Earlier, I wrote on how crucially an unreliable sources of power such as wind depend on fossil fuels. Based on real world production data from around the world, I noted that even with massively distributed production wind power is very variable and necessitates a reliable backup power source (typically from fossil fuels) which must be able to produce essentially all the power society consumes. A way around this problem would be a massive energy storage, but I found the size of the required storage to be unreasonably large.

One typical response to findings such as these, is to brush them aside by claiming that even if true, the results will not matter since we will have many different renewable energy sources acting together (as if there is some “harmony” in two essentially random signals). Most importantly quite a few people base their vision of future energy production on a mixture of wind and solar power. For this reason I felt the need to return to this problem so that also solar power is considered. Unfortunately, I have yet to find a good source for real world production data for solar power. The best I have come up with are images (typically of the daily production), but raw data is better hidden.

However, since solar power (without storage) production is proportional to insolation we can use meteorological data as a reasonable starting point. US has a National solar radiation database which has large collection of insolation modelling data around USA. From this data they have also formed a “typical meteorological year 3 (TMY3)” datasets. (There are some quirks in the construction of TMY3 that I frown upon. For example, after El Chichón and Mount Pinatubo eruptions insolation was reduced, but these periods were apparently excluded from the TMY3 as atypical. Of course they were atypical, but they are still things that do happen and whose effects must be considered. However, I suspect that the effect due to eruptions was still minor in US.) As my insolation data I take the average of TMY3 data from six different class I sites (class I has the best data) in three different states: Prescott Love and Tucson Airport in Arizona, Arcata Airport and Fresno Yosemite Airport in California, and Denver Airport and Limon in Colorado. These sites have an average latitude similar to southern Spain.(Why did I choose these sites? Well, being lazy I started from the entries listed in alphabetical order by states and picked the first southern states I encountered.)

Somewhat annoyingly only hourly data is provided. We know from BNC among others that solar power (especially PV) can have large swings on shorter timescales. Therefore, this limitation may have important consequences. Nevertheless, let us ignore the torpedoes with an understanding that the solar power we talk about here is such that sufficient storage has been already implemented to smooth out hourly variation in production. So keep in mind, that the starting assumptions for solar production have a bias towards the optimistic side. Since the production data for wind power is given every 5 minutes I will linearly interpolate the solar insolation data to deduce the production of solar power every 5 minutes (link to the data here). As in the earlier study the data corresponds to one year starting July the 1st. and the consumption data corresponds to the Bonneville Power Authority load with a possible scale factors to suit my needs.

Now that we have rather massively distributed production of both wind and solar power, what do we find? In Fig. 1 I show the average insolation from six US locations (the wind data I have discussed earlier). Daily variation is apparent as is also the large seasonal variation between summer and winter. In this system the solar power has an impressive 20% capacity factor. OK, now that we have the relevant data let us then proceed to check what backup requirements we have if we are to integrate this solar production in such away that production and consumption match (as they must).

Figure 1: The average insolation as an average over 6 sites in USA. The figure shows both the yearly data as well as an example of one random 7 day period.

If we choose the installed solar capacity such that the solar power produces the same amount of electricity over the year as our model society consumes, we find that a massive 55% percent of the electricity is generated with reliables (typically fossil fuels). These reliable power plants must be able to produce 97% of peak demand and they are running at a capacity factor of 36%. Solar power itself sees its capacity factor drop to 9%. These results are essentially caused by the seasonal variation of insolation (too little production in the winter) and the fact that solar power reliably produces nothing when it is dark. It is perhaps not worth pointing out that this scenario is not compatible with the goal of decarbonizing our societies.

How about mixing solar and wind? Since the sun shines during the day when consumption is higher one can guess that unreliables production matches the consumption better if there is some amount of solar in the mix. On the other hand the solar output varies even more than the wind output since, unlike wind, it predictably produces nothing when it is dark. (Of course, if the sun stops shining for good, eventually the winds disappear as well.) So presumably one shouldn’t push the fraction of solar production too high. This suggests some “sweet spot” for the fraction of installed solar capacity if we are to match the production of wind and solar optimally to consumption.

