NEURAL NETWORKS, WAVELET AND DATA MINING TECHNIQUES. Z.Y. Dong X. Li Z. Xu K. L. ... School of Information Technology and Electrical Engineering.
WEATHER DEPENENT ELECTRICITY MARKET FORECASTING WITH NEURAL NETWORKS, WAVELET AND DATA MINING TECHNIQUES Z.Y. Dong
X. Li
Z. Xu
K. L. Teo
School of Information Technology and Electrical Engineering The University of Queensland, St. Lucia, QLD 4072, Australia Abstract With the presence of competitive electricity market, accurate load and price forecasting have become essential for both system operator as well as general participants. Presented in this paper is an adaptive neuro-wavelet model for Short Term Electricity Load Forecast (STLF). Both historical load and temperature data, which have important impacts on load level, are used in forecasting by the proposed model. To enhance the forecasting accuracy by neural networks, the Non-decimated Wavelet Transform (NWT) is introduced to pre-process these data. The proposed model has been evaluated using actual data of electricity load and temperature of Queensland, Australia. The simulation results demonstrate that the model is capable of providing a reasonable forecasting accuracy in STLF. In addition, a forecasting scheme based on the presented model and data mining technique has been outlined for future research, which aims at forecasting electricity price with outliers. 1.
INTRODUCTION
The deregulation of power industries in Australia was recommended to the Federal and State Governments in 1991 [1]. Since then, competitive electricity markets, including wholesale and retail sectors, have been slowly but firmly introduced into serval states, resulting in formal launch of Australian Nation Electricity Market (NEM) in 1998. The fundamental objective of the deregulation is to increase the efficiency of electricity generation and distribution while maintaining sufficient security of operation. With the presence of electricity market, forecasting electricity demand and price become a necessity. Proper forecasting of electricity load would ensure adequate electricity generation to meet the consumers’ demands in the near and far future. In a deregulated electricity market, the penalty for inadequate load supply is very high. A generation company may lose its entire year’s revenue due to unforeseen loss of generation caused by contingencies
[2], usually out of system operation’s control. One solution to overcome and to manage such contingencies is by proper system operational planning based on STLF, which forecasts the load of a few minutes, hours, or days ahead. The aim of STLF is to predict the future electricity demand based on the recognition of similar repeating trends of patterns from historical load data. However, other important factors, such as social events and especially the weatherrelated variables, must be considered [3], [4], [5], [6] and [7]. Traditionally forecasting models are mostly linear methods, such as Autoregressive Moving Average (ARMA) model, which have limited abilities to capture the nonlinearities in the time series such as electricity demand. In recent years, modern techniques based on artificial intelligence have shown promising results. The Neural Network (NN) based methods have gained most attention [8]. The NN is regarded as an effective approach and is now being used for electricity demand and price forecast. The reason of its popularity exists in its ease of
use and ability of function approximation of high complexity. Among different types of NNs that have been implemented, the Multilayer Percetrons (MLP) or Feed-forward NN has been proven to give satisfactory results for time series predictions [8] and [9]. In this paper a forecasting scheme has been developed. In addition to the historical electricity demand data, the weather (temperature), which has significant impacts on energy consumption, has also been used in the proposed method. By pre-processing these data using Non-decimated Wavelet Transform (NWT), the forecasting accuracy has been enhanced. An example using realworld data from Australia NEM has demonstrated the proposed method can provide reasonable accuracy in STLF. Furthermore, future scope of applying the scheme with data mining techniques in forecasting electricity spot price has been discussed. 2. THE PROPOSED WEATHER DEPENDANT SHORT TERM LOAD FORECASTING MODEL The proposed model has three stages for STLF, including data pre-processing using NWT, NN forecasting using feed-forward
NN and data post-processing by NWT. Figure 1 shows the overall structure of the proposed model. 2.1
Data pre-processing
Both the historical data of electricity load and temperature are treated as time series signals. NWT is used as the pre-signal processor in the proposed model. The à trous transform is an example of nondecimated wavelet transform. This algorithm is used in our approach to extract the hidden patterns of both the historical time series of electricity demand and temperature. If we consider a given time series signal, the à trous wavelet transform filters the signal through a series of low and high pass filters. The result from each filtering stage is the approximation (low frequency information) and detail (high frequency information) coefficient series obtained at different resolution levels. The number of filter stages depends on the highest resolution level determined for the filtering process. Comparing to classical wavelet algorithm, the NWT does not drop any data (non-decimation) and keep the time-invariance in decomposition, therefore has been adopted in the model.
