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

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362 10.4 Design of wind pump systems

opt

dHg

. (10.34)

As for radial centrifugal pumps, the value of the pressure number only shows

slight variation (

opt

= 0.9 to 1.1), the entire wind pump system is determined by

the two equations (10.33) and (10.34). Fig. 10-26 shows the result of such a sys-

tem design, which gave an optimum transmission ratio i

opt

= 1:3.8. The additional

curves for the other transmission ratios i = 1:2 and 1:6 illustrate the consequences

of deviating from the optimum transmission gear ratio found. More details on the

design of wind pump systems with centrifugal pumps, also for the case with free

choice of the pump parameters, for designing a particular pump, are found in [3].

References

[1] Interdisziplinäre Projektgruppe für Angepasste Technologie (IPAT): Der Einsatz von

Windpumpsystemen zur Be- und Entwässerung (The use of wind pump systems

for irrigation and drainage), Schriftenreihe des Fachbereichs Internationale

Agrarentwicklung der TU Berlin (Series of the Department for International Agricul-

tural Development at the Technical University Berlin), No. 120, Berlin, 1989

[2] Jongh, J.A. de: Low Head / High Volume Wind Pumps for the Fleuve Region in

Senegal, CWD, Wind Energy Group, Technical University Eindhoven, 1988

[3] Twele, J.: Ertragsoptimierung windgetriebener Kreiselpumpen (Yield optimization of

wind-driven centrifugal pumps), Fortschritt-Berichte (Progress reports) VDI, series 7,

No 181, Düsseldorf, 1990

[4] Pfleiderer, C.; Petermann, H.: Strömungsmaschinen (fluid flow machines), 5th edition,

Springer-Verlag, Berlin Heidelberg New York London Paris Tokyo, 1986

[5] Lysen, E.H.: Introduction to Wind Energy, CWD, Amersfoort, The Netherlands, 1982

[6] Dijk, H. van: The Volume of Storage Tanks in Water Supply Systems with Windmill

Driven Pumps in Cap Verde, International Institute for Reclamation and Improvement,

Wageningen, The Netherlands, 1984

[7] Staassen, A. J.: A Model of a Centrifugal Pump Coupled to a Windrotor, Wind Energy

Group, University of Technology Eindhoven, 1988

[8] Cleijne, H., u.a.: Pump Research by CWD: The influence of starting torque of single

acting piston pumps on water pumping windmills, European Wind Energy Associa-

tion, Conference and Exhibition, 7.10.-9.10.1986, Rome, Section E10, p. 163-167

[9] Meel, J. van; u.a.: Field Testing of Water Pumping Windmills by CWD, European

Wind Energy Association Conference and Exhibition, 7.10.-9.10.1986, Rome, Section

F15, p. 423-430

[10] Mier, M.; Siekmann, H.; Twele, J.: Optimization of Winddriven Centrifugal Pumps,

1st International Congress on Fluid Handling Systems 10.9.-12.09.1990, Essen

[11] Kortenkamp, R.: Die Optimierung von Windpumpsystemen mit Kreiselpumpe unter

Berücksichtigung des instationären Betriebsverhaltens (The Optimisation of

wind pump systems with centrifugal pumps, taking into account unsteady operating

behaviour), Fortschritt-Berichte (Progress reports), VDI, series 7, No 235, Düsseldorf,

1993

R. Gasch and J. Twele (eds.), Wind Power Plants: Fundamentals, Design, Construction 363

and Operation, DOI 10.1007/978-3-642-22938-1_11, © Springer-Verlag Berlin Heidelberg 2012

11 Wind turbines for electricity generation -

basics

Presently wind turbines are used primarily for electrical power generation. Three-

phase alternators (AC generators) are used almost exclusively. Even for applications

that require DC the lower-cost alternator/rectifier configuration has superceded

the DC-generator. When a three-phase generator feeds directly into a grid,

that operates at a fixed frequency (e.g. 50 Hz in Europe, 60 Hz in the U.S.A.) the

angular velocity of the generator is fixed - or almost fixed. In this situation the

power generation capability of the wind turbine will be fully utilized for just one

value of wind speed (approximately 8 m/s in Fig. 11-1a). Thanks to the highly

developed converter technology of today it is now possible to operate with variable

generator speeds even for grid-connected generators (see Fig. 6-18). This yields

better utilization of the wind turbine; during gusty winds it also substantially

decreases the mechanical stresses in the blades and the shaft between turbine and

generator.

10v

12v

Fig. 11-1 Operating points of wind turbine and generator: a) directly grid-connected operation;

b) stand-alone operation as a battery charger

Fig. 11-2 Grid connection of a wind turbine: a) Direct grid connection of asynchronous (ASG)

or synchronous generator (SG); b) synchronous generator feeding into the grid via a frequency

converter with intermediate DC circuit

364 11.1 The alternator - single-phase AC machine

We have already considered extensively the aerodynamic properties of rotors in

chapters 5 and 6. In the present chapter we will focus on electrical generators and

AC-DC-AC converters. This will lead us to an understanding of the overall sys-

tem. Concepts of control and of plant layout will then be introduced in chapters 12

and 13. Chapter 14 will be devoted to issues of grid connection.

