The motivation for this work is the study and prediction of wind ramp events occurring in a large-scale wind farm located in the US Midwest. In this paper we introduce the SHREA framework, a stream-based model that continuously learns a discrete HMM model from wind power and wind speed measurements. We use a supervised learning algorithm to learn HMM parameters from discretized data, where ramp events are HMM states and discretized wind speed data are HMM observations. The discretization of the historical data is obtained by running the SAX algorithm over the first order variations in the original signal. SHREA updates the HMM using the most recent historical data and includes a forgetting mechanism to model natural time dependence in wind patterns. To forecast ramp events we use recent wind speed forecasts and the Viterbi algorithm, that incrementally finds the most probable ramp event to occur. We compare SHREA framework against Persistence baseline in predicting ramp events occurring in very short-time horizons.
Ramping is one notable characteristic in a time series associated with
a drastic change in value in a set of consecutive time steps. Two
properties of a ramping event i.e. slope and phase error, are important
from the point of view of the System Operator (SO), with
important implications in the decisions associated with unit commitment or
generation scheduling. Unit commitment decisions must prepare the
generation schedule in order to smoothly accommodate forecasted
drastic changes in wind power availability [
The development of the SHREA framework is the answer to the three main issues available in ramp event forecasting. How can we describe and get insights on the wind power, and wind speed, timedependent dynamic and use this description to predict short-time ahead ramp events? How can we combine real valued historical wind power and speed measurements and Numerical Weather Predictions (NWP), specially wind speed predictions, to output reliable real-time predictions? How can we continuously adapt SHREA to accommodate different natural weather regimes yet producing reliable predictions?
To answer these questions we designed a stream-based framework
that continuously learns a discrete Hidden Markov Model (HMM)
and uses it to generate predictions. To learn and update the HMM the
SHREA framework uses a supervised strategy whereas the HMM
parameters are estimated from historical data, the state transitions
probabilities are estimated from wind power measurements and the
emission probabilities, at each state, are estimated from wind speed
observations. To estimate the state probability transitions, first, we
combine a ramp filter, a derivative alike filter, and a user-defined
threshold to translate the real-valued wind power time series into
a labeled time-series, coding three different types of ramp events:
ramp-up, no-ramp and ramp-down. Then, the transitions occurring
in this labeled time series are used to estimate the transitions of the
Markov process hidden in the HMM, i.e., to model the transitions
between the three states associated with the three types of ramp events.
To learn the HMM emission probabilities, first we combine a ramp
filter and the SAX algorithm [
When we analyze wind power historical data we observe both seasonal weather regimes and short-time ahead dependence of the recent past wind power/speed measurements. Thus, to accommodate these issues, in SHREA we included a strategy that forgets old weather regimes and continuously updates the HMM with the most recent measurements, both wind power measurements and wind speed measurements.
To generate ramp event predictions occurring in short-time ahead
window we use the wind speed forecast, obtained from a major NWP
provider, and the current HMM. First, we run a filter over the wind
speed forecast signal to obtain a signal of wind speed variations.
Next, we run the SAX algorithm to translate the resulting real-valued
time series into a string. Then, we run the Viterbi algorithm [
It is important to observe that wind speed measurements and forecasts, mainly short time horizon predictions, are approximately equally distributed over time. Moreover, the wind power output of each turbine is related to wind speed measurements.
In this work we run the SHREA framework to describe and predict
very short-time ahead ramp events occurring in a large-scale wind
farm located in the US Midwest. We present a comparison against
the Persistence model that is known to be hard to beat in short-time
forecasts [
Despite the difficulty of the ramp forecasting problem, in this work we make the following contributions: Develop a stream-based framework that predicts ramp events and generates both descriptive and cost-effective models; Introduce a forgetting mechanism so that we can learn a HMM using only the most recent weather regimes; Use wind speed forecasts as observations of a discrete HMM to predict short-time ahead ramp events.
