Geophysical constraints on the reliability of solar and wind power worldwide

If future net-zero emissions energy systems rely heavily on solar and wind resources, spatial and temporal mismatches between resource availability and electricity demand may challenge system reliability. Using 39 years of hourly reanalysis data (1980–2018), we analyze the ability of solar and wind resources to meet electricity demand in 42 countries, varying the hypothetical scale and mix of renewable generation as well as energy storage capacity. Assuming perfect transmission and annual generation equal to annual demand, but no energy storage, we find the most reliable renewable electricity systems are wind-heavy and satisfy countries’ electricity demand in 72–91% of hours (83–94% by adding 12 h of storage). Yet even in systems which meet >90% of demand, hundreds of hours of unmet demand may occur annually. Our analysis helps quantify the power, energy, and utilization rates of additional energy storage, demand management, or curtailment, as well as the benefits of regional aggregation.

Supplementary Note 1. Explanation for near constant solar resource around daytime peak.
In this work, many of the derived solar capacity factors are quite flat around noon, as opposed to showing a discrete peak near the middle of the day. This midday flatness can be explained by the adjustment of the direct sunlight component as explained below.
During the calculation of solar capacity factors, the incoming surface shortwave radiation is first separated into its direct and diffuse components. The direct solar radiation is then divided by the cosine of the zenith angle to estimate the total incoming direct solar radiation, and multiplied by the incidence angle to estimate in-panel direct radiation. Because the cosine zenith angle is small near noon, it could result in large vertical direction incoming direct radiation. To constrain the abnormally large incoming direct solar radiation, we applied a Beer-Lambert Law using both top-of-atmosphere and surface shortwave radiation, which sets an upper limit for the maximum surface solar radiation. Our analysis shows that due to factors including cloud cover, the Beer-Lambert constraint does not always give a maximum value at the daytime peak hour. The shape of the solar capacity factor daily cycle could be distorted further by averaging across a large geophysical area, in which grid cells at different local times exist. The abovementioned factors together produce the midday plateau in solar capacity curves for many countries presented here.

Supplementary Note 2.
The development of statistical model to predict reliability.
In this study, we developed an expression that can be used to predict the reliability given country size, the level of annual generation, and the capacity of energy storage (Supplementary Table 3). The expression (S1) developed here is shown as following: where represents the predicted reliability with excess annual generation and storage, 0 represents the reliability with no excess annual generation and no storage, represents the land area, b represents the level of annual generation relative to annual demand (i.e. 1, 1.5, and 3), represents the capacity of energy storage relative to mean hourly electricity demand (i.e. hours of storage), k , k , and k represent parameters that are estimated form the Macro Energy Model simulations.
k , k , and k are estimated as 0.149612, 0.419976, and 16.4896, respectively, by means of maximum likelihood. The predicted reliability and actual reliability show a good fit with the correlation coefficient (R) equaling 0.95 (R 2 =0.90; Supplementary Figure 15).

