In the previous example with the ARR screening curve, you may have noticed that the higher a plant's capacity factor (meaning the more often that it runs throughout the year) the higher the ARR. The logic here is simple - the more often a plant runs, the more fuel or other operating costs it incurs and the more revenue it needs to bring in to break even.

To convince yourself of this, take our natural gas plant from the previous section. This was a 500 MW natural gas plant with a total installed cost of $500 million. The plant has a capacity factor of 25%, a heat rate of 7 mmBTU per MWh and faces a fuel price of $3 per mmBTU. Assume that r = 10% and T = 15 years.

If the capacity factor of the plant is 100% (operates all the time), you should find that it has an ARR of $315,433 per MW-year.

If the capacity factor of the plant is 0.5% (operates just a handful of hours each year), you should find that it has an ARR of $123,393 per MW-year.

Now look back at the LCOE equation, where we divide by Q (annual output). This means that if a power plant is used less often (lower capacity factor), its LCOE will increase. Take our same natural gas plant and calculate its LCOE assuming capacity factors of 100%, 25% and 0.5%. You should get:

- Capacity factor = 100%, LCOE = $36.01/MWh
- Capacity factor = 25%, LCOE = $81.03/MWh
- Capacity factor = 0.5%, LCOE = $3,022/MWh

Look at how the LCOE blows up as the capacity factor becomes really tiny! The figure below shows the LCOE for our natural gas plant as a function of the number of operating hours per year. Notice that once the plant operates less than 500 hours per year (about three weeks per year), its LCOE skyrockets.

The lesson here, which we will come back to later in the course when we discuss deregulated electricity markets, is that building a power plant to operate it only a few hours a year is an incredibly expensive thing to do. It explains much of the reason that prices in deregulated electricity markets get very volatile during the summer months.