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Analysis and performance comparison of an OWC wavepower plant equipped with Wells and Impulse turbines

Eugnio V. Corvelo

Abstract

The paper deals with numerical simulation on time domain of the performance of an OWC

wave power plant equipped with two parallel electric turbo-generators sets equipped with

Wells or with Impulse turbines. It is also studied the performance of the OWC equipped with

Wells turbine and a fast relief valve in parallel. An algorithm to control the turbines rotational

speed for maximum power output and energy quality is also presented.

1 Introduction

Oscillating water column (OWC) wave

energy power plants are to date those that

have known a more extensive

development. Full-scale prototypes have

been built in some countries. The device is

constituted by a hydro-pneumatic chamber,

generally similar to a large parallelepiped

(or cylinder) shape with the side walls

partially submerged in the water. The

hydro-pneumatic chamber form inside a

free-surface, that oscillates by the action ofwaves. This rising and falling of the water

level promotes an air flow that drives one

or more air turbines coupled to electric

generators. The air flow is non-steady,

with the flow changing direction twice per

wave cycle, and the amplitude of the air

flow oscillations changing in different time

scales. Therefore designing a self-

rectifying turbine to respond satisfactorily

to these operating conditions is a

challenge.

In the late seventies, a self-rectifying

turbine to equip OWC was invented: The

Wells turbine. However, this type of

turbine has the disadvantage of presenting

severe and abrupt drops in power due to

flow separation around the blades,

depending on flow velocities and turbine

rotation speed. In order to overcome these

drawbacks, other types of self-rectifyingturbines have been proposed for this

purpose, namely Impulse turbines.

Although the efficiency peak of theseturbines is lower than the Wells efficiency

peak, they do not exhibit the sudden power

drop, characteristic of Wells turbines. This

study aims to compare these two types of

turbines in situations of real operation, ie,

as integral parts of the energy conversion

chain of an OWC.

The comparison has necessarily to be made

on time domain, because the relation

between flow coefficient and pressurecoefficient of impulse turbine is non-linear.

Further, it is known that turbine flow

characteristics affect the absorption

capacity of hydro-pneumatic chamber. It

was also required to understand how the

turbine affects the amount and the quality

of electric energy, related to a strategy to

control turbine rotation speed.

In order to obtain realistic results, the

numeric simulations were performed based

on previous studies for the wave power

plant proposed to integrate the new

breakwater at the mouth of Douro River,

Oporto. The site wave climate and the

hydro-pneumatic chamber hydrodynamic

coefficients were used. Turbine flow

characteristics were obtained

experimentally at IST laboratories [1].

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2 HydrodynamicsThe hydrodynamic coefficients of the

pneumatic chamber were calculated using

the software WAMIT [2]. This software

uses the panel method to calculate several

characteristic coefficients of bodieshydrodynamic behavior subjected to wave

field action. For OWC devices, it is

necessary to calculate the transfer function

that relates the diffracted flow, with the

amplitude of the incident wave, and the

function that relates the flow radiated by

pressure inside the chamber. Thus,

assuming that () is the excitation-

volume-flow coefficient for regular

incident waves of frequency and

amplitude , we have [3, 4]:

= A . 2.1 For the radiated flow we have

+ = . 2.2

Linear water wave theory allows us todecompose the water flow that enters and

exits the hydro-pneumatic chamber, ,into diffracted flow , and radiatedflow [4]:= + 2.3

Fig 1 Hydrodynamic coefficients: excitation-volume flow coefficient for different waves

directions, (

1blue, for 60;

2green, 50;

3red, 40; 4black, 30).

Fig 2 Hydrodynamic coefficients: radiation

conductance, (solid line, red), radiationsusceptance (dashed line, blue).Wave climate of 46 sea states,

characterized by significant wave height,energy periods and frequency of

occurrence, was used in the present study.

In the calculation of hydrodynamic

coefficients, it is assumed that the system

behaves linearly. Therefore, the nonlinear

losses were not taken into consideration in

calculating the hydrodynamic coefficients

and hydrodynamic behavior. Thus, in order

not to ignore these losses, it is assumed

that they correspond to a decrease in

incident energy, which is reflected as a

significant reduction in height of waves at

the site.