Table 11.1 presents the symbols for the circuit elements that we will use. Note

that the table contains elements from semiconductor electronics in addition to the

classical electrical components Resistor R, Capacitor C, and Coil L. The dynamic

behaviour of the elements is summarised in the second column of the table. For

the electronic components the input/output transfer with sinusoidal inputs is

shown. These semiconductor components, which are increasing in importance,

and their uses will be the topic of section 11.3.

11.1 The alternator - single-phase AC machine

11.1.1 The alternator (dynamo) in stand-alone operation

When a conductor moves through the lines of flux of a magnetic field a source

voltage e(t) will be induced in it, Fig. 11-3. Faraday’s law tells us that we will

have

e(t) = B l v(t). (11.1)

Here B is the flux density of a uniform magnetic field and l is the length of a con-

ductor that moves with the velocity v(t) through the magnetic field perpendicular

to the lines of flux. The flux density B is commonly expressed in Tesla units

(1 T = Vs/m

). In an alternator, this effect is used to generate a single-phase alter-

nating voltage.

The most elementary implementation consists of a single one-turn coil rotating

in a field of a permanent magnet, Fig. 11-4. The effective conductor length is 2 l

in that case. The voltage e(t) is delivered by two slip rings. Given that the angle

t is relative to the horizontal axis the voltage e(t) turns out to be:

e(t) = B 2 l r :sin :t = E

sin :t. (11.2)

11 Wind turbines for electricity generation - basics

365

Table 11.1 Electrical components and their dynamic behaviour

Electrical components and their dynamic behaviour

Widerstand R

Resistor

Resistance R

Widerstand R

Resistor

Resistance R

iRu 

Voltage = resistance x current

Kondensator

Kapazität C

Capacitor

Capacitance C

Kondensator

Kapazität C

Capacitor

Capacitance C

dti

Spu le

Induktivität L

Inductor

Inductance L

Spu le

Induktivität L

Inductor

Inductance L

Diode

Sperrbereich

Blocking zone

Sperrbereich

Blocking zone

Thyristor

Zündimpuls

Firing pulse

Zündimpuls

Firing pulse

Transistor

366 11.1 The alternator - single-phase AC machine

Fig. 11-4 shows that the velocity r

sin(

t) is the component of the circumfer-

ential velocity r

which intersects the lines of the magnetic field at right angles,

i.e. it corresponds to v(t) in Fig. 11-3. The amplitude E

of the source voltage e(t)

is proportional to the circumferential velocity r

, and therefore, it is proportional

to the angular velocity

and the rotational speed n,

= 2

n. It is also propor-

tional to the magnetic flux density B, and to the number of windings of the coil

which is one in Fig. 11-4. The highest voltage is always induced when the change

of magnetic flux

)

 = 2 B (l r)cos

t within the one-turn coil is largest, see Fig.

11-5.

For real electrical machines, it is often too complex to determine the operating

behaviour based on the exact physical relations. Therefore, equivalent circuit dia-

grams are used in that case. They only represent the most important physical

characteristics.

v(t)

e(t)

Fig. 11-3 Moving a conductor in a uniform magnetic field. Induction of the voltage e(t)

sinr:



Fig. 11-4 Left: alternator (dynamo); right: active velocity component

11 Wind turbines for electricity generation - basics

367







Fig. 11-5 Voltage e(t) and magnetic flux ĭ(t) in a dynamo

The equivalent circuit diagram of an alternator connected to a load resistance R

is shown in Fig. 11-6 where e(t) is the source voltage; R

and L

are the internal

rotor resistance and the rotor inductance, respectively. If the machine is at standstill,

the ohmic resistance R

can directly be measured. The source voltage is obtained

by measuring the terminal voltage at the open circuit terminals.

The inductance is obtained from a short circuit experiment (with low voltage

level). All electrical machines can be represented by such equivalent circuit dia-

grams. The required parameters can be usually determined by simple experiments

[1, 10, 13, 15].











Fig. 11-6 Equivalent circuit diagram of a dynamo with the load resistance R

, the internal rotor

resistance R

, and the rotor inductance L

Now, we will analyze how an alternator behaves if it is connected to a resistive

load R

, e.g. an electrical heater.

According to Kirchhoff’s voltage law the induced source voltage e(t) is

absorbed by the inductance L

, and the resistances R

and R

, as shown in Fig. 11-6.

The differential equation

)(

iLi

LiRiR 

, (11.3)

is valid; as the voltage drop in the coil is not proportional to the current, but to the

current change versus time di/dt.

