[ieee 2012 ieee international conference on power and energy (pecon) - kota kinabalu, malaysia...

Probabilistic wind speed forecast for wind power

prediction using pseudo ensemble approach

Sultan Al-Yahyai , Adel Gastli

Department of Electrical & Computer Engineering

Sultan Qaboos University

Muscat, Oman

[email protected], [email protected]

Yassine Charabi

Department of Geography

Sultan Qaboos University

Muscat, Oman

[email protected]

Abstract— Accurate wind forecast at a wind farm is an essential

process in wind energy industry and marketing. Numerical

Weather Prediction (NWP) models can be used but they provide

wind forecast as a single value for a given time horizon.

Therefore, forecasting wind speed as a deterministic value

doesn’t represent the uncertainty of the wind speed forecast.

Ensemble NWP forecast can be used to calculate the probability

of occurrence of different wind speeds classes. The main

disadvantage of this approach is the extensive computational

resources required to run multiple copies of the NWP model.

This paper, explores the possibility of using pseudo ensemble

method for generating probabilistic wind forecast for wind farm

applications. The proposed method utilizes the spatial and

temporal neighborhoods of the forecast point to generate forecast

dataset and then calculate the required probabilities. A case

study using the proposed method is tested and validated using

wind data from NWP model and measurements from three ground weather stations in Oman.

Keywords- probabilistic forecast; pseudo ensemble; wind speed;

Oman

I. INTRODUCTION

Due to the cubic relation between wind speed and theoretical power contents of the wind, it is necessary to accurately estimate the future wind speed at wind farm site. Accurate wind forecast is needed by wind farm developers and operators. It is used to ensure high security of supply [1] in term of optimizing the scheduling of conventional power plants, optimizing the value of produced electricity in the market and planning the maintenance ‎[2].

There are two main stages in wind power forecast [3]. The first‎stage‎is‎the‎“meteorological”‎stage,‎where‎the‎wind‎speed‎is forecasted at the farm site for different time horizons. The second‎stage‎is‎the‎“energy‎conversion”‎stage,‎where‎the‎wind‎speed information is transformed to power for the whole wind farm. The better the wind forecast the better the estimate of the generated power can be performed.

Numerical Weather Prediction (NWP) Models are used among others to provide the wind forecast in the “meteorological”‎stage‎‎[4]. However, since they predict single value of wind speed at a given space and for a given time, they are considered as a deterministic forecasting tool.

Different NWP models such as HIRLAM in[5], ECMWF in [6] and COSMO in [7] were used to forecast wind condition for different sites. Based on the available computational resources, different model resolutions were used. Using the conventional deterministic NWP model forecast, NWP wind forecast is extracted for a single grid point (deterministic) that corresponds to the wind farm site ‎[8]. NWP models forecast wind condition at different vertical layers which are not necessarily‎ matching‎ the‎ wind‎ farm’s‎ turbines‎ hub‎ height.‎Therefore, the second step is to conduct local site refinement according to the hub heights and the site roughness.

It is well known that NWP models have systematic bias[4]. As a result, statistical calibration is performed using long-term historical site observations. Wind speed forecast is converted to power‎using‎turbine’s‎power‎curve.‎The‎forecasted‎power‎of‎a‎single turbine is then aggregated to represent the whole wind farm [9]. Finally, single representative wind farm is used to conduct regional upscaling and generate power prediction for a group of wind farms [10].

As described earlier, that NWP model forecast is deterministic by its nature. This represents a limitation, especially, for wind energy applications since no information is provided about the possible variation from the expected value [11]. Hence, precautionary action planning is limited [12]. In addition to the chaotic nature of the atmosphere, the intermittent behavior of the wind is subject to seasonal and diurnal cycles. Therefore, forecasting wind speed as a single (deterministic) value for a given time horizon does not provide the uncertainty of the wind speed forecast. Besides, when trading future production on electricity market, the use of probabilistic forecast can lead to higher benefits than those obtained by deterministic forecast [12]. Therefore, it is important to develop techniques to transform the wind speed forecast from deterministic to probabilistic domain. Among these techniques we can find the prediction error, ensemble forecast, poor man ensemble forecast and pseudo-ensemble method.

The prediction error approach is a simple technique to provide added value to the deterministic forecast through adding information about the historical deviation of the model forecast from the measurements‎ [13]. Simple evaluation scores such as standard deviation and root mean square error (RMSE)

2012 IEEE International Conference on Power and Energy (PECon), 2-5 December 2012, Kota Kinabalu Sabah, Malaysia

978-1-4673-5019-8/12/$31.00 ©2012 IEEE 127

are used. The need for long-term data set to evaluate the systematic errors is the main disadvantage of this approach.

