A novel power-driven fractional accumulated grey model and its application in forecasting wind energy consumption of China

Autoři: Peng Zhang aff001;  Xin Ma aff002;  Kun She aff001
Působiště autorů: School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, China aff001;  School of Science, Southwest University of Science and Technology, Mianyang, China aff002;  State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China aff003
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0225362


Wind energy is one of the most important renewable resources and plays a vital role in reducing carbon emission and solving global warming problem. Every country has made a corresponding energy policy to stimulate wind energy industry development based on wind energy production, consumption, and distribution. In this paper, we focus on forecasting wind energy consumption from a macro perspective. A novel power-driven fractional accumulated grey model (PFAGM) is proposed to solve the wind energy consumption prediction problem with historic annual consumption of the past ten years. PFAGM model optimizes the grey input of the classic fractional grey model with an exponential term of time. For boosting prediction performance, a heuristic intelligent algorithm WOA is used to search the optimal order of PFAGM model. Its linear parameters are estimated by using the least-square method. Then validation experiments on real-life data sets have been conducted to verify the superior prediction accuracy of PFAGM model compared with other three well-known grey models. Finally, the PFAGM model is applied to predict China’s wind energy consumption in the next three years.

Klíčová slova:

Alternative energy – Differential equations – Humpback whales – Oils – Optimization – Wind – Wind power


1. Saidur R, Islam MR, Rahim NA, Solangi KH. A review on global wind energy policy. Renewable and Sustainable Energy Reviews. 2010;14(7):1744–1762. doi: 10.1016/j.rser.2010.03.007

2. Zhang P. Do energy intensity targets matter for wind energy development? Identifying their heterogeneous effects in Chinese provinces with different wind resources. Renewable Energy. 2019;139:968–975. doi: 10.1016/j.renene.2019.03.007

3. Liu H, Chen C, Lv X, Wu X, Liu M. Deterministic wind energy forecasting: A review of intelligent predictors and auxiliary methods. Energy Conversion and Management. 2019;195(January):328–345. doi: 10.1016/j.enconman.2019.05.020

4. Yang Z, Wang J. A hybrid forecasting approach applied in wind speed forecasting based on a data processing strategy and an optimized artificial intelligence algorithm. Energy. 2018;160:87–100. doi: 10.1016/j.energy.2018.07.005

5. do Nascimento Camelo H, Lucio PS, JB VL Junior, de Carvalho PCM. A hybrid model based on time series models and neural network for forecasting wind speed in the Brazilian northeast region. Sustainable Energy Technologies and Assessments. 2018;28:65–72. doi: 10.1016/j.seta.2018.06.009

6. Xiao L, Qian F, Shao W. Multi-step wind speed forecasting based on a hybrid forecasting architecture and an improved bat algorithm. Energy Conversion and Management. 2017;143:410–430. doi: 10.1016/j.enconman.2017.04.012

7. Liu H, O’Connor T, Lee S, Yoon S. A process optimization strategy of a pulsed-spray fluidized bed granulation process based on predictive three-stage population balance model. Powder Technology. 2018;327:188–200. doi: 10.1016/j.powtec.2017.12.070

8. Santhosh M, Venkaiah C, Vinod Kumar DM. Ensemble empirical mode decomposition based adaptive wavelet neural network method for wind speed prediction. Energy Conversion and Management. 2018;168:482–493. doi: 10.1016/j.enconman.2018.04.099

9. Du P, Wang J, Yang W, Niu T. A novel hybrid model for short-term wind power forecasting. Applied Soft Computing Journal. 2019;80:93–106. doi: 10.1016/j.asoc.2019.03.035

10. Liu D, Niu D, Wang H, Fan L. Short-term wind speed forecasting using wavelet transform and support vector machines optimized by genetic algorithm. Renewable Energy. 2014;62:592–597. doi: 10.1016/j.renene.2013.08.011

11. Xiao L, Dong Y, Dong Y. An improved combination approach based on Adaboost algorithm for wind speed time series forecasting. Energy Conversion and Management. 2018;160:273–288. doi: 10.1016/j.enconman.2018.01.038

12. Kong X, Liu X, Shi R, Lee KY. Wind speed prediction using reduced support vector machines with feature selection. Neurocomputing. 2015;169:449–456. doi: 10.1016/j.neucom.2014.09.090

13. Zhang CY, Chen CLP, Gan M, Chen L. Predictive Deep Boltzmann Machine for Multiperiod Wind Speed Forecasting. IEEE Transactions on Sustainable Energy. 2015;6(4):1416–1425. doi: 10.1109/TSTE.2015.2434387

14. Liu H, Mi X, Li Y. Smart deep learning based wind speed prediction model using wavelet packet decomposition, convolutional neural network and convolutional long short term memory network. Energy Conversion and Management. 2018;166:120–131. doi: 10.1016/j.enconman.2018.04.021

15. Yu C, Li Y, Bao Y, Tang H, Zhai G. A novel framework for wind speed prediction based on recurrent neural networks and support vector machine. Energy Conversion and Management. 2018;178:137–145. doi: 10.1016/j.enconman.2018.10.008

