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SPATIAL AND TEMPORAL INTERACTIONS OF SOLAR AND WIND RESOURCES IN THE
NEXT GENERATION UTILITY
Bryan Palmintier
Lena Hansen
Rocky Mountain Institute
1820 Folsom St.
Boulder, CO 80302
bpalmintier@rmi.org
lhansen@rmi.org
Jonah Levine
ECE-Eng-Elecl/Comp Admin
University of Colorado at Boulder
425 UCB
Boulder, CO 80309-0425
jonah.levine@colorado.edu
Abstract
The “next generation” electric utility must incorporate
variable renewable resources, including wind and solar, in
much larger quantities than conventionally thought possible.
While resource variability presents a challenge, it should be
possible to reduce and manage that variability by
geographically distributing renewables, combining them
with different renewables, and having more dynamic control
of electric loads.
This study shows that interconnecting individual solar
generation sites into geographically diverse arrays can
reduce power output variability, and that including solar
generation sites in arrays of geographically diverse wind
sites can further reduce the total variability beyond what is
possible for either resource type alone. Specifically,
optimized portfolios offer an average decrease in variability
of 55% below the average of all individual sites. Finally, it
was observed that, in the modeled system, only a small
subset of the potential sites in an interconnected array need
to be included to achieve these variability reductions.
1 INTRODUCTION
The ever-growing energy demands of the 21st century are
dependent upon a power infrastructure designed for the
early 20th century. Advances in digital communications and
renewable energy technologies could facilitate a transition
to a “next generation utility” that fully integrates both
supply- and demand-side resources in a way that can enable
significantly larger penetrations of variable renewable
energy technologies than conventionally thought possible.
This paper begins with a brief overview of the “next
generation utility” concept, then turns to the ability of the
next generation utility to incorporate solar and wind power
on a large scale, driven by geographical dispersion of both
solar and wind resources at utility and larger scales, cross-
firming of solar and wind resources, and increased grid
flexibility to absorb and mitigate variability.
2 THE NEXT GENERATION UTILITY
A new electric utility paradigm is needed to meet increasing
demands for power quality and reliability and to
significantly reduce global greenhouse gas emissions
generated by electricity production. A new generation of
power technology is developing, however, and can enable
the “next generation utility”, which will involve (see Fig. 1):
• Fully capturing the potential of energy efficiency and
demand response;
• De-carbonizing electric supply through greatly
increased penetration of renewable and distributed
supply technologies; and
• Electrifying or substituting clean, renewable fuels for
loads that would otherwise depend on fossil fuel,
including vehicles.
Fig. 1: The next generation utility will turn generation
infrastructure on its head, with a mix dominated by
efficiency and renewables with minimal coal and nuclear.
A key tenet of the next generation utility concept is that it
should be possible to provide the energy services required
by our modern society using significantly less “baseload”
coal and nuclear power. Doing so requires increased
reliance on variable renewable sources and more dynamic
control of energy demand, and consequently, more focus on
short time scales.
Taken together, the components of the next generation
utility can be thought to interact as seen in the load duration
curve in Fig. 2 below. Specifically, radical gains in building
energy efficiency should reduce the entire demand
significantly. Demand is then met largely through an
intelligently designed portfolio of variable and “firm”
renewable resources. Finally, remaining demand is met
through a combination of distributed generation (combined
heat & power and combined cooling, heat & power),
demand response and plug-in hybrid electric vehicles.
Fig. 2: Conceptual load duration curve for a next generation
utility.
The design of the next generation utility concept is currently
under development by Rocky Mountain Institute. This paper
describes research around new strategies for integration of
large-scale variable renewable resources.
3 BACKGROUND
One of the primary goals of electric utilities is maintaining
the reliability of the electric system—the implication being
that the reliability of any individual generator is only
important in the larger context of system reliability. This
insight also recognizes that all generators, both conventional
and variable, have some probability of failure. The forced
outages of conventional generators result from unplanned
mechanical failures, whereas the effective “forced outages”
of variable generators are due to the risk of “fuel” (i.e., wind
or sun) availability. These two factors lead to the conclusion
that we must evaluate variable renewable generators for
their contribution to overall system reliability, rather than
the reliability of an individual renewable generator.
