A more realistic view of the cost of solar wind and nuclear energy

There is no more critical issue today than energy. Energy affects our health, standard of living, environment, and national security. The establishment view is that solar, wind, and batteries will cheaply and easily power the world.

President Biden declared that renewable energy is the cheapest form of energy. Larry Summers, one of the most influential economists, convinced senator Joe Manchin to vote for the inflation reduction act because renewable energy is so cheap, even subsidizing it will reduce inflation. Mark Z Jacobson, Stanford professor, and the world’s most influential renewable energy advocate, recently claimed that the cost of “new utility solar is 2.5 to 5 cents/KWh”, and therefore California should close Diablo Canyon nuclear plant rather than invest more money into keeping it running.

Are these statements valid? A growing number of energy experts think that nuclear power is a better choice. Are they right? This paper will answer these questions.

Levelized cost of electricity

To compare the cost of various kinds of electricity generation, analysts use a concept called levelized cost of electricity (LCOE). The cost unit is usually dollars per megawatt-hour ($/MWh). Dividing by ten converts this to cents per kilowatt-hour (cents/KWh). So, when Jacobson claims the cost of new solar is 2.5 to 5 cents/KWh, he means the LCOE of solar. LCOE only considers the cost of the generation, it excludes the cost of transmission, distribution, and administration. Thus, it should not be confused with the retail cost of electricity. The National Renewable Energy Lab (NREL) recommends the following formula to calculate the unsubsidized LCOE.¹

Equation 1

There is no need to understand this equation, but the capacity factor is an especially important idea that this paper will often refer to. The common definition of capacity factor for a power plant is the amount of electricity it produces in a typical year, divided by what it could produce if it ran at full power continuously for that year. Capacity factors can be defined for any time period, not just years.

To calculate the LCOE for various electrical plants, we will use the most recent (2023) report by the Energy Information Agency (EIA).² This report lists the assumptions needed for each kind of power plant to plug into equation 1. Table 1 below shows the data from the report in black. The blue columns are data from other sources. Average capacity factors come from an EIA report that can be found here.³ The red column is the LCOE calculation.

The assumptions are all based on a national average, hence, the LCOE can be lower in some regions or higher in others. The weighted average cost of capital (WACC) is assumed to be 8%. WACC is the effective interest rate – it is a combination of debt and equity. Note that equity interest rates are much higher than debt interest rates.

Table 1

The last two rows come from non-EIA sources. Nuclear power is a special case. There is simply no good data in which to compute an accurate LCOE. Lazard (a common source for LCOE calculations) is using data from the last 2 nuclear plants built in the US - Vogtle 3 and 4. Vogtle 3 and 4 are first-of-a-kind nuclear plants called AP1000. The project was way over budget and took about double the time expected to build. Lazard is using the first-of-a-kind cost which dramatically inflates the expected cost of building future nuclear power plants.

For nuclear power, the best we can do is to use a projected nth-of-kind cost. The idea is that if we build the same plant design repeatedly, the cost will come down dramatically due to industrial and regulatory learning throughout the entire supply chain. This effect is seen in every product manufactured. The last row in table 1 uses information from an MIT study to predict the LCOE after building 10 AP1000s, assuming an 80-year payback period, and pre-covid productivity.⁴

Table 1 reveals that combined cycle natural gas is the cheapest form of electrical energy, not any kind of renewable energy. In fact, offshore wind, and rooftop solar (even before including the cost of batteries) are more expensive than Vogtle 3. The projected nth-of-kind cost of nuclear is comparable to solar and wind, even before adding the cost of batteries.

Often cited LCOE calculations for solar and wind are less than those reported in table 1. The reasons for this include:

1. They include subsidies. Subsidies do not lower the cost to society. Federal production subsidies are worth $26/MWh. In addition, there are private sector subsidies in the form of renewable energy credits (RECs). For every MWh produced, the owner can sell a REC. The US REC market in 2023 was 12.1 billion dollars.

2. They use a projected WACC that is lower than 8%. No one can predict future interest rates.

3. They use capacity factors that are higher than those listed in table 1.

4. They use outdated information as capital costs for solar and wind power have been slowly rising in recent years (shown in recent EIA reports). If China starts making these with clean energy, or if production is brought back to the US, these prices may continue to rise.