3 Turbine

The numerical simulations conducted in

this study were based on the dimensionless

curves obtained experimentally for the

Wells and Impulse turbine [1]. These

curves allow to relate the mass flow

, to

the differential pressure in the hydro-pneumatic chamber . Applyingdimensional analysis for incompressible

flows, we can write:

= , = ,where,

=

, 3.1

0 0.5 1 1.5

w@radsD

0

200

400

600

800

G1HwL,

G2HwL,

G3HwL

,G4HwL

@m

2sD

0 0.5 1 1.5 2

w @radsD

-0.04

-0.02

0

0.02

0.04

0.06

BHwL,

CHwL

@m

4sgkD

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= , 3.2

=

=

, 3.3

where is the pressure coefficient, the

flow coefficient, the power coefficient

and , , and , the density of air, therotational speed and diameter of the

turbine, respectively. The characteristic

curves for the Wells turbine are plotted in

Figures 3, 4 and 7

Fig 3 Wells turbine power coefficient versus

flow coefficient.

Fig 4 Wells turbine pressure coefficient versus

flow coefficient.

For the Impulse turbine, the characteristics

curves are plotted in Figures 5, 6 and 7.

Fig 5 - Impulse turbine power coefficient versus

flow coefficient.

Fig 6 - Impulse turbine pressure coefficient versus

flow coefficient.

Figure 7 shows the aerodynamic efficiency

curves for the two turbines depending onthe normalized flow coefficient.

Fig 7 Wells and Impulse turbines aerodynamic

efficiency versus normalized flow coefficient

4-System Mathematical Model

For a bottom-mounted OWC power plant,

the mass balance is given by:

= + , 4.1

0,000

0,0000

0,000

0,0010

0,001

0,000

0,00

0,000

0,00 0,0 0,0 0,0 0,0 0,10

P

F

0,00

0,0

0,10

0,1

0,0

0,

0,0

0,00 0,0 0,0 0,0 0,0 0,10

Y

F

0,01

0,0

0,10

0,1

0,0

0,

0,0

0,

0 0,0 0,1 0,1 0, 0, 0,

P

F

0,0

0,

1,0

1,,0

,

,0

,

0 0,0 0,1 0,1 0, 0, 0,

Y

F

0,

0,0

0,

0,

0,

0,

0,0 0, 1,0 1, ,0 , ,0 , ,0 , ,0

h

FFh

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where and are the density andvolume of air under no perturbation,

respectively.

Assuming that:

= ;

=

;

= ; , equation (4.1)can be written as:

= . 4.2

The radiated flow is given by [5]:

=

, 4.3 where = c isthe system memory function.

From equation (2.3) and equation (4.2)

results the following expression

representing the system dynamics, which

should be solved numerically [6]:

= + . 4.4

5-Results of Numerical Simulation

Simulations were conducted for each sea

state, and each rotor diameter in order to

optimize the turbine rotational speed. The

optimum rotational speed for each seastate, and each rotor diameter is calculated

by varying the turbines rotational speed in

increments of 5 rad/s, and calculating the

shaft power output. It is assumed that

rotational speed does not change by wave

cycle or wave groups effects, or if there is

rotational speed variation, this is small

enough so its influence can be ignored.

Physically, this means that the inertia of

rotating parts is large enough so that

prevents significant variations of rotationalspeed for a given sea state. The time span

for computational simulation of the plant

operation is 20 minutes for every sea state,

solving equation (4.4) with time

increments of = 0.1 seconds. It isaccepted that 20 minutes is a time window

long enough to have results statisticallysignificant. It was found that with time

increments of one tenth seconds solving

equation (4.4), the obtained results were

sufficiently accurate.

The rotor diameters considered for the

Wells turbine with and without by-pass air

valve were, 1.5, 2.0, 2.5, 3.0 m. For the

Impulse turbine were 1.2, 1.7, 2.2, 2.7 m.

Fig 8 Wells turbine average shaft power versus

optimum rotation speed without rotation speedlimits.

The data points resulting from numerical

simulations, line up nearly perfectly in

accordance with an equation of type .Because of sonic effects, the rotational

speed of the Wells turbine has to be

limited. It is assumed that tip velocity limit

is 160 m/s. Figure 8 shows the relationship

between average shaft power and optimum

turbine rotational speed.

0

50

100

150

200

250

0 100 200 300

Pu[kW]

N [rad/s]

D=1.5

D=2

D=2.5

D=3

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optimum rotation speed with rotation speed limits.

Figure 3 shows that for flow coefficients

around =0.045, the Wells turbine suffers

a sharp decrease in shaft power output, by

the effect of flow separation on the blades.This effect is even more important the

smaller the diameter of the turbine, ie

turbines with smaller diameters enter in

aerodynamic loss more often. This effect

can be avoided with the installation of

rapid relief valves in parallel with the

turbine, to control the maximum pressure

in the pneumatic chamber, and thereby

limit the flow rate through the turbine.