Because of the implications for reliability, capacity credit—
the amount of capacity that can be counted on to contribute
to system reliability—has financial value and can therefore
greatly improve the cost-effectiveness of wind power.
Conventional wisdom holds that capacity credit is given to
an individual site based on the individual site characteristics.
(Milligan 2002) This philosophy generally leads to the
assumption that wind farms have little or no capacity value
because the degree of the resource’s variability is so high at
each individual site. (Kirby, et al 2002)
Similarly, while solar is more predictable than wind, it is
still variable and therefore given little credit for contributing
to system reliability.
However, modern financial portfolio theory offers a
different way of looking at the world. A financial portfolio
consists of a combination of individual stocks. Developed
by Harry Markowitz in 1952, modern portfolio theory
enables the creation of minimum-variance portfolios for a
given level of expected return. This theory is based on
diversification—the lower the correlation between the
individual assets that make up the portfolio, the lower the
portfolio variance, or risk. (Alexander 1996)
Portfolio theory can be easily applied to energy resources.
In this context, a renewable portfolio can comprise a
geographically dispersed set of wind farms and solar electric
systems. This paper seeks to analyze the reliability value,
and therefore capacity value, of a set of wind and solar
generators dispersed across the U.S. Midwest.
4 DATA AND METHODS
4.1 Data Sources
This study attempts to maximize the use of high quality
measured wind speed and solar insolation data. All data
were recorded at hourly intervals. The wind data was
measured at or near a 50-80 meter hub height and the solar
data includes separate direct and diffuse radiation values.
This initial analysis is limited to the Midwest Reliability
Organization (MRO) for the 2004 calendar year. This region
and timeframe were selected from among those previously
analyzed by Hansen & Levine (2008) because they provided
the highest number of corresponding sites for which
measured solar data was available.
The wind data was chosen from the RMI/UC-Boulder wind
database compiled by Levine and Hansen (Levine 2007,
Hansen & Levine 2008). The original source for the MRO
wind data was the University of North Dakota Energy &
Environmental Research Center (EERC) hosted Plains
Organization for Wind Energy (POWER) database.1 Thirty-
five (35) wind sites from MRO were included in this
analysis.
All solar data was taken from the National Solar Radiation
Database (NSRDB) 1991-2005 Update maintained by the
National Renewable Energy Lab (NREL).2 Though this
database contains radiation data for 1,454 sites, only 40 of
these sites include measured data.
For the region and period of interest – MRO in 2004 – three
solar insolation sites were selected with measured data for
90% or more of the time. An additional five modeled sites
were selected to increase the spatial diversity of the dataset.
These modeled sites were carefully selected to be class-I
sites with 100% low data uncertainty during 2004. (NREL
2007)
4.2 Data Preparation
Both wind speed and solar insolation data were first cleaned
to remove any negative, grossly out of range values, or
flagged as invalid points. These removed points were
conservatively set to zero. The measurement times were also
normalized to coordinated universal time (UTC) to ensure
data alignment across time zones.
For wind, the raw wind speed was converted to a consistent
80-meter or greater hub height using the methodology
described in detail in Hansen and Levine (2008). In
summary, all data gathered at lower than 40m were
discarded, data gathered between 40m and 80m were scaled
up to 80m, and all data gathered at or above 80m were left
at the recorded height. Wind speeds were adjusted for height
using the one-seventh-power rule.
For solar, both direct (beam) insolation and diffuse
horizontal collector data was included. Where measured
solar data was not available on an hour-by-hour or site-by-
site basis, modeled data was substituted when possible.
4.3 Wind Power Production Model
As described further in Hansen & Levine (2008), the 2 MW
Vestas V80 was chosen to model power production. The
turbine’s power curve was adjusted for elevation and air
density at each site.
4.4 Solar Power Production Model
Solar power production was modeled for an idealized 1-axis
polar mount tracking photovoltaic system with a maximum
power point (MPP) tracker. Although solar thermal systems
1 Available on line at:
www.undeerc.org/programareas/renewableenergy/wind/default.asp
2 Available on-line at:
http://rredc.nrel.gov/solar/old_data/nsrdb/1991-2005/
are more common for utility scale solar power, a
photovoltaic system was chosen in this analysis because:
• The NSRDB-Update modeled direct insolation data
does not adequately capture some frequency
components important for solar thermal analysis
(Renné, et al 2008); and
• Concentrating solar power production, including solar
thermal is less suited for areas, such as MRO, where
diffuse radiation comprises a substantial portion of the
total insolation.