The EIA uses maximum capacity factors in their LCOE calculations (solar = 29%, wind = 43%).⁵ The highest capacity factor in a US state for solar is about 27.9% in Nevada, and wind is about 42.9% in North Dakota. The EIA source for capacity factors for table 1 are average capacity factors. However, the EIA uses maximum capacity factors in their LCOE calculations for the purpose of comparing technologies, but this makes solar and wind power look cheaper than they really are.

The worst sin of our three thought leaders, however, is not that they minimize the LCOE of renewable energy, but that they use the LCOE to compare the cost of reliable energy to the cost of solar and wind energy. For all the types of energy in table 1, except solar and wind, there is a control room somewhere in the plant. In that control room there is a dial such that if you turn it one way, the power rises, the other way, the power lowers. This paper will henceforth call this reliable energy. For solar and wind there is no such dial, the electrical output varies with the whims of the weather. This paper will henceforth call this variable energy. This means that variable energy is an incomplete form of energy.

By using the LCOE to compare variable energy to nuclear power, Jacobson is implying that the cost of batteries is free. Of course he knows this, but he does it anyway. As we will soon see, this inappropriateness goes well beyond assuming that batteries are free.

Estimating the cost of powering a region with reliable energy is simple to do. You determine the maximum electrical consumption in a year, then calculate the amount of capacity needed to satisfy that peak consumption. You then add enough extra capacity to account for the time the plants are offline for maintenance and refueling. For variable energy, however, there is no straightforward way to do this. We need to find a way of estimating the cost of converting variable energy into reliable energy. Only with reliable energy can we perfectly match our power output with fluctuating consumer demand. This is called load balancing.

Turning variable energy into reliable energy

To turn variable energy into reliable energy we need to employ four key strategies: energy storage, overbuilding, grid expansion, and backup. Each of these adds additional costs that are not normally incurred with reliable energy. If these costs are not accounted for, we significantly underestimate the cost of variable energy.

In a typical region in the US, solar farms only produce energy about 24% of the year, and wind farms only produce energy about 35% of the year. This can be increased by storing energy when conditions are favorable, then releasing it when conditions are poor. The common forms of storage today are pumped-hydro and batteries. Hydrogen storage is a possibility for the future. In this paper we will focus on batteries as pumped-hydro is not scalable. Hours of storage means the hours that batteries alone can supply 100% of consumer demand.

Batteries alone can never make variable energy even close to 100% reliable. This is because there can be several days of simultaneous low performance of solar and wind energy and batteries are too expensive to compensate for this. Even worse, there are severe seasonal variations. For instance, summer output of solar energy is almost 3 times greater than winter output, and wind energy is about 2 times greater in late fall than in summer. We therefore must overbuild variable energy to make it more reliable for all seasons.

The overbuild factor is the amount of variable energy we overbuild with respect to annual consumer demand. An overbuild factor of 1 means that the amount of variable energy produced in a year is equal to the annual consumer demand. An overbuild factor of 0 means that we have no variable energy. An overbuild factor of 2 means that the amount of variable energy produced in a year is double the annual consumer demand. The overbuild factor ranges from 0 to infinity.

The grid we have today was built to carry reliable energy from power plants to load centers (cities). Switching over to variable energy will pose many challenges. First, solar and wind energy are very low-density sources, hence they need a lot of space. New transmission will have to be built to reach out to rural areas where there is enough available space. Second, the power output of a solar or wind farm ranges from 0 to many times greater than its annual average. This is because of the low capacity factor of variable energy, where most of the time it produces 0 energy, thus it must overproduce when conditions are favorable.

Reliable energy, however, only fluctuates with respect to consumer demand, hence it transmits power close to its annual average. This means that the power lines will have to handle much more peak power at high percentages of variable energy, unless the plants are load balanced before they transmit their energy. This can be done by co-locating batteries at the plant.

We have two main choices on how to load balance variable energy. One approach is to transmit all the variable energy from all the solar and wind farms before load balancing so that the energy can mix. This will smooth out some of the fluctuations. When location A has good conditions, it can power location B where conditions are poor. At other times it will be B powering A. Think of the grid as if it was a giant sheet of copper. This will reduce the amount of storage and overbuilding necessary to achieve reliability, but it will require extremely expensive grid upgrades.

