Solar pv Payback logic error ... ?

zeupater

Hi All

Well, firstly this thread could have had one of numerous other titles, such as 'Who's pulling the..' or 'The great FiT logic error' being amongst them. I'd guess that most reading this are thinking 'Where is this going ?', so I'll elaborate.

Wherever you look for information on solar pv justification and payback issues you will see the following basic calculation for annual savings :-

Payback Value (£p)pa = Feed in Tariff (£x)pa + Exported Value (£y)pa + Value of generated energy self consumed (£z)pa

Excellent, but everyone really misses the obvious flaw in this simplistic logic, including organisations such as the EST (and they should know better !), which is simply :-

THE ENERGY COST PER UNIT MUST VARY IN THE CALCULATION.

.... and this is true whether the site concerned is on a mains supply tariff which has a separate standing charge, or one with banded costs.

To help explain this let's consider a basic new installation of 3.6kWh, somewhere in the middle of England (Meriden), facing due South with a 35 degree unshaded roof slope providing an estimated 3033kWh with the following production profile :-

Q1 - 499 kWh / Q2 - 1099 kWh / Q3 - 1038 kWh / Q4 - 397 kWh

with an average electricity consumption of 3200kWh with quarterly usage weighted as being :-

Q1+Q4 - 1760kWh / Q2+Q3 - 1440kWh

The Saving calculation would probably look something like :-

Feed in Tariff (£0.413 x 3033kWh) = £1253pa
Exported Value @ 60% production (3033kWh x 60% x £0.03/kWh) = £55pa
Value of generated energy self consumed (3033kWh x 40% x £0.13/kWh) = £158pa
Payback Value (1253+55+158) = £1466pa

However, in real terms the calculation is complicated by the imbalance of generation in the summer and also the likely day/night usage pattern (which will be different for each household), so lets just consider a simplified model ....

Winter Q4+Q1 - Require 1760 KWh / Generate 896 kWh / Use while generating (40% x 896kWh) = 358kWh / Export (896-358) = 538 kWh

Summer Q2+Q3 - Require 1440kWh / Generate 2137 kWh .... whoops an imbalance, let's assume that 40% of the requirement is at night and 60% is during the day, therefore the daytime requirement is (1440 x 60%) = 864kWh and that a whopping 80% of this requirement is provided by the pv array (just to keep the EST happy) then .. / Use whilst generating (864 x 80%) = 691 kWh / Export (2137-691) = 1446kWh (67.6%)

The Summer imbalance calculation above shows that an assumption of exporting 60% of annual production is possibly flawed and unless you have an export meter you'll probably be handing over a considerable number of electrons to the grid for free, but let's not worry about that here as it's not the point in hand. The situation above describes a position where the imported electricity changes as follows :-

Import

---

Before pv / With pv
Winter - 1760kWh / (1760-358) = 1402kWh
Summer - 1440kWh / (1440-691) = 749kWh

Now let's look at the cost of the electricity, both before and after the installation. For this I'm going to use the rate I'm on which is BG Click 6, I'll make things a little better for the likes of the EST or any installers by not including dual fuel discounts, or any other methods of reducing the costs further, and just use the following:-

Tier 1 (<125kWh/Qtr) = £0.19366/kWh / Tier 2 = £0.08480/kWh

As each quarter uses >125kWh lets take that as being a fixed £24.21/Qtr and apply the Tier 2 to the remainder.
Before

Winter = 48.42+((1760-250)x0.0848) = £176.47 = 10.03p/kWh
Summer = 48.42+((1440-250)x0.0848) = £149.33 = 10.37p/kWh
Total = £325.80 = 10.18p/kWh

After

Winter = 48.42+((1402-250)x0.0848) = £146.11 = 10.43p/kWh
Summer = 48.42+((749-250)x0.0848) = £90.74 = 12.11p/kWh
Total = £236.85 = 11.01p/kWh

So surely the overall Saving calculation as a result of this would be a realistic :-

Feed in Tariff (£0.413 x 3033kWh) = £1253pa
Exported Value @ 60% production (3033kWh x 60% x £0.03/kWh) = £55pa
Real value of generated energy self consumed (£325.80 - £236.85) = £89pa
Payback Value (1253+55+89) = £1397pa

Therefore a (£1466-£1397) £69 difference

Remember 1984/3033 kWh is also being exported (65.4%) so 5.4% of generated capacity is being 'given' to the supplier, which they then sell back to you !!

