# Frequency and duration of low-wind-power events in Germany

Nils Ohlendorf<EMAIL_ADDRESS>Wolf-Peter Schill<EMAIL_ADDRESS>Mercator Research Institute on Global Commons and Climate Change (MCC), EUREF
Campus 19, Torgauer Straße 12-15, 10829 Berlin, Germany  German Institute for
Economic Research (DIW Berlin), Mohrenstrasse 58, 10117 Berlin, Germany
Energy Transition Hub, Climate & Energy College, The University of Melbourne

###### Abstract

In the transition to a renewable energy system, the occurrence of low-wind-
power events receives increasing attention. We analyze the frequency and
duration of such events for onshore wind power in Germany, based on 40 years
of reanalysis data and open software. We find that low-wind-power events are
less frequent in winter than in summer, but the maximum duration is
distributed more evenly between months. While short events are frequent, very
long events are much rarer. Every year, a period of around five consecutive
days with an average wind capacity factor below 10% occurs, and every ten
years a respective period of nearly eight days. These durations decrease if
only winter months are considered. The longest event in the data lasts nearly
ten days. We conclude that public concerns about low-wind-power events in
winter may be overrated, but recommend that modeling studies consider multiple
weather years to properly account for such events.

###### keywords:

Wind power; Low-wind-power events; Reanalysis data;

††journal: arXiv

##  1 Introduction

The Paris Agreement calls for an extensive decarbonization of the global
economy. A major strategy for achieving this goal is a massive expansion of
variable renewable energy sources, in particular solar photovoltaics (PV) and
wind power [de Coninck et al., 2018]. While power generation from solar PV
largely follows diurnal and seasonal cycles with annually repeating patterns,
wind power is subject to more irregular inter-annual as well as intra-annual
variations which are relevant from a security of supply perspective. In
countries with growing shares of wind power, the occurrence of low-wind-power
(LWP) events thus receives increasing attention.

This is particularly true in Germany. In the context of its energy transition,
Germany is one of the global front-runners in wind power deployment. In 2018,
a total capacity of 52.5 GW of onshore wind power was installed in Germany,
generating 90.5 TWh of electricity. This corresponds to 15% of German gross
electricity consumption [BMWi, 2019]. Given the government’s targets to expand
the share of renewables in electricity consumption to 65% by 2030 and at least
80% by 2050 [Bundesregierung, 2019], the dependence of the German energy
system on wind power is set to increase strongly in the future. Concerns about
LWP events have been discussed in German media [Wetzel, 2017, 2019] and in the
German parliament [Deutscher Bundestag, 2019a], and LWP events are also
mentioned in the government’s energy transition reporting [Deutscher
Bundestag, 2019b]. In this context, the term Dunkelflaute is increasingly
used. It refers to a persistent situation with very low power generation from
wind and solar PV, which would be especially challenging in the German winter
season where PV availability is low and electric load has its peak. Yet no
clear definition of this concept has been provided so far [Wissenschaftliche
Dienste, 2019], and quantitative evidence on the frequency and duration of
such events is missing. In Table $15$ of Deutscher Bundestag [2019b], an
independent expert commission generally assumes a no-wind-no-solar period of
two weeks.

Yet research on LWP events is sparse so far. In this paper, we contribute to
filling this gap, focusing on onshore wind power in Germany. We provide an in-
depth analysis of the frequency, duration, and magnitude of LWP events, making
use of reanalysis data for 40 full years (1980 to 2019) and power curves of
recently installed wind turbines. In doing so, we propose two definitions of
LWP events and investigate three different thresholds of capacity factors (2%,
5% and 10%). We also compare the spatial distributions of the most persistent
LWP event and the mean electricity generation. Parts of our analysis
explicitly focus on winter months: these are particularly relevant, as power
generation from solar PV is relatively low during this season, while the
German peak load also occurs in winter. In order to allow for the highest
degree of transparency and reproducibility, we provide the source code of our
analysis under a permissive open-source license [Ohlendorf, 2020].