As the relation is analyzed for a steady rotational speed

, the source voltage is

368 11.1 The alternator - single-phase AC machine

e(t) = E

sin

t. (11.4)

For the current, a more general sinusoidal function will be tried:

i(t) = I

sin :t + I

cos :t (11.5a)

= :I

cos :t - :I

sin :t. (11.5b)

A pure sine approach would not be sufficient, as will be seen soon. Inserting

(11.4) and (11.5) into the differential equation (11.3), and assorting according to

sine and cosine terms, which each have to be balanced, the following system of

equations for the current amplitudes results:



:

:

Lii

iLi

RRL

LRR

. (11.6)

The top row of (11.6) is a collection of terms that had contained sin

:t. The

bottom row originates from the terms which contain cos

:t. The right side in the

bottom row is zero since the source voltage does not have a cosine term. Solving

the equation (e.g. applying the Cramer’s rule) we obtain:



( :



LRR

(active current) (11.7a)



( :



LRR

(reactive current). (11.7b)

Both current amplitudes are proportional to the source voltage amplitude E

. The

sine amplitude I

, which is in phase with the source voltage, disappears if there is

no ohmic resistance (R

+ R

= 0) in the circuit. The cosine amplitude disappears

if no inductance is present (L

= 0).

The cosine amplitude is negative, equation (11.7b). This will be discussed later.

For the time history of the current we obtain

:

:

:





LRR

Eti cossin

()(

)(

iLi

. (11.8)

11 Wind turbines for electricity generation - basics

369

The sine term is called active current, and the cosine term reactive current. The

reasons become immediately clear if we calculate the power, which is the product

of voltage and current

P(t) = i(t) e(t)

P(t) = E

sin

:t + E

sin :t cos :t . (11.9)

Active power Reactive power

The first term, the active power, is always positive. However, due to



:

2cos1

sin

(11.10)

it oscillates around the mean value, cf. Fig. 11-7,

SSm

)()(

)2(

LRR

rlBIEP

:



(11.11)

The oscillation occurs at twice the frequency

:. The second term, the reactive

power, oscillates at twice the frequency, too. However, its mean value is zero,

therefore it is also called wattless power.

It is common when discussing AC currents to combine the sine and cosine

components of equation (11.5a):

i(t) = I

sin :t + I

cos :t

= î sin (

:t +

). (11.12)

î is the amplitude of the current i(t), and the phase angle

gives the shift of the

current relative to the source voltage e(t) = E

sin

t. These two values are deter-

mined from I

and I

tan

andIIi 

. (11.13)

370 11.1 The alternator - single-phase AC machine

e(t)

source voltage

active current

tsinI

tcosI

reactive current

active

tsinIE

active power

reactive

tcostsinIE



reactive power

Fig. 11-7 Active and reactive power from multiplication of voltage and current

The derivation shall be mentioned only briefly. Due to

î sin (

:t + ĳ) = î (sin :t cos ĳ + cos :t sin ĳ)

the comparison of the coefficients with (11.12) gives I

= î sin ĳ; I

= î cos ĳ.

From this follow the two equations (11.3). The advantage of the representation by

amplitude and phase angle is obvious, Fig. 11-8: both these values are easily

measured – e.g. using an oscilloscope.

The fact that the cosine amplitude of the alternator is negative in equation

(11.7b) is considered in Fig. 11-8. Here, it can be seen as well that the current

maximum follows the voltage maximum which is typical for a system of inductors

and resistors: current follows voltage. The time curves of voltage and current may

be considered as projections of the vectors in the diagrams to the left in Fig. 11-8.

11 Wind turbines for electricity generation - basics

371

ȍ t

t = 0

e(t) = E

sin ȍ t

ȍ t

sin ȍ t

îsin(ȍ t + ĳ)

cos ȍ t

ȍ t

t = 0

e(t) = E

sin ȍ t

ȍ t

sin ȍ t

îsin(ȍ t + ĳ)

cos ȍ t

ȍ t

Fig. 11-8 Vector diagram of current and power at the time t = 0; current amplitude î; phase angle

ĳ; (left); time curves of current and power versus

t (right)

With this representation of the current time curves we obtain the momentary

power, equation (11.9), in the form which was already discussed in connection

with Fig. 11-7:

P(t) = i(t) e(t)

= E

î cos ĳ [sin

:t] + E

î sin ĳ [cos :t sin :t] . (11.14)

Active power Reactive power

The amplitudes of active and reactive current are î cos ĳ = I

and î sin ĳ = I

, cf.

Fig. 11-8.

The integration of the reactive power (i.e. wattles power) over the period T

yields zero (cf. Fig. 11-7 right) and for the active power, as given in equation

(11.11) we obtain the mean value of

= (1/2) E

î cos ĳ = (1/2) E

. (11.15)

The amplitude of the reactive power is E

î sin

= E

, but it oscillates with

twice the frequency around zero.

For historical reasons, in the daily work of electrical engineering, not the

amplitudes of the sinusoidal voltages and currents (E, î) are used but the so-called

effective values.

The effective value corresponds to about 70% of the amplitude

value, I

eff

= I/ 2 and E

eff

= E/ 2 , respectively. Using this convention (analogous