Saturday, August 9, 2008

Coal / Solar Cost Comparison - Final Draft

Note: This article is under revision, considering current fluctuations in price. The Concept is sound (IMO) as a way to make rough comparisons in cost, but the Prices are presently off.

Also note, the 33% Insolation that is used as a basis for comparison, is very high for a stationary system, but well within the range of a tracking system. For more information on Insolation, see "A Note on Units of Energy and Insolation."





I'll set up two equivalent scenarios using Coal and Solar, and will then make comparisons.




Note: I make numerous assumptions, and will mention these where appropriate.




For this thought experiment, we'll imagine that both of these industries are starting from scratch with equal Energy Production Capacities. In reality, of course, Coal has tremendous existing Scale Advantage over Solar.

This will be a demonstration of how fuel costs could affect the long term comparative cost of the Coal Energy vs. Solar Energy.

First, imagine two industries; Solar and Coal. The goal of both of these industries is to produce Energy.




Now, divide each of the industries into three groups.




Group One:

Group One is made up of those segments of the Industries that produce the actual Electrical Generation Facilities.

In the case of Coal, this is the industry that produces the actual Power Plant. It would include everything from the ground up, like the steelworks that made the metal, to the quarries that produced the Concrete. It would include the Engineers, Managers, and Laborers for the Plant Construction, as well as the Lawyers and Lobbyists required to work with the Government and Public to support the plant's construction.

In the case of Solar, this would include all of the players from TCS, Wafers, Crucibles, and Modules, through the final Solar Power Plant Installation. Once again, it would include all of the extraneous support required for the project.


Group Two:

This group is made up of everyone associated with supplying the fuel for the Power Plants that were produced by Group One, above.

- For Coal, this would include everything from the actual Mining of the Coal; the engineers, geologists, equipment operators, supervisors, etc. This group would also include the Transportation of the Coal to the Power Plant.

- For Solar, there is no Second Group. There is no Delivery of fuel to the Solar Plant.


Group Three:

This is all of those involved in the upkeep over time of the power plants. I'll ignore this group, and give Coal a freebie. I think it's safe to say that Solar will beat Coal on Upkeep Costs over time.



Notes and Assumptions:




Note: The Solar Plant is going to have to be rather larger in peak rating than the Coal Plant, since Sunlight isn't constant. 33% is a fair conversion for a very sunny place, so our Solar Plant has to be three times the rated output of the Coal Plant (Say, 350MW Coal = 1050MW Solar). Whatever actual output we settle on, we just want the total yearly output of Energy from both plants to be the same for comparison purposes.

Note: Solar does not provide a base load like Coal. We're just looking at total Energy Output, not the convenience or timing of the final product. Ultimately, for future base-loads, we'll need a heck of a grid, plus some other provider like Sequestered Coal, Geothermal, or something else like that.

Note: I have Silicon-based Photovoltaic Solar in mind in writing this.

Note: PV Solar lends itself to a decentralized solution. Therefore, when talking about a 1050 MW Installation, we don't have to assume that some company has bought 1050 MW worth of Panels and Installed them as a single project. Instead, we can talk about a total of 1050 MW of Panels installed anywhere, in any distribution. Whether Centralized, or not, a Watt of Solar Energy offsets a Watt of Fossil-based Production.

Note: The referred-to Spreadsheet is likely not entirely clear to anyone but myself. I did try to add descriptions to help, but there are a lot of numbers involved. Feel free to counter my numbers with your own if you think that I'm off on anything.

Assumption: I've worked out several Cost scenarios involving guesses on future Inflation / Coal Price Increases. Of course there's no telling how the price of Coal will vary over the next 25 Years. There are numerous reasons to suggest, however, that the price of Coal will not remain static, particularly in the face of Peak Fossil and US Dollar Depreciation. Even if Coal is not near Peak, Peak Oil will put increasing upward price pressure on Fuel to support Coal Deliveries. Nearly all of the price pressures in the foreseeable future point towards a continued Increase in the Price of Coal, particularly in the price of non-local Coal that requires long distance transport.

Assumption: No cost factors related to future Climate Change Regulations are included in this Document. This gives a huge Freebie to Coal, as Sequestration and Carbon Credits will add greatly to the cost of Energy Production from Coal Sources over the next 25 Years.

Assumption: No cost factors related to Increased Healthcare Costs due to the Burning of Coal. This is another Freebie for Coal as far as this paper is concerned.

