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By Alfonso Velosa III, Research Director at Gartner and Manhal Aboudi, Principal at Solar Consulting Center
Investors in the PV solar industry have worked to properly understand
and price their solar projects, and thus determine the return on their
investments. The PV solar industry has responded by moving the pricing
discussion from a capacity basis to an energy generation basis. IE they
have moved from a cost per watt conversation to a cost per
kilowatt-hour. The cost of this energy generation is usually represented
by an estimated "levelized cost of electricity" or "LCOE". Yet, since
the real purpose of the LCOE is to help price projects, it helps to be
clear on what assumptions to have built into your LCOE. Otherwise, you
may not have properly calculated your cost versus revenues or understood
the magnitude of the margin of error in the LCOE estimate. And this
will not just damage your portfolio - it will damage your reputation.
Levelized Cost of Electricity Formulas: Fancy Formulas for Simple Summations
In order to understand your LCOE, it is always a good idea to go back to
basics. The basic formula to determine your LCOE starts with equating
your costs and revenues. This can be represented in the simple formula
below.
Cost structure = electricity output * cost of electricity
Therefore the cost of the electricity of your LCOE can be defined as:
LCOE = (Cost Structure / Electricity Output)
Now let us clarify what is in the denominator and in the numerator.
Don't get scared by the following formulas. All they really show is
that you have additions over time. Then you factor the time period by
bringing it to the present value - that is what these slightly fancy
equations are meant to show you:
Your cost structure is defined as incorporating your project cost plus
the present value of your annual operations (AO) expenditures and
subtracting the present value of any residual value (RV) for the solar
system, all of this based on your discount rate (DR).
Your electricity output would be defined as the present value of the
kilowatt hours of your system based on the insolation of your region and
the thermal and the DC-to-AC derating of your specific system
multiplied by the expected annual degradation of your system. If you
want to get really fancy you can factor in an uptime factor to reflect
your assumptions on what fraction of the time your system is actually
"up" and generating electricity.
It is important to have these two elements clearly defined, since this
is where most of the assumptions that sales and marketing personnel make
are incorporated. Or as the case may be - not incorporated. Let us look
at 2 examples of LCOE formulas and the estimates you get from these
formulas.
Basic LCOE Formula
Starting from our defined elements, we can translate all this into a formula so that we can calculate our cost of electricity:
This looks pretty straightforward and you can construct a straightforward spreadsheet model to calculate it.
Leveraged LCOE Formula
Yet it is too simple. For example, does the annual cost incorporate
anything beyond maintenance and monitoring? Is insurance included?
Does it contain a factor for eventual inverter replacement cost? What
about the financial and tax factors such as depreciation, interest?
Thus we can take the basic calculation and make it a bit more complex by
addition these factors and you get the following formula that we used
to build our spreadsheet:
| LCOE = Levelized Cost of Electricity |
AO = Annual operations costs |
DEP = Depreciation |
| PCI = Project Cost minus Investment Tax Credit |
RV = Residual Value |
LP = Loan Payment |
|
DR = Discount Rate |
INT = Interest Paid |
|
TR = Tax Rate |
N = Number of years for system |
Now your cost structure incorporates your cost after the investment tax
grant minus the present value of your residual value plus the present
value of several factors. These factors include subtracting the tax
benefit of your depreciation, adding the loan payment if you finance
part of your system, subtracting the tax benefit of your interest, and
finally factoring in all your annual costs after you account for the tax
benefit they provide you. We would still use the same electricity
output formula.
Case Study: Proposed Plant for Austin Energy
So far all of this has been a rather academic exercise. It is a bit more
interesting if you start to use some of the proposed projects out there
and figure out the potential LCOE of a system. What we will show next
is an analysis that we have done of the project Gemini and Austin Energy
are working on. Figure 1. Assumptions for the analysis of a PV System
in Webberville, Texas
Assumptions
30 MW AC System - derated to 35 MW DC
Installed system cost - $4/w for a total of $141 million
30% tax grant cuts costs to $99 million
Tax benefits based on 30% tax rate
Single Axis Trackers
Austin Energy provides land
O&M cost - $4.6/panel (includes insurance) with a 4% cost escalator
Discount rate - 8.1%
Solar RECs sold at $15/MW
Sunlight hours / year - 2000
Initial KWh per year - 60 million
Annual degradation - 0.5%
Figure 1 Source: Estimates by solarconsultingcenter.com. Please note that these are our assumptions and should not be considered to be data from the firms referenced.