16. Yang W, Wang J, Lu H, Niu T, Du P. Hybrid wind energy forecasting and analysis system based on divide and conquer scheme: A case study in China. Journal of Cleaner Production. 2019;222:942–959. doi: 10.1016/j.jclepro.2019.03.036

17. Du P, Wang J, Yang W, Niu T. A novel hybrid model for short-term wind power forecasting. Applied Soft Computing. 2019;80:93–106. doi: 10.1016/j.asoc.2019.03.035

18. Shukur OB, Lee MH. Daily wind speed forecasting through hybrid KF-ANN model based on ARIMA. Renewable Energy. 2015;76:637–647. doi: 10.1016/j.renene.2014.11.084

19. Aasim, Singh SN, Mohapatra A. Repeated wavelet transform based ARIMA model for very short-term wind speed forecasting. Renewable Energy. 2019;136:758–768. doi: 10.1016/j.renene.2019.01.031

20. Ding S, Hipel KW, guo Dang Y. Forecasting China’s electricity consumption using a new grey prediction model. Energy. 2018;149:314–328. doi: 10.1016/j.energy.2018.01.169

21. Xu N, Dang Y, Gong Y. Novel grey prediction model with nonlinear optimized time response method for forecasting of electricity consumption in China. Energy. 2017;118:473–480. doi: 10.1016/j.energy.2016.10.003

22. Bianco V, Manca O, Nardini S. Electricity consumption forecasting in Italy using linear regression models. Energy. 2009;34(9):1413–1421. doi: 10.1016/j.energy.2009.06.034

23. Wang ZX, Li Q, Pei LL. A seasonal GM(1,1) model for forecasting the electricity consumption of the primary economic sectors. Energy. 2018;154:522–534.

24. da Silva FLC, Cyrino Oliveira FL, Souza RC. A bottom-up bayesian extension for long term electricity consumption forecasting. Energy. 2019;167:198–210. doi: 10.1016/j.energy.2018.10.201

25. Tang L, Wang X, Wang X, Shao C, Liu S, Tian S. Long-term electricity consumption forecasting based on expert prediction and fuzzy Bayesian theory. Energy. 2019;167:1144–1154. doi: 10.1016/j.energy.2018.10.073

26. Bahrami S, Hooshmand RA, Parastegari M. Short term electric load forecasting by wavelet transform and grey model improved by PSO (particle swarm optimization) algorithm. Energy. 2014;72:434–442. doi: 10.1016/j.energy.2014.05.065

27. Yang Y, Xue D. Continuous fractional-order grey model and electricity prediction research based on the observation error feedback. Energy. 2016;115:722–733. doi: 10.1016/j.energy.2016.08.097

28. Wu L, Gao X, Xiao Y, Yang Y, Chen X. Using a novel multi-variable grey model to forecast the electricity consumption of Shandong Province in China. Energy. 2018;157(2018):327–335. doi: 10.1016/j.energy.2018.05.147

29. Hamzacebi C, Es HA. Forecasting the annual electricity consumption of Turkey using an optimized grey model. Energy. 2014;70:165–171. doi: 10.1016/j.energy.2014.03.105

30. Sen D, Günay ME, Tunç KMMM. Forecasting annual natural gas consumption using socio-economic indicators for making future policies. Energy. 2019;173:1106–1118. doi: 10.1016/j.energy.2019.02.130

31. Zhang W, Yang J. Forecasting natural gas consumption in China by Bayesian Model Averaging. Energy Reports. 2015;1:216–220. doi: 10.1016/j.egyr.2015.11.001

32. Li J, Wang R, Wang J, Li Y. Analysis and forecasting of the oil consumption in China based on combination models optimized by artificial intelligence algorithms. Energy. 2018;144:243–264. doi: 10.1016/j.energy.2017.12.042

33. Wang Q, Song X. Forecasting China’s oil consumption: A comparison of novel nonlinear-dynamic grey model (GM), linear GM, nonlinear GM and metabolism GM. Energy. 2019;183:160–171. doi: 10.1016/j.energy.2019.06.139

34. Wu W, Ma X, Zeng B, Wang Y, Cai W. Application of the novel fractional grey model FAGMO(1,1,k) to predict China’s nuclear energy consumption. Energy. 2018;165:223–234. doi: 10.1016/j.energy.2018.09.155

35. Tang L, Yu L, He K. A novel data-characteristic-driven modeling methodology for nuclear energy consumption forecasting. Applied Energy. 2014;128:1–14. doi: 10.1016/j.apenergy.2014.04.021

36. Wang H, Lei Z, Zhang X, Zhou B, Peng J. A review of deep learning for renewable energy forecasting. Energy Conversion and Management. 2019;198(April):111799. doi: 10.1016/j.enconman.2019.111799

37. Wu L, Zhao H. Discrete grey model with the weighted accumulation. Soft Computing. 2019;3.

38. Wang Q, Liu L, Wang S, Wang JZ, Liu M. Predicting Beijing’s tertiary industry with an improved grey model. Applied Soft Computing Journal. 2017;57:482–494. doi: 10.1016/j.asoc.2017.04.022

39. Xia J, Ma X, Wu W, Huang B, Li W. Application of a new information priority accumulated grey model with time power to predict short-term wind turbine capacity. Journal of Cleaner Production. 2019; p. 118573.

