Air-flow velocity (m/s) r Mean radius (m)

tω Turbine angular velocity (rad/s) tC Torque coefficient

phy Flow coefficient (can be expressed as angle) b Blade height (m) l Blade chord length (m) n No. of blades

inP Pneumatic incident power (W). The torque and power developed by the turbine can be

computed based on power coefficient and torque coefficient against the flow coefficient [9].

These are the characteristic curves of the turbine under study and their shape may be seen on figures 2 and 3.

From the equation (5), it may be observed that when air-flow velocity increases, the flow coefficient also increases provoking the aforementioned stalling behaviour in the turbine.

This behaviour is clearly observable also in Fig. 3 when phy approaches 0.3(this value may change depending of the characteristic curve of each turbine)..

A standard input pressure drop to the turbine may be experimentally modelled as 7000sin(0.5t) Pa, as it is shown in Fig. 4.

With this input, the variation of the flow coefficient for the uncontrolled system (the external rotor resistance for the generator being 0 Ω) may be seen in Fig. 5. It can be observed that its value is higher than 0.3, which corresponds to the

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

2

4

6

8

10

12

14←--

Ca

(Pow

er C

oeff

icie

nt)

phy (Flow Coefficient)

Fig. 2. Power coefficient vs flow coefficient

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

X: 0.3Y: 0.34

Ct

( T

orqu

e C

oeff

icie

nt)

phy ( Flow Coefficient )

Fig. 3. Torque coefficient vs flow coefficient

118 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP118 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP

stalling behaviour threshold value for our turbine. In this sense, Fig. 6 shows the power extracted from the

turbine with the rotor external resistance value set to rx = 0 Ω (uncontrolled case). As indicated before, it may be clearly observed that the power to be extracted by the turbine is limited by its stalling behaviour.

IV. CONTROL STATEMENT

The undesired stalling behaviour can be avoided or delayed if the turbine accelerates fast enough in response to the incoming airflow, which can be accomplished by adding external resistances (rx) in series with the rotor winding of the induction generator [10].

The control system for flow coefficient is achieved by varying the rotor resistance of the induction generator. This can be done by adding either two resistance switching or continuous resistance switching.

In this work we have chosen to use a continuous resistance switching depending on the pressure drop.

Our purpose is to calculate the maximum pressure drop across the rotor of the turbine without stalling behaviour. To do

so, numerous simulations have been carried out in order to study the variation of the flow coefficient for different pressure drops and external resistances of the generator rotor.

The results may be observed in Table I which shows the variation of flow coefficient for different values of pressure drop (dP) and external resistances (rx) in series with the rotor winding of the induction generator. Using this table, we have derived the optimum range for rx as a function of the pressure drop avoiding the stalling in the turbine. This study may be extended to other Wells turbines, presenting all them similar behaviours.

In turn, Fig. 7 shows the torque generated by the turbine which also presents a loss proportional to the drop in power.

V. SIMULATION RESULTS

The model of the Wells turbine presented in Section III and the induction generator have been implemented using Matlab-SIMULINK software, as shown schematically in Fig.8.

The parameters used in the model for the turbine are shown in Table II.

0 10 20 30 40 50 600

1000

2000

3000

4000

5000

6000

7000

time(s)

Pre

ssur

e dr

op (

Pa)

Fig. 4. dP=7000sin(0.5t) Pa

0 10 20 30 40 50 600

0.1

0.2

0.3

0.4

0.5

time (s)

phy

Fig. 5. phy vs time for dP=7000sin(0.5t) Pa and rx=0 Ω

0 10 20 30 40 50 60-1

0

1

2

3

4

5

6x 10

4

time (s)

Tur

bine

pow

er (

W)

Fig. 6. Pt vs time for dP=7000sin(0.5t) Pa and rx=0 Ω

0 10 20 30 40 50 60-100

0

100

200

300

400

500

600

700

tiime(s)

Tur

bine

Tor

que

(N·m

)

Fig. 7. Tt vs time for dP=7000sin(0.5t) Pa and rx=0 Ω

POWER QUALITY, ALTERNATIVE ENERGY AND DISTRIBUTED SYSTEMS 119

TABLE I PHY VS PRESSURE DROP AND RX RESISTANCE

dP (Pa) phy (Flow coefficient) rx (Ω) 1000sin (0.5t) 0 – 0.0541 0 3000sin (0.5t) 0 – 0.1612 0 5000sin (0.5t) 0 – 0.2708 0 5500sin (0.5t) 0 – 0.2985 0 5550sin (0.5t) 0 – 0.3080 0 5800sin (0.5t) 0 – 0.2992 0.1 5900sin (0.5t) 0 – 0.3090 0.1 6000sin (0.5t) 0 – 0.2988 0.2 6100sin (0.5t) 0 – 0.3032 0.2 6200sin (0.5t) 0 – 0.2975 0.3 6300sin (0.5t) 0 – 0.3015 0.3 6500sin (0.5t) 0 – 0.2990 0.4 6600sin (0.5t) 0 – 0.3024 0.4 6800sin (0.5t) 0 – 0.2993 0.5 6900sin (0.5t) 0 – 0.3028 0.5 7100sin (0.5t) 0 – 0.2981 0.6 7200sin (0.5t) 0 – 0.3006 0.6 7500sin (0.5t) 0 – 0.2981 0.7 7600sin (0.5t) 0 – 0.3007 0.7 8000sin (0.5t) 0 – 0.2989 0.8 8100sin (0.5t) 0 – 0.3010 0.8 8500sin (0.5t) 0 – 0.2981 0.9 8700sin (0.5t) 0 – 0.3015 0.9

