Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012
Evaluating the Impact of Wind Power Uncertainty on
Power System Adequacy
Esteban Gil
Departamento de Ingeniería Eléctrica
Universidad Técnica Federico Santa María
Valparaíso, Chile
esteban.gil@usm.cl
Abstract— This paper discusses how wind power uncertainty
affects power system adequacy from an operational point of view.
A method is presented to produce wind power generation
simulated data to feed a Monte Carlo scheme. The Monte Carlo
scheme randomly selects forced outage patterns for each
conventional generator and wind power simulated patterns in
order to evaluate how system adequacy metrics, such as Loss of
Load Probability (LOLP) and Loss of Energy Expectation
(LOEE) change with the introduction of wind power into the
system. The method is tested on a model of the Chilean Northern
Interconnected system. Results show how LOLP and LOEE
change for different capacity reserve margin levels and different
levels of wind penetration.
Keywords- wind energy generation, power system reliability,
power system adequacy, capacity value, Monte Carlo techniques,
LOLP, LOEE
I.
INTRODUCTION
As wind generation technology matures and becomes more
competitive with conventional generation technologies, its
penetration and impacts on power systems will continue to
grow. Therefore, system operators and regulatory bodies need
to be prepared not only for wind power promised benefits but
also for the novel operational and regulatory challenges that a
larger wind power penetration will bring.
Because of their different operational characteristics, wind
energy generators can become a substantial challenge to
incorporate in electricity grids long dominated by conventional
thermal and hydro technologies. Depending on the scope of the
beholder, the challenges brought by renewable technology
integration will lie on one of these three categories: i)
operational challenges, such as system transient stability
problems caused by the low inertia of the wind farms, or
additional operational burden due to the intermittent or
undispatchable nature of wind power; ii) planning challenges,
such as how much wind power can be accommodated into the
market so as to maintain acceptable system reliability; and iii)
regulatory changes, such as policy changes necessary in order
to incentivize investments on renewable technologies and with
the purpose of capitalizing on their perceived benefits. Of
course, many of the integration issues brought by wind power
also encompass complex modeling efforts in order to represent
their particular characteristics and special operating regimes
adequately into our existing models, and this has caused a
boom of research efforts [1]-[2].
Many different studies have been conducted on integration
of wind power into existing grids (see [3]-[5] for reviews and
[6]-[11] for detailed studies). In particular, many of these
studies deal with evaluating the impact that uncertainty in wind
farm output has on power systems, generally with one or both
of these objectives in mind: 1) To estimate the wind resource
capacity value, that is, the contribution of each wind power
generator to power system adequacy, and/or 2) To determine
the additional amount of operational reserves that the system
must carry to account for the uncertainty on wind power
output. Hence, while the first objective is oriented to evaluating
the contribution to reliability of the generator itself, the second
objective attempts to evaluate the preventive actions that the
system operator must take on face of the additional uncertainty
such that system reliability remains within acceptable
boundaries. Either of these objectives requires understanding of
how power system adequacy, that is, the capacity of the system
supply to meet its demand taking into account unexpected
outages of generators or transmission infrastructure and
possible constraints on the primary energy resource [12],
changes under different operating conditions.
The results presented in this paper correspond to a pilot
study conducted to evaluate the impact on reliability that the
possible incorporation of wind power into the Chilean Northern
Interconnected System (Sistema Interconectado del Norte
Grande, SING) might have. The SING is an almost purely
thermoelectric system with about 3.7 GW installed generation
capacity in 2010 and most of its load being industrial and
relatively flat. Although the SING has not wind power installed
so far, the Chilean market for renewable generation projects
has accelerated its development over the last few years, mainly
driven by the removal of barriers of entry and increasing
electricity demand and prices. Recent changes to the regulatory
framework seek to ensure that the characteristics of nonconventional renewable energy (NCRE) technologies are
properly accounted for so that they can be effectively
incorporated into the electricity market [13]. There are two
main objectives for this study: 1) To develop and evaluate a
method to produce wind power generation simulated data and
2) Use the simulated data in a Monte Carlo scheme that will
allow a better understanding of how system adequacy metrics,
such as Loss of Load Probability (LOLP) and Loss of Energy
Expectation (LOEE) change with the introduction of wind.