The ensemble forecast is the most direct approach to calculate the probability of certain event to occur from a set of possible events and scenarios [1][14]. It has been used in [4],[10] and [15] to provide probabilistic wind forecast for different wind farms in Europe. Ensemble forecast describes the possible physical state of the atmosphere through different possible NWP models, initial states and boundary conditions ‎[12].‎The‎Ensemble‎member’s‎ forecast‎ is‎ sampling‎the distribution of expected event. Disagreement between the member’s‎ forecasts‎ represents‎ a‎ quantitative‎ estimate‎ of‎ the‎uncertainty in the prediction [16]. On the other hand, the main disadvantages of this approach are the extensive computational resources required to run multiple copies of the NWP model and the amount of data generated by the models that require exclusive management.

The poor man ensemble forecast ‎ was used as a workaround method to overcome the computational requirement of the ensemble forecast approach [17]. The main idea is to use the overlapping runs of the NWP model from different starting times for given point in time to form the ensemble members. The main disadvantage of this approach is that the forecast quality degrades with time.

The pseudo-ensemble method was also proposed to overcome the computational requirement of the ensemble forecast for precipitation prediction [18]. The pseudo ensemble is based on spatial-temporal neighborhoods of the model forecast for certain site. The pseudo ensemble was used to describe the uncertainty in the precipitation forecast and provides low cost and online prediction. So far, this method is not yet used for wind speed forecast.

This paper presents an improvement to the pseudo-ensemble method that was initially used for precipitation forecast and explores the possibility of using it for generating probabilistic wind forecast for wind power applications. A case study using the proposed method is tested using wind data from NWP model and measurements from three weather stations in Oman. The rest of this paper is organized as follows. Section 2 describes the proposed method. The case study is presented in section 3. Finally, section 4 concludes the paper.

II. PROPOSED APPROACH

Beside the improvement on the forecast quality, height resolution‎ model’s‎ forecast‎ does‎ not‎ necessarily‎ match‎ the‎observation at any particular grid point. Small shift in time or space can cause large difference in the validation scores for certain observation point. Therefore, spatial model validation [19][20] was introduced to consider spatial patterns validation than single point-to-point approach. In addition, probability of certain event to occur at specific location can be judged subjectively by experienced forecasters. They look to the model output around the location and based on the forecast patterns the probability is judged. This natural behavior is based on that high resolution model forecast is not taken as a fact but rather as a guidance of what may happen around certain location and time.

Therefore, the proposed approach looks into the Spatio-Temporal neighborhood of a grid point (location) to get a set of possible wind forecasts. Then, it uses this set to derive probabilistic forecast for that specific location. One major issue to address in this approach is the size of the Spatio-Temporal neighborhood. Spatial neighborhood is expressed in multiples of model‎ horizontal‎ resolution‎ (Δx)‎ while‎ temporal‎neighborhood is expressed in multiples of model output frequency‎(ΔT).

Figure 1 shows the Spatio-Temporal neighborhood representation for grid point (x0,y0) at forecast time horizon T0. Figure 1 (A), shows the spatial neighborhood in (x,y)-plane with‎ neighborhood‎ (shaded)‎ size‎ of‎ (3Δx).‎ The‎ Temporal‎neighborhood‎ (3ΔT)‎ is‎ shown‎ in‎part‎ (B)‎ in‎ (x,t)-plane. Both spatial and temporal neighborhoods are combined in part (C).

In [18], fixed size of Spatio-Temporal neighborhood was used to generate precipitation probabilistic forecast for the whole domain. Three different configurations were presented namely small, medium and large. Small configuration is with neighborhood‎ size‎ of‎ (6Δx-3ΔT),‎medium‎with‎neighborhood‎size of‎(12Δx-4ΔT)‎and‎large‎configuration‎with‎neighborhood‎size‎of‎(20Δx-6ΔT).

Based on verification results such as in [21] of different models, it is known that quality of model forecast vary from one location to another based on different factors such as the initial condition of the model and the complexity of the topography surrounding the location. Therefore, it is believed that fixed neighborhood size is not the best choice. In this paper, it is proposed to use site dependent neighborhood size.

Specific analysis for each site is required to determine the optimum neighborhood size. Figure 2 shows the proposed procedure to select the optimum neighborhood size for each site. The selection is based on the Brier score (BS) which is essentially the mean square error of the probabilistic forecast [22] as represented in eq. (1). Where yk is the forecast probability and ok is the observed probability.

