Energy, Money, and Time

There is a deep link between energy use and economic growth. Access to energy brings economic benefits. Every energy source also has costs from causes as diverse as any other human activity. Understanding and reducing these costs is key to enabling large-scale changes in patterns of world energy use. 

Those costs can be classed in four general areas, with different relationships to the time period for economic payback and the scale of resource utilization.

Cost typeCost vs. scale Time period
Research and development Sub-linear Before capital investment Energy source may be inaccessible before R&D investment
Capital roughly linear amortized over capital lifetime Replacement after capital depreciation with new technology
Operational:
fuel, maintenance, etc.
Scales with total During payback period May be super-linear due to resource depletion
Environmental Usually scales with total Usually after payback May be super-linear if buffering capabilities of natural systems are exceeded.

Costs vs scale
Figure 1: Sample trends of costs relative to scale of resource usage - in this case the resource scale could either be relative to the technically recoverable potential for a non-renewable resource, or to the maximum ongoing technical potential for a renewable resource.

Costs vs time
Figure 2: Sample trends of costs vs. time, for a non-renewable resource. Same information as in the first figure, but shown relative to the time the costs are incurred, rather than the extent of resource utilization.

For transport, heating, or other industrial uses there are a wide variety of cost issues related to capital and R&D investment in end-application technology that complicate things. The following discussion focuses on the slightly simpler situation for electric power production.

Major energy pathways can have a chain of dependent components with separate allocations of these cost categories, some of which may be internalized in prices and therefore in operational costs downstream, but others of which should remain in their respective categories in a full analysis. For example, fuel extraction requires capital investment in mining and refining, even aside from the associated capital invested in an electric power plant that might be using that fuel. To the extent the costs are internalized in fuel prices, those become part of the operational costs of the power plant. Environmental costs of fuel extraction and refining, if not internalized in fuel prices, would also be considered part of the environmental costs of the power plant.

R&D and environmental costs are usually ignored in the economic decision to build power plants: for an established design the R&D costs are generally already sunk anyway, and the environmental costs don't directly accrue to the producers. That leaves capital and operational costs with the main impact on the direct economics, and the resulting cost of energy (cents per kilowatt-hour at the wholesale level).

Capital cost is usually expressed as cost per peak kW. However, no power source is available and in use at peak capacity full time, so the measure relevant to economic payback is capital cost per average kW, or the per peak number multiplied by the inverse of average capacity factor (percent of time effectively running at full capacity). Even if a wind turbine's capital cost per peak kW is the same as that for a coal-fired power plant, the wind capacity factor of about 30% relative to coal's capacity factor of about 70% still makes the wind turbine more than twice as expensive in capital cost per average kW.

The other two factors related to capital cost that feed into electric power costs are plant lifetime and the "cost of money" - the rate of return expected from the capital investment for it to be economically useful. This last is often misunderstood or neglected, but it is a real cost to be accounted for. This may be more than the interest rate paid out to those who put up the capital, as that rate is often subsidized for large energy projects, or backed by government guarantees that eliminate the risk to investors if a project fails and goes bankrupt.

For a given real risk, there are many worthy projects that could provide economic returns and make more capital available in future. The limited supply of capital at that risk level coupled with this range of available worthwhile projects means those projects with the highest returns should be funded first. The boundary between those that can be funded and those that cannot determines the cost of money and effective interest rate expected for that level of risk (an opportunity cost). If capital is devoted to a power plant that could have gone to something with a higher rate of return, there's a real loss to economic growth that diminishes human wealth.

The issue of risk is important - the "risk free" rate of return is usually the few percent that a central bank provides; for a given industry and type of company over a number of years a financial risk level establishes itself (through variations in return on investment) and that risk level adds a standard premium to the cost of capital for that industry or company; these may be 10%-15% or more above the "risk free" rate.

To come up with the full effect of capital cost in cents per kwh, cost of capital must also be combined with amortization of plant investment over expected lifetime; typically electric power systems are long-lived and this is a small effect. However, there are some costly electric power components with much shorter expected lifetimes - for example, batteries which may have to be replaced after about 5 years - their amortization costs can be much larger than typical cost-of-capital levels. Figure 3 shows the effective cost of capital for a given plant lifetime and several different interest rate levels, assuming a plant that provides a constant economic return after start-up (so that the capital embodied in the plant is reduced year after year, similar to mortgage payments reducing principal owed).

Effective capital cost rate
Figure 3: The effective capital cost rate is a combination of the interest rate r with the expected lifetime T over which the original investment must be amortized; the general formula for this effective rate is: r/(1 - e-rT). For short lifetimes the effective rate is just the inverse lifetime (e.g. somewhat over 20% for 5 years); for long lifetimes it comes close to the interest rate alone.