Section II of this paper will present the Monte Carlo
scheme and discuss issues related to generation dispatch and
664
Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012
pre-dispatch under uncertainty while Section III will discuss
the generation of simulated wind data. Section IV will describe
the test system and present preliminary simulation results.
II.
METHODOLOGY
A. Overview
Evaluating the impact of a particular generator on power
system adequacy is usually performed by using the Effective
Load Carrying Capability (ELCC) approach. The ELCC
approach consists on evaluating the additional amount of
demand that the system is able to handle, while preserving the
same system adequacy, given the addition of the generator
being studied. This general idea, introduced by Garver in 1966
[14], has been successfully applied for decades to conventional
generators and it may certainly prove valuable when dealing
with intermittent generators such as wind. For example, the
reliability equalization technique, based on ELCC principles,
replaces the generator of interest by some benchmark
generation unit of a variable capacity, and then varies its
capacity until some system adequacy metric (e.g. LOLP) is the
same than with the generator being evaluated. Despite ample
acceptance of these ideas, there are quite a lot of dissimilarities
in terms of their implementation. For example, no clear rules
exist regarding the type of benchmark generator to use when
doing reliability equalization, or about the most appropriate
system adequacy metric to use (LOLP, LOLE, LOEE,
etc.)[15]. Traditionally, ELCC-based ideas have been
implemented by applying convolution to the probability
distributions of the generators’ availability and the demand
[16]-[17]. This method does not need simulation and works
well if the variables are independent. But since availability of
wind is usually correlated to system demand, simulation
methods should be used instead.
The Monte Carlo simulation scheme presented in this paper
can be summarized as follows: Using a forecast of wind power
for the following day, a detailed hourly unit commitment is
obtained for each day. Then, the unit commitment decisions are
fixed and a Monte Carlo simulation is applied to the economic
load dispatch in order to obtain LOLP and LOEE versus
capacity reserve margin. The Monte Carlo sampling is done to
randomly determine forced outage patterns for each
conventional generator, and to randomly select a wind power
simulated pattern that preserves the correlation between load
and wind power generation. Considering that having un-served
energy is a rare event, the process usually requires a large
number of simulation samples as it tries to make estimations
about the tail of the probability distribution of the balance
between demand and supply.
B. Pre-dispatch
To model realistically how pre-dispatch decisions are made,
on the Unit Commitment (UC) algorithm the generators are
scheduled to operate or not based on a prediction of demand
and wind output for the next 24 hours, considering a hard
operating reserve requirement to account for unexpected
outages and errors in the load and wind forecasts. Because
most of the generating units in the SING are large inflexible
coal and gas-fired units, most on-off decisions need to be
modeled as integers and the unit commitment becomes a
relatively large Mixed Linear Integer Program to solve.
Although some authors have suggested the use of stochastic
programming [18]-[22] for this type of problems, its use would
increase substantially simulation time and thus it is considered
to be out of the scope of this preliminary study. Once a solution
has been obtained, the algorithm then fixes the UC decisions of
the most inflexible conventional generators and passes them
down to the Economic Load Dispatch (ELD) algorithm.
C. Load dispatch using Monte Carlo
The UC decisions from the previous stage are fixed for the
inflexible units, and load dispatch is conducted for different
Monte Carlo samples. In this stage only peaking and fast
intermediate generation units can change their commitment
decision, thus the mathematical optimization problem is
considerably faster to solve. The Monte Carlo sampling
randomly selects forced outage patterns for each conventional
generator, and also randomly selects a wind power simulated
pattern created as per described in Section III.