For each site, the idea is to select the spatial and temporal

dataset combination that gives the better BS compared to that

of the deterministic model. Therefore, the probability of

different wind classes to occur in measurements, deterministic

forecast and different spatial and temporal neighborhood size’s‎ datasets‎ are‎ calculated.‎ For‎measurements,‎ ok=1 if the

event occurs and ok=0 otherwise. Similarly, for deterministic

forecast, yk=1 if the event occurs and yk=0 otherwise.

Neighborhood sizes that give the optimum average BS is selected for both spatial and temporal datasets. Then, the

datasets of both optimum spatial and temporal neighborhood

sizes are combined to form the optimum dataset (pseudo

ensemble) for that specific site. This procedure is repeated for

each wind farm site.

Using this approach, the NWP data are not extracted for the

site location grid point only as in the deterministic approach,

but also for the surrounding area based on the optimum

neighborhood size.


128

Figure 1: Spatio-Temporal neighborhood representation

Figure 2: Dataflow diagram for selecting the best Spatio-Temporal neighborhood size

Site measurements dataset

Calculate probability of each wind class

Select the best spatial

neighborhood with best

average score

Deterministic forecast dataset

Spatial neighborhood datasets for different

neighborhood sizes

Temporal neighborhood datasets for different neighborhood sizes

Brier score for

probabilistic forecast

Select the temporal

neighborhood size with best

average score

Combine the datasets for both spatial and

temporal neighborhoods

Calculate probability of each wind class for the new dataset

(A) (B)

(C)


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Local refinement is still needed to provide the wind forecast at

the hub height for the whole neighborhood dataset. Wind

speed for the whole dataset is then converted to power using

the wind turbine power curve. The next step would be the

probability calculation for different power or wind classes

from the dataset. Since the approach is applied on large dataset, data representation is an important step. Box-plot and

Probability Density Functions (PDF) are the most common

representation for probabilistic information. Box-plot

describes the dataset distribution and then the uncertainty of

the forecast can be judged. PDFs are used to represent the

probability of occurrence for each wind and power class.

III. CASE STUDY

The main objective of this case study is to illustrate and

validate the proposed approach for probabilistic wind

prediction. The approach is illustrated and validated over three

weather stations in Oman. Currently there is no wind farm in

Oman; therefore the approach is validated using the wind speed data measured at three different weather stations. The

three selected weather stations are located in the mostly

suitable sites for future wind energy applications in Oman

(Figure 3). NWP data for the case study was generated from

the COSMO model COSMO model at 2.8km resolution for

the year 2009‎ [21].

Figure 3: Location of the selected weather stations used in the

case study

A. Validation and neighborhood size selection

The spatio-temporal pseudo ensemble approach is validated

against the deterministic approach. RMSE for probabilistic

forecast (Brier score) is used. The validation results are then

used to select the optimum spatio-temporal size. Following the

procedure illustrated in Figure 2, the probability of different

wind speeds is generated for the observation, deterministic

wind forecast, and different spatial and temporal

neighborhood size datasets. Figure 4 shows the BS for the

deterministic forecast and different spatial neighborhood size

datasets for the Masirah Island site. It is clearly seen that the

BS for the spatial neighborhood datasets is better than the BS

of the deterministic forecast. Similar results are obtained for

the other two sites (not shown). It can also be seen that,

different neighborhood size datasets has different BS values

for‎different‎wind‎classes.‎For‎example,‎the‎10Δx‎dataset‎has‎

better‎BS‎ than‎3Δx‎dataset‎ for‎4m/s‎wind‎speed‎compared‎to‎8m/s. Therefore, it is essential to select the neighborhood size

which fits most of the wind classes.

Figure 5 shows the average BS of all wind classes for the

Masirah Island site. For spatial neighborhood (A), it can be

seen that the BS improves as the neighborhood size increases

until‎3Δx‎where‎it‎stabilized‎at‎a‎value‎around‎0.45.‎Therefore,

in‎ ordered‎ to‎ minimize‎ computational‎ costs,‎ 3Δx‎ can‎ be‎

considered as the optimum spatial neighborhood size. On the

other‎ hand,‎ 6ΔT‎ can‎ also‎ be‎ considered‎ as‎ the‎ optimum‎

temporal neighborhood size, above which the BS did not

improve further as shown in part (B). Finally, after combining

both spatial and temporal datasets, the total BS is improved to a value of 0.4 compared to previous values of 0.45 and 0.44

using individual spatial and temporal datasets respectively as

shown in part (C). From this, it can be concluded that the

optimum combination of the spatio-temporal neighborhood

size for‎the‎Masirah‎Island‎is‎(3Δx-6ΔT).

