The climatological renewable energy deviation index (credi)

The highly variable nature of the wind and solar resources makes that a straightforward 30-year daily mean does not result in a useful definition of their climate (see SI section A). The same holds for an initial estimate by averaging each ordinal hour over 30 years (figures 2(a) and (c)). Though this simple average-based climatology does capture the mean expected behaviour on annual timescales, the random fluctuations from day-to-day and hour-to-hour cannot be explained by physical processes in this climatological definition. To remove these random fluctuations more data would be needed to obtain the desired, physical, smooth , but physical, climatology. However, considering a period longer than 30-years is ineffective, as climate change would start to influence the result [28]. Applying a simple running mean to this simple average-based climate timeseries is undesirable, as that would remove the diurnal cycle, which has a physical origin and is of large importance for our application in the energy sector.

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We therefore define an hourly rolling window climate, meaning that we first group the same time of day, and then, for each 'hour-of-the-day'-group, we apply a 30-year running mean (see SI section A.2). The hourly rolling window climate (C) of a renewable resource potential P for hour-of-the-year h is computed by:

$$\begin{align} C_P\left(h\right) & = \frac{1}{n}\sum_{y = 1}^n\ \sum_{h^{^{\prime}} \in \left\{h+24d\right\}_{d = -\Delta}^{d = +\Delta}} \ \frac{P\left(y, h^{^{\prime}}\right)}{2 \Delta +1} , \notag\\ h & = 1,2,\ldots,8760 \end{align} \tag{ 1 }$$

where n is the number of years, h is the hour of the year from 1 to 8760, Δ is half the window size (days) and $P(y,h^{^{\prime}})$ is the generation potential for hour hʹ of year y. In line with [27] an unweighted average and $n =$ 30 years are used. See figure 2 for a comparison between the different methods.

It should be noted that two details where omitted in formula (1). First, the hour-of-the-year is cyclic in nature, meaning that the first hour of year y follows the last hour of year y − 1. While this is implemented, for reasons of clarity this is not included. Second, to deal with leap years, we discard 29 February when computing the climatology. The climatology of each hour of the day for 29 February is then defined by the mean value of that hour of the day of 28 February and 1 March. This addresses the lack of data for 29 February and keeps a simple formalism.

The choice for the size of the rolling window is somewhat arbitrary. Sensitivity tests indicate that the window size should be bigger than 20 days to smooth any remaining nonphysical day-to-day variability, but smaller than 60 days to avoid over-smoothing the annual cycle (SI section A.3). Within this range the exact size of the window does not affect the use of the index. Here, we choose a window size of 40 days.

By using the hourly rolling window climate, both the importance of the various timescales and the need for more data points to get a smooth climatological function are addressed. It is essential that the climatological definition used in the calculation of the deviation index for wind or solar energy is physical (i.e. does not contain random fluctuations), such that anomalies represent variability due to the weather, decoupled from the climate.

We define the credi to be the cumulative anomaly of a renewable resource with respect to its climate over a specific time period of interest from a chosen starting point in two steps (figure 1). First, we determine the anomaly of a renewable resource, as the difference between the hourly generation potential of that resource and its climate (i.e. its expected value), taken from the computed hourly rolling window climate. Second, from an initial chosen starting point we sum these anomalies over a time period of interest.

More formally: let $P(y,h)$ denote the generation potential for ordinal hour h of year y, and let $C_P(h)$ denote the climate for ordinal hour h for that potential P. The anomaly $A_C(y,h)$ of a renewable resource for ordinal hour h of year y is then defined as:

$$\begin{align} A_C\left(y,h\right) = P\left(y,h\right) - C_P\left(h\right).\end{align} \tag{ 2 }$$

The credi over a given period of time is defined as the cumulative sum (or running total) of A_C over that period. For example, if we align the starting point with the start of the year, the credi on the ith hour of that year (y) is:

$$\begin{align} {\tiny \textrm{CREDI}}\left(y,i\right) & = \sum_{h = 1}^{i} A_C\left(y,h\right), \notag\\ i & = 1,2,\ldots,8760.\end{align} \tag{ 3 }$$

When interpreting the index, the following should be considered. A change in credi over time is an indication of either an excess or deficit of the renewable resource potential with respect to its climatic normal (figure 1(b)). A stable credi over a period indicates nominal renewable resource potential with respect to its climate.