The Monte Carlo simulation results can then be used to
obtain various power system adequacy metrics. In this case we
selected a capacity adequacy metric (LOLP) and an energy
adequacy metric (LOEE). It must be observed that different
periods carry different risk, as the balance between demand and
supply is not always the same. Thus, the focus of this paper
will be on obtaining a relationship between the reserve capacity
margin and the power system adequacy metric of choice.
Notice that the capacity reserve margin varies through the year
as a result of load variation, scheduled outages of generators
and transmission lines, and as a result of the connection of new
power plants.
In this preliminary stage of the study 200 Monte-Carlo
samples per case are being considered. However, based on
uncertainty estimates of the adequacy metrics, over 1000
samples may be necessary in later stages in order to reduce the
uncertainty of the estimates, especially in low-risk/high
capacity reserve margin periods.
III.
MODELING OF THE WIND
A. Modeling issues
In general, generators such as thermal plants burning fossil
fuels, thermonuclear plants, or hydroelectric plants can be
considered to be available as long as the unit is not on
maintenance or an unexpected outage occurs. In contrast, wind
generation output depends on meteorological factors outside
direct operator control. The following will discuss different
aspects and challenges related to the operation and integration
of wind generation, and will indicate certain guidelines that
need to be followed to properly simulate the effect that wind
generation uncertainty will have on UC and ELD decisions.
1) Dispatchability
Dispatchability of a generation unit refers to the ability of
the system operator to program or decide (dispatch) in advance
if and how much a unit will be generating within a specified
timeframe. In the formulation of the mathematical problem,
dispatchability of a unit refers to the suitability of the unit
generation in a given period to become a decision variable in
the UC and the ELD optimization problems. Since the
665
Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012
operational costs of wind power tend to be small or negligible
compared to the operational costs of conventional thermal
power plants, there are no transmission or unit commitment
constraints, wind generation will only be limited by the
availability of the renewable resource. However, due to the
intermittent nature of the wind resource, wind generation is
treated not as a decision variable (either generated
deterministically or stochastically) but as an input of the
optimization problems.
2) Average capacity factor and seasonal patterns
The average capacity factor of wind generation changes
over time as a result of cyclic behaviors of the weather (e.g.
day and night; Winter and Summer). As the load also manifests
such cyclic behavior, it is important to represent these cycles in
the modeling since the correlation between load and wind
power output may play a very significant role in evaluating its
contribution to power system adequacy.
3) Correlation between load and wind output
Evaluating the impact of wind power on system adequacy
must take into account how much capacity the generator can
make available at high system risk periods [5]-[23]. That is,
when a generator is needed the most its contribution to system
adequacy will be greater. In consequence, the capacity value of
a generator able to inject energy into the system during the
periods of high system risk (usually the periods of high
demand) will be higher than the capacity value of a generator
unable to do so.
4) Variability and Predictability
Variability of a generator refers to the extent to which its
output can exhibit undesired or uncontrolled changes [24].
Thus, a metric for variability will describe how far the
generator’s output lies from its average generation. Obviously,
the variance or standard deviation of a generator’s output is a
metric for the generator’s variability.
Although all types of generation are subject to some
variability as a result of unexpected outages, in wind generators
this characteristic is more accentuated. For example, wind
speeds, and therefore wind power output, can be highly
variable at different timescales: hourly, daily and seasonally.
2.
Simulated wind data should be a good representation of
historical wind data: Seasonal patterns in the data should
be reproduced, and each simulated data pattern should
have autocorrelation and partial autocorrelation functions
similar to the ones of the historical data.
3.
Correlation between wind power availability and load
should be preserved, as wind power capacity value can be
very dependent on this correlation.
4.
Uncertainty in the first few periods of the forecast should
be smaller than in later periods: Wind power can be
predicted reasonably accurately for the next few hours, but
not very accurately for periods far-ahead. This should be
reflected in that the simulated data for the Monte Carlo
simulation should increase its variance as time progresses.