Figure 1 The proposed forecast model 2.2
Neural network forecasting
In this stage, the wavelet coefficients obtained from NWT decomposition are fed into neural networks to predict future data at
one more time steps ahead. A set of feedfroward NNs are allocated to forecast the wavelet at different resolution levels. These networks contain only one hidden layer, which is adequate to approximate functions
of any complexities [10]. The Scaled Conjugate Gradient algorithm (SCG) is used in training the NNs, due to its advantage of fast computational time for a large NN size.
Figure 2 Wavelet Recombination Process
2.3
Data post-processing
For post signal processing, the same wavelet technique and resolution level as mentioned in Stage 1 is used. In this stage, the outputs from the signal predictors (NNs) are combined to form the final predicted output. This is achieved by summing all the predicted wavelet coefficients. Figure 2 illustrates the recombination process. 3.
SIMULATION AND RESULTS
3.1
Results
The proposed model is tested with eight sets of historical data containing the electricity load and temperature data for the month of January 2001; one set of electricity demand data of Queensland Market and seven sets of temperature data from seven different locations (higher power consumption regions) of Queensland. It should be noted that the load data is with half-hour basis. The reason for using seven sets of temperature data is a compromise due to the unavailability of a general set of average temperature data for Queensland. The
forecasting performance is measured by the mean absolute percentage error (MAPE)
MAPE =
1 N xi − yi ∑ N i =1 xi
* 100%
(1)
where N is the number of points measured, xi is the actual values and yi is the predicted values. The model is trained with one week (336 points) of combined demand and temperature data for fifty cycles. The performance of the forecast model was evaluated and the results are as shown in Figures 3 to 5. Table 1: Summary of MAPEs
No. of forecasted points
MAPE (%)
336 (7 days)
1.4134
384 (8 days)
1.6198
432 (9 days)
2.0048
The MAPE values were calculated based on the forecasted values and the original time series. The MAPEs are recorded in Table 1.
Figure 3. 7-day ahead forecasting (336 points)
Figure 5. 9-day ahead forecasting (432 points) 3.2
Discussion
From the simulation results, it can be seen that the proposed model produces a reasonable accuracy in STLF. In our case study, training of the proposed model was conducted with only 336 points (one week) of the recent temperature and electricity historical data. Once the model is trained, it can be used to forecast the electricity load data for 48 times, each time forecasting one point ahead and with MAPE less than 1.7%, without the need to be retrained. Figure 4. 8-day ahead forecasting (384 points)
Figure 6. The proposed model for multi-step forecasting
Nevertheless, there is a limitation with the forecasting schemes that can be used for the model. The model can only predict one point
ahead, which makes it unfeasible for the STLF of Queensland. To resolve the limitation, the model can be modified to
features of the electricity and the power systems. Especially, the outliers or spikes in the price series have made the forecasting extremely difficult, although market participants rely much on this information for finical management. With the model proposed in this paper, we have further proposed an electricity forecasting scheme. Basic forecasting function will be achieved using the model developed in this paper, while the data mining technique is employed to account for outlier prediction.
predict more points ahead. This modification can be done by including more prediction units into the model, which are used to predict the temperatures. The proposed model for multi-step prediction is shown in Figure 6. 4. DATA MINING APPROACH TO ELECTRICITY PRICE FORECASTING
From the simulation results, it can be seen that the proposed model produces a reasonable accuracy in STLF. Once the model is trained, it can be used to forecast the electricity load data of future. However, the model can only predict one point ahead, which limits its application. To resolve the limitation, the model can be modified to predict more points ahead in future.