In the next Section we introduce the ramp event forecast problem. In Section 3 we present a detailed description of our framework. In Section 4 we present and discuss the obtained results. Last, we present some conclusions and present future research directions. 2
One of the main problems in ramp forecasting is how to define a
ramp. In fact, there is no standard definition [
The authors in [
In [
Definition 1 A ramp event is considered to occur at time point t, the end of an interval, if the magnitude of the increase or decrease in the power signal is greater than the threshold value, the Pref : | P (t) − P (t − Δt)| > Pref
The parameter Δt is related to the ramp duration and defines the
size of the time interval considered to identify a ramp. In [
A comprehensive analysis of ramp modeling and prediction may
be found in [
input : Three time series: PT , wind power measurements; OT , wind speed measurements; and JT , wind Speed forecasts; a, the forecast horizon; Pref , threshold to identify ramp events; Δt, the ramp definition parameter; W, the PAA parameter that specifies the amount of signal aggregation; σ, a forgetting factor output: A sequence of predictions Qrd . . . Qrd+a for each period/window d = 1, . . . fcoor ueanchtpTeriimod/ewPindeorwidoddos ← 0; flag ← 0; Acount ← 0; Bcount ← 0; countT imeP eriods + + Preprocessing Psd ← fitSpline(Pd), Osd ← fitSpline(Od), Jsd ← fitSpline(Jd) Pfd ← rampDef(Psd, Δt), Ofd ← rampDef(Osd, Δt), Jfd ← rampDef(Jsd, Δt) Ld ← label(Pfd , Pref ); // Label Data Odn ← znorm(Ofd ), Jdn ← znorm(Jfd ) Osdtr ← SAX(PAA(Odn)), OFsdtr ← SAX(PAA(Jdn)) Learn Supervised HMM π ← (δ(Ld(r) = rampDown), δ(Ld(r) = noramp), δ(Ld(r) = rampUp)) λd(A, B, π) ← LearnHMM(Osdtr (1, . . . , r), Ld(1, . . . , r), Acount, Bcount) Predict Ramp Events using the learned HMM Qrd . . . Qr+a ← V iterbi(λ, OFsdtr(r + 1, . . . , r + a))
d λd(A, B, π) ← updateHMM(Osdtr(r + 1, . . .), Ld(r + 1, . . .)) Forgetting mechanism if (countTimePeriods==σ) then
Acaouuxnt ← Acount; Bcaouuxnt ← Bcount; flag ← 1 if (countTimePeriods mod σ == 0 & flag==1) then
Acount ← Acount − Acaouuxnt; Bcount ← Bcount − Bcaouuxnt 3
In this section we present SHREA framework, a stream-based framework that uses a supervised learning strategy to obtain a HMM. SHREA continuously learns a discrete HMM on a fixed size nonoverlapping moving window and, at each time period, uses the updated HMM to predict ramp events. We introduce a forgetting mechanism to forget old wind regimes and to accommodate weather global changes. The SHREA architecture has three main steps (see algorithm pseudo-code in Algorithm 1): preprocessing phase, where a ramp filter and the SAX algorithm are used to translate real valued signals into events/strings; learning phase, where a supervised strategy is used to learn a HMM; and prediction phase, where the Viterbi algorithm is used to forecast ramp events. In the following lines we describe each one of these phases. 3.1 Preprocessing In the preprocessing phase we translate the real-valued points occurring in a given time period d, i.e. occurring inside a non-overlapping fixed size window, into a discrete timeseries suitable to be used at HMM learning and prediction time. First, we fit a spline to both the wind power and wind speed measurements time series obtaining, respectively, two new signals, Psd and Os . We d run the same procedure over J time series, a wind speed forecast, and d obtain Js . We fit splines to the original data to remove high frequencies that can be considered noisy data. Second, we run ramp definition one, presented above in Section 2, to filter the three smoothed signals and obtain three new signals: Pf , Ofd and Jf . These signals d d are wind power and speed variations, derivative alike signals, suitable to identify ramp events. Third, we use a user-defined power variation threshold, the input parameter Pref value, to translate the wind power signal Pfd into a labeled time series Ld(1, . . . , r + a), where 1 is the first point of the time window, r is the forecast launch time and a is the time horizon. We map each wind power variation into one of three labels/ramp events: ramp-up, ramp-down and no-ramp. These three labels will be the three states of our HMM and the transitions will be estimated using the points of the Ld time series.