The model system was tilted at an angle above horizontal
equal to the site latitude. The Maximum Power Point (MPP)
current was assumed to vary linearly with insolation.
Temperature effects and decreased MPP voltage at lower
insolation levels were not included. An isotropic sky is
assumed and implies equal diffuse radiation intensity in all
directions. Reflected radiation is conservatively assumed to
be zero. Other losses, including conversion and inverter
efficiencies were assumed to be constant. Since the system
was scaled to a fixed total AC nameplate power it was not
necessary to quantify these other losses. The resulting
equations for insolation and power production are:
!
I1"axis =IBcos
#
+IDH
1+cos(
$
+
#
)
2
%
&
'
(
)
*
!
P
1"axis =I1"axis #Pnameplate
Where IB=direct (beam) insolation, IDH=horizontal diffuse
insolation, δ=solar declination, and ζ=zenith angle. (adapted
from Masters 2004)
Though this model is very simple, it is adequate to capture
the time variability of the solar resource, which is the
primary concern in this study. Further efforts are underway
to refine this model to both include non-idealities and the
balance of system hardware and to compare other solar
power system designs including fixed photovoltaics and
concentrating solar technologies.
4.5 Scaling and Interconnection
As described in section 3, this study combined multiple
individual generation sites to create portfolios of
geographically and resource (wind vs. solar) diverse
generation. This analysis does not consider the constraints
and losses associated with an interconnecting transmission
system and other infrastructure components.
To facilitate comparisons of results for different scenarios,
all individual wind and solar site date was scaled to a
nameplate power rating of 100 MW AC. For solar, this
scaling was done on the AC power rating at 1-sun (1000
W/m2). When multiple sites were interconnected to form a
portfolio, individual site output power was scaled such that
the total nameplate power for the portfolio was kept at 100
MW. The selection of 100 MW was arbitrary, and the
results can be readily scaled up (or down) as needed. The
use of 100 MW also affords easy conversions to/from
percent of nameplate load.
4.6 Variability and Output Metrics
The variability of site (or portfolio) output was quantified as
the standard deviation, σ, of the (combined) hourly power
production in MW. The standard deviation also has units of
MW. The output was quantified as the arithmetic mean of
the hourly power production in MW. If desired, this average
output measure can be converted to annual energy
production in MWh by multiplying by the number of hours
in a year.
In addition to representing important considerations for
integrating a variable resource into a utility load, the choice
of mean and standard deviation allow for significant
computational savings when optimizing large portfolios.
This is because, rather than having to recalculate the hour-
by-hour power output at each optimization step, it is only
necessary to scale the covariance matrix and mean.
The computation of the portfolio mean power output,
!
pp
,
for n sites is straightforward:
!
pp=aipi
i=1
n
"
where ai is the percent share, or weight, of generating
capacity for an individual site. And
!
pi
is the mean of the
hourly output series, Pi, of the corresponding site.
The computation of the portfolio standard deviation, σp,
takes advantage of the fact that the variance (σ2) of the sum
of a set of random variables, Xi, is equal to the sum of the
elements in their covariance matrix. Namely,
!
Var(X1+X2KXn)=Cov(Xi,Xj)
j=1
n
"
i=1
n
"
And the property that the covariance of scaled random
variables is equal to the scaled covariance of the original
variables:
!
abCov(X,Y)=Cov(aX,bY )
As a result, the portfolio output power standard deviation is
given by:
!
"
p
2=aiajCov(Pi,Pj)
j=1
n
#
i=1
n
#
or in Matrix form:
!
"
p
2=aTµa
where:
!
a=
a1
M
an
"
#
$
$
$
%
&
'
'
'
!
µ=
Var(P
1)LCov(P
1,P
n)
M O M
Cov(P
1,P
n)LVar(P
n)
"
#
$
$
$
%
&
'
'
'
since Cov(X,X) = Var(X).
4.7 Optimization Methodology
The portfolio variability was minimized using Monte Carlo
methods subject to a constraint on the average output power:
!
minimize(
"
p)
subject to
!
pp"plimit
This portfolio power constraint, plimit, was varied from the
minimum to maximum single site output average power, pi,
for the set of sites in a scenario.
