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Wind Energy Exercises Week 7
Introduktion til vindenergi (46000)
Danmarks Tekniske Universitet
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46000 Introduction to Wind Energy
Exercise: Role of wind energy in Danish Energy
Supply and Economy
1. How big is Danish electricity production relative to the total energy consumption?
2. Use the annual Nord pool system price graph in the slides to read off the spot market elec-
tricity price for the year shown. Calculate the mean value and the standard deviation.
3. How is ’full-load hours’ defined?
4. Download the spreadsheet ’anlaegprodtilnettet’ from ens. Find a typical mod-
ern wind turbine. How many full load hours did it have last year? Repeat for four other wind
turbines, same model. What’s the average capacity factor?
5. Based on the average market price of (2), what electricity income would you expect for
a year of operation?
6. Compare wind energy and wave energy with respect to costs.
7. For the wind turbine model investigated in (4), estimate the initial cost.
8. Estimate the annual running expenses with information from 2 sources. Compare and dis-
cuss.
9. Make an NPV calculation for a 20 year life time. Assume a discount rate of 11%. What
is NPV?
10. What is IRR?
11. What is the simple pay-back time?
12. Introduce a fluctuation in the electricity price corresponding to your answer from (2). How
does that effect IRR?
Solution
1. How big is Danish electricity production relative to the total energy consumption?
From slide information:
ratio = 109350 TJ
781 PJ
= 0 = 14% (1)
Here it is noted that electricity is not a ’primary energy source’ but is produced from primary
energy sources such as coal and renewables. The result may seem small. This is due to the
energy amounts that goes into heating and transport.
2. Use the annual Nord pool system price graph in the slides to read off the spot market elec-
tricity price for the year shown. Calculate the mean value and the standard deviation.
The prices are read off and typed into a spreadsheet. We get a mean value of 24. 9 øre/kWh and
a standard deviation of 8. 1 øre/kWh.
3. How is ’full-load hours’ defined?
Full load hours is the ratio of energy produced and the rated power of the wind turbine. Ex-
pressed in hours.
4. Download the spreadsheet ’anlaegprodtilnettet’ from ens. Find a typical modern
wind turbine. How many full load hours did it have last year? Repeat for four other wind
turbines, same model. What’s the average capacity factor?
The Vestas V117 turbine is chosen. It has a rated power of 3 MW and a rotor diameter of
117 m. Five turbines at five locations are looked up:
Place Enery production 2019 Full load hours Capacity factor
Købelev 14350691 kWh 3986 0.
Askø 12157573 kWh 3377 0.
Kerteminde 10817426 kWh 3005 0.
Holstebro 9904750 kWh 2751 0.
Kalbygaard 10247717 kWh 2847 0.
The average capacity factor is 0. For the first turbine it is 0 which is relatively large. We
go ahead with this turbine later.
5. Based on the average market price of (2), what electricity income would you expect for
a year of operation?
The income per unit energy is equal to the spot price so is 24. 9 øre/kWh.
The expected income is 14. 4 · 109 Wh × 0. 249 · 10 − 3 DKK/Wh = 3. 6 MDKK
Sheet
Page 1
NPV calculation
####### rated power 3,60E+06 W
####### capacity factor 4,55E-
####### energy pr year 1,44E+10 Wh
####### tariff 2,49E-04 DKK/W
####### initial costs 3,02E+07 DKK
####### running expens 5,39E+05 DKK/year
####### discount rate 1,10E-
####### year cost energy prod year income net income PV of earning Cash NPV
####### DKK Wh DKK DKK DKK DKK DKK
####### 0 3,02E+07 0,00E+00 -3,02E+07 -3,02E+07 -3,02E+07 -3,02E+
####### 1 5,39E+05 1,44E+10 3,58E+06 3,04E+06 2,74E+06 -2,72E+07 -2,75E+
####### 2 5,39E+05 1,44E+10 3,58E+06 3,04E+06 2,46E+06 -2,42E+07 -2,50E+
####### 3 5,39E+05 1,44E+10 3,58E+06 3,04E+06 2,22E+06 -2,11E+07 -2,28E+
####### 4 5,39E+05 1,44E+10 3,58E+06 3,04E+06 2,00E+06 -1,81E+07 -2,08E+
####### 5 5,39E+05 1,44E+10 3,58E+06 3,04E+06 1,80E+06 -1,51E+07 -1,90E+
####### 6 5,39E+05 1,44E+10 3,58E+06 3,04E+06 1,62E+06 -1,20E+07 -1,74E+
####### 7 5,39E+05 1,44E+10 3,58E+06 3,04E+06 1,46E+06 -8,98E+06 -1,59E+
####### 8 5,39E+05 1,44E+10 3,58E+06 3,04E+06 1,32E+06 -5,94E+06 -1,46E+
####### 9 5,39E+05 1,44E+10 3,58E+06 3,04E+06 1,19E+06 -2,91E+06 -1,34E+
####### 10 5,39E+05 1,44E+10 3,58E+06 3,04E+06 1,07E+06 1,30E+05 -1,24E+
####### 11 5,39E+05 1,44E+10 3,58E+06 3,04E+06 9,64E+05 3,17E+06 -1,14E+
####### 12 5,39E+05 1,44E+10 3,58E+06 3,04E+06 8,68E+05 6,20E+06 -1,05E+
####### 13 5,39E+05 1,44E+10 3,58E+06 3,04E+06 7,82E+05 9,24E+06 -9,74E+
####### 14 5,39E+05 1,44E+10 3,58E+06 3,04E+06 7,05E+05 1,23E+07 -9,04E+
####### 15 5,39E+05 1,44E+10 3,58E+06 3,04E+06 6,35E+05 1,53E+07 -8,40E+
####### 16 5,39E+05 1,44E+10 3,58E+06 3,04E+06 5,72E+05 1,84E+07 -7,83E+
####### 17 5,39E+05 1,44E+10 3,58E+06 3,04E+06 5,15E+05 2,14E+07 -7,31E+
####### 18 5,39E+05 1,44E+10 3,58E+06 3,04E+06 4,64E+05 2,44E+07 -6,85E+
####### 19 5,39E+05 1,44E+10 3,58E+06 3,04E+06 4,18E+05 2,75E+07 -6,43E+
####### 20 5,39E+05 1,44E+10 3,58E+06 3,04E+06 3,77E+05 3,05E+07 -6,06E+
####### total 1,08E+007 6,07E+007 -6,06E+
Figure 1: NPV calculation.
Wind Energy Exercises Week 7
Kursus: Introduktion til vindenergi (46000)
Universitet: Danmarks Tekniske Universitet