Specifically, the credi score has the unit full load hours (FLH) and at a given time informs the user of the cumulative surplus or deficit generation potential over the period considered with respect to its nominal behaviour. So given a fixed time window, the distribution of the credi score calculated then provides insight into the properties of a connected storage unit, like the (dis-)charge potential. FLHs depend on the installed capacity, therefore if the installed capacity of a resource is known or assumed, the index allows for direct assessment of the storage volume and power needed to always generate nominally within the fixed time window used.

For clarity, when the index is applied to a specific resource, we first refer to the resource before the index acronym is given. For example, the wind credi refers to an assessment of the credi of wind energy potential, and similarly for solar.

The index can be used to assess the temporal development of anomalous renewable energy generation. In line with the application of hydrological drought indices, a physical storylines approach [31, 32] could be used. This approach can use regional climate change information while avoiding the strict limitations of a normal confidence-based approach applied in climate science. Storylines can be used to gain more insight into the driving processes, identify event analogues, and investigate similar events in alternative energy systems or under future climate conditions. Utilising these insights in, for example, resource adequacy assessments or system design studies, will likely lead to a more robust energy system.

Selection of relevant events can be based on historical adequacy assessments (like the [33] Adequacy Outlook). As shown by Van der Wiel et al [12, 32], event analogues can then be found in large energy-climate datasets that incorporate climate change [1, 11]. By studying these analogues the physical processes and likelihood of these events can be assessed.

To demonstrate the index at different timescales and to highlight relevant considerations in the application of the credi, we selected the years 1996, 1998, 2003 and 2016 as storylines. The year 1996 was chosen specifically, as one of the most challenging years for resource adequacy in the Netherlands and Germany in a future net-zero emission energy system [33, p 56]. In the analysis of the potential for hydrogen generation from wind, 2003 and 2010 where found to be anomalously low [33, pp 58–61]. Both 1998 and 2016 where chosen as they represent the most anomalous years of the index for solar and wind, respectively.

At annual to decadal timescales the index can be used to assess the impact of large scale oscillations in the ocean and atmosphere on the availability of a renewable energy resource. These long-term deviations from the climate are relevant, e.g. because they offer sources of meteorological predictability [37, 38], or because stakeholders look at 10 year time periods to estimate return of investments [33].

Over the past 30 years, large inter-annual variation is observed in the wind credi (figure 3(a)). The cumulative effect of variations at seasonal scales resulted in higher than expected wind generation potential from 1991 to 2002, while from 2010 onwards wind credi declined indicating lower than expected wind generation potential. These general variations are in line with those found by Stoop et al [15] and Wohland et al [39].

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Similarly, the solar credi shows inter-annual variability. From 1991 to 2003 solar credi shows a general decrease, indicating less than average potential generation from solar. Within this period, a strong reduction in the periods 1993–1995 and 1998–2002 is observed (figure 3(b)). In the period 2005–2018, solar credi is flat, showing that the solar potential was as expected from climate. After this period a steady increase in the solar credi is observed, indicating higher than expected potential generation.

The values of solar credi are generally lower than those of the wind credi. This is directly related to the diurnal cycle, which by definition gives zero solar potential at night and low values in the morning and evening. Consequently, the sum of the anomalies over a given period is smaller than for wind potential, which has values for all 24 h in a day.

Finally, while the impact of the relative observed variability depends on the ratio of installed capacities, we observe that the inter-annual energy-meteorological variability is mainly driven by the wind resource in the analysed region (i.e. the northern of the Netherlands). And though the wind and solar credi s show strong anti-correlated behaviour during some years (e.g. from 1991 to 2002), in others this is not the case (e.g. from 2004 to 2005). At decadal timescales, wind and solar balance the system somewhat, but they are not suited to fully negate the variability of their counterpart.