The other alternative is to co-locate batteries with the solar and wind farms and load balance before transmitting the energy, thus we get similar performance as with reliable energy. This approach will reduce the amount of required grid upgrades but will increase the amount of storage and overbuilding needed to achieve reliability. The reason is because there will be no complimentary effect from mixing fluctuating energy.

A grid capable of full mixing will be called a super grid; a grid like our current grid will be called a standard grid. Building a super grid involves a combination of increasing the voltage of the current power lines and building new ultra-high voltage power lines. Higher voltages are necessary to increase the transmission capacity. At low levels of variable energy, we can do some mixing even with the standard grid because currently there is a lot of excess transmission capacity. We can also do some energy mixing with only a partial super grid. In this paper we only consider the two extremes - a super grid or a standard grid.

Eliminating all blackouts with only variable energy is going to be extremely difficult. We therefore need to maintain a fossil fuel backup system unless 100% solar and wind can be achieved. The preferred energy source for the backup system is natural gas. As the percentage of variable energy increases, the backup system will become less utilized and thus the unit cost of this energy becomes more expensive. This happens because even when we do not use the plant, the fixed costs do not go down, we only save money on fuel. This must be counted as an additional cost associated with variable energy.

Simulation

To calculate the realistic cost of variable energy we need to first specify some metric associated with its quantity. We can do this in at least two ways. One way is to specify the percentage of variable energy that makes up the total annual energy consumed. For example, 90% of our consumed energy comes from a combination of solar and wind. The second way is to specify a percentage of CO₂ reduced with respect to say 100% natural gas. For example, we have deployed enough solar and wind capacity to achieve a 90% reduction in CO₂ emissions compared to a grid that is 100% natural gas.

The next step is to calculate the overbuild factor, hours of storage, percentage of solar, percentage of wind, and amount of gas backup that achieves the specified metric, at the lowest possible cost. With these factors we can compute the total cost of electricity and land usage.

There is no easy way to perform the above task. The only apparent way is to build a model that can perform a simulation of time series data. I have built such a model; it is called VES (Variational Energy Solver). The EIA publishes hourly data of consumer demand, solar energy produced, and wind energy produced, for each grid region in US. VES first normalizes this data with known capacity factors of solar and wind energy for that region, then rescales it to test a specific scenario. VES iterates through each hour of this data, increasing or decreasing storage, tracking amount of curtailment, calculating the hours of gas backup needed to avoid blackouts, while accounting for all the known losses.

VES is written in Excel, using VBA functions to perform the simulation. To specify the variable energy metric, VES is paired with Solver. Solver is Excel’s built-in constrained optimizer. Solver takes control of VES to find the overbuild factor, hours of storage, percent solar, and percent wind, that achieves the specified goal, at the lowest possible cost.

The EIA data is the total of all energy produced in the region of interest. This means that all the energy acts as though it is perfectly mixed, as though the grid was a giant sheet of copper. Building a super grid capable of this level of mixing will be extremely expensive and may never be built. VES therefore has an option to simulate a standard grid with minor upgrades. This is more complicated because VES must synthesize hourly data as there is no source of hourly data for individual solar and wind farms. VES does this by using weather data published by NASA then employs models to produce synthetic data to emulate an individual solar or wind farm. VES can then simulate load balancing at the plant before energy is transmitted to the grid.

More details and assumptions used by VES can be found here.

Why it is difficult to make solar and wind energy reliable

The data in this section comes from Midcontinent Independent System Operator (MISO). MISO is a grid region made up of 15 states. MISO is a good representation of powering the US with solar and wind energy because it is close to having the average conditions for them in the US. The demand, solar, and wind data are from the EIA, normalized and rescaled by VES, using national capacity factors for solar and wind (24.3%,35%). VES produced all the figures in this section.

The conditions for figures 1 through 6 assume the following: 95% of the annual energy comes from solar and wind, the mixture is 36.2% solar, and 63.8% wind, an overbuild factor of 1.84, and 7.94 hours of batteries. The optimizer found that these values produced the lowest possible cost for 95% variable energy consumed. VES used natural gas to supply the rest of the energy. All the solar and wind data are the total for all of MISO; hence, we assume a super grid spanning MISO. Yellow is solar, blue is wind, red is demand, and black is natural gas.

Figure 1 shows the result of hourly simulation in May. Both solar and wind are fluctuating evenly with respect to demand. This is because the overbuild factor is nearly ideal for May. Batteries can manage short term fluctuations; hence, we load balance without using any gas.

