How should we generate electricity?

Last post, we discussed the various power sources from the perspective of the grid and briefly discussed energy storage. This post will put together the results of Parts I & II in a simple model to test different strategies for moving away from using fossil fuels to generate our electricity.

The simplifications in the model will make the transition away from fossil fuels look easier than it is. But they should be a fair comparison between the different strategies we might use.

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Prerequisites: Part II: The Perspective of the Grid.

Originally Written: March 2021.

Confidence Level: Calculations are approximate, but are the right order of magnitude.

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Consider a hypothetical country which produces and uses 100 GW of electricity. This is about the size of Japan. To convert to a major European country or to Texas, divide all of the numbers by 2. To convert to the entire US, multiply all of the numbers by 5.

I will include daily fluctuations in the model. This country uses 120 GW of electricity during the day and 80 GW at night. Day and night each last for 12 hours. I will ignore seasonal variability in demand (and day length) and surge demand. Including these would make my model more complicated – and would make the transition away from fossil fuels harder. In real grids, you should always have some spare capacity to deal with demand surges or other unexpected events.

Instead of explicitly calculating maintenance, I will estimate maintenance as the cost to replace power sources when they get too old. To make this reasonable, I slightly underestimate how long everything lasts.

I focus on four ways of generating electricity:

• Hydroelectric is on demand. We have 10 GW already built and we cannot build any more.
• Natural gas represents all fossil fuels and is on demand. It is also already built.
• Solar and wind are combined, in the right ratio to even out their seasonal dependence. They are intermittent. A megawatt of capacity costs $1.5 million to build,^[1]Solar costs $\$$1.2 million and wind $\$$1.8 million. uses 50 acres of land,^[2]Solar uses 30 acres and wind uses 75 acres. and has to be replaced every 20 years.^[3]Solar lasts for 25 years and wind lasts for 20 years. The capacity factor is 33%,^[4]Wind has a capacity factor of 30%-40%, while solar has 10%-30%. so 100 MW of solar / wind capacity produces only 33 MW of power on average, when we include nights and windless days.
• Nuclear is steady. A megawatt of capacity costs $6 million to build and has to be replaced every 40 years. The capacity factor is 100%.^[5]This is slightly higher than the actual capacity factor of 90%, but 33% is a bit high for combined solar/wind too.

Note that these prices are stated for a megawatt (MW). Building a gigawatt (GW) of capacity would cost 1,000 times as much.

I will also include batteries in some of the strategies. They cost $125 million per GW-hr and have to be replaced every 5 years.

All costs are using 2020 prices. Technological development or regulatory reform could significantly change the prices of any of these. I will not try to guess which technologies will improve the fastest in the future.

For intermittent sources, we will have to worry about lulls. On windless nights, there is no electricity generated by solar or wind. Cloudy, windless days might be even worse because the demand is higher, but at least some light gets through the clouds. I will use windless nights as estimates for the lulls.

The main comparison I will look at is between solar / wind and nuclear. I will not include discuss mixed strategies here, to keep this from getting too long. Nuclear costs 4 times as much to build, but has 3 times the capacity factor and lasts twice as long.

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Initial Scenario

We start with our electricity dominated by fossil fuels. We have 10 GW of hydroelectric capacity and 110 GW of natural gas capacity. Together, these cover the 120 GW of power needed during the day.

Both power sources are on demand, so we can always choose how much of them we need. Hydroelectricity is prioritized, so some natural gas power plants shut off at night.

Here is the capacity and average production for our initial scenario:

	Hydroelectricity	Natural Gas	Wind / Solar	Nuclear
Capacity	10 GW	110 GW	0 GW	0 GW
Production	10 GW	90 GW	0 GW	0 GW

Our goal is to build new capacity to move away from natural gas.

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Building Solar / Wind At Capacity

We need 120 GW of solar / wind during the day, so let’s build 120 GW of solar / wind capacity.

The total cost of this plan is 120,000 MW $\times$ $\$$1.5 million per MW = $\$$180 billion.

Since solar panels and wind turbines last about 20 years, we would need to replace 1/20th of our capacity every year. This is an annual cost of $\$$9 billion per year.

The total land area needed is 120,000 MW $\times$ 50 acres per MW = 9,400 square miles = 24,000 square kilometers. This is about the size of New Hampshire or Wales.

These sources have a capacity factor of 33%, so 120 GW of capacity only produces 40 GW of electricity on average. The rest has to be supplied by other sources: hydroelectricity and natural gas.

To deal with windless nights, we need 80 GW of on demand backup. Hydroelectricity accounts for 10 GW of this, but the other 70 GW have to come from natural gas.

Here is what the capacity and average production look like if we build solar / wind at capacity:

	Hydroelectricity	Natural Gas	Wind / Solar	Nuclear
Capacity	10 GW	70 GW	120 GW	0 GW
Production	10 GW	50 GW	40 GW	0 GW

Building solar / wind at capacity only partially moves us away from fossil fuels.

This is approximately what Germany is doing now. They get about 50% of their electricity from renewables (including hydroelectricity and biofuels), 10% from nuclear power (which they are shutting off), and 40% from coal and natural gas.

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Building Solar / Wind Over Capacity

Let’s just build more solar / wind.

Instead of building 120 GW of new solar / wind capacity, let’s build 300 GW. The average power produced by solar / wind now matches the average power demand.

The total cost of this plan is 300,000 MW $\times$ $\$$1.5 million = $\$$ 450 billion.

Replacing 1/20th of the solar panels and wind turbines costs about $22 billion per year.

