Wind-solar complementarities

This is a short summary of the paper 

Good news: wind and solar are complementary! This is important because the variability of wind and solar is the main challenge for their integration into electricity markets. Being complementary means that when combining both technologies we obtain a more stable generation pattern that is easier to manage. 

The easiest way to look at the complementarities of wind and solar is by looking at the correlation of their generation profiles. Figure 1 shows that wind and solar are very complementary at the seasonal level because their correlation is strongly negative for all European countries. This is great because seasonality is the hardest level of variability to tackle due to the difficulty of storing electricity for a long time (for more on storage, check the great, open access book, Monetizing energy storage). 

Wind and solar are also complementary at the daily level. Solar only generates only during the day whereas wind generates more during the night than during the day. Wind and solar are also complementary at the hourly level although the negative correlation is weaker than at the monthly and daily levels.

Because different regions have different generation patterns, we can allocate wind and solar capacities to optimize the trade-off between obtaining the maximum possible capacity factor (production per unit of installed capacity) at the minimum possible generation variability (here measured as the standard deviation of the capacity factor). In this paper, we apply the mean-variance framework (optimizing this trade-off) to see how coordinating the deployment of wind and solar capacities across European countries could smooth the aggregate generation profile while still having a high capacity factor (and thus lower generation cost).

Figure 1. Wind-solar correlation at different time-scales

With this method we can create efficient frontiers of portfolios (shares of installed capacity of each technology in each country) that minimize generation variability (standard deviation) for each attainable level of capacity factor. Within each of these efficient frontiers (lines in Figure 2), we can identify the optimal portfolio that maximizes the capacity factor per unit of variability (or equivalently, minimizes the coefficient of variation - points along the lines in Figure 2). Finally, we can compare the frontiers and optimal portfolios with individual countries in autarky (grey points in Figure 2) to quantify the potential benefits of spatial integration and deployment coordination, in terms of higher capacity factor and lower variability.

Figure 2 explores how optimally distributing solar (panels a and c) and wind (panels b and d) capacities across European countries at hourly (panels a and c) and monthly (panels b and d) improves the capacity factor-variability trade-off. The efficient frontiers show incremental geographical areas: (i) CWE: Central West Europe (Benelux, France and Germany), (ii) NWE: North-Western Europe (CWE, Great Britain, the Nordics and the Baltics), and (iii) Europe: full dataset.

Comparing panels a and c we can see that the frontiers are much farther from the individual countries for wind (c) than for solar (a), meaning that the benefits of combining wind patterns across countries are much higher than for solar. This is because wind generation is highly location-specific and more heterogeneous across countries, while solar generation patterns are more similar across countries in the same hemisphere. Whereas there is usually a positive correlation between capacity factor and its standard deviation, this correlation reverses at the monthly scale for solar (panel b), because countries closer to the equator have both higher average production and lower seasonality. Finally, we can conclude that the larger the spatial integration, the greater the potential benefits, as the larger configuration frontiers are more to the left and higher than the smaller ones, implying lower variability and higher capacity factor, respectively.

Figure 2. Trade-off between capacity factor and variability. Countries in autarky in grey. Efficient frontiers for larger geographical areas (CWE: Central-Western Europe, NWE: Northern-Western Europe, Europe), and optimal portfolios (highlighted points along the frontiers).

Instead of integrating into larger geographical areas, countries could optimize the shares of solar and wind (onshore and offshore) in autarky (grey points in Figure 3.a). In the studied countries, the optimal technological combination is around 40-45% for solar and the remaining for onshore and offshore wind (Figure 3.b). Whereas optimizing technologies within countries would bring some benefits, integrating larger areas and optimizing capacities at those levels has higher potential benefits, as shown in Figure 3.a, by the fact that the efficient frontiers are all superior to the individual countries in autarky.

Figure 3. (a) Capacity factore-variability trade-off: optimized individual countries (grey dots) and efficient frontiers (lines) for larger spatial configurations (CWE: Central-Western Europe, NWE: Northern-Western Europe, Europe). (b) Optimal technological shares for each individual country. All results are at the hourly level.

In conclusion, this paper explores the complementarities between wind and solar in Europe, for each technology across countries, for each country across technologies, and for all countries and technologies together. We study these complementarities at three timescales: hourly, daily, and monthly, and for two points in time: current installed capacity and future expected capacities. We conclude that optimally allocating capacities can provide higher capacity factors (and thus lower unit cost of electricity) and lower variability (and thus lower integration costs).  All code and data are available on Zenodo ( Check the paper for details (