There are only few dedicated analyses on the frequency and duration of LWP
events. Early contributions address reliability aspects of spatially dispersed
wind power in California [Kahn, 1979] or in the midwestern United States
[Archer and Jacobson, 2007]. Analyses explicitly focusing on LWP events only
recently emerged. Yet these differ from our work, amongst other factors, with
respect to geographical and temporal coverage, data sources used, and
methodologies applied. In particular, previous low-wind analyses mostly draw
on local measurement data and either evaluate wind speeds [Leahy and McKeogh,
2013, Patlakas et al., 2017] or wind power [Handschy et al., 2017, Kruyt et
al., 2017]. Leahy and McKeogh [2013] and Patlakas et al. [2017] investigate
low-wind events for Ireland and the North Sea area, respectively. Both studies
firstly evaluate low-wind events that are constantly below a given wind speed
threshold, and secondly determine annual minimum moving average wind speeds
for given durations, using extreme value distributions. Kruyt et al. [2017]
and Handschy et al. [2017] go one step further and calculate respective power
generation from wind speeds for Switzerland and the United States, using a
power curve. While the findings of these studies are necessarily idiosyncratic
to the specific geographical applications, some common findings emerge. First,
low-wind events are less frequent and less persistent if more, and spatially
more dispersed, measurement stations are used. Second, there are generally
less events in winter than in summer.

The measurement-based analyses face challenges related to their data sources.
In general, studies that draw on measured wind speeds are spatially biased,
have low measurement densities, and extrapolation from measurement height to
hub height is challenging because of distorting effects of terrain, elevations
or buildings [Sharp et al., 2015]. Measurement data may further be subject to
inconsistencies caused by changing equipment and measurement errors. Extreme
event analyses further require consistent measurements over large time periods
to sufficiently capture climatic variations.

These issues can be addressed by using long-term meteorological reanalysis
data. Such data is increasingly applied for onshore wind energy modelling.
Several studies focus on data accuracy and on validating models of wind power
generation [Decker et al., 2012, Sharp et al., 2015, Olauson and Bergkvist,
2015, Rose and Apt, 2015, Staffell and Pfenninger, 2016, González-Aparicio et
al., 2017, Germer and Kleidon, 2019]. Other analyses deal with variability
aspects of wind power, but do not focus on extreme low-wind events. For
example, Grams et al. [2017] explain longer-term fluctuations in European wind
power generation with different types of weather regimes, based on MERRA-2
data. With similar approaches, Collins et al. [2018] investigate inter-annual
variations of European wind and solar power, and Santos-Alamillos et al.
[2017] explore optimal allocations of renewable generation capacity in a
European super grid. For the contingent U.S. states, Shaner et al. [2018]
investigate the reliability of future power systems dominated by wind and/or
solar PV, and Kumler et al. [2019] explore inter-annual renewable variability
for Texas. Yet none of these studies explicitly focuses on the frequency and
duration of extreme low-wind-power events.

A notable reanalysis study that does focus on extreme wind events is conducted
by Cannon et al. [2015] for Great Britain. Using 33 years of MERRA as well as
ERA-Interim data, the authors conclude that the frequency and duration of low-
wind-power events can be approximated by a Poisson-like process. Weber et al.
[2019] also use ERA-Interim data for a superstatistical analysis of extreme
wind power events at nine specific European sites, including one German
onshore location. They find that the distribution of low-wind events has a
heavy tail, as low-wind events may result from a combination of different
weather and circulation patterns.111Weber et al. [2019] base their analysis on
wind speeds, not wind power generation, with a cut-off threshold of $4$ m/s.
In another analysis based on ERA-Interim reanalysis data and other sources,
Raynaud et al. [2018] define and investigate the occurrence of renewable
“energy droughts”, which are measured relative to average daily generation.
They find that wind power droughts are both relatively frequent and relatively
short in most European countries, compared to hydro power droughts.

We contribute to this emerging literature with a dedicated open-source,
reanalysis-based study that investigates LWP events in Germany in detail. To
the best of our knowledge, we are the first to use MERRA-2 data in this
context, i.e., spatially and temporally consistent reanalysis data covering 40
years at 50 m above surface. Compared to Cannon et al. [2015], we also make
use of not only one, but three recent power curves to represent different
types of wind turbines that are characteristic for different locations defined
by mean wind speeds. Complementary to Raynaud et al. [2018], we further
present an alternative approach to defining and evaluating LWPs by looking
either at hours that are constantly below a threshold, or at hours with a mean
below a threshold.