The total land area used is 300,000 MW $\times$ 50 acres = 23,000 square miles = 61,000 square kilometers. This is about the size of West Virginia or Croatia. If we scale this up to the US electricity production,^[6]Multiply all the numbers by 5. this would cover almost 4% of the continental United States. This is in line with other estimates for land use needed to power developed countries primarily using solar and wind.^[7]Estimates for different locations range from 0.5% to 5% of land used. Source.

We would have a lot of extra power on sunny and windy days. The maximum excess power produced would be 180 GW. This isn’t necessarily a problem. New uses for the irregularly available electricity would likely arise.

We still have to deal with lulls. To deal with windless nights, we still need 80 GW of on demand backup, including 10 GW of hydroelectricity and 70 GW of natural gas.

I don’t have a good estimate of how common lulls are (and it varies for different locations). I’m going to make up a number and use it for the chart. Lulls occur in my hypothetical country 8% of the time.

Here is what the capacity and average production look like if we build solar / wind over capacity:

	Hydroelectricity	Natural Gas	Wind / Solar	Nuclear
Capacity	10 GW	70 GW	300 GW	0 GW
Production	1 GW	7 GW	92 GW	0 GW

Building significantly more solar / wind capacity does reduce how much electricity is produced by fossil fuels. It does not reduce how much natural gas capacity is needed as backup. Since the natural gas power plants only produce electricity during a lull or during a demand surge, they are likely to be unprofitable. But letting them go out of business makes the grid unreliable. They will likely have to be subsidized or allowed to charge significantly higher prices than other electricity sources.

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Building Solar / Wind with Batteries

Start with the previous scenario. We have built 300 GW of solar / wind capacity. Then add batteries to store the extra energy from sunny and windy times to use during lulls. How many batteries do we need to eliminate the natural gas backup?

The simplest lull is a single windless night. Nights last for 12 hours. During this night, we would only have the 10 GW from hydroelectricity. We would need to store enough energy for 70 GW for 12 hours, or 840 GW-hr. This corresponds to storing 8-9 hours of our average electricity production.

Lulls can come from weather systems and so can last multiple days. A more severe but still plausible lull would involve several days of windless and cloudy weather. There would still be some production during this time, but not enough to recharge the batteries. Battery backup should be at least 1-2 days of average electricity production.

Let’s approximate this to 36 hours, or 3600 GW-hr, of battery backup. This would cost $450 billion to build.

Replacing 1/5th of the batteries every year costs about $90 billion per year. This requires 720 GW-hr of new batteries every year, which is 15 times the current lithium ion battery production in the US.

These costs are in addition to the costs of building solar / wind over capacity. Combined, this plan would cost $\$$900 billion to build and $\$$112 billion per year to maintain.

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Building Nuclear At Capacity

Since nuclear is a steady power source, it makes sense to use nuclear for the baseline electricity demand.

Let’s build 80 GW of nuclear power.

The total cost of this plan is 80,000 MW $\times$ $\$$6.0 million per MW = $\$$ 480 billion.

Replacing 1/40th of the nuclear power plants every year would cost about $12 billion per year.

Land use would be less than the initial scenario. Nuclear power plants take up about the same area as fossil fuel power plants. Uranium mining requires less land than fossil fuel mining.^[8]Because nuclear fuel has a much higher energy density than fossil fuels.

At night, all of the electricity comes from nuclear. During the day, we need 40 GW of additional on demand power. 10 GW of this comes from hydroelectricity, so we would still need to have 30 GW from natural gas. On demand electricity only produces half the time: during the day.

Here is what the capacity and average production look like if we build nuclear at capacity:

	Hydroelectricity	Natural Gas	Wind / Solar	Nuclear
Capacity	10 GW	30 GW	0 GW	80 GW
Production	5 GW	15 GW	0 GW	80 GW

Building nuclear at capacity replaces most, but not all, of the production from fossil fuels.

This is approximately what France is doing now. They get about 70% of their electricity from nuclear power plants, 10% from hydroelectricity, 10% from solar / wind, and 10% from fossil fuels.

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Building Nuclear Over Capacity

We could instead build 110 GW of nuclear power.

The total cost of this plan is 110,000 MW $\times$ $\$$6.0 million per MW = $\$$ 660 billion.

Replacing 1/40th of the nuclear power plants every year would cost about $17 billion per year.

During the day, electricity would be generated by a combination of nuclear and hydroelectricity. At night, all of the electricity is generated by nuclear power.

There would be 30GW of extra electricity at night. We would likely find new uses for this extra electricity available at night.

Here is what the capacity and average production look like if we build nuclear over capacity:

	Hydroelectricity	Natural Gas	Wind / Solar	Nuclear
Capacity	10 GW	0 GW	0 GW	110 GW
Production	5 GW	0 GW	0 GW	95 GW

Building nuclear over capacity completely removes the need for fossil fuel power plants.

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Building Nuclear with Batteries

If we scale up our battery production, we could build only 90 GW of nuclear power. With the 10 GW of hydroelectricity, this matches the average electricity demand. Building 90 GW of nuclear power costs $\$$ 540 billion to build and $\$$14 billion per year to maintain.

This strategy has a 20 GW surplus of electricity at night and a 20 GW deficit of electricity during the day.

For a 12 hour day, this means that we need to store 240 GW-hr of energy. This corresponds to 2.4 hours of total power production.

Let’s approximate this to 3 hours, or 300 GW-hr, of battery backup. This would cost $38 billion to build.

Replacing 1/5th of the batteries every year costs about $8 billion per year. This requires 60 GW-hr of new batteries every year, which is 1.2 times the current lithium ion battery production in the US.

These costs are in addition to the costs of building 90 GW of nuclear power.

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In the next post, I will compare these strategies and describe what I think the best policies are.