[RE-wrenches] Cost per kWh - LCoE

Sun Mar 7 10:23:07 PST 2010

I pretty much agree with what Matt is saying. Here is my take. One can do
the calculation with varying levels of sophistication, and each of us can
draw the line where we want. Matt includes net purchase price (including
finance charges), O&M and increase in property value, and a term of 25
years. However, I would think the increase in property value is not revenue,
unless you actually sell the property, which you might do at the end of the
term, and one should account for its residual value only (e.g. if you take
depreciation). I think Matt's approach gives an approximate number, good for
an initial calculation.

At the other end of the spectrum (the full-up calculation if you wish) is
called Levelized Cost of Energy (Electricity) LCoE, and it includes
everything (trust me). There is a fairly good paper written by Matt Campbell
of SunPower, titled "The drivers of the Levelized Cost of Electricty for
Utility-Scale Photovoltaics". Also the Solar Advisory Model (SAM) offered by
NREL has LCoE built in. Finally if you are doing a PPA or working on a large
commercial project, you have to use LCoE.

One of the interesting aspects of LCoE is the time-rate-of-change of three
important factors: (1) Cost of Money, (2) Utility Rates, and (3) PV
production. This is the aspect that Matt doesn't include in the first-order
calculation.

The first just says that a dollar today is worth more than a dollar you
might receive tomorrow; because you could put it into the bank and earn
interest. Conversely if you have to pay for something, defer making the
payment as long as you can because you will be using cheaper money. To
arrive at this rate you should look at your return on an investment of
similar risk. In the case of PV, I use the 20-year T-bill, which has
historically been under 5%. So if you are calculating future revenues, you
need to discount the revenue in order to bring it back to the present.

The second says that utility rates will go up over time and the energy
produced by a plant is of greater value as time goes on. I use 7% for
southern California (I know it varies with utility, and fluctuates a lot).

The third says that PV production goes down over time. There is a lot of
controversy on this point as to the value of the degradation. NREL (or a
related party) published data to show that the number was close to 0.5%/yr.
This is old data and covered PV modules manufactured in the 60's. More
recent data (based on newer PV modules) suggest that the number is much less
than 0.5%/yr (maybe less than 0.1%/yr).

LCoE should also include depreciation and any repairs not captured under O&M
(e.g. inverter).

The reason I have taken the time this Sunday morning to send this out is to
hook up with other folks who want to develop a working knowledge of LCoE. I
have just downloaded SAM, and it will take me some time to understand how it
works. Maybe an Excel spreadsheet would be a simpler approach. In any event
I am willing to share what I begin to understand with like minded souls
(off-line I guess is the best approach).

And Matt, keep up the good work! Your approach should work for the vast
majority of clients who want to look at the long term economic value of PV.

- Peter

Peter T. Parrish, Ph.D., President
California Solar Engineering, Inc.
820 Cynthia Ave., Los Angeles, CA 90065
CA Lic. 854779, NABCEP Cert. 031806-26
peter.parrish at calsolareng.com  
Ph 323-258-8883, Mobile 323-839-6108, Fax 323-258-8885

  _____  

From: re-wrenches-bounces at lists.re-wrenches.org
[mailto:re-wrenches-bounces at lists.re-wrenches.org] On Behalf Of Matt
Lafferty
Sent: Saturday, March 06, 2010 4:28 PM
To: 'RE-wrenches'
Subject: Re: [RE-wrenches] Cost per kWh

Holt says: Can't put my hands on the equation for determining cost per kWh
of a system

Holt,

Are you looking to calculate Cost or Value of the system? Both calculations
are important.

The simple $/kWh COST for a residential PV System is calculated as follows:
Lifetime $/kWh Cost = (Purchase $ after incentives + Finance Charge $ +
Lifetime O&M $) / Lifetime kWh Generated
Example: A system that has a capital cost of $20,000 including finance
charges generates 150,000 kWh over its 25 year life. The O&M costs over the
same period total $5,000, for a Total Cost of $25,000. The Lifetime Cost of
the electricity generated = $25,000/150,000 kWh = $0.1667/kWh.

The Net $/kWh VALUE for a PV System includes some other factors, which will
vary on a system-by-system basis. The driving element here is the $/kWh of
the Offset Utility Energy. This is, after all, the comparative value of the
energy in the first place. I also believe that the net-change in value of
the property is valid to consider. I don't like all the BS mumbo jumbo about
NPVs and wild-ass guesstimates about the cost of money at arbitrary points
in the future and whether or not the inflation rates of electric rates will
be higher or lower than $ deflation rates in a given time period and only if
the customer turns 65 during the life of the system and due to divorce in
Year 11 the customer's effective tax rate changes and...... Screw that. My
crystal ball ain't that good. It is what it is. 

Calculate the VALUE of the PV System in $/kWh as follows:
Net $/kWh Value = ((Offset Utility Energy $ + Net Change Property Value $) -
Total Cost) / Lifetime kWh Generated
Example: A system generates 150,000 kWh over its 25 year life. The Offset
Utility Energy $ is $27,000 and the Net Change in Property Value is $10,000.
The system has a Total Cost of $25,000. The Net Value of the electricity
generated = (($27,000 + $10,000) - $25,000) = $12,000. The The Net $/kWh
Value = $12,000 / 150,000 kWh = $0.08/kWh.

Two of the biggest underlying factors are the assumed Service Life of the
System in Years and the O&M costs during that period. Like I said, my
crystal ball ain't that good. I can share that 

Hope this is helpful,

Matt Lafferty

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.re-wrenches.org/pipermail/re-wrenches-re-wrenches.org/attachments/20100307/075e2926/attachment-0004.html>