From the data set (see Figure 7), it can be seen that the total electricity demands (TED) are more or less periodical. The price spikes in RRP (regional average price) are correlated to the peak time of TED. As a result the price forecasting can be constrained by employing data mining for prediction of the time of the price spikes by correlation with the demand series in the following steps:
Comparing to load data, forecasting the fairly chaotic electricity price is more complex. The high volatility of electricity price is attributed to the many exclusive 7000 6000 5000 4000
TOTALDEMAND
3000
RRP
2000 1000 253
239
225
211
197
183
169
155
141
127
99
113
85
71
57
43
29
15
1
0
Figure 7. The correlation between total demands and price (RRP)
1. Calculate the correlation coefficient r (Pearson’s r) between the Total Demand and RRP: r=
∑(x ∑(x
i − X
i − X
) ( yi − Y )
(2)
)2 ( yi − Y ) 2
2. For a given time series database D, at time t, with the window size w, we take a
sub-series s in the time period the t-w, to search D for a match s’ that satisfies the minimum pre-defined Euclidean distance d between s and s’. 3. For s’ the RRP(Δt) * r will be the predicted price value.
Price series
Preprocessing
Price Spikes
Base Series Demand series
Correlation Processing Module
Base Series NNWavelet Forecast Module
Final Processing
Final forecasted price signal
Weather series
Figure 8 Proposed price forecasting scheme with outlier detection
Combining the data mining technique with the forecasting model developed, the price forecasting scheme with outliers detection is illustrated in Figure 8. With the proposed outline, further research on electricity price forecasting with appearance of outliers is underway. 4.
CONCLUSIONS
This paper proposed a STLF model with a high forecasting accuracy. The NWT has been successfully implemented in the model. The implementation of NWT has reasonably enhanced the learning capability of the NNs in the model, thus minimizing their training cycles as shown in the simulations. Temperature has a close relationship with electricity load and its feasibility to be included for STLF has been proven with reasonable accuracy achieved from the simulations. In summary, the inclusion of temperature data (as an additional input variable) and the use of NWT (as the data processing tool) for the proposed STLF model have been proved to provide enhanced accuracy in STLF. The NN based forecast model can be further explored by combining data mining techniques in forecasting of electricity price signals, mainly price peaks based on the covariance between load and price data series of an electricity market. 5.
REFERENCES
[1] National Electricity Market Management Co Ltd (NEMMCO), Statement of Opportunities 2002.
[2] F. F. Wu and P. Varaiya, “Coordinated multilateral trades for electric power networks: theory and implementation 1,” Electrical Power and Energy Systems 21 (1999) 75-102. [3] G. Chicco et al, “Load pattern clustering for short-term load forecasting of anomalous days,” Proc. IEEE Porto PowerTech 2001, Sep. 2001. [4] D. W. Bunn, “Forecasting loads and prices in competitive power markets,” Proc. of the IEE, vol. 88, no. 2, Feb. 2000, pp. 163-169. [5] B. L. Zhang and Z. Y. Dong, “An adaptive neural-wavelet model for short term load forecasting,” Electric Power Systems Research 59 (2001) 121-129. [6] D. K. Ranaweera et al, “Effect of probabilistic inputs on neural networkbased electric load forecasting,” IEEE Trans. on Neural Networks, vol. 7, no. 6, Nov. 1996, pp. 1528-1532. [7] A. D. Papalexopoulos and T. C. Hesterberg, “A regression-based approach to short-term system load forecasting,” IEEE Trans. on Power Systems, vol. 5, no. 4, Nov. 1990, pp. 1535-1547. [8] H. S. Hippert et al, “Neural networks for short-term load forecasting: A Review and Evaluation,” IEEE Trans. on Power Systems, vol. 16, no. 1, Feb. 2001, pp. 4454. [9] W. R. Foster et al, “Neural network forecasting of short, noisy time series,” Computers Chem. Enging., vol.16, no.4, 1992, pp. 293-297. [10] S. Haykin, “Neural Networks,” Macmillan College Publishing Company, Inc. 1994.
