# Measuring the Dunkelflaute: How (not) to analyze variable renewable energy
shortage

Martin Kittel<EMAIL_ADDRESS>Wolf-Peter Schill<EMAIL_ADDRESS>DIW Berlin,
Department of Energy, Transportation, Environment, Mohrenstraße 58, 10117
Berlin, Germany  Technical University Berlin, Digital Transformation in Energy
Systems, Einsteinufer 25 (TA 8), 10587 Berlin, Germany

###### Abstract

As variable renewable energy sources increasingly gain importance in global
energy systems, there is a growing interest in understanding periods of
variable renewable energy shortage (“Dunkelflauten”). Defining, quantifying,
and comparing such shortage events across different renewable generation
technologies and locations presents a surprisingly intricate challenge.
Various approaches exist in different bodies of literature, such as hydrology,
wind and solar energy analysis, or energy system modeling. The subject of
interest in previous analyses ranges from single technologies in specific
locations to diverse technology portfolios across multiple regions, focusing
either on supply from variable renewables or its mismatch with electricity
demand. We provide an overview of methods for quantifying variable renewable
energy shortage. We explain and critically discuss the merits and challenges
of different approaches for defining and identifying shortage events and
propose further methodological improvements for more accurate shortage
determination. Additionally, we elaborate on comparability requirements for
multi-technological and multi-regional energy shortage analysis. In doing so,
we aim to contribute to unifying disparate methodologies, harmonizing
terminologies, and providing guidance for future research.

CAZ

    Constantly-Above-Zero
CBT

    Constantly-Below-Threshold
CSP

    Centralized Solar Power
ENTSO-e

    European Network of Transmission System Operators for Electricity
FLH

    Full-load hours
FMAZ

    fixed-duration MAZ
FMBT

    fixed-duration MBT
LWP

    low-wind-periods
MAZ

    Mean-Above-Zero
MBT

    Mean-Below-Threshold
NTC

    Net Transfer Capacity
PRL

    positive residual load
PV

    photovoltaics
RoR

    Run-of-River
SPA

    Sequent Peak Algorithm
SPAadj

    adjusted Sequent Peak Algorithm
TYNDP

    Ten Year Network Development Plan
VMAZ

    variable-duration MAZ
VMBT

    variable-duration MBT
VRE

    variable renewable energy

###### keywords:

Variable renewable energy , Dunkelflaute , Energy shortage , Variable
renewable energy droughts , Positive residual load events , Methodological
exploration

††journal: arXiv

2.5cm2.4cm1.5cm2cm

##  1 Introduction

Motivation: Dunkelflauten. Wind and solar power are cornerstone technologies
for achieving climate-neutral energy systems around the world [1]. Because of
their variable generation profiles, their system integration requires an
increasing amount of temporal and spatial power sector flexibility. This
includes, for example, different types of energy storage, demand-side
flexibility, and geographical balancing [2, 3, 4, 5, 6, 7]. While various
implications of renewable variability have been explored in the literature,
attention has recently shifted to the occurrence of prolonged periods with
extremely low wind and/or solar availability, also referred to as
“Dunkelflauten”. This applies to both the research and the energy policy
discourse in many countries [8, 9, 10, 11, 12, 13].

Relevance of VRE shortage analysis. There is a growing interest in the
questions as to how frequent and severe such shortage events may become in
future energy systems heavily relying on variable renewable energy (VRE), and
how to deal with them. Periods of VRE shortage will particularly require the
use of long-duration energy storage [14, 15] as the potential for geographical
balancing may be limited. This is because of the synoptic scale of these
weather events, arising across thousands of kilometers [16]. However, a unique
and generally accepted definition of VRE shortage events has not yet been
established. This is because defining and quantifying VRE shortage events is a
surprisingly intricate task that can be addressed from different angles,
requiring a range of methodological choices and parameter assumptions. With
this paper, we aim to provide comprehensive guidance for the analysis of VRE
shortage conditions.

Diverse approaches in VRE shortage analysis. VRE shortage events can be
analyzed using different types of input data. One approach focusing on energy
supply is to detect periods with low VRE availability, which can be either
derived from measurements, modeled weather variables, or further processed
recognizing technological assumptions and spatial distribution of the
installed capacity. Many different terms have been used in the literature for
such shortage events (Figure 1), e.g., “wind drought” [17], “wind and solar
resource drought” [18], or“energy production droughts” [19] in the literature.
Alternatively, analyses may consider not only VRE generation potentials but
also how these relate to electric load profiles. This can be done by analyzing
residual load, sometimes also referred to as net load, which represents the
net balance of electricity demand and VRE supply. Again, there is no consensus
in the literature on how to term such shortage events (Figure 1), which, for
example, have been referred to as “energy supply droughts” [19], “energy
deficits” [20], or “energy shortfall events” [21]. For clarity, we propose the
following terminology: “VRE droughts” for periods with low resource
availability of a single or multiple VRE technologies, “ positive residual
load (PRL) events” for periods where VRE supply falls short of electric load,
and “VRE shortages” as a generic term that captures both concepts (Figure 1).

variable renewable energy shortage
---
generic term including both approaches
variable renewable energy droughts
---
focusing on resource availability,
considering VRE availability time series only
extreme low wind generation events |  Cannon et al. [22]
low wind generation events |  Potisomporn & Vogel [23]
low wind speed events |  Potisomporn et al. [24]
wind droughts |  Potisomporn et al. [17]
hydrologic droughts |  Yevyevich [25]
streamflow drought |  Fleig et al. [26]
extreme low wind events |  Abdelaziz et al. [27]
extended periods of low wind events |  Leahy & McKeogh [28]
low wind speed events |  Patlakas et al. [29]
extreme low-wind-power events |  Ohlendorf & Schill [30]
energy production droughts |  Raynaud et al. [19]
wind & solar resource droughts |  Rinaldi et al. [18]
wind & solar energy droughts |  Gangopadhyay et al. [31]
low generation events |  Kies et al. [32]
renewable energy droughts |  Kapica et al. [33]
renewable energy droughts |  Hu et al. [34]
dark lulls |  Breyer et al. [35]
low wind & solar production events |  Kaspar et al. [36]
Dunkelflauten |  Mockert et al. [37]
Dunkelflaute |  Mayer et al. [38]
dark doldrums |  Ohba et al. [39]
energy production droughts |  Otero et al. [40]
energy production droughts |  Allen & Otero [41]
wind and solar (power) droughts |  Brown et al. [16]
wind and solar energy drought |  Bracken et al. [42]
energy production drought |  Bracken et al. [42]
low wind & solar production events |  van der Wiel et al. [21]
positive residual load events
---
focusing on supply gaps, considering
imbalances of electric load and VRE availability
energy supply droughts |  Raynaud et al. [19]
gaps between VRE supply & demand |  Rinaldi et al. [18]
Dunkelflaute in high demand period |  Mayer et al. [38]
energy compound events |  Otero et al. [43]
high residual load droughts |  Otero et al. [40]
energy supply droughts |  Allen & Otero [41]
energy deficits |  Ruhnau & Qvist [20]
wind-drought-peak-demand |  Dawkins & Rushby [8]
electricity supply deficit |  Francois et al. [44]
low resource days |  Plain et al. [45]
energy supply drought |  Bracken et al. [42]
energy shortfall events |  van der Wiel et al. [21]
Figure 1: Proposal for a distinctive terminology and overview of previously
used terms for VRE shortage conditions.

