Cost per KWh

drraptor · June 2014

I came up with this formula for calculating the total cost of electricity produced per KWh over a period of 25 years.:-)

Rate of Panels per watts x Size of array in watts + Rate of batteries/Ah x Size of battery bank/Ah x No of banks required in 25 years + Inverter or chargers's price = Total Cost for a period of 25 years

Annual production = Size of array x 365 x Total sunhours in a year x 0.77% (derate factor)

Cost per KWh = Total Cost for a period of 25 years / (annual production x 25 years)

Is it good enough or does it need any modification.

Cariboocoot · June 2014

Re: Cost per KWh

How about:

Equipment cost amortized over lifespan = cost per year.
Cost per year / annual kW hour production = cost per kW hour.

You're trying to predict in advance the kW hour production, which is not so easily done. To go that route:

Array size * derating (0.77 typical) * hours of good sun (varies with time of year and weather) * days = annual production.

This is why there is PV Watts, where the history of local conditions is already factored in so you can make a reasonable prediction of production for a year. But it (like the formula above) does not include batteries.

Toss them in the mix and you have a new game. For one thing it varies the cost, sometimes unpredictably (oops! Fried that set.) For another it alters the efficiency of the system; it could be as low as 52% over-all, depending on how much of the power usage is 'stored' and how much is 'direct' (obtained with batteries full so making use of PV power that would otherwise not be realized at all).

There: did that help complicate things?

Photowhit · June 2014

Re: Cost per KWh

It pretty much can't be calculated in the manner your pursuing. You calculating available production, not what is actually produced and used. In the end anything on that tangent will produce skewed numbers. I've got a thread somewhere where I did my projected use and costs and even that doesn't include time and care for a system...

BB. · June 2014

Re: Cost per KWh

Remember that a Grid Tied system has a virtually "unlimited" storage capacity in the AC grid (mine is actually 1 year net metering). I can draw negative in winter and recharge during summer.

With an off grid system--You nominally only have 2 days of storage... Some days you use less and simple leave "unused" charging capacity from the array (probably only run ~66 to 75% of daily average "available" predicted power.

And some days, you will use more power than the off grid system can generate (poor weather, winter, etc.)--And those days you may need to use a genset to supply energy.

So, as above:

total cost of installation + 20 years of maintenance (new batteries, new inverter/charge controller) divided by the estimated 20 years of "useful" power you can realistically use = $$$ / KWH.

-Bill

South Africa · June 2014

Re: Cost per KWh

I have a very simplistic view, it worked very well for me to date:
For grid tie or hybrid systems:
1) Cost of solar system divided over shortest possible period. Lets say X (cost of system) / Y (months) = Z
2) Will you get Z 'savings' on average per month on your grid bill over Y months?

And if you are 100% off grid:
Investigate the lowest possibly consumption electrical equipment that you really need, they cost a pretty penny, but it will substantially reduce your solar outlay. Then do the numbers with the replacement of that equipment factored in.

That adds another level of complexity. :-)

For me it was a very sobering insight into the cost of solar systems.

pleppik · June 2014

Re: Cost per KWh

One more thing you should take into account is the "cost of money," which can be a lot over 25 years.

Even if you can afford to pay cash for the system, you will be losing whatever interest you would have earned over 25 years. Of course if you borrow to pay for the system you will have to pay the interest out of pocket.

Calculating compounding interest is more complicated, but as a simple first approximation you can go to a mortgage calculator (there's a lot of them online) and find out the monthly payment for a mortgage where the principal amount is the cost of your system, the length of the mortgage is the lifetime of your system, and the interest rate is whatever you would have earned from your savings (or the rate you would pay for a loan).

The monthly mortgage payment you get out will be a pretty good approximation to what your PV system costs on a monthly basis, including the cost of money. Divide that by the average kWh you expect to generate each month (or 1/12 the expected annual production) to get the cost/kWh.

zoneblue · June 2014

Re: Cost per KWh

pleppik wrote: »

One more thing you should take into account is the "cost of money," which can be a lot over 25 years.

True. So i tidied up the rough cost benefit analysis i did on our system, and uploaded it here: www.zoneblue.org/files/solar-cba.xls

It works out around 40c/kWh using a 5% discount rate. The model appears to most sensitive to expected power production (so get that right). Grid pricing is also high because of the low user rate. If you use more power, like many things in the modern world its cheaper in bulk.

Still for our usage, off grid price parity is almost here.

South Africa · June 2014

Re: Cost per KWh

Very interesting calc. The calcs for me with Grid rate of increase at 8%, no discount, leaving the rest the same, has a 25 year cumulative of grid @ 49 113 and solar at 21 158.

And every year in July, when the increases are done for grid power, the grid will keep on getting even more expensive, and solar cheaper due to panels coming down.

And when, sorry, if, the new coal fired power stations come online one day, their estimated cost per kw, as of today, is going to be even more expensive than solar is today. :-)

It is good for the solar industry.