Figure 1

Figure 2 shows what happens in November. In the first week, both solar and wind are fluctuating above the demand. This is because the overbuild factor is too high for this week. When this happens, our batteries fill quickly, then we must discard the surplus. This is called curtailing. Curtailing is wasteful and drives up costs.

Figure 2

Figure 3 shows what happens in the summer. Wind energy falls well below demand for three weeks during August. The overbuild factor is too low for this season, and batteries are insufficient; hence, load balancing will require gas-powered peaking plants. Notice that on 13-Aug, just after sundown, consumer demand was peaking, the batteries were empty, and the wind went to almost zero. The peaking power plants had to provide the grid with about 90% of the electricity. This shows that even at ultra-high levels of variable energy, very few gas plants can be retired unless 100% reliability is achieved.

Figure 3

Figure 4 shows what happens in the winter. Solar and wind both fall below demand for an entire week in the middle of January. The Germans call this dunkelflaute. Note that from 17-Jan to 18-Jan peaking power plants were supplying nearly all the electricity. Even though the overbuild factor is already 1.84 and there are 8 hours of batteries, to achieve 100% solar, wind, and batteries, without gas, an astronomical amount of overbuilding and batteries will be required.

Figure 4

Figure 5 shows the capacity factors for each month for wind, solar, and a mixture of the two. Notice the seasonal variation. Wind energy has a sharp drop in the summer. To avoid using gas, we must compensate for this by overbuilding. Batteries alone cannot achieve reliability. The problem with this is that we will then get too much wind energy in late fall. When this happens, we must curtail the surplus. Solar energy has the same problem in the winter. We can reduce the seasonal variation by mixing the solar and wind together, but only if the grid can transmit large power spikes.

Figure 5

Figure 6 shows a reduction in the statistical variance when the energies are mixed. Note the capacity factor for the mixture is a little lower than for wind alone, but optimization shows we still benefit by adding some solar energy. We can only find the ideal mixture with optimization. The ideal mixture will vary depending on the capacity factors of the solar and wind energy in the region being simulated.

Figure 6

For figures 7 and 8 we are assuming a standard grid. This scenario is 95% variable energy, where 100% of that is wind energy. The standard grid is typically composed of lower voltage power lines than the super grid. This means that at high levels of overbuilding, power spikes which occur when there is good solar and wind energy output cannot be transmitted without melting the power line. The solution is to load balance at the plant (locate the batteries near the plant). The plant will then only have to transmit close to its average power, instead of its peak power - more like a reliable plant does.

The reason there is no solar is because without the super grid there is no mixing, thus the optimizer determined 100% wind is the cheapest. To simulate this, VES synthetizes the wind data. The charts below represent a typical wind farm in central Minnesota. Minnesota is chosen because its wind capacity factor is near the average for the US.

Figure 7 shows the winter wind output when the wind speeds are robust. Notice how much more volatile the output is when compared to figures 1 to 6. The peaks are much higher, while the lows go to zero. The peaks flatten out because when the wind speed reaches a certain level, a windmill feathers its blades to prevent damage. A large amount of curtailing is happening here. It is common for wind output from a single wind farm to fall to zero because windmills need a minimum wind speed to make electricity, thus we need a lot of overbuilding and batteries to avoid using gas.

Figure 7

Figure 8 shows the summer wind output. For most of July, the output is below demand. Making a windfarm in this season 100% reliable with just overbuilding and batteries is going to be nearly impossible.

Figure 8

Unit cost of reliable energy

In the previous two sections we saw that making variable energy more reliable involves a combination of overbuilding, battery storage, enhancements to the grid, and gas backup. In contrast, a reliable energy plant only needs a small amount of overbuilding. The equation below shows the structure of the total cost of electricity for nuclear energy.

Equation2:

Cost of nuclear = LCOE_b*COF + T + D                                 

LCOE_b is the baseline levelized cost of electricity. Baseline simply means LCOE without including the effects of overbuilding and storage - the values in table 1. COF is the Consumer Overbuild Factor. We need enough energy to supply the grid when the consumer demand is at its highest point of the year. For MISO this is 1.59 times the average demand. The COF for MISO is thus 1.59 (for zero CO₂). T is the cost of transmission for a standard grid, and D is the cost of distribution plus administration. The transmission lines are the high voltage lines that carry power to the load centers (cities). The distribution lines are the lower voltage lines in the cities. Administration is all the other costs that appear on an electric bill.

