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Probabilistic wind power forecasting using a novel hybrid intelligent method

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Abstract

As a consequence of increasing wind power penetration level, it will be a big challenge to control and operate the power system because of the inherent uncertainty of the wind energy. One of the ways to deal with the wind power variability is to predict it accurately and reliably. The traditional point forecasting-based technique cannot notably solve the uncertainty in power system operation. In order to compute the probabilistic forecasting, which yields information on the uncertainty of wind power, a novel hybrid intelligent method that incorporates the wavelet transform, neural network (NN), and improved krill herd optimization algorithm (IKHOA), is used in this paper. Also, the extreme learning machine is exerted to train NN and calculates point forecasts, and IKHOA is applied to forecast the noise variance. The robust method called bootstrap is regarded to create prediction intervals and calculate the model uncertainty. The efficiency of proposed forecasting engine is evaluated by usage of wind power data from the Alberta, Canada.

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Abbreviations

\(b_{i} ,b^{^\circ }\) :

Biases of ELM and approximated models

B PI :

Number of the bootstrap duplicates

ϑ (α) :

Indicator of PICP

LS :

Cost function of the gradient-based learning algorithm

\(DS_{{s^{2} }}\) :

Generated dataset for training the models of noise variance estimation

f D ():

Output function

φ():

Activation function of neural network

H :

Hidden-layer output matrix

\(H^{\dag }\) :

Moore–Penrose generalized inverse of the hidden-layer output matrix

D :

Number of hidden nodes

\({\mathcal{L}}_{t}^{\alpha }\) :

Lower bound of PI

\({\mathcal{U}}_{t}^{\alpha }\) :

Upper bound of PI

m :

Dimension of the output vector

n :

Dimension of the input vector

N :

Number of training samples

\(N_{{\mathcal{T}}}\) :

Number of test samples

IS α t (x i ):

Interval score

\(T, t\) :

Matrix of targets, targets/length of time series, time period

v :

Input weights of ELM

v ♢ :

Approximated input weights

z :

Input variables

L :

True regression

\(\hat{L}\) :

Trained neural network

∂1−α/2 :