Potter y Negnevitsky - 2007 - Investigating Using Stochastic Methods to Generate

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Investigating Using Stochastic Methods to Generate Training Data for
Windpower Prediction
Article in Australian Journal of Electrical and Electronics Engineering · January 2007
DOI: 10.1080/1448837X.2007.11464154
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Investigating Using Stochastic Methods to Generate
Training Data for Windpower Prediction
Cameron Potter
School of Engineering
University of Tasmania
Sandy Bay, Tasmania, Australia
[email protected]
ABSTRACT
This paper investigates the potential capability of
stochastic methods to generate data for windpower
prediction purposes. Stochastic models have been used
to develop data before, however, this paper shows that a
simplistic single histogram model will not suffice for
windpower purposes. The need to generate data is
important as often there is only a short period of data
available for use in developing a prediction system. This
need is then exaggerated if information from multiple
wind turbines is desired for the data input.
1.
INTRODUCTION
Windpower is presently the fastest growing power
generation sector in the world. It is predicted that in the
next year alone, windpower generation in the United
States of America could increase by 50% [1]. In
Australia, Tasmania and South Australia have a large
number of wind farm installations planned. Present
installations in Tasmania total to a capacity of 67MW, or
a potential wind penetration of 5.7% based on average
demand (although the installations have not been
operating long enough for an accurate yearly
assessment). Expansions presently under development
will take the total to 143MW. Furthermore, there are
proposals being investigated for a further 674MW [2, 3].
This means there is a potential for almost 50% wind
penetration in Tasmania. South Australia is in a similar
situation. One reason for this growth is the comparably
short lead time necessary to construct wind farms,
allowing for rapid response to increases in demand.
However, windpower does have significant problems
that must be addressed and these become more severe as
the wind penetration increases [4]. Wind is intermittent,
hence power generated from wind is also intermittent
[5]. The loss of generation from a minor wind farm
could be absorbed by the grid, yet larger wind farms
(some are as large as 300MW) pose more risk. This is
exacerbated by the tendency for close grouping of wind
farms, often feeding into the same utility line [4]. The
problem stems from the fact that energy from wind
generation is impractical to store. Storing large amounts
of generated energy is presently inefficient or expensive
(or both). The additional cost, either directly or through
loss of efficiency, would then impact upon the viability
of using windpower – which already needs supporting
through government incentives [4, 6].
A good example of government incentives is Australia’s
Mandatory Renewable Energy Target (MRET). This
scheme supplements the ability of renewable energy to
Michael Negnevitsky
School of Engineering
University of Tasmania
Sandy Bay, Tasmania, Australia
[email protected]
compete with fossil-fuel produced power through the
purchase of MRET credits. The MRET credits are
traded in a market independent of the energy market [6].
MRET sets targets for the amount of renewable energy
production and aims to achieve these targets through
financial penalties. Each distributor must purchase
enough of these credits to cover a given percentage of
their electricity supplied – actual percentages supplied in
[6]. This occurs regardless of which distributor is
actually purchasing the renewable energy, all must buy
the MRET credits separately in order to avoid the fines.
This means that renewable energy generators are gaining
revenue for the electricity they produce, but also for the
fact that they are contributing MRET credits.
2.
OPERATING SYSTEMS WITH HIGH WIND
PENETRATION
Operating a system with significant amounts of
unschedulable (or automatically scheduled) power is a
new challenge. To solely use spinning reserve to
provide security for a large amount of windfarm
generation would mean a low efficiency across the entire
network. However, the most efficient way to “store”
energy from a windfarm is to operate the other stations
in accordance with the windfarm generation. When the
windfarm is producing electricity, other stations can be
ramped back (saving energy), when the windfarm is not
producing electricity the other stations must be ramped
up to cover the demand. This differs from spinning
reserve in that rather than operating at low efficiency in
case of contingencies, the other generators instead would
use normal operations. Forecasting the generation from
the windfarm would be similar to forecasting demand. If
the operators knew that more non-windfarm generation
was required, non-windfarm generators would be
scheduled and the converse would be true too. To be
able to trade efficiently, make best use of transmission
line capability and address concerns with system
frequency in a re-regulated system, accurate short-term
windpower prediction is essential.
