Probabilistic wind speed forecast for wind power prediction using pseudo ensemble approach Sultan Al-Yahyai1, Yassine Charabi2, Adel Gastli1 1
[email protected] [email protected] [email protected] 2 Department of Electrical & Computer Engineering Department of Geography College of Engineering College of Arts & Social Sciences Sultan Qaboos University, Muscat, Oman
Abstract Accurate wind and power forecast is essential process in wind energy marketing. Due to the intermittent nature of the wind, it is necessarily to provide information about predictability of different wind speeds. Numerical Weather Prediction (NWP) provides wind forecast as a single value for a given time horizon. Therefore, forecasting wind speed as deterministic value doesn’t represent the uncertainty of the wind speed forecast. Ensemble NWP forecast is 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 model. Poor man ensemble method is used to overcome extensive computational resources requirement of the approach through utilizing the overlapping runs of the NWP model from different starting times for given point in time. This paper, explores the possibility of using pseudo ensemble method for generating probabilistic wind forecast for wind power applications. This 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 using wind data from NWP model and measurements from three weather stations in Oman.
Key words: Probabilistic power forecast, pseudo ensemble, Oman 1. 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 and power 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 scheduling the maintenance planning [2].
There are two main stages in wind power forecast [1][3]. The first stage is the “meteorological” stage, where the wind speed is forecasted at the farm site for different time horizon. The second stage is the “energy conversion” stage, where the wind speed information is transformed to power for the whole wind farm[4]. It can be imagine that the better the wind forecast the better generated power can be estimated. With recent technological developments, Numerical Weather Prediction (NWP) Models are used to provide the wind forecast in the “meteorological” stage [5]. NWP models forecasts the wind condition for citrine site location for different time horizon. NWP model forecast is deterministic by its nature. Therefore, the forecast don’t provide any information about predictability of certain event. Figure 1 Shows the steps use single NWP model forecast in wind power prediction chain [2][6] [7]. Different NWP models such as HIRLAM in [8], ECMWF in [9] and COSMO in [10] were used to forecast wind condition for different sites. Based on the available computational resources, different model resolutions were used. In this approach, the NWP wind forecast is extracted for a single grid point (deterministic) that correspond to the wind farm site[7]. NWP models forecasts wind condition at different vertical layers which are not necessarily match 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. Local refinement can be calculated using the logarithmic low [11] or interpolation of the forecast from two different vertical layers. NWP wind speed forecast at different horizon (12h, 24h, 36h …etc) for the site
Local site refinement (hub height, roughness …)
Statistical Calibration
Wind power calculation using power curve
Regional Upscaling
Figure 1: Data flow diagram for using deterministic NWP model forecast in wind power prediction
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 power for single wind turbine using wind turbine power curve. Different approached were implemented to use turbine manufacture’s power curve or through building power curve based on measured wind speed, direction and generated power [4]. The forecasted power of a single turbine is then aggregated to represent the whole wind farm [12]. Finally, single representative wind farm is used to conduct regional upscaling and generate power prediction for a group of wind farms [13] . As described earlier, that NWP model forecast is deterministic by its nature. This represents limitation especially for wind energy applications since no information is provided about the variation from the expected value [14]. Hence, precautionary action planning is limited [15]. 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 don’t represent the uncertainty of the wind speed forecast. The description of the uncertainty is an essential step for any scientific prediction. That is, single deterministic forecasts are not consistent with the “scientific method”, in the sense that the result from any scientific prediction is not complete without an estimate of the likely error associated with measurement and other experimental inaccuracy [4]. It has been widely experienced that the single deterministic model is unreliable during extreme events [4]. On the other hand extreme events are very important to secure the power supply when the wind is calm and to secure the wind turbines during severe wind conditions. Therefore, probabilistic forecast provides the probability for one or more events to occur. It has been shown that, when trading future production on electricity market, the use of probabilistic forecast can lead to higher benefits than those obtained by one single forecast [15]. Hence, it is necessarily to develop techniques to transform the wind speed forecast from the deterministic domain to the probabilistic domain. Prediction error approach [16] 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. Simple evaluation scores such as standard deviation and root mean squire error (RMSE) are used. The need for long-term data set to evaluate the systematic errors is the main disadvantage of this approach. In addition, it is only providing constant value for each time horizon. Ensemble forecast [17] is the most direct approach to calculate the probability of certain event to occur from a set of possible events and scenarios[1]. It has been used in [5][13][18] 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 [15]. The Ensemble members forecast is sampling the distribution of expected event. Disagreement between the member’s forecasts represent a quantitative estimate
of the uncertainty in the prediction[19]. 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 date generated by the models that require exclusive management. Poor man ensemble forecast [20] was used as a work around method to overcome the computational requirement of the ensemble forecast approach. 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 degrade with time. To overcome computational requirement of the ensemble forecast, pseudo ensemble method was proposed in [21] for precipitation forecast. Pseudo ensemble is based on spatial-temporal neighborhoods of the model forecast for certain site. Pseudo ensemble was used to describe the uncertainty in the precipitation forecast and provides low coast and online prediction. This paper introduces improvement in the proposed method and explores the possibility of using pseudo ensemble method 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. 2. Proposed approach Beside the improvement on the forecast quality with the recent use of height resolution model, point to point model validation shows low skill scores. On the other hand, operational forecasters confirm the added value given by the NWP models for their forecasts. Small shift in time or space can cause large difference in the validation scores for certain observation point. Therefore, spatial model validation [23][24] 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 nature 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. Based on the above clarification, the proposed approach looks into the Spatio-Temporal neighborhood of grid point (location) to get set of possible wind forecasts. Then uses this set to derive probabilistic forecast for that location. 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 temporal neighborhood is expressed in multiples of model output frequency (ΔT).