At this point we already have the data needed to estimate the
transitions of the Markov process hidden in the HMM process. Now we
need to transform wind speed data into a format suitable to estimate
emission probabilities of the discrete HMM that we are learning. We
combine Piecewise Aggregate Approximation (PAA) and SAX
algorithms [
In the HMM that we learn, compactly written λ(A, B, π), the
state transitions, the A parameter, are associated with wind power
measurements and the emissions probabilities, the B parameter, are
associated with wind speed measurements. In Figure 2 we show a
HMM learned by SHREA at the end of the 2010 winter. To estimate
these two parameters we use the ramp labels, Ld(1, . . . , r), and the
d
wind speed mesurements signals, Ostr(1, . . . , r), and run the
wellknown and straightforward supervised learning algorithm described
in [
We now explain how to update the model in the time. We design our framework to improve over the time with the arriving of new data. At each time period d SHREA is fed with new data and the HMM parameters are updated to include the most recent historical data. At each time period d we update the HMM parameters by counting the state transitions and state emissions coded in the current vectors Osdtr(1, . . . , r) and Ld(1, . . . , r), obtaining the number of state transitions and emissions at each HMM state, the Acount and Bcount. Then, we compute the marginal probabilities of each matrix and obtain the updated HMM, the model λd(Ad, Bd, πd) that will be used to predict ramp events. The learned HMM, λd, will be used to predict ramp events occurring between r and r + a. In the next time period (i.e. the next fixed sized time window) we will update the λd HMM, using this same strategy but including also the transitions and emissions of the time period d that were not used to estimate λd, i.e., we update Acount and Bcount with the wind measurements of the time period d occurring after d’s launch time and before d + 1 period launch time, the r point. By using this strategy we continuously update the HMM to include both the most recent data and all old data. By using this strategy, and with the course of time, the HMM can become less sensitive to new weather regimes. Thus we introduce a forgetting strategy to update the HMM using only the most recent measurements and forgetting the old data. This strategy relies on a threshold that specifies the number of time periods to include in the HMM estimation. This forgetting parameter, σ, is a user-defined value that can be set by experienced wind power technicians. Considering that at time period d we have read σ time periods and that we backup the current counts into Acaouuxnt and Bcaouuxnt temporary matrices. After reading 2σ time periods we will use the following forgetting mechanism: Ac2oσunt = Acount − Acaouuxnt and Bc2oσunt = Bc2oσunt − Bcaouuxnt.
2σ Then, we reset Acaouuxnt and Bcaouuxnt equal to the updated Acount and 2σ Bc2oσunt matrices, respectively. Next, to predict ramp events occurring in the time periods following 2σ, we will update and use the HMM parameters obtained from the Ac2oσunt and Bc2oσunt to forecast ramp events. Every time we read a number of time periods that equals a multiple of σ we apply this forgetting mechanism using the updated auxiliary matrices.
we use the HMM learned in time period d, the λd, and the string d Jstr, obtained from wind speed forecasts, to predict ramp events for the time points ranging from r to r + a. Remember that r is the prediction launch time and a is the forecast horizon.
To obtain the ramp event predictions we run the Viterbi
algorithm [
d d d
Regarding the π parameter, we introduce a non classical approach to estimate this parameter. We defined this strategy after observing that it is almost impossible to beat a ramp event forecaster that predicts the ramp event occurring one step ahead to be the current observed ramp event. Thus, we set π to be a distribution having zero probability for all events except the event observed at launch time, the r time point. In the pseudo code we write π ← (δ(Ld(r) == rampDown), δ(Ld(r) == noramp), δ(Ld(r) == rampU p),) where δ is a Dirac delta function defined by δ(x) = 1, if x is T RU E and δ(x) = 0, if x is F ALSE. 4
In this section we describe the configurations, the metrics and the results that we obtain in our experimental evaluation. b c
Costs 1:
ed down itcd no re up P
events in a large-scale wind farm located in the US Midwest. To
evaluate our system we collected historical data and, to make
predictions, use wind speed power predictions (NWP) for the time
period ranging between 3rd of June 2009 and 16th of February 2010.