Another driver for short-term wind forecasting is that the
rapid growth of windfarming is making existing
scheduling methods inefficient [7]. At present, the
National Electricity Market (NEM) accepts all windfarm
production straight into the market. Until recent years,
there has been no need for a bidding system as the wind
generation has been insignificant in comparison with
total system requirements. However, as generation from
wind sources increases, so too does the influence of
these sources on the market. For this reason, the National
Electricity Market Management Company (NEMMCO)
is reviewing the scheduling policy, one possible outcome
could result in the generators having to bid their wind
assets into the market, like traditional generators.
Accurate forecasts of power generation are also of
importance to electricity transmission. As windfarms
grow in capacity, the strain they place on the
transmission grids also becomes more pronounced. This
is then further compounded by the fact that many
windfarms are being built in remote areas with “stringy”
transmission grids. This means that operation near
transmission limits will not be unusual for wind
generation and the transmission capability could be a
constraint to electricity transfer. Fig. 1 shows a clear
example of wind farms at the end of sparse transmission
grids. The six farms in the western side of the map all
depend on one transmission line.
N
separately for ‘raise’ and ‘lower’. Fast FCAS operates
on a six second response time, slow FCAS on a sixty
second response time and delayed FCAS on a five
minute response and returns the system to normal
operating conditions; see Fig. 2.
Fig. 2: Plot of fast, slow and delayed lower FCAS
after a contingency.
Due to Tasmania’s low level of interconnection with a
large grid, the operating regulations are more flexible.
However, given the way the FCAS requirements are
calculated by NEMMCO, even the more flexible
constraints are still effectively stricter towards Tasmania.
Consider the fast lower requirement:
FCAS FL = max( SingleLoad) − SD * LRF * ( BL / 50Hz )
SD = System Demand
LRF = Load Relief Factor
BL = Boundary Limit for a Load Event
Fig. 1: South Australian windfarms and transmission grid.
2.1.
THE TASMANIAN S ITUATION
Tasmania is in a unique situation in the field of power
generation; it is an isolated system in which 98.5% of all
power production is through renewable means.
“Basslink”, a HVDC underwater cable, will soon link
Tasmania’s grid to the NEM. This link will provide an
interconnection with a much larger, mainland system.
Ireland can be compared to Tasmania and may provide
some interesting conclusions [8]. Both systems are
islands with a HVDC connection to a larger power grid.
Both systems have the potential to install windfarm
capacity over half of the average demand. Both islands
are presently investigating this wind potential keenly.
Thus, Tasmania can learn from the concerns being raised
by the Irish Research Council for Science, Engineering
and Technology. These concerns include the fault ride
through capabilities as well as the power system
security, reliability and quality [8].
To maintain the power systems within the frequency
deviation standards, a sufficient level of frequency
control ancillary services (FCAS) are required. In the
NEM, FCAS is traded competitively in each region and
split into eight subgroups [9]. These subgroups are:
regulation, fast, slow and delayed FCAS each traded
For Tasmania, the maximum single load is around
100MW, while system demand range is approximately
950MW to 1800MW. The load relief factor is 1 and the
limit for a load event is 1Hz [10]. For an average system
demand of 1200MW, this would require a fast lower
FCAS of 76MW.
Consider mainland Australia:
maximum single load is around 350MW, average
demand is approximately 20,000MW, the load relief
factor is 1.5 and the operation boundary is 0.5Hz. This
gives a fast lower FCAS requirement of only 50MW, for
a much larger system.
Another problem with FCAS in Tasmania is from where
the services must be sourced. In general, NEMMCO
does not consider from where the region might source its
required FCAS. However, since Tasmania has a single
connection to the mainland grid, this is vitally important.
•
•
•
If Basslink is not operating, all of Tasmania’s FCAS
requirements must be sourced locally.
If Basslink is operating at it’s maximum export
limit, all of Tasmania’s lower FCAS requirements
must be sourced locally.
If Basslink is operating at it’s maximum import
limit, all of Tasmania’s raise FCAS requirements
must be sourced locally.
The requirement to supply sufficient FCAS according to
NEM standards will be a challenge for Tasmania.
Furthermore, windpower will only compound these
problems, unless it is well predicted. The standards are
set considering the effects that the maximum single
contingency event could cause. However, due to the
unschedulable
nature of windpower, the power
fluctuations from large scale wind developments will
adversely affect the system operation, unless the changes
are well predicted.
Tasmania’s potential 50% wind penetration would be
one of the highest windpower penetrations in the world.
This makes the concerns such as the reduction in wind
farm output coinciding with the loss of another generator
a relevant concern. For this reason, accurate prediction
of windpower production in Tasmania is vital.
