02 July 2006

Incremental Capital Investment Advantage of Renewable Energy Sources

A comment Nick made about interest on the capital costs of a photovoltaic power plant got me thinking: maybe one of the reasons that wind and solar power are experiencing such explosive growth is their small incremental capital cost. Wind turbines typically come with a power rating of 1000 - 300 kW while photovoltaic systems can be built in any practical increment. On the other hand, a nuclear power plant, a hydroelectric dam, or any other centralized power plant can only be built in extremely large increments (300+ MW). The capital cost for a nuclear or coal power plant is three or four orders of magnitude higher than that of a wind turbine. Because of this, a wind power investment can grow much closer to the exponential curve than big thermal power plants.

The financial advantage essentially works like this: assume that you have a nuclear plant and a wind farm and that both systems have the same rate of return. For my case study, I will assume that the system's net revenue is 20 % of its capital cost every year. Nominally you could build a new centralized power plant every five years if you reinvested all of your profits. Consider instead a wind farm that produced the same average power (with the same capital cost per Megawatt). If each turbine cost 1/1000th that of a major nuclear plant then a new one could be purchased every two days. As it will become apparent, the law of compound interest greatly favours the source that can be built in smaller increments.

In order to test this theory I constructed a model to compare the growth of an abstract wind farm and nuclear plant investment. Both the nuclear and wind farm investor took a loan sufficient to build 1000 MW of capacity. This is assumed to be average capacity, with the capacity factor of each already included. I will also incorporate a 2 % interest rate − indexed to inflation − on all cash balances held (positive or negative). The last thing I would like to model is a delay between the allocation of funds and the power plant actually coming on-line. For the 'nuclear' the delay is two years to account for construction, for 'wind' the delay is thirty days.

The interest rate is quite small compared to the profit on the plants so it should take approximately five years for the nuclear plant to payoff the loan, another five years to accumulate enough capital to pay for a new one, and two more years to actually build the plant. That's twelve years before the second nuclear plant can be constructed. For wind, it will take the same five years to payoff the loan but then it will only take two days to earn enough money to build another turbine and then thirty days for the turbine to be installed. One can guess that this is not going to turn out well for the nuclear option but nothing illustrates this better than a figure.
Figure 1: Step-like growth of large capital nuclear power plants (red) versus
more continuous small capital wind turbine farm (blue). Exponential
growth curve (black) at given rate of return (0.2/annum) added for reference.

After twenty years the wind farm will already have outgrown the nuclear capacity by a factor of 17850 MW to 5000 MW. The wind-based power system will provide 3.6x more power than the nuclear based system. This doesn't let wind power off the hook with regard to its intermittent nature but it certainly goes a long way to explain why solar and wind are seeing such explosive growth around the world. One could certainly play with my model to include other factors, change the rate of return or interest rates. However, the big picture isn't going to change unless the large capital investment power installations can massively outperform solar and wind with regards to the rate of return.

The growth rate advantage is not the whole story, of course. It is much easier to secure a few million in financing than a few billion. Similarly, the incremental risk of putting up a new wind turbine is quite low. The risk is also reduced by the fact that there are no fluctuating fuel costs associated with renewables versus fossil or nuclear fuels.


Robert Schwartz said...

Here are some issues.

First. I do not think that the lumpiness of your nuclear graph is justified. Financial markets can and do bridge temporal gaps between investment and return all the time and at fairly modest cost. The only factor that is relevant to the analysis is the rate of return on the project.

Second, not considering the intermittent nature of solar/wind is a major distortion. Either they are part of a system that must include other fast cycle sources (e.g. nat gas fired turbines) that can pick up when they go offline, or you must include the equipment necessary to smooth their power supplies out, such as flywheels or pumped water storage. In either event you are raising the capital cost of the project dramatically.

Robert McLeod said...

Well the 'lumpiness' of the graph for the nuclear or coal case is largely unavoidable. The y-axis on the graph is megawatts. Unless they start building nuclear plants that only produce 10 MW each those large increments are unavoidable. The wind curve would also look quite lumpy if you increased the time resolution sufficiently.

My ratio of 20 % rate of return to 2 % interest on outstanding balances is a 10:1 ratio, which you wouldn't see in the real world. Increasing the amount of interest isn't going to benefit the nuke/coal case. Regardless of the financing scheme you chose to fund your large thermal power plant, you will still have a long lead time between your first loan and when the plant comes on-line and starts making money.

On the second point, that disregards the abstract nature of this parameter. What I am saying is that, all other things equal, the energy source with the smaller incremental capital cost will outgrow the larger one. I specifically held all the numbers on rate of return, and capital investment per megawatt constant for both cases.

Alex said...

Another good point regarding what we may as well term "incrementality" is that it radically increases adaptability and reduces risk. If you are working in 10MW increments, stopping, going faster, putting them somewhere else, or using different equipment is much less of a problem than if you are working in 1GW, decade-project lumps.

Also, it means you are likely to get closer to flow-production for the sub-assemblies, which means reduced (sometimes drastically reduced) marginal cost.

Robert McLeod said...

All good additional advantages that point to 'incrementalism'. I haven't seen this as part of the narrative for renewables but it's clearly a major production advantage.

Just considering the research and development cycles the smaller incremental nature is another big advantage. We're on perhaps the 3.5 generation of nuclear plants. Solar and wind seem to go through such a development cycle every 6 - 12 months.

Having those big incremental steps certainly gives the nuclear engineers the opportunity to step-back and 'think-big' but so few proposals ever reach the marketplace. In comparison we've seen all sorts of crazy solar schemes trial on the market without destroying the industry.

Alex said...

Just added you to my RSS reader, btw.

Anonymous said...

I wonder if comparing the turbine to the powerplant is apples-to-apples. Wouldn't it be more appropriate to compare the powerplant to a turbine assembly plant? Of course, while a powerplant's energy output is constant, for a turbine assembly plant it grows linearly - so your basic point is still valid. But if you are talking logistics (permits, time delays etc.) you have to acknowledge that there is substantial infrastructure behind the wind turbine itself and the ramp-up is not as smooth as you present it.

Fractal Psychologist said...

is in america still exist a microhydro turbine?