Guest essay by Philip Dowd

Here is a simple example that illustrates why current solar technology will be hard-pressed to replace existing carbon-fired power plants.

Let’s suppose that a power company is planning to scrap a coal-fired power plant and wants to replace it with a new plant. Furthermore, let’s assume that the old plant to be scrapped is in Arizona. The options for the new plant are natural gas and solar. The company wants a simple, ball-park analysis of the front-end cost to build each of these options.

The requirements:

1. Electricity demand on this facility is 4,800 MWh/day, about the demand for a community of 160,000 average households[i]

2. The “up time” of both plants must be equal. That is, both must be equally reliable and produce the demand for the same fraction of time over the course of one year.

Assumptions:

1. The solar plant will consist of a Photovoltaic (PV) panel and a battery. The PV panel will generate enough electricity during the day to produce the necessary output and charge the battery. The battery will generate the necessary output at night.

2. Night time demand equals day time demand.

3. The new plant will be built in Arizona, a good spot for a solar plant

The Analysis

The analysis is in the form of an annotated spread sheet, showing the two options and the steps required to derive the solution.

I. Capital Cost to Generate Electricity

II. Capital Cost of Storage for Night Time Demand

The solar option requires a battery that would supply night time demand. For this purpose we will use technology known as “Pumped Storage”. This method stores energy in the form of potential energy of water, pumped from a lower elevation reservoir to a higher elevation reservoir. In our example, about half of the electric power from our solar facility produced during the day would be used to run the pumps and fill the upper reservoir. Then, at night, the stored water would be released through turbines to produce the electricity that would run the night time economy.

For more on this see: https://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity

III. Total Capital Cost Including Storage ($millions)

For our exercise let’s consider the Bath County facility, located in the northern corner of Bath County, Virginia[vii]. It was constructed in 1977-85 and is currently the largest pumped storage facility in the world.

Here are its relevant specifications:

So, at this point in the exercise we have the relative costs of the two options to generate electricity over a twenty-four hour period, assuming normal operations for both. The capital cost of the solar option is about 14 times the cost of the gas option.

Conclusion

This back-of-the-envelope analysis suggests that a solar (PV) power plant that could deliver that same results as a gas-fired power plant would cost about 14 times the gas-fired option to build. It is worth noting that the solar option cost excludes any subsidies, investment tax credits, etc, that could narrow the range, but it is obvious from this little exercise that until solar technology improves dramatically, there is little chance that it will replace natural gas as the “go-to” option for new power plants.

Bill Gates, the co-founder of Microsoft, has said that it was “fantastic” that the UN, national governments, and environmental campaigners had raised awareness of climate change and were taking steps to counter it. However, he argued that current technologies could only reduce global CO2 emissions at a “beyond astronomical” cost. “The only way you can get to the very positive scenario is by great innovation,” he said. “Innovation really does bend the curve.”[xiv]

I totally agree. Mr Gates intends to invest $2 billion in renewable energy over the next five years — innovation to bend the curve. Solar energy is going to need lots of it if it is ever to become a viable substitute for carbon-based energy.

References:

[i] Average household in US consumes about 900 kWh/month or about 30 kWh/day

http://insideenergy.org/2014/05/22/using-energy-how-much-electricity-do-you-use-each-month/

[ii] Net Capacity = electricity demand for one day ÷ 24 hrs or x/24

[iii] http://www.eia.gov/forecasts/aeo/electricity_generation.cfm

Scroll down to the table. Capacity factor is found in col 2.

The number for gas is “Conventional Combined Cycle”

The number for solar is ”Solar PV”

[iv] Gross Capacity required = net capacity ÷ capacity factor

[v] http://www.eia.gov/forecasts/aeo/assumptions/pdf/electricity.pdf#page=4

The cost used comes from col 5 in this chart: “Base Overnight Cost in 2014”

The entry for gas is “Conventional Gas/Oil Combined Cycle”

The entry for solar is “Solar PV”. Note that this cost excludes any subsidies.

[vi] Gross Capacity Required x Capital Cost

[vii] http://en.wikipedia.org/wiki/Bath_County_Pumped_Storage_Station

[viii] The equation here is Capital Cost at time of construction x adjustment for inflation

For Bath = $1,600 mil x 2.6 = $4.1 billion (inflation adjustment is for the period 1981 – 2014)

For inflation adjustment use this site: http://www.usinflationcalculator.com/

[ix] The equation here is Capacity x Time to Empty Upper Reservoir

For Bath = 3,000 MW x 14.3 hours = 43.0 GWh

[x] Assume night time demand = day time demand so night time demand on the solar battery = ½ total daily demand

[xi] Cost of Storage = Capital Cost ÷ Stored Energy = $4.1 billion ÷ 43 GWh ≈ $100/kWh

[xii] Capex to store night time demand = $100/kWh x 0.5X kWh = $50X

[xiii] Total here is the “Total Capital Cost” in Sec I plus the “Cost of Storage” in Sec II

[xiv] http://www.ft.com/intl/cms/s/2/4f66ff5c-1a47-11e5-a130-2e7db721f996.html#axzz3kyDZjQxG

Errata and notes: The $4.1 trillion capex for the Bath County facility is a typo; yes, should be $4.1 billion, both in the body of the article and the footnotes. This has been corrected. All of the other numbers in the body of the article are correct and the conclusion that the capex of the solar plant is 14 times the gas plant stands.

The assumption of night time demand = day time is just for convenience. I know its not true, but this is just a ball park analysis and I’m trying to keep it simple.

The analysis deals only with capital cost, not levelized or life cycle, again just to keep it as simple as possible. – Philip Dowd

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