Diverse scope of VRE shortage analyses. VRE shortage analyses can be done with
various methods, ranging from stylized, assumption-based projections of future
energy mixes to more sophisticated, optimizing energy system models. Further,
the scope of VRE shortage analyses is broad, ranging from the assessment of
individual renewable technologies in specific locations to optimized
portfolios of generation technologies and demand flexibility across large
balancing areas, encompassing multiple countries. Consequently, the
definitions and identification methods for VRE shortage events should
facilitate meaningful comparisons across various renewable generation
technologies and regions.

Literature: wind analysis. Different bodies of literature contribute to the
analysis of VRE shortage events, primarily related to meteorology or energy
research. One literature strand focuses on wind energy. Notably, wind droughts
in the United Kingdom are well-studied. Cannon et al. [22] explore extreme
onshore wind power events in the UK based on reanalysis data covering 33
years. Thresholds correspond to percentiles of the cumulative frequency
distribution of investigated data. Potisomporn & Vogel [23] study the spatial
and temporal correlation of low-wind-power events for offshore wind locations
in the United Kingdom given a historical and projected distribution of
offshore wind farms. Potisomporn et al. [24] contrast low-wind speed events
derived from ERA5 reanalysis data to measured data from 205 onshore and
offshore wind locations in the United Kingdom. The same authors [17] compare
different identification methods for low-wind events in the United Kingdom
based on 72 years of ERA5 reanalysis data, deploying concepts for analyzing
hydrological droughts [25, 26]. Abdelaziz et al. [27] assess offshore wind
speed droughts in the United Kingdom. They identify consecutive days with
daily average wind speed below a given threshold. There are related studies
analyzing other regions. Leahy & McKeogh [28] and Patlakas et al. [29] study
the persistence of low-wind speeds for different locations in Ireland and the
North Sea based on historical records. They search for events with wind speeds
constantly below a threshold and for annual minimal values of moving average
wind speeds over pre-defined intervals, applying extreme value theory.
Thresholds are based on a range of exogenously set wind speeds. Ohlendorf &
Schill [30] investigate the duration and frequency of low onshore wind power
events in Germany based on reanalysis data and exogenously set thresholds.

Literature: VRE portfolio analysis. While the first VRE drought analyses
focused on wind power, research interest in energy droughts of VRE portfolios
that also include solar photovoltaics (PV) is growing. Raynaud et al. [19]
investigate droughts for wind, solar, and hydro, both separately and combined
as a portfolio, for 12 European regions and 30 years of data. They employ
relative regional thresholds as fractions of the mean daily availability
factor. Rinaldi et al. [18] draw on Raynaud et al. [19] for identifying wind,
solar, and wind-solar droughts in the Western U.S. for 39 years of data for
different thresholds relative to mean daily generation. Gangopadhyay et al.
[31] apply a similar approach to India, drawing on 5000 years of synthetic
data. Kies et al. [32] compare seven VRE availability datasets for Europe.
Using a composite VRE portfolio time series that combines wind and PV
availability, they search for periods constantly below a range of exogenous
thresholds. Kapica et al. [33] compare energy droughts for solar PV and wind
in Europe, either separately or as a combined portfolio, for historical and
future weather conditions retrieved from eight regional climate models. Their
identification method again draws on [19] with thresholds relative to seasonal
and regional averages. Hu et al. [34] explore the risk of simultaneously
occurring VRE droughts for European countries for single VRE technologies and
a VRE portfolio, and compare it to droughts arising across all of Europe
assuming perfect electricity exchange. Breyer et al. [35] model
decarbonization pathways for Europe until 2040 or 2050, using the weather year
2005. They screen their model outcomes for drought periods constantly below a
range of thresholds relative to the maximum availability of wind and PV
separately and combined for Germany and Europe. Kaspar et al. [36] analyze
wind and PV separately and combined for Germany based on reanalysis data. For
given averaging intervals, they scan for moving averages below exogenously set
thresholds. Mockert et al. [37] also study VRE droughts in Germany in the
context of prevailing weather regimes and lean on Kaspar et al. [36] for
drought identification. Mayer et al. [38] analyze concurrent PV and wind
droughts in Hungary by identifying consecutive time steps with availability
from both technologies below exogenous thresholds. Ohba et al. [39] link wind
and solar droughts, both separately and combined as a portfolio, to four
typical weather patterns arising in eastern Japan using an exogenously set
threshold and neural network learning.

Literature: residual load analysis. Finally, VRE shortage events are analyzed
in the context of residual load. In addition to their VRE drought analysis,
Raynaud et al. [19] investigate the imbalance of demand and VRE supply in
Europe. Van der Wiel et al. [21] test whether low wind and solar generation as
well as high residual events are linked to large-scale weather regimes arising
over Europe. Otero et al. [43] investigate periods with simultaneously low
wind and solar generation and high demand across 27 European countries based
on absolute thresholds. Otera et al. [40] use copula analysis to analyze VRE
droughts based on a threshold relative to a ten percent fraction of its mean
availability, and residual load events above the 90% percentile of its
distribution in Europe based on ERA5 reanalysis. Allen & Otero [41] introduce
standardized VRE droughts indices derived from meteorological indicators that
incorporate both VRE generation and electricity demand. They showcase the
proposed method for droughts in Europe. Ruhnau & Qvist [20] retrieve residual
load time series from a model analysis of a least-cost decarbonized Germany
power sector scenario and search for persistent positive residual load events.
Dawkins & Rushby [8] characterize wind droughts and residual load events that
qualify as droughts in the United Kingdom based on percentile thresholds.
Francois et al. [44] explore positive residual load events (coined electricity
deficits) for run-of-river hydropower and solar PV net of demand for Northern
Italy. They deploy Complete-Time-Analysis, which is focused on return periods
lasting from single hours up to several years. Based on the assumption of
sufficient storage availability, Plain et al. [45] identify low-solar periods
using 21 years of satellite data to size microgrids power systems in Africa
based on the mismatch between solar production and demand. Bracken et al. [42]
characterize VRE droughts across the U.S. concerning frequency, duration,
magnitude, and seasonality given the existing energy infrastructure in 2020.
They investigate single VRE technologies, VRE portfolios, and positive
residual load events.

Contribution - harmonization. The review shows that different bodies of
literature, e.g., hydrology, wind and solar energy, or energy system modeling,
use a wide range of methodological approaches for defining and quantifying VRE
shortage. Respective studies differ in terms of the technological,
geographical, and temporal scope of the investigated system, based on partly
inconsistent terminology. This could be a result of the disconnect of involved
research fields. Communities at the intersections of these previously
disconnected fields have established, bridging the gap between meteorology and
energy research [46, 47]. Yet, the literature lacks a structured overview and
explanation of different methodological approaches for VRE shortage analyses
using harmonized terminology. We aim to contribute to the literature by
closing this gap.