3.
WINDPOWER PREDICTION
Forecasting is a vital part of business planning in today’s
competitive environment.
However, there is no
dominant system for the very short-term windpower
prediction [11]. Windpower prediction research is
extremely topical. At the last IEEE Power Engineering
Society General Meeting (San Francisco, 2005) 193 out
of 611 papers made reference to windpower. This is a
disproportionate number considering the low windpower
penetration worldwide. This is because as an emerging
technology, wind energy is a hot research topic. This is
not so much because the technology is very new, more
because the proliferation of windpower has become far
wider. Accordingly, it is having a greater impact on
market behaviour; hence the research interest.
3.1.
TIME S ERIES P REDICTION
A time series can be defined as a set of observations of a
parameter, or set of parameters, taken at a number of
time intervals. These intervals are usually (although not
always) of a regular length. If the time step between
data points is not consistent, or there is data missing, this
should be corrected to a regular time step if the data is to
be used for forecasting. Real-world time series are
diverse. Some time series data changes slowly and
relatively smoothly. Monthly electricity demand may
represent such a time series. Other time series can
exhibit comparably chaotic behaviour, making
prediction difficult. A windspeed time series, such as
the one shown in Fig. 3, possesses these characteristics.
Fig. 3. Wind time series with a 2.5 minute time step.
3.2.
P RESENT WIND P REDICTION S YSTEMS
Wind prediction is complex due to the wind’s high
degree of volatility. The usual forecast scales for power
engineering do not necessarily apply.
Efficient
windpower operation needs 2-3 minute forecasts to
handle wind gusts, accurate prediction out to 30 minutes
for dispatch, and longer forecasts for planning. To
achieve accurate forecasts, a number of different systems
must be developed and maintained.
Three main classes of techniques have been identified
for wind forecasting. These are numeric weather
prediction (NWP) models, statistical methods and
methods based upon artificial neural networks (ANN).
The NWP methods are based on mathematical fluid
mechanics models and have been found to dominate the
meteorological literature, almost exclusively. NWP
methods are the accepted technique for forecasts over an
hour ahead. However, due to extensive computation
time, accurate NWP models cannot be used for the 30
minutes ahead predictions. For the very short-term
prediction, statistical and ANN methods perform more
accurately [12, 13]. It has been shown that accurate
results can be obtained for the 2-3 minute prediction
[14]. These results were superior to the “persistence”
method, which meteorologists use as a benchmark for
very short-term wind prediction. Persistence uses the
assumption that wind will not change drastically from
time t to time t+1.
Longer-term wind forecasts have been extensively
developed by meteorologists and are successful. Papers
are available showing very short-term wind prediction
can be accurately achieved. However, after discussions
with industry, it is clear that there is no system that
predicts windpower accurately out to 30 minutes ahead.
As recently as 2003, NEMMCO received advice that
forecasts in the 5 minute to 30 minute range should be
based upon persistence [15]. However, this is not
sufficiently accurate and other techniques must be
considered.
The major problem with ANN and statistical techniques
is the reliance on large amounts of data to achieve
accurate prediction. Often this quantity of data can be
difficult to obtain. The data must have a sufficiently
small time step to be useful for 30 minute prediction.
The data should also be sourced from several years to
allow for annual (or even longer-term) weather patterns
such as El Niño and La Niña.
4.
GENERATING DATA FOR TRAINING
Generating data for testing or training of a system in
power engineering is not a new innovation. There are
many examples where a probabilistic model (otherwise
known as the “Monte Carlo” method) has been used to
develop data. The procedure is well documented [16].
However, the procedure is intended such that if, as an
example, seven variables are required, each of those
seven variables have insignificant correlations to each
others’ existence and/or value. However, for short-term
wind prediction, the inputs are often derived from a
single time series of points (although this might be
supplemented with additional data). This provides a new
challenge that must be met if a probabilistic model is to
be used to develop training data for a windpower
prediction system.
There are two conceivable ways to overcome the
problem of generating data for a time series. One is to
develop a way to create the time series so that the points
are not correlated during creation (like normal), but are
correlated in the same manner as the real data after the
data creation is complete. This may be achievable
through grouping the generated data points, however
sufficient accuracy would be difficult. The other method
is to try to develop the data in such a way that the
correlations are modelled due to the design itself. This
approach is considered more likely to be successful.