Figure 2: How well the solar and wind production match the consumption as a function of solar capacity.

In Fig. 2 I show how the function
Σ(Production-Consumption)2/Σ Production2
behaves. If production matches the consumption exactly (as it does in the real world), this function vanishes. We note that optimally the installed solar capacity should be about 21% of the installed wind capacity. (Not that this split gives rise to production which matches consumption. It is just somewhat less worse than other choices.)

For comparison, European renewable energy council and Greenpeace postulate a more ecumenical figure close to 50/50 for the split between wind and solar. (Since no explanation for this split was apparent, cynic in me is left wondering if this choice simply reflects the relative turnovers of respective industries which presumably correlate with spending on lobbyist.) However, if we are to use such a mix and produce as much power with wind and solar as we consume, it turns out that we need reliable power plants with a capacity of 91% of peak demand. They will have a capacity factor of 17% and amount to 24% of total production. Combined capacity factor of wind and solar has now dropped to around 19%. This case is presented in Figs. 3 and 4. In my earlier study with just wind power I found that fossil fuel power plants accounted for 21% of production (and with a capacity 88% of peak demand). So adding this much solar into the system has actually made things worse! The culprit is again the seasonal variation of insolation which reaches minimum during the winter (in northern hemisphere) when the consumption is often greater.

Figure 3: A snapshot of the production and consumption during a one week interval when solar and wind capacities were equal.

Figure 4: The yearly production and consumption together with the reliables output when solar and wind capacities were equal.

(As an aside: Another way to understand the challenges involved is to compare standard deviations relative to mean for wind and solar production as well as for the consumption. For the consumption this number is around 0.15, for wind power it is much larger 0.47, and for solar power it is huge 1.32. However, keep in mind that the underlying distributions are anything but normal. They cannot really be described properly by just the mean and standard deviation.)

How about choosing the solar capacity to be the “optimal” 0.21 of wind power capacity? Then we need reliable power plants with a capacity of 89% of peak demand. They will have a capacity factor of 14% and amount to 19% of total production. So, yes! Adding solar power to the mix can sometimes help, by reducing the electricity produced with fossil fuels from 21% to 19%. Unfortunately, the required capacity of reliable power plants is actually slightly higher than with wind only. I will not dare to compute the cost of CO2 abatement under such a scenario.

Figure 5: Solar capacity is 21% of the wind capacity. Weekly snapshot.

Figure 6: Solar capacity is 21% of the wind capacity. Yearly data.

Finally, few words about storage. Maybe adding solar into the mix would help us to live with a smaller energy storage? Unfortunately, also that hope is misplaced. Due to seasonal variation systems with solar power actually need MORE storage. In the earlier study with only wind power I estimated that in order phase out fossil fuels AND keep the lights on, we need an energy storage for about 9% of yearly production. Repeating the exercise (storage doesn’t decay and 20% round trip loss) for the system combining wind and solar, we find that we need storage for 13% of production in the 50/50 case while about 10% is enough with solar capacity limited to 21% of wind capacity. (Also, in the 50/50 scenario we would have to be able to store energy at a rate which is nearly 2.5 times the average power consumption of the surrounding society. Otherwise capacity factors are reduced and/or dependence on reliables reappear.)

To conclude, I note that adding solar power and wind without massive storage to the mix does next to nothing to remove the need for fossil fuel based energy infrastructure. Scenarios based on wind and solar power are fundamentally reliant on fossil fuels and sooner this is understood the better it is for climate. Currently the mirage of purely unreliables based energy production essentially maintains the use of fossil fuels for as long as the eye can see both for technical and financial reasons.

While doing these exercises I occasionally get a feeling that I am fencing with a tetraplegic. You might say this is not sportsmanlike, but unfortunately the political reality is that the mirage of solar and wind based solutions is a tetraplegic which hampers us from confronting the real and difficult issues with respect to climate change. By offering an easy “alternative” this mirage effectively acts as a cover for the damage anti-nuclear activities are causing for attempts to mitigate climate change. Unfortunately fencing must continue since this cover must be removed.

(This posting also appeared as a guest post in Brave New Climate.I encourage you to read the discussion there.)