Contribution - VRE supply & residual load. We provide a methodological
overview of different approaches for identifying VRE droughts across multiple
regions and VRE technologies from the perspective of the energy system. We
discuss possible definitions of VRE droughts and identification methods,
focusing on renewable availability time series. As VRE potentials vary across
technologies, space, and time, we elaborate on how to enable comparability
across these dimensions. We further discuss how VRE drought analysis can be
extended to also include electric load, i.e., how to evaluate extreme PRL.
This allows for identifying compound low-VRE availability and high-demand
events indicating the need for dispatchable capacity. Drawing on the proposed
method for VRE availability time series, we discuss how to analyze PRL events
and discuss essential points of criticism.

##  2 Concepts for defining variable renewable energy droughts

###  2.1 Drought definitions

VRE availability factors. When exploring VRE droughts, i.e., VRE shortage
focusing on the energy supply side, one approach is to detect periods with low
wind speeds or solar irradiation. According data can originate from
measurements (in-situ or by satellites) or meteorological models.
Alternatively, drought analyses can use VRE availability time series, also
referred to as capacity factors, either derived from measurements or converted
from modeled weather variables. These indicate how much electricity (e.g., in
megawatt hours) a VRE source can generate at a given time step $t$, normalized
by its installed generation capacity (e.g., in megawatt). In other words, an
availability factor is a measure of a VRE generator’s capture efficiency of
the meteorological resource [48]. While our analysis focuses on discrete time
series of VRE availability factors $\phi_{t}^{VRE}\in[0,1]$, the discussed
methods generally apply to all of the above-mentioned data types. For clarity,
we start with a single technology and one region, and later turn to renewable
technology portfolios and larger regions.

Drought threshold. Given a VRE availability time series, VRE droughts can
generally be defined as periods below a certain drought qualification
threshold $\tau\in[0,1]$ (gray lines in Figure 2).

(a) Drought windows with fixed duration below a drought threshold $\tau=0.1$.
(b) Drought events with variable duration below two drought thresholds
$\tau_{1}=0.1$ and $\tau_{1}=0.2$. Using higher thresholds generally leads to
longer, but fewer, events.

Figure 2: Comparison of VRE drought definitions. The window perspective
underestimates drought duration and overestimates the number of droughts.

Drought definition: window perspective. There are different definitions for
VRE drought periods. One option is searching for ’drought windows’ with
predefined duration [19, 33, 18]111These studies search for periods of
consecutive daily averages below some threshold with a cut-off every 24
hours., e.g., a given number of time steps below a given threshold (Figure
2a). Implementing a respective search algorithm for a specified window
duration is straightforward. Yet, droughts identified via predefined windows
may be shorter than actual droughts (Figure 2a). Further, consecutive windows
that form one longer combined drought may be counted individually (Figure 2a,
right windows). Thus, this definition systematically underestimates drought
duration and overestimates the number of droughts.

Drought definition: event perspective. An alternative approach is searching
for complete ’drought events’ below a threshold, which last as long as a
drought qualification criterion is met. That is, drought duration is not
predefined by setting a window length, but, for example, the result of a
search on how many consecutive time steps are below a given threshold [25, 26,
17]. This ensures that identified events are completely captured, and
consecutive droughts are properly accounted for (Figure 2b). We thus consider
the drought event perspective to be a superior concept for identifying VRE
droughts, and focus on it henceforward.

Threshold intuition. Higher thresholds generally identify less severe, but
longer-lasting drought events. This tends to reduce the number of obtained
droughts, as events that are considered to be separate for lower thresholds
may integrate into combined ones (Figure 2b).

###  2.2 Drought identification methods

Identification method: CBT. Numerous methods exist for identifying VRE
droughts. We focus on a selection222We limit our selection to methods that
appear useful for investigating VRE droughts. Other methods in different
bodies of literature can be found, e.g, the Inter-event time method that was
developed for hydropower [49] and was recently evaluated in [17]. in the
following (Figure 3). A Constantly-Below-Threshold (CBT) event relates to a
period of consecutive time steps during which availability factors are
constantly below a threshold $\tau$ [50, 28, 22, 29, 30, 23, 17, 38]. In the
hydrologic literature, this method has been first introduced as ’runs
analysis’ [25]. The boolean function $\psi_{t}^{CBT}$ determines whether time
step $t$ qualifies as drought (1) or not (0):

$\psi_{t}^{CBT}=\begin{cases}1&\text{if $\phi_{t}^{VRE}<\tau\ \ \forall\ \
t$}\\\ 0&\text{if $\phi_{t}^{VRE}\geq\tau\ \ \forall\ \ t$}\end{cases}$ (1)

Figure 3: The upper panels shows exemplary VRE availability time series (bold
line) and identification methods CBT, FMBT, VMBT, and SPA. The gray line
represents the drought threshold $\tau=0.1$. Green and orange areas highlight
the energy deficit obtained by CBT and FMBT, respectively. The lower panel’s
horizontal bars illustrate the varying event duration $\delta$ identified by
each method.

CBT duration & energy deficit. The duration of a CBT event $\delta^{CBT}$ is
the number of consecutive time steps with $\psi_{t}^{CBT}=1$. Suppose $t_{k}$
and $t_{l}$ are the first and the last time steps of an event. Then the
event’s cumulative energy, also referred to as energy deficit or drought
severity [25, 17], is defined as follows:

$\epsilon^{CBT}=\sum_{t_{k}}^{t_{l}}\tau-\phi_{t}^{VRE}\ \ \forall\ \
t_{k}\leq t\leq t_{l}$ (2)

Limitation CBT. The CBT notion identifies VRE droughts regardless of
availability factors in adjacent periods, even if their availability is
briefly above the drought threshold (Figure 3).

Identification method: MBT. Addressing this limitation, Mean-Below-Threshold
(MBT) events define consecutive time steps during which a moving average of
availability factors $\Phi_{t}^{VRE}(\omega)$ is below a threshold [19, 30,
36, 37, 17]. This approach smooths out short-term fluctuations over the
lagging averaging interval $[t-\omega,t]$333We propose using a lagging
averaging interval, which is is common in time series analyses. Using a
leading interval would also be possible, but appears non-intuitive. Likewise,
a centered interval is also not recommended as dealing with border time steps
for an uneven number of time steps is ambiguous. with a predefined duration
$\omega$. Equivalent to $\psi_{t}^{CBT}$, the function $\psi_{t}^{MBT}$
evaluates each time step $t$ as follows:

$\psi_{t}^{MBT}=\begin{cases}1&\text{if $\Phi_{t}^{VRE}(\omega)<\tau\ \
\forall\ \ t$}\\\ 0&\text{if $\Phi_{t}^{VRE}(\omega)\geq\tau\ \ \forall\ \
t$}\end{cases}$ (3)

Fixed-duration MBT. The MBT method can be applied in two different ways.
First, the fixed-duration MBT (FMBT) searches for MBT events based on a fixed
averaging interval $\omega^{FMBT}$ [36, 37, 17]. The duration of an FMBT event
$\delta^{FMBT}$ corresponds to the number of consecutive time steps with
$\psi_{t}^{FMBT}=1$ (e.g., $\delta^{FMBT}=15$ for $\omega=10$ in Figure 3).
The energy deficit $\epsilon^{FMBT}$ is computed analogously to
$\epsilon^{CBT}$ (i.e., using $\Phi_{t}^{VRE}(\omega)$ instead of
$\phi_{t}^{VRE}$) and decreases due to the smoothing effect of the moving
average. One option to avoid this is evaluating the energy deficit based on
the original time series $\phi_{t}^{VRE}$ instead of $\Phi_{t}^{VRE}(\omega)$,
i.e., reporting $\epsilon^{CBT}$ instead of $\epsilon^{FMBT}$ corresponding to
the identified FMBT event [17].

