These authors contributed equally to this work.

Maps showing the mean wind speed only give an inaccurate indication of the quality of locations for future wind power developments. Calculating the capacity factor and plotting that on a map gives a better indication of the expected mean power output, but the outcome depends on the turbine choice. In this article, we introduce a general step-by-step method for improved visualisation of potential wind power locations. First, the mentioned dependency on turbine choice is compensated for by putting the expected mean power output in relation to the expected mean power output of all other wind parks of the region. This

The

Spatial diversification can help to reduce or limit variance (instead of compensating for it). This approach is gaining increasing importance for the siting of renewable energy sources, and it is an effective countermeasure to limit the increasing variance of the power output from weather-driven renewable energy sources such as wind power

The European Green Deal and the European Commission's dedicated offshore renewable energy strategy envision more than 300 GW of offshore wind parks in Europe

When looking further into the future, it will become important to spread wind power development better in space. This can be driven either politically by strategic selection of wind development areas in a dispersed manner (internationally) or economically by investors who actively seek to avoid co-location with too many existing wind parks for improving potential market revenues. To support this needed spatial diversification, a new comprehensive visualisation tool has been developed: Renewable Energy Complementarity (RECom) maps. The tool is described in this article.

RECom maps combine information about the energy resource at a given location and the expected market value of power capacity installed in this location, resulting in an indicative revenue potential. The cost for wind power developments at these locations (depending e.g. on water depth and distance to shore) is, however, not included; the RECom only addresses revenues, not costs.

Somewhat similar approaches exist that map wind power according to estimated levelised cost of energy (

We show RECom maps applied to an example of offshore wind power, but the methodology is not wind-power-specific and can likely be used for solar power or for mixes of different weather-driven renewable energy sources.

Here, we have chosen to focus on offshore wind as a single parameter to keep the message clear and because it is a particularly important factor in the North Sea region. Adding more parameters could give a more accurate estimation of future market values but at the cost of introducing more assumptions and uncertainties, obscuring the main message of the article. The main point of the article is to provide a general method for visualising the quality of locations for future wind power development without relying on market modelling. To be useful in this way, it needs to rely on as few assumptions and input parameters as possible. To be clear, such a visualisation tool is certainly not an alternative to detailed energy system modelling and market analysis but a useful supplement for the general discourse surrounding the energy transition.

Wind park power curve

Geographical resolution.

This section describes the data used for estimating wind power resources in the North Sea and assumptions regarding future deployment of offshore wind parks.

Assumed wind power capacity in the North Sea.

To estimate future wind power time series for arbitrary locations in the North Sea area, we use numerical weather model data for historical years. This is a common approach. In our case, we have obtained wind speed data at a 100 m height for the 5-year period from 2018 to 2022 from the MERRA-2 dataset

Wind speed time series have been converted to wind power per installed capacity by applying a power curve

The Gaussian filtering method to obtain wind park power curves is a simplification that does not include wake effects, and the estimated capacity factors are therefore high. However, for the present study we consider this approach sufficient, especially since this upward bias is compensated for later on (see Sect.

In reality, a wind park power curve is influenced by several factors (e.g. the choice of the wind turbine type and wind turbine spacing). As these influencing parameters are selected according to the wind resource, the wind park power curve depends on the related wind resource. These considerations are, however, not accounted for in the approach presented here, and for simplicity a single power curve has been used for all cases.

The assumed hub height for wind speeds, the implicit wind shear assumption, the rough geographical resolution and the simple wind power curve are all simplifications/assumptions that create certain biases in the calculations. However, as the final results are concerned with relative comparisons of different locations, uniform biases will tend to drop out and therefore be less important for the maps.

The wind speed and wind power time series were generated for a latitude–longitude lattice at 1.0° intervals in the latitude direction and 1.5° intervals in the longitude direction. This is indicated by the black dots in Fig.

To plot a RECom map, it is necessary to know the main parameters of all wind parks in the considered region. This can be either the real situation, as it is today, or a future scenario, as applied in this article.

Assumptions for the total offshore wind power capacity per country have been based on ENTSO-E Ten-Year Network Development Plan (TYNDP) 2022 “distributed energy” storyline assumptions

The geographical distribution of the wind power capacity has been obtained using public information available via the

Using these data sources, the wind deployment scenarios for 2025, 2030, 2035 and 2040 have been determined according to the following principles (see Fig.

In cases where the Emodnet data indicate too high a capacity for a country, wind parks are (randomly) included until the target capacity is reached.

In cases where the Emodnet data indicate too low a capacity for a country, the missing capacity is added to planned wind park areas that have an unspecified capacity in the dataset.

For 2040, some wind park locations are added manually in line with tentative plans for the various countries

Finally, capacity is scaled up or down so that the sum per country matches the country target for the specific year.

For 2035, the averages of 2030 and 2040 target capacities were assumed.

The state of the art to assess the suitability of locations for wind power developments is to draw wind speed maps, often called a wind atlases.