You'll notice that the difference is quite close to the calculated 'Export Value' in the above example and that I have been very generous in favour of the ' This House believes in pv' side of the debate. In my own case the before usage figures are about 75% of the example (which has a much more pronounced affect on change in the imported average cost/kWh) and there are also the dual fuel and direct debit discounts, the array is S/W, and the capacity is targeted as being 3.96kWp, the total effect being a difference well above the export value (and don't forget the assumption that a whopping 80% of summer daytime demand can be satisfied by the array). Applying this logic to your own calculations will provide a reasonably accurate picture of what the payback calculations should look like (and I'm not getting involved in that debate !), but as a general rule-of-thumb, it would probably be better to forget the double-accounting affect by just ignoring the export value from rough calculations.

Please also note that, as mentioned earlier, the assertion that the unit cost per kWh is not a constant also stands for supplies with standing charges when the standing charge is amortised back across the consumption, as that's effectively the result of the Tier 1 inflated cost per unit anyway.



Regards
Z

albyota

or...from Scottish & Southern's website...

Your energy making you money

Purchase Price* £8,187
Total Payable: £8,187
Average annual income from FiT tariff** £484.45
Average saving from using generated electricity*** £137.63
Average annual income from unused generated electricity exported to the grid £3.51
Average total yearly income generated : £625.59
25 year combined income and savings from electricity generated: £15,639.75


1. Subject to terms and conditions of manufacturer's warranty.
*Cost based on a Yingli 1.38kWp system, fully installed, including delivery and VAT (Other modules are available). Price subject to survey.
**41.3p/kWh as mandated by the Government plus 3p/kWh as an export tariff from Southern Electric.
***13p/kWh energy price, based on an annual output of 1173 kWh and 90% of the energy consumed within the house and the other 10% fed back into the power grid – south facing roof at 30 degree pitch.

zeupater

albyota wrote: »

or...from Scottish & Southern's website...

Your energy making you money

Purchase Price* £8,187
Total Payable: £8,187
Average annual income from FiT tariff** £484.45
Average saving from using generated electricity*** £137.63
Average annual income from unused generated electricity exported to the grid £3.51
Average total yearly income generated : £625.59
25 year combined income and savings from electricity generated: £15,639.75


1. Subject to terms and conditions of manufacturer's warranty.
*Cost based on a Yingli 1.38kWp system, fully installed, including delivery and VAT (Other modules are available). Price subject to survey.
**41.3p/kWh as mandated by the Government plus 3p/kWh as an export tariff from Southern Electric.
***13p/kWh energy price, based on an annual output of 1173 kWh and 90% of the energy consumed within the house and the other 10% fed back into the power grid – south facing roof at 30 degree pitch.

Hi

Agree, there's absolutely no allowance for a change in the cost per unit(kWh) of imported power as a result of lower import requirements at all and there really should be.

What is interesting here though is that a household with a 1.38kWp system would actually consume 90% of production, that's one very large 'background' usage, mine varies between say 50W and about 250W as a background consumption as appliances cut in/out, probably at 50W most of the time, so in that case on a nice sunny day generating a healthy 1kW the system would be exporting 95% and it doesn't take many days of doing that to really question their savings logic ....

Regards
Z

Cardew

Wow Zeupater!

Surely everyone will 'use up' the 125kWh tier 1 slice per quarter at night, or when the PV is not generating sufficient to cover consumption? Therefore you can treat that as a 'standing charge' in the same way as someone paying a daily standing charge and a flat rate for their electricity.

So logically you can only use the tier 2 rate in any calculation in savings calculations - in your case 8.48p/kWh. The 13p/kWh you use to reach £158 in the first set of calculations is way too high IMO and should be £103.(3033kWh x 40% x 8.48p)

IMO your later calculations to reach a figure of £89pa for the "Real value of generated energy self consumed (£325.80 - £236.85)" is flawed.

If you take 3033kWh x 60% it equals 1820kWh(which is where you correctly get the £55 figure) So the remaing 40% comes to 1213kWh.

By concluding that this 1213kWh has a value of £89 you are pricing each kWh used in the house at 7.34p/kWh. Way lower than your Tier 2 price.

