1. Solar Energy Commercialization Application to PV Systems
SEC598S18
Solar Energy Commercialization
Session 17
Economic Analysis
Application to PV Systems
March 13, 2019

2. Session 17 - Learning Outcomes
An understanding of essential economic considerations as applied to PV systems, including:
Present Worth calculations
Life Cycle Costing
Levelized Costs

3. Class Components Interesting youtube video Economic Analysis
Economic Analysis
Present Worth Factors
Life Cycle Costs
Levelized Costs
LCOE
LCOS

4. Economic Analysis
The following considerations form the basis of an economic analysis appropriate to PV commercialization:
What is the initial cost of the system?
What are the maintenance costs?
What are the component replacement costs?
What incentives are available?
What will be the cost of electricity?
Should the money to fund the project be borrowed?

5. Economic Analysis Issues to grasp: The Levelized Cost of Storage
Life Cycle Costing
Apart from the initial construction cost, LCC analysis takes into account all the user costs and agency costs related to future activities, including future periodic maintenance and rehabilitation. All the costs are usually discounted and totaled to a present day value known as net present value (NPV).
The Levelized Cost of Electricity (LCOE)
The Levelized Cost of Storage

6. Value to class members
The Levelized Cost of Electricity (LCOE) is extensively employed in the energy industry, as it is used to compare costs among energy sources, or to compare the cost of energy from variations in the same technology.
The Levelized Cost of Storage (LCOS) is a recently proposed adjunct to the LCOE to consider the costs and impacts of battery and other storage options in PV systems.

7. Economic Analysis Time Value of Money
The value of money at a future point of time would take account of interest earned or inflation accrued over a given period of time. This notion exists both because there is an opportunity to earn interest on the money and because inflation will drive prices up, thus changing the "value" of the money.
Put money (N0) in a savings account that pays an annual interest rate of d. In Economics 101 this is called the “discount rate”:
Albert Einstein is reputed to have said: “The most powerful force in the universe is compound interest”

8. Economic Analysis Time Value of Money
Now consider the initial price of an item (C0) in an economy subject to an annual inflation rate of iINF. Inflation reflects an annual devaluation of purchasing power (i.e., annual increase in item price)
Interesting economic decision presents itself: if the cost of an item increases at a rate that exceeds the rate of saved money, maybe the item should purchased right away. But if the item cost decreases with time (deflation), should one delay the purchase? Maybe not – the use of the item is postponed until purchase!

9. Economic Analysis Present Worth
Now consider the case when C0 equals N0. Then the following factor emerges:
The quantity FPV is the Present Worth Factor, and of course, can be used to calculate this quantity:

10. Economic Analysis Present Worth
The Present Worth Factor, FPW, is given by:
And the Present Worth (PW) is the amount of money needed at the present time (invested at d) in order to purchase an object at a future time (with inflation rate of iINF)

11. Economic Analysis Present Worth
Note: If there is no inflation, or if the impact of inflation is not included, then the Present Worth Factor at the nth year becomes:
And the annual PW factor is then:
This is sometimes called the discount factor

12. Economic Analysis Life-Cycle Cost
Here is a webpage that shows the US inflation rate in the recent past:
And for discount rates:

13. Levelized Cost of Electricity
LCOE is defined as an energy source’s total lifetime cost of operation divided by the total lifetime energy production:
Its main function is to provide a way to compare the relative cost of energy produced by different energy-generating sources regardless of project scale or operating time frame
Note: LCOE is a metric with units $/kWh

14. LCOE Rewriting the previous equation
Both sides of the equation have the units of $ - the left side is the value of the energy generated and the right side is the total LCC – so both must be present worth calculations:

15. LCOE
Rearranging these equations

16. LCOE
Rearranging these equations, using discount calculation only:

17. One LCOE Resource
“Levelized Cost of Electricity,” T.Yates & B.Hibberd, in SolarPro, V5N3, April/May 2012

18. LCOE factors Costs Incentives Energy
Initial investment or capitol cost
O&M costs
Financing costs
Insurance costs
Taxes (County, State and Federal)
Return on Investment
Decommissioning
Incentives
Tax credits (State and Federal)
Depreciation (MACRS)
Incentive revenue
Energy
Estimated year one production
Annual degradation
System availability

19. LCOE Expanding the previous equation where: I = Initial capital cost
D = Depreciation
T = Tax rate
O = Annual operating cost (O&M, loan payments, insurance, etc.)
R = Incentive revenue
S = Salvage value
Q1 = Year one energy production
d = Degradation rate

20. LCOE Effect of location
Yates & Hibbard also analyze other factors, inside one technology:
Effect of location

21. LCOE
In the paper by Yates & Hibbard, then LCOE calculation is used to analyze and predict the LCOE for future power –plants

22. LCOE
A more recent calculation by First Solar shows
$/kWh

23. LCOE
Sensitivity to factors in the equation

24. LCOE
Effect of module cost and degradation rate

25. LCOE There are some limitations to the value of LCOE calculations
It calculates energy value in the analysis period, but does not calculate how valuable the power is. This can be an important factor with time variable energy sources
A project with a lower LCOE is not necessarily the preferred project. It is a good macro-perspective design tool, but not always the most useful when making decisions about a specific project

26. Payback
The numerator of the LCOE equation can be examined alone, to help estimate the payback period for a PV system
But if various factors turn on (or turn off) at different times, then the equation has to be modified.

27. One LCOS Resource
M.B.Krause & D.Brearly, “Economics of Residential Energfy Storage,” SolarPro, V9N4, July/August 2016

28. Energy Storage Applications
Uses
Backup power (uninterruptible power supply)
PV self-consumption (zero-export)
Time-of-use (energy arbitrage)
Demand reduction (peak shaving)
Ancillary services (power factor, load following, etc)

29. Levelized Cost of Storage
LCOS is defined as a storage system’s total lifetime cost of operation divided by the total lifetime use and cycling practices:
Its main function is to provide a way to compare the relative cost to store energy produced by different storage means to retail electricity prices
Note: LCOS also has the units $/kWh

30. LCOS factors Costs Incentives Use and Cycles
Initial installed cost of storage system and associated power electronics
O&M costs
Financing costs
Insurance costs
Taxes (County, State and Federal)
Return on Investment
Salvage
Incentives
Tax credits (State and Federal)
Depreciation (MACRS)
Use and Cycles
Usable capacity
Cycles
Efficiency

31. LCOS Expanding the previous equation where: I = Initial capital cost
D = Depreciation
T = Tax rate
O = Annual operating cost (O&M, loan payments, insurance, etc.)
R = Incentive revenue
S = Salvage value
C1 = Year one energy storage capacity
N = Number of cycles
h = Efficiency

32. LCOS Effect of System Cost and Capacity
Krause and Brearly examine a Tesla Powerwall system
Effect of System Cost and Capacity

33. LCOS
Krause and Brearly also consider this battery degradation timeline

34. LCOS
Krause and Brearly also examine an Adara battery system
Effect of Cycling

35. LCOS sonnenBatterie guarantees its eco-series:
“10,000 cycles or 10 years”
For one daily cycle (charge-discharge) would produce 3650 cycles in 10 years – so 2.7 cycles/day required to get to 10,000 cycles in 10 years
So the battery system has to be deployed to provide more than one service – application stacking

36. LCOS
Application Stacking

37. Additional Reading
Lazard, “Lazard’s LCOS Analysis, Version 3.0”, November 2017, lazard.com Rocky Mountain Institute, “The Economics of Battery Energy Storage,” October, 2015, rmi.org Other references listed on class webpage