Solar payback assumptions

[sensij]

It isn't that I can't follow SAM's LCOE calculations... they helpfully make a spreadsheet available that details the calculations

The problem is that the calculations they are performing are gobbledegook.

One thing they do is apply a time value to energy. They discount the actual energy used 5 years from now, as though energy and dollars are the same thing. They are not. Dollars are subject to inflation, energy is not. Dollars can be invested elsewhere with a projected return, energy can not. By discounting the energy, the denominator in the (Total dollars) / (Total Energy) is reduced relative to straight addition, which increases the apparent LCOE.

Even worse, they don't keep the discount rate constant between dollars and energy. In "Real LCOE", they discount the energy by the real rate, but discount the dollars by the nominal rate.

Also, the SAM method doesn't take into account the energy you still need to buy from the utility, it is only calculating LCOE of the production from the PV system. You would need to replicate the calculation for the energy and costs associated with the utility portion of the usage, and make sure you do it with the same weird discounting equations or else it is not an even comparison. Finding "grid parity" is an interesting goal, but I'd would argue the method I described in my previous post helps you minimize overall LCOE, which seems to me to more directly capture the intent of a solar installation.

[J.P.M.]

1.) While I agree that the concept of LCOE is straightforward, I've found that like many things, the devil is in the details.

2.) Those details can be, depending on user inclination, quite complicated. I've done the SAM LCOE calc's by hand following along and using SAM's logic and methods and they seem straightforward if cumbersome and somewhat iterative at times. Others may have different opinions.

3.) Some of the difference between your analysis and SAM's method may be in the utility rates and rate structure. Some in the rates of energy cost inflation vs. general inflation which can affect the discount rate. Lots of other sources as well.

4.) There is an NREL manual: NREL/TP-462-5173. It covers a lot of pertinent stuff much too lengthy for this forum. Download it or find it through SAM's help screens. I don't agree with all of the applications, but they seem logical and probably as good as any for the purpose.

5.) Given the uncertainty introduced by guessing at future conditions and, similar to compound interest calc's where a small change in initial conditions can have a large effect over time, process economics and life cycle costing calc's, while usually necessary and useful, are still a guess and may be most useful in comparing alternatives when making decisions. I'd suggest being careful to remember the sensitivity to initial assumptions, and that probability of predictions being off increases as f(length of analysis). As you allude, parametric analysis can often help identify sources of uncertainty, or probabilistic ranges for rolling the decision dice.

6.) To your points about the NREL LCOE calculator or other questions you ask:
IMO, the NREL LCOE calculator is not a bad 1st shot provided the instructions are followed. I referenced that more as one of my examples why I questioned your LCOE's of ~~ .025/kWh than a comparison to SAM's or other process costing methods.
The analysis period I use for my system is 12 years. PM me if you want the gory details. FWIW, the rest of the SAM analysis using my assumptions seems to match reality to a fair degree, at least for the 1st year - whatever that means.

[sensij]

Running my system w/ SAM gives me a real LCOE of about $.194/kWh.

I'm finding that I don't understand SAM's LCOE calculation. LCOE should be straightforward...

LCOE = (total cost of energy) / (total energy)

What makes it slightly more complicated is that since the costs occur over a number of years, they should be discounted to present value.

For example, in the 11500 kWh / yr test case we've been using, you get the following annual costs without solar, assuming 2.5% cost increase per year for inflation:

0---0
1---3333
2---3416
3---3501
4---3589
5---3679
6---3771
7---3865
8---3961
9---4061
10--4162

Applying a 6% discount rate to that gives a net present value of $25620.
The total energy over 10 yrs is 11500 * 10 = 115000 kWh.
Levelized cost of energy = $25620 / 115000 kWh = $0.223 / kWh.

Now, SAM and I pretty much agree on the savings each year due to solar with the 6.9 kW system. The new annual electric costs look like this:

0---25530 (system cost)
1---(7555) (tax credit + 1st years bill)
2---107
3---122
4---138
5---155
6---172
7---190
8---209
9---229
10--249

Using the same 6% discount rate gives a NPV of $18376.
Levelized cost of energy = $18376 / 115000 kWh = $0.160 / kWh.