As an aside, equation 2 slightly overstates the cost. This is because LCOE_b*COF has the effect of multiplying COF times the cost of the fuel, but the cost of the fuel is not proportional to COF. However, since the cost of the fuel is less than 10% of the total cost, this is a small effect. VES does not use equation 2 to calculate the cost of nuclear power, but equation 2 is useful to draw out some interesting points in a simple way.

For variable energy, we have 4 more costs. The equation below shows the structure of the total cost for variable energy.

Equation3:

Cost of variable = LCOE_b*COF*VOF + S + T + ExT + D + B         

VOF is the Variable energy Overbuild Factor. This is the overbuilding that is done specifically for compensating the effects of fluctuating solar and wind outputs throughout the seasons. The general overbuild factor discussed in earlier sections = COF*VOF. S is the cost of storage. ExT is the cost of enhancing a standard grid to behave more like a super grid. The super grid is only needed for variable energy. There is no material difference in the distribution and administrative costs when comparing reliable to variable energy.

B is the extra cost of gas backup needed to load balance variable energy. We saw in the last section that even at ultra-high percentages of variable energy, we still need most of the gas capacity to avoid blackouts. In addition, we replaced highly efficient gas plants with less efficient gas peaking plants that have fast ramping capabilities to support highly volatile variable energy. Therefore, some of the fixed and fuel costs of gas plants must be considered an extra cost to support variable energy. Note that this effect does not happen with nuclear energy because as nuclear plants are built, gas plants can be retired, and we do not need to build new peaking plants. VES will calculate the exact amount of backup capacity that is needed to avoid blackouts.

In summary, VOF, S, ExT, and B are extra costs that are incurred because of variable energy. Moreover, as the percentage of variable energy increases, VOF, S, and ExT increase exponentially. The cost of B goes down as the percentage of variable energy increases, but mostly only the fuel costs. The fixed cost of gas plants goes down only slightly, unless 100% variable energy is achieved. All this means that the cost of variable energy is highly dependent on what the percentage of the variable energy is. It will be impractical to derive a general formula.

Table 2 shows the results of VES simulations as the percentage of variable energy consumed increases. The data is actual data from MISO, normalized and rescaled by VES. VES normalized the data using 24.3% and 35.0% as the capacity factors for solar and wind because these are the capacity factors for the US. A super grid is assumed. The baseline energy source from which comparisons are made is 95% natural gas combined cycle (NGCC), and 5% natural gas combustion turbine (NGCT). The baseline average cost of electricity is 106.6 $/MWh.

The NGCT is needed initially to manage fluctuations in consumer demand. As the percentage of variable energy increases, VES changes this distribution so that the percentage of NGCT equals the percentage of variable energy plus the original 5%. All costs are unsubsidized costs. The scope of the simulation is for current electrical consumption only.

Table 2

Price increases remain stable until about the 60% mark, then start to rise exponentially. Subsidies should be able to hide the price increases until then. Note that at 50% variable energy, CO₂ emissions only fell by 31.2%. This is because NGCT has replaced NGCC. NGCT is needed to load balance due to its fast-ramping ability, but it burns 50% more fuel. The optimizer found no need for batteries until the 80% mark. In a region like California with better solar and worse wind, batteries will come in much sooner. This shows the power of optimization. The optimizer usually prefers wind over solar in MISO, but oddly at 100% it switched to solar.

EROEI means energy returned on energy invested. This is a measure of the overall health of an energy system. The EROEI is for the entire system. It is calculated using the specific energies for gas plants, solar farms, wind farms, and batteries. Transmission is not included in the EROEI calculation as there is no data available for this. The EROEI tells us the amount of energy created that must be reinvested back into building the energy infrastructure. Percent of output energy that must be reinvested back into creating energy = 1/EROEI*100%.

Land use is the percentage of the US not counting Alaska. Land use only considers the land needed for solar and wind farms. Note that these simulations are for current electrical consumption (~4,000,000 GWh), so land use will be substantially higher in the true net zero scenarios. The land use assumption for solar is 7 acres/MW. The land use assumption for wind is 60 acres/MW. This is halfway between an NREL study⁶ (national average of 82 acres/MW) and the ideal location (40 acres/MW). The NREL study is from 2009, so VES splits the difference, assuming wind farms are better managed today.