Figure 2 shows the Spatio-Temporal neighborhood representation for grid point (x0,y0) at forecast time horizon T0. Figure 2 (A), shows the special neighborhood in (x,y)-plane with neighborhood (shaded) size of (3Δx). The Temporal neighborhood (3ΔT) is shown in part (B) in (x,t)-plane. Both spatial and temporal neighborhoods are combined in part (C).
(A)
(B)
(C) Figure 2: Spatio-Temporal neighborhood representation
In [20][21], 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), medium with neighborhood size of (12Δx-4ΔT) and large configuration with neighborhood size of (20Δx-6ΔT). Based on verification results [25] of different models, it is known that quality of model forecast vary from one location to another based on different factors such as initial condition of the model and the complexity of the topography surrounding the location. Therefore, it is believed that 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 best neighborhood size. Figure 3 shows the proposed procedure to select the best neighborhood size for each selected site. The selection is based on the Brier score (BS) which is essentially the mean square error of probabilistic forecast [22] as represented in eq. (1). Where yk is the forecast probability and ok is the observed probability. ∑
(1)
For each site, the idea is to select the special and temporal dataset combination that gives the better brier score compared to the BS 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. For measurements ok=1 if the event occurs and ok=0 otherwise. Similarly, for deterministic forecast, yk=1 if the event occurs and yk=0 otherwise. Site measurements dataset
Deterministic forecast dataset
Special neighborhood datasets for different neighborhood sizes
Temporal neighborhood datasets for different neighborhood sizes
Calculate probability of each wind class
Brier score for probabilistic forecast
Select the temporal neighborhood size with best average score
Select the best spatial neighborhood with best average score
Combine the datasets for both spatial and temporal neighborhoods
Calculate probability of each wind class for the new dataset
Figure 3: Dataflow diagram for selecting the best Spatio-Temporal neighborhood size
Neighborhood sizes that give the best average BS is selected for both spatial and temporal datasets. Then, the datasets of both best spatial and temporal neighborhood sizes are combined to form the best dataset (pseudo ensemble) for that specific site. This procedure is repeated for each specific wind farm site. After selecting the best spatio-temporal neighborhood size, the steps described in Figure 1can then be revised and extended as shown in Figure 4 . These steps are performed after each daily run of the NWP model to generate the probabilistic prediction. Extract NWP forecast using the best spatio-temporal neighborhood size
Local site refinement (hub height, roughness …)
Statistical Calibration of the deterministic forecast Wind power calculation using power curve for the whole neighborhood dataset
Probability calculation for each power classes in the neighborhood dataset
Probabilistic representation of the forecast such as box-plot and PDF
Regional Upscaling Figure 4: Data flow diagram for using spatio-temporal pseudo ensemble approach for probabilistic wind and power prediction
It the proposed procedure, 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 best neighborhood size. In the new procedure, local refinement is still needed to provide the wind forecast at the hub
height for the whole neighborhood dataset. Unlike local refinement, statistical calibration can only be performed at the measurement site which is normally corresponding to the location of the deterministic forecast. Wind speed for the whole dataset is then converted to power using the power curve. 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 in 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. Similar to the deterministic approach, Regional upscaling is the final step in the procedure. 3. Case study The main objective of this case study is to illustrate and validate the proposed approach for probabilistic wind and power 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. The three selected weather stations are located in the mostly suitable site for future wind energy applications in Oman [25]. Figure 5 shows the location of the selected sites. NWP data for the case study was generated from the operational COSMO model at the Directorate General of Meteorology and Air Navigation (DGMAN). COSMO model was run at 2.8km resolution for the year 2009.