C. Modeling of wind power uncertainty
For the purposes of this work two types of wind data will
be needed. First, we need a time series corresponding to the
forecast of the wind for the next 24 hours for use in the UC
algorithm. Second, we need a set of time series of simulated
wind power data for use in the Monte Carlo simulations.
The historical wind data is from 20 months of generation
data from a 62MW wind farm relatively close but not
connected to the SING. The data was normalized to values
between 0 and 1 to allow later resizing. All statistical analyses
of the data were conducted in R [25].
1) Removing seasonal variations
Despite not having enough historical wind power data to
properly identify yearly seasonal patterns, their existence is
strongly suggested by the analysis of historical wind speed
data, and as a boxplot indicating the 25, 50, and 75 percentiles
of hourly wind generation of the wind farm for each month
illustrates in Figure 1. It is observed that during the first half of
the year the wind farm capacity factor remains relatively low
and then increases with the Spring, peaking in September.
Thus, to account for this seasonal variation a linear model of
the wind generation data using the month as a factor was fitted.
Predictability of a generator refers to the extent to which
the output of the generator can be inferred in advance (for the
next hour, day, week, month or year) [24]. Intermittent
generators’ predictability is directly related to the autocorrelation and seasonal patterns present in the time series of
its output. For example, while wind farm production in the
short term (a few hours ahead) can be predicted with some
precision, it is not possible to do so on the long term (at least
hourly) because of the chaotic nature of the weather.
B. Guidelines for generating simulated wind data
Based on the previous discussion, a set of guidelines for
generating simulated wind data is suggested:
1.
Wind generation must not be treated as a decision variable.
Instead, wind generation patterns must be created
externally (preferably stochastically) and fed to the UC
and ELD problems.
Figure 1. Boxplot of wind generation versus month
666
Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012
algorithm outlined in [26] and implemented in R´s forecast
package. Using this procedure, the best model turned out to be
a SARIMA(1,0,1)x(1,0,0){24} model with parameters outlined
in Table I.
The diagnostics for the model fitting of the remainder can
be seen in Figure 4. The model is considered to satisfactorily
represent the data, as the autocorrelation function of the
SARIMA model residuals is very flat and the p-values of the
Lung-Box statistic are all small.
TABLE I.
PARAMETERS OF THE SARIMA(1,0,1)X(1,0,0) {24} MODEL
ar1
ma1
sar1
0.9306
0.1536
0.0645
coefficient
0.0033
0.0088
0.0085
standard error
sigma^2 estimated as 0.005761: log likelihood=16138.04
AIC=-32266.09 AICc=-32266.09 BIC=-32228.38
intercept
0.0000
0.0114
Figure 2. Boxplot of wind generation versus hour
A boxplot of the data using the hour of the day as a factor is
shown in Figure 2. The boxplot suggests a strong daily
seasonal pattern, as a result of predictable weather variations
between night and day. In order to get rid of the daily seasonal
pattern, we applied a local polynomial regression fitting
procedure to the residuals of the previously fitted linear model.
The residuals of the new model are shown in Figure 3.
Figure 4. Diagnostic of the fitted SARIMA(1,0,1)x(1,0,0)[24] model
3) Using the fitted model to produce forecasted and
simulated data
For each day, a forecast and a set of simulated data are
produced using the previous values of the time series, the
parameters of the SARIMA(1,0,1)x(1,0,0){24} model, and the
seasonal patterns identified earlier.
Figure 3. Time series of the residuals after removing the yearly and daily
seasonal effects
2) SARIMA model fitting
According to the partial autocorrelation function of the
residuals, there is strong evidence of an implicit autoregressive
process and a remaining seasonal autoregressive process. The
autocorrelation function also shows the signature of a moving
average process. Based on a KPSS test, we identified no need
for first-differencing, and based on a CH test we identified no
need for season-differencing.