The baseline cost of new transmission is 40 billion dollars annually. Annual transmission costs start rising sharply above 60%. The transmission cost here is for building a super grid. This should not be confused with the kind of grid expansion currently proposed in many studies. The goal of the super grid is to perfectly mix all the variable energy. When overbuilding starts to rise, it becomes far more expensive to do this. Note that energy analysts, in their simulations, assume a super grid, but then fail to account for the cost of building it. The paper referenced at the end of the simulation section explains how these costs are calculated.

The cost of power is the cost of electricity not including transmission, distribution, and administration cost. The cost of power begins to rise exponentially at high levels of variable energy. This exponential rise is caused by the exponential rise in overbuilding and storage. The exponential rise in overbuilding and storage is caused by the need to produce enough energy during dunkelflaute. Note that as the cost of power rises, industry becomes noncompetitive. This is because industry currently pays about 70 $/MWh for their electricity. This situation will become exasperated as more industrial processes are electrified.

The average cost of electricity is the average of retail, commercial, and industrial prices. This includes transmission, distribution, and administrative costs. If the costs at 100% seem too high, please review the charts in the previous section. Perfect load balancing during dunkelflaute requires a gargantuan amount of storage, overbuilding, and transmission.

These results are going to be lower bound estimates because all the variables are perfectly optimized. In reality, variable energy is developing in a haphazard way. Results here also depend on the super grid performing perfectly with no bottlenecks. All solar is utility ground based single axis tracker, and all wind is onshore. Cost input assumptions come from table 1. WACC is assumed to be 8%. Any use of rooftop solar or offshore wind will result in higher prices.

Table 3 shows the results of simulation for a standard grid. VES synthesizes solar power from weather data in central Illinois because the solar capacity factor there matches the US. VES synthesizes wind power from weather data in central Minnesota, because the wind capacity factor there matches the US.

Table 3

The transmission costs are much lower, but the overall costs are higher. This shows the value of mixing the energies in a super grid. The optimizer used 100% wind. This is not surprising because without mixing, there is no complementary benefit from mixing solar and wind, thus only the cheapest solution is used. In MISO, wind power is a cheaper form of energy due to its lower variance. If we had optimized for land use, solar would have won. The cost at 100% is absurd, but this should not be that surprising after reviewing figure 8.

A common argument that solar and wind power advocates often make might seem to contradict these results: “Region X gets a high percentage of its energy from renewable sources and its electricity is still fairly cheap.” Upon close examination there are always problems with this claim:

1. Region X’s renewable energy is composed largely of reliable forms of non-scalable renewables such as hydroelectric, geothermal, and biomass.

2. Region X exports a substantial portion of its pre-load balanced variable energy; thus, it must load balance a much lower percentage than if it had to load balance all it produces. A region only has to load balance what it consumes – NOT all that it produces. The cost before load balancing is LCOE_b – subsidies, very cheap indeed.

3. Region X imports a lot of reliable energy during dunkelflaute, thus a neighboring region with a lower percentage of variable energy is doing X’s most difficult load balancing. To achieve net zero globally with variable energy, ALL regions will have to suffer the pain of load balancing during dunkelflaute.

Table 4 shows the average cost of electricity for nth-of-a-kind nuclear energy at rising percentages. Once nth-of-a-kind pricing for Nuclear is achieved, the price is always cheaper than solar and wind. The optimizer was free to bring in solar or wind, but it did not. The reason is because there is no complementary effect of mixing nuclear with variable, in fact doing so is parasitic to nuclear. Notice that the optimizer did bring in .74 hours of batteries at the 100% level. The batteries not only lower the energy cost slightly, but as a bonus, they make it easier for the nuclear plants to load balance.

Table 4

Table 5 shows the most relevant comparison between variable and nuclear energy. Here we use an optimization constraint to calculate the percentage of CO₂ emissions reduced. The actual percentage of variable or nuclear energy vs gas should not matter because the fundamental goal is to reduce CO₂ emissions. For variable energy, a super grid is assumed. The cost difference between variable and nuclear is greater vs comparing table 2 to table 4. The reason is because variable energy causes the replacement of higher efficient gas plants, with lower efficient peaking plants, as higher percentages of variable energy are deployed.