It is common to use maps that show the mean wind speed for the goal of assessing good locations for potential new wind parks

Mean wind speed at hub height [m s

Mean wind speed is indeed a valid indicator for the quality of a site for wind park developments, but it does not give the full picture, as the relationship between wind power and wind speed is highly non-linear. This can be best shown with an unrealistic example:

Site A has 6 months of 25 m s

Site B has 12 months of 12.5 m s

Both sites have identical mean wind speeds and will appear the same on such a mean wind speed map. However, the energy output of a wind park at site A will be significantly lower than for site B. This phenomenon is not accounted for when using mean wind speed maps. It is therefore better to plot capacity factor maps, as explained in the following section.

A better indicator of wind power potential is the expected capacity factor

In addition to data for wind speeds, this step requires assumptions about the power curve (Sect.

Using the capacity factor is already an improvement compared to the mean wind speed map, as it gives a more accurate indication of the expected energy output of a wind park. However, there is still a problem: the result depends on the power curve

If a power curve with large rotor is used (low specific power), 45 % might not be very good.

For another power curve with a smaller rotor (high specific power), 45 % might actually be quite good.

We define the

First, we write the expression for the normalised aggregated wind power output, which is used as the

The relative capacity factor

Relative capacity factor

Even though the shown wind power map nicely indicates how much power can be expected to be harvested at given locations, it lacks an indication of the revenue that can be expected from that generated power. Wind power that is generated simultaneously with many other wind parks will be valued less on the electricity market. It is therefore not enough to only look at the wind resource for identifying good locations for potential new wind parks. It is important to also look at the placement of other wind parks and the

Even though the relative capacity factor map provides a good overview of which location will likely provide a good power output, it does not say anything about which location will provide good revenue on the electricity market.

Due to the merit order effect

The covariance between two time series

The

The

For the variance of a sum of independent variables, the following general expression holds:

Covariance is a mathematical operation that is very useful for spatial planning of renewable energy. Often correlation coefficients are discussed for such purposes, but that has disadvantages as they only indicate the similarity of the fluctuations of the weather between two locations and no information about the amplitude of the fluctuations. Covariance includes both and is therefore more appropriate for assessing potential sites.

An example is two nuclear power stations giving an almost flat output profile, with tiny but identical fluctuations. Is that correlated? Yes. Is it a problem? No. The tiny fluctuations might be highly correlated, but that does not matter because they are so small. In this case correlation is high, but covariance is low.

Let us introduce some simplifying notation. We express power time series in terms of capacity and normalised power output,

For a candidate new wind park (indicated with the index “

We also define the relative covariance

The relative covariance consists of two terms. The first term,

The product of these two terms,

The relative covariance can be interpreted as the ratio of how much the overall variance increases when adding a new wind park of infinitesimal capacity at a specific location

Similarly, if we scale up existing capacity by the same amount,

Covariance equivalent installed capacities

Now we can summarise what different values of the relative covariance for a new wind park at location

Based on the relative covariance, an expression for the covariance equivalent installed capacity can be formulated:

The covariance equivalent installed capacity has the unit watts (

The covariance equivalent installed capacity with full correlation with

The covariance equivalent installed capacity gives an indication of how correlated a potential wind park at location

In Fig. 6, we show the covariance equivalent installed capacity maps for all the four scenario time steps. The plots nicely illustrate how the situation gets worse over time as more wind power capacity is added.

However, the covariance equivalent installed capacities shown do not directly indicate good or bad sites for new wind parks. A value of 50 GW might be bad in 2025, but it is good in 2040, as the levels then are generally much higher.

Adding a new wind park in the yellow area of Fig.

In this section, we develop Renewable Energy Complementarity (RECom) maps, which aims to address the drawbacks for normal wind resource maps and which accounts for covariance with existing wind parks.

Now, based on the relative covariance

A map displaying the complementarity factor is shown in Fig.

Higher values indicate better sites.

Average sites score a value of 1.

Complementarity factor

The parameter

The complementarity factor

Let us try to define a quantity that is an indicator of market value. The obtained income from a wind park depends on the capacity factor and the market price. Wind power has low marginal costs, so more wind power generally means lower prices. For simplicity, let us consider the price

With this assumption, we can compute an expression for the capture price, i.e. the mean value of the electricity price weighted according to energy production. For wind park

Here,

The parameter

The market value factor

For the data we use in this article,

Remember that

It should be noted that the calculation of the market value factor is based on a strongly simplified and idealised linear market model, which cannot fully represent the complexity of the power market price-setting mechanisms. It only captures the general trend and cannot include non-linearities of the merit order curve and other relevant phenomena. The influence of the electricity transmission network is not included, leaving out grid congestion and power market price zones that can have significant influence on the revenues. Such simplification was assessed to be necessary to realise a simple index, where the main aspect to capture was the general trend. National legislation can also influence the revenue potential for a wind park (e.g. though support schemes and renewable energy policies), but such phenomena are not accounted for here.

To represent the relation between wind power output and electricity market revenue, a simplified linear relation was used; see Eq. (

The relative covariance

To assure that the market value factor

converges towards zero for large positive input,

diverges towards infinity for large negative input,

behaves similar to the previously used linear function in the realistic range for wind power data.