Therefore, new simulations were

performed considering the action of a fast

relief valve. It was considered that the

valve would have an ideal behavior. Figure

10 shows the relationship between average

shaft power and rotational speed under

these conditions. A significant increase in

turbine power output is observed, when the

plant is equipped with a fast relief valve.

It was found that the root mean square of

pressure in the pneumatic chamber is avariable that represents very well the plant

operation state.

Table 1 shows the results for the plant

annual average shaft power (plant

equipped with two equal turbo-electric

generator sets). It shows the turbines gross

power; shaft power, pneumatic power as

well as mechanical and aerodynamic

efficiencies, and capture widths of


optimum rotation speed with rotation speed limits

and fast relief valve.

Fig 11 Impulse turbine average shaft powerversus optimum rotation speed without rotation

speed limits.

hydro-pneumatic chamber for the four

scenarios, and various diameters of the

turbine rotor. It is found that the best

scenario is achieved by the plant equipped

with Wells turbines and fast relief valves.

However, it should be noted that the model

implemented considers an ideal relief

valve. Thereby it is expected that for a real

situation the power output should be lower.

The ideal model for the fast relief valves

do not take into account the expected

losses in valves or the power consumed for

valves control, as well as difficulties

associated to control the valves opening

and closing times. Therefore, smaller

differences are expected in real situations

for the power output of the plant equipped

with Wells turbine and fast relief valve,

compared to power output by plant

equipped with Impulse turbines. It is

expected that in real situation, the lastshould be the best scenario.

0

50

100

150

200

250

0 50 100 150 200 250

Pu[kW]

N [rad/s]

D=1.5

D=2

D=2,5

D=3

0

50

100

150

200

250

0 50 100 150 200 250

Pu[kW]

N [rad/s]

D=1.5

D=2

D=2,5

D=3

0

50

100

150

200

250

0 50 100 150

Pu[kW]

N [rad/s]

D=1,2

D=1,7

D=2,2

D=2,7

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()

()

.

()

haer hm haer.hm

()

haer.hm.CW

(m)

1. 1. . 10.1 0. 0. 0.1

.0 1. .1 1. 0. 0. 0.

. . . 11. 0. 0. 0.

.0 . . 1. 0. 0. 0.

1. . . 1.0 0. 0. 0. . .

.0 .1 0. 11.0 0.0 0. 0. 1. .

. . . 1. 0. 0. 0.1 1. .

.0 . . 1. 0. 0. 0. 1. .0

1. 0. 1. 11. 0.1 0. 0.0

.0 1. . 1.0 0.1 0. 0.0

. 10. 10. 1. 0.0 0, 0.

.0 10. 10. 1. 0. 0. 0.

1. 0. . 10. 0. 0. 0. . .

1. . . 10.1 0. 0. 0. 11. .1

. . 10. 1. 0. 0. 0. 1. .

. 10. 10. 1. 0. 0. 0. 1.1 .0

Table 1 Annual average shaft power; annual average turbines total power; pneumatic power; aerodynamic

efficiency; mechanic efficiency and annual average capture width for turbines different diameters.

(1 )

() ()

. .

()

.01 .

()

.1 .0

()

. 1.

Table 2Maximum annual average shaft power for

optimum turbine diameters.

Table 2 shows the turbines optimaldiameters as well as the maximum shaft

power for each of the four scenarios under

consideration. Note that if the plant is

equipped with Wells turbines and fast

relief valves, the maximum annual average

shaft power is 2x52.0 kW for Wells

turbines with 2.81 m rotor diameter. For

Impulse turbines, the maximum annual

average shaft power is 2x51.5 kW, with

rotor diameter of 2.59 m. It is therefore

expected to be lost over 1 kW if the model

for the rapid relief valves is more realistic.

In this sense, it seems evident that the best

solution would be achieved with impulse

turbines. It should be noted that the

analysis does not consider turbine

rotational speed control.

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6-Turbine Rotational SpeedControl

An effective way to improve turbine

efficiency for different sea states and wave

grouping is to allow variations of turbinerotational speed. Note that on the best

turbine efficiency point (b.e.p.), flow rate

and power output are proportional to and, respectively. The possibility to varythe turbine rotational speed permits the

ability to set up rotational speed to each

sea state, and thereby maximize the turbine

average power output. It also has the

beneficial effect to store energy in the form

of kinetic energy, which allows smooth

short time variations of electrical powersupplied to the grid. Turbine aerodynamic

efficiency, and the amount and quality of

electric power, will naturally be strongly

dependent on the strategy adopted to

control instantaneous rotational speed.