BB. · June 2014

Re: Cost per KWh

Then you can get into the "value" of power...

The value of simple GT solar power that is only available when the sun is shining and cannot be "throttled" is not near as much as a power source that can be turned on anytime (day or night) and can be throttled to meet required loads.

Say you had the "ideal" gasoline engine that got 100 miles per gallon. But it only could be turned on or off and connected that to your car.

You made the engine to output 5 hp (on). Then proceeded to drive. Around town, that would be pretty difficult driving, either On or Off, that was it. And on the freeway / going up hills, you would need to fire up a second engine to supply more power when needed.

It sounds odd to have an engine with no throttle, but early WWI air craft did not have throttles either, or needed a bunch of manual control of mixture+throttle--and simply killed the ignition when power was not needed:

http://en.wikipedia.org/wiki/Sopwith_Camel

The Gnome "mono" engines did not have throttles and were at full "throttle" while the ignition was on – they could be "throttled" with a selector switch which cut the ignition to some of the cylinders to reduce power for landing. The Clerget, Le Rhone and BR1 had throttles, although reducing power involved simultaneously adjusting the mixture and was not straightforward, so it became common during landing to "blip" the engine (turn the ignition off and on) using a control column-mounted ignition switch, the blip switch, to reduce power.

You can make do with what you have--But it is not always the optimum solution.

-Bill

zoneblue · June 2014

Re: Cost per KWh

The 'discount rate' is the price of capital, and hence integral to net present value calculations. So leave it in. We used to use a figure up in the 6 or 7 percent region back in the 90s, 00s. But i think 5% is closer to it now.

The worldwatch institute recently priced the installation cost of nuclear at $6 per watt, which is twice PV at $3/W. Yet people are still building the wretched things. As bill says thats grid tie pricing without factoring storage.

For anyone that needs a dose of solar inspiration there is nothing like the words of Hermann Scheer.
http://www.youtube.com/watch?v=nr-grdspEWQ

drraptor · June 2014

Re: Cost per KWh

Cariboocoot wrote: »

How about:

Equipment cost amortized over lifespan = cost per year.
Cost per year / annual kW hour production = cost per kW hour.

You're trying to predict in advance the kW hour production, which is not so easily done. To go that route:

Array size * derating (0.77 typical) * hours of good sun (varies with time of year and weather) * days = annual production.

This is why there is PV Watts, where the history of local conditions is already factored in so you can make a reasonable prediction of production for a year. But it (like the formula above) does not include batteries.

PV watts isn't available for my area. I have to calculate on my own or else I have to contact the Pakistan Meteorological Departmen http://www.pmd.gov.pk/ which might be a headache itself.

Toss them in the mix and you have a new game. For one thing it varies the cost, sometimes unpredictably (oops! Fried that set.) For another it alters the efficiency of the system; it could be as low as 52% over-all, depending on how much of the power usage is 'stored' and how much is 'direct' (obtained with batteries full so making use of PV power that would otherwise not be realized at all).

There: did that help complicate things?

With modes such as Mini-Grid, Grid-zero, and Backup modes on inverter we can maximize the PV array use http://www.outbackpower.com/downloads/documents/radian_7048e_3548e/gs_7048e_3548e_operator.pdf :-)

BB. · June 2014

Re: Cost per KWh

http://solarelectricityhandbook.com/solar-irradiance.html

Seems to be about the same as PV Watts (in areas with overlap), and covers a lot of regions around the world.

I like it because is it simple and gives "hours of sun"--Just plug those into our equations and away you go.... Some of the more complex calculators do a lot of other deratings/conversions and it is a bit more work to "unwind" them to figure out what they are doing.

-Bill

drraptor · June 2014

Re: Cost per KWh

Photowhit wrote: »

It pretty much can't be calculated in the manner your pursuing. You calculating available production, not what is actually produced and used. In the end anything on that tangent will produce skewed numbers. I've got a thread somewhere where I did my projected use and costs and even that doesn't include time and care for a system...

can you please post your spreadsheet or any calculation you did

drraptor · June 2014

Re: Cost per KWh

BB. wrote: »

http://solarelectricityhandbook.com/solar-irradiance.html

Seems to be about the same as PV Watts (in areas with overlap), and covers a lot of regions around the world.

I like it because is it simple and gives "hours of sun"--Just plug those into our equations and away you go.... Some of the more complex calculators do a lot of other deratings/conversions and it is a bit more work to "unwind" them to figure out what they are doing.

-Bill

made of spreadsheet, please check whether I have calculated it right. https://docs.google.com/spreadsheets/d/1vz_36FsKLZfqDb1pYwtEZlY2ukFX_UohZ0_9K5ECc5c/edit?usp=sharing

drraptor · June 2014

Re: Cost per KWh

pleppik wrote: »

One more thing you should take into account is the "cost of money," which can be a lot over 25 years.