Assumption: I assume for the initial calculations that the lifespan of the Coal Plant and the Solar Plant are equal to 25 Years. The lifespan of either a Coal Plant or a Solar Plant is certainly greater than 25 Years. I'll look back at this in a later section.

Assumption: I assume for the initial calculations that the Conversion Efficiency of the Solar Panels stay constant throughout the life of the plant. Again, I'll look back at this in a later section.



Imagine both a Coal Industry and a Solar Industry, each capable of producing a single Power Plant per year (or arbitrary unit of time, really).




Year One: Both a Coal and a Solar Plant are built.

By the end of year One, both the Coal Plant and the Solar Plant have produced one Yearly Energy Unit. The Coal Plant has consumed it's required yearly supply of Coal.

Year Two: Both a Coal and a Solar Plant are built.

By the end of this year, the Plants that were built last year, each produce their total yearly capacity in Energy. In addition, the new plants being constructed this year have each produced a Yearly Energy Unit. The two Coal Plants consume a total of 2 Units of Coal for the year.

The Total Amount of Coal burned since the first Year is 3 Units.

Year Three: Both a Coal and a Solar Plant are built.

By the end of this year, the Plants that were built in the two previous years, each produce their total yearly capacities in Energy, for a total of 2 Units of Energy from Solar and Coal Plants. In addition, the new plants from this year have each produced a Yearly Energy Unit. The three Coal Plants consume a total of 3 Units of Coal for the year.

The Total Amount of Coal burned since the first Year is 6 Units.



Now, to make some Comparisons between Coal and Solar based on the above setup.




Comparison One: Side-by-Side – Energy Output

Take a look at this spreadsheet, I'll take it out 25 Years.

See Sheet 1.

This first set just shows that over 25 years, the total Energy Output of both our Coal and Our Solar Industries are the same. Easy enough, that was part of the basic assumption.


Comparison Two: Side-by-Side – Feedstock Demand

This next set shows how the total demand for Coal Feedstock grows over time.

See Sheet 2.

Per Plant, of course, it's linear; just One Unit of Coal Fuel per Year per Plant; however, as the number of plants increases, the Total Yearly Demand for Coal for the Industry increases exponentially based on the rate of increase of demand. This is a recipe for increased cost of that fuel over time, particularly since the Coal is utterly destroyed in the process of burning; there is no recycling or conservation of raw materials.

In fact, over the first 25 years of the scenario, the yearly demand for Coal from the Power Plants has increased 25 times. Unless supply increases similarly, prices will have to increase due to the additional demand.

This is where our assumption that the Coal Industry isn't actually a behemoth in comparison to Solar comes in. Of course, the Industry is so large that an extra 25 Plants worth of Demand isn't going to stress out the Suppliers too much. However, the ability of the Coal Industry to increase supply to meet demand is not infinite, particularly since, once the coal is gone from a site, it's gone and the total production from that site has to be replaced by production from a new site. Finding new sites gets more difficult over time, particularly as International Politics and Dependence on Support from Sovereign Governments creates Long Term Complications and various forms of Blowback.

Looking at some actual Coal Consumption Numbers (See P.35), we see that in 10 years between '97 and '07, consumption of Coal increased from 2317 to 3177 (Millions of Tons of Oil Equivalent), or by 37%. According to The World Coal Institute, "at current production levels coal will be available for at least the next 147 years." They specify at "current production rates," which says to me that they are not taking into account increases in Demand / Production, as production rates would either have to increase to meet demand, or else price would have to go through the roof to take into account the discrepancy. Oddly enough, at the beginning of the writing of this paper, the World Coal Institute estimation was that we had 155 years worth of Coal remaining, but now, having confirmed my links, I see that they've updated this number to 147 Years, which means that in about two weeks of time, the World Coal Institute revised their estimate down by eight years*. For a counter opinion on the timing of Peak Coal, see this article which concludes that it could be in as soon as 15 years.


Comparison Three: Costs – Inflation Scenarios

Looking at a specific example, I'll take a look at some samples of Coal Plants, to see how much coal they each go through in a year. I've grabbed a couple of examples from the web, which gives some idea of how much coal a plant will go through, compared to its rated power output. It looks like Milliken Station on Cayuga Lake is quoted as the most efficient plant of the four that I found (in Energy per ton of Coal), so I'll use that plant as an example, and support it as within a reasonable estimation with some averages from www.powerofcoal.com.

See Sheet 3.

