Levelized Cost of Energy

This appendix is a more elaborate discussion concerning the cost of various types of electricity. The Levelized Cost of Energy (LCOE) is used by various organizations as a way to compare the cost of various types of generating plants. Simply knowing the LCOE is not a complete measure of the value of a plant. In the real world, many other factors weigh heavily. For example, how fuel is transported to the plant, how electricity is carried to the users, and other more technical problems, such as the need for reactive power.

Formally, the LCOE is the cost of electricity such that the present value of the revenue streams less the present value of the cost streams, equals the present value of the cost of the project. That is, the gross profit is just enough to pay for the plant, or put it another way it is the cost of electricity when the plant operates at break even. The present value of a stream of payments assumes that payments in the future have a lower value now, discounted by a discount rate for each year into the future. We use a discount rate of 8%. It is not necessary to fully understand present value to follow the discussion here.

A simplified version of LCOE is used here. In the calculations, it is assumed that the generating plant has a contract to deliver electricity over a period of years at a fixed price. For example, deliver electricity for $80 per megawatt hour for 25 years. If that stream of revenue is just enough to pay for the building the plant and for the operating costs of the plant, then the $80 per megawatt hour is the LCOE. Of course, $80 per megawatt hour is 8-cents per kilowatt hour.

To further simplify the comparison of various types of generating plants we ignore minor expenses that would complicate the calculations. An example of a minor expense is property tax.

In the real world, the developer of a generating plant needs to make a profit, so the contract price generally must be higher than the LCOE, because the LCOE is a no-profit price. Roughly add 15% to our LCOE to get a real-world price including profit and minor expenses. Most discussions comparing power plants use the LCOE, no profit price, as do we.

For wind or solar plants the most critical factors are the capital cost, the capacity factor and the fixed maintenance costs. The capital cost is expressed as dollars per kilowatt of nameplate capacity. The nameplate capacity is the amount of power that can be produced when operating at full possible power, or at 100% capacity factor.

Wind Farm Example

For (on shore) wind plants, we use a capital cost of $1733 per kW of capacity. The capital cost is taken from the National Renewable Energy Laboratory[1] (NREL). The 36% capacity factor is typical of operating wind farms and close to the NREL mid suggestion. The fixed maintenance cost is taken as $52.50 per year per kW of capacity, also from NREL. We use middle values from NREL and adjust them by 5% to change 2015 dollars to 2018 dollars.

Using these numbers for a wind plant, a 100-megawatt wind plant would cost $1733 per kW of capacity to build, or $173.3 million. With a capacity factor of 36% it would, on average, generate 36 megawatts, or 315,360 megawatt hours per year (8760 hours per year).

In order to compute the annual capital cost, we assume the plant is financed by a 25-year loan at 8% interest rate. Excel has a function PMT to calculate the annual payment, just as one would for a home mortgage:

=-PMT(.08,25,173300000) = $16,234,532

The annual payment on the plant mortgage is just over $16 million or $51.48 per megawatt hour. (16,234,532/315360)

For a wind farm, the capital cost is the greatest cost as no fuel is used.

The fixed maintenance cost of $52.50 per kW of capacity consists largely of labor costs, so we inflate that by 2.5% per year. To avoid having a different charge for maintenance each year, we levelize the maintenance cost by using an inflation adjustment factor of 1.273. If we multiply the $52.50 maintenance by 1.273 we get maintenance of $66.83 per year per kW. In other words, a maintenance charge of 52.50 escalating by 2.5% per year is equivalent to a charge of $66.83 the same every year for the 25 years. The total maintenance cost will be $6.683 million per year or $21.19 per megawatt hour. The total LCOE is the sum of the capital cost and the maintenance cost or $72.67 per megawatt hour.