TABLE II

TURBINE PARAMETERS

The parameters used for the induction generator are shown

in the Table III. Our control aims to vary the generator rotor resistance in order

to alter the torque/slip characteristic, so as to get higher velocities of the system and avoid the stalling behaviour [8].

Fig. 8. System scheme

TABLE III INDUCTION GENERATOR PARAMETERS

The control block implemented changes the value of the rotor

resistance of the induction generator according to the parameters studied Section III and the optimal values of rx for each specific range of pressure drop are presented in Table I.

For this controlled case it has been used the same pressure drop input to the turbine as the one used for the uncontrolled case (7000sin(0.5t) Pa) and shown in Fig. 4.

Fig. 9 shows the variation of flow coefficient for this case. As it may be seen, now the flow coefficient does not exceed the stalling threshold value 0.3.

In this sense, Fig. 10 shows the power extracted from the turbine in the controlled case. The control action applied avoids the stalling behaviour, allowing to maximize the power that may be extracted by the turbine. In turn, Fig. 11 shows the torque generated by the turbine in this controlled case.

These results may be compared with those of the uncontrolled case, shown in figures 5, 6 and 7, where considering the same pressure drop at the input, the stalling behaviour threshold value for phy was reached and hence the power and the torque that could be extracted from the turbine were reduced.

Figs. 12 and 13 show the power generated by the induction generator in both cases. It is remarkable how the power generated increases when the stall is controlled. When the waves produce a variation in pressure drop of 6000sin(0.5t) Pa, the undesired behaviour can be observed too. In turn, fig. 14 shows the power extracted from the turbine in the uncontrolled case.

Turbine n=8

K=0.7079

r=0.7285

a=1.1763

Generator p=4

rs=0.0181

xs=0.13 xm=7.413

rm=107.303 rr=0.0334

xr=0.16

0 0.2 0.4 0.6 0.8-0.1

0

0.1

0.2

0.3

0.4

0.5

X: 0.3Y: 0.34

Stalling Phenomenom

dP

Gearbox

Wells turbine

Control

Grid

rx

Angular velocity

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

time (s)

phy

Fig. 9. phy vs time for dP=7000sin(0.5t) Pa and rx=0.6 Ω

120 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP120 2009 COMPATIBILITY AND POWER ELECTRONICS CPE2009 6TH INTERNATIONAL CONFERENCE-WORKSHOP

In contrast, the controlled power generated is increases, as shown in Fig. 15. The same performance can be observed when the input pressure drop is 8000sin(0.5t) Pa, Fig. 16 and Fig. 17.

Finally, Table IV shows the average power generated by the turbine for different pressure drops and external resistances (rx) in series with the rotor winding of the generator. The turbine

efficiency is calculated from equation (7). The table shows that the generated power of the turbine is highly improved in the controlled case and that there exist only one optimum value within the calculated range.

TABLE IV TURBINE EFFICIENCY VS PRESSURE DROP AND RX RESISTANCE

dP (Pa) PtAVERAGE (KW)

PinAVERAGE (KW)

μ (%) rx (Ω)

5500sin (0.5t) 25.053 51.798 48.37 0

6500sin (0.5t) 24.020 72.934 32.93 0

6500sin (0.5t) 32.194 66.626 48.32 0.4

6500sin (0.5t) 31.753 65.500 48.48 0.5

7500sin (0.5t) 17.834 98.006 18.20 0

7500sin (0.5t) 39.670 82.437 48.12 0.7

7500sin (0.5t) 38.609 79.818 48.37 0.9

8500sin (0.5t) 14.198 126.410 11.23 0

8500sin (0.5t) 18.367 121.300 15.14 0.3

8500sin (0.5t) 47.673 99.528 47.90 0.9

0 10 20 30 40 50 60-1

0

1

2

3

4

5

6

7

8x 10

4

time (s)

Tur

bine

pow

er (

W)

Fig. 10. Pt vs time for dP=7000sin(0.5t) Pa and rx=0.6 Ω

0 10 20 30 40 50 60-5

-4

-3

-2

-1

0

1

2

3

x 104

time (s)

Pow

er g

ener

ated

(W

)

Fig. 12. Pgen vs time for dP=7000sin(0.5t) Pa and rx=0 Ω.