Linear vs. exponential function.

Market value factor

Relative capacity factor, market value factor and RECom index (2040) (

Recall that the Taylor expansion of the exponential function is

It behaves similarly at the baseline point but ensures acceptable global behaviour (staying always positive). The relation between the linear function and exponential function is shown in Fig.

The resulting market value factor in its exponential form is plotted in Fig.

Market value factor

RECom index

Based on the relative capacity factor

Recall that

The RECom index is plotted in Fig.

the wind resources,

the covariance with all other wind parks,

the advantage of production in low-wind hours.

An average wind park has an index value of 1. Higher capacity factors result in higher index values. Less covariance with the wind power fleet will also result in higher values.

An RECom index larger than 1 indicates good sites.

An RECom index smaller than 1 indicates bad sites.

The RECom index is the quantity we have been seeking, and we propose to use this as a basis for maps that visualise the quality of potential wind power sites and the benefits of spatial diversification.

In this section, we discuss the sensitivity of the RECom map towards several influencing parameters.

The conversion of the linear value function in Eq. (

values larger than 1 (green/blue) are amplified,

values lower than 1 (orange/red) are damped.

The influence of the exponential formulation can be concluded from Fig.

As the data considered are rather close to the baseline point (

The RECom index depends for a large part on the scenario and the wind parks considered. It is therefore clear that it will change over time as more and more wind parks are deployed. This development over time is shown in Fig.

It can be observed that the dotted line, which represents

Hourly data were used for this study. Figure

RECom index 2040 based on time series with different sampling rates.

Again, we observe good robustness, as the changes are limited. Only in the extreme case of converting to weekly data do significant changes occur. It can be concluded that the performance of the RECom index does not highly depend on high-resolution data.

The most influential parameter is

RECom index 2040 with different values of the

Comparing the different maps shows the following:

For

For large values of

Our choice of

In reality, the most appropriate choice for

It is, however, not within the scope of this article to perform detailed analysis of future energy system scenarios to determine

The RECom index and the related RECom maps are useful tools to support spatial diversification by visualising the need and potential for it. They give a comprehensive indication of the expected revenue of potential wind park locations. Compared to the well-known wind resource maps, which display the mean wind speed, RECom maps add significant value, as they include more highly relevant information. Their simple and comprehensive nature is intended to visualise the matter also for people, such as politicians and the general population, who are not familiar with many of the underlying principles.

The RECom index is lower in areas with a lot of wind parks due to the high covariance and resulting lower expected wind power market value. The reality might even exaggerate this, as co-location with other wind parks might depress market value due to not only the merit order effect but also the power output. Areas with a lot of wind parks might be confronted with lower capacity factors (lower than expected) due to wake and blockage effects of nearby wind parks. These wave and blockage effects have, however, not yet been included in the RECom index in its current form.

Even though RECom maps can show a lot more than a mean wind speed map can, one must be careful to be aware of its limitations. A few of these limitations are listed here:

The calculation is based on a strongly simplified and idealised linear market model, which cannot fully represent the complexity of the power market price-setting mechanisms.

The choice of the parameter

The electricity transmission network is not included, leaving out grid congestion and power market price zones that can have significant influence on revenues.

The mean electricity price differs between countries and price zones, and the parameter

National legislation can influence the revenue potential, but renewable energy policies and support schemes are not accounted for here.

It is obvious that a market value estimation based on a very simple model never will show the full picture. However, it is not meaningful to get distracted by comparing the simple RECom index with a complex and time-consuming power market study of a future scenario. Instead, the RECom index and the related RECom maps need to be compared to mean wind speed maps, where the RECom index adds significant value.

RECom maps only show the benefits of having a wind park at a given location and not the cost of establishing a wind park there. For finding suitable locations, cost drivers such as water depth and distance to shore need to be considered as well. These considerations will, to some extent, counteract the benefits of the “good” locations identified by the RECom map, which tend to lay far offshore in deeper waters. This is to be addressed in future work.

Another aspect to be addressed in future work is the conversion of wind data into power output data, which at the moment is performed in a simplified way. It is to be investigated how accuracy can be improved without adding too much complexity to calculation of the RECom index.

The focus of this article is on wind power, but the methodology is not wind-power-specific and can likely be used for solar power. An adaptation of the RECom index for mixes of different weather-driven renewable energy sources will be considered in future work.

The code to download weather model data and create the maps is available on Zenodo:

All data used in this study are publicly available and can be obtained together with the code (wind power capacity scenario) or are obtained by running the code (weather model data). Data used for this study are as follows: the MERRA-2 reanalysis dataset obtained via Renewables.ninja,

TKV had the idea behind this activity and contributed to developing it and writing this article. HGS contributed to developing the activity, realised it in Python and contributed to writing this article.

The contact author has declared that neither of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This research has been supported by the Ocean Grid project, which is a Green Platform project financed in part by The Research Council of Norway (grant no. 328750).

This paper was edited by Anca Hansen and reviewed by two anonymous referees.