# Forecasting Monthly Electric Energy Consumption Using Feature Extraction

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Feature Extraction and Forecasting Algorithms

#### 2.1. Feature Extraction Based on DWT

_{j}

_{,k}(t) can be written as:

^{j}is a scale function and ka

^{j}b is a translation function, both of which are derived from a continuous wavelet transform (CWT) by discreteness.

_{j}

_{,k}is derived from:

_{L}) and high-frequency coefficients (y

_{0}− y

_{L}). The low-frequency and high-frequency coefficients comprise the approximate features and the details of f(t), respectively. The relationship between these values is defined by f(t) = z

_{L}+ y

_{0}+ y

_{1}+ … + y

_{L}.

#### 2.2. GM for Exponential Trend Forecasting

_{1}, b

_{2}, and b

_{3}are the shape parameters. In fact, by adjusting the parameters of b

_{1}, b

_{2}, and b

_{3}, Equation (4) can simulate any smoothing convex trend. The optimum parameters of Equation (4) cannot be obtained by minimizing the residual sum of square (RSS) because of the location of b

_{3}. Deng [23,24] proposed a method for solving this problem.

^{(0)}(k) (k = 1,2,…) refers to the raw series, and x

^{(1)}(k) (k = 1,2,…) stands for the accumulated generating series and is written as ${x}^{(1)}(k)={\displaystyle \sum _{i=1}^{k}{x}^{(0)}(i)}$.

**N**= [x

^{(0)}(2) x

^{(0)}(3) … x

^{(0)}(n)]

^{T},

**A**= [a u]

^{T}, and $B=\left[\begin{array}{cc}-\frac{1}{2}[{x}^{(1)}(1)+{x}^{(1)}(2)]& 1\\ -\frac{1}{2}[{x}^{(1)}(2)+{x}^{(1)}(3)]& 1\\ \vdots & \vdots \\ -\frac{1}{2}[{x}^{(1)}(n-1)+{x}^{(1)}(n)]& 1\end{array}\right]$

^{(1)}(1) as a particular solution will yield the following solution for Equation (5):

^{(0)}is derived as follows:

#### 2.3. RBF NNs for Periodical Waves

_{j}is the output value of jth node in the hidden layer, x is the input vector of the hidden layer, w

_{j}is the center of the Gauss function of the jth node, σ

_{j}

^{2}is the spread of the Gauss function, and N

_{1}is the number of nodes in the hidden layer. Based on Equation (12), the output of each Gauss function will be between 0 and 1. Furthermore, each Gauss function has a reflection (significantly unequal 0) only when the input vector is very close to the space center (w

_{j}).

#### 2.4. Forecasting Model Design

## 3. Experimental Setup and Forecasting Results

^{8}kWh) in China from January 1990 to December 2006 were selected to validate the aforementioned methods. Data were obtained from the website of the Chinese Economic and Financial Database of the China Center for Economic Research (CCER) [25]. The monthly electric energy consumption curve (Figure 3) obviously exhibits a basic exponential rising trend and is characterized by numerous waves.

Actual Data | Method 1 | Error (%) | Method 2 | Error (%) | Method 3 | Error (%) | Method 4 | Error (%) | |
---|---|---|---|---|---|---|---|---|---|

Jan. 2005 | 1914.89 | 1934.16 | 1.01 | 1811.98 | 5.37 | 1797.75 | −6.12 | 1931.2 | 0.85 |

Feb. | 1601.06 | 1686.78 | 5.35 | 1770.77 | −10.6 | 1741.73 | 8.79 | 1684.61 | 5.22 |

Mar. | 1940.47 | 1879.17 | −3.16 | 1912.86 | 1.42 | 1893.04 | −2.44 | 1877.78 | −3.23 |

Apr. | 1892.06 | 1843.68 | −2.56 | 1906.05 | −0.74 | 1878.43 | −0.72 | 1843.17 | −2.58 |

May | 1924.7 | 1957.53 | 1.71 | 1950.29 | −1.33 | 1907.51 | −0.89 | 1957.53 | 1.71 |

Jun. | 2006.75 | 2075.33 | 3.42 | 2006.39 | 0.02 | 1962.02 | −2.23 | 2074.67 | 3.38 |

Jul. | 2178.9 | 2148.25 | −1.41 | 2160.61 | 0.84 | 2096.35 | −3.79 | 2146.74 | −1.48 |

Aug. | 2162.05 | 2124.62 | −1.73 | 2158.88 | 0.15 | 2092.78 | −3.2 | 2122.05 | −1.85 |

Sep. | 2053.25 | 2035.17 | −0.88 | 2083.3 | −1.46 | 2018.1 | −1.71 | 2031.7 | −1.05 |

