1. Lecture 4: Energy systems and energy technologies – Focus on economical aspects UNIK4820/ UNIK: 08/ Arne Lind

2. Outline Course content
Part 0: Outline
Outline
Course content
Methodology to assess and compare costs for different technologies
Wind power
Description of costs
LCOE
Learning curve
Hydropower
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3. Part 0: Outline
Course content (1/6)
Lecture 1 (17th of January): Introduction, motivation and the Norwegian energy system
Objective, requirements, learning outcome, course content, etc
Why we use models?
An introduction to the Norwegian energy system
Lecture 2 (25th of January): Energy systems and energy technologies (technology focus)
Electricity production (hydropower, wind power, gas power, etc)
Energy storage and fuel cells
Combined heat and power generation
Lecture 3 (1st of February): Energy systems and energy technologies (technology and economic focus)
Solar power
Nuclear power
Energy storage
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4. Part 0: Outline
Course content (2/6)
Lecture 4 (8th of February): Energy systems and energy technologies (focus on economical aspects)
Investment and operational costs for various technologies
Learning curves, discount rates, economic lifetime, etc
Definition of levelized cost of electricity (LCOE)
Assignment 1 (15th of February): Energy systems and energy technologies (technology and economic focus)
Calculation of levelized cost of electricity (LCOE) for various technologies
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5. Methodology to assess and compare costs for different technologies
Part 1: Methodology
Methodology to assess and compare costs for different technologies
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6. Time points and periods
Part 1: Methodology
Time points and periods
Time points and periods are crucial factors in an analysis
Critical time points in an analysis
Base year: Year to which all cash flows are converted
“Currency” year: Year to which base year results are converted and reported
Investment year: Year in which the actual investment occurs
Important time periods for the analysis
Investment useful lifetime (economic lifetime): Estimate of a particular investment’s useful life
Analysis period: Period of time for which an evaluation is conducted
Depreciation period: Period of time over which an investment is amortised (e.g. for tax purposes)
Finance period: Period of time for which an investment’s financing is structured
Levelisation period: Period of time used when calculating a levelised cash flow stream
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7. Part 1: Methodology
Discount rates (1/2)
Time value is the price put on the time an investor waits for a return on an investment
A dollar received today is worth more than a dollar received tomorrow
The dollar today can be invested to earn interest immediately
A dollar received tomorrow is worth less than a dollar received today
Opportunity to earn interest on the dollar is lost
The discount rate acts as a measure of this time value
Is central to the calculation of present value
Are often used to account for the risk inherent in an investment
The choice of discount rate is important to any economic analysis
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8. Discount rates (2/2) 𝑑 𝑟 = 1+ 𝑑 𝑛 1+𝑒 −1
Part 1: Methodology
Discount rates (2/2)
Analyses can be done by using either current or constant cash flows (in relevant monetary units)
Important to be consistent throughout the analysis
A discount rate is used to calculate the present value of a future payment
Can include the effects of inflation (nominal) (dn)
Excluding effects of inflation (real) (dr)
𝑑 𝑟 = 1+ 𝑑 𝑛 1+𝑒 −1
e = inflation
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9. Present value (1/3) 𝑃𝑉𝐼𝐹 𝑛 = 1 (1+𝑑) 𝑛 𝑃𝑉= 𝑃𝑉𝐼𝐹 𝑛 × 𝐹 𝑛
Part 1: Methodology
Present value (1/3)
Present value is used to calculate today’s worth of a transaction that will occur in the future to account for changing monetary unit variations
Present value is a measure of today’s value of revenues or costs to be incurred in the future
The present value of a dollar received (or paid) in the future can be calculated by multiplying the future cash flow by a present value discount factor (PVIFn)
Used to discount future cash flows back to the present
Present value (PV):
𝑃𝑉𝐼𝐹 𝑛 = 1 (1+𝑑) 𝑛
𝑃𝑉= 𝑃𝑉𝐼𝐹 𝑛 × 𝐹 𝑛
Fn = cash flow n years in the future
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10. Present value (2/3) 𝑃𝑉= 1 (1+𝑑) 𝑛 × 𝐹 𝑛 𝑃𝑉= 𝑛=1 𝑁 𝑃𝑉𝐼𝐹 𝑛 × 𝐹 𝑛
Part 1: Methodology
Present value (2/3)
𝑃𝑉= 1 (1+𝑑) 𝑛 × 𝐹 𝑛