Supplementary Note 3.
The sensitivity tests of different solar tracking systems and another reanalysis weather data on the electricity system reliabilities.
Our study assumes a horizontal single-axis tracking system when calculating the solar capacity factors. In order to test the impacts of different solar tracking systems on the electricity system reliabilities, we further estimate the solar capacity factors adopting dual-axis (both a horizontal and a vertical axis) tracking system. In our dual-axis assumption, the panels will always be oriented towards the sun with an incident angle of zero, representing the maximum solar-system energy production potential. The reliability changes are shown in Supplementary Figure 10, we find that, the solar tracking systems have small impacts on the electricity system reliabilities and the reliability change ratios are within ±5%. Especially under the high-level of annual generation relative to annual demand (3x generation; Fig. S10c), the impacts would be very small. it is noted there are relatively large impacts on the system reliabilities in some countries, for example, in Russia, Canada, and Sweden, it is because that these countries are located the high latitude area, and the panels will always be oriented towards the sun with the dual-axis solar tracking system while the tilted panels are used with single-axis tracking system. In summary, there are very small impacts on the system reliabilities regardless of solar tracking systems.
In addition, to investigate uncertainties of our results associated with reanalysis weather data used here (i.e., MERRA-2), we apply the same estimation process for capacity factors of solar and wind using ERA5 provided by European Centre for Medium-Range Weather Forecasts (ECMWF). Hourly historical (from 1980 to 2018) variables, such as top of atmosphere and surface incoming solar radiation, surface air temperature, and 100-meter wind speed that are required to calculate the potential power generation, are downloaded and re-gridded into the same horizontal resolution as MERRA-2. Previous studies comparing MERRA-2 and ERA5 have shown that bias exists in both reanalysis products 30,31 . Our estimates of the system reliabilities by using ERA5 data in the 42 major countries are in good agreement with results of MERRA-2: under 1x generation and the most reliable mixes without storage, reliability under the different loads varies on average from -9.4% to 1.3% (see Fig. S11a). The differences are similar in systems with excess generation (Figs. S11b-c). We also compared the magnitude and duration of unmet demand in 16 major countries like Figure 4 (see Supplementary Figure 12). The data products of MERRA-2 and ERA5 both can essentially capture the number of hours each year that such a gap occurred. By contrast, the MERRA-2 data has a better performance of meeting hourly demand in larger countries (i.e. Russia and Canada) but a similar performance in small countries (i.e. United Kingdom). The somewhat different patterns of resource variability in the two datasets do not alter our main conclusions.

Supplementary Note 4. The sensitivity tests of various demand characteristics.
In this study, only one-year of demand data is employed to assess the geophysical constraints of 39-year solar and wind resources. We realize that load profiles for electricity in many of countries would be different over the past 30 years and in future, there will impact the electricity system reliability, especially under the case of no additional energy storage to dispatch the electricity. Therefore, considering the limits of computing resources, we combined the load profiles of other countries and regions (i.e. 192 countries and regions) and the solar and wind capability (i.e. capacity factors) of the U.S. to evaluate their impacts on the electricity system reliabilities. We analyze systems ranging from 100% solar (no wind) to 100% wind (no solar), in which total annual generation ranged from equal to annual demand ("1x generation") to up to three times of annual demand ("3x generation") with no available energy storage. As shown in Supplementary Figure 14, without any excess annual generation or energy storage, the impacts of various load profiles on the system reliabilities are within ±10% (Fig. S14a), and the most reliable solar-wind generation mixes (25% solar and 75% wind) are not changed. With the level of annual generation relative to annual demand increasing (from "1x generation" to "3x generation"; Fig. S14), the impacts on the electricity system reliabilities are much smaller, especially under the most reliable mixes (i.e. ≤±0.2%).
In conclusion, we think there are relatively small impact on reliability especially under the high level of annual generation relative to annual demand, and the impact would be further reduced if there is energy storage.

Supplementary Figure 1 | Temporal variability of solar and wind resources and electricity demand.
Climatological variability of the area-weighted median power from sun (orange) and wind (blue) resources around each selected country from six continents during the 39-year period 1980-2018: India (a, g, m), Japan (b, h, n), Russia (c, i, o), United Kingdom (d, j, p), France (e, k, q), and Canada (f, l, r). And the left column (a-f) for the daily and seasonal, the middle column (g-l) for hourly summer (June, July, and August), the right column (m-r) for hourly winter (December, January, and February) variability. The lines represent the median, the dark shading represents the inner 50% of observations (25th to 75th percentile) and the light shading represents the outer 50% of observations (0th to 100th percentile). Red curves in each panel represent electricity demand for a single but latest available year for each country. The time of day shown is local time zone of each country and expressed as Coordinated Universal Time (UTC). Note that the middle of local time zones has been selected for the countries with multiple time zones. The solar, wind, and demand data are each normalized by their respective 39-year mean value.