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 [email protected] Ph 323-258-8883, Mobile 323-839-6108, Fax 323-258-8885
_____ From: [email protected] [mailto:[email protected]] 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
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