Even if you can afford to pay cash for the system, you will be losing whatever interest you would have earned over 25 years. Of course if you borrow to pay for the system you will have to pay the interest out of pocket.

Calculating compounding interest is more complicated, but as a simple first approximation you can go to a mortgage calculator (there's a lot of them online) and find out the monthly payment for a mortgage where the principal amount is the cost of your system, the length of the mortgage is the lifetime of your system, and the interest rate is whatever you would have earned from your savings (or the rate you would pay for a loan).

The monthly mortgage payment you get out will be a pretty good approximation to what your PV system costs on a monthly basis, including the cost of money. Divide that by the average kWh you expect to generate each month (or 1/12 the expected annual production) to get the cost/kWh.

Interest is Haraam in Islam so can't consider that

http://en.wikipedia.org/wiki/Riba

BB. · June 2014

Re: Cost per KWh

I am not sure I understand your calculations... Take January: You have 355 and 314 Watt array? And the math:

355 Watt array * 3.25 Hours of Sun * 31 days * 0.77 derating = 27,540 Hours of sun (not 24,358 WH)

This is for a grid tied system (derating is 0.77).

And you have hours of sun for vertical surface--Is this a horizontal surface?

-Bill

Photowhit · June 2014

Re: Cost per KWh

drraptor wrote: »

can you please post your spreadsheet or any calculation you did

I did long ago;

http://forum.solar-electric.com/showthread.php?17055-It-s-going-to-be-close-to-cost-effective!-or-Off-grid-at-26-cents-a-KWh!

For What It's Worth, the system has been up and running well, I never replaced the inverter, I sold my cabin system and added that inverter to the mix, though largely as a spare or when using electric chainsaw or weed eater in the yard. The now 4 year old battery(originally on my cabin system) has an ugly cell, literally it it's electrolyte appears dark but it has always been one of the highest SGs on the battery. I wonder if it had a higher concentration of acid originally. I have yet to add a mini split, but have opened the area that is available for the single window unit to include the bathroom and 2nd bedroom, so it's duty cycle is much longer.

Not included installation expenses should include about $1000-1200 to install a wood stove, since I can no longer heat with electric.

drraptor · June 2014

Re: Cost per KWh

BB. wrote: »

I am not sure I understand your calculations... Take January: You have 355 and 314 Watt array? And the math:

355 Watt array * 3.25 Hours of Sun * 31 days * 0.77 derating = 27,540 Hours of sun (not 24,358 WH)

This is for a grid tied system (derating is 0.77).

And you have hours of sun for vertical surface--Is this a horizontal surface?

-Bill

Actual size of array is because of this equation [VMP+VMP] * IMP (Smaller of the two). I have recalculated it.

Yes panel was almost on a horizontal surface (it was typing mistake on my part) , for best production in summers; but now I adjusted the angle and now it is more close to 73 degrees.

drraptor · June 2014

Re: Cost per KWh

Photowhit wrote: »

I did long ago;

http://forum.solar-electric.com/showthread.php?17055-It-s-going-to-be-close-to-cost-effective!-or-Off-grid-at-26-cents-a-KWh!

For What It's Worth, the system has been up and running well, I never replaced the inverter, I sold my cabin system and added that inverter to the mix, though largely as a spare or when using electric chainsaw or weed eater in the yard. The now 4 year old battery(originally on my cabin system) has an ugly cell, literally it it's electrolyte appears dark but it has always been one of the highest SGs on the battery. I wonder if it had a higher concentration of acid originally. I have yet to add a mini split, but have opened the area that is available for the single window unit to include the bathroom and 2nd bedroom, so it's duty cycle is much longer.

Not included installation expenses should include about $1000-1200 to install a wood stove, since I can no longer heat with electric.

Isn't the Window unit less efficient than a split or inverter based unit ?

Photowhit · June 2014

Re: Cost per KWh

Yes...

If you want to buy me one, I'd be glad to have you do that. Do you want my Email to drop the money in my PayPal account?

The back bedroom is about 15x14 and lower ceilings than a 'normal' home (7'), our heat comes with sun, so the small (5200btu) window unit works fine for that. It actually has been fine cooling the bath and second bedroom as well, but we haven't hit the 'heat of the summer yet, still a month away. Plans are still to have a mini split in the kitchen/living room area @15x30, just don't have the money to throw at it.

zoneblue · June 2014

Re: Cost per KWh

drraptor wrote: »

Interest is Haraam in Islam so can't consider that http://en.wikipedia.org/wiki/Riba

My recollection is rusty, but in the islamic world loans attracted equity positions in lieu of interest, or something like that. How does that work exactly? How does your central banking system regulatee money supply? Maybe pegged to US dollar or something?

But unless you have zero inflation, any model that compares costs both now and far in the future will need to compensate for the changing value of money over time.

Cost per KWh

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