In order to determine the order of the most adequate
Seasonal Autoregressive Integrative Moving Average
(SARIMA) model, we conducted a recursive search using the
While for the 24-hour ahead forecast the model error is
assumed to be zero and the predicted values are simply a linear
function of the previous values, the simulated data series errors
are generated by randomly sampling from a normal distribution
with zero mean and variance as given by Table I. After
applying the SARIMA model to the data and the randomly
generated errors, simulated wind generation patterns are then
reconstructed by summing up the seasonal components.
IV.
SIMULATION RESULTS
A. Test system
The test system is the Chilean Northern Interconnected
System (Sistema Interconnectado del Norte Grande, SING).
667
Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012
The energy market simulations were conducted using
PLEXOS. PLEXOS is a Mixed Integer Linear Programming
(MILP) based electricity market simulation and optimization
software. PLEXOS co-optimizes thermal, hydro, and ancillary
services and is able to perform stochastic simulations [28].
Once PLEXOS formulates the mathematical program, it is
solved using Xpress [29].
The CDEC-SING, the SING independent system operator
(ISO), provides on their website a PLEXOS database of their
system for purposes of their weekly generation programming
containing detailed production and network data. For this work,
the collection of databases for a whole year (Nov. 2010 to Oct.
2011) were merged, tested, and adapted to suit the purposes of
this study. The outputs of the simulations were benchmarked
against actual system outputs to check for correctness and
consistency. Then, by using Monte Carlo simulation following
the procedure outlined in Section II, system adequacy metrics
(LOLP and LOEE) for the system at different capacity reserve
margins were obtained.
B. Results
Results for LOEE versus capacity reserve margin for
different-sized wind farms are shown in Figure 5. LOLP results
are shown in Figure 6. Both LOLP and LOEE are observed to
decrease exponentially as the mismatch between available
capacity and peak load (capacity reserve margin) increases.
100%
LOLP (%)
The SING is an almost entirely thermal system with about 3.7
GW installed generation capacity serving mainly flat industrial
loads (mining) and a small percentage of residential loads
(about 10%). It has several old baseload coal units with
relatively inflexible operating regimes (57.8% of total
generation in 2010), some newer combined-cycle and opencycle gas-fired units (26.8%), some fuel-oil and diesel-based
peaking plants (15%), and a small amount of hydro generation
(0.4%) [27]. Despite the system having relatively large
capacity reserve margins (over 70%), an inflexible generator
mix coupled with a number of transmission constraints cause
many instances of unserved energy to occur.
10%
1%
40
60
80
100
120
140
160
180
200
Capacity reserve margin (%)
No Wind
Wind 100MW
Wind 2x100MW
Wind 200MW
Exponencial (No Wind)
Exponencial (Wind 100MW)
Exponencial (Wind 2x100MW)
Exponencial (Wind 200MW)
Figure 6. System LOLP versus capacity reserve margin for wind farms of
different size
The results in Figures 5 and Figure 6 show that system
adequacy is reduced (as LOLP and LOEE increased) when
wind farms are introduced to the system. This decline in
adequacy will eventually need to be compensated by increasing
the operational reserves carried by the system, in order to
restore adequacy to acceptable levels. Table II shows LOEE
values in MWh for different capacity reserve margin levels. At
the lowest capacity reserve margin (80%), the introduction of
100MW of wind increases the LOEE by about 4 MWh, while
at higher capacity reserve margins the impact of wind power
uncertainty on system adequacy is reduced.
TABLE II.