Figure 5: location of the weather stations used in the case study
3.1 Validation and neighborhood size selection In this section, the spatio-temporal pseudo ensemble approach is validated against the deterministic approach. The RMSE for probabilistic forecast (Brier score) was used. The validation results were then used to select the best spatio-temporal size. Following the procedure in Figure 3, probability of different wind speeds was generated for the observation, deterministic wind forecast, and different spatial and temporal neighborhood size datasets. Figure 6 shows the Brier score (BS) for the deterministic forecast and different spatial neighborhood size datasets for 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 were obtained for the other two sites. It also can be seen that, different neighborhood size datasets has different BS values for different wind classes. For example, the 10Δx dataset has better BS than 3Δx dataset for 4m/s wind speed compared to 8m/s. Therefore, it is necessarily to select the neighborhood size which fits most of the wind classes. 0.3
Spatial Neighborhood Size Deterministic 1Δx 2Δx 3Δx 4Δx 5Δx 6Δx 8Δx 10Δx
0.25
0.2
BS
0.15
0.1
0.05
0
Wind Speed (m/s) Figure 6: Brier score (BS) for deterministic forecast and different spatial neighborhood size datasets for Masirah island site
Figure 7 shows the average BS of all wind classes for Masirah island site. For spatial neighborhood (A), it can be seen the BS continued to improve as the neighborhood size increase until 3Δx where it stabilized at 0.45. Therefore, 3Δx is the best spatial neighborhood size. On the other hand, 6ΔT is the best temporal neighborhood size where the BS did not improve further as shown in part (B). Finally, after combining both spatial and temporal datasets, the total BS got
improved to 0.4 compared to 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 best spatio-temporal neighborhood size for Masirah Island is 3Δx-6ΔT.
(A)
(B)
(C)
Figure 7: Average Brier score (BS) for deterministic forecast and different spatial-temporal neighborhood size datasets for Masirah island site
Similarly, Figure 8 shows the average BS using different neighborhood sizes for both Thumrait. With respect to the spatial neighborhood, it can be seen that the BS was improved using 1Δx size and then got worse after that until 5Δx size. This is due to the complex mountainous topography surrounding the station. Increasing neighborhood size, allowed points with large different wind regime to be aggregated. This increased the Brier Score. When the neighborhood size was increased further, more flat areas were included and then the error was smoothed out as seen with neighborhood size 20Δx. In this case, neighborhood size of 1Δx was selected as the best size to avoid increasing the extraction time with insignificant reduction of the BS. Therefore, the best spatio-temporal neighborhood sizes for Thumrait is 1Δx-6ΔT.
(A)
(B)
(C)
Figure 8: Average Brier score (BS) for deterministic forecast and different spatial-temporal neighborhood size datasets for Thumrait site
(A)
(B)
(C)
Figure 9: Average Brier score (BS) for deterministic forecast and different spatial-temporal neighborhood size datasets for Joba site
Similarly, Figure 9 shows that the best spatio-temporal neighborhood size for Joba is 5Δx-7ΔT respectively. From the three cases, it can be concluded that the spatio-temporal neighborhood approach was better than the deterministic forecast approach for the wind speed data.
3.2 probabilistic prediction and representation One disadvantage of the deterministic approach is that the forecast don’t inform the end users about the variation from the expected value. Figure 10 Shows an example of deterministic wind speed that can be then converted to power for Masirah island
Figure 10: 24h Deterministic wind forecast for Masirah island site for 2 nd Aug 2009
Unlike deterministic forecast, spatio-temporal neighborhood (pseudo ensemble) approach enable 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 significant for prober planning and securing the supply. Figure 11shows Box-Plot of 24h wind speed forecast using the spatio-temporal neighborhood approach over Masirah island for 2nd Aug 2009. Deterministic forecast and observed wind speeded were added to the plot for comparison purposes. 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 value, while the upper whisker represents the maximum forecasted wind speed. Empty circles represent the wind 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 like inside the box. Using the proposed approach, it can be seen that almost all observations fell 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 from the observed values and outside the most significant 50% of the distribution.
Figure 11: 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 12 shows the probability of occurrence for different wind classes based on the forecast for 2nd Aug 2009 over Masirah island
site. Red starts indicate the observed wind class. The most significant part of the forecast distribution (25%-75%) was used to calculate the probability.
Figure 12: probability of occurrence for different wind classes for the forecast for 2nd Aug 2009 over Masirah island site. Red starts indicate the observed wind class
Figure 13 shows the Brier Score validation of the case. It can be seen that the spatio-temporal neighborhood approach has better Brier Score for all wind classes below 10m/s. It also can be seen that the spatio-temporal neighborhood approach reduced the average Brier Score by almost 50%.
Figure 13: Briar Score Validation for 2nd Aug 2009 case over Masirah island site
4. Conclusion The main objective of this paper was 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 prediction. 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 DGMAN, Oman. 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.
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