##  2 Methods and data

###  2.1 General approach

Based on wind speeds and power curves, we derive an hourly aggregated time
series of capacity factors for wind power in Germany. First, we take wind
speeds at 50 m above surface from the MERRA-2 reanalysis dataset, which covers
40 years from 1980 to 2019, and extrapolate to hub heights.222See Section A
for further information on the use of reanalysis data for energy modelling.
Second, capacity factors of each MERRA-2 grid cell are calculated based on
power curves of recently installed wind turbines. Third, we spatially
aggregate these capacity factors using a weighting scheme that considers the
current spatial distribution of onshore wind power capacity in Germany.
Finally, we investigate the resulting time series of hourly aggregated
capacity factors by applying a narrower and a wider definition of LWP events.

###  2.2 Wind speeds derived from reanalysis data

We use the MERRA-2 dataset provided by NASA [Gelaro et al., 2017]. Data is
available starting from the year 1980. In contrast to several other global
reanalysis datasets which have time resolutions of 3 to 6 hours and provide
wind speeds at 10 m above surface, MERRA-2 includes hourly wind speed data at
50 m, which allows better modelling of wind power generation.

Figure 1: MERRA-2 grid points (blue) and grid cells that intersect with
Germany.

The MERRA-2 grid consists of 576 longitudinal and 361 latitudinal horizontal
grid points, i.e., a resolution of $0.625^{\circ}$ x $0.5^{\circ}$ which for
Germany roughly corresponds to 50 x 50 km [Bosilovich et al., 2016]. Figure 1
shows the grid points in blue and all grid cells extrapolated from these
points that intersect with Germany. For each grid cell, MERRA-2 provides
hourly northward and eastward wind speed data at 50 m above surface. Our
dataset further includes surface roughness data for the year 2019.

###  2.3 Aggregated wind power derived from wind speeds using power curves

We calculate the magnitude of the horizontal wind speed ($U$) for each MERRA-2
grid point based on northward ($u$) and eastward components ($v$) at 50 m
(Equation 1).

$U=\sqrt{(u^{2}+v^{2})}$ (1)

In line with Kruyt et al. [2017], we use the logarithmic power law to
extrapolate wind speeds to hub-height ($h$) with $U_{hub}$ as the wind speed
at hub height and $z_{0}$ as the surface roughness data for every grid point
and each hour of the year 2019 (Equation 2).

$U_{hub}=w\frac{\ln\frac{h}{z_{0}}}{\ln\frac{50}{z_{0}}}$ (2)

Figure 2: Wind speed zones in Germany. Dark blue implies high mean wind
speeds, blue medium wind speeds, and light blue low mean wind speeds.

We define three types of wind zones, based on mean local wind speeds over 40
years for each MERRA-2 grid cell (Figure 2), and assign typical hub heights
for wind turbines. For high-wind-speed sites, we assign a hub height of 100 m,
for medium-wind-speed sites of 125 m, and for low-wind-speed sites of 139 m
[Wallasch et al., 2015]. These values reflect the mean hub heights of recently
installed wind power plants in respective German wind speed zones.

We calculate hourly capacity factors for each grid cell by applying power
curves characteristic for the three wind zones. The power curves are based on
manufacturer data of currently available wind turbines for low-, medium- and
high-wind sites, respectively. Both the low- and high-wind site power curves
represent an average of four wind turbines of similar diameters and
capacities. We consider turbines from six manufacturers (see B), among them
four large companies which cover 87% of the capacity installed in Germany in
2015 [Lüers, 2016].

Manufacturers generally provide discrete capacity factors ($CF_{disc}$) for
wind speed intervals of 1 m/s. For both the low- and high-wind curves, we
first calculate discrete mean capacity factors for each wind speed and then
calculate continuous capacity factors using a generalized logistic function
(Equation 3).

$CF_{cont}=A+\frac{C}{(1+Te^{-B(U_{hub}-M)})^{1/T}}$ (3)

Here, $CF_{cont}$ is the continuous capacity factor and $A$, $B$, $C$, $M$ and
$T$ are fitted coefficients based on minimising the squared deviations between
$CF_{disc}$ and $CF_{cont}$. For both the low- and the high-wind power curve,
cut-in wind speeds of around 3 m/s emerge, and the resulting capacity factors
are capped at 0% and 100%. The medium-wind power curve represents the average
of the low- and high-wind curves (Figure 3).

