Monday, December 12, 2011

Trying to understand system wide costs of energy

Some time ago in Brave New Climate Peter Lang wrote an interesting post on the CO2 abatement costs in Australia. He found that nuclear power is not the cheapest abatement method under Australian circumstances. His post was followed by interesting discussion and several wondered that can one arrive at sufficiently decarbonized electricity supply by always choosing the lowest cost alternative, should we not only include options that actually get all the emissions reductions we need, and what is the proper way to account for and discount costs. Since I have wanted to understand cost calculations better for quite some time, I decided to use this problem as one of my own exercises. For background you might want to read my earlier postings on related things (here and here, or in finnish here and here). Here I attempt to sketch system wide cost and CO2 abatement consequences of wind and nuclear based options. (In case you want to play and have access to Matlab, you can download some poorly documented macros I used.)

Throughout I will use the discount rate of 7.5%, a payback period of 20 years for wind power, 50 years for hydro and nuclear (this is longer than usual, but assumption is not hugely important for my needs), and 40 years for natural gas and coal. I won't bother to list all the input parameters here, but most of them I have picked up from the typical market prices for different fuels as well as from the National Renewable energy laboratory. As a calibration I find following levelized costs of energy:

Source Capacity factorLCOE ($/kWh)
Coal 0.85 0.066
Gas 0.85 0.071
Wind 0.29 0.102
Hydro 0.5 0.046
Nuclear 0.9 0.063

Few remarks are in order. There is no single LCOE since the costs are different in different places and different cost components keep changing. In Asia, for example, the costs of nuclear can be considerably lower than the above estimate, but under American style regulatory framework maybe higher. For gas prices I used a value of 8$/MMBtu. This is higher than the current gas prices in US, but lower than the European ones. The LCOE for wind power is lower than the typical feed-in tariffs in Europe and electricity spot price in the Nordic region fluctuates around 7.5 cents/kWh. The fact that Finnish utilities want to build nuclear power also suggests that compared with alternatives economics for it are favorable in our circumstances. Changing the assumptions can of course change the above values somewhat, but overall I think the numbers pass the sanity check. In what is to follow the figures above are not even that important since they mainly set the starting point and after that the cost trends are determined by the changing energy mix and the capacity factors.

I will now compare two different scenarios for decarbonizing the electricity supply. In the first scenario we start with the fossil fuel dominated system where coal provides baseload power corresponding to the minimum yearly demand (as before I take the demand pattern from the Bonneville power authority load). I make drastic approximation that the output power of coal burning power plants does not vary at all and that the load following is only done with hydro (with capacity of 15% of average demand) and natural gas. Somewhat unrealistically I also assume that the hydrocapacity is always available. (This assumption makes the systems appear to have somewhat lower emissions than in reality where hydro power might have a capacity factor of around 50%.) I then start increasing the amount of electricity generated with wind. The production profile of wind power is derived from combining the Irish, south-eastern Australian, and Bonneville power authority wind production. The details are explained in an earlier posting. The wind production is taken to have a priority access to the grid. To generate the remaining electricity, we use coal at a power corresponding to the minimum demand once the contribution of wind power has been subtracted from the demand. The rest is generated with hydro and natural gas in that order. I further assume that production can always respond so rapidly that no capacity has to be in the spinning mode. (Our imaginary state has an average demand of 10000MW.)  In the first movie, I demonstrate how the mix of different sources of electricity evolve under this scenario.
video

In the second scenario the starting point is the same, but rather than increasing the amount of wind power, we increase the amount of nuclear power. Like coal, this nuclear power is taken to produce constant power so that it first displaces baseload coal and then starts replacing natural gas. When nuclear power starts to replace gas used for load following its capacity factor starts to take a hit. The 2nd movie illustrates the mix of different sources of electricity in this scenario.
video

These two scenarios are naturally not the only ways to satisfy electricity demand, but they are possible ways and with the numbers shown in the movies production always matches demand. Since the required capacities and capacity factors change with increasing wind or nuclear penetrations, the LCOE for different sources do not stay the same. For the society (although not necessarily for the individual investor) what matters most is the cost of typical kWh rather than the LCOE for each individual component of the electricity supply. I will take the cost of typical kWh to be the weighted average of each separate LCOE. The weights are given by the relative amounts of electricity produced from each source.

I think one clear error in what I do, is to implicitly assume that the underlying energy infrastructure stays the same over the payback period. As we decarbonize the electricity generation, capacities and capacity factors change with time and this should, in principle, be taken into account. On the other hand, since we do not live in a planned economy postulating construction plans decades in advance would also be dubious. The best the society might be able to do, is to try to reduce uncertainty and ensure that the market pressures always act in the right direction of ever lower GHG emissions.
So what do I find? In Figure 1, I summarize how the system evolves under the first scenario while Figure 2 summarizes the costs involved. For the wind based solution increasing share of wind power first lowers the space occupied by the base load power plants. This implies shutting down coal power plants and replacing them with gas plants.If methane leakage is bravely assumed not to be an issue, at this phase some CO2 emissions are avoided due to swapping for somewhat cleaner fuel. At higher penetrations capacity factors of wind, gas, and hydro power are reduced and costs continue to increase. (Btw. Getting someone to invest in new gas infrastructure might be tricky if the investors expect the demand growth early on the decarbonization path to be short lived. Presumably they do not believe this to be the case which, if accurate, would be bad news for the climate.) Even with very large wind power capacity one needs a reliable backup that can produce almost all the power consumed. For this reason after rapid rise in the capacity of power plants burning natural gas, their capacity declines only very slowly with increasing wind penetration.