In fact, it appears that the fuel cost that I derive for Milliken Station is slightly above the average in the Industry. Per PowerofCoal. Working out the Cost per Watt from Milliken Station over 25 Years at $100 / ton gives $6.26/Watt*25 Years. This compares to the National Average, which works out to $5.18/Watt*25 Years. Note that since this “PowerofCoal” reference was dated, most Coal Prices have increased quite dramatically, so the national average costs have probably increased by 25% or more.

Note: Per “Checking my Numbers,” below, it appears that Milliken Station is very close to the theoretical maximum in terms of Energy Production / Ton of Coal. Therefore the PowerofCoal Numbers are likely skewed in some way, likely due to the Particularly large amount of easily recoverable Coal in the Powder River Basin in Wyoming, and possibly also due to Government incentives at some stage of the Coal Energy Production Cycle.

Over the first 25 years of this plant's life, it costs a total of around $2.6 Billion in initial Construction Costs and Yearly Deliveries of Coal Fuel. Of course, this assumes that the price of Coal doesn't increase over this 25 years, and it assumes that the plant costs nothing in maintenance. As shown on Sheet 3, if Inflationary factors are considered, total cost for this near average plant over 25 years could actually approach $6+ Billion.

For Fuel Cost Estimation for other Coal Plants, see Sheet 4.

Ok, now to look at an equivalent Solar Installation (1050MW @ 33% of Peak in Total Energy Output). There are alot of different ways to work out sample prices for equivalent Solar Installations. The first, and ugliest example would be to use the retail price data from Solarbuzz.

According to Solarbuzz, the average US Retail Price for Panels is $4.82 Watt, and the Total Cost of the Project is about Twice the cost of the PV Modules. Using this method arrives at an end resulting cost of between about 2 and 5 times the cost of an equivalent Coal Plant over 25 years (Depending on Future Inflation). At this price, the total cost of the Installation would be $4.82/W * 1MillionW/MW * 1050MW * 2 = $10.12 Billion (compared to $2-$6 Billion for an equivalent Coal Plant). Wow! Ok, but this number reflects the many inefficiencies of small-scale retail distribution and installation. It also represents the current high demand / low supply that we see in the World PV Market, reflected among other things by a cost of Polysilicon of 5-10 times (or more) the cost of its production (Polysilicon costs are around 40% of the total cost of producing Solar Panels at this time).

So, with a 25 Year window, it's tough to compare the Best-case scenario for Coal to the Worst-case scenario for Solar at present Solar Prices. We'll get back to this one a bit later.

Instead, I'll try to gauge the cost of some existing large scale PV Solar Installations. Attached you'll see a few price references to indicate the Cost / Peak Power that is currently available for mid-size Installation sizes.

See Sheet 5.

This spreadsheet shows some examples of Solar Power Plants in the real World, their output, and their projected costs. Remember, that I've chosen a 1050MW Solar Plant to be equivalent to a 350MW Coal Plant in annual Energy Output.

The Price per Watt ranges from $5.33 -$8.05. So, using this range of prices to construct a theoretical Solar Plant of 1050MW would give us costs ranging from $5.8-$8.5 Billion. Remember, this is compared to a cost for coal of my just slightly above US average Coal Power Production Costs of $2.6-$6.5 Billion.

Personally, I think that assuming future inflation to be zero is ludicrous, and can't help but think that the much safer bet is that Coal Fuel Prices will increase significantly faster in the near and mid-term future than we're used to thinking about. If this is the case, then there are cases in this scenario in which Solar Installation would be the best economic choice for installation RIGHT NOW.


Comparison Three A: Costs – Inflation Scenarios – Extended to 50 Years

We know that a Coal Plant Lifespan isn't limited to 25 Years. We know that Solar Panels are typically warranted out to 25 Years. We also know, however, that Solar Panels can last significantly longer than 25 Years. Sheet 7 gives some idea of what kind of useful lifespan we are looking at as far as Solar Panels, based on a .5% degradation in output per Year. Considering this degradation would certainly throw off the previous Calculations, so I'll consider it for this scenario. I'll also cut down the total output of the Panels by 5% due to Inverter Losses, and by 10% for High Temperature Loss. In addition, I'll take into account the Panel Output loss over that 50 Years using the Chart on Sheet 7 by reducing the overall Output by an extra 12.5%. All of this means that now, instead of needing 1050MW to equal the 350MW Coal Plant, we're going to need a 1364MW Solar Plant.

As before, using Solarbuzz, $4.82/W * 1MillionW/MW * 1364MW * 2 = $13.15 Billion for the entire Solar Installation.