Figure 3: Power curves of three types of wind turbines

Aggregated hourly capacity factor time series for overall Germany are derived
by weighting all grid cells with the current distribution of installed wind
power generation capacity. The latter is extracted from Open Power System Data
[Open Power System Data, 2017, Wiese et al., 2019] and open-source GIS data.
The red points in Figure 4 indicate the installed wind capacity of locally
aggregated wind power plant sites in Germany and the blue squares show the
corresponding relative capacity distribution of the MERRA-2 grid cells. Grid
cells only partly intersecting with the German land area receive lower weights
according to the overlapping area. We implicitly assume that the transmission
infrastructure allows geographical balancing of wind power in Germany, which
is currently largely the case.333This assumptions is particularly valid for
low-wind periods. During high-wind, high-load periods, the German transmission
grid can be constrained in North-South direction.

Figure 4: Distribution of currently installed wind power capacity in Germany.
Darker colors indicate a larger share of total or relative installed capacity.

###  2.4 Definition of low-wind-power events

We propose two different measures of low-wind-power periods, a narrower and a
wider one (Figure 5). We further consider three alternative capacity factor
thresholds of 2%, 5%, and 10%.

As for the narrower definition, we consider LWP events to be consecutive hours
in which the aggregated capacity factors are Constantly Below the Threshold
(CBT). This concept bears some resemblance to the “runs analysis” by Leahy and
McKeogh [2013] or the “duration given intensity” method by Patlakas et al.
[2017]. Starting in the first hour, we list annual LWP events for durations
starting from five consecutive hours and report the number of hours constantly
below the given capacity factor threshold. We then increase the duration in
hourly steps and repeat until there are no further events listed.

To provide a wider definition, we consider LWP events to consist of
consecutive hours in which the moving average of capacity factors is under the
same threshold, i.e., Mean Below the Threshold (MBT). Again, we list all LWP
periods until we reach the threshold value, ensuring that LWP periods do not
overlap. By definition, the MBT method results in more low-wind-power events
for a given duration and also results in longer events for each threshold,
compared to CBT.

Figure 5: Illustration of the two LWP event definitions

The average annual amount of LWP events per duration over all 40 years equals
the expected value of events per year. Further, the reciprocal value of the
annual average provides the return period, that is the expected temporal
distance between two similar reoccurring events. Periods overlapping annually
or monthly are assigned to the year or month in which more than 50% of the
hours are located444 Accounting for annually overlapping periods requires
December data from the previous year, and January data from the subsequent
year. For the two boundary years 1980 and 2019, we substitute the missing data
for December 1979 (January 2020) with data from December 1980 (January 2019).
.

##  3 Results

###  3.1 Seasonal distribution and frequency of low-wind-power events

Figure 6 shows that LWP events are generally most frequent in summer (here
defined as June-August) and least frequent in winter (December-February). The
results for spring (March-May) and autumn (September-November) are mostly
close to the annual average. Accordingly, respective findings made for other
European countries [Leahy and McKeogh, 2013, Cannon et al., 2015, Kruyt et
al., 2017] are also valid for Germany.

Figure 6: Average seasonal duration (horizontal axis) and frequency (vertical
axis) of LWP events in Germany

The frequency of events for a given duration is about 1.5-3 times higher for
the wider MBT definition compared to the narrower CBT concept. For both
metrics, the frequency of LWP events increases substantially with the capacity
factor threshold value. For example, a 10-hour event below a capacity factor
of 2% occurs on average around 0.2 times per winter for CBT and slightly less
than once per winter for MBT. For a 10% capacity factor threshold, there are
on average around eight such winter events for CBT and 13 for MBT. In general,
we find that short LWP events with a duration of up to around half a day are
relatively frequent and may occur several times per year, especially under the
wider MBT definition. Longer LWP events, in contrast, are much less frequent.

To provide a complementary perspective, we calculate the return periods for
different durations of LWP events (Table 1). The return periods are the
reciprocal of the average (annual or seasonal) frequency of LWP events for
different durations, considering both definitions and all three thresholds
(cf. Figure 6). For example, an LWP event with an average frequency of 0.2 for
a given duration leads to a return period of 5 years for this specific
duration. The longer a given duration, the lower its average frequency and the
longer its return period.