Comparison CBT & FMBT. Unlike CBT, the FMBT approach allows for instances
above the drought threshold before, between, and after potentially multiple
CBT drought events that are filtered out by pooling them together (compare CBT
and FMBT events in Figure 3) [17]. In the hydrology literature, such CBT
events are referred to as ’mutually dependent’ [26]. For prolonging averaging
intervals, the moving average smoothing becomes more pronounced. Hence, the
choice of $\omega^{FMBT}$ determines to which extent shorter CBT events are
filtered out.444The FMBT method converges to CBT as the length of the
averaging interval $\omega^{FMBT}$ approaches the granularity of the original
time series. By design, for a given threshold, the CBT approach identifies
more drought events than FMBT, whereas FMBT finds fewer but longer-lasting
events. Thus, the CBT method may overestimate the number of drought events
while underestimating the duration and energy deficit, which is particularly
relevant for characterizing the cumulative energy of extreme VRE droughts. In
contrast, the FMBT method acknowledges natural fluctuations in VRE
availability by accounting for brief periods of higher availability within an
overall low-availability period. FMBT therefore provides a more realistic view
of prolonged VRE droughts and the corresponding power sector flexibility
needs.

Limitation FMBT. However, there is no clear relation between a power sector
attribute and $\omega^{FMBT}$, whose parameterization remains arbitrary. VRE
availability time series could be evaluated for a range of different
$\omega^{FMBT}$. Yet, drought events based on different $\omega^{FMBT}$ may
partially overlap, creating ambiguity in their characteristics like duration,
energy deficit, and frequency. In fact, results may substantially change with
varying $\omega^{FMBT}$ (compare the moving averages
$\Phi_{t}^{VRE}(\omega=10)$ and $\Phi_{t}^{VRE}(\omega=50)$ in Figure 3, with
the latter obtaining no drought at all). Consequently, VRE droughts identified
via the FMBT approach are valid only for a specific parameterization of
$\omega^{FMBT}$, limiting the applicability of this concept.

Variable-duration MBT. Addressing this limitation, we introduce the variable-
duration MBT (VMBT) method, which to the best of our knowledge is a novelty.
It obtains unique VRE droughts, ranging from very long-lasting events, e.g.,
months, to such that last only a few time steps. This is achieved by deploying
the MBT perspective for a large number of different averaging intervals,
iteratively adjusting $\omega^{VMBT}$ in descending order. Importantly, to
ensure that no long-duration events with $\delta^{VMBT}>\omega^{VMBT}$ are
missed, the first iteration should start with a very high $\omega^{VMBT}$, so
that the moving average $\Phi_{t}^{VRE}(\omega)>\tau$ across the entire time
series (in the example shown in Figure 3, compare the moving average
$\Phi_{t}^{VRE}(\omega^{VMBT}=50)$). In subsequent iterations, $\omega^{VMBT}$
is reduced and $\Phi_{t}^{VMBT}$ updated, until the first drought event is
identified at $\Phi_{t}^{VMBT}<\tau$ (compare the moving average
$\Phi_{t}^{VRE}(\omega=25)$ in Figure 3). Its duration equals the averaging
interval $\delta^{VMBT}=\omega^{VMBT}$. The respective period is then excluded
in later iterations, where $\omega^{VMBT}$ decreases further and additional
(shorter) drought events are identified, and so on. For a given drought
threshold $\tau$, this iterative process effectively captures all unique
drought events, without any overlap or double counting, each accurately
recorded with its maximum possible duration. Compared to FMBT, this renders
the VMBT approach a more accurate and informative method for drought
identification.

Limitation VMBT. Note that the VMBT energy deficit $\epsilon^{VMBT}$ is
insignificant due to the close proximity of the moving average to the
threshold. Further, this method involves a trade-off between accuracy and
computational efficiency. Iteratively reducing the interval of the moving
average ($\omega^{VMBT}$), with an incremental change that equals the
resolution of the underlying time series, ensures captures all unique drought
events, but requires numerous iterations and may lead to long processing time.

Identification method: SPA. Finally, the Sequent Peak Algorithm (SPA)
identification method searches for the maximum cumulative energy deficit of a
drought event, while accommodating intermediate periods where renewable
availability may surpass the threshold. Originating in hydrology [51, 26], SPA
has been extended to other bodies of literature, such as wind energy analysis
[17]. A similar concept has also been applied to characterizing renewable
surplus events [52]. The cumulative energy deficit is defined as follows:

$\epsilon_{t}^{SPA}=\begin{cases}\epsilon^{SPA}_{t-1}+\tau-\phi_{t}^{VRE}&\text{if
$\epsilon^{SPA}_{t-1}+\tau-\phi_{t}^{VRE}>0\ \ \forall\ \ t$}\\\ 0&\text{if
$\epsilon^{SPA}_{t-1}+\tau-\phi_{t}^{VRE}\leq 0\ \ \forall\ \ t$}\end{cases}$
(4)

SPA duration. The SPA measures event duration $\delta^{SPA}$ from the first
instance when the cumulative energy deficit of a single SPA event becomes
positive to its global555Here, “global” refers to the maximum of a single SPA
event, not to the maximum of all potential SPA events of the underlying VRE
availability time series. maximum. This maximum occurs when the VRE
availability curve intersects with the threshold for the last time during an
SPC event, i.e., when $\phi_{t}^{VRE}\geq\tau$ (Figure 3). This algorithm
requires no iterations or assumptions on averaging intervals, and only a
single straightforward computation of cumulative energy deficits for the
underlying VRE availability time series. It allows for long-duration events
that include brief periods with above-threshold availability.

Comparison SPA & VMBT: Unlike VMBT, SPA events start when VRE availability
falls below the threshold and thus depends on threshold parameterization. In
contrast, the VMBT method allows for high or low availability periods before
SPA events, making it less reliant on specific threshold parameterization. For
a given threshold, both VMBT and SPA obtain a unique and unambiguous set of
VRE drought events, and thus appear to be superior to the CBT of FMBT
approaches. SPA is computationally less demanding than VMBT, as it requires no
iterations over averaging intervals. Yet, SPA may not recognize minor events
that follow a longer-lasting drought, which has been criticized in the
literature [17].

Comparison duration CBT, FMBT, VMBT, SPA. As indicated by Figure 3, for a
given threshold, the VMBT approach generally leads to the longest drought
duration of all four identification strategies explained above. The SPA method
identifies events with extended duration, albeit shorter than VMBT, followed
by FMBT events with moderate duration. On the other end of the spectrum, the
CBT method leads to the shortest drought duration.

Limitation of energy deficits in VRE drought analysis. While often reported in
other bodies of literature, energy deficits of VRE droughts identified purely
based on VRE availability are hard to interpret as they do not allow for
drawing direct energy system conclusions.

Threshold parameterization. Note that an effective threshold parameterization
is methodologically challenging and subject to user discretion (see Section
2.3 for further discussion).

