Enhanced Forecasting Approach for Electricity Market Prices and Wind Power Data Series in the Short-Term
Abstract
:1. Introduction
2. Proposed Approach
2.1. Wavelet Transform
2.2. Differential Evolutionary Particle Swarm Optimization
2.3. Adaptive Neuro-Fuzzy Inference System
2.4. Hybrid Proposed Approach
- Step 1: Initialize the HWDA approach with a historical data matrix of EMP or wind power, respectively, considering the forecasting time-scale of each forecast field;
- Step 2: Choose a set of historical data of the previous step to run the pre-processing process carried out by the WT tool. This step is performed by a backtracking process, in order to attain a smaller error at the end by choosing the best set of candidates. Also, the approach considered in this paper uses , , and steps as inputs for the next step;
- Step 3: Train the ANFIS tool with the previous sets of constitutive historical data obtained from WT. The optimization process of the ANFIS membership function parameters will be achieved with the DEEPSO method. All parameters considered from all methods are summarized in Table 1.
- Step 4: until the best results are obtained or convergence is reached:
- ○
- Step 4.1: Jump to Step 4 in the case of EMP if convergence is not reached;
- ○
- Step 4.2: Jump to Step 2 in the case of wind power forecasting, refreshing the historical data matrix.
- Step 5: Apply the inverse WT. The output of the proposed HWDA approach is attained; that is, the forecasted EMP or wind power results are ready to be presented;
- Step 6: Compute the forecasting errors of EMP or wind power results with different criteria to validate the proposed HWDA approach and show the results.
2.5. Forecasting Error Evaluation
3. Case Studies and Results
3.1. Electricity Market Prices Forecasting
3.1.1. Spanish Market Results
3.1.2. PJM (Pennsylvania-New Jersey-Mary) Land Market Results
3.2. Wind Power Forecasting
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature
WT scaling integer variable | |
ANFIS linguistic label | |
ANFIS contribution parameter set | |
WT approximation coefficient | |
WT translation integer variable | |
DEEPSO actual global position | |
DEEPSO global position provided by a new weight | |
ANFIS linguistic label | |
ANFIS contribution parameter set | |
ANFIS contribution parameter set | |
WT detail coefficient | |
Discrete wavelet transform set | |
Error at hour | |
WT father-wavelet function | |
WT length of set | |
DEEPSO integer time-step from global search space | |
ANFIS number of nodes | |
ANFIS output node | |
ANFIS layer | |
Mean absolute percentage error | |
WT integer scaling parameter | |
Length of observed values points | |
DEEPSO random Gaussian variable with 0 mean and variance 1 | |
Normalized mean absolute error | |
Normalized root mean square error | |
WT integer translation parameter | |
Average value for the forecasting horizon | |
DEEPSO probabilistic diagonal binary matrix | |
Data forecasted at hour | |
Total wind power capacity installed | |
ANFIS parameter set of membership function | |
Real data at hour | |
WT mother-wavelet function | |
WT signal input | |
ANFIS parameter set of membership function | |
ANFIS parameter set of membership function | |
Error variance from the forecasting horizon | |