For a return period of ten years, we find a duration of 17 hours (2% capacity
factor threshold), 41 hours (5%) and 77 hours (10%) under the narrower CBT
definition, and a duration of 34 hours (2%), 79 hours (5%) and 188 hours (10%)
under the wider MBT concept. In other words, every ten years the German energy
system has to deal with a period of nearly eight days of average wind power
generation (MBT) below 10% of the installed capacity.

Table 1: Duration in hours for LWP events in winter or in any season for different return periods | Constantly below threshold (CBT) | Mean below threshold (MBT)
---|---|---
| Winter | Any season | Winter | Any season
Return period | 2% | 5% | 10% | 2% | 5% | 10% | 2% | 5% | 10% | 2% | 5% | 10%
1 year | 5 | 15 | 29 | 11 | 23 | 45 | 8 | 30 | 63 | 18 | 58 | 122
2 years | 7 | 21 | 40 | 13 | 32 | 57 | 12 | 45 | 92 | 21 | 69 | 144
3 years | 8 | 23 | 44 | 14 | 33 | 60 | 14 | 52 | 101 | 23 | 71 | 161
4 years | 9 | 30 | 48 | 14 | 33 | 63 | 16 | 62 | 112 | 27 | 72 | 173
5 years | 10 | 32 | 57 | 15 | 35 | 65 | 22 | 68 | 113 | 28 | 75 | 178
6 years | 10 | 32 | 57 | 15 | 35 | 67 | 25 | 69 | 114 | 29 | 76 | 182
7 years | 12 | 33 | 60 | 15 | 36 | 67 | 27 | 70 | 114 | 31 | 76 | 186
8 years | 14 | 33 | 63 | 17 | 37 | 69 | 28 | 72 | 117 | 33 | 79 | 186
9 years | 14 | 33 | 63 | 17 | 37 | 69 | 28 | 72 | 117 | 33 | 79 | 186
10 years | 14 | 33 | 64 | 17 | 41 | 77 | 28 | 72 | 126 | 34 | 79 | 188
15 years | 17 | 36 | 67 | 18 | 41 | 77 | 31 | 76 | 129 | 38 | 82 | 189
20 years | 19 | 41 | 77 | 19 | 49 | 81 | 34 | 79 | 131 | 45 | 89 | 221
25 years | 19 | 41 | 77 | 19 | 49 | 81 | 34 | 79 | 131 | 45 | 89 | 221
30 years | 19 | 41 | 77 | 19 | 49 | 81 | 34 | 79 | 131 | 45 | 89 | 221

To better interpret these return periods, we provide an example for the German
onshore wind power capacity of 52.5 GW installed in 2018. For this wind
turbine fleet, average power generation is expected to not exceed around five
GW, i.e., 10% of capacity, during a period of around five consecutive days
every year (122 hours, MBT for ’Any Season’ in 1). Every ten years, this
period increases to nearly eight days, and every twenty years to more than
nine full days. Looking only at LWP events in winter, these durations decrease
to less than three days every winter, less than five days every tenth winter,
and around five and a half days every twentieth winter. The remaining load has
to be covered by other generators, energy storage or demand-side measures.
However, wind power still contributes some generation capacity above the 10%
threshold during some of these hours, as indicated by much lower CBT return
periods.

###  3.2 Magnitude of the most extreme low-wind-power events

The most extreme LWP events over the entire 40 years analyzed can be
interpreted as worst cases from an energy system planning perspective. In an
annual perspective, the most extreme events occurred in 1985 for all capacity
factor thresholds (Figure 7). Under the narrower CBT definition, there are
nearly four consecutive days with wind power generation constantly below 10%
in 1985, and still around two consecutive days with generation constantly
below 5%. Under the wider MBT definition, the duration of this most extreme
event increases to nearly ten days (10%) or around four days (5%).

Figure 7: Most extreme LWP events per year. The vertical axis shows the
duration of the longest event per year for the three capacity factor
thresholds.

While this 1985 event is the most extreme one under both CBT and MBT, the
ranking of the second most extreme yearly events differs between the LWP
definitions. For example, the second-longest event occurred in 1984 under the
CBT definition. Yet under MBT, the duration of the most extreme event in 1984
is only average. In general, the definition of LWP events and the chosen
thresholds have a substantial impact on quantitative results. Under MBT, the
most extreme annual events are generally around twice as high compared to CBT.