SYSTEM LOEE (MWH) VERSUS CAPACITY RESERVE MARGIN
Capacity reserve margin
80%
100%
120%
11.6
6.6
3.8
15.6
8.9
5.1
19.8
11.3
6.5
20.2
11.5
6.6
No Wind
Wind 100MW
Wind 2x100MW
Wind 200MW
LOEE (MWh)
100
10
1
40
60
80
100
120
140
160
180
200
Capacity reserve margin (%)
No Wind
Wind 100MW
Wind 2x100MW
Wind 200MW
Exponencial (No Wind)
Exponencial (Wind 100MW)
Exponencial (Wind 2x100MW)
Exponencial (Wind 200MW)
Figure 5. System LOEE versus capacity reserve margin for wind farms of
different size
As the wind farm size increased, adequacy with respect to
the ‘no wind’ case decreased. Additionally, we tried to
compare if wind resource diversity played an important role for
this particular system by comparing the performance of a
single 200 MW capacity wind farm against 2x100 MW wind
farms, but our results were inconclusive. Since unserved
energy events are of rare occurrence, a large number of
simulations might be necessary in order to properly estimate if
the system adequacy metrics are significantly different for both
cases.
V.
CONCLUSIONS
Numerical results show that system adequacy, as measured
by both LOLP and LOEE, decreases exponentially as the
capacity reserve margin for the system is reduced. Our
preliminary results for the SING showed that at the lower
capacity reserve margin every 100 MW of wind generation
added to the system increased the LOEE by about 4 MWh as a
result of wind power uncertainty. This constitutes a clear signal
668
Proceedings of PMAPS 2012, Istanbul, Turkey, June 10-14, 2012
to the ISO about how much additional operational reserve to
carry in order to keep system adequacy at its original level.
On subsequent simulations we have observed the impact of
wind uncertainty on power system adequacy to be quite
dependent on specific characteristics of the system, such as
generation technology mix, load shape, operational reserve
carried, transmission conditions, and ramping characteristics of
the thermal units. The statistical properties of the wind power
time series data are also very relevant in this type of analysis.
As shown in Figure 2, the wind data we used for this study has
a very strong daily pattern, which makes its uncertainty to be
less troubling than simulated data generated from different
wind data sets.
A follow-up study will evaluate the additional operational
reserves that this system will need to carry per each MW of
wind power installed using additional wind data. We also
expect to elucidate if wind resource diversity will play a
significant role in the impact that wind power uncertainty has
on power system adequacy.
ACKNOWLEDGEMENTS
The author acknowledges the support of the Chilean
National Commission for Scientific and Technological
Research (CONICYT) under grant Fondecyt 11110502.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
National Renewable Energy Laboratory (2011, Nov 22). NREL’s Wind
R&D Success Stories [Online]. Available: http://www.nrel.gov.
CONICYT (2011, Nov 22). The energy sector in Chile: Research
capabilities and science & technology development areas [Online].
Available: http://www.conicyt.cl.
J. DeCesaro et al., “Wind Energy and Power System Operations: A
Review of Wind Integration Studies to Date,” The Electricity Journal,
vol. 22, N°10, pp.33-43, 2009.
E. Ela et al., “Evolution of operating reserve determination in wind
power integration studies,” in IEEE Power and Energy Society General
Meeting, Minneapolis, MN, Jul. 2010.
M. Milligan et al., “Operating reserves and wind power integration: an
international comparison”, in Transmission Networks for Offshore Wind
Power Plants Conf., Québec, Canada, Oct. 2010.
R. Piwko et al., “The Effects of Integrating Wind Power on
Transmission System Planning, Reliability, and Operations: Report on
Phase 2,” The New York State Energy Research and Development
Authority, New York, NY, Tech. Rep., Mar. 2005.
R. Zavadil et al., “Final Report 2006 Minnesota Wind Integration Study:
Volume I,” The Minesota Public Utilities Comission, Saint Paul, MN,
Final Rep., Nov. 2006.
P. Meibom et al., “Final Report for All Island Grid Study - Workstream
2(b): Wind Variability Management Studies,” Department of
Communications, Energy and Natural Resources, Dublin, Ireland, Final
Rep., Jul. 2007.
D. Corbus et al., “Eastern Wind Integration and Transmission Study,”
National Renewable Energy Laboratory, Golden, CO, Final Rep., Feb.