To accomplish the result of modelling the correlations
between continuous data points, it is important to
consider the way that wind time series prediction
operates. An accurate prediction of very short-term
windspeed can be achieved by using only the time series
of previous points measured at a location [14]. This
shows that there must be some characteristic of the
inputs that makes the prediction possible. The only
information available in the input stream is the wind
vector magnitude, the vector orientation (ie North/South
or West/East) and the data point separation. The last two
characteristics are implicitly known as they are constant.
The wind vector magnitude is the only useful
information, as constant characteristics provide no
further information once declared. This means that an
input pattern of magnitudes must provide sufficient data
to predict the next point. The single previous vector
value is of some use (as shown by persistence).
However, the fact that better predictions are possible
shows that the change from data point to data point must
have a correlated relationship. This relationship cannot
be produced with the usual probabilistic model design.
Fig. 4 shows the recorded data at a wind site in
Tasmania, during Spring. It shows that westerlies are
the predominant wind pattern, but also has a large
reading at zero windspeed. The shape of the histogram
approximates a distorted Gaussian distribution. This
raises two issues with probabilistic data creation.
Firstly, the unusual shape (while supported by real data)
shows a level of unpredictability. The likelihood of a
weak westerly is low, yet the likelihood of a zero (or
very close to zero) reading is high. These noncontinuities are a problem that must be overcome to
attain an accurate prediction. Using more data to better
represent the histogram would be desirable, but there is
not always more data available. The second, and more
serious, concern is that if this histogram was used to
develop data, there would be no correlation between
time t and t+1. The chance of a 4m/s westerly being the
next reading, at t+1, would be equally likely whether the
present reading, t, is –5m/s, 5m/s or even 20m/s. This
does not represent the true behaviour of wind.
windspeed. The shape of this histogram is consistent,
with no unusual spikes on the curve. Even though the
data that Fig. 4 and Fig. 5 were derived from was the
same, the two histograms are significantly different. The
most common differenced values occur more than twice
as frequently as the most common values from the
original data. Thus, the histogram is more representative
through a higher concentration of data and hence is more
reliable. If the current windspeed is –5m/s, the chance
of the next value being 4m/s (a change of 9m/s) is
extremely unlikely. The most likely result is that either a
small change (or no change) would occur.
Fig. 5. ‘Difference’ histogram using same data as Fig. 4.
To create data using a difference histogram, the initial
point would have to be randomly chosen based upon the
recorded data histogram. This is done through creating a
cumulative probability density function (PDF), shown in
Fig. 6. A random number is generated and used as the yvalue this is then cross-referenced to the x-axis, which
provides the result. For the purposes of this example,
consider the initial generated point to be x(t). The next
point would be created using the cumulative PDF of the
differenced data histogram, shown in Fig. 6 as the dotted
trace. The output in this instance would be added to the
value of x(t) to create x(t+1). This would be repeated to
create x(t+2) and continued until the desired input
pattern length was achieved. An example of such an
input pattern is shown in Eq. 1.
X = [x (t ) x (t + 1) x (t + 2 ) x (t + 3)]
(1)
Fig. 6. Cumulative probability density functions
for the histograms in Fig. 4 and Fig. 5.
Fig. 4. West/East histogram of recorded values
from a windsite in Tasmania, during Spring.
Fig. 5 is derived from the same data as Fig. 4, but instead
presents the difference between one point and the next.
The result is an almost perfect Laplacian distribution
showing a strong likelihood for little or no alteration in
4.1.
MODEL WITH M ULTIPLE H ISTOGRAMS
The previous section shows that a difference histogram
will produce better results when modelling a time series
in a probabilistic data creation method. However, even
this is not ideal. One of the key features of many time
series data sets is that over the data range the spectral
density is not consistent [17]. The more information that
can be separated out from the raw data, the better the
probabilistic model will replicate the real data.
One of the key features of wind is that because it is
generally a stochastic process, the behaviour of the wind
is not consistent over the range. However, consultation
with experts revealed that a large change when the
windspeed is low is less likely than when the windspeed
is high. This is because high windspeeds tend to be
more gusty than low windspeeds. This was examined by
creating a set of histograms over the range of
windspeeds. The resultant histograms showed that the
wind was indeed more erratic at the higher windspeeds,
as shown in Fig. 7.
available wind turbines has a power output that is
approximately represented by the curve shown in Fig. 9.
There other factors such as air density and turbine-blade
inertia and momentum. For very short-term data blade
inertia/momentum can cause significant differences in
the expected power output compared with the actual
power output. The inertia and momentum also perform
a smoothing effect; as the power output cannot change as
rapidly as the wind changes.