Rotational speed control is accomplished

by acting on instantaneous electric

generator torque imposed to turbine.

Oscillations of electrical power supplied to

the grid may be split into three time scales:

i) Fluctuations of short time duration,typically on the order of half wave period,

ie between 4 and 8 s, ii) Fluctuations of

average time duration, associated with

wave groups with time scales on the order

of few tens of seconds; Long time duration

oscillations, associated with variations of

sea states. It is expected that the kinetic

energy accumulated by flywheel effect can

filter the power oscillations of short

duration and help filter out the oscillations

of average duration.

In this study, a strategy is developed for

controlling turbines rotational speed. The

strategy took into consideration several

factors: i) Rotational speed limit imposed

to turbines by mechanical issues,

aerodynamics, or imposed by the rotational

speed range of electrical generator, ie

. ii) The rotation speed

will have to adjust to sea states in order tomaximize the turbine power output. iii)

Electric energy quality to be supplied to

the grid. iv) The power plant overall

efficiency, given that variation in rotational

speed change the pressure drop across the

turbine, which influences the first stage of

energy conversion chain, ie wave energy topneumatic energy. v) The power plant

monitoring procedure should be realistic,

and the control algorithm should take as

input, variables easily measurable and be

suitable for on-line implement at the power

plant Programmable Logic Control.

The strategy adopted in this study was to

control the torque of the electric generator,

based on turbines average power curves

functions of optimal rotation speed foreach sea state. The electric generator

torque must balance the turbine torque

over long periods of time, so that the

average speed of rotation is approximately

the optimum rotation speed for a given sea

state, ie:

1

= , , , . 6.1 Having knowledge of strategies previously

developed, and the problems arising [7],

after several attempts to define a more

appropriate control law, we concluded that

the following equation would have to be

fulfilled:

> 6.2 A piecewise function of the following kind

could respond adequately to the objectives

and requirements needed:

= >

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Where , , , are constants calculatedaccording to each sea state. is theturbine rotation speed which limits each

section of the control law. , is therated generator power,

is the inertia of

rotating parts, and = /, the timederivative of the instantaneous electricalpower accepted by grid. and areconstants funded by solving the following

system of two equations:

= = 1 6.4Being

, , the optimum value of turbine

rotational speed, and power output, foreach sea state, respectively. In the control

strategy developed, the values of , and for each sea state, are determined bycorrelations between them and the pressure

root mean square in the pneumatic

chamber. dN is a variable to be defined

according to the allowed rotational speed

oscillation range around the optimum value. It is found that turbines power output issensitive to the rotational speed oscillation

range. The inertia of rotating parts isextremely important with regard to the

quality of electrical energy produced, and

it can become critical for the more

energetic sea states.

For the numerical simulations performed

with the control law defined above, it was

decided that the diameters of the turbines

would be D=2.0 m for the Wells turbines,

and D=1.7 m for the Impulse turbine. For

the Wells turbine, and Wells turbine in

parallel with fast release valve (D=2.0 m),

it was assigned a value of dN=20 rad/s,

with a rotational parts inertia of 600 kg.m2.

For the Wells turbine it was needed a rated

generator power of 250 kW. For the Wells

turbine in parallel with fast release valve it

was needed a rated generator power of 300

kW.

For Impulse turbine (D=1.7 m) was

assigned a value of dN=13.2 rad/s, and ainertia of 1200 kg.m

2. It was needed a

rated generator power of 300 kW. It was

found to be extremely difficult to control

the rotational speed for this turbine for

smaller rotational parts inertia.

The control law developed in this work,has the ability to self-adjust appropriately

to each sea state, taking as input only the

pressure root mean square, which is a

variable easy to measure, and little

influenced by errors of pressure reading.

The following figures show the behavior of

the control law for dN=20 rad/s, and

dN=60 rad/s, and the turbine shaft power

curve,

. The

, and

, curves

intersection represents the optimumoperation point for the Wells turbine with a

diameter of 2 m, an inertia of, = 100kg.m2, = 84 kWs-1, and a ratedgenerator power of = 250 kW, fora sea state characterized by Hs=2.2m;

Te=15.3s. For this sea state, the optimal

operating point, has an average rotational

speed of N=143.6 rad/s, for which the

turbine can delivery a average shaft power

of = 50.0 kW. It can be observed in thefigures that the higher the value of dN, thesmoother the progress of curve, andtherefore higher rotational speed

oscillations. It was observed that in

general, this control strategy led to very

good results in terms of quantity and

quality of produced electricity, reasonably

fulfilling the Portuguese electric grid

regulation for almost all sea states

regarded.