###  2.3 Comparability and the choice of threshold

Comparability issues. Research interest is increasingly moving beyond single
technologies at particular regions (e.g., [22, 23, 24, 27, 30]) towards a
characterization of VRE drought patterns of portfolios of different renewable
generation technologies for multiple regions (e.g., [19, 18, 32, 33]). For
this, enabling comparability across VRE technologies and regions when
analyzing VRE drought events is imperative.

Differences in generation potentials: single technologies. Previous research
draws on absolute, exogenously set thresholds for availability factors, e.g.,
0.01, 0.02, 0.05, or 0.10 [28, 29, 36, 30, 32, 17]. Yet, such analyses face
compatibility issues when analyzing systems with different technologies and/or
across several regions. This is because applying absolute thresholds on
normalized availability factor time series implies assuming uniform generation
capacity (e.g., in megawatts) across all compared systems. However, these
systems may have very different annual generation potentials (e.g., in
megawatt hours) depending on the meteorological conditions of the location and
the VRE technology. VRE availability duration curves, sorting availability
factor time series in descending order, highlight the discrepancies in
generation potentials between different technologies and regions (Figure 4a).

(a) Availability duration curves of single VRE technologies. (b) Availability
duration curves of VRE portfolios with different exemplary capacity mixes.

Figure 4: Annual generation potentials of onshore wind power, solar PV, and
portfolios with different mixes of these technologies in Germany and Spain in
2010, visualized as the area below the availability duration curves. The data
is retrieved from the Pan-European Climate Database [53].

Differences in generation potentials: technology portfolios. The same applies
to energy systems transitioning towards variable renewables. Here, the optimal
capacity mix of VRE technologies depends on their respective generation
potentials as well as cost parameters, and may vary substantially across
regions. This results in diverse generation potentials for such VRE portfolios
based on the location and the capacity mix (Figure 4b).

Challenges with absolute thresholds: FLH bias. Full-load hours (FLH) serve as
a commonly used metric for comparing annual average generation (or generation
potential before potential curtailment). This metric indicates how long a
generator (or technology aggregate) would operate at full capacity to provide
its annual energy (potential). An analysis based on a uniform, exogenously set
threshold for each compared system does not account for discrepancies in
annual generation potentials. Consequently, such analyses (e.g., [36, 32, 39,
38]) are biased by a FLH effect, which puts their validity into question.

Threshold scaling relative to maximum availability factor. As a remedy, the
drought threshold can be scaled to account for FLH differences between VRE
technologies and locations. Threshold scaling relative to different time
series attributes can be found in the literature. One option is to scale
thresholds relative to their system-specific maximum availability factor
[35].666Technically, in this study, thresholds scale with the maximum
generation. Discarding potential curtailment, this is equivalent to scaling
with the maximum availability factor.. Focusing on the VRE availability of a
single point in time (i.e., the peak point of the duration curves in Figure
4), this approach ignores general availability patterns over the course of a
year. Consequently, it does not mitigate differences in FLH.

Thresholds scaling relative to the distribution of availability factors.
Another option is to use a percentile of the availability time series
distribution as threshold [26, 22, 45]. Duration curves are a graphical
representation of availability factor distributions (Figure 4). A percentile
refers to the availability factor below a certain fraction of the population
of time steps falls and depends on the shape of the distribution, which may
vary across technologies and regions. Unlike scaling relative to the maximum
availability factor, this method recognizes all VRE availability states.
However, the percentile approach does not fully adjust for FLH differences.

Thresholds scaling relative to mean availability factor. An effective option
for this is to align the drought threshold with each system’s mean
availability factor $\bar{\phi}^{VRE}$. This method inherently scales with the
system’s FLH and, therefore, enables comparability across technologies or
technology portfolios, regions, and, in the case of comparing multiple years,
time [19, 18, 31, 40, 33].

Effective threshold ranges. A priori, a meaningful parameterization of the
fraction $\alpha$ of the mean availability factor $\bar{\phi}^{VRE}$ for
drought identification is not straightforward. Previous studies use various
fractions of the mean [25]. While lower thresholds, e.g.,
$\tau=0.1\bar{\phi}^{VRE}$, find very severe but potentially brief and
isolated VRE drought events, higher fractions closer to $\bar{\phi}^{VRE}$ may
result in identifying extended periods of below-average availability rather
than true VRE droughts. Relevant fractions likely lie between these extremes.
It therefore appears useful to explore a range of thresholds,
$\tau=\alpha*\bar{\phi}^{VRE}$, for example with $\alpha$ ranging between 0.1
and 0.9. Obtained events reflect different degrees of low VRE availability,
which may be relevant for different types of flexibility options in renewable
energy systems.

###  2.4 Technological and spatial scope of analysis

VRE drought analyses scopes. The scope of a VRE drought analysis focusing on
VRE supply may differ in terms of technological and spatial scope. Each of
these dimensions demands specific assumptions, weighting, as well as
comparability requirements.

Portfolio time series in multi-technology analyses. In contrast to single-
technology drought analyses, according investigations of a VRE portfolio
require a composite time series that combines the availability factors of
different VRE technologies. It can be computed as the weighted average of the
technology-specific time series. Weighting factors correspond to the
technology shares in the assumed overall capacity mix. Considering the
temporal and spatial complementarity of wind and solar power [54, 55], such a
composite time series allows for within-portfolio balancing, which reflects
the generation dynamics of power sectors with high shares of variable
renewables. This is in line with several related studies [19, 43, 20, 44].
Another approach excludes or limits such balancing by applying a definition of
compound VRE drought events as periods with simultaneously arising drought
conditions of multiple VRE technologies [18, 38]. This discards VRE
complementarity, hence potentially overestimating droughts characteristics of
a VRE portfolio.

Interconnection states in multi-regional analysis. For multi-regional
settings, drought analyses using VRE availability time series can be based on
two extreme scenarios regarding regional interconnection777Here we abstract
from within-region grid congestion.: i) perfect interconnection, which
abstracts from grid limitations (often referred to as the “copper plate”
assumption), and ii) complete isolation, where regions are treated as “island
systems” without electricity exchange. When comparing VRE droughts of such
island systems, FLH-adjusted threshold scaling is required as discussed above.
Realistic patterns of cross-regional electricity exchange fall between these
extremes and typically necessitate more sophisticated energy system modeling
beyond simple VRE time series analysis.

Cross-regional time series. Similar to the technology portfolio case, multi-
regional settings with assumed perfect interconnection require a composite
time series that collectively represents all regions. It can be generated as
the weighted average of respective regional time series. The weights are
assigned based on the relative share of each region’s capacity within the
overall system. Unless multiple cross-regional composite time series are to be
compared, no FLH-adjustment of the threshold is required. For VRE portfolios
across regions, weighting factors need to reflect both within-regional and
across-regional shares in the capacity mixes.

##  3 Extending the methodology to positive residual load events

###  3.1 Positive residual load event definition

Motivation: kalte Dunkelflauten. In addition to focusing exclusively on VRE
supply, research interest on the dynamics between VRE droughts and periods of
high electricity demand is intensifying. This becomes more relevant as many
countries plan to electrify their heat, transport, and industry sectors, and
respective additional loads enter the power sector. Notably during the heating
season, electrified heating appliances such as heat pumps increase electricity
demand with characteristic profiles [56, 57, 58]. Compound high-demand and VRE
drought events, sometimes also referred to as “cold dark doldrums” or, in
German, “kalte Dunkelflauten” are emerging as a challenge for decarbonized
energy systems that rely on VRE.

