Gasch R., Twele J. (Eds.) Wind Power Plants: Fundamentals, Design, Construction and Operation

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342 10.3 Operation behaviour of wind pumps

Drinking-water

supply

Livestock

watering

Irrigation

Drainage

Q low, H high

(H >

20 m)

Q: medium, H: medium

(5 m <

H < 20 m)

Q high, H low

(H < 5 m)

Piston pump A

Multistage

centrifugal pump E

Eccentric screw

pump C

Mammoth pump H

Single-stage centri-

fugal pump D

Diaphragm pump B

Screw pump F

Chain pump G

Type of application Pumping conditions Pump type

Drinking-water

supply

Livestock

watering

Irrigation

Drainage

Q low, H high

(H >

20 m)

Q: medium, H: medium

(5 m <

H < 20 m)

Q high, H low

(H < 5 m)

Piston pump A

Multistage

centrifugal pump E

Eccentric screw

pump C

Mammoth pump H

Single-stage centri-

fugal pump D

Diaphragm pump B

Screw pump F

Chain pump G

Type of application Pumping conditions Pump type

Fig. 10-9 Types of application, pumping conditions and pump types

The selection of a pump design for a particular application is influenced by a

number of criteria which have to be assessed individually. These can be physical,

technical and economic criteria. Considering the types of application and the

related pumping conditions, cf. Fig. 10-3, the correspondingly suitable pump types

can be identified, Fig. 10-9.

10.3 Operation behaviour of wind pumps

10.3.1 Suitable combinations of wind turbines and pumps

The design of the wind pump is determined, on the one hand, by the pumping

conditions of the particular type of application which is the main selection crite-

rion for the pump type choice, Fig. 10-9. On the other hand, the wind turbine, the

transmission ratio, and the pump have to be adapted to each other, taking the local

wind conditions of the intended site into account.

To find a suitable combination of wind turbine and pump, the torque-speed

characteristics of the wind turbine and the pump have to be compared, as it is

common practice for the coupling of an engine and a machine. Fig. 10-6 shows the

M-n characteristics of the different pump types. Two issues are important for

selecting a combination of wind turbine type and pump type. The rotational speeds

of the wind turbine and pump under operation have to be adapted to each other by

10 Wind pump systems 343

a transmission component, e.g. gears or belt drive. Moreover, the starting torque

has to be taken into account in order to achieve a favourable starting behaviour of

the wind pump already at low wind speed.

Fig. 10-10 shows the typical ranges of rotational speeds and total heads for

different pump types. The figure also contains the ranges of rotational speeds of

the various wind turbine types considering a reference diameter d

= 5 m of the

wind turbines

)

. It becomes clear that in many cases the rotational speeds have to

be adapted by a gearbox, as the wide range of speeds of the likely suitable pump

type is not covered by the much narrower range of rotational speeds of likely suit-

able wind turbines. For the pump types on the left of Fig. 10-10, gearing-down is

usually required. For the pump types on the right, gearing-up is required. In some

cases, the rotational speeds match without gears. Fig. 10-10 illustrates, that on one

hand, wind turbines with a low tip speed ratio are suitable for pump types A, B, F,

and G. On the other, wind turbines with a high tip speed are more suitable for

operation with pump types C, D, and E.

The transmission ratio i is selected so that the highest system efficiency possible

over the entire operating range of the wind pump is achieved for a given wind

turbine and pump. Usually, to determine of the transmission gear ratio, a rated

wind speed where both wind turbine and pump reach their maximum efficiency, is

chosen from the given wind conditions, cf. section 10.4.2.

Apart from matching the rotational speeds, any combination of wind turbine

and pump type has to take into consideration whether the torque of the wind tur-

bine is sufficiently large in order to start the pump. Positive displacement pumps

(A,B and C), such as piston pumps, diaphragm pumps and eccentric screw pumps

require a high starting torque. In contrast, centrifugal pumps (D,E) require only a

low torque, cf. Fig. 10-6.

A comparison of the starting torque required by the pumps with the starting

torque provided by the wind turbines (see chapter 6, Fig. 6-10) gives the following

suitable combinations: Wind turbines with a low tip speed ratio match with posi-

tive displacement pumps and wind turbines with a high tip speed ratio match with

centrifugal pumps. A suitable compromise has to be found for eccentric screw

pumps (C) between favourable start-up behaviour and sufficiently high rotational

speed under operation, as the eccentric screw pump has both a high starting torque

and a relatively high operating speed. A solution for this can be the use of a

centrifugal clutch and of a gearbox with a variable transmission ratio, for instance.

)

The rotor diameter d

= 5.0 m is representative for the wind turbine capacities

which have a very high application potential in rural areas (cf. Fig. 10-4).