2011.
[10] D. Lew et al., “Western Wind and Solar Integration Study,” National
Renewable Energy Laboratory, Golden, CO, Final Rep., May 2010.
[11] ERCOT (2011, Nov. 22). ERCOT Methodologies for Determining
Ancillary Service Requirements [Online]. Available: www.ercot.com.
[12] NERC Board of Trustees, “Glossary of terms used in reliability
standards,” NERC, Tech. Rep., Feb. 2008.
[13] R. Palma et al., “Non-Conventional Renewable Energy in the Chilean
Electricity Market,” Comision Nacional de Energía, Santiago, Chile,
Final Rep., Oct. 2009.
[14] L. Garver, “Effective Load Carrying Capability of Generating Units,”
IEEE Trans. Power App. Syst., vol. PAS-85, pp.910-919, Aug. 1966.
[15] P. Aguirre et al., “Realistic calculation of wind generation capacity
credits,” Integration of Wide-Scale Renewable Resources Into the Power
Delivery System, 2009 CIGRE/IEEE PES Joint Symposium, pp.1-8, Jul.
2009.
[16] M. Amelin, “Comparison of Capacity Credit Calculation Methods for
Conventional Power Plants and Wind Power,” IEEE Trans. on Power
Syst., vol. 24, pp. 685-691, May 2009.
[17] L. Soder and M. Amelin, “A review of different methodologies used for
calculation of wind power capacity credit,” in IEEE Power and Energy
Society General Meeting, pp. 1-5, July 2008.
[18] P. Carpentier et al., “Stochastic optimization of unit commitment: A new
decomposition framework,” IEEE Trans. Power Syst., vol. 11, pp. 10671073, May 1996
[19] S. Takriti et al., “A stochastic model for the unit commitment problem,”
IEEE Trans. Power Syst., vol.11, pp.1497-1508, Aug 1996.
[20] R. Barth et al., “A Stochastic Unit-commitment Model for the
Evaluation of the Impacts of Integration of Large Amounts of
Intermittent Wind Power,” in Proc. 9th Int. Conf. on Probabilistic
Methods Applied to Power Systems (PMAPS), Ames, IA, 2006.
[21] A. Tuohy et al., “Benefits of stochastic scheduling for power systems
with significant installed wind power,” in Proc. 10th Int. Conf.
Probabilistic Methods Applied to Power Systems (PMAPS), Mayaguez,
PR, 2008.
[22] P. Ruiz et al., “Applying Stochastic Programming to the Unit
Commitment Problem,” in Proc. 10th Int. Conf. on Probabilistic
Methods Applied to Power Systems (PMAPS), Mayaguez, PR, 2008.
[23] M. Milligan and K. Porter, “The Capacity Value of Wind in the United
States: Methods and Implementation”, The Electricity Journal, vol. 19,
N° 2, March 2006, pp. 91-99.
[24] G. Sinden, “Assessing the Costs of Intermittent Power Generation”, UK
Energy Research Centre, London, UK, Tech. Rep., Jul. 2005.
[25] R Development Core Team, “R: A Language and Environment for
Statistical Computing,” R Foundation for Statistical Computing, Vienna,
Austria, 2011.
[26] R. Hyndman and Y. Khandakar, “Automatic time series forecasting: The
forecast package for R,” Journal of Statistical Software, vol. 26, N°3,
2008.
[27] CDEC-SING, “2010 Annual Report: Statistics and Operation,” CDECSING, Santiago, Chile, Annual Rep., 2011.
[28] Energy Exemplar (2011, Nov 22). PLEXOS for Power Systems–Power
Market Simulation and Analysis Software [Software]. Available:
www.energyexemplar.com
[29] B. Daniel, “Modeling with Xpress,” Fair Isaac Corporation, Leam
House, UK, FICO Xpress Optimization Suite Whitepaper, May 2009.
669