Wind Farm Discussion

The estimate of 72.67 per megawatt hour is unsubsidized. Other authorities have lower estimates. The Lazard Company has an estimate of about $60 per megawatt hour. They use similar numbers to ours but include tax equity financing, really a government subsidy. NREL has a value of about $50 per megawatt hour but they include both tax equity financing and a much lower interest rate of 4.4%. Additional cost factors associated with wind are related to the fact that good wind is mainly in the Midwest. Our assumption of full financing at 8% interest would be unrealistic except for government policy guaranteeing market and pricing. It is questionable that wind turbines will actually last for 25 years considering that the 2.4 cent production tax credit expires in 10 years and a constant payment per megawatt hour becomes less valuable as time passes, due to inflation. In any case, it makes little difference to the overall analysis whether the LCOE is $50 or $70 per megawatt hour.

Natural Gas Plant Example

Calculating the LCOE for a natural gas plant is similar to Wind or Solar except that there is a fuel cost of about $22 per megawatt hour. We only consider a combined cycle natural gas plant – the most efficient type. A combined cycle plant uses a gas turbine as the first stage, then the hot exhaust of the gas turbine is used to make steam and drive a steam turbine. These plants are capable of extracting over 60% of the theoretical energy in the gas. Other types of fossil fuel plants don’t get much over 40%. Although a combined cycle plant can run at near 100% capacity factor, in practice it is closer to 50% due to reduced usage at night and perhaps throttling up and down to follow wind or solar. Due to the reduced capacity factor, thermal efficiency also runs low, at about 50%. (There is no connection between 50% capacity factor and 50% thermal efficiency.)

The cost of natural gas over a 25-year period is difficult to predict. Gas is priced in dollars per million Btu (MMBtu). Currently the price is about $3.20 per MMBtu. 3420 Btu is the same amount of energy as a kilowatt hour. If the gas plant operates at 50% efficiency, the 6840 Btu is needed to generate one kWh. The fuel cost per kWh is then $3.20/(1000000/6840) = 2.2 cents per kWh. The price has been declining due to the growth of fracking. It is not clear if the price will increase or decrease in the longer term. If fracking becomes widespread in other countries, supply could greatly increase. On the other hand, exports of natural gas should tend to support the price. As a compromise, we assume a constant price in dollars. The construction cost of natural gas plants has also been declining

The spreadsheet below calculates LCOE for wind, solar and natural gas. The Excel spreadsheet can be downloaded at:

dumbenergy.com/cost-of-electricity.html

This appendix is a more elaborate discussion concerning the cost of various types of electricity. The Levelized Cost of Energy (LCOE) is used by various organizations as a way to compare the cost of various types of generating plants. Simply knowing the LCOE is not a complete measure of the value of a plant. In the real world, many other factors weigh heavily. For example, how fuel is transported to the plant, how electricity is carried to the users, and other more technical problems, such as the need for reactive power.

Formally, the LCOE is the cost of electricity such that the present value of the revenue streams less the present value of the cost streams, equals the present value of the cost of the project. That is, the gross profit is just enough to pay for the plant, or put it another way it is the cost of electricity when the plant operates at break even. The present value of a stream of payments assumes that payments in the future have a lower value now, discounted by a discount rate for each year into the future. We use a discount rate of 8%. It is not necessary to fully understand present value to follow the discussion here.

A simplified version of LCOE is used here. In the calculations, it is assumed that the generating plant has a contract to deliver electricity over a period of years at a fixed price. For example, deliver electricity for $80 per megawatt hour for 25 years. If that stream of revenue is just enough to pay for the building the plant and for the operating costs of the plant, then the $80 per megawatt hour is the LCOE. Of course, $80 per megawatt hour is 8-cents per kilowatt hour.

To further simplify the comparison of various types of generating plants we ignore minor expenses that would complicate the calculations. An example of a minor expense is property tax.

In the real world, the developer of a generating plant needs to make a profit, so the contract price generally must be higher than the LCOE, because the LCOE is a no-profit price. Roughly add 15% to our LCOE to get a real-world price including profit and minor expenses. Most discussions comparing power plants use the LCOE, no profit price, as do we.