Positive & negative residual load events. PRL events, characterized by high
demand and a shortage of VRE supply, indicate the need for firm capacity from
thermal generators, or flexibility provided by electricity storage, imports,
or demand-side measures [59, 60, 61]. In contrast, negative residual load
events represent VRE surplus generation. This surplus can be integrated into
the power sector through electricity storage or exports to other areas, or
used for electrified loads from coupled sectors, such as heat provision or
transport [62]. Alternatively, it can be curtailed [52, 60]. Note that the
latter is not an option for PRL periods, which makes them more challenging to
deal with than negative residual loads. Accurately quantifying both positive
and negative residual load events is relevant for capacity planning of
weather-resilient energy systems.

PRL characteristics. Key PRL characteristics, e.g., duration and energy
deficits, can be analyzed using residual load time series $\phi_{t}^{RL}$
(Figure 5). While this can be done analogously to VRE drought analysis, the
energy deficit of PRL events can directly be associated with the need for
energy that has to be provided by, for instance, long-duration storage.
Importantly, the maximum capacity need can be inferred from peak residual load
(compare left-most value of the residual load duration curve in Figure 5) and
does not require a dedicated analysis of PRL events.

Implicit threshold parameterization. Unlike VRE drought analysis, there is no
need for deliberate threshold parameterization to identify PRL events.
Instead, PRL events are simply obtained as periods above zero (gray line in
Figure 5). In previous PRL analysis other approaches such as percentile-based
thresholds were used [40]. However, positive residual load directly relates to
the need for energy from firm generators, storage, or imports. Hence, from the
perspective of a power sector, diverting from thresholds aligned with the zero
line appears counter-intuitive.

Figure 5: Exemplary residual load time series and identification methods CAZ,
FMAZ, VMAZ, SPA (with or without recovery), and SPAadj (upper panel). The
green and orange areas indicate the obtained CAZ and FMAZ energy deficit,
respectively. The lower panel’s horizontal bars illustrate the varying event
duration $\delta$ identified by each method.

###  3.2 Identification methods

Identification methods: CAZ & MAZ. We adapt the VRE droughts identification
methods discussed in Section 2 to PRL events. Unless stated otherwise, the
algorithmic routine is equivalent but recalibrated to identify periods where
residual load $\phi_{t}^{RL}$, or its average $\Phi_{t}^{RL}$, is above zero,
rather than below a designated threshold. Analogously to CBT and MBT, we
denote Constantly-Above-Zero (CAZ) and Mean-Above-Zero (MAZ) as:

$\displaystyle\psi_{t}^{CAZ}=$ $\displaystyle\begin{cases}1&\text{if
$\phi_{t}^{RL}>0\ \ \forall\ \ t$}\\\ 0&\text{if $\phi_{t}^{RL}\leq 0\ \
\forall\ \ t$}\end{cases}$ $\displaystyle\psi_{t}^{FMAZ}=$
$\displaystyle\begin{cases}1&\text{if $\Phi_{t}^{RL}(\omega)>0\ \ \forall\ \
t$}\\\ 0&\text{if $\Phi_{t}^{RL}(\omega)\leq 0\ \ \forall\ \ t$}\end{cases}$
(5)

Identification methods: FMAZ & VMAZ. Accordingly, the fixed-duration MAZ
(FMAZ) and variable-duration MAZ (VMAZ) concepts emulate the FMBT and VMBT
approaches.

Duration CAZ, FMAZ, VMAZ.. Analogously to VRE drought analysis, the PRL event
duration $\delta^{CAZ}$ and $\delta^{FMAZ}$ corresponds to the number of
consecutive time steps with $\psi_{t}^{CAZ}=1$ and $\psi_{t}^{FMAZ}=1$,
respectively. The duration of VMAZ event equals the iteration-specific
averaging interval $\delta^{VMAZ}=\omega^{VMAZ}$.

Energy deficit CAZ, FMAZ, VMAZ. The VMAZ energy deficit is near zero and hence
insignificant. With $t_{k}$ and $t_{l}$ as the start and end points of a PRL
event, the CAZ and FMAZ event’s energy deficit (green and orange areas in
Figure 5) are defined as:

$\displaystyle\epsilon^{CAZ}=$
$\displaystyle\sum_{t_{k}}^{t_{l}}\phi_{t}^{RL}$
$\displaystyle\epsilon^{FMAZ}=$
$\displaystyle\sum_{t_{k}}^{t_{l}}\Phi_{t}^{RL}$ $\displaystyle\forall\ \
t_{k}\leq t\leq t_{l}$ (6)

Limitations of CAZ, FMAZ, and VMAZ. The limitations associated with CBT, FMBT,
and VMBT discussed in Section 2 also extend to their PRL counterparts. The CAZ
method, while directly linking event duration, its energy deficit, and its
temporal occurrence to for example the required generation and dispatch period
of a capacity-constrained firm generator, ignores brief periods of negative
residual load adjacent to PRL events (compare the two CAZ events on the left
in Figure 5). This can lead to underestimating the need for energy-constrained
flexibility options, such as long-duration electricity storage. As for FMAZ,
the parameterization of the averaging interval $\omega^{MAZ}$ lacks a directly
attributable power sector reference and remains arbitrary. As identified FMAZ
events may substantially change with varying $\omega^{MAZ}$, they are
ambiguous. Further, their interpretation is not straightforward. In general,
longer averaging periods may lead to an underestimation of actual PRL
challenges as averaging already assumes temporal balancing, for instance, in
real-world power systems carried out by electricity storage or other
flexibility options. The VMAZ approach, in contrast, obtains unique events.
Yet, its relevance remains limited in PRL analysis as it only allows for
evaluating PRL event duration but not energy deficit, which converges to zero
by design.

Identification method: SPA. The SPA identifies unique PRL while obtaining a
meaningful energy deficit. Unlike for VRE droughts, SPA does not require
setting an arbitrary threshold for PRL detection, precluding a respective
shortcoming in the case of VRE drought identification. SPA allows for brief
periods with negative residual load and detects all PRL events within a single
iteration. Consequently, we regard it as particularly well-suited for
identifying PRL events. Analogously to VRE droughts, its cumulative energy
deficit is denoted as:

$\epsilon_{t}^{SPA}=\begin{cases}\epsilon^{SPA}_{t-1}+\phi_{t}^{RL}&\text{if
$\epsilon^{SPA}_{t-1}+\phi_{t}^{RL}>0\ \ \forall\ \ t$}\\\ 0&\text{if
$\epsilon^{SPA}_{t-1}+\phi_{t}^{RL}\leq 0\ \ \forall\ \ t$}\end{cases}$ (7)

SPA duration and recovery period. The SPA event duration $\delta^{SPA}$ refers
to the period beginning when the cumulative energy deficit of a single SPA
event becomes positive to its global maximum. The SPA method further allows
for quantifying a recovery period $\sigma^{SPC}$. Originating from the
hydrology field [63], this period represents the balancing time required for
the surplus VRE energy from intermediate and subsequent negative residual load
events to offset the energy deficit of a PRL event. It corresponds to the
period following the peak cumulative energy deficit $\epsilon_{t}^{SPA}$ to
the point in time where this deficit returns to zero $\epsilon_{t}^{SPC}=0$
(Figure 5).

