## Your own grid parity PV system January 24, 2012

Posted by Maury Markowitz in solar.
Tags: , ,

I was talking shop a couple of days ago and we started throwing around numbers for PV prices moving forward. In case you haven’t heard, equipment costs, even on small systems, have hit the $2 mark in USD. That means a mid-size plant, where the construction costs are spread out, should go in around USD$3 a watt. In capital terms PV is now one of the least expensive forms of power available.

So, yeah, GOOD!

But that’s talking about the problem in the lingo of the power industry, where everyone talks about the cost of building the plant (the “CAPEX”) and not so much about the cost of electricity it produces. That makes more sense than you might think, because if the plant can’t make competitive electricity you simply don’t build it.

But for you, the reader, all you care about is the cost of the power. So follow along while we explore the wonderful world of the Levelized Cost of Electricity

### LCoE

We’ve covered the basics of what follows here on Energy Matters before, in terms of trying to come to grips with the differences in operational costs that different power systems face, and especially when considering the economic value of putting solar panels in space. But in this post I’m going to get a lot more specific, and show you exactly how to carry out these calculations yourself. If you plug these into a spreadsheet, you’ll be able to compare systems and see why this downward price pressure is so important.

Very basically, the “levelized cost of electricity” or “LCoE” is the total amount of money you spent on a system over its lifetime divided by all the power it produced in that same period. You can choose any units you like, but since you’re electricity bill comes in “cents per kilowatt-hour”, we’ll use that so the numbers are easy to understand.

### Start simple…

First up, because of it’s simplicity, is a set of solar panels on your roof. Right now panels that deliver 250 Watts of power under “STC” condition are fairly common. Let’s consider a system with four such panels for a total “peak capacity” of 1,000 Watts, or 1 kW. If you factor in everything, those panels should produce 1150 kilowatt-hours, or kWh, a year. In actual fact, they should produce closer to 1250 kWh a year, but we’ll stay with this semi-official lower number.

Right now you can get the system, equipment costs only, for around $2.50 per Watt, so our 1000 Watt system should cost about$2,500. The panels themselves will make it to 25 years with zero maintenance, and if they don’t you get a free one under warrantee. The electronics, notably the “inverter”, probably won’t make it that long and you should budget in one replacement. Right now that costs about $500, but by the time you need it I suspect it will be much lower. So what’s left is the cost to install. This can vary widely depending on the demands of your local power company. For argument’s sake, let’s call it$1,000, that’s two guys for two days. We’ll explore this more in a later section, because it becomes very important.

So where are we… $2,500 for the gear,$500 for a replacement inverter, and $1,000 for installation. That’s$4,000 all-in.