On a more general point unless you have an export meter( and many will?) I simply cannot see how you can argue that 60% is unfair.

It is impossible to know how much you are using in the house and hence the percentage you are exporting. I really cannot see how you reach a figure of 65.4%. or indeed the relevance of the before and after PV figures.

Your 75% and 80% figures are also a puzzle.

The larger the array, the higher the percentage, exported. Take the Scotish and Southern example above of a small 1.38kWp array. They take the view that 90% will be used in the house and only 10% exported. Yet whilst only exporting 10% they will be paid for 60%(if no export meter)

On the other hand a 4kWp array in SW England could be generating 5,000kWh per year and if the occupants were out during the day it is quite possible that they could be exporting 80%+.

Mankysteve

The biggest mistake is calculating PV payback is forgetting opportunity lost.

zeupater

Hi Cardew

The point behind the post is to highlight the fact that the more energy you generate and use yourself, the more you actually pay for each kWh of imported electricity. The above post shows an increase of about 10% in the cost per kWh imported, mine is considerably higher due to the variables described in the post. I'll try to clarify the post by addressing your points as raised.

Cardew wrote: »

Surely everyone will 'use up' the 125kWh tier 1 slice per quarter at night, or when the PV is not generating sufficient to cover consumption? Therefore you can treat that as a 'standing charge' in the same way as someone paying a daily standing charge and a flat rate for their electricity.

Actually I agree, and that's mentioned early in the post and confirmed in the last paragraph As you correctly point out a long as the 125kWh is used up the following logic applies :-
The difference between Tier 1 pricing @ £0.19366/kWh and Tier 2 @ £0.08480/kWh shows a premium for the Tier1 element of £0.10886/kWh which equates to a fixed premium of £13.61/Qtr. As long as at least 125kWh is consumed in each quarter this is effectively the same as a standing charge.

Cardew wrote: »

So logically you can only use the tier 2 rate in any calculation in savings calculations - in your case 8.48p/kWh. The 13p/kWh you use to reach £158 in the first set of calculations is way too high IMO and should be £103.(3033kWh x 40% x 8.48p)

This is the crux of he point in hand. You logically SHOULD NOT use the tier 2 rate on either side of the equation and you SHOULD NOT use the same cost per imported kWh on both sides either. The example above clearly shows that the unit cost of imported electricity increases due to the proportion of the total imported cost element made up from either the inflated Tier 1 price or the standing charge. The overall average cost/kWh must logically be used as calculated both before and after the pv installation, and this changes as described.
The 13p/kWh is the figure which has been used both in the quotations I have received and most calculations I have seen (including albyota's S&S example), and this is part of the point being raised as the higher the unit cost, the higher the calculated payback value (conveniently!). I therefore agree with your 13p observation, but the figure was used to convey what the savings calculation would look like on a received quotation and is therefore the correct figure to use as a baseline.

Cardew wrote: »

IMO your later calculations to reach a figure of £89pa for the "Real value of generated energy self consumed (£325.80 - £236.85)" is flawed.

If you take 3033kWh x 60% it equals 1820kWh(which is where you correctly get the £55 figure) So the remaing 40% comes to 1213kWh.

By concluding that this 1213kWh has a value of £89 you are pricing each kWh used in the house at 7.34p/kWh. Way lower than your Tier 2 price.

The methodology utilised in the post actually stands up well when compared to any other possible calculations. I know that it's a different way of addressing the saving, but it's totally logical if you think about it. Before the installation of the pv array the imported electricity cost would be £325.80 and after the installation the cost would be £236.85, therefore having the array on the roof only saves the difference, trying to price this difference in terms of cost per unit is irrelevant because those are the import figures before and after and, quite simply, the difference is the saving.

Cardew wrote: »

On a more general point unless you have an export meter( and many will?) I simply cannot see how you can argue that 60% is unfair.

It is impossible to know how much you are using in the house and hence the percentage you are exporting. I really cannot see how you reach a figure of 65.4%. or indeed the relevance of the before and after PV figures.

.