The last two rows show the cost of CO₂ reduction in $/MWh. This is calculated by subtracting the cost of electricity at each percentage of CO2 reduction from the baseline cost, then dividing that by the percentage of CO₂ reduced. Ideally the cost to reduce CO2 would be zero, but the cost at 100% reduction is 449 $/MWh for variable energy and 56 $/MWh for nuclear. At 100% reduction of CO₂, variable power is thus 8 times more expensive than nuclear power from the standpoint of the cost over the baseline.

Table 5

Nuclear energy will get cheaper as the energy transition proceeds. The reason is because heat pumps and EVs will flatten out the annual demand curve, thus COF in equation 2 will become closer to 1. The opposite is true for variable energy. The reason is because there is currently a complementary effect between high solar production in the summer and the heavy use of air conditioners. In the future, heat pumps and EVs will create heavy nighttime demand in the winter when solar is poor, thus more overbuilding and batteries will be required. Nuclear power can also supply process heat to industry at a fraction of the cost of electrification with variable energy.

Here is a list of common errors that solar and wind advocates make when comparing variable energy to nuclear energy:

1. They compare the subsidized cost of variable energy to the unsubsidized cost of nuclear energy.

2. They compare the nth-of-a-kind cost of variable energy to the first-of-a-kind cost of nuclear energy.

3. They fail to account for the cost of batteries required to make variable energy more reliable.

4. They fail to account for the cost of overbuilding variable energy that is required to overcome seasonal fluctuations.

5. They fail to account for the cost of the grid enhancements that are required to make variable energy more reliable, and to reach rural areas where there is space for low density variable energy.

6. They fail to account for the excess fixed and capital cost of backing up variable energy with underutilized fossil fuel (or hydrogen) plants.

7. They use maximum capacity factors for variable energy in cost calculations. For example, they imply the cost of wind power in Iowa applies to other states with lower wind speeds. For nuclear power, its average capacity factor currently equals its maximum.

8. They cite a LCOE for utility solar and onshore wind, then advocate for the wide scale use of rooftop solar and offshore wind which are each about 3 times more expensive (see table 1).

Conclusion

Using the LCOE of solar or wind energy from the EIA or Lazard will underestimate the true cost of solar and wind energy by a huge margin. Recently both sources have added a new LCOE for solar or wind plus storage. This is just as useless. Without simulation it is impossible to understand the benefit (or liability) of adding X hours of batteries to the grid. Advocates of solar and wind power need to get serious about proving their case because time is being lost. To get the cost of nuclear energy down will require many years of building the same designs over and over, and only China is doing this.

This study shows that solar and wind energy are substantially more expensive than nuclear energy. In addition, land usage is 7% of the lower 48 states to decarbonize current consumption. It will be 3x or more for true net zero. Nuclear energy, however, is still more expensive than natural gas. We need a global effort to make the cost of nuclear energy more competitive to natural gas, not only to save money, but to increase the odds of achieving CO₂ reductions.

At the current rate of global CO2 emissions increase per year, not only will we fail to eliminate CO2 emissions by 2050, but we will be lucky to even reduce them. History teaches us that people, in the pursuit of acquiring energy, will kill every whale, cut down every tree, and burn every lump of coal, unless they have an affordable alternative.

This paper only considers the current consumption. If the current grid is decarbonized, this will result in about a 31% reduction in CO₂ emissions. To achieve true net zero is far more complicated and difficult. VES models true net zero as well as current consumption. For those interested, a longer paper describing how this can be done is available here. The case for nuclear grows even stronger when looking at the total picture. The referenced paper also provides the references, and enough details, such that anyone with modest programming skills can replicate the results of this paper.

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1. NREL LCOE: https://atb-archive.nrel.gov/electricity/2018/equations-variables.html

2. EIA, LCOE assumptions: https://www.eia.gov/outlooks/aeo/assumptions/pdf/elec_cost_perf.pdf

3. EIA capacity factors: https://www.eia.gov/electricity/annual/html/epa_04_08_b.html

4. MIT AP1000 study: https://web.mit.edu/kshirvan/www/research/ANP193%20TR%20CANES.pdf

5. EIA Capacity factors for solar and wind: https://www.eia.gov/outlooks/aeo/pdf/electricity_generation.pdf

6. NREL study of land usage for wind: https://www.nrel.gov/docs/fy09osti/45834.pdf