344 10.3 Operation behaviour of wind pumps

rpmrpm

Fig. 10-10 Operating ranges of different types of wind turbines (diameter d

= 5 m) and

pumps [5]

Fig. 10-11 shows schematically the suitable combinations of wind turbine and

pump types which result from the discussion so far, and their attainable total head

H. Every wind pump shown has a limited application range where it reaches a

good efficiency. The application range is mainly determined by the operating

characteristics of the combined components. There is no such thing as a univer-

sally applicable wind pump. If the wind pump is operated outside this application

range, the yield will be reduced since the wind energy available is converted into

hydraulic energy less efficiently.

10 Wind pump systems 345

Fig. 10-11 Suitable combinations of wind turbines and pumps [3]

10.3.2 Qualitative comparison of wind pump systems with piston

pump and centrifugal pump

In the following, piston and centrifugal pumps are taken as examples, since they

are the most important pump types. The H-Q diagrams in Fig. 10-12 show the dif-

ferent characteristic behaviour of these two pump types. The pump’s rotational

speed n is the parameter used to clarify the effect of varying rotational speeds on

the performance characteristics.

Piston pump Centrifugal pump

Fig. 10-12 H-Q diagram of a piston pump and a centrifugal pump

346 10.3 Operation behaviour of wind pumps

The flow rate Q of the piston pump (Fig. 10-7) is

volK

volHub

nVQ (10.9)

with the stroke volume V

hub

of the pump, the piston diameter d

, the crank radius

, and the volumetric efficiency

vol

which takes into account the filling degree

and the leakage losses of piston and valves (

vol

> 0.9). So the flow rate is pro-

portional to the rotational speed, whereas the head is nearly independent from it,

Fig. 10-12 and the description of Fig. 10-7.

For the centrifugal pump (the most common pump type) it has to be pointed out

that according to the laws of similarity [3], there is a characteristic dependency of

total head H and flow rate Q on the rotational speed n:

H ~ n

and Q ~ n.

Therefore, the curves can be transformed for the different rotational speeds, as

long as the Reynolds’ number values are above certain limits. If a measured H-Q

curve for a certain rotational speed n

is given, Fig. 10-13, it is possible to calcu-

late for another rotational speed n

the corresponding H-Q curve using these laws

of similarity. Moreover, it follows from equation (10.1) that the hydraulic power is

proportional to the cube of the rotational speed.

hydr.1

hydr.2

(10.10)

0246810

Flow rate in m³/h

Total head in m

= 2 n

Fig. 10-13 H-Q diagram of a centrifugal pump with measured characteristic curve for rotational

speeds n

and calculated similar curve for n

10 Wind pump systems 347

large pipe diameter,

small losses

geo

small pipe diameter, large losses

large pipe diameter,

small losses

geo

small pipe diameter, large losses

Fig. 10-14 H

-Q diagram with characteristic curves of the hydraulic system for different head

losses

Usually the pump is integrated in a piping system which conducts the flow. The

pipes that are attached at the pump’s suction and pressure side (delivery side) are

called the hydraulic system. The head H

of the hydraulic system is calculated on

the basis of the geometry of the well and the pipes. In most cases, it is the sum of

the geodetic head H

geo

which is the height difference that has to be overcome

between system entry and exit, and the head loss H

= H

geo

+ H

(10.11)

The head loss H

results from the pressure losses (mainly friction) in the pipes,

depending on their geometry and surface. It increases with the square of the flow

velocity in the pipe, and is therefore proportional to the square of the flow rate Q.

Other components (e.g. bends, valves, fittings) also cause pressure losses. The

characteristics of the hydraulic system show the system head H

versus the flow

rate Q , Fig. 10-14. Thus, the characteristics of pump and hydraulic system may be

drawn in one diagram, Fig. 10-15, to determine the operating points. These are

given by the intersections of pump and hydraulic system curves.

Piston pump Centrifugal pump

H H

pump

system

Q Q

pump

system

Piston pump Centrifugal pump

H H

pump

system

Q Q

pump

system

Fig. 10-15 Operating points of a hydraulic system and the pump

348 10.3 Operation behaviour of wind pumps

In Fig. 10-15 one and the same hydraulic system operates with a piston pump

(left) and a centrifugal pump (right).

In order to design wind pump systems which are compatible with the different

types of application, the selected pump type has to be combined with a suitable

wind turbine. So, the requirements of the pump type have to be taken into account

when choosing the wind turbine.

Fig. 10-17, left, shows for a piston pump the curve of the mean torque M

(required at the pump shaft) versus the rotational speed n. The mean torque of a

single acting piston pump is constant, i.e. independent of the rotational speed. By

contrast, the torque of a centrifugal pump increases with the square of the rota-

tional speed, Fig. 10-17, right. It cannot be determined analytically, and therefore

has to be taken from the measured characteristic curve. This shows that for the

choice of a suitable wind turbine, these two pump types, piston pump and the

centrifugal pump, have completely different requirements.