Assume a discount rate of 5% and a cash inflow of 1€ one year from now
PV = 1/(1+0.05) x 1€ = 0.95€
0.95€ is approximately the present value of the future cash flow of 1€
If 0.95€ was invested at a 5% interest rate, it would be worth 1€ one year from now
The same basic formula can be used to evaluate cash flows in any future period or from now to some point in the future
𝑃𝑉= 𝑛=1 𝑁 𝑃𝑉𝐼𝐹 𝑛 × 𝐹 𝑛
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11. Assume a cash flow of 1€ one year from now
And a cash inflow of 5€ two years from now
Annual discount rate of 5%
𝑃𝑉 1 = 1 (1+0.05) 1 ×1= ×1=0.95€
𝑃𝑉 2 = 1 (1+0.05) 2 ×5= ×5=4.54€
These cash flows can be added once they are converted to present value
𝑃𝑉=𝑃𝑉 1 + 𝑃𝑉 2 =0.95€+4.54€=5.49€
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12. Present value (3/3) 𝑃𝑉=𝐹× (1+𝑑 ) 𝑁 −1 𝑑×(1+𝑑) 𝑁
Part 1: Methodology
Present value (3/3)
If future cash flows are fixed in size and occur regularly over a specific number of periods -> Annuity
Formula for present value (PV) of an annuity:
𝑃𝑉=𝐹× (1+𝑑 ) 𝑁 −1 𝑑×(1+𝑑) 𝑁
F = cash flow in each of N future years
d = annual discount rate
If we assume a cash flow of 100€ per year for the next 5 years at a discount rate of 10%:
𝑃𝑉=100× (1+0.1 ) 5 −1 0.1×(1+0.1) 5 =379.08€
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13. Part 1: Methodology
Taxes
Taxes represents additional costs that are no different from other costs
All relevant taxes should be included in an economic analysis
The most complete analysis of an investment in a technology takes into account all costs; including taxes
In analyses from a societal perspective, taxes can be omitted
An analysis could indicate that a given technology is beneficial from society’s perspective
However, tax distortions could prevent that technology from being economically viable from an investor’s viewpoint
In some instances it may therefore be advantageous to analyse a project’s viability both with and without taxes
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14. Methodology and general assumptions
Part 1: Methodology
Methodology and general assumptions
In order to compare energy costs for various technologies it is common to use something called Levelized Cost of Energy (LCOE)
This is the energy cost over the technology lifetime
More precise: The total cost divided by the total production during the technologies’ lifetime
LCOE represents the income or energy costs savings (in e.g. NOK/kWh) that is necessary in order to “break even” for energy production or for energy efficiency measures
LCOE allows alternative technologies to be compared when different scales of operation, different investment and operating time periods, or both exist
LCOE could be used to compare the cost of energy generated by a renewable resource with that of a standard fossil-fueled generating unit
LCOE can also be used for ranking different alternatives
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15. Levelized Cost of Energy (LCOE)
Part 1: Methodology
Levelized Cost of Energy (LCOE)
LCOE = Levelized cost of energy (NOK/kWh)
It = Investment and development costs (NOK)
Mt = Operation and maintenance costs (NOK)
Ft = Energy and fuel costs (NOK)
Et = Energy production (kWh)
r = discount rate (-)
t = Economic lifetime (years)
𝐿𝐶𝑂𝐸= 𝑡=0 𝑛 𝐼 𝑡 + 𝑀 𝑡 + 𝐹 𝑡 (1+𝑟) 𝑡 𝑡=0 𝑛 𝐸 𝑡 (1+𝑟) 𝑡
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16. Part 2: Wind power
Wind power
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17. Wind power: Description of costs (1/2)
Part 2: Wind power
Wind power: Description of costs (1/2)
Wind power requires large investments in connection with the purchase of wind turbines and construction of the plant
Relatively low operating and maintenance costs over the lifetime of a project
Wind turbines account for the greatest proportion of the investment cost
Investment and production costs are very sensitive in terms of fluctuations in wind turbine prices
Distribution of investment costs
5 Norwegian facilities
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18. Wind power: Description of costs (2/2)
Part 2: Wind power
Wind power: Description of costs (2/2)
Project specific costs
Spread in costs between different projects depend mainly on prices of wind turbines, infrastructure and grid connection
Turbine prices are very project specific as the prices often include charges for shipping and assembly of turbines
Power and construction costs are also project specific, and can become much higher for projects on very isolated or hilly places
Operating and maintenance costs for wind power is relatively low compared with many other forms of power generation