Note that in this particular case, the LCOE could actually have been reduced slightly to $0.154 / kWh by installing only 20 panels, instead of 23. I guess if you knew for sure you had a 10 year horizon, and agreed with all of the other assumptions, that would be optimum. For me, who would personally have a more optimistic outlook, the 23 panel system covering close to 100% of usage looks awesome.

Note that installing a system that covered only the Tier 3 / Tier 4 power would also be slightly sub-optimal over 10 years. That would be a system supplying about 7000 kWh, or around 14 panels, and would have an LCOE of $0.159 / kWh.

So this has been a dive into the weeds, but I think this supports the idea that sizing only for Tier 3/4 power in San Diego is optimal in only a narrow set of assumptions that require a short time horizon and a pessimistic view of the economics of solar (IE, utility electric rates won't increase faster than inflation).

In other parts of the country, with cheaper electricity and less direct sun, the math will definitely be different.

[sensij]

Are you sure about that? http://www.sdge.com/clean-energy/ove...view-nem-rates didn't say TOU has to be commercial. When I put up the solar I talked to SDGE and was told I could pick either EV-TOU2 (since I already have an EV) or DR-SES (which is TOU), unless they changed it. You might want to call and verify. TOU makes solar even more valuable, but the calculation is more complicated.

Yeah, you're right... I hadn't looked at DR-SES, which is available to net metering solar customers. Even without solar, I think we can expect to see TOU plans available sometime next year. DR-SES has a multiplying factor of about 1.5X between off-peak and on peak which seems less generous than other TOU plans I've seen talked about here. However, every little bit helps, and for someone who does not heavily use peak power, it seems like it could be a nice way to get more value out of a smaller system.

[thejq]

As far as I can tell, TOU is only available from SDG&E for EV and commercial customers at this time, although it will be made available to all residential next year.

Are you sure about that? http://www.sdge.com/clean-energy/ove...view-nem-rates didn't say TOU has to be commercial. When I put up the solar I talked to SDGE and was told I could pick either EV-TOU2 (since I already have an EV) or DR-SES (which is TOU), unless they changed it. You might want to call and verify. TOU makes solar even more valuable, but the calculation is more complicated.

[sensij]

I've corrected the decimal point error that creeped in when I copied the results over, but otherwise, I think the results are correct. As far as I can tell, TOU is only available from SDG&E for EV and commercial customers at this time, although it will be made available to all residential next year. The analysis is sensitive to any of the assumptions, including the rate plan.

Just to clarify, although I reported the Tier electric rates as averages, I actually used monthly rates representing summer and winter generation typical for my rate plan. Also, the solar generation was modeled monthly based on PVWatts expectations for a south facing unshaded system in San Diego.

I will also model this test case in SAM to see how it compares, but I like to start with a spreadsheet where I have more visibility of how the calculations are being performed. There are some formatting things to clean up, but I could share the spreadsheet if requested.

The NREL LCOE calculator has a lot of factors involved that aren't relevant for residential calculations, so I have avoided it. When you calculate LCOE with SAM, what analysis period are you using? LCOE is totally dependent on the time period over which the costs are being levelized, which is why I explored that parametrically here.

[J.P.M.]

I'm not sure I understand some of your #'s, particularly the LCOE's given.

While I haven't done my own est. using your assumptions, if I understand correctly what you are saying, I'm not sure I'd come up with an LCOE of around $.025/kWh.

Running my system w/ SAM gives me a real LCOE of about $.194/kWh.

The NREL LCOE calculator with your data as input for 20 yrs. gives an LCOE of $.204/kWh using what may be a somewhat generous capacity factor of 18%.

I won't take a whole lot of issue with your annual bills or using constant usage except to comment that they're probably OK to use as long as you keep in mind that there are winter and summer rates, 4 climate zones, and basic and "all electric" rates which all in all allow for 16 different annual bills for a particular annual usage. And that's for tiered schedule only, not T.O.U.

[sensij]

The responses in this thread were interesting enough that I went through a somewhat more involved thought experiment. I used Slopoke's system as test case, since it seems typical for a higher tier user. For power each month, I scaled my own data to achieve the right annual usage.