DEEPSO learning parameter | |
WT time-step | |
DEEPSO actual velocity | |
DEEPSO new velocity of the particle | |
DEEPSO new weight with self-adaptive features | |
DEEPSO mutated weights of inertia, memory and cooperation | |
ANFIS firing strength | |
ANFIS output firing strength | |
ANFIS input data | |
DEEPSO actual position | |
DEEPSO new position of the particle | |
DEEPSO set of best ancestors from the swarm | |
DEEPSO set of recorded positions of the swarm | |
ANFIS input data | |
ANFIS defuzzification parameters data |
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Methods | Parameters | Type or Size |
---|---|---|
WT | Decomposition Direction | Row |
Level of Decomposition | 3 | |
Mother-Wavelet Function | Db4 | |
Denoising Methods | “sqtwolog”–“minimaxi” | |
Multiplicative Thresholds Rescaling | “one”–“sln” | |
DEEPSO | Communication Probability | 0.10 |
Final Inertia Wight | 0.01–0.15 | |
Initial Inertia Weight | 0.50–0.90 | |
Initial Population Size | 100 | |
Initial Sharing Acceleration | 0.50–2.00 | |
Initial Swarm Learning Process | 1.00–2.00 | |
Initial Swarm Sharing Process | 2.00 | |
Learning Parameter | 1 | |
Maximum Value of New Position | Set of Max. Inputs | |
Minimum Value of New Position | Set of Min. Inputs | |
Necessary iterations | 100–1000 | |
ANFIS | Structure Type | Takagi-Sugeno |
Style of Membership Function | Triangular | |
Number of Inference Rules | Automatic | |
Membership Functions | 2–15 | |
Number of Epochs | 2–50 | |
Number of Nodes | 3–9 | |
Number of Inputs / Outputs | 2–5/1 |
Methods | Winter | Spring | Summer | Fall | Average | Enhancement |
---|---|---|---|---|---|---|
NN [13], 2007 | 5.23 | 5.36 | 11.40 | 13.65 | 8.91 | 54.66% |
FNN [11], 2006 | 4.62 | 5.30 | 9.84 | 10.32 | 7.52 | 46.28% |
HIS [12], 2009 | 6.06 | 7.07 | 7.47 | 7.30 | 6.97 | 42.04% |
AWNN [14], 2008 | 3.43 | 4.67 | 9.64 | 9.29 | 6.75 | 40.15% |
CNEA [15], 2009 | 4.88 | 4.65 | 5.79 | 5.96 | 5.32 | 24.06% |
CNN [16], 2009 | 4.21 | 4.76 | 6.01 | 5.88 | 5.22 | 22.61% |
HNES [17], 2010 | 4.28 | 4.39 | 6.53 | 5.37 | 5.14 | 21.40% |
MI+CNN [22], 2012 | 4.51 | 4.28 | 6.47 | 5.27 | 5.13 | 21.25% |
WPA [19], 2011 | 3.37 | 3.91 | 6.50 | 6.51 | 5.07 | 20.32% |
HEA [44], 2014 | 3.04 | 3.33 | 5.38 | 4.97 | 4.18 | 3.35% |
HWDA | 3.00 | 3.16 | 5.23 | 4.76 | 4.04 | - |
Methods | Winter | Spring | Summer | Fall | Average | Enhancement |
---|---|---|---|---|---|---|
NN [13], 2007 | 0.0017 | 0.0018 | 0.0109 | 0.0136 | 0.0070 | 82.86% |
FNN [11], 2006 | 0.0018 | 0.0019 | 0.0092 | 0.0088 | 0.0054 | 77.78% |
AWNN [14], 2008 | 0.0012 | 0.0031 | 0.0074 | 0.0075 | 0.0048 | 75.00% |
HIS [12], 2009 | 0.0034 | 0.0049 | 0.0029 | 0.0031 | 0.0036 | 66.67% |
CNEA [15], 2009 | 0.0036 | 0.0027 | 0.0043 | 0.0039 | 0.0036 | 66.67% |
CNN [16], 2009 | 0.0014 | 0.0033 | 0.0045 | 0.0048 | 0.0035 | 65.71% |
WPA [19], 2011 | 0.0008 | 0.0013 | 0.0056 | 0.0033 | 0.0027 | 55.56% |
MI+CNN [22], 2012 | 0.0014 | 0.0014 | 0.0033 | 0.0022 | 0.0021 | 42.86% |
HNES [17], 2010 | 0.0013 | 0.0015 | 0.0033 | 0.0022 | 0.0021 | 42.86% |
HEA [44], 2014 | 0.0008 | 0.0011 | 0.0026 | 0.0014 | 0.0015 | 20.00% |
HWDA | 0.0007 | 0.0008 | 0.0022 | 0.0010 | 0.0012 | - |
HNES [17], 2010 | Hybrid [44], 2010 | CNEA [15], 2009 | HEA [44], 2014 | HWDA | |
---|---|---|---|---|---|