The torque of a piston pump of one revolution is a half-sine wave curve,

Fig. 10-16. The mean torque

of the piston pump results from integrating this

half-sine wave over one revolution of the crank drive:

max

(10.12)

However, the calculation of the starting process cannot be based on the mean

torque of the piston pump, because in order to start up the pump, the wind turbine

has to provide the maximum torque M

max

. During operation, the system has

kinetic energy, and the oscillating torque curve can be replaced by the mean pump

torque

max

Position of the crank drive

max

Position of the crank drive

Fig. 10-16 Torque curve of the piston pump for one revolution

10 Wind pump systems 349

Equating mechanical and hydraulic power

g H V

Hub

n (10.13)

gives the mean torque of the piston pump under operation

rdHg

. (10.14)

The mechanical efficiency

takes into account the mechanical losses of the pis-

ton pump. The torque of the piston pump is directly proportional to the head H,

the crank radius r

, and the square of the piston diameter d

. It is independent of

the rotational speed n.

The operation behaviour of the wind pump is derived from the superposition of

torque and power curves of both wind turbine and pump. Fig. 10-17 shows power

and torque characteristics of a wind turbine for different wind speeds and the load

curves of the piston pump (left), and the centrifugal pump (right) respectively. The

intersection of wind turbine torque curve for the actual wind speed and the pump

torque curve, respectively of wind turbine power curve and pump power curve,

gives the actual operating point of the wind pump.

In the consideration, a constant total head H is assumed, i.e. in the hydraulic

system the head loss H

is negligible compared to the geodetic head H

geo

(short

pipe length, large pipe diameter). It is evident that the characteristic power curve

of the centrifugal pump matches much better with the power characteristics of the

wind turbine than that of the piston pump. The piston pump achieves an optimum

loading of the wind turbine only at one single operating point, and at higher wind

speeds it does not utilise the maximum power of the turbine.

Being a rotodynamic machine (like the wind turbine), the centrifugal pump

shows an optimum matching with the wind turbine characteristics at almost all

wind speeds if a suitable rotational speed adaption (transmission gear ratio) is

used, cf. section 10.4.4.

The wind speeds v and the rotational speeds n of the operating points can now

be taken from the diagram. For the piston pump, the corresponding flow rate Q is

according to equation (10.9)

Q = V

Hub

vol .

(10.15)

On the contrary, an analytical determination is not possible for the centrifugal

pump. The flow rates Q of the operating points have to be taken from the H-Q

diagram (see Fig. 10-15, right) at the intersections of the pump curves with the H

-Q

curve of the hydraulic system.

350 10.3 Operation behaviour of wind pumps

Piston pump

Centrifugal pump

system

Piston pump

Centrifugal pump

system

Fig. 10-17 Operating points of a wind pump with a piston pump and a centrifugal pump

Q Q

Piston pump

Centrifugal pump

Q Q

Piston pump

Centrifugal pump

Fig. 10-18 Flow rate Q versus wind speed v of a wind pump with a piston pump and a centrifu-

gal pump (discharge curves)

If the flow rates are plotted versus the corresponding wind speeds, the result is the

‘discharge curve’ Q = Q(v) of the wind pump (Fig. 10-18). This diagram relates

the characteristic value of the wind energy, the wind speed v, to a value representing

10 Wind pump systems 351

the hydraulic energy, the flow rate Q. The wind pump begins to discharge at the

start-up wind speed v

For a constant total head H, the curve of the total efficiency

of the wind

pump versus the wind speed v (Fig. 10-19) can be determined immediately, as

the ratio of hydraulic power and the theoretical power in the wind

Wind

= (

U

/2)

(

d /4)



HQg

(10.16)

In Fig. 10-19 the advantage of the better matching of the wind turbine and

centrifugal pump is obvious, as this kind of wind pump has a wider range of high

efficiencies in its efficiency curve, in comparison to the one with a piston pump.

The latter has a more distinct efficiency peak, and the efficiency is then reduced

rapidly with growing wind speeds.

So far, the total head H has been assumed to be constant, but in reality it in-

creases with higher wind speeds because the correspondingly growing flow rate

(higher velocity in the pipe) leads to higher pipe friction losses. Additionally, the

water level in the well often decreases during continuous pumping at high winds,

so the geodetic head increases, too. A qualitative illustration of how a change in

the head influences the discharge curve Q = Q(v), valid for both piston and cen-

trifugal pumps, is given in Fig. 10-20.

The discharge curve Q = Q(v) describes the technical system wind pump re-

garding the conversion of wind energy into hydraulic energy. The calculation of

the yield of the wind pump requires a description of the wind conditions. The yield

is defined as the discharge volume during the period under consideration, e.g. the

daily discharge volume V

. The wind conditions are measured using a wind meas-

uring system with a classification function which provides a wind speed histogram

(cf. section 4.3).

The discharge volume V of the wind pump is determined by wind speed histo-

gram and discharge curve. The total time T of the period under consideration is

multiplied by the summation of the frequencies h

of the individual wind class v

and the corresponding flow rate Q

hQTV

. (10.17)