The elements that then enter into a conversion of capital costs to final "cents per kwh" cost numbers are then:

  1. initial capital cost per peak kW (including any interest accumulated over the construction period, before a plant becomes fully operational)
  2. capacity factor to get an effective capital cost per average kW
  3. cost of money (risk free interest rate plus risk premium)
  4. plant lifetime (to get an effective cost of capital rate)

Operational costs are more straightforward: fuel costs or maintenance costs per kwh of power produced. Combining the two with relatively realistic numbers and a range of effective capital cost rates yields the picture seen in Figure 4.

Cost per kwh
Figure 4: Production costs for electricity, in cents per kwh, for operational costs of 1 and 3 cents/kwh, over a range of capital costs per average kW, for several different effective capital cost rates.

Note that the capital cost rate issues have a relatively small effect on production costs for capital costs under $1000 per average kW, but are much more significant for capital costs on the order of $3000 or more per average kW (given operational costs of 3 cents or less/kwh). For low capital costs, production costs are dominated by operational costs; for high capital costs, production costs are dominated by the costs of capital.

These production costs relative to market prices for electricity determine whether a plant has positive payback for the owners - can they sell at a profit? But understanding the full societal cost/benefit requires acounting also for the wider benefits, and wider costs, of additional production.

Energy availability contributes to economic growth at the rate of about 33 cents/kwh, based on worldwide average energy intensity of 11 MJ/$ (1990 US dollars, from Smil). Improving energy intensity increases that monetary amount slightly over time - nevertheless, there are strong connections, for example in this interesting graph of nations' per capita GDP vs transportation distance: http://www.worldchanging.com/images/schafer.png. Given the heat rate effect - the 11 MJ is a primary (thermal) energy number - electric power may contribute as much as $1/kwh. For production costs (including the externalities we haven't really talked about yet) of 5 cents/kwh, the economic payback may be as high as 20:1. Even with retail electric rates as high as 20 cents/kwh, the primary economic payback from electric power production accrues to society as a whole, not directly to the producers. The centrality of energy supply to economic activity also explains many military and political developments of the past century.

Aside from the economic payback ratio, there is another more physically meaningful - the energy payback ratio. What is the ratio of energy produced to that expended in capital and operations? The energy industry is more energy intensive than world averages, so that energy payback will be somewhat less than the economic payback ratio; the economic payback number is an upper bound.

What about R&D and environmental costs? R&D typically involves small numbers on the scale of eventual production levels; nevertheless, a long lead time without other productive payback from the R&D investment effectively adds that R&D (plus interest) to initial capital costs for the first generations of a new technology in energy production, although the majority of those costs may have been externalized by government funding.

For example, if we spend $10 billion on fusion research and then receive no economic payback for 20 years, that $10 billion would represent $40 billion (including interest at 7%) in effective capital cost that should be amortized over the first production plants - so those would have to be built at a scale on the order of 40 GW average capacity to justify the expense (the R&D investment then adds only $1000/kW). If the $10 billion can be delayed 10 years and still result in productive reactors 10 years thereafter, the initial production scale could be half as large for the same averaged costs. This suggests the importance of focusing the largest portion of R&D dollars on areas with the quickest economic payback; nevertheless long-term R&D should not be neglected, and if fusion scales to the 1000 GW or more level of installed capacity we hope for after 50 years, $10 billion now would add less than $300/kW then (if not already amortized in an earlier plant generation).

Environmental costs, for the most part being post production (other than the destruction caused by mining and extraction), work in reverse to R&D costs - large future environmental costs make some sense reduced by interest-rate levels to the present time. On the other hand, being in the future they can be difficult to estimate. One way to measure these is to estimate the cost of mitigation - returning the environment to a state similar to that beforehand. Concerns about environmental costs of greenhouse warming from CO2 have added considerably to perceived externalized costs of fosil fuels. The fact that the mitigation effects of CO2sequestration is being seriously considered as an option for "clean coal" electric production suggests that the environmental costs even in this case may not add substantially to the full societal costs of electric power. Unfortunately, only time will give us a full accounting of these cost issues; one interesting effect is an increase in the risk premium that traditioanl utilities may see, internalizing some of these environmental costs over time.

This is still an incomplete overview of the economic issues in energy production; nevertheless the key points reviewed here of risk, lifetime, and capital costs for the electric power sector need to be more widely understood.

References:
Vaclav Smil, Energy at the Crossroads: Global Perspectives and Uncertainties, MIT Press (2003).

Created: 2005-02-20 05:58:10 by Arthur Smith
Modified: 2005-03-01 04:36:59 by Arthur Smith