Calculating the estimated LCOE for this installation based on our assumptions we get two results:
Basic Model: $0.12 per kWh
Leveraged Model: $0.08 per kWh
This gives you an idea of how broad the range can be for estimates on
LCOE. This can be further tweaked by the modeler based on the factors
they have incorporated into the model. In particular, if they are
optimistic and use ideal conditions of insolation, uptime and limited
degradation, you can get very low estimates that may not align with
reality. Keep in mind the following things based on this analysis:
Depending on the formula you pick, you can get a broad range of LCOE estimates
Your starting assumptions are hugely critical factors for your LCOE estimates
You do not get the margin of error for the LCOE estimate from this formula
Most importantly - this is just an estimate
Sensitivity Analysis of this Case Study
A simple sensitivity analysis strongly reinforces the central point that
this is an estimate. Keep in mind for this graphical analysis is that
some things you can control and some things you cannot. Below we have
the leveraged LCOE for a scenario where you control the factors - IE the
price you pay for a system, and then 2 scenarios where you only have
limited control - IE system performance in the field. Figure 2.
Leveraged LCOE Sensitivity Analysis for Three PV System Factors
Source: Estimates by solarconsultingcenter.com. Please note that
these are our assumptions and should not be considered to be data from
the firms referenced. Also note that Leveraged LCOE is charted on the
y-axis with a range of $0.07 to $0.09 per kWh.
The first graph of Figure 2 is pretty straightforward. Assuming that the
quality of the PV system is the same for all cases, the LCOE should
decrease as system cost decreases.
The next two graphs start to show us some of the complications for the
LCOE analysis. For higher insolations, you get more electricity output
so your LCOE will be lower. For higher levels of panel degradation, you
will get less electricity output and thus a higher LCOE.
The insolation of any particular site should average out to a steady
state over the long term. Yet in the short term, you can get very
significant variations that can affect your energy output and thus your
revenue stream. They may not be as extreme as these show on the second
graph, but you will need to consider it. The commercial activity in your
neighborhood may end up throwing extra dirt or soot on your system and
impairing its performance. Panel mismatches may drag down the output of
your system. Plus your panels may have a sharp degradation spike in the
first year or two of performance, with a low degradation in the out
years. Operations, maintenance and monitoring are critical for ensuring
your LCOE is tracking your estimates.
Again, this is a simple analysis that does not capture the reality in
field. But then - an LCOE estimate is based on a simplified set of
factors.
Conclusion - Beware the Assumptions in the PV Industry
In today's PV market, everyone you talk to tells you stories based on
their LCOE. System owners brag about their LCOE. Start-up thin-film PV
firms and microinverter firms will tell you about their calculated LCOE.
When you hear them, you need to ask yourself:
What assumptions did they factor in and what did they exclude?
Did they factor in all the degradation / uptime /other issues?
Are they dealing with real or nominal dollars?
Do you want to factor in the sale of s-RECs as part of the
calculation of your LCOE, or just factor it in afterwards in your ROI
analysis?
What is the margin of error of this estimate?
Your due diligence on any project should include an analysis of both the
cost of the capacity - IE the cost per watt peak for the installed
system - and the cost of the energy output - IE the LCOE of the system.
Revisit the assumptions for the LCOE of any PV solar project you look
at. Any of the formulas for calculating LCOE are useful since they help
you compare your system to other PV systems as well as average utility
rates. For example, the basic formula may apply if you have sold all
your tax benefits to investors and just want to deal with nominal 2010
dollars. After all, you can subtract the sale of the tax benefits from
your cost and proceed with your analysis.
Once you take the time to properly factor the assumptions built into a
vendor's or investor's LCOE estimates, you can start to parse the risks
on the rate of return for a project, and how realistic the assumptions
were. And this is the most critical step you can take to maintain your
reputation. |
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