Rather than running a separate optimization for each Plimit,
in which any runs that did not meet the constraint must be
thrown out, the results of each Monte Carlo trial were
binned according to output level. In this way the simulation
lets us run multiple constrained optimizations
simultaneously.
Also, to more fully explore the potential value of sparse
portfolios, at the start of each trial random weights were
assigned not to all n sites, but to a randomized subset, N, of
the available sites. This was necessary since the probability
of multiple zero or near-zero share members existing in a
portfolio of randomly weighted sites drops precipitously
with increasing n.
4.8 Treatment of Constrained Number of Sites
During the analysis, it was noticed that the optimal portfolio
rarely contained all of the sites. Further investigations were
conducted to determine the impacts of restricting the
number of sites included in the portfolio.
This introduced an additional constraint to the optimization:
!
length(N)"nlimit
Separate simulations were run for each value of nlimit.
In these scenarios, the subset of sites with nonzero output
shares was randomly selected for each trial from the entire
appropriate set of power data (e.g. all wind sites). In this
way, the members in the subset of sites was allowed to vary
to achieve the optimal results across a spectrum of output
levels. The sites represented at low output levels for a given
nlimit would typically be different than those included in a
higher output portfolio for the same nlimit.
5 RESULTS AND DISCUSSION
5.1 Wind alone
Given the growing body of literature on the subject (Archer
& Jacobson 2007, for example) and the results of prior
studies by the group using different optimization methods
(Hansen & Levine 2008), it was not surprising to find that
the power production for an optimized portfolio of wind
assets was less variable than that for its sites individually.
Specifically, optimized wind portfolios for MRO in 2004
reduced output variability an average of 45%3 compared to
the individual sites and increased the capacity factor from
0.19 to 0.254. The 80/90/95/99% available output level also
increased from an average of 1.5/0/0/0MW to 9/6/4/1MW5.
5.2 Solar alone
Similar to wind, combining solar generating assets into an
optimal portfolio reduced the output variability compared to
that of the individual sites. Optimized solar only portfolios
for MRO in 2004 reduced output variability an average of
15% compared to the individual sites and increased the
capacity factor from 0.23 to 0.25. Because the sun sets, the
power output for individual solar sites is zero at least half of
the time. When combined into a portfolio, this increased to
8 MW of firm output capacity available 50% of the time.
A major factor in this reduced variability comes from the
range of longitudes included in a portfolio. Increasing
longitudinal spans makes it possible for the sun to be
available to some collector in the portfolio for more hours of
3 All portfolio averages include the two middle quartiles of the set
of optimal portfolios.
4 CF for portfolio with moderately high output and standard
deviations (bin 15/20) vs site average.
5 Increased guaranteed output levels for portfolio with moderately
high output and standard deviations (bin 15/20.)
the day. Spatial diversity of solar also reduces the impact of
patchy clouds covering the sun, since it is likely that the sun
will be unobscured at one of the other sites.
In this analysis, the variability reduction was less dramatic
than for wind, largely because solar radiation is more
correlated between sites than wind speed. In fact, the
minimum covariance between individual solar sites is 50x
higher than that for wind sites.
5.3 Solar & Wind Together
When combined, solar and wind resources provide optimal
portfolios which offer further decreases in power variability
beyond that of either alone.
Fig. 3: (top) Load-duration-style output curves for optimal
portfolios. A high, flat line that is never at zero is best.
(bottom) Zoom in on the lower right showing significantly
improved firmness of output for portfolios. 6
In this analysis, both the wind-only and solar-only
covariance matrices were strictly positive, indicating that
the resource specific power production was more or less
correlated. In the combined solar & wind scenario, negative
elements appear corresponding to an anti-correlation
between the solar and wind resources which is a powerful
indicator for the potential of cross-firming.
Optimized portfolios offer an average decrease in variability
of 55% below the average of individual sites. This
represents a 13% lower average variability than the optimal
for wind only and 60% lower than the optimal solar. The
6 The portfolios depicted as optimal in these figures are those with
moderately high output and standard deviations. (bin 15/20). See
section 5.4 for further discussion.
combined optimal capacity factor was 0.25 and the
80/90/95/99% available output increased to 11/7/4/2 MW.
