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

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

Class Components Interesting youtube video Economic Analysis   https://www.youtube.com/watch?v=KjIiTjs2fjw Economic Analysis Present Worth Factors Life Cycle Costs Levelized Costs LCOE LCOS

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?

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

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.

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”

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!

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:

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)

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

Economic Analysis Life-Cycle Cost Here is a webpage that shows the US inflation rate in the recent past: http://www.usinflationcalculator.com/inflation/current-inflation-rates/ And for discount rates: http://www.bankrate.com/rates/interest-rates/federal-discount-rate.aspx

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

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:

LCOE Rearranging these equations

LCOE Rearranging these equations, using discount calculation only:

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

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

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

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

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

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

LCOE Sensitivity to factors in the equation

LCOE Effect of module cost and degradation rate

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

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.

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

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)

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

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

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

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

LCOS Krause and Brearly also consider this battery degradation timeline

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

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

LCOS Application Stacking

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