Now, for the Coal Plant, we'll figure out the cost over 50 Years assuming some inflation rate. This time I'll assume a rate of 4%. See Sheet 8. It seems that assuming 4% Inflation in the price of Coal over these 50 Years, even with all of the negative offsets that I've just added to the cost of the Solar Installation, the Coal Plant LOSES with a total fuel cost of $13.4 Billion.

Remember, Solarbuzz Numbers are Retail. How much money can we save for a utility-scale operation by buying bulk? I'm going to take a wild guess.

In the real World, Trina Solar recently reported an ASP, or Average Selling Price, of $3.85 / Watt, which is relatively high relative to other Solar Manufacturers, but well below Retail. Given a direct relationship with a Modulemaker such as Trina, and the ability to buy at around $3.85 / Watt, brings the cost of our 1364MW Solar Plant cost down by $2.6 Billion to $10.50 Billion.

We can do more. Solarbuzz says that the total cost of the Installation is twice the cost of the Modules. Well, clearly this reflects the cost of Installation on the Retail Level, which will certainly be higher than the cost of Installation on a Utility Scale. It is much more challenging to do thousands of Individual Installations on unique rooftops all over a region, than it is to take a piece of land and set up a large scale array of panels. Another Efficiency factor to be found in Large-scale installations will be the savings due to an efficiently engineered wiring and electrical design. For instance, a large scale system won't need the vast number of small inverters that would be required for an equally powered Residential Distribution. I think it's pretty safe to assume that 20% in efficiencies could be found in this situation, so we work out a Installation cost per Watt of $3.85, or $2.6 Billion Dollars off of the cost of the 1364MW Installation, leading to a total cost of $7.9 Billion Dollars.

So, the results of this scenario show that over 50 Years, our 1364W Installation should compare very favorably with Coal. The Total Installation Cost of $7.9 Billion is much lower than the Coal Plant's 50 Year Cost of $13.4 Billion assuming a low low inflation rate of 4%. Is fact, just considering a low 4% Inflation Rate, the Solar Plant breaks even with the Coal Plant at 39 Years. Anything beyond this time is Icing.



A Note on Scale




So far I've been assuming that 1050MW or 1364MW of Solar panels could be even bought on the Open Market. This is a questionable assumption.

According to the Chart on Sheet 5, the total annual installation for 2007 was 2.2 GW. However, as can be seen on the same chart, the rate of increase of installation capacity (limited by production capacity) is taking off, and is expected to increase by Eighteen Hundred Percent, to 37GW Annually, in the next Four Years.

This is when things will start to get interesting, because Utility-scale Developers will for the first time ever, have the opportunity to supply large-scale plants with decreasing lead times, and at the prices that I have talked about in this document, or less.



Conclusion




Well, so far, what I've shown is that there is overlap in the long term price of a Solar Installation and Coal Installations. Much depends on the future rate of Inflation, or at least Inflation in terms of increased Price of Coal. However, given that Future Inflation is not knowable, but in today's World Economic Climate could be explosive, Solar, even at today's high prices, fills a lucrative Energy Niche as a hedge against increasing Coal prices.

As it is, Solar Producers have more than enough Customers to easily sell all the product that they can make at today's prices. Industry Production Capacity is increasing incredibly fast, though, and will likely soon outstrip demand. However, long term Coal Generation costs would indicate that a price bottom for Solar Products will arrive as defined by projections of long-term production costs from Fossil Fuels similar to what I've shown above.

In a future Post I will look at Comparisons between Solar and Natural Gas Electricity Production, which is really a much closer fit to the particular niche that Solar fills, but in this first case I wanted to compare the costs to Coal, which is typically acknowledged as the cheapest current source of Electricity.



Checking my Numbers




Energy Capacity per Ton of Coal:


Is it reasonable to assume that a Coal Plant like Milliken Station actually consumes 876000 Tons of Coal per Year in order to produce its 350MW of Power?

Per Wikipedia, Coal Plants produce approx. 2KW*Hour/KG of Coal.

I want to solve the equation (2KW*Hour/KG)*X Tons of Coal Burned / Year = 350 MW * Year.

I'll convert to Years because because I want the Annual Average to make Comparisons to. As for the Mass, I want Long Tons, which are equal to 1016 KG, and for Power I want Megawatts.

