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.
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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.
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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.
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