LCoE = cost / power

= ($2,500 +$500 + $1,000) / (1150 kWh a year x 25 years) = 4000 / 28750 = 13.9 cents/kWh ### Wait, what? My last electricity bill came out to 14.7 cents/kWh. That’s right, based on the assumptions above, it’s cheaper for me to put panels on my roof than it is to buy the power from the grid. And that means we’ve hit grid parity, right? Well no, as you’ll see, it’s more complex. But basically we have a rule of thumb here, and now you know why PV is the fastest growing power source in the world. But it also brings up the first important thing to consider. In this case, I’m comparing the cost of power on the retail side of the meter. If I look at my bill, the actual price for the electricity is not 14.7 cents, it’s somewhere around 8 to 9 cents. The rest is made up of delivery charges, fees, debt retirement and taxes. Its perfectly valid for you to compare the retail rate of power to the LCoE of panels on your roof, because that’s what you’d actually pay. However, if we’re not talking about your roof, but a larger plant out in a field somewhere, then that power has to be shipped off to the customers. In that case, the plant is going to have to pay all those same “adders”, and competing with the retail price is no good, the plant has to compete with the wholesale rate. But that’s the beauty of PV. Until we can buy Mr. Fusion, PV is pretty much the only practical power source that can be installed on the retail side of the meter. Any other practical source, from nuclear to wind, all connect in on the grid side. ### So… is this grid parity or not? Well, yes and no, depending on your definition. To avoid this confusion, the Japanese helpfully defined several types of grid parity. They order them depending on the delivered cost of electricity: 1. parity with the consumer retail rate 2. parity with the commercial/industrial retail rate 3. parity with the wholesale rate The easiest benchmark to hit is on the residential side, which they call “1st phase”. We’re almost there now, and we’ve already hit it in places where power is expensive (like Hawaii). “2nd phase” is when rooftop systems hit the price of power for large commercial or industrial users, who pay less than residential users. The “3rd phase” is when the power source is the same cost as existing systems on the wholesale side, and we’re a long way from that yet. So people who like PV say we’re already there, while people who don’t say we’re not even close. Both answers are correct. ### The nitty gritty But if we’re going to really compare energy systems on that “3rd phase” criterion, we need to get a little more complicated. That’s because most forms of power on the grid are very large industrial systems that take years to build. These systems start with a bank loan to pay for the construction, and don’t start paying that off until the plant is operational. So while the physical construction costs might be very low, once you factor in the interest payments, things can get really crazy. Compared to the “overnight cost” (the price if you could build it in one day), power plants might have real-world costs twice as high. Another consideration is inflation. You’re buying a power plant now, using today’s dollars. However, it’s delivering power for years. That dollar of power it produces today is worth more than the dollar it produces in 25 years. And if your plant takes years to get up and running, then this effect is even more pronounced – get it wrong, and the plant might never be able to pay for itself. So, what’s the formula look like when you put everything in? Well, sadly, it’s something like this… ${LEC} = \frac{\sum_{t=1}^{n} \frac{ I_t + M_t + F_t}{\left({1+r}\right)^t} }{\sum_{t=1}^{n} \frac{E_t}{\left({1+r}\right)^{t}} }$ This isn’t quite as bad as it looks. Basically what it’s saying is that you break things down year-by-year instead of calculating it all in one lump, and then add up each year’s calculation. So for any given year ,”t“, you calculate all the money you spent operating it that year (I + M + F), including the interest payments (I), maintenance (M) and fuel (M), and then you apply the “discount rate”, “r” to adjust for inflation. Do the same for the power produced (E, on the bottom), to account for the effect of inflation of the value of the power. Still with me? Seriously, it’s not that hard, the only odd bit is the discount calculation, but that’s basic a financial calculation use all over the place – like when they calculate your mortgage payments. ### So let’s try this again Ok, so let’s run our original scenario again, but this time we’ll say the homeowner borrows the money from the bank as part of their mortgage at 3.5% interest. That gets you annual payments of just under$250. We’ll also budget that inverter replacement for year 12 instead of up front. And we’re assuming that the discount rate is about the same as the interest rate (argue that amongst yourselves).

Right? So now we’ll look at the cost side of things this year by year…

1. 250 / 1.0035 = 249.13
2. 250 / 1.00701225 = 248.26
3. 250 / 1.01053679 = 247.39
4. 243.96
5. 245.67
6. and so on… but in year 12 it’s 496.35 because of the new inverter.

When you add it all up, it comes to $4,451.27, expressed in today’s dollars. Not that much different than what we calculated using the easy method. That’s one half. The other half is the power you expect to produce. In the earlier example we assumed it would produce the same amount of power every year. That’s not true, as there is a little degradation over time. The exact amount is subject to intense debate, but for this calculation we’re going to use a fixed value of 0.5% a year. This works almost exactly like the discount rate adjustment above, but it’s 0.5% instead of 3.5%, and everything is off by one year because the panels degrade at the end of the year. There’s one last twist. Let’s ignore the panel degradation for a second and pretend that they make that 1150 kWh a year through their lifetime. Our LCoE is calculating the value of the electricity in today’s money. So while the panels might produce 1150 kWh a year 25 years from now, the economic value of that power is less. How much less? Well that’s another matter of intense debate, because power prices have borne little relationship to inflation over the years. Nevertheless, the basic method is to use the same discount as you did on the cash. So then, we lower the power output and adjust by the discount rate. The series looks like this… 1. 1150 / 1 / 1.0035 = 1150 2. 1150 / 1.005 / 1.00701225 = 1,144.28 3. 1150 / 1.01 / 1.01053679 = 1138.59 4. 1132.92 5. 1127.28 6. and so on… So when you add all of this up, you get 18,022. Again, that’s not raw power, which you get by ignoring the discount rate and returns 27,097. As before, we’ll use the “bad one”. So… LCoE =$4,451.27 / 18.022 = 24.7 cents/kWh

So by this measure, we haven’t hit grid parity. However, if we assume electricity prices will go up at the rate of inflation, then you might want to use this version instead…