The top chart in Fig. 3 compares the output duration
improvements for the optimal combined portfolios with
those of the individual technology portfolios and those of an
arbitrary subset of the individual sites. The upper plot shows
that all of the optimal portfolios and the combined
wind+solar and the wind-only profiles in particular, have a
relatively flatter profile, illustrating that a narrower range of
output levels is produced for a majority of the time. The
combined portfolio produces the flattest profile, illustrating
its further variability reductions. The flat regions of the
curve are also higher than those of the individual sites,
indicating an increase in reliable output power during these
periods of reduced variability.
The bottom chart in Fig. 3. shows that the optimal combined
and wind-only portfolios eliminate the amount of time with
zero output. This represents a significant improvement
above the roughly 15% of the time the wind sites in this
analysis have zero output. The optimal solar-only portfolio
also shows a large reduction in zero output from 50% to
40% of the time.
Some of the ways in which the solar and wind resources
compliment each other are illustrated in Fig. 4. At night, the
wind generators provide power when the sun can’t. During
the afternoon of May 27th and all day on May 28th solar
output is able to compensate for low wind power output to
produce a lower variability output.
Fig. 4: Generation profile of optimal portfolios.
5.4 Trade-offs
For each scenario there is a set of optimal portfolios that
represent a trade-off between variability (standard
deviation) and power output (
!
pp
).
This concept is represented graphically with the efficient
frontier shown in Fig. 5 This plot shows the trade-off
between risk (variability) and reward (output). Individual
sites appear as points, while optimal portfolios lie along a
curve. Moving toward the left (lower variability) and up
(higher output) represent desired trajectories. A utility can
pick from along the curves to select the best-suited balance
of output and variability.
Fig. 5: Tradeoff of output power vs variability. Upper left is
best.
In the figure it is clear that in all cases – wind-alone, solar-
alone, combined solar and wind – the optimal portfolios
offer decreased variability (standard deviation) for a given
output level and/or increased average power output for a
given variability compared to their associated individual
sites alone. This figure also clearly shows the added value of
cross-firming wind with solar to allow a few percentage
points of increased output or decreased variability.
5.5 Effect of Number of Site Constraints
This study conducted preliminary analysis on the impacts of
limiting the number of sites selected for a portfolio. As seen
in Fig. 6, including only a few of the available sites can
achieve the majority of reductions in variability (or
increases in output). A marked improvement in variability is
achieved by interconnecting portfolios as small as two sites
and portfolios of only six optimally chosen sites are nearly
indistinguishable from the unconstrained optimums.
Furthermore, the actual number sites that make up the
optimal portfolios for less-constrained simulations is
observed to be much lower than nlimit as seen in Table 1.
This could plausibly be due to the difficulty of finding
optimal solutions from the extremely large number of
combinations of sites and weights for high nlimit scenarios.
However, increasing the number of trials, which should
increase the odds of locating an optimal portfolio with a
high number of sites, has instead been observed to further
reduce the number of sites in optimal portfolios. This
observation taken together with the trend that increasing
nlimit beyond a certain point does not significantly affect the
variability, provides support for the theory that the optimal
portfolio for a given output level does not contain all of the
sites.
Fig. 6: Improvement in variability for a given output can be
had with only a few optimally selected sites.
This analysis shows rapidly diminishing returns for
decreasing variability by increasing nlimit for a given
geographic region. Others, including Archer and Jacobson
(2007), have shown seemingly contradictorily results that
the variability of power output tends to decrease
monotonically with the number of sites interconnected in an
array with only gradually diminishing returns. One possible
explanation is that the number of sites available to draw
from when creating a portfolio, rather than the actual
number of interconnected sites is the key to reducing
variability Further investigation is required to better
understand this phenomenon.
TABLE 1: OPTIMAL PORTFOLIO RESULTS
(WIND+SOLAR)
Max Sites
Constraint
Avg # Sites in
Best Portfolios
Average Drop in
Std. Dev.7
2
2.0
9.0 MW
4
4.0
13.0
6
5.5
13.4
12
8.8
13.7
20
9.8
13.8
43 (all)
8.18
13.8
7 Relative to the average std. dev. of individual sites of 25MW
8 The full portfolio is the result of 5-10x as many simulations as
the other sites.