Here's the assumptions:
1) Annual usage is constant at 11505.5 kWh
2) Tier 1: 0.156 / kWh, Tier 2: 0.18 / kWh, Tier 3: 0.36 / kWh, Tier 4: 0.38 / kWh
3) Electricity price inflation: 2.5% / yr
4) Tier thresholds are based on data from my own bills
5) Panels - 300 W, up to 23 installed at $3.70 / W (this obviously wouldn't hold if only a couple panels were installed), less 30% federal rebate
6) Panel degradation, 97% after year 1, 0.7% / yr thereafter (matching LG 300 datasheet)
7) Discount rate: 6%
8) Assume the installation has zero value to a future buyer. In words, all payback stops at the time the house is sold.

With these assumptions, I came up with a current annual electric bill of $3333. Yikes!

Next, I calculated the LCOE ($ / kWh) over time periods from 1 year to 20 years, assuming the house was sold in that year, and using NPV to keep all costs in today's dollars. Note that this has the effect of reducing LCOE when longer time periods are considered, because the discount rate used is higher than inflation. For each end year, I found the number of panels that minimized the LCOE over that period.

First column is the year the house is sold.
2nd column is the LCOE if solar wasn't installed
3rd column is the minimum LCOE with solar
4th column is the number of panels installed in year 0 to get that minimum

1---0.26---0.26---0
2---0.25---0.25---0
3---0.25---0.25---0
4---0.25---0.25---0
5---0.24---0.24---6
6---0.24---0.22---11
7---0.23---0.20---13
8---0.23---0.18---16
9---0.23---0.17---18
10--0.22---0.15---20
11--0.22---0.14---21
12--0.22---0.13---22
13--0.21---0.12---23

In other words, under these assumptions, installing solar that covers close to 100% usage is the optimum solution only if the house will not be sold for 13 years. If the house would be sold in 5 years, might as well not install solar at all.

I've tried in these assumptions to create the *least* convincing case for solar that I could. Many people might have assumptions that are more optimistic, and that could change the results significantly. However, I think I understand better now some of the arguments that have been used to caution against over-installing.

[inetdog]

And if you lose track of this thread and want to find the calculator later, you will find a banner ("FREE SOLAR CALCULATOR") linking to it on every forum page (as long as you do not use an ad blocker in your browser.)

[solar pete]

Solar Payback Calculator

Hey guys there is a good tool that you can use to run solar numbers its the free solar calculator on the front page of the forum.
It is the leading solar payback calculator in the US. Once you enter your zipcode, utility and power bill it tells you how much solar you need to wipe out your bill. It also shows the rebates and incentives that are available in your area and your payback period (or return on investment)

[J.P.M.]

Lots to consider.
Some thoughts:
1.) If the latest rate of solar installs in the SDG & E service area were to remain constant, the 5% NEM cap will be reached in about 33 months. As things ramp up I'd SWAG that down to 18 to 24 months. The 30% fed. tax credit will expire 12/31/2016 unless changed by legislation.

2.) NPV is one way to look at costs. I'd favor LCOE as a more useful tool although both and indeed all other methods of life cycle costing and process economics are SWAGs with a lot of sensitivity to assumptions about the future - something most people are unaware of or forget.

Depending on how you guess(ed) costs, both present and future rates of increase and tier (re)structure (or T.O.U.), provided any solar ( the 1st Watt installed ) has an LCOE less than the LCOE of the highest tier (last) kWh you buy, ramp up the solar size, bringing down the LCOE until it equals the LCOE of the last kWh bought for that largest system size. That's one way to estimate the most cost effective system. If the solar LCOE/kWh is higher than your highest POCO LCOE/kWh, solar is not cost effective under your assumptions.

3.)The mandates of AB 327 as regards rate restructuring will change a lot of the assumptions used in this thread. One of the bills purposes is to do some rate leveling. There may be 2 tiers, or more. What looks to be the thinking at this time, and as the bill at least strongly implies is that lower tiers are increasing and upper tiers are coming down.

[JCP]

For us, if we did not break out of tier 2, we would not have looked into solar. We average 11,500 or so kWhs per year and get into tiers 3 and 4 most months. Using this forum for my research, I used PVWatts as the calculator and with the numbers it spit out, it estimated that we needed a 6.9 kW system to offset around 80% of our usage. Getting bids for the system configuration that we wanted and armed with the price per watt I felt comfortable paying using the CSI data, we pulled the trigger at $3.70 per watt. With that, our estimated break even was just under 7 years. PVWatts was a little conservative on the production and it looks as if our system might offset almost our entire annual consumption and our adjusted break even point will be a few months less than anticipated. All of our calculations were based on todays actual costs and the tax credit, no inflation or other factors were used.

One of my neighbors did a lease three years ago with a system real close to what we were looking at and he showed me their numbers when I was doing our price research. Well, their lease over 20 years will be $71,000 in money just to the leasing company, plus the cost of electricity from PG&E. Roll the time forward to a few months ago, one of my coworkers did a zero out of pocket lease and the cost of any electricity they will use is 15 cents per kWh, big difference in prices!

Most likely, tiers 3 and 4 will go away. Tier i and 2 will go up though.

Currently, with a decent roof exposure, the Fed tax credit and not taking into account the time value of money, your average installation will produce electricity at 10 cents a KWh over the next 20 years. With net metering, it's a no brainer in CA. Fast forward a few years, and without net metering or Federal tax credits, it's going to be tough slogging go forward unless costs go down another 30%.

[slopoke]

Really, I'm honestly trying to understand why some believe the average homeowner in San Diego, with Tier 2 usage, should not see going solar as economically beneficial. If I've misunderstood the advice given in other threads, or am making bad assumptions, please set me straight.

For us, if we did not break out of tier 2, we would not have looked into solar. We average 11,500 or so kWhs per year and get into tiers 3 and 4 most months. Using this forum for my research, I used PVWatts as the calculator and with the numbers it spit out, it estimated that we needed a 6.9 kW system to offset around 80% of our usage. Getting bids for the system configuration that we wanted and armed with the price per watt I felt comfortable paying using the CSI data, we pulled the trigger at $3.70 per watt. With that, our estimated break even was just under 7 years. PVWatts was a little conservative on the production and it looks as if our system might offset almost our entire annual consumption and our adjusted break even point will be a few months less than anticipated. All of our calculations were based on todays actual costs and the tax credit, no inflation or other factors were used.

One of my neighbors did a lease three years ago with a system real close to what we were looking at and he showed me their numbers when I was doing our price research. Well, their lease over 20 years will be $71,000 in money just to the leasing company, plus the cost of electricity from PG&E. Roll the time forward to a few months ago, one of my coworkers did a zero out of pocket lease and the cost of any electricity they will use is 15 cents per kWh, big difference in prices!

[sensij]

I'd like to say I'm more of a logic enthusiast. I'm talking narrowly about the financial justification for solar here, I haven't done enough research on the other aspects to be confident. For example, is the environmental aspect truly net positive? Making all those panels and inverters surely involves some nasty chemicals and emissions, and requires energy. How does that compare against what a clean burning power plant would produce? A true solar enthusiast might know, but I don't. It is good that there are people trying to figure it out.

To your other point, maybe my error is in overestimating the value of solar in a home sale. Requiring a breakeven NPV of 7 years (or less) makes a lot of sense if the new buyer is unwilling to pay for the electric production capacity. Buyers definitely *are* willing to pay for the revenue stream a rentable in-law apartment might produce, but solar is barely moving out of niche here and may not yet be fully appreciated. The real estate market here is so dynamic, it is hard to predict how solar will be seen in the future. Based on how many of my neighbors seem aware of it and interested in installing systems, I'm optimistic about the long term asset value.

I am definitely not saying that anyone in the forum is trying to steer people wrong. In fact, I like this forum because it seems to have more thoughtful analysis than many others. I'm just trying to bridge the gap between my understanding and theirs.

[thejq]

Really, I'm honestly trying to understand why some believe the average homeowner in San Diego, with Tier 2 usage, should not see going solar as economically beneficial. If I've misunderstood the advice given in other threads, or am making bad assumptions, please set me straight.

You definitely sounded like a solar enthusiast. I'm with you. I wish everyone who can afford it should have it. It's good for the environment, our children, and by extension their children etc. But the matter of fact is that most people can't plan 10-15 yrs in advance. There was a statistics (can't remember when) that people in CA on average stay in their home for 7 years. That's why 5,7 ARM was so popular. So it's easier to suggest ROI that fits that time frame, and the only way it can happen is to assume Tier 3 or 4. Because solar is so new, price will drop in the long term and sizing is very personal, it's hard to estimate its value when you're selling your house. But as the end consumer, it's import to take those expert advice and apply it accordingly to your objectives and not blindly. Personally I don't think any expert here is trying to steer people in the wrong direction.