LCoE = $4,451.27 / 27,097 = 16.4 cents/kWh And if power prices do what we’ve seen in Ontario, and they’re going up faster than the inflation rate, then the equivalent rate could be anything./ So, as you see, depending on your assumptions, we’re either very close to grid parity, or not very close at all. Again, depending on whether or not you like PV, you’ll pick one or the other number to support your point. ### Let’s play! So now let’s see what happens when you start playing with you assumptions. This way we can get a feel for what parts of the equation are actually important in the outcome, a “stress test”. So here’s a bunch of things we can throw at it – I’ll spare you the year-by-year… Basic assumption: 24.7 cents/kWh • Production really is 1250 a year, not 1150: 22.5 cents/kWh • Panels degrade at 1% a year, often used in LCoE: 25.9 cents/kWh • Panels degrade at 0.25% a year, the measured value: 24.1 cents/kWh • Interest rate is 6.5%, yearly payments become$321:  30.1 cents/kWh
• Interest rate is 1.5%, yearly payments become $192: 19.5 cents/kWh • Equipment is$1.50 a Watt, payments become $180: 18.1 cents/kWh So you can see that the system isn’t very sensitive to changes in actual energy production (like the degradation rate). Even some major swings in the inputs cause little change to the LCoE, on the order of a few pennies. But change the interest rate and it goes up by 5 cents, or drop the cost of the panels and it drops by 7 cents. It’s all about the cost of money! So now let’s work backwards… what’s the total system price have to be in order to reach parity with my 15 cent/kWh bill?$2,500. If we keep the labor and wiring the same at $1,000, that means the panels and inverters have to go to just under$1.50 a Watt.

That is completely doable. In fact, it’s almost certain to happen in the next two to three years.

UPDATE in June 2014: It happened in 1.5 years. You can buy complete pre-bundled systems for small installs at about $1.50/W, and here in Ontario a completely installed 10k system goes in for$26,000 ($2.60/W). Commercial systems in the US, fully installed and commissioned, were$1.98/W at the end of 2013.

### How does this compare?

Ok so back to our baseline again… is 24.7 cents a lot or a little? It’s certainly more than you pay now, but that’s not saying much because practically every fuel is expected to go up in price, and sunshine is still free. We’re not looking at prices today, we need to know what we expect the price of other power to be in 25 years. Because if the price of power system “X” is expected to be 25 cents in 25 years, we’re better off building PV now.

So let’s compare this with a new nuclear plant.

If you call me today to put a PV system on the roof, you’ll have it up and running in a couple of months. In the meantime you keep the money in the bank. But if you want to start building a new nuclear plant today, it won’t be running for 10 to 12 years, and you’re going to have to pay people millions of dollars through that whole period. That’s true of any big-capital project.

So here’s the thing, in our calculations above, you were paying off the debt while making money. That meant that the discount rate applied equally on both sides. But in this case, I’m paying today’s dollars for construction, but getting 12-years-from-now dollars back. Do you see what this does? It makes the value of the power cheaper compared to the capital, which is a bad place to be. And if anything goes wrong with your schedule, you’re in serious, serious trouble.

Because this effect can change things so much, it’s common to see two completely different prices for a nuclear plant. One is the “overnight cost”, the price of the parts and labour if you could build it today. The overnight cost is the best analog to the price of a PV system, because those go up practically overnight. But since the construction of a nuke takes so long, it’s also common to include the price of borrowing the money during the construction phase. This is the “all in cost”, and it can be as much as double the overnight.

Ok, let’s get some numbers going.

There’s all sorts of numbers being thrown around on the cost side. We do know that CANDU6 plants go in for around $4 a Watt, judging by the known builds. However, it’s not entirely clear what number to use for new plants, because AECL’s recent bid for Darlington B was at least$26 billion for a 3.2 billion Watt plant, or about $8.25 a Watt. I believe that was the all-in figure, but that still suggests a price of around$5 a Watt overnight. Moody’s estimated new plants would be between $5 and$6, while the DoE suggests it’s around $3. I’m going to average all this out and call it$5, you can play with that yourself.

Cost of capital? Now that’s a big issue. It’s easy enough to get a couple of thousand rolled into your mortgage, but it’s another thing entirely to get tens of billions with no collateral. Borrowing costs are going to be at least 6.5%, the basic unsecured rate at the banks today. Don’t think that’s fair? Pickering and Bruce borrowed at 8 to 9%, Darlington started at 9 and went to 18%. Imagine what carrying billions of dollars at 18% does to the LCoE…

No, don’t imagine, do it! Using the same methodology you see for the PV case above, you get payments of $410 a year for a 1000 Watt reactor (scaling everything to “dollars per Watt” to keep it even). The cost side remains the same, paying$410 a year for 25 years and discounting as before. On the power side though, years 1 through 12 get you nothing, and then you get power for 25 years after that (year 37). When you do that math, you get 5.0 cents/kWh not including fuel, operating costs, decommissioning or anything else.