Oct. | 2010.97 | 1916.54 | −4.7 | 2093.51 | −4.1 | 2024.17 | 0.66 | 1912.9 | −4.88 |

Nov. | 2041.89 | 1970.19 | −3.51 | 2130.93 | −4.36 | 2052 | 0.5 | 1966.37 | −3.7 |

Dec. | 2246.59 | 2195.55 | −2.27 | 2250.09 | −0.16 | 2145.64 | −4.49 | 2191.91 | −2.43 |

Jan. 2006 | 2063.39 | 2107.82 | 2.15 | 2057.61 | 0.28 | 2049.61 | −0.67 | 2104.61 | 2 |

Feb. | 1962.01 | 1990.85 | 1.47 | 1954.98 | 0.36 | 1927.18 | −1.78 | 1988 | 1.32 |

Mar. | 2161.62 | 2128.15 | −1.55 | 2160.16 | 0.07 | 2137.9 | −1.1 | 2125.66 | −1.66 |

Apr. | 2116.6 | 2059.6 | −2.69 | 2137.18 | −0.97 | 2114.38 | −0.1 | 2057.53 | −2.79 |

May | 2175.28 | 2165.91 | −0.43 | 2172.42 | 0.13 | 2153.48 | −1 | 2164.19 | −0.51 |

Jun. | 2301.93 | 2289.92 | −0.52 | 2228.76 | 3.18 | 2215.43 | −3.76 | 2287.68 | −0.62 |

Jul. | 2517.14 | 2422.73 | −3.75 | 2370.46 | 5.83 | 2368.84 | −5.89 | 2419.8 | −3.87 |

Aug. | 2570.49 | 2468.77 | −3.96 | 2361.52 | 8.13 | 2371.35 | −7.75 | 2465.09 | −4.1 |

Sep. | 2364.75 | 2426.81 | 2.62 | 2258.85 | 4.48 | 2288.2 | −3.24 | 2422.4 | 2.44 |

Oct. | 2324.3 | 2300.76 | −1.01 | 2266.56 | 2.48 | 2308.43 | −0.68 | 2296.04 | −1.22 |

Nov. | 2363.36 | 2199.24 | −6.94 | 2298.88 | 2.73 | 2346.64 | −0.71 | 2194.15 | −7.16 |

Dec. | 2573.4 | 2439.59 | −5.2 | 2391.33 | 7.08 | 2462.79 | −4.3 | 2434.3 | −5.41 |

