logo

SCIENTIA SINICA Informationis, Volume 48, Issue 10: 1300-1315(2018) https://doi.org/10.1360/N112018-00075

Decomposition-optimization-ensemble learning approach for electricity price forecasting

More info
  • ReceivedMar 30, 2018
  • AcceptedMay 25, 2018
  • PublishedOct 9, 2018

Abstract

The accurate forecasting of electricity price, which is an indispensable indicator of the current market situation, can help market players avoid risks and maximize economic profits as the electricity market undergoes continuous development and reform. This study aims to propose decomposition-optimization-ensemble (DOE), which is a new hybrid approach, for the predicting electricity price data in the power market. First, we decomposed electricity price data into a series of intrinsic mode functions and a residual sequence using the fast ensemble empirical mode decomposition method. Next, we optimized the convergence speed, accuracy, and searching ability of the whale optimization algorithm. We then used the improved whale optimization algorithm to optimize the expansion coefficient of the RBF neural network. The improved model was used to predict the values of intrinsic mode functions and the residual sequence. Finally, we applied the ensemble method to calculate the final predicted values of the original electricity price data. We performed mid-long-term and short-term predictions with the electricity price data of the PJM electricity market in the United States to verify the forecasting performance of the DOE model. The empirical results showed that the DOE model can achieve high accuracy in both horizontal and directional precisions.


Funded by

国家自然科学基金(61773401,61304067,11601524,61761130081,11571368)


References

[1] Maciejowska K, Nowotarski J, Weron R. Probabilistic forecasting of electricity spot prices using Factor Quantile Regression Averaging. 2016, 32: 957-965 CrossRef Google Scholar

[2] Conejo A J, Plazas M A, Espinola R. Day-Ahead Electricity Price Forecasting Using the Wavelet Transform and ARIMA Models. 2005, 20: 1035-1042 CrossRef ADS Google Scholar

[3] Xu W, Zhou H, Cheng N. Internet of vehicles in big data era. 2018, 5: 19-35 CrossRef Google Scholar

[4] Zhang C S. Challenges in machine learning. Sci Sin Inform, 2013, 43: 1612--1623. Google Scholar

[5] Itaba S, Mori H. An Electricity Price Forecasting Model with Fuzzy Clustering Preconditioned ANN. 2018, 138: 90-98 CrossRef ADS Google Scholar

[6] Saadaoui F. A seasonal feedforward neural network to forecast electricity prices. 2017, 28: 835-847 CrossRef Google Scholar

[7] Xiao Q, Zeng Z. Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales.. 2017, 47: 2984-2994 CrossRef PubMed Google Scholar

[8] Wu A, Liu L, Huang T. Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments.. 2017, 85: 118-127 CrossRef PubMed Google Scholar

[9] ?zgüner E, T?r O B, Güven A N. Probabilistic day-ahead system marginal price forecasting with ANN for the Turkish electricity market. 2017, 25: 4923-4935 CrossRef Google Scholar

[10] Zhu S, Yang Q, Shen Y. Noise further expresses exponential decay for globally exponentially stable time-varying delayed neural networks.. 2016, 77: 7-13 CrossRef PubMed Google Scholar

[11] Zhang W, Zhang H, Liu J. Weather prediction with multiclass support vector machines in the fault detection of photovoltaic system. 2017, 4: 520-525 CrossRef Google Scholar

[12] Ma Z, Zhong H, Xie L. Month ahead average daily electricity price profile forecasting based on a hybrid nonlinear regression and SVM model: an ERCOT case study. 2018, 6: 281-291 CrossRef Google Scholar

[13] Shao Z, Yang S L, Gao F. A new electricity price prediction strategy using mutual information-based SVM-RFE classification. 2017, 70: 330-341 CrossRef Google Scholar

[14] Yan X, Chowdhury N A. Mid-term electricity market clearing price forecasting using multiple least squares support vector machines. 2014, 8: 1572-1582 CrossRef Google Scholar

[15] Mareda T, Gaudard L, Romerio F. A parametric genetic algorithm approach to assess complementary options of large scale windsolar coupling. 2017, 4: 260-272 CrossRef Google Scholar

[16] Gu W, Yu Y, Hu W. Artificial bee colony algorithmbased parameter estimation of fractional-order chaotic system with time delay. 2017, 4: 107-113 CrossRef Google Scholar

[17] Heydari A, Keynia F. A new intelligent heuristic combined method for short-term electricity price forecasting in deregulated markets. 2016, 13: 258-267 CrossRef Google Scholar

[18] Liu H, Mi X, Li Y. An experimental investigation of three new hybrid wind speed forecasting models using multi-decomposing strategy and ELM algorithm. 2018, 123: 694-705 CrossRef Google Scholar

[19] Sun S, Wang S, Zhang G. A decomposition-clustering-ensemble learning approach for solar radiation forecasting. 2018, 163: 189-199 CrossRef ADS Google Scholar

[20] Mirjalili S, Lewis A. The Whale Optimization Algorithm. 2016, 95: 51-67 CrossRef Google Scholar