Jan. 20 | 4.98 | 3.71 | 4.73 | 3.29 | 3.22 |
Feb. 10 | 4.10 | 2.85 | 4.50 | 2.80 | 2.71 |
Mar. 5 | 4.45 | 5.48 | 4.92 | 3.32 | 3.27 |
Apr. 7 | 4.67 | 4.17 | 4.22 | 3.55 | 3.42 |
May 13 | 4.05 | 4.06 | 3.96 | 3.43 | 3.40 |
Feb. 1–7 | 4.62 | 5.27 | 4.02 | 3.11 | 3.09 |
Feb. 22–28 | 4.66 | 5.01 | 4.13 | 3.08 | 3.02 |
Average | 4.50 | 4.36 | 4.35 | 3.23 | 3.16 |
Enhancement | 29.78% | 27.52% | 27.36% | 2.17% | - |
CNEA [15], 2009 | Hybrid [44], 2010 | HNES [17], 2010 | HEA [44], 2013 | HWDA | |
---|---|---|---|---|---|
Jan. 20 | 0.0031 | 0.0010 | 0.0020 | 0.0010 | 0.0010 |
Feb. 10 | 0.0036 | 0.0015 | 0.0012 | 0.0009 | 0.0008 |
Mar. 5 | 0.0042 | 0.0033 | 0.0015 | 0.0011 | 0.0010 |
Apr. 7 | 0.0022 | 0.0013 | 0.0018 | 0.0011 | 0.0011 |
May 13 | 0.0027 | 0.0015 | 0.0013 | 0.0012 | 0.0012 |
Feb. 1–7 | 0.0044 | 0.0037 | 0.0016 | 0.0012 | 0.0011 |
Feb. 22–28 | 0.0035 | 0.0025 | 0.0017 | 0.0017 | 0.0016 |
Average | 0.0034 | 0.0021 | 0.0016 | 0.0012 | 0.0011 |
Enhancement | 67.65% | 47.62% | 45.45% | 8.33% | - |
Winter | Spring | Summer | Fall | Average | Enhancement | |
---|---|---|---|---|---|---|
NN [29] | 9.51 | 9.92 | 6.34 | 3.26 | 7.26 | 53.58% |
NF [32] | 8.85 | 8.96 | 5.63 | 3.11 | 6.64 | 49.25% |
WNF [34] | 8.34 | 7.71 | 4.81 | 3.08 | 5.99 | 43.74% |
WPA [35] | 6.47 | 6.08 | 4.31 | 3.07 | 4.98 | 32.33% |
HEA [45] | 5.74 | 3.49 | 3.13 | 2.62 | 3.75 | 11.28% |
HWDA | 5.08 | 3.19 | 2.96 | 2.27 | 3.37 | - |
Winter | Spring | Summer | Fall | Average | Enhancement | |
---|---|---|---|---|---|---|
NN [29] | 0.0044 | 0.0106 | 0.0043 | 0.0010 | 0.0051 | 76.47% |
NF [32] | 0.0041 | 0.0086 | 0.0038 | 0.0008 | 0.0043 | 72.09% |
WNF [34] | 0.0046 | 0.0051 | 0.0021 | 0.0011 | 0.0032 | 62.50% |
WPA [35] | 0.0021 | 0.0035 | 0.0016 | 0.0011 | 0.0021 | 42.86% |
HEA [45] | 0.0019 | 0.0015 | 0.0010 | 0.0008 | 0.0013 | 7.69% |
HWDA | 0.0017 | 0.0016 | 0.0007 | 0.0006 | 0.0012 | - |
Winter | Spring | Summer | Fall | Average | Enhancement | |
---|---|---|---|---|---|---|
NN [29] | 5.22 | 3.72 | 2.35 | 2.15 | 3.36 | 84.23% |
NF [32] | 4.86 | 3.36 | 2.09 | 2.05 | 3.09 | 82.85% |
WNF [34] | 4.58 | 2.89 | 1.78 | 2.03 | 2.82 | 81.21% |
WPA [35] | 3.56 | 2.28 | 1.60 | 2.02 | 2.37 | 77.64% |
HEA [45] | 2.73 | 1.48 | 0.74 | 1.10 | 1.51 | 64.90% |
HWDA | 0.94 | 0.49 | 0.28 | 0.39 | 0.53 | - |
Winter | Spring | Summer | Fall | Average | Enhancement | |
---|---|---|---|---|---|---|
HEA [45] | 3.60 | 3.18 | 1.78 | 2.07 | 2.66 | 39.47% |
HWDA | 2.19 | 1.27 | 1.81 | 1.18 | 1.61 | - |
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Share and Cite
Osório, G.J.; Gonçalves, J.N.D.L.; Lujano-Rojas, J.M.; Catalão, J.P.S. Enhanced Forecasting Approach for Electricity Market Prices and Wind Power Data Series in the Short-Term. Energies 2016, 9, 693. https://doi.org/10.3390/en9090693
Osório GJ, Gonçalves JNDL, Lujano-Rojas JM, Catalão JPS. Enhanced Forecasting Approach for Electricity Market Prices and Wind Power Data Series in the Short-Term. Energies. 2016; 9(9):693. https://doi.org/10.3390/en9090693
Chicago/Turabian StyleOsório, Gerardo J., Jorge N. D. L. Gonçalves, Juan M. Lujano-Rojas, and João P. S. Catalão. 2016. "Enhanced Forecasting Approach for Electricity Market Prices and Wind Power Data Series in the Short-Term" Energies 9, no. 9: 693. https://doi.org/10.3390/en9090693