Each turbine in the wind farm has a Supervisory Control and Data
Acquisition System (SCADA) that registers several parameters,
including the wind power generated by each turbine and the measured
wind speed at the turbine, the latter are 10 minute spaced point
measurements. In this work we consider a subset of turbines and
compute, for each time point, the subset mean wind power output and
the subset mean wind speed, obtaining two time series of
measurements. The wind speed power prediction for the wind farm location
was obtained from a major provider. Every day we get a wind speed
forecast with launch time at 6 am and having 24 hours horizon. The
predictions are 10 minute spaced point forecasts. In this work we
run SHREA to forecast ramp events occurring 30, 60 and 90
minutes ahead, the a parameter. We start by learning a HMM using five
days of data and then use the learned, and updated, HMM to
generate predictions for each fixed size non overlapping time window.
Moreover, we split the day in four periods and run SHREA to learn
four independent HMM models: dawn, period ranging between zero
and six hours; morning, period ranging between six to twelve hours;
afternoon, period ranging between twelve and eighteen hours; nigh,
period ranging between eighteen and midnight. The last four models
were only used to give some insight on the ramp dynamics and were
not used to make predictions. We define a ramp event to be a change
in wind power production higher than 20% of the nominal capacity,
i.e., we set the Pref threshold equal to 20% of the nominal capacity.
Moreover, we run a set of experiments by setting Δt parameter equal
to 1, 2 and 3 time points, i.e., equal to 30, 60 and 90 minutes. We run
SHREA using thirty minute signal aggregation, thus each time point
represents thirty minutes of data. In these experiments we also
consider phase error corrections. Phase errors are errors in forecasting
ramp timing [
Furthermore, as SHREA is continuously updating the HMM, we set the forgetting parameter σ = 30, i.e., each time the system reads a new period of 30 days of data, the system forgets 30 days of old data. The amount of forgetting used in this work results from a careful study of the wind patterns.
For this configuration we compute and present the Hanssen &
Kuippers Skill Score (KSS) and the Skill Score (SS) [
In Figure 2 we present an example of HMM generated by SHREA in February. This model was learned when running SHREA to predict 90 minutes ahead events and setting Δt = 2. This HMM has three states, each state is associated with one ramp type, and each state emits six symbols, each representing a discrete bin of the observed wind speed. The lower level of wind speed is associated with the a character and the higher level of wind speed is associated with the f character. The labels in the edges show the state emissions and the state transition probabilities.
The HMM models that we obtained in our experiments uncover
interesting ramp behaviors. If we consider all the data used in these
experiments, when we set Δt = 1 we found that there were
detected 7% more ramp-up events than ramp-down events. When we
set Δt = 3 we get the inverse behavior, we get 4% more
rampdowns than ramp-ups. This behavior is easily explained by the wind
natural dynamics that causes steepest ramp-up events and smooth
ramp-down events. If we analyze independently the four periods of
the day we can say that we have a small number of ramp events,
both ramp-ups and ramp-downs, in the afternoon. If we compute the
mean number of ramps, for all Δt parameters we get approximately
30%(15%) more ramp-up(ramp-down) events at night than in the
afternoon. Overall, we can say that we get more ramp events at night
and, in second place, at the dawn period. Moreover, we can say that
in the summer we get, both for ramp-up and ramp-down events, wind
speed distributions with higher entropy, we get approximately 85%
of the probability concentrated in two observed symbols. Different
from this behavior, in the winter we have less entropy in the wind
speed distribution associated with both types of ramp events. In the
winter we have approximately 91% of the probability distribution
concentrated in the one symbol. The emission probability
distribution of the ramp-down state is concentrated in symbol a and the
emission probability distribution in the ramp-down state is concentrated
in symbol f. These two findings are consistent with our empirical
visual analysis and other findings [
As is illustrated in Figure 2 we identified a large portion of selfloops, especially ramp-up to ramp-up transitions in the winter nights. The percentage of self-loops range between 12%, when we run SHREA with Δt = 1, and 55% when we set Δt = 3. This self-loop transition shows that we have a high percentage of ramp events having a magnitude of at least 40% of the nameplate, two times the Pref threshold. Furthermore, in the winter we get a higher proportion of ramp-up to ramp-down and ramp-down to ramp-up transitions than in the summer. This is especially clear at the dawn and night periods. This phenomena can be related with the difference in the average temperatures registered in these time periods.