[21] Wang J, Du P, Niu T. A novel hybrid system based on a new proposed algorithm-Multi-Objective Whale Optimization Algorithm for wind speed forecasting. 2017, 208: 344-360 CrossRef Google Scholar

[22] Bento P M R, Pombo J A N, Calado M R A. A bat optimized neural network and wavelet transform approach for short-term price forecasting. 2018, 210: 88-97 CrossRef Google Scholar

[23] Wang D, Luo H, Grunder O. Multi-step ahead electricity price forecasting using a hybrid model based on two-layer decomposition technique and BP neural network optimized by firefly algorithm. 2017, 190: 390-407 CrossRef Google Scholar

[24] Shayeghi H, Ghasemi A, Moradzadeh M. Day-ahead electricity price forecasting using WPT, GMI and modified LSSVM-based S-OLABC algorithm. 2017, 21: 525-541 CrossRef Google Scholar

[25] Wang Y H, Yeh C H, Young H W V. On the computational complexity of the empirical mode decomposition algorithm. 2014, 400: 159-167 CrossRef ADS Google Scholar

[26] Gu J, Gu M, Cao C. A novel competitive co-evolutionary quantum genetic algorithm for stochastic job shop scheduling problem. 2010, 37: 927-937 CrossRef Google Scholar

[27] Zhan S, Huo H. Improved PSO-based task scheduling algorithm in cloud computing. J Inf Computat Sci, 2012, 9: 3821--3829. Google Scholar

[28] Lewis C. International and Business Forecasting Methods. London: Butter-Worths, 1982. Google Scholar

  • Figure 1

    (Color online) Hybrid learning framework of FEEMD-IWOA-RBF

  • Figure 2

    (Color online) Original data of electricity price in PJM market

  • Figure 3

    (Color online) Electricity price decomposed by FEEMD

  • Figure 4

    (Color online) Related error of mid-long-term prediction of forecasting models

  • Figure 7

    Related error of short-term prediction of hybrid models

  • 图 8

    (网络版彩图) 模型的RMSE结果对比图

  • 图 13

    (网络版彩图) 模型的$D_s$结果对比

  •   

    Algorithm 1 IWOA算法

    Initialize the whales' population $X_i~(i=1,2,\ldots,n)$ and calculate the fitness of each whale;

    $X^*_{\rm~prey}=$ the fittest whale (a similar position of the prey);

    while $l<$ maximum number of iterations

    for each whale

    Update $a,~A,~C,~t$ and $p$;

    if1 $p<0.5$

    if2 $|A|<1$

    update the position of the current whaleby 13;

    else if2 $|A|>1$

    Select a random whale $X_{\rm~rand}$;

    Update the position of the current whale by 5;

    end if2

    else if1 $p>0.5$

    Update the position of the current whale by 7;

    end if1

    Using quantum method to update the positions of all the whales by 10;

    Choose the better updating method by comparing the fitness of 5, 7, 13 and 10;

    end for

    Check if any whale goes beyond the search space and amend it;

    Calculate the fitness of each whale;

    Update $X^*_{\rm~prey}$ if there is a better solution;

    $l=l+1$;