So, X Tons / Year = (350MW * Year)/(2KW*Hour/KG)

Then, X Tons / Year = (350MW * Year)/(2KW*Hour/KG*1MW/1000KW*1Year/8760Hours*1016KG/1Ton)

Finally, X Tons / Year = (350MW * Year)/(.000232MW*Year/Ton) = 1.5 Million Tons of Coal / Year. Wow, this is rather a lot higher than my estimated Coal Fuel Demand for a 350MW Plant, which makes the Solar Plant considerably cheaper in Comparison.

Let's try another estimation. A physicist friend of mine, who works in Coal, estimated for me that a Ton of Thermal Coal, when burned, produces 26 GJ of Energy (Wikipedia has it at 24 GJ/Ton (after some conversions)). Using an Online Converter, 26 GJ works out to 7.22 MW*Hour. Not all of that Energy is converted into Electricity at the Coal Plant, only between 30%-35% is typically converted with a theoretical limit at about 45%.

Using 35% Efficiency would put the Energy / Ton of Coal at 9.1 GJ/Ton, or 2.52 MW*Hour/Ton.

Using the same process as above, for a 350 MW Power Plant, this works out to 1.22 Million Tons of Coal / Year, also higher than my earlier Estimation for Milliken Station.

Let's go one step better for Coal. I've seen reference to 30 GJ per Ton and 42% Conversion Efficiency at a particular plant. I'll work out the Tons of Coal / Year for a 350MW Coal Plant under these Conditions.

30 GJ per Ton = 8.33 MW*Hour/Ton.

At 42% Efficiency in converting this energy to Electricity at a Coal Plant, we get 3.5 MW*Hour/Ton.

Calculating as above, at this incredibly efficient example we come up with Total Tons per Year = (350MW * Year)/(3.5 MW*Hour/Ton*1Year/8760Hours) = 877,000 Tons per Year. This almost exactly matches our estimation for Milliken Station. Nice!



PowerofCoal Data Check:


PowerofCoal Claim: The Average Cost of Production of all US Coal Plants (as of Jan '08) = $23.68 per MW*Hour

In Comparison Three I used this number to calculate a Cost / Watt over 25 Years of $5.18/Watt*25 Years. To do this, I did the following conversion:

Average Cost / Watt*Year = ($23.68/MW*Hour)(1MW/1,000,000W)(365Days/1Year)(24Hours/1Day) = $0.20 / Watt*Year = $5.18 / W*25Years or $10.36 / W*50Years.

Note: These numbers for PowerofCoal.com include all of the cost of production, including presumably, maintenance and upkeep. So, they should be slightly more representative of the actual costs to produce Energy with Coal in the US, however, as shown above, Milliken Station is close to the peak of Efficiency in terms of Energy Output to Coal Consumed, so in order to arrive at a lower average cost than Milliken Station, the average cost of Coal to these US Coal Plants must be much lower than $100 / Ton, or else the cost to produce Coal Energy in the US must be Subsidized. We can see from the Chart that the US does indeed have access to very cheap Coal from Powder River Basin, though from the same Chart we can also see that other Coal Sources are increasing their prices dramatically.

Using the above numbers as a starting place, and then calculating in 4% in Inflation Increases per year, gives $8.63 / W*25Years or $31.63 / W*50Years.



Additional References




Commodity Price Data (Pink Sheets)

PV Costs to Decrease 40% by 2010

China Spurs Coal-Price Surge -WSJ



* Note on World Coal Institute Archives. Based on Archived Reports :

2008 Estimated Reserves: 147 Years
2007 Estimated Reserves: 147 Years
2006 Estimated Reserves: 155 Years
2005 Estimated Reserves: 164 Years
2004 Estimated Reserves: 190 Years
2003 Estimated Reserves: 200 Years
2001 Estimated Reserves: 200 Years

Conclusion, since 2001, we've used 53 Years worth of Coal. LOL!



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3 comments:

Anonymous said...

Your forgot to include the time value of money. If you invest in a safe return of 2% above inflation the difference in capital outlay between solar and coal, solar can't win.

It is amazing how much better this looks for solar than 10 years ago however. Wait another 5 years and do the calcs again.

milt said...

Hi,
Interesting calculation, but I think you have made a mistake regarding time value of money. You are using 2010 dollars for your solar cost, while using 2010-2060 dollars for your coal costs. Properly calculate coal in 2010 dollars and unfortunately it is much cheaper than solar.
Milt

D Pickard said...

It's been a long time, but I recall that the reason I did this was because the costs of Solar are frontloaded to the initial installation, whereas coal has a much lower immediate price, but requires a constant supply of coal during the plant's lifetime.