We further find very large inter-annual variations. Considering the 10%
threshold, the longest event for the MBT definition lasted for almost 10 days
in 1985, but in 2005 the longest duration was only three days for the same
threshold. The relative difference between the longest events for each year
increases with the threshold. These large variations of the most extreme
annual LWP events complement the findings made by Collins et al. [2018], who
determine large inter-annual variations of average renewable availability.

We next look at the most extreme LWP event in a monthly perspective,
irrespective of the year in which these occur (Figure 8). The most extreme
events for the 10% threshold occur in March for both definitions. This is the
1985 event discussed above, with durations of nearly four (CBT) or nearly ten
consecutive days (MBT).

Figure 8: Most extreme LWP events per month. The vertical axis shows the
duration of the longest event of all respective months for the three capacity
factor thresholds.

Considering all thresholds and both LWP definitions, there is no clear trend
of the most extreme monthly LWP events. That is, substantial extreme events
may occur throughout the year, and also in winter months. This contrasts the
previous finding that the frequency of LWP events is generally much higher in
summer than in winter, as shown in Section 3.1. Under CBT, the most extreme
events in each of the winter months are even longer than those in summer
months for the 10% capacity threshold. This finding is, however, not confirmed
under the MBT definition.

###  3.3 Spatial distribution of wind power during most extreme LWP event

To also explore the spatial dimension of LWP events, we compare the
distribution of capacity factors during the most extreme LWP of 1985 to the
distribution of annual mean capacity factors in the same year (Figure 9).

Figure 9:  Spatial distribution of wind power. Left: Average wind power during
most extreme LWP event (10% capacity factor, MBT) in dataset in March 1985
(Scale: From 0% to 20% of mean capacity factors). Right: Mean wind power in
the entire year 1985 (Scale: From 5% to 50% of mean capacity factors).

The spatial pattern of annual mean capacity factors (Figure 9, right panel)
largely resembles that of average wind speeds in Germany (Figure 2). Mean
capacity factors are generally higher in Northern than in Southern Germany.
They are highest close to the Northern and the Baltic Sea, and lowest in the
southern Alpine region.

The spatial pattern of mean capacity factors during the most extreme LWP event
(Figure 9, left panel) substantially deviates from the distribution of the
means. In particular, capacity factors of the north-eastern region and parts
of the northern region are relatively low. The respective spatial
distributions of capacity factors for other thresholds under both the CBT and
MBT definitions of the same event also show substantial deviations from annual
means.

Accordingly, the spatial distribution of capacity factors during extreme LWP
events does not necessarily correspond to the annual mean pattern. This
indicates that low-wind events can be very pronounced even in regions with
very good average wind resources.

##  4 Conclusions

We analyze the seasonal distribution, frequency and magnitude of onshore low-
wind-power events in Germany, as well as spatial aspects of the most extreme
events, based on MERRA-2 reanalysis data and open software. We propose and
evaluate two definitions of low-wind-power events for three capacity factor
thresholds.

We synthesize three key results from the analysis. First, LWP events are
generally most frequent in summer and least frequent in winter. Nonetheless,
substantial events occur in all months of the year, and also in winter. The
most persistent LWP event in the dataset occurred in March.

Second, while short events with a duration of up to around half a day are
relatively frequent, very long events are much rarer.555Weber et al. [2019]
argue that low-wind event statistics do not follow a simple exponential
distribution, but have “heavy tails”, i.e. the probability decreases rather
slowly with increasing duration. Every year, the German energy system has to
deal with a period of around five consecutive days during which average wind
power generation is below 10% of the installed capacity. Every ten years, a
respective period of nearly eight days is to be expected. Looking only at
winter months, the durations of these expected events decrease to less than
three days every winter and less than five days every tenth winter. The most
persistent low-wind event in the entire dataset has a duration of nearly ten
consecutive days of average wind power generation below a 10% capacity factor.

Third, the spatial pattern of LWP events may be very different from the one of
average wind power resources. During the most persistent LWP event, we find
average generation to be particularly low in several regions which have some
of the best wind resources.