Accounting for efficiency losses: adjusted SPA. In real-world energy systems,
long-duration electricity storage is a key option for dealing with PRL events
[20]. Storage always incurs conversion losses, i.e., the amount of electricity
recovered from storage is always smaller than previous storage charging. The
standard SPA method does not account for such losses. To address this, we
introduce an adjusted Sequent Peak Algorithm (SPAadj) method, which
incorporates storage efficiency losses arising when balancing positive and
negative residual load periods.888For simplicity, we assume that electricity
storage does not have any binding capacity constraints with respect to
charging, discharging and storage energy. This can be achieved by adjusting
all negative residual load values to account for storage round-
trip999Technically, this adjustment allots the conversion losses from both
charging and discharging to storage charging occurring in intermediate and
subsequent negative residual load periods, whose surplus energy is used to
offset the energy deficit of a PRL event. efficiency $\eta^{LDS}$ as denoted
by:

$\phi_{t}^{RL,adj}=\frac{\phi_{t}^{RL}}{\eta^{LDS}}\ \ \forall\ \
\phi_{t}^{RL}<0$ (8)

Adjusted recovery period. In the SPAadj method, the adjusted energy deficit
$\epsilon_{t}^{SPA,adj}$ is calculated equivalently to $\epsilon_{t}^{SPA}$.
However, assuming that long-duration electricity storage is the relevant
flexibility option for dealing with a PRL event, the round-trip efficiency
adjustment prolongs the recovery period $\sigma^{SPA,adj}$ to reflect the time
needed to recharge the storage to its pre-PRL state of charge (Figure 5). This
approach results in an extended recovery period $\sigma^{SPA,adj}$ and event
duration $\delta^{SPC}$ when compared to calculations without considering
efficiency losses. This adjustment leads to a more realistic representation of
the energy system flexibility need during compound peak demand and VRE drought
events. Note that real-world storage options may also incur relevant standing
losses, depending on how long the energy is stored. Incorporating these into
the SPA concept would be significantly increase complexity and should rather
be studied using appropriate energy models.

###  3.3 Comparability, scope of analysis, and critical appraisal

Implicit comparability. Unlike VRE droughts, analyzing PRL events does not
require pre-processing, such as a FLH adjustment, to enable comparability. PRL
events are denoted in energy (e.g., megawatt hours), which is readily
comparable across different technological, spatial, and temporal scopes.

Setting: Exogenous residual load. The analysis of residual load time series
can be approached in two ways. On option is to use exogenous assumptions for
both VRE availability factors and demand time series. This setup facilitates
the exploration of various user-specific VRE capacity mix scenarios.

Setting: Optimized residual load. Alternatively, residual load time series can
be retrieved from a scenario optimized by an energy system model. This method
is more resource-intensive due to the need for comprehensive input data and
complex modeling assumptions, but also less dependent on exogenous capacity
assumptions. It further enables an analysis of policy-relevant scenarios, such
as those outlined in strategic documents like the Ten Year Network Development
Plan for the European electricity infrastructure [64].

Interpretation of PRL characteristics. Characterizing extreme PRL events,
i.e., their duration, energy deficit, frequency, etc., allows exploring the
need for power sector flexibility, which can be provided by long-duration
storage or other flexibility options. The SPAadj, accounting for energy losses
of such flexibility options, appears to be particularly useful in this
respect.

General Limitation. During an extreme PRL events, brief periods with very high
VRE generation requiring partial curtailment may occur. None of the discussed
identification methods is able to account for such curtailed energy, which can
lead to underestimating the energy deficit and duration of extreme PRL events
[20]. More importantly, insights from PRL event analysis are only applicable
to specific assumptions on the VRE portfolio and load, or driven by the
parameterization of optimizing models. Therefore, when discussing
characteristics such as the duration, frequency, or energy deficit of PRL
events, contextualization is essential. This is particularly important for a
meaningful comparison of the findings of different studies, and for
communication with policy-makers or the general public.

Limitations: exogenous residual load. By design, an exogenously derived
residual load time series does not account for electricity exchange and
potentially neglects flexibility from conventional demand and electrified
loads from the heating, transport, or industry sector. Accurately estimating
the operation of these loads without the use of an energy system model is
challenging and may require numerous assumptions.

Limitations: optimized residual load. As for residual load time series
generated by optimizing energy system models, model outcomes rely on the used
modeling framework and its underlying optimization rationale, the level and
detail of technology representation, and techno-economical assumptions, such
as available technologies, costs, meteorological resources [65, 66, 67]. For
instance, ceteris paribus, changes in storage investment costs can
significantly affect storage investment and usage in a modeled scenario, thus
altering the energy deficit or duration of obtained PRL events.

Note that an optimized residual load resulting from energy system modeling
already takes into account the optimal capacities and dispatch decisions of
electricity storage and other flexibility options. This inherently affects PRL
event characteristics.

##  4 Conclusion and recommendations

###  4.1 Contribution

Gap in literature & suggested terminology. VRE shortage has drawn research
interest from various fields, including hydrology, wind and solar energy,
energy system modeling, or climatology, and has been analyzed using a range of
methods and disparate naming. Yet, there is no structured overview and
explanation of these methods using harmonized terminology. It thus remains
unclear as to what methodological approach is useful for different settings of
VRE shortage analysis, which can be studied based on time series of VRE
availability or positive residual load. For clarity, we suggest “variable
renewable energy shortage” as a generic term covering both “variable renewable
droughts” as periods with low resource availability of a single or multiple
VRE technologies and “positive residual load events” as periods with a net
imbalance of electric load and VRE supply.

Contribution. This paper addresses this gap by providing a methodological
overview and guidance for defining and quantifying VRE shortage events across
technologies and regions, discussing different approaches for both VRE
availability and PRL time series. While not claiming to be exhaustive, we
categorize and discuss relevant existing shortage event definitions and
identification methods, propose methodological improvements, and elaborate on
how to enable compatibility in cross-technology or multi-regional analyses.
Our work seeks to support the harmonization of terminology across related
fields. We also aim to aid in advancing future research on VRE shortage events
by facilitating a better interpretation of such studies’ potential findings.

###  4.2 What (not) to do in variable renewable energy shortage analysis

Good practices. We identify a range of good practices for VRE shortage
analysis to obtain accurate, broadly applicable, and easy-to-interpret
findings on the duration, frequency, and energy deficit of VRE shortage
events. This is important for guiding policy or infrastructure decisions for
future energy systems with high VRE penetration.

Good practices: specify method. We advocate for future work to clearly and
unambiguously specify the shortage period definitions and identification
methods used, as well as key parameter choices such as thresholds or averaging
intervals. Methods that are poorly defined or not transparent hinder the
accurate interpretation and contextualization of findings, in both research
and policy discourse.