When assessing the seasonal energy-meteorological variability using the credi, the starting point determines the way the temporal development of the index is perceived. In line with definitions of hydrological drought, the starting point determines the separation between energy surplus (wet) and deficit (dry) years. As the index is intended to capture the energy-meteorological variability, the start date is picked such that the biggest range if credi at the end of, and throughout, the year is observed.

Comparing credi starting points for each month of the year, we found that these should not be the same for wind and solar (SI section B). We use May 1st as the starting point for wind, as it gives the widest distribution of the index at the end of the analysis window in this particular region. For solar no clear distinction is found between a December or January starting point, we chose to use January 1st here.

For the yearly wind credi, it is obvious that an individual year can either be anomalously positive or negative, and that variations throughout a year are large (figure 4(a)). This results in a wide range of yearly storylines. The 25%–75% spread of the index grows to ±180 FLH over a year (figure 4(b)). The most extreme negative year in the period considered for wind credi was 2016. In that year, from about September onwards, the wind potential was almost consistently below expected with 350 less FLHs at the end of the analysed period.

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As an example of the use of wind credi for storyline analysis we look at 1996. From May to October the index is relatively flat, indicating that the wind potential was as expected from its climate (red line in figure 4(b). Then, a strong reduction is observed in the wind credi from December to the end of January, indicating much lower then average potential generation from wind. Part of this deviation is compensated by higher than normal generation potential in February of 1997.

As noted earlier, values of yearly solar credi are smaller than of wind credi (figure 5(a)), with an average spread (25%–75%) of ±18 FLHs, and uncommon spread (10%–90%) of ±35 FLHs spread over a year (figure 5(b)). This indicates that ~18 FLHs of total energy is needed to cover the deficit of the installed solar capacity in 50% of years and ~35 FLHs to cover 80% of years (figure 5).

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The most extreme year of high solar potential was 2003; the most extreme year of low solar potential was 1998. Especially 2003 is remembered for its extremely warm and sunny summer [40].

At sub-seasonal timescales, similar to seasonal, the start point determines the way the temporal development of the index is perceived. We use 'energy'-seasons to capture the large scale changes on sub-seasonal timescales. For wind we define two seasons of interest: September to March, and April to August. For brevity, only the results found for wind in the winter 'energy'-season are shown here, see SI section C for the other and solar. Alternative definitions of 'energy'-seasons can be relevant, especially for regions that have different sub-seasonal behaviour then the 'NL1'-region shown here.

It is obvious that different years show quite different characteristics (figure 6(a)) and individual winter seasons can differ greatly. As expected, the sub-seasonal timescale is emphasised more. For instance, the anomalous index-development in 1996 described in section 4.2 is more clearly visible. Especially the strong reduction in wind credi from December to the end of January stands out as a period of much lower than normal wind generation potential.

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Finally, short-term events, e.g. Dunkelflautes, can pose significant risk to highly renewable energy systems [12, 41–44]. A 8-day window for credi aligns with previous work [33], and is investigated here, see SI section D for additional figures and the top 50 eight-day events.

For short-term event analysis we do not pre-define the start point, all eight-day windows are considered. Overlapping events that share a five or more days, are removed from the analysis. While we only consider the lowest final credi value for our event selection, other impact selection methods as described by Van der Wiel et al [32] can be used.

Again we noted the large weather-caused variability between different eight-day periods (figure 7(a)). The computed spread in figure 7(b) considers events throughout the year. This can also be investigated on a seasonal basis for winter or summer-specific event information, or for shorter or longer events.

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The most extreme event is from 16–24 January 2017 and the analysis year 2016 is present three times in the top 50 events. While the specific eight-day event found in TenneT [33] is not the most extreme event, the analysis year 1996 does show up four times in the top 50 events. Indicating that the analysis year 1996 indeed stands out as quite exceptional.