We conclude that energy modeling studies that only consider one historic
weather year are likely to substantially underestimate the occurrence of low-
wind-power events and related system implications. In particular, analyses
with an energy system planning perspective should take less frequent LWP
events into account, e.g., the discussed events with a return period of ten
years, or even the most extreme event identified here. This is particularly
important when the complementary role of other variable and dispatchable
generators, energy storage, or demand-side measures in highly-renewable energy
systems is to be explored.666This is demonstrated, for example, by Schill and
Zerrahn [2018] in an analysis of storage requirements for renewable energy
integration in a sensitivity analysis with one artificial no-wind week.

Further, analyses dealing with the pros and cons of either more decentralized
or more centralized renewable energy systems should consider the spatial
dimension of LWP events. Although not in the focus of our analysis, our
results indicate that LWP events are more pronounced for smaller geographic
areas.

From an energy policy perspective, our findings on LWP events occurring in
winter may be most relevant. Our analysis indicates that concerns about
frequent and persistent LWP events in German winters appear to be overrated,
considering that the longest event with an average capacity factor below 10%
and a ten-year return period in winter has a duration of less than five days.
We further recommend that policy makers or regulators develop a proper
definition of the Dunkelflaute term, which currently appears to be used in a
rather qualitative way. Our two definitions of LWP events proposed here may be
useful in this context.

While our analysis deliberately focuses on LWP events of onshore wind power in
Germany, we see an avenue for future research that would ideally combine the
analysis of low production periods of onshore and offshore wind power as well
as solar PV with time series of load, while expanding the geographic focus
beyond Germany. The open-source provision of the tool used for the present
analysis may be a useful starting point for such research.

## Acknowledgment

This analysis is a result of the research project P2X, funded by the German
Federal Ministry of Education and Research (FKZ 03SFK2B1). Wolf-Peter Schill
carried out parts of the work during a research stay at the University of
Melbourne. Nils Ohlendorf mainly worked on this project while employed at DIW
Berlin, and partly also after being employed at MCC. We thank the participants
of the DIW Sustainability Cluster Seminar in April 2017, Strommarkttreffen
Berlin November 2017, IAEE International Conference Groningen 2018 and Enerday
Dresden 2018 for valuable comments on earlier drafts.

## Data availability statement

The data that support the findings of this study have been created with
software that is openly available under an MIT license at
https://doi.org/10.5281/zenodo.3694373.

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##  Appendix A Reanalysis data and its use for energy modelling

Reanalysis data is increasingly used for energy modelling as it provides
consistent global time series of long-term atmosphere data such as wind speed,
temperature and air pressure in regular spatial and temporal resolutions. The
underlying global circulation models extrapolate measurement station data on
wind speeds, temperature, moisture and surface pressure as well as data from
satellites and precipitation measurements [Decker et al., 2012]. Several
publicly available second-generation global reanalysis datasets have been
released since the early 2000s. We use MERRA-2, which builds on and improves
the previous MERRA dataset, using advanced models and data sources [Molod et
al., 2015].

Decker et al. [2012] evaluate the accuracy of several reanalysis datasets
(MERRA, NCEP, ERA-40, ERA-Interim, CFSR and GLDAS) using flux tower
measurements in the Northern Hemisphere. Almost all products overestimate the
monthly and 6-hourly wind speeds and their variability. MERRA and ERA-Interim
show the lowest values root-mean-square error and bias for diurnal cycles.
Sharp et al. [2015] review other data validation studies of different
reanalysis datasets. Three studies derive Pearson’s correlation coefficients
for MERRA between 0.75 and 0.89 based on measurement stations in Sweden,
Portugal, Norway and Denmark [Liléo and Petrik, 2011, Liléo et al., 2013,
Carvalho et al., 2014]. Staffell and Pfenninger [2016] propose country-
specific wind speed bias correction factors for MERRA and MERRA-2 to increase
the correlation with national capacity factors. Without such correction,
average capacity factors for Germany based on raw MERRA or MERRA-2 wind speeds
would be overestimated. Staffell and Green [2014] make a similar point for the
UK. In contrast, Cannon et al. [2015] do not use correction factors in a UK
application. Even if MERRA wind speeds turn out to be not particularly valid
for single measurement points, spatial aggregation of mean wind speed over all
stations results in a correlation coefficient of 0.94. This indicates a high
validity of MERRA data for large-scale wind patterns. Following Cannon et al.
[2015], we also refrain from introducing correction factors and instead make
use of the error-smoothing effect of spatial aggregation. In doing so, we also
avoid model artefacts, particularly as the usefulness of correction factors
has only been demonstrated for average wind speeds, but not for extreme
values.