Good practice: methodical requirements. For accurate identification, VRE
shortage analysis should meet a range of methodological criteria. First, VRE
shortage periods should be defined according to the event perspective, i.e.,
capturing the full extent of qualifying periods allowing for event duration
ranging from just a few time steps to extensive weeks or even months. Second,
identified shortage events should be unique, avoiding double counting and
overlap with adjacent events. Third, the method should allow for pooling of
closely occurring events to include periods that independently may not qualify
as VRE drought or PRL events but are adjacent to periods of low availability
or high residual load.

Good practice: recommended VRE shortage characteristics. In general, reporting
the VRE shortage duration appears to be equally relevant to VRE drought and
PRL analyses. Yet, claims on identified durations have to be contextualized,
as they depend on the identification method used. Further, evaluating energy
deficits of PRL events is valuable for understanding the demand for firm
generation or long-duration storage energy in renewable power sectors.
Conversely, even tho this metric is commonly applied in VRE drought analysis
across different bodies of literature, it appears to be less relevant in such
settings, as it strongly depends on the threshold parameter choice and cannot
be associated with a power sector attribute.

Good practice: recommended methods. For VRE droughts analysis, the VMBT and
SPA methods align well with these methodological requirements. The VMBT method
finds events with the longest duration but lacks meaningful energy deficits,
which is a reasonable cost for accurate duration identification. In the case
of PRL analyses, we recommend the use of SPA or its adjusted version, SPAadj.
Besides adhering to the outlined criteria, these methods allow for accurately
quantifying both duration and the energy deficit of PRL events.

Good practice: comparative analyses. Analyzing VRE droughts across multiple
regions and/or for different VRE technologies or technology portfolios poses
comparability challenges. It is essential to base the analysis on uniform
average generation (or generation potential) across compared systems to avoid
a FLH bias in obtained drought characteristics. Threshold scaling for each
investigated system according to a fraction of the mean capacity factors is an
effective option for enabling comparability.

Good practice: threshold selection. The selection of the respective fraction
remains a sensitive parameter choice and requires careful consideration. Too
high thresholds may identify long-lasting periods with below-average VRE
availability rather than actual VRE droughts. Conversely, very low thresholds
may find very severe but potentially brief and isolated droughts. We advise
exploring various threshold values between these extremes, ranging from near-
zero to the average availability factor. This ensures a comprehensive capture
of the full spectrum of drought events, from mild to very severe.

Good practices: open code and data. For transparency and reproducibility, it
further appears vital to document and provide the underlying data and the
algorithms used, adhering to open-source and open-data principles [68]. Such
practices will not only foster transparency and replicability, but also
strengthen the overall accuracy and practical usefulness of VRE drought
analyses.

Bad practices. Based on our analysis, we identify a range of bad practices for
VRE shortage analysis. Searching for fixed-duration shortage windows
underestimates shortage duration while inflating the number of identified
shortage periods. We thus strongly recommend not using the window perspective.
Methods yielding ambiguous sets of events that may change for varying method
parameterization, such as FMBT and FMAZ, should be avoided due to the limited
applicability of obtained shortage characteristics. Next, we advise against
the use of methods incapable of pooling mutually dependent shortage events,
such as CBT and CAZ, as obtained results overestimate the number of events
while underestimating event duration and energy deficit. Finally, in VRE
drought studies, using absolute thresholds can further lead to misleading
comparisons based on normalized generation capacities rather than actual
energy production, resulting in potentially flawed conclusions.

###  4.3 Methodological trade-offs and outlook

Trade-offs between VRE drought and PRL analysis. Renewable energy shortage can
be studied based on time series of VRE availability or positive residual load.
While both approaches have their merits, a trade-off between policy relevance
and the universality of insights emerges. VRE drought analysis based on VRE
availability data typically requires fewer assumptions, yielding conclusions
with broader applicability. PRL events analyses aim to be more policy-
oriented, as they quantify the mismatch between electricity demand and VRE
supply, which is especially relevant for highly renewable decarbonization
scenarios. However, the latter approach requires extensive assumptions on the
composition of the renewable generation portfolio and demand-side flexibility.
This may necessitate detailed energy system modeling, whose outcomes hinge
upon underlying optimization rationales, technology representation, and
parameterization. This potentially limits the validity of PRL analyses to the
particular scenarios investigated.

Trade-offs between single and multiple technologies VRE drought analysis. Such
a trade-off also applies to the technological scope of VRE drought analysis.
Aside from methodological assumptions inherent to the generation of VRE
availability time series, e.g., such for reanalysis, insights from single-
technology analysis are broadly applicable but less policy-relevant for future
energy systems that rely on a mix of VRE technologies. Conversely, analyzing a
VRE portfolio is more policy-oriented but involves energy modeling or
exogenous assumptions on the composition of the investigated capacity mix. VRE
capacity mixes determined by an energy modeling are optimal only in the
context of the other optimized system components and flexibility options that
are represented in the model (e.g., storage, electricity exchange, or direct-
electrified applications from the heat, industry, or transport sector).
Similarly, exogenous capacity mixes rely on user-specific assumptions. These
aspects limit the validity of insights to investigated scenarios.

Outlook. While we provide general guidance on the advantages and drawbacks of
different VRE shortage identification methods, a thorough quantitative
comparison would be desirable, ideally for a range of VRE technologies and
electric load profiles for different world regions and weather years. Another
key aspect that requires attention is the choice of the threshold parameter,
particularly in distinguishing between severe VRE droughts and prolonged
periods of below-average availability. This distinction could support the
selection of relevant weather years to enable weather- and climate-resilient
energy system analyses and well-informed decarbonization policies.
Additionally, assessing the sensitivity of outcomes to different VRE
availability datasets would be useful and could be valuable feedback to the
meteorological research community that provides and continuously improves such
datasets [47].

## Acknowledgments

We thank the entire research group “Transformation of the Energy Economy” at
the German Institute for Economic Research (DIW Berlin) for valuable inputs
and discussions, as well as conference participants of the EGU General
Assembly 2022, the International Energy Workshop 2022, the Conference on
Climate, Weather and Carbon Risk in Energy and Finance 2022, the Next
Generation Energy and Climate Workshop 2022, and the International Conference
Energy & Meteorology 2023 for valuable comments on earlier drafts. We
acknowledge research grants by the Einstein Foundation (grant no. A-2020-612)
and by the German Federal Ministry of Education and Research via the “Ariadne”
projects (Fkz 03SFK5NO & 03SFK5NO-2).

## Author Contributions

Martin Kittel: Conceptualization (equal), methodology, software,
investigation, data curation, visualization, writing - original draft, review
and editing (equal). Wolf-Peter Schill: Conceptualization (equal), writing -
review and editing (equal), project administration.

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  *[VRE]: variable renewable energy
  *[PRL]: positive residual load
  *[PV]: photovoltaics
  *[CBT]: Constantly-Below-Threshold
  *[FMBT]: fixed-duration MBT
  *[VMBT]: variable-duration MBT
  *[SPA]: Sequent Peak Algorithm
  *[MBT]: Mean-Below-Threshold
  *[FLH]: Full-load hours
  *[CAZ]: Constantly-Above-Zero
  *[FMAZ]: fixed-duration MAZ
  *[VMAZ]: variable-duration MAZ
  *[SPAadj]: adjusted Sequent Peak Algorithm
  *[MAZ]: Mean-Above-Zero