For wind or solar plants the most critical factors are the capital cost, the capacity factor and the fixed maintenance costs. The capital cost is expressed as dollars per kilowatt of nameplate capacity. The nameplate capacity is the amount of power that can be produced when operating at full possible power, or at 100% capacity factor.

Wind Farm Example

For (on shore) wind plants, we use a capital cost of $1733 per kW of capacity. The capital cost is taken from the National Renewable Energy Laboratory[1] (NREL). The 36% capacity factor is typical of operating wind farms and close to the NREL mid suggestion. The fixed maintenance cost is taken as $52.50 per year per kW of capacity, also from NREL. We use middle values from NREL and adjust them by 5% to change 2015 dollars to 2018 dollars.

Using these numbers for a wind plant, a 100-megawatt wind plant would cost $1733 per kW of capacity to build, or $173.3 million. With a capacity factor of 36% it would, on average, generate 36 megawatts, or 315,360 megawatt hours per year (8760 hours per year).

In order to compute the annual capital cost, we assume the plant is financed by a 25-year loan at 8% interest rate. Excel has a function PMT to calculate the annual payment, just as one would for a home mortgage:

=-PMT(.08,25,173300000) = $16,234,532

The annual payment on the plant mortgage is just over $16 million or $51.48 per megawatt hour. (16,234,532/315360)

For a wind farm, the capital cost is the greatest cost as no fuel is used.

The fixed maintenance cost of $52.50 per kW of capacity consists largely of labor costs, so we inflate that by 2.5% per year. To avoid having a different charge for maintenance each year, we levelize the maintenance cost by using an inflation adjustment factor of 1.273. If we multiply the $52.50 maintenance by 1.273 we get maintenance of $66.83 per year per kW. In other words, a maintenance charge of 52.50 escalating by 2.5% per year is equivalent to a charge of $66.83 the same every year for the 25 years. The total maintenance cost will be $6.683 million per year or $21.19 per megawatt hour. The total LCOE is the sum of the capital cost and the maintenance cost or $72.67 per megawatt hour.

Wind Farm Discussion

The estimate of 72.67 per megawatt hour is unsubsidized. Other authorities have lower estimates. The Lazard Company has an estimate of about $60 per megawatt hour. They use similar numbers to ours but include tax equity financing, really a government subsidy. NREL has a value of about $50 per megawatt hour but they include both tax equity financing and a much lower interest rate of 4.4%. Additional cost factors associated with wind are related to the fact that good wind is mainly in the Midwest. Our assumption of full financing at 8% interest would be unrealistic except for government policy guaranteeing market and pricing. It is questionable that wind turbines will actually last for 25 years considering that the 2.4 cent production tax credit expires in 10 years and a constant payment per megawatt hour becomes less valuable as time passes, due to inflation. In any case, it makes little difference to the overall analysis whether the LCOE is $50 or $70 per megawatt hour.

Natural Gas Plant Example

Calculating the LCOE for a natural gas plant is similar to Wind or Solar except that there is a fuel cost of about $22 per megawatt hour. We only consider a combined cycle natural gas plant – the most efficient type. A combined cycle plant uses a gas turbine as the first stage, then the hot exhaust of the gas turbine is used to make steam and drive a steam turbine. These plants are capable of extracting over 60% of the theoretical energy in the gas. Other types of fossil fuel plants don’t get much over 40%. Although a combined cycle plant can run at near 100% capacity factor, in practice it is closer to 50% due to reduced usage at night and perhaps throttling up and down to follow wind or solar. Due to the reduced capacity factor, thermal efficiency also runs low, at about 50%. (There is no connection between 50% capacity factor and 50% thermal efficiency.)