Most wind turbines have a certified life of 20 years
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19. 𝐿𝐶𝑂𝐸= 𝑡=0 𝑛 𝐼 𝑡 + 𝑀 𝑡 + 𝐹 𝑡 (1+𝑟) 𝑡 𝑡=0 𝑛 𝐸 𝑡 (1+𝑟) 𝑡
Calculation of LCOE for wind power
Assume investment cost of kNOK/MW
Installed capacity = 100 MW
Operating hours = 3200 hours
Operating and maintenance costs = 150 kNOK/GWh
Economic lifetime = 20 years
Annual energy production of = 100*8.76*(3200/8760) = 320 GWh
Use
𝐿𝐶𝑂𝐸= 𝑡=0 𝑛 𝐼 𝑡 + 𝑀 𝑡 + 𝐹 𝑡 (1+𝑟) 𝑡 𝑡=0 𝑛 𝐸 𝑡 (1+𝑟) 𝑡
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20. LCOE for wind power: Example (1/2)
Part 2: Wind power
LCOE for wind power: Example (1/2)
0.56 NOK/kWh
LCOE = NOK/kWh
Increasing economic lifetime
Decreasing economic lifetime
0.34 NOK/kWh
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21. LCOE for wind power: Example (2/2)
Part 2: Wind power
LCOE for wind power: Example (2/2)
0.64 NOK/kWh
LCOE = NOK/kWh
Increased production
Decreased production
0.31 NOK/kWh
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22. Learning curve Part 2: Wind power LCOE Source: NVE
Investment costs [MNOK/MW]
LCOE
16% reduction in LCOE
20-30% reduction is assumed by IEA Wind Task 26
Source: NVE
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23. Part 3: Hydropower
Hydropower
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24. Hydropower: Description of costs (1/2)
Part 3: Hydropower
Hydropower: Description of costs (1/2)
Hydropower costs are often expressed through the parameter specific development costs
Defined as investment costs divided by the annual production
Expressed as NOK/kWh
Simplified conversion between specific development costs and LCOE for various discount rates:
LCOE
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25. Hydropower: Description of costs (2/2)
Part 3: Hydropower
Hydropower: Description of costs (2/2)
Development costs (in either NOK/kW or NOK/kWh) can vary a lot
Between different power plant types
From project to project
Differences in geographical conditions have a significant impact
Best projects have a cost of 2 NOK/kWh (or lower)
Upper limit for investment: 5 NOK/kWh (rule of thumb)
Operation and maintenance costs are around 1% of the investment, or in the range from 2 to 6 øre/kWh per produced unit
Project specific costs vary mainly due to location specific conditions
The length of the waterway can result in large differences for projects that are otherwise relatively equal (installation, production)
The cost of the waterway can be a relatively large portion of the overall building costs
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26. 𝐿𝐶𝑂𝐸= 𝑡=0 𝑛 𝐼 𝑡 + 𝑀 𝑡 + 𝐹 𝑡 (1+𝑟) 𝑡 𝑡=0 𝑛 𝐸 𝑡 (1+𝑟) 𝑡
Calculation of LCOE for hydro power
Assume investment cost of kNOK/MW (cheap)
Installed capacity = 5 MW
Operating hours = 2400 hours
Operating and maintenance costs = 40 kNOK/GWh
Economic lifetime = 40 years
Annual energy production of = 5*8.76*(2400/8760) = 12 GWh
Use
𝐿𝐶𝑂𝐸= 𝑡=0 𝑛 𝐼 𝑡 + 𝑀 𝑡 + 𝐹 𝑡 (1+𝑟) 𝑡 𝑡=0 𝑛 𝐸 𝑡 (1+𝑟) 𝑡
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27. LCOE for hydropower: Example (d = 0.04)
Part 3: Hydropower
LCOE for hydropower: Example (d = 0.04)
LCOE = NOK/kWh
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28. LCOE for hydropower: Example (d = 0.06)
Part 3: Hydropower
LCOE for hydropower: Example (d = 0.06)
LCOE = NOK/kWh
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29. Economic lifetime and learning curves
Part 3: Hydropower
Economic lifetime and learning curves
Hydroelectric power is (very) reliable
With good maintenance procedures the plants can be in operation for a long period without significant costs or new investments
Upgrading and expansion of existing hydropower plants will increase the production
The most common upgrading measures include increasing the efficiency of the turbine, generator and transformer and reduction of head loss in waterways
Expansion includes increased installation, new transfers and increased magazine capacity
In Norway the typical economical lifetime is 40 years
Hydropower is a (very) mature technology
Learning curves are not suitable to project future energy costs for hydropower
It is common to assume identical cost level in the future
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30. Part 4 : Summary
Summary
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31. Falling costs of renewables
Part 4: Summary
Source: IRENA
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32. Part 3: Hydropower
Assignment 1
Assignment 1 will include further examples of the calculation of LCOE for the following technologies:
Solar PV
Coal-fired power plant
Nuclear
Gas power
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