Figure 1: Capacities, capacity factors, and the share of fossil fuels as the fraction of wind generated electricity increase.

Figure 2: LCOE under the wind based scenario.
For the nuclear based scenario 2, the corresponding results are shown in Figures 3 and 4. Now the system wide LCOE actually decreases slightly until nuclear power produces around 75% of the demand (at this point around 10% is produced with natural gas). After this the cost increases with the reduced capacity factors in NPPs. However, the kind of cost escalation apparent in the wind power based solution is absent since there is no need to maintain large amounts of reliable capacity running at low capacity factors. In these examples I made no assumptions about learning curves. If the capital costs of nuclear power are reduced by about 10% for each doubling in capacity until 10000MW (around 30% reduction in capital costs in total), the final LCOE of the decarbonized system is actually lower than the starting point. Similar cost reductions of wind power over the decarbonizing pathway used here do not avoid escalation of costs since cost increases are largely caused by the reduced capacity factors. It seems that one can also make a plausible case that the increased cost at high nuclear penetrations is an artifact of the simplifying assumptions I made. Eventually smart grid solutions can increase the share of base load power, NPPs can load follow, and lower capital cost NPPs which are better suited for load following can be engineered.

Figure 3: Capacities, capacity factors, and the share of fossil fuels as the fraction of nuclear generated electricity increase.

Figure 4: LCOE under the second scenario.
Finally in Figure 5, I compare the most relevant metrics of both scenarios. The costs diverge dramatically with the fraction of chosen carbon free energy. Nuclear based solution ends up with fairly constant LCOE over the pathway leading to decarbonization, while costs escalate with wind based solution. The installed carbon free capacity is drastically higher in wind based solution, suggesting greater challenges in construction and grid design. Finally, the fraction of electricity generated from fossil fuels is higher in the wind based solution. Together with increasing costs this implies dramatically lower "bang for the buck" at large wind penetrations. In contrast by the time nuclear power produces the same amount of electricity as the yearly demand, share of fossil fuels has dropped to less than 2%.


Figure 5: Comparison between wind and nuclear based scenarios.
It should be noted that in the above in addition to many simplifying assumptions I ignored the additional transmissions costs for the wind based scenario. I am quite clueless as to what kind of grid upgrades are needed, but it seems clear that with wind capacity in excess of 5 times the average demand changes would be substantial. Where I live the transmission costs amount to around one third of my electricity bill so changes in transmission costs would have a large impact on the cost of electricity.

In this post I also focus on electricity production only. To decarbonize our societies we will also have to decarbonize heating and transport. If we were to use excess wind power to heat water, it is easy to see that the rise in the cost of warm water would be even greater than the cost increases in electricity (home work exercise). In case of nuclear power warm water could be a by-product of electricity generation (although this reduces the electrical power somewhat). Furthermore, if this warm water is produced close to the wind turbines, transporting it to consumers will cost more than moving electricity around. Similar conclusions apply for liquid fuels.

Do these kind of cost differences matter? I find it shocking that so many (typically wealthy westerners) seem to have an attitude that energy costs are almost irrelevant and that the question is basically analogous with a choice of buying a PC or a Mac. Some even seem to view rising energy costs as a good thing. We spend roughly 8% of our GDP on energy and this energy use pretty much makes all the rest possible. It is useful to remind how much we actually spend on some things that are widely valued. I will take the figures from my home country of Finland, but they are probably quite representative of industrialized countries in general.

Spending on Share of GDP
Public health care 7%
Education 6%
Pensions 12%
Pensions (2030 esimate) 15%
Development aid 0.5%
Ministry of environment <0.2%

In the past few decades the income differences have increased also in Finland so that today our richest 10% have around 2-3% greater share of the GDP than in 1990. My impression is that most environmentalists find this terrible. The aging population causes our pension costs to increase and this increase is cause of anxiety for many both left and right. So we can very easily see that the energy costs in our society are comparable to many big spending categories for which it is already hard to find resources. Large increases in energy costs can easily have far greater social consequences than most people probably realize. Fantasizing that this is something to be promoted not only borders on insane, but is morally dubious. I have yet to find an explanation for why a society that spends more on energy rather than, for example, on education and health care is a better place for its inhabitants?

You might try to rescue the fantasy by somehow assuming that the same GDP could be produced with so much lower energy consumption that the total costs remain the same. However, as is clear from the above estimates this would require so drastic reductions in energy use that it cannot be taken seriously as a basis for responsible climate policy. There is nothing to suggest that this is doable and especially in the case of poorer countries that this is desirable. (Also, why would economically justified energy savings measures be incompatible with nuclear power is not clear to me.)  Once the discussion strays into this territory, I often end up confused by the inconsistency of the arguments in favor of the paleogreen consensus. Construction of ideologically favored energy sources is typically touted (not entirely convincingly) as being good for the economy, but the same people might in a different context condemn economic growth and express desire for degrowth. Which one is it? Surely one cannot have it both ways?

Do I seriously believe that the societies will choose the path of ever increasing energy costs? Of course not. As soon as the effects of cost increases become apparent and start to affect other priorities people have, different choices will be made. As I see it, choosing the wrong way initially implies wasteful spending and unnecessary CO2 emissions since it delays the day when we eventually do choose policies that can eliminate the GHG emissions from the energy sector for good.

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