Method 1 | Method 2 | Method 3 | Method 4 | |
---|---|---|---|---|

MaxAPE | 6.94 | 10.6 | 8.79 | 7.16 |

MAPE | 2.67 | 2.76 | 2.76 | 2.73 |

MdAPE | 2.42 | 1.44 | 2.01 | 2.44 |

GMARE | 0.61 | 0.33 | 0.51 | 0.63 |

## 4. Conclusions

## Acknowledgements

## References

- Papalexopoulos, A.D.; Hesterberg, T.C. A regression-based approach to short-term load forecasting. IEEE Trans. Power Syst.
**1990**, 5, 1535–1550. [Google Scholar] [CrossRef] - Rahman, S.; Hazim, O. A generalized knowledge-based short-term loadforecasting technique. IEEE Trans. Power Syst.
**1993**, 8, 508–514. [Google Scholar] [CrossRef] - Abdel-Aal, R.E.; Al-Garni, A.Z. Forecasting monthly electric energy consumption in Eastern Saudi Arabia using univariate time-series analysis. Energy
**1997**, 22, 1059–1069. [Google Scholar] [CrossRef] - Saab, S.; Badr, E.; Nasr, G. Univariate modeling and forecasting of energy consumption: The case of electricity in Lebanon. Energy
**2001**, 26, 1–14. [Google Scholar] [CrossRef] - Hong, W.C.; Dong, Y.; Lai, C.-Y.; Chen, L.-Y.; Wei, S-Y. SVR with Hybrid Chaotic Immune Algorithm for Seasonal Load Demand Forecasting. Energies
**2011**, 4, 960–977. [Google Scholar] [CrossRef] - Reis, A.J.R.; Silva, A.P.A.D. Feature extraction via multiresolution analysis for short-term load forecasting. IEEE Trans. Power Syst.
**2005**, 20, 189–198. [Google Scholar] [CrossRef] - Kandil, N.; Wamkeue, R.; Saad, M.; Georges, S. An efficient approach for short term load forecasting using artificial neural networks. Int. J. Electr. Power Energy Syst.
**2006**, 28, 525–530. [Google Scholar] [CrossRef] - Lauret, P.; Fock, E.; Randrianarivony, R.N.; Manicom-Ramsamy, J.-F. Bayesian neural network approach to short time load forecasting. Energy Convers. Manag.
**2008**, 49, 1156–1166. [Google Scholar] [CrossRef] - Xiao, Z.; Ye, S.-J.; Zhong, B.; Sun, C.-X. BP neural network with rough set for short term load forecasting. Expert Syst. Appl.
**2009**, 36, 273–279. [Google Scholar] [CrossRef] - Amjady, N.; Keynia, F. A new neural network approach to short term load forecasting of electrical power systems. Energies
**2011**, 4, 488–503. [Google Scholar] [CrossRef] - Amjady, N.; Keynia, F. Day-ahead price forecasting of electricity markets by mutual information technique and cascaded neuro-evolutionary algorithm. IEEE Trans. Power Syst.
**2009**, 24, 306–318. [Google Scholar] [CrossRef] - Amjady, N.; Keynia, F. A new prediction strategy for price spike forecasting of day-ahead electricity markets. Appl. Soft Comput.
**2011**, 11, 4246–4256. [Google Scholar] [CrossRef] - Hagan, M.T.; Demuth, H.B.; Beale, M.H. Neural Network Design; PWS Publishing Company: Boston, MA, USA, 1996. [Google Scholar]
- Haykin, S. Neural Networks: A Comprehensive Foundation; Pearson Education Inc.: Upper Saddle River, NJ, USA, 2009. [Google Scholar]
- Parkpoom, S.J.; Harrison, G.P. Analyzing the impact of climate change on future electricity demand in Thailand. IEEE Trans. Power Syst.
**2008**, 23, 1441–1448. [Google Scholar] [CrossRef] - Abdel-Aal, R.E. Univariate modeling and forecasting of monthly energy demand time series using abductive and neural networks. Comput. Ind. Eng.
**2008**, 54, 903–917. [Google Scholar] [CrossRef] - Chang, P.-C.; Fan, C.-Y.; Lin, J.-J. Monthly electricity demand forecasting based on a weighted evolving fuzzy neural network approach. Int. J. Electr. Power Energy Syst.
**2011**, 33, 17–27. [Google Scholar] [CrossRef] - Zhao, S.; Wei, G.W. Jump process for the trend estimation of time series. Comput. Stat. Data Anal.
**2003**, 42, 219–241. [Google Scholar] [CrossRef] - González-Romera, E.; Jaramillo-Morán, M.A.; Carmona-Fernández, D. Monthly electric energy demand forecasting based on trend extraction. IEEE Trans. Power Syst.
**2006**, 21, 1946–1953. [Google Scholar] [CrossRef] - González-Romera, E.; Jaramillo-Morán, M.A.; Carmona-Fernández, D. Forecasting of the electric energy demand trend and monthly fluctuation with neural networks. Comput. Ind. Eng.
**2007**, 52, 336–343. [Google Scholar] [CrossRef] - González-Romera, E.; Jaramillo-Morán, M.A.; Carmona-Fernández, D. Monthly electric energy demand forecasting with neural networks and Fourier series. Energy Convers. Manag.
**2008**, 49, 3135–3142. [Google Scholar] [CrossRef] - Saravanan, N.; Ramachandran, K.I. Incipient gear box fault diagnosis using discrete wavelet transform (DWT) for feature extraction and classification using artificial neural network (ANN). Expert Syst. Appl.
**2010**, 37, 4168–4181. [Google Scholar] [CrossRef] - Deng, J.-L. Control problems of grey systems. Syst. Control Lett.
**1982**, 1, 288–294. [Google Scholar] [CrossRef] - Deng, J.-L. Grey Forecasting and Decision; Huazhong University of Science & Technology Press Co.: Hangzhou, China, 2002. [Google Scholar]
- China Center for Economic Research (CCER). Chinese Economic and Financial Database 2011. Available online: http://www.ccerdata.com (accessed on 30 April 2011).

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**MDPI and ACS Style**

Meng, M.; Niu, D.; Sun, W.
Forecasting Monthly Electric Energy Consumption Using Feature Extraction. *Energies* **2011**, *4*, 1495-1507.
https://doi.org/10.3390/en4101495

**AMA Style**

Meng M, Niu D, Sun W.
Forecasting Monthly Electric Energy Consumption Using Feature Extraction. *Energies*. 2011; 4(10):1495-1507.
https://doi.org/10.3390/en4101495

**Chicago/Turabian Style**

Meng, Ming, Dongxiao Niu, and Wei Sun.
2011. "Forecasting Monthly Electric Energy Consumption Using Feature Extraction" *Energies* 4, no. 10: 1495-1507.
https://doi.org/10.3390/en4101495