6 SOLAR AND WIND IN A NEXT GENERATION
UTILITY
While geographical dispersion of variable resources and the
combination of different variable resources can significantly
reduce portfolio variability, as described in this paper, the
remaining variability must be managed in order to balance
demand and supply on the hourly, minute, and second
scales.
This balancing currently happens through the use of
automated generation control and ancillary services.
However, with greatly increased penetrations of variable
renewables, more flexible capacity will be required. Given
advances in communications and control technologies,
much of this remaining variability could be met effectively
through the dynamic use of:
• Responsive Loads—demand response has traditionally
been used to clip and shift on-peak demand to off-peak
periods in order to defer building new generation
capacity. Increasing the magnitude and duration of
demand response contributes to controlling absolute
demand growth. Furthermore, developing demand
response techniques that can operate at more than just
peak periods should allow demand response to provide
ancillary grid services and help manage renewable
variability. Previous pilot projects in California and
Nevada have shown that automated technologies with
two-way digital communications can successfully drive
demand response;
• Energy Storage— powerful system performance
synergies can be derived from the integration of the
electric and transportation sectors through the use of
plug-in hybrid electric vehicles and full electric
vehicles. For the electric utility, PHEVs and EVs
(collectively xEVs) offer responsive off-peak load, the
potential for dispatchable on-peak capacity from
vehicle-to-grid (V2G) connections, and the prospect of
economic electric storage, since the high capital costs
of batteries would be shared with drivers; and
• Intelligent Grid Communications—Increased use of
responsive load and xEVs requires advanced grid
communications technologies. Utilities must be able to
communicate in real-time with loads and xEVs to make
most effective use of the firming capabilities of those
resources. Such capabilities are being explored in on-
going research into “smart grid” technologies.
7 CONCLUSIONS
This study shows that, as is the case for wind,
interconnecting individual solar generation sites into
geographically diverse arrays can reduce the variability of
the power output. It also shows that including solar
generation sites into arrays of geographically diverse wind
sites can further reduce the total variability beyond what is
possible for either resource type alone. Finally, it was
observed that, at least in the modeled system, only a small
subset of the potential sites in an interconnected array need
to be included to achieve these variability reductions.
8 NEXT STEPS
To expand and enhance this analysis for incorporation into
the next generation utility concept, there are several
additional elements of analysis that will be addressed,
including:
• Other geographic areas—this analysis covers only the
Midwest Reliability Organization (MRO). As with the
wind-only analysis conducted by Hansen & Levine in
2008, this analysis will be expanded into the Southwest
Power Pool (SPP) and the Electric Reliability Council
of Texas (ERCOT). Additionally, both the wind-only
analysis and the wind and solar analysis will be
expanded into the Western Electric Coordinating
Council (WECC). Once these regions have been
analyzed, the majority of good wind and solar sites
within the continental United States will have been
addressed.
• Longer time periods—this analysis comprises only the
year 2004. To more accurately capture the variability
over time of both wind and solar power, hourly data
over at least three years should be analyzed. This
expanded analysis will be conducted as possible given
the availability of hourly data in a consecutive three-
year period.
• Match to load shape—as discussed at the beginning of
this paper, renewable resource variability is only
important in the context of system load. Therefore, a
complete analysis includes the covariance of
renewables with load over the same time period. This
type of analysis, frequently referred to as the effective
load carrying capability (ELCC) of a renewable
resource, is dependent in part on the ability to acquire
accurate hourly load data.
• Integration with demand-side resources—finally, the
next generation utility project will analyze the
interactions between variable renewable resources and
demand-side resources, including responsive load and
xEVs. The ability of these resources to manage
renewable variability largely depends on the duration
and possible rate of change of each resource.
• Economic drivers—the viability of the next generation
utility concept is dependent on the cost-effectiveness of
the system and its components. The theory put forward
in this paper is that the intelligent combination of
resources can reduce the cost of the portfolio. However,
this and other economic drivers, including the cost of
various technologies and of the transmission capacity
needed to connect them, must be explicitly addressed.
9 ACKNOWLEDGEMENTS
The authors would like to thank Joel Swisher, Ph.D., P.E.,
and the Energy & Resources Team of the Rocky Mountain
Institute for their collective work on the next generation
utility concept. This research is funded through the generous
support of the William and Flora Hewlett Foundation.
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