Energy conversion

The energy of the wind can be captured using drag and/or lift. The drag principle has a lower theoretical efficiency. Most wind power plants today deploy the lift principle. They convert the kinetic energy of the wind into mechanical energy of rotor blades rotating around a horizontal axis. The mechanical energy is then converted into electricity with a generator.

Most wind turbines start rotating from a start-up wind speed of 2 - 3 m/s with a low coefficient of performance c_p that increases with wind speed. At nominal output capacity of the electricity generator, the power extracted from the wind is limited so that even at higher wind speeds, the generator would not be overloaded. At a specific cut-off wind speed, the mechanic stress of the whole plant becomes so big that power extraction is regulated down and the rotor is turned out of the main wind direction in order to protect it from damages. The power extraction from the wind can be regulated by either the stall (rotor blade design makes the wind stall above a specific wind speed) or the pitch approach (rotor blades are rotated along their centrelines in order to control the lift forces). Modern wind power plants are regulated down over a certain interval of wind speeds until the rotor is completely turned out of the wind and the electricity generation is stopped.

The power curve of a wind power plant is its power output plotted against the wind speed. As a basis for calculating the potential power output at given wind speeds, the power curve of the ENERCON E82 (ENERCON 2007) wind turbine with a rotor diameter of 82 m was used.

The start-up wind speed is 2 m/s, nominal power output is reached at 12 m/s. Cut-off was set to start at 25 m/s and to end at 35 m/s, with a linear decrease in between these two wind speeds. The resulting power curve is shown in figure 4.3.2.

The technical development until the year 2050 was assumed to result in higher nominal power output. The same coefficients of performance and the same wind speeds for start-up, reaching nominal capacity, start and end of cut-off were used for the higher power outputs.

The rotor diameters d_rot^WIND were chosen so as to match the respective nominal power output

at the wind speed of 12 m/s. Hub heights h_hub^WIND were assumed to increase as well. The values for d^WIND_rot and h_hub^WIND are listed in table 4.3.1.

Figure 4.3.2: Power curve for analysing the wind power electricity generation potential, based on (ENERCON 2007).

When wind turbines are grouped in wind parks, losses due to shading and losses in the cables linking the wind turbines to the grid occur. Technical blackout times and time for maintenance were taken into account by an overall availability factor _fav^WIND (Kuehn 2008).

The values for the loss factor _floss^WIND and the availability factor _fav^WIND are also given in table 4.3.1.

Table 4.3.1: Technical parameters of wind power plants. Based on (Kaltschmitt, Wiese et al. 2003), (Kuehn 2008).

Symbol Unit 2010 2020 2050

Onshore wind turbines

Nominal capacity ^{WIND ON}

Pnom ^_ kW 1950 3400 5500

Hub height ^{WIND ON}

hhub ^_ m 112 122 132

Rotor diameter d_rot^WIND_ON m 77.47 102.29 130.1

Distance factor f_dist^{WIND_ON - 6 6 6}

Area-specific installable capacity p^WIND_inst,max^_ON kW/km2 10422 10423 10423 Losses: shading, cables ^{WIND ON}

floss ^_ - 0.15 0.15 0.15

Availability factor f_av^WIND_ON - 0.95 0.95 0.95

Offshore wind turbines

Nominal capacity P_nom^WIND_OFF kW 3000 6000 12000

Hub height h_hub^WIND_OFF m 80 102 140

Rotor diameter d_rot^WIND_OFF m 96.09 135.89 192.17

Distance factor f_dist^WIND_OFF - 6 6 6

Area-specific installable capacity p^WIND_inst,max^_OFF kW/km2 10422 10422 10423 Losses: shading, cables f_loss^WIND_OFF - 0.15 0.15 0.15 Availability factor f_av^WIND_OFF - 0.95 0.95 0.95

In order to calculate the nominal output capacity that can be installed on a usable base area of known size, the distance between the wind turbines must be defined. The bigger the