Fig. 9. Rating curve for Vestas V66 1.75MW turbines.
4.2.
Fig. 7. Aggregated histograms over the entire
windfarm within different windspeed limits.
Fig. 7 shows a number of histograms aggregated across
an entire windfarm. The location of the windsite and
actual values are withheld as the data is commercially
sensitive. Even so, the results express the increased
variability of wind data. As the windspeed boundaries
increase, the histogram widens. This means that in the
data set used, windspeeds over 18m/s were
approximately three times as variable as windspeeds
under 3m/s. The largest difference in variability comes
from the ability for wind to swiftly reduce. Another
indicator of the stochastic nature of wind is
demonstrated by considering multiple traces from
different towers superimposed upon each other. An
example of this is shown in Fig. 8. The left plot has the
same number of towers, and hence traces, as the right
plot. However, the plot for lower windspeeds overlap
more tightly showing that the behaviour of the wind is
more consistent across the windfarm at lower
windspeeds than it is at higher windspeeds.
P OWER O UTPUT H ISTOGRAMS
To examine the characteristics of power output (rather
than windspeed) a second set of histograms were
developed. These histograms showed similar trends to
the wind patterns. However, the power output curves
have some differences, as shown in Fig. 10. Curves up
to 900kW are very even traces and make almost perfect
Laplacian distributions – whereas the windspeed
histograms were not so consistently shaped. Also the
windpower histograms from 900kW to 1500kW all have
similar shaped traces. The last (and possibly most
important) difference is for the highest histogram
bracket. For windspeed the highest histogram was
erratic and broad, indicating a wide variability. The
windpower histogram for the highest range histogram is
in fact very narrow. The reason for this is because of the
shape of the power rating curve for the wind turbines,
see Fig. 9. Any windspeed over 15m/s will produce the
same power output. Thus, if the windspeed stays above
this limit, even if the wind is changing, the output will
remain constant (or at least close to constant).
Fig. 8. Histograms for low and high windspeeds.
The variability of windspeed has clear ramifications on
the power output from a turbine. One of the comercially
Fig. 10. Aggregated histograms over the entire
windfarm within different windpower limits.
5.
RESULTS
When modeling a windpower site, it is possible to see
that higher windspeeds produce greater variability. This
must be considered when generating data for windpower
prediction purposes. Other results that have been found
from this research show that at low windspeeds, the
histograms for towers on the same site vary only
slightly; while at higher windspeeds the variation
between towers is accentuated. A larger data sample,
would provide more values at the higher windspeeds,
possibly resulting in more similar histograms. However,
as shown in Fig. 8, the results from the different towers
may not overlap for high windspeeds, but they do still
follow the same approximate Laplacian shape.
The third conclusion this paper draws is that power
output histograms are smoother and more consistent than
the corresponding windspeed histograms. This supports
the hypothesis that the inertia and momentum of the
turbines blades have a smoothing effect at short-term
intervals. Furthermore, the highest windspeeds (where
the wind is least predictable) are less variable as the
power output is limited above 15m/s. The histogram
curves from 900kW to 1500kW are also similar,
meaning that these could be combined into a single
histogram for data generation purposes – simplifying the
design.
6.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
CONCLUSIONS
Accurate wind prediction is vital for power system
operation; especially given the growth of wind energy
penetration. However, there is no very short-term wind
prediction package commercially available [11]. There
are promising systems available [14], but to be able to
use site averages or total site power output requires
either an extremely severe quality assurance program for
data collection or many years worth of data. Thus, often
the desired data is simply not available. This means that
the data must be generated. The usual approach to data
generation would not model a wind time series
sufficiently well, so instead a more detailed system
design must be used.
The research, reported in this paper, indicates that
generating data that accurately represents possible time
series patterns for a windfarm is best done considering
the power output. However, this approach needs to use
multiple histograms to model the variation of the wind
driving the turbine. The data developed can then be used
for system studies, simulation and/or training of
adaptive/learning algorithms for prediction purposes.
[9]
[10]
[11]
[12]
[13]
[14]
ACKNOWLEDGMENT
The authors would like to thank Hydro Tasmania for
their collaboration and provision of time series data for
our research on power system prediction models.
Specific thanks go to Kieran Jacka, Roger Allen, Mico
Skoklevski, Robert Stewart and Gerard Flack for their
personal assistance in the research.
View publication stats
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