    end while

    return $X^*_{\rm~prey}.$

  • 1   Table 1Error analysis results of improved models of mid-long-term prediction
    Error reduction (100%)
    Evaluating FEEMD-IWOA-RBF FEEMD-IWOA-RBF FEEMD-IWOA-RBF IWOA-RBF IWOA-RBF
    indicator vs. vs. vs. vs. vs.
    VMD-IWOA-RBF IWOA-RBF RBF WOA-RBF RBF
    RMSE 89.6009 64.0848 77.8211 17.1842 38.2465
    NRMSE 89.6047 64.1062 77.8208 17.1842 38.2088
    MAPE 92.9205 60.0071 72.0683 8.6842 30.1584
    MAE 57.3394 $-$350.000 10.5769 82.6923 82.6923
    TIC 88.2116 63.9967 77.3153 5.9384 36.9927
    $D_s$ 38.5564 34.6831 33.6268 0.5392 1.5915
  • 2   Table 2Error analysis results of improved models of short-term prediction
    Error reduction (100%)
    Evaluating FEEMD-IWOA-RBF FEEMD-IWOA-RBF FEEMD-IWOA-RBF IWOA-RBF IWOA-RBF
    indicator vs. vs. vs. vs. vs.
    VMD-IWOA-RBF IWOA-RBF RBF WOA-RBF RBF
    RMSE 88.0326 54.2226 77.1650 20.2163 50.1173
    NRMSE 88.0379 54.2376 77.1725 20.2168 50.1174
    MAPE 92.9313 54.0561 75.1738 21.5856 45.9642
    MAE 85.6757 48.6835 89.4479 79.4372 79.4372
    TIC 63.4663 54.3258 76.3710 73.8163 48.2661
    $D_s$ 46.3414 36.5854 26.8292 $-$10.3449 10.3449
  • 3   Table 3DM test results of electricity price mid-long-term forecasting
    Benchmark model
    Tested model FEEMD- VMD- VMD- IWOA- WOA-RBF RBF BPNN SVR
    WOA-RBF IWOA-RBF WOA-RBF RBF
    FEEMD- 1.1368 9.2603 9.2547 0.4285 2.1887 1.6479 3.3695 42.7820
    IWOA-RBF (0.8720) (1.0000) (1.0000) (0.9546) (0.9855) (0.9501) (0.9996) (1.0000)
    FEEMD- 4.3688 4.3695 $-$0.7944 $-$0.6698 2.2486 1.0601 6.6285
    WOA-RBF (1.0000) (1.0000) (0.2136) (0.2516) (0.9876) (0.8533) (1.0000)
    VMD- 1.0925 $-$10.8100 $-$10.6180 $-$2.1621 $-$4.2964 1.7575
    IWOA-RBF (0.8621) (2E$-$16) (2E$-$16) (0.0155) (9.9E$-$6) (0.9604)
    VMD- $-$10.8030 $-$10.6120 $-$2.1632 $-$4.2976 1.7535
    WOA-RBF (2E$-$16) (2E$-$16) (0.0154) (9.9E$-$6) (0.9600)
    IWOA-RBF 2.0274 1.4617 2.9284 28.5080
    (0.9875) (0.9278) (0.9982) (1.0000)
    WOA-RBF 1.3862 2.8616 27.7560
    (0.9169) (0.9978) (1.0000)
    RBF $-$0.1602 3.0827
    (0.4364) (0.9989)
    BPNN 8.3562
    (1.0000)
  • 4   Table 4DM test results of electricity price short-term forecasting
    Benchmark model
    Tested model FEEMD- VMD- VMD- IWOA- WOA-RBF RBF BPNN SVR
    WOA-RBF IWOA-RBF WOA-RBF RBF
    FEEMD- 1.3318 3.6532 3.6557 1.6066 1.8730 1.2870 2.3400 $-$0.5259
    IWOA-RBF (0.9053) (0.9997) (1.0000) (0.9426) (0.9855) (0.9664) (0.9882) (0.3007)
    FEEMD- 3.6433 3.6459 1.4351 1.7937 1.2824 2.3266 2.7214
    WOA-RBF (0.9997) (0.9997) (0.9211) (0.9604) (0.8970) (0.9878) (0.9955)
    VMD- 0.7011 $-$3.7150 $-$3.5472 $-$0.5841 $-$1.8705 1.8132
    IWOA-RBF (0.7566) (0.0003) (0.0004) (0.2810) (0.0338) (0.9619)
    VMD- $-$3.7182 $-$3.5506 $-$0.5862 $-$1.8738 1.8121
    WOA-RBF (0.0003) (0.0003) (0.2803) (0.0036) (0.9618)
    IWOA-RBF 1.2284 1.2394 2.2119 2.7012
    (0.8873) (0.8893) (0.9841) (0.9952)
    WOA-RBF 1.2368 2.1159 2.6719
    (0.8889) (0.9802) (0.9948)
    RBF $-$0.5259 1.9896
    (0.3007) (0.9738)
    BPNN 2.5081
    (0.9922)
  • 5   Table 5PT test results of electricity price forecasting
    FEEMD- FEEMD- VMD- VMD- IWOA- WOA- RBF BPNN SVR
    IWOA-RBF WOA-RBF IWOA-RBF WOA-RBF RBF RBF
    Mid-long-term 24.9790 20.5746 $-$8.1915 $-$8.1915 4.5563 4.1174 4.7664 0.1540 0.9324
    forecasting (0.0000) (0.0000) (2.0000) (2.0000) (5.2E$-$6) (3.8E$-$5) (1.8E$-$6) (0.8876) (0.3511)
    Short-term 7.9825 7.3510 NAN NAN 0.6061 1.7474 2.0263 0.9509 0.6397
    forecasting (1.3E$-$15) (2.0E$-$13) NAN NAN (0.5444) (0.0806) (0.0427) (0.3417) (0.5224)
  • 6   Table 6Error analysis results of compared models of mid-long-term prediction
    Evaluating indicator FA-BP VMD-FA-BP FEEMD-FA-BP FEEMD-VMD-FA-BP
    RMSE 9.2260 27.4947 6.3783 5.8784
    NRMSE 35.9376 107.0991 24.8451 22.8979
    MAPE 20.9548 102.1828 14.0246 14.2400
    MAE 0.0010 0.0269 0.0102 0.0072
    TIC 0.1841 0.3227 0.1714 0.1709
    $D_s$ 55.5887 52.0119 53.8003 55.8867
  • 7   Table 7Error analysis results of compared models of short-term prediction
    Evaluating indicator FA-BP VMD-FA-BP FEEMD-FA-BP FEEMD-VMD-FA-BP
    RMSE 9.2260 23.7100 6.4677 5.1113
    NRMSE 39.9836 105.1287 28.6773 22.6630
    MAPE 26.7387 101.5876 13.8441 12.2035
    MAE 14.3056 19.4101 2.7301 3.0527
    TIC 0.1917 0.3760 0.2068 0.2036
    $D_s$ 61.7021 46.8085 53.1915 63.8298

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有

京ICP备18024590号-1