0 10 20 30 40 50 60-100

0

100

200

300

400

500

600

700

800

900

time (s)

Tur

bine

Tor

que

(N·m

)

Fig. 11. Tt vs time for dP=7000sin(0.5t) Pa and rx=0.6 Ω

0 10 20 30 40 50 60-5

-4.5

-4

-3.5

-3

-2.5

-2

x 104

time (s)

Pow

er g

ener

ated

(W

)

Fig. 13. Pgen vs time for dP=7000sin(0.5t) Pa and rx=0.6 Ω

0 10 20 30 40 50 60-1

0

1

2

3

4

5

6x 10

4

time(s)

Tur

bine

pow

er (

W)

stalling behabiour

Fig. 14. Pt vs time for dP=6000sin(0.5t) Pa and rx=0 Ω

POWER QUALITY, ALTERNATIVE ENERGY AND DISTRIBUTED SYSTEMS 121

VI. CONCLUSIONS

In this paper the performance of the Wells turbine has been improved, studying its stalling behaviour when the flow coefficient (phy) reaches a specific characteristic value. A control scheme is proposed, aimed to avoid or delay the stalling behaviour, increasing the allowed slip of the induction generator coupled to the turbine. The control system for the flow coefficient is achieved by varying the rotor resistance of the induction generator.

It is stated that there exist an optimal value of rx for each specific range of pressure drop and it is verified that greater input pressure drop does not imply higher power output unless the stalling behaviour is avoided.

It has been demonstrated that the proposed control method used for this purpose clearly improves the performance of the system, maximizing the power generated by the turbine.

ACKNOWLEDGEMENT

The authors are very grateful to UPV/EHU and MICINN (formerly MEC) by its support through research projects EHU 06/88 and GIU07/08, and projects DPI2006-01677 and DPI2006-00714, respectively. They are also grateful to the Basque Government by its partial support through the research projects S-PE07UN04 and S-PE06UN10.

REFERENCES [1] European Commission. Joint Research Center. Directorate-General.

Institute for Energy. Energy Systems Evaluation Unit. Report on the Workshop on Hydropower and Ocean Energy – part I & II: Ocean Energy.http://ec.europa.eu/energy/res/setplan/expert_consultation_en.htm

[2] L. Christiansen, E. Friis-Madsen. PowerGen 2006.Worlds Larges Wave Energy Project 2007 in Wales

[3] Strategy on Renewable Energy 2010.EVE.The Euskadi 2010 Energy strategy. http://www.eve.es/index_hi.asp

[4] “Wave energy converters and their impact on power systems” Polinder, H.; Scuotto, M. Future Power Systems, 2005 International Conference on Volume, Issue , 18-18 Nov. 2005 Page(s):9 pp. - 9 Digital Object Identifier 10.1109/FPS.2005.204210.

[5] T.J.T. Whittaker, S. Raghunathan, A. Thompson.”ICE Proc water maritime and energy”, nº 124, 189-201, ISBN 09650903, (1997).The Islay wave power project – an engineering perspective

[6] A. Brito-Melo, L.M.C. Gato, A.J.N.A. Sarmento “Analysis of Wells turbine design parameters by numerical simulation of the OWC performance” .Ocean Engineering 29 (2002),pp. 1463–1477.

[7] Bimal K. Bose. Condra chair of excellence in power electronics. Modern power electronics and AC drives

[8] The Queen’s University of Belfast. Islay Limpet wave power plant. The European commission – Non nuclear energy programme JOULE III (1/11/1998 to 30/4/2002).

[9] T. Setoguchi, K. Kaneko, H. Tanisyama, H. Maeda, M. Inoue.”Impulse Turbine with self pitch controlled guide vanes connected by links” International. Journal of Offshore and Polar Engineering, Vol.6 Nº.1, March 1996. ISSN 1053-5381.

[10] V. Jayashankar, K. Udayakumar, B. Karthikeyan, K. Manivannan, Niranjan Venkatraman, S. Rangaprasad.”Maximizing Power Output From A Wave Energy Plant” Power Engineering Society Winter Meeting, 2000.IEEE. ISBN: 0-7803-5935-6 Volume: 3, pp.(s): 1796-1801 vol.3,2000. 0 10 20 30 40 50 60

-1

0

1

2

3

4

5

6x 10

4

time(s)

Tur

bine

pow

er (

W)

stalling behaviour

Fig. 16. Pt vs time for dP=8000sin(0.5t) Pa and rx=0 Ω

0 10 20 30 40 50 60-1

0

1

2

3

4

5

6x 10

4

time(s)

Tur

bine

pow

er (

W)

Fig. 15. Pt vs time for dP=6000sin(0.5t) Pa and rx=0.2 Ω

0 10 20 30 40 50 60-2

0

2

4

6

8

10x 10

4

stalling behaviour

Fig. 17. Pt vs time for dP=8000sin(0.5t) Pa and rx=0.8 Ω

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