I agree. If you can justify an export meter then one should be fitted. What the post is attemping to show is that although the figure of 60% could be fair, with the size of array above and average usage there is an imbalance between the summer generation and usage, which would probably result in more than 60% being exported.
If you re-check the logic you'll see that in every respect the calculations are designed to err on the side of caution. Remember that the calculation assumes that 80% of anticipated daytime hours consumption is satisfied by the array, which probably suggests that, if anything, the 65.4% is possibly on the low side.
The real solution here would simply be for the scheme to employ a system of net metering, where the imported and exported units are netted off against each other over a period of time and there is a simple charge or payment for the difference, but then again, considering the subject being discussed, why do you think that the utility companies would be against this .

Cardew wrote: »

Your 75% and 80% figures are also a puzzle.

Okay then, first the 75%. This relates to my consumption which is approximately 75% of that in the example which logically increases the effect of the fixed tier 1 element of £13.61/Qtr described above (or standing charge if applicable). Reducing the Tier 2 imported units has a more pronounced effect on the average price per unit in situations where the total consumption is lower. The effect of this is to further increase the average cost per kWh of imported electricity as a result of installing solar generating capacity. It really does, try it out on a spreadsheet.

Next, the 80%. Note that ths relates to the 'Whopping 80%' which is a basic assumption for the proportion of daytime summer consumption which a 3.6kWp array could supply. This was, as referred to earlier, a figure which was chosen speciffically to err on the side of caution so as not to upset anyone who might think that 'I was cooking the figures' in favour of the anti-solar brigade. Almost every time that a high consumption appliance such as the hob, cooker, kettle, washing machine, tumble dryer, toaster, vacuum cleaner etc are needed, an array sized at a nominal 3.6kWp would struggle to cope with demand, so in reality the 80% is probably far too high, but lowering it would only increase the imported unit requirement and further reduce the calculated payback value.

Cardew wrote: »

The larger the array, the higher the percentage, exported. Take the Scotish and Southern example above of a small 1.38kWp array. They take the view that 90% will be used in the house and only 10% exported. Yet whilst only exporting 10% they will be paid for 60%(if no export meter)

On the other hand a 4kWp array in SW England could be generating 5,000kWh per year and if the occupants were out during the day it is quite possible that they could be exporting 80%+.

Totally agree, and this confirms what was being described. In my case, with a both a lower usage and a larger array, although the higher capacity of the array would cope better with the peak consumption demand and therefore slightly reduce the import requirement (note the use of slightly), it is obvious that more generation would be availabe to export than described in the example.
The Scottish & Southern example, conveniently from the point of a provider, really heavily depends on the summer daytime usage pattern. I find it very hard to visualise a usage pattern which would satisfy a healthy 90% of generated power being consumed locally in a domestic environment. If you think about it from the two extremes, that would mean that at any particular point in time the household requirement would need to be between 90% of array output for 100% of the generation time, and 100% of array output for 90% of the generation time. To achieve this you would need a continuous base load of somewhere around 900W on the sunniest days, which is more suited to a commercial environment (shop/pub etc).

Regards
Z

Cardew

Hi zeupater,
We could bounce these figures backwards and forwards and not reach agreement on some points; but the thrust of your argument is accepted.

Obviously it suits those promoting PV to put a higher value on the benefits. However IMO it is not normally* the 60% factor that is the problem in slightly exagerating the returns but the high price they put on the electricity consumed in the house. Typically 13p/kWh or higher is used, where 10p/kWh or less is more realistic - when you take the Tier 2 rate and factor in the various discounts.

* obviously the illustration above where they assume 90% will be consumed in the house is not realistic and on a small system serves to greatly exagerate the expected savings.

On the 60% issue, I was looking at Yakky58's figures for a 2kWp sytem that generated 2059kWh last year. He exported 52% of that total. Obviously he has an export meter but had his set-up been eligble for FITs etc and got an assumed 60% for his exports he would have gained.

That said the FIT is the major source of income, and we both agree that the 'fudging' of expected returns is not going to change the overall returns by a great deal.

My bigger concern in the way PV is marketed is they totally ignore the loss of interest on the money invested.

If someone said borrow £100,000 on a mortgage and pay back £5,000 a year and you will have paid it off in 20 years, they would be laughed at!!!

The other issue I have is that none of these wonderful estimates for savings over the next 25 years ever mention repairs to the system. Yet a 2 year warranty is the norm. Even if it were longer, what is the chance of the installer being about after 5 or 10 years - or at least trading under the same name! It seems to be standard practice to cease trading and start up another firm with the same people/equipment but no responsibility for previous work.