Applications of extension grey prediction model for power system forecasting. (English) Zbl 1282.90152

Summary: Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literature’s show its performance could be further improved. For this purpose, this paper proves that the growth rate of the simulated value of the grey model GM(1, 1) is a fixed value. If the growth rates of the primary sequence are equate, the fitted value deriving from GM(1, 1) is the same as the primary sequence, otherwise greater error would occur. In order to overcome shortcoming of the fixed growth rates, extend the traditional GM(1, 1) model by introducing linear time-varying terms, which can predict more accurately on non geometric sequences, termed EGM(1, 1). Finally, compared with the other improved grey model and ARIMA model, experimental results indicate that the proposed model obviously can improve the prediction accuracy.


90C27 Combinatorial optimization
90C90 Applications of mathematical programming
Full Text: DOI


[1] Guo R, Love E (2005) Fuzzy set-valued and grey filtering statistical inferences on a system operation data. J Qual Maint Eng 11(3):267-278
[2] He WZ, Song G (2005) Estimation of grey model parameter based on genetic algorithm. J Syst Eng 20(4):432-436 · Zbl 1331.62102
[3] Hsien CH (2002) Grey neural network and its application to short term load forecasting problem. IEICE Trans Inf Syst 2:897-902
[4] Hsu L-C (2011) Using improved grey forecasting models to forecast the output of opto-electronics industry. Expert Syst Appl 38(11):13879-13885
[5] Julong D (2002) The basis of grey theory. Huazhong University of Science & Technology, Wuhan
[6] Li FQ, Liu JG (2008) Study on the improvement of grey forecasting model by data transformation. Stat Decis 6(6):15-17
[7] Li B, Wei Y (2009) Optimized grey derivative of GM(1,1). Syst Eng, Theory Pract 9(2):100-105
[8] Li, GD; Yamaguchi, D.; Nagai, M., Application of improved grey prediction model to short term load forecasting, 1-6 (2006)
[9] Li D, Chang C, Chen W, Chen C (2011) An extended grey forecasting model for omnidirectional forecasting considering data gap difference. Appl Math Model 35(10):5051-5058 · Zbl 1228.62162
[10] Liu B, Liu SF (2003) Optimum time response sequence for GM(1,1). Chin Manag Sci 11(4):54-57
[11] Luo D, Liu SF, Dang YG (2003) The optimization of grey model GM(1,1). Eng Sci 5(8):50-53
[12] Mu Y (2003) An unbiased GM(1,1) model with optimum grey derivative’s whitening values. Math Practice Theory 33(3):13-16
[13] Song ZM, Zhang SH (2002) Separated modeling method in grey system. Syst Eng, Theory Pract 22(5):103-107
[14] Wang J, Zhu S, Zhao W, Zhu W (2011) Optimal parameters estimation and input subset for grey model based on chaotic particle swarm optimization algorithm. Expert Syst Appl, 38(7):8151-8158
[15] Xie NM, Liu SF (2009) Discrete grey forecasting model and its optimized. Appl Math Model 33:1173-1186 · Zbl 1168.62380
[16] Yunbai L, Ping Y, Bin S, et al. (2001) Prediction of the gas dissolved in power transformer oil by the grey model. Proc CSEE 21(3):65-69
[17] Zeng XY, Xiao XP (2009) Study on generalization for GM(1,1) model and its application. Control Decis 24(7):1092-1096
[18] Zhang H, Hu SG (2001) Accurate solution for GM(1,1) model. Syst Eng Theory Methodol Appl 10(1):72-74
[19] Zhang DH, Jiang SF, Shi KQ (2002) Theoretical defect of grey prediction formula and its improvement. Syst Eng, Theory Pract 22(8):140-142
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