The cost of natural gas over a 25-year period is difficult to predict. Gas is priced in dollars per million Btu (MMBtu). Currently the price is about $3.20 per MMBtu. 3420 Btu is the same amount of energy as a kilowatt hour. If the gas plant operates at 50% efficiency, the 6840 Btu is needed to generate one kWh. The fuel cost per kWh is then $3.20/(1000000/6840) = 2.2 cents per kWh. The price has been declining due to the growth of fracking. It is not clear if the price will increase or decrease in the longer term. If fracking becomes widespread in other countries, supply could greatly increase. On the other hand, exports of natural gas should tend to support the price. As a compromise, we assume a constant price in dollars. The construction cost of natural gas plants has also been declining

The spreadsheet below calculates LCOE for wind, solar and natural gas. The Excel spreadsheet can be downloaded at:

dumbenergy.com/cost-of-electricity.html

**Capacity Factor for Solar**

Some critics have suggested that the 19% capacity factor for solar is too low, citing surveys recording much higher capacity factors for solar, even over 30%. There are two factors at play here. My 19% capacity factor refers to panels with a fixed tilt, facing south. Systems that modify the panel tilt dynamically to follow the sun will naturally have a higher capacity factor, but such systems are more expensive. The choice between fixed tilt and tracking is generally a close call, so performing the analysis for fixed tilt will generate costs that are also close for tracking systems. The second factor is panel degradation over time. Panels lose roughly 2% of capacity in the first year and about 0.8% each year after. Over the life of the system the average, discount weighted, loss of capacity is roughly 8%. So a 19% capacity factor is equivalent to about 27% capacity factor at system startup. An additional factor that may be in play is manufacturer understating initial panel efficiency to give a margin of error for warranties. That will raise the observed capacity factor. So, I suggest that 19% is a generous capacity factor, even for excellent locations in Arizona, and far higher than found outside of the sunny Southwest.

About Interest Rates

I use and interest rate of 8%. The boosters of wind and solar, such as Lazard, use similar or identical interest rates. This makes one suspect the 8% is too low. If wind and solar were not 70% subsidized no one would build such installations and no source of credit would offer credit to obviously untenable enterprises. In an unsubsidized market without government mandated quotas for renewable energy, why would a utility or a public utilities commission pay 7 cents per kWh in order to save 2 cents worth of fuel in its existing fossil fuel plants?

The 8% interest rate represents interest rates for actual deals in the subsidized and mandated environment in which deals are being done. In an unsubsidized environment deals would have to be done for cash and the investor would at best be able to sell the electricity for 2 cents per kWh. If a deal is done for cash the cost per kWh would be the cost of the project, divided by the value of the total kWh produced discounted by the time value of the kWh plus discounted operating costs. If an 8% discount is experienced in the current environment, in the riskier environment without the subsidies and assured markets, a 12% discount rate might be more reasonable. If a 12% discount rate is applied to the 100-megawatt solar example above, the effective kilowatt hours would be about 1/3 the total kWh produced and the cost per kWh would be about 10 cents rather than 7 to 8 cents.

Other Cost Estimates

The Energy Information Administration (EIA) has published cost estimates for wind power that amount to 4.8 cents per kWh, exclusive of subsidies. That compares to my estimate of 7.27 cents. They use a capacity factor of 42% compared to my 36%. If the EIA used 36%, then its estimate would be closer to my estimate. It is not clear if the EIA is including a tax equity subsidy in their calculation.

Lazard gives a wind estimate of 6 cents per kWh. If you take tax equity financing out of their analysis, their estimate would be higher.

Capacity factor for wind turbines depends on the quality of the wind resource and the design of the turbine. The advocates of wind frequently assume a high capacity factor. If you really want more cost-effective power, the turbine needs to be bigger and taller. Wind is better higher up. If you can increase the turbine power output more than you increase the cost, cost-efficiency is increased.

Although I have made an effort to make my cost estimates generous, giving away much to the advocates of green energy, the critics will always have plenty of ammunition given the murky complications involved in computing the cost of electricity at the plant fence.

[1] The NREL annual technology baseline at https://atb.nrel.gov/