##  Appendix B Wind power turbines

The low- and high-wind power curves used in our analysis are based on data of
eight wind power turbines by six manufacturers, namely Nordex, Senvion,
Enercon, Vestas, Gamesa and Vensys. Specifically, we use the following high-
wind power turbines:

  * 1.

Nordex N90-2.5MW

  * 2.

Vestas V90-2.0MW

  * 3.

Gamesa G97-2MW

  * 4.

Vensys 100-2.5MW

Analogously, we use following low-wind power turbines:

  * 1.

Nordex N131-3.3MW

  * 2.

Senvion 3.2M122

  * 3.

Enercon E126 EP4/4.2MW

  * 4.

Vestas V126-3.3MW

##  Appendix C Discussion of limitations

We briefly discuss some limitations of our analysis and how these may
qualitatively impact results.

First, there are general limitations of using reanalysis data which have been
discussed in the literature, for example spatial biases or issues with
upscaling to hub heights [Sharp et al., 2015, Olauson and Bergkvist, 2015,
Rose and Apt, 2015, Staffell and Pfenninger, 2016]. It is, however, not clear
if there are specific distortions with respect to extreme low-wind events
derived from reanalysis data. A limitation specific to the MERRA-2 dataset is
the relatively coarse 50x50 km grid cell size, which insufficiently represent
local impacts on wind speeds. Regional reanalysis data with more refined
geographical resolutions may resolve this issue, e.g. COSMO-REA2 with 2x2 km,
or COSMO-REA6 with 6x6 km [Hans Ertel Zentrum, 2019], yet these are only
available for shorter periods of time. The global coverage of MERRA-2 further
allows repeating our open-source analysis for other countries and world
regions.

Second, we use power curves of currently available wind turbines and assume
hub-heights of recently constructed plants. We may thus overestimate wind
power generation compared to the currently existing fleet of wind turbines in
Germany, which includes many older and smaller turbines, and in turn
underestimate the magnitude of current LWP events. Conversely, we may
underestimate power generation of future turbines, and accordingly
overestimate the magnitude of future low-wind-power events, assuming that
turbine efficiency and hub height increases further, with corresponding upward
shifts in the power curves. Once LWP events become more relevant for the
overall energy system, this may also trigger specific technology improvements
toward lower cut-in speeds and a steeper slope of the power curve on the very
left-hand side. Quantifying the potentially mitigating effects of such
developments on LWP periods is left for future research.

Third, we use the current spatial capacity distribution of German wind power
plants for deriving an aggregated capacity factor time series. We implicitly
assume that this distribution also persists in the future. In reality, a
relative increase of wind power deployment at sites with lower wind resources
may occur, for example in southern Germany. From the results presented in
Section 3.1, we infer that a more even spatial dispersion of wind turbines
could slightly mitigate LWP events.

Next, climate change has an impact on wind speeds. Future time series of wind
power capacity factors will thus differ from the historic ones investigated
here. Tobin et al. [2016] find that wind power variability in Europe may
generally increase, but Schlott et al. [2018] conclude that this has no
substantial effect on optimal deployment of onshore wind power in highly
renewable future scenarios. Moemken et al. [2018] find that climate change
will increase the occurrence of low wind speeds.

Finally, the focus of this analysis is a detailed but selective investigation
of onshore LWP events in Germany. This geographic focus helps to keep the
analysis tractable and avoids making implicit assumptions on continental
electricity transmission infrastructure. It is also relevant from an energy
policy perspective, which often includes national energy security
considerations. Yet expanding the geographic scope of the analysis would allow
raising complementary insights on larger-scale spatial patterns of extreme LWP
events. Focusing on onshore wind power, and not including other renewable
energy sources such as offshore wind power and solar PV, allows for
parsimonious model assumptions, and findings remain valid for any level of
installed capacity. Analyses that would combine periods of low production from
various renewable energy sources, and also explore their correlation with
electric load, appear to be a promising field for future research. The work of
Raynaud et al. [2018], albeit with lower temporal and spatial detail compared
to our analysis, can be considered as a first step in this direction.