Figure 4: Brier score for deterministic forecast and different spatial neighborhood size datasets for Masirah island site

Similarly, the same procedure was applied to the other two sites (Thumrait, Joba). Figure 6 shows the Average BS for deterministic forecast and the optimum spatial-temporal neighborhood datasets for Thumrait and Joba. The optimum neighborhood‎size‎was‎found‎to‎be‎(1Δx-6ΔT)‎and‎(5Δx-7ΔT) for Thumrait and Joba respectively.

Based on the three cases, it can be concluded that the spatio-temporal neighborhood approach is better than the deterministic forecast approach for the wind speed data.

B. Probabilistic prediction and representation

One disadvantage of the deterministic approach is that the forecast does not inform the end users about the variation from the expected value. Unlike deterministic forecast, spatio-temporal neighborhood (pseudo ensemble) approach enables the user to expect the variation in the forecasted wind speed and power and provide the probability of occurrence of each wind speed and power class. This added value information is


130

significant for proper planning and better security of the supply.

Figure 5: Average Brier score for deterministic forecast and

different spatial-temporal neighborhood size datasets for

Masirah island site

Figure 6: Average Brier score for deterministic forecast and

the optimum spatial-temporal neighborhood datasets for

Thumrait and Joba

Figure 7 shows the Box-Plot of 24h wind speed forecast using the spatio-temporal neighborhood approach over Masirah Island for 2

nd Aug 2009. Deterministic forecast (blue triangles)

and observed (red square) wind speeds were added to the plot for the sake of comparison only. It can be seen that the spatio-temporal neighborhood approach is more informative compared to the deterministic approach. The pox-plot represents the wind forecast data distribution for different time horizon. The lower whisker of the box-plot represents the minimum forecasted wind speed, while the upper whisker represents the maximum forecasted wind speed. Empty circles represent the wind speed forecasts that are considered as outliers. The lower edge of the box represents the 25% quintile and the upper edge represents the 75% quintile. Therefore, the most significant 50% of the forecast occurs inside the box. The

median of the distribution is marked by the dark horizontal line inside the box.

Using the proposed approach, it can be seen that almost all observations fall inside the box which is the most significant 50% of the distribution. On the other hand, it can be seen that in many cases, the single deterministic forecast is away different from the observed values and outside the most significant 50% of the distribution.

Figure 7: Box-Plot for Masirah island site, based on 24h

forecast for 2nd Aug 2009 using the spatio-temporal

neighborhood approach

While Box-Plot is an important representation to understand the uncertainty of the forecast, it is very important for the wind farm daily operation to know the probability of occurrence for different wind classes and then different power classes. Figure 8 shows the probability of occurrence for different wind classes based on the forecast for 2nd Aug 2009 over Masirah island site. Red stars indicate the observed wind class. The most significant part of the forecast distribution (25%-75%) is used to calculate the probability.

Figure 9 shows the BS validation of the case. It can be seen that the spatio-temporal neighborhood approach has better BS for all wind classes below 10m/s. It also can be seen that the spatio-temporal neighborhood approach reduces the average BS by almost 50%. Similar results are obtained for both Thumrait and Joba site. Table 1 summarizes the BS obtained for this case in all the selected sites.

Figure 8: Probability of occurrence for different wind

classes for the forecast for Aug 2nd 2009 over Masirah island

site. Red stars indicate the observed wind class

(Thumrait) (Joba)

(A) (B)

(C)


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TABLE 1: Brier Score for Aug 2nd 2009 case using

deterministic and Spatio-Temporal approach

Site Deterministic

forecast

Spatio-

Temporal

forecast

Brier Score

Reduction

(%)

Masirah 0.079 0.04 51

Thumrait 0.079 0.044 56

Joba 0.083 0.046 56

Figure 9: Briar Score Validation for 2nd Aug 2009 case over

Masirah island site

IV. CONCLUSION

The main objective of this paper is to investigate the possibility of using spatio-temporal neighborhood method for generating probabilistic wind and power prediction. The proposed approach works as post processing procedure to derive probabilistic forecast from deterministic NWP predictions. Unlike the deterministic forecast approach, this approach provides additional information about the forecast uncertainty. In addition, it provides low cost and online forecast compared to the ensemble NWP approach. The proposed method was applied to the operational NWP (COSMO) model at Directorate General of Meteorology and Air navigation. The results were validated against the observed wind speed data from three weather stations. Results showed that the proposed method scored better than the deterministic model. The proposed method is an enhancement of the wind power forecast process which is essential in wind energy marketing.

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