40. Liu X, Xie N. A nonlinear grey forecasting model with double shape parameters and its application. Applied Mathematics and Computation. 2019;360:203–212. doi: 10.1016/j.amc.2019.05.012

41. Hu Y. Electricity consumption prediction using a neural-network-based grey forecasting approach. Journal of the Operational Research Society. 2017;68(10):1259–1264. doi: 10.1057/s41274-016-0150-y

42. Wang ZX. An optimized Nash nonlinear grey Bernoulli model for forecasting the main economic indices of high technology enterprises in China. Computers and Industrial Engineering. 2013;64(3):780–787. doi: 10.1016/j.cie.2012.12.010

43. Zeng B, Li C. Forecasting the natural gas demand in China using a self-adapting intelligent grey model. Energy. 2016;112:810–825. doi: 10.1016/j.energy.2016.06.090

44. Li L, Wang H. A VVWBO-BVO-based GM (1,1) and its parameter optimization by GRA-IGSA integration algorithm for annual power load forecasting. PLoS ONE. 2018;13(5):e0196816. doi: 10.1371/journal.pone.0196816 29768450

45. Wang Z, Hao P. An improved grey multivariable model for predicting industrial energy consumption in China. Applied Mathematical Modelling. 2016;40(11-12):5745–5758. doi: 10.1016/j.apm.2016.01.012

46. Zeng B, Li C. Improved multi-variable grey forecasting model with a dynamic background-value coefficient and its application. Computers and Industrial Engineering. 2018;118(March):278–290. doi: 10.1016/j.cie.2018.02.042

47. Zeng B, Duan H, Zhou Y. A new multivariable grey prediction model with structure compatibility. Applied Mathematical Modelling. 2019;75:385–397. doi: 10.1016/j.apm.2019.05.044

48. Ma X, Liu Z. The GMC (1, n) Model with Optimized Parameters and Its Application. Journal of grey system. 2017;29(4):122–138.

49. Wu L, Liu S, Yao L, Yan S, Liu D. Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation. 2013;18(7):1775–1785. doi: 10.1016/j.cnsns.2012.11.017

50. Mao S, Gao M, Xiao X, Zhu M. A novel fractional grey system model and its application. Applied Mathematical Modelling. 2016;40(7-8):5063–5076. doi: 10.1016/j.apm.2015.12.014

51. Ma X, Mei X, Wu W, Wu X, Zeng B. A novel fractional time delayed grey model with Grey Wolf Optimizer and its applications in forecasting the natural gas and coal consumption in Chongqing China. Energy. 2019;178:487–507. doi: 10.1016/j.energy.2019.04.096

52. Ma X, Wu W, Zeng B, Wang Y, Wu X. The conformable fractional grey system model. ISA Transactions. 2019;. doi: 10.1016/j.isatra.2019.07.009

53. Zeng B, Liu S. A self-adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application. Mathematical Methods in the Applied Sciences. 2017;40(18):7843–7857. doi: 10.1002/mma.4565

54. Ma X, Xie M, Wu W, Zeng B, Wang Y, Wu X. The novel fractional discrete multivariate grey system model and its applications. Applied Mathematical Modelling. 2019;70:402–424. doi: 10.1016/j.apm.2019.01.039

55. Xu H, Liu S, Fang Z. Optimization of grey action quantity of GM(1,1) model. Mathematics in Practice and Theory. 2010;40(2):27–32.

56. Mirjalili S, Lewis A. The Whale Optimization Algorithm. Advances in Engineering Software. 2016;95:51–67. doi: 10.1016/j.advengsoft.2016.01.008

57. Gharehchopogh FS, Gholizadeh H. A comprehensive survey: Whale Optimization Algorithm and its applications. Swarm and Evolutionary Computation. 2019;48(November 2018):1–24. https://doi.org/10.1016/j.swevo.2019.03.004

58. Shaikh F, Ji Q, Shaikh PH, Mirjat NH, Uqaili MA. Forecasting China’s natural gas demand based on optimised nonlinear grey models. Energy. 2017;140:941–951. doi: 10.1016/j.energy.2017.09.037


60. Ma X, Liu Z. Predicting the Cumulative Oil Field Production Using the Novel Grey ENGM Model. Journal of Computational and Theoretical Nanoscience. 2016;13(1):89–95. doi: 10.1166/jctn.2016.4773

61. Chen PY, Yu HM. Foundation Settlement Prediction Based on a Novel NGM Model. Mathematical Problems in Engineering. 2014;2014:1–8.

Článek vyšel v časopise


2019 Číslo 12
Nejčtenější tento týden