So is that a fair calculation? Well considering that Ontario Power Generation is paid 5.5 cents/kWh for the power from their reactors, yes, it seems like this is a very good calculation to use.

Update!

But what about new plants. I’m updating this article to reflect the recent news that two new rectors have been approved in the US, two of the new AP1000’s will go in at Vogtle in Georgia.

How’s that work out? Well the numbers given at the time of the release were $6.26 a Watt, which is outside the worst-case calculated by Moody’s, and especially disconcerting considering they already have the land and power distribution system. In fact, to get that power out of the plant, there’s another$3 billion in wiring, so the real cost is $7.73 a Watt. This is starting to sound a whole lot like the price of the ACR, in spite of all the rhetoric of the AP1000 being cheaper because it’s “assembly lined”. However, as the paperwork’s already been in process for ages, the time-to-power is expected to be only five years. Yeah yeah yeah, with a five-year delay to production, 6.5% interest and a 25 year lifespan with no degradation… LCoE = 7.6 cents/kWh, just for CAPEX alone! Now lets do the same for a large industrial PV system, in Mohave where they get 1650 kWh/kW a year. Systems are going in right now at$3 a watt, and we’ll assume a 40 year life with three inverter replacements, and the same discount and interest rates…

LCoE = 11.5 cents/kWh, all in.

### Ok, so PV’s out, right?

If a reactor generates power for around 7.6 cents, and “big PV” at 11.5 cents, then we do nuclear right?

It’s simply not that easy. Here’s a couple of very important things to consider:

1. the price of PV is going down very rapidly, while the price of nuclear is basically the same as it was 40 years ago
2. we’re in the midst of what the Brits call a “credit crunch”, big-capital projects simply don’t happen
3. we need green energy now, not 12 years from now
4. fuel costs… fuel represents a small part of the LCoE for a nuke plant, but the price of fuel these days is basically a proxy for oil

That first item is the real big issue. Right now industrial PV is going in at under $3 a Watt, but that price, as I noted early, has come down 70% in the last two years. To hit the same price as the AP1000, it has to go in at$2 a Watt (try it yourself). That’s a 50% decrease compared to current prices. And we have five years to get to this point, because that’s when we get the first power from Vogtle.

And therein lies the debate. Will PV hit $2 in the next five years? Everyone says yes. Everyone. ### All in! And that’s why this paper is causing such a ruckus right now. It’s not the first to go down this path, but it is one of the most influential. We’ll have to see if the industry starts using these new numbers, because at this point we only need another year or two before we have widespread grid parity on the customer side. So, go try this yourself! Here’s a great little form to play with. ## Comments» 1. Roland - March 18, 2012 Installation costs for panels are too high. Shingles will change that. Installing/replacing a shingle roof is something you have to do anyway, so (most of) it is “sunk cost.” Maury Markowitz - March 24, 2012 Agreed. And the electrical only needs to be done once. Unfortunately no one’s made one that’s economical – yet. 2. rathelm - April 25, 2012 Very intriguing write up. I am curious on your thoughts on the consumer market. You have all your math done for 25 years, but wouldn’t it seem that the average person would only finance something like this for 5 to 10 years? Is the only way to get your money out of this is to bake the cost into the home loan? With that said what is the return value on PV when you sell the property (assuming a normal housing market)? As an example, swimming pools only recover a fraction of their cost. Maury Markowitz - April 25, 2012 Absolutely rath, and this is certainly a big problem on the consumer side (not commercial, where they can do the math). In spite of every suggestion to the contrary, people still consider their house to be an ephemeral item that they’ll dump the second the price is right. And, as a result, they’ll only consider systems that pay off in some short period of time, say 5 years. If they sell the house, they don’t want to keep paying for the loan. There is a good solution to this problem – loan the money from the local government and pay it back through property taxes. That way it doesn’t matter who owns the house, and the payment period can be anything you want, even 25 years. Since the payments will be lower than the income (using the values above) then there’s really no reason not to do it right now. As to the property *value*, that’s a matter of some debate. There was a paper a few years back that claimed that every$1 in panels gets you $1 in resale. When I looked into the paper, it turned out the research had nothing to do with solar, and they were making what I believed was an extremely questionable comparison. However, there’s been a couple of newer papers since then that have looked at real PV properties in California, and guess what?$1 in panels = \$1 in value!

rathelm - April 25, 2012

Hmm.. Interesting is the 1 to 1 value at current market values or is there expected depreciation rates? The reason I ask is in the next 2 years I was contemplating getting back into the housing market and I was seriously considering an investment in PV if the price was right (also want an electric car). I live in Southern Nevada so sun is something we have plenty of.