Fig 12 Turbine shaft power versus optimum

rotation speed (blue line) and electric power control

law imposed by electric generator to the turbine(red line); dN=60 rad/s Wells turbine D=2 m.

120 140 160 180 200N @radsD

50

100

150

200

250

300

uPHNL,

ePHNL,

@

Wk

D

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Fig 13 Turbine shaft power versus optimum

rotation speed (blue line) and electric power control

law imposed by electric generator to the turbine

(red line); dN=20 rad/s Wells turbine D=2 m.

7-Power plant operation timeevolution

Figures 14, 15 and 16, show the turbineinstantaneous shaft power (blue lines) and

instantaneous electric power (red lines) for

the Wells turbine, Wells turbine in parallel

with fast relief valve and for the impulse

turbine, for a sea state characterized by

significant height Hs=2.9m and energy

period Te=11.2s. It can be observed (Fig.

14) for this energetic sea state, that the

Wells turbine spend significant operation

time on aerodynamic stall conditions,

which leads to a significant powerreduction. For this sea state, the installation

of a fast relief valve can avoid the turbine

aerodynamic stall which improves the

turbine aerodynamic performance and

power output (Fig. 15). The impulse

turbine has the advantage of not suffering

the effects associated to aerodynamic stall

(Fig. 16).

Fig 14 Instantaneous turbine shaft power (blueline) and instantaneous electric power versus time

(red line) for Wells turbine (Hs=2.9 m; Te=11.2s,D=2m, no relief valve).


(red line) for Wells turbine (Hs=2.9 m; Te=11.2s,

D=2m, with relief valve).


(red line) for Impulse turbine (Hs=2.9 m; Te=11.2s,

D=1.7m).

8-Conclusions

The integration in the power plant of fast

relief valves prevents the rapid power loss

of Wells turbine, avoiding the major

drawback of this type of turbine. It was

observed that the integration of fast relief

valves in parallel with the Wells turbine

has a very beneficial effect in terms of

electricity produced, which will enable to

reduce the optimum turbine diameter, andconsequent construction costs. It is

possible to significantly increase the

energy produced by the power plant if

equipped with impulse turbines, compared

to the energy production if the power plant

is equipped with Wells turbine without

relief valves. For the case of Wells turbine

operating in parallel with fast relief valves,

the energy produced by the Impulse

turbine is only slightly lower. However the

model used in numerical simulations for

the fast relief valve, assumes, that it

120 140 160 180 200

N @radsD

50

100

150

200

250

300

uPHNL,

ePHNL,

@

Wk

D

200 400 600 800 1000

10x t @sD

0

100

200

300

400

500

600

top

.lit;

top

.lec@

Wk

D

200 400 600 800 1000

10 x t @sD

0100

200

300

400

500

600

top.

lit;

top

.lec@

Wk

D

200 400 600 800 1000

10 x t @sD

0

100

200

300400

500

600

top.

lit;

top

.lec@

Wk

D

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behaves optimally. Furthermore the energy

required to control and operates the relief

valves is ignored. Therefore, it is expected

that a more realistic model for the

operation of fast relief valves will lead to a

reduction of produced energy compared towhat can be achieved by the Impulse

turbine. Taking into account the quality of

energy produced, some difficulties were

found on the effective rotation speed

control of the Impulse turbine. For some

sea states, it was not possible to produce

electricity with the quality required by the

grid.

9-References

[1] L.M.C. Gato, Internal

comunication, IST, 2008

[2] P.A.P. Justino, Internalcommunication, INETI, 2008.

[3] A.F. de O. Falco, Frequency

domain, time domain and stochastic

modeling of wave energy

converters, Coordination Action inOcean Energy Report, IST, 2005.

[4] A.F. de O. Falco, R.J.A.

Rodrigues, Stochastic modeling of

OWC wave power plant

performance, Applied Ocean

Reserch 24, 59-71, 2002

[5] A. F de O. Falco, P. A. P. Justino.

OWC wave energy devices with

air flow control OceanEngineering 26, 1275-1295, 1999

[6] P.A.P. Justino; A.F. de O. Falco,

Rotacional speed control of an

OWC wave power plant, Journal of

Offshore Mechanics and Arctic

Engineering 121, 65-70, 1999

[7] A.F de O. Falco, Control of an

oscillating-water-column power

plant for maximum energy

production, Aplied Ocean Reserch

24, 73-82, 2002

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