Before presenting the forecast performance, it must be said that the quality of ramp forecasting depends a great deal on the quality of meteorological forecasts. Moreover, as the HMMs represent probability distributions it is expected that SHREA will be biased to predict no-ramp events. Typically SHREA over predicts no-ramp events but makes less severe errors. This biased behavior of SHREA is an acceptable feature since it is better to forecast a no-ramp event when we observe a ramp-down(ramp-up) event than predicting a rampup(ramp-down) event. In real wind power operations (see Table 1) the cost of the later error is several times larger than the former errors.
In Table 2 we present the mean (inside brackets we present the associated standard deviation) KSS, SS and Expected Cost metrics that we obtained when running SHREA, and the reference model, to predict ramp events occurring in the last hundred days of the evaluation period.
Before presenting a detailed discussion of the obtained results, we must say that, if we consider the same Δt parameter, in all experiments we obtained better, or equal, results than the baseline algorithm, the Persistence algorithm. Moreover, we must say that when we generate predictions for the 30 minute horizon (one time point ahead, since we use 30 minutes aggregation) we get the same results as the Persistence model. This phenomena is related with the strategy that we used to define the HMM initial state distribution. Remember that we set the HMM π parameter equal to the last state observed.
As expected, the KSS results worsen with the increase of the time horizon. It is well known that the forecast reliability/fit worsens as the distance from the forecast launch time increases. Moreover we can say that we obtained better KSS values for the morning period than in the other three periods of the day. For lack of space we do not present a detailed description of the results that we obtain when we run SHREA to predict ramp events occurring in each one of the four periods of the day. This can be related with the wind speed forecasts launch time. The wind speed forecast that we use in this work is updated every day at 6 am.
The analysis of the Δt parameter shows that the mean KSS values increase with the increase in the Δt value. Again, this can be explained by the wind patterns, typically the wind speed increases smoothly during more than 30 minutes. In Table 2 we can see clearly that SHREA performance improves with the increase in Δt parameter. We observe the same behavior when inspecting the results that we obtained by running the Persistence algorithm. Concerning the SS, we can see that we obtain improvements over the Persistence forecast that ranges between 0% and 16%.
Concerning the phase error technique, we get important improvements for the two phase error parameter values considered in this study. The amount of improvement that we obtained by considering the phase error can be valuable in real time operations. The technicians can prepare the wind farm to deal with a nearby ramp event. In Table 2 we present the results without considering the phase error technique, phE = 0, and considering one time point (30 minutes), phE = 1, and two time points (60 minutes), phE = 2, phase errors corrections.
We also introduce a misclassification cost analysis framework that can be used to quantify the management decisions. We define a misclassification cost scenario (see Table 2) and show that SHREA produces valuable predictions. In this real scenario, SHREA generates significant lower operational costs and better operational performance than the baseline model.
In this work we obtained some insights on the intricate mechanisms hidden in the ramp event dynamics and obtain valuable forecasts for very short-time horizons. For instance, we can now say that steepest and large wind ramps tend to occur more often in the winter. Moreover, typically there is a rapid wind speed increase followed by a more gradual wind speed decrease. Overall, with the obtained HMM models we both obtained insights on the wind ramp dynamics and generate accurate predictions that prove to be cost beneficial when compared against a Persistence forecast method.
The performance of SHREA is heavily dependent on the wind speed forecasts quality. Thus, in a near future we hope to get special purpose NWP suitable to detect ramp events and having more frequent daily updates. Moreover, we will study multi-variate HMM emissions to include other NWP parameters like wind direction and temperature.
Acknowledgments: This manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne“). Argonne, a U.S. Dep. of Energy Office of Science laboratory, is operated under Contract No. DE AC02-06CH11357. The authors also acknowledge EDP Renewables, North America, LLC. This work was is also funded by the ERDF - through the COMPETE programme and by National Funds through the FCT Project KDUS.