The levelized-cost-of-fuel (LCF) is a very useful value to calculate for different sources of electrical energy. Essentially, the LCF is the levelized-cost-of-electricity (LCOE) with the capital and operations terms removed. Since many regulatory bodies, including most state-level public service commissions (or public utility commissions) make their determinations about generation capacity around the LCOE, it is important to understand the role of the LCF.

In simplest terms, the LCF is the thermal cost of fuel multiplied by the heat rate of the plant. Here are two calculations of the LCF based on combined-cycle natural-gas-fired turbines (CCGT) and steam-turbine power plants heated by Powder River Basin coal (PRBC).

   

   

The thermal costs of Henry Hub natural gas (at $2.42/MMBTU) and Powder River Basin coal (at $0.81/MMBTU) were looked up recently. The heat rate is calculated by taking the value of a megawatt-hour in MMBTU (1 MWh = 3.6 GJ = 3.412 MMBTU) and dividing it by the thermal efficiency of the power plant. Combined-cycle plants have a high thermal efficiency, around 55%, while coal-fired power plants have a lower thermal efficiency of around 38%.

The thermal cost of the fuel is often published so power generators and the markets they serve can assess their LCF. For instance, one can find published data about the thermal cost of natural gas at various distribution hubs. One can also find published data about the thermal cost of coal, of various grades, from government websites. In the United States, this thermal cost is usually given in dollars per million BTU (British thermal unit). Another way this data could be published might be in dollars per gigajoule or euros per gigajoule. It is a fascinating coincidence that a gigajoule is within about 5% of the same thermal value as a million BTUs.

   

The heat rate describes the amount of thermal energy needed to generate a single unit of electrical energy. As such, it can also be thought of as another way to express the thermal efficiency of the plant. Thermal efficiency is unitless, but the heat rate has units chosen to make it compatible with the published fuel costs. So in the United States it would be typical to see a heat rate published in millions of BTU per electrical megawatt-hour. And in Europe and elsewhere we might see instead as gigajoules per electrical megawatt-hour. Both would reduce to the inverse of the unitless thermal efficiency, if we were to “boil them down”, but that is how the heat rate of the plant is typically given.

A lower heat rate is “better”, because it means that you used less fuel to generate the same amount of electrical power. Plants used to publish their heat rates, and try to compete against one another to get the lowest heat rate. Since the heat rate is the inverse of thermal efficiency expressed with units, this is equivalent to saying that plants were trying to get the highest thermal efficiency.

Natural-gas-fired plants and coal-fired plants will often calculate and publish their LCFs, but we don’t often find nuclear plants describing themselves this way.

   

Why not? Well, it’s not the heat rate. We can calculate the heat rate for a nuclear plant pretty easily, since nearly all of them operate on subcritical steam turbines and at comparatively low thermal efficiencies. We can be pretty confident that the thermal efficiency for today’s reactors is 30-35%.

The big question mark is the thermal cost of nuclear fuel.

If the thermal cost of nuclear fuel were published in ways that allowed easy comparisons with coal and gas, I think that would be very enlightening to the consumer. It might also be very enlightening to utility managers and executives, and to elected officials that are charged with making choices that lead to the lowest rates for the consumers that they serve.

So let’s attempt to calculate the thermal cost of nuclear fuel. The thermal cost of the fuel is simply the cost of the fuel, per unit mass, divided by the thermal output of the fuel, per unit mass. If we were doing this calculation with natural gas or coal, it’s pretty well-known how much energy you get out of a pound or kilo of gas or coal, and so if you knew how much you had to pay for that pound or kilo, you’d have all the information you needed to get the thermal cost of the fuel. This is so well-known for gas and coal that they simply skip this step and publish the thermal cost.

But for nuclear fuel, both the cost of the fuel and the expected thermal release from the fuel are strong functions of the enrichment of the fuel. The higher the enrichment, the more that the fuel costs, and the more energy you can expect to get from the fuel. When you have two aspects like this that are seeming to move in ways that counterbalance one another, you really have to turn to actual math calculations to see which effects prevail.

For instance, a CANDU reactor uses natural (unenriched) uranium with only 0.71% U-235 content. The fuel doesn’t cost a lot but it also doesn’t put out as much energy, per kilogram. The LCF comes out to be:

   

A typical pressurized-water reactor (PWR) is enriched to about 3.5% U-235 content. The fuel costs a lot more, but it also puts out a lot more thermal energy per unit mass. The LCF ends up still being close to the unenriched uranium case.

   

A high-temperature gas-cooled reactor (HTGR) will probably use uranium enriched to 20% in the form of TRISO fuel. It costs a lot of money, but it also puts out a lot more energy, and at those high temperatures it can achieve higher thermal efficiencies, and thus have a lower heat rate.

   

These calculations are based on some economic assumptions. We assume that natural uranium is fed into an enrichment system at 0.71% and at a cost of $277.03/kgU as UF6. This is based on a feed cost of $80.00/lb of U3O8 and the ConverDyn conversion factor of 2.61285 lbU3O8/kgU, added to a conversion cost of $68.00/kgU. The tails fraction from the enrichment system is 0.25% and their disposal costs $5.00/kgU. Separative work costs $176.00/kgSWU, with a cost multiple of 1.50 applied to separative work from 5% to 10%, and a multiple of 10.00 applied to enrichment greater than 10%. Uranium dioxide fuel fabrication is assumed to cost $400/kgU and TRISO fuel fabrication is assumed to cost $4000/kgU.