0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 wind speed [m/s]

power in kW

0.00 0.10 0.20 0.30 0.40 0.50 cp

power output P coefficient of performance cp

distance is, the lower the losses through turbulence emissions and the higher the yield per wind turbine are. On the other hand higher distances mean lower absolute numbers of turbines, lowering the potential wind energy yield from a defined area. The distance between the turbines is given as a multiple of the rotor diameter, the so called distance factor f_dist^WIND. According to (Kaltschmitt, Wiese et al. 2003), values for f_dist^WIND lie between 6 and 15 when no wind direction is prevalent and with a prevalent wind direction, f_dist^WIND is chosen between 8 and 10 in the prevalent wind direction and between 4 and 5 normal to it, resulting in a much denser formation. When areas are rare, smaller distance factors are sometimes chosen.

Here, f_dist^WIND was set to 6 without distinguishing between different wind directions. The area that one wind turbine occupies can be calculated from eq. 18 (Kaltschmitt, Wiese et al.

2003).

 

²

4

3 WIND

rot WIND dist WIND

turb f d

A   ^{eq. 18}

where A^WIND_turb Area occupied by one wind turbine

WIND

fdist Distance factor

WIND

drot Rotor diameter

The area-specific installable output capacity p^WIND_inst,max is calculated by dividing the nominal output capacity of one turbine P_nom^WIND by the area it occupies.

WIND turb WIND WIND nom

inst A

p _,max  P eq. 19

The maximum installable capacity in a raster cell can be calculated from the area-specific capacity, the area of the raster cell, the share of the base area in the raster cell and the usable area share:

WIND inst WIND au WIND lc RC WIND

RC

inst A f f p

P _,max,     _,max eq. 20

where P_inst^WIND_,max,RC Maximum installable wind turbine capacity in a raster cell ARC Area of the raster cell

WIND

flc Share of base-area landcover in the raster cell

WIND

fau Usable area share

For each raster cell the power output P_max,^WIND_RC^,timeis calculated according to eq. 21.

 

_WIND

nom WIND inst av WIND loss wind

p wind WIND rot wind time

WIND

RC P

f P f

v c v A

P_max, ^{, 3} (1 ) ^,max

2

1       

  ^{eq. 21}

where time Time step index

time WIND

P_max,RC^, Power output of the maximum installable capacity in a raster cell

wind Density of the air

vwind Wind speed

) ( _wind

p v

c Coefficient of performance, depending on wind speed

WIND

Arot Area swept over by the rotor blades

WIND

floss Loss factor

WIND

fav Availability factor (accounting for maintenance times and technical blackouts) The annual integral of the power output of the maximum installable wind power capacity

time WIND

P_max,RC^, over a whole year is the annual electricity generation potential in the raster cell.

4.3.3.2 Costs

Economic parameters for wind power plants for the year 2010 and anticipated values for the years 2020 and 2050 were taken from (BMU 2010). They are listed in table 4.3.2. Levelised electricity costs and cost potential curves were calculated as described in chapter 4.1.3.2.

Table 4.3.2: Economic parameters of on- and offshore wind power plants, based on (BMU 2010). All costs in €2009.

Symbol Unit 2010 2020 2050

Onshore wind turbines

Investment costs c^WIND_inv ^_ON €/kW 1160 1030 900

Fixed operation costs¹⁾ f_c^WIND_{_fixop}^_ON - 0.04 0.04 0.04 Fixed operation costs (absolute) - €/kW 46 41 36

Variable operation costs c^WIND_varop^_ON €/kWh 0 0 0

Life-time N^WIND_ON a 18 18 18

Offshore wind turbines

Investment costs c^WIND_inv ^_OFF €/kW 3300 2100 1300 Fixed operation costs¹⁾ fc^WIND_fixop^_OFF - 0.055 0.055 0.055 Fixed operation costs (absolute) - €/kW/a 182 116 72

Variable operation costs c^WIND_varop^_OFF €/kWh 0 0 0

Life-time N^WIND_OFF a 18 18 18

1) Annual share in investment costs

Im Dokument Renewable energy based electricity supply at low costs : development of the REMix model and application for Europe (Seite 59-62)