Solar payback assumptions

[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]

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.

[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]

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.

[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.

[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]

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.]

Opinions vary. I think it does a decent job. Not perfect, but then not much is. Explanations could be a bit more forthcoming, there is a land mine or two in there and some results are squirrely for reasons unclear. But, I've found my patience usually rewarded and there is always Paul Gilman at NREL.

[sensij]

J.P.M. was kind enough to share some of his system data and SAM analysis he used when evaluating solar, so that the calculations could be reviewed with a known set of assumptions. Those assumptions are:

1) 5.232 kW system (16 x Sunpower 327 with 5 kW inverter)
2) First year production set to 9389 kWh (predicted in SAM)
3) 0.4% annual degradation (Sunpower is better than most panels)
4) $4.50 / W installation cost (pre-incentive)
5) 30% federal tax credit + $912 state rebate (CA state rebates are no longer available for residential customers)
6) SDG&E Inland All Electric DR rate schedule ("All Electric" allows much higher baseline usage in winter for heating), September 2013 pricing
7) Annual usage of 10307 kWh, seasonally distributed to yield $0.21776 / kWh average cost.
8) Total electric rate inflation of 3.08% (2.33% base inflation + 0.75% electric rate inflation)
9) System is purchased cash, not financed or leased
10) Nominal discount rate of 6% (for zero-down financing, it would be reasonable to use the loan APR).
11) Analysis period of 12 years
12) Asset value of the system is zero at the end of the analysis period
13) Effects on assessment and property taxes are ignored.
14) Nothing is spent on maintenance.

With these assumptions, the following table can be built:
1st column = year
2nd column = cost of electricity without solar
3rd column = cost of electricity with solar
4th column = amount saved by solar


0_____________0____23572____(23573)
1__________2244____(7802)_____5558
2__________2313______186_____2127
3__________2384______189_____2195
4__________2458______193_____2265
5__________2533______197_____2336
6__________2612______200_____2412
7__________2692______204_____2488
8__________2775______207_____2568
9__________2860______211_____2649
10_________2948______214_____2734
11_________3039______218_____2821
12_________3133______221_____2912
____________________________$3939 = NPV of savings
LCOE (nom)_0.253____0.205
PVEC (nom)_0.167____0.135

The LCOE (levelized cost of energy) and PVEC (present value energy cost) are both reported in $ / kWh, by taking (total cost) / (total energy). LCOE is an industry recognized calculation that uses the NPV of costs divided by the NPV of usage, using the same nominal discount rate to calculate both. The PVEC calculation is as I described earlier in the thread, in which the NPV of costs is divided by the SUM of usage, since I see no reason to discount the future energy production.

Despite the difference in calculations, both averaging methods and also the simple NPV of solar savings agree that the breakeven point occurs early in year 10. Breakeven is the point at which the cost of electricity with solar is equal to the cost of electricity without solar.

For systems in San Diego, breakeven seems to typically be somewhat over 10 years when the system is sized to cover 100% of energy usage. For systems sized to cover only tiers 3 / 4 power, the breakeven point will occur much more quickly, although the long term cumulative savings may be less. If you live in another part of the country and would like some help applying these calculations to your system, just PM or email me and I would be happy to help.

Whether you use SAM, your own calculations, or whatever the solar salesman has pitched you, make sure that the assumptions being used are realistic! This kind of analysis is a powerful way to estimate the cost-effectiveness of solar, or any long term investment, and is not too difficult to perform.

Despite my frustration with SAM's LCOE calculation, it has a lot going for it. Among those are the ability to easily incorporate property taxes and other operating or maintenance costs, along with other cost models that are less uniform than the assumptions I've used here. It also has some interesting production estimation tools, including a 3D shading modeller.

[J.P.M.]

A comment or 2:

I suggested Sensij share his results with the forum. The data is indeed for my system and were supplied by me.

1.) The real LCOE from my SAM analysis for my system using data and electric rates from my 10/17/2013 startup is $.18112/kWhr.

2.) Sensij's methods are his, not mine. While respecting his opinion, I believe his analysis is incomplete and flawed in some ways. I'll continue to use the LCOE method similar to SAM's as I believe it to be a better, more thorough and more accepted way of doing an energy cost analysis.

3.) FWIW, that analysis used 3% fouling. So far with 4 days to go to the 1st anniv. of startup, the system has produced 9,489 kWh.

J.P.M.

[sensij]

@J.P.M. as you say, it's a free country. do what you like.

For others who are interested in payback assumptions and calculations, I would love to continue a dialog about best practices and ways in which the industry standards may not represent the interests of the typical homeowner. You can see I strongly advocate supporting opinions with data, and understanding the data well enough to explain how it is derived. Based on the sales pitches I have been receiving, there are many in the industry who are willing to profit on ignorance, and encourage decision making that may not be in our best interests.

Having said that, solar in San Diego is a rational economic decision under many sets of assumptions, and I hope that others who might be on the fence are willing to take a close look and see if their situation is consistent with those assumptions.

[scswickman]

We just moved from our smaller home of 20 years into a much larger house, and SDG&E was nice enough to send us a $1,000+ electric bill for the August-September billing cycle. Granted, we ran quite a bit of AC and we have an electric car, but holy guacamole! Hard to see how solar would not pencil out for us, especially since SDG&E has aggressively increased rates and shows no signs of ceasing such practice in the future.

[J.P.M.]

We just moved from our smaller home of 20 years into a much larger house, and SDG&E was nice enough to send us a $1,000+ electric bill for the August-September billing cycle. Granted, we ran quite a bit of AC and we have an electric car, but holy guacamole! Hard to see how solar would not pencil out for us, especially since SDG&E has aggressively increased rates and shows no signs of ceasing such practice in the future.

Be careful what you believe about rates. They are changing. Your money, your choice, but a bit of homework may change your opinion some about the future of SDG & E and other CA POCO rate increases. If SDG & E is to be believed (???), they published something recently that said they intend to go to 2 tiers with rates much closer together, by an approx. increase in what were the lower tier rates of about 8%, and a DECREASE in what were the upper tier rates of about 30%, pending PUC approval. They intimated about a 2+yr. phase in. Thus, large users will probably see their bills go down some. Small bills will increase some. Root around on their website for confirmation. I'd suggest being skeptical of what those with money to make by using consumer ignorance to fear monger folks into solar or other things with unsubstantiated and often exaggerated claims about supposed rate increases that may or may not happen as much as being skeptical of the POCO's blurbs.

Nothing cuts an electric bill as effectively as not using the POCO's product. Conservation is usually the next most cost effective measure. Solar electric is about the least cost effective and only then probably to a point of replacing most of a conservation reduced bill, rather than the whole thing.

[sensij]

The comments above may be sourced here.

The impact on solar payback is interesting. On one hand, the marginal reward for replacing upper tier consumption drops significantly, and the increase in monthly fee hurts solar payback across the board. It isn't clear if the fee will be instead of the existing $0.17 minimum charge per day (which is effectively $5.17 / mo), or on top of it. On the other hand, the relatively large increase in the lower tier rates improves the marginal reward for replacing that energy with solar.

If your payback analysis under the existing rate structure shows optimum reward for replacing all or nearly all of your electric with solar, then the new structure is unlikely to change that conclusion. In that scenario, your last panel is replacing low tier power in either case, and that is likely to be more valuable in the future, not less. However, the overall benefit may be reduced, since the Tier 3/4 replacement is not contributing as much.


Some other documentation that is related is SDG&E's filing for rate increases in 2015 at the beginning of the year. The projected impact, as detailed on page 59, is a 4.2% increase for the "average" consumer of 500 kWh per month, while net decreases would result for the upper tier consumers.

That filing was updated here, at the end of February.

It is clear from the documentation that a significant factor in the rate and tier restructuring (over 5 years) will include redefining the "baseline" usage to a level at or near the legislative minimums. For users who are near the upper limit of tier 2 today, it is reasonable to believe at least a portion of the usage will be classified as "upper tier" in the new structure.

Hearings are ongoing, but clearly, changes will be coming.

[sensij]

Apparently, I'm not the only one who sees LCOE as inadequate for evaluating residential rooftop solar. My understanding of it above was incorrect, due in part to the way NREL has chosen to present its calculations in their spreadsheet (and also in part to my initial lack of reading comprehension while reviewing their detailed manuals). After a query with NREL and further review of their documentation, the energy is not in fact being discounted, the cash flow is essentially being discounted and then un-discounted. The result is that LCOE is not meant to be interpreted as a present value lifecycle metric, but instead simply satisfies the equation: Average Energy cost (in year n) = LCOE (constant over all years) x energy consumed (in year n). It is a neat math trick, but even its usefulness in the economics of large scale generation is questioned.

Alternatively, the analysis I described above attempts to answer the question, "What $ / kWh will I pay in today's dollars for my electricity consumption over the next N years?". Neither this, nor LCOE is very suitable for evaluating energy efficient upgrades, since reducing energy consumption reduces the denominator and therefore understates the value of the upgrade. Simple NPV cost calculations are a better starting point for those types of decisions, but studies have shown that many of us pursuing solar are already aware of the benefits of conservation.

Solar payback analysis is not a wheel that has already been invented, but is evolving. The approach I've described to this problem is not new or innovative, but is a simple enough formulation that I can understand it and communicate it to others, and since it is based on established total lifecycle cost methods, the accuracy will be as good as the starting assumptions. Sensitivity analysis of those assumptions is an extension of the analysis that can help determine how trustworthy the results really may be.

Why the deep dive into cost calculations? I've hypothesized that a current tier 2 electric user in San Diego could benefit from switching to solar, and a solid framework in which that hypothesis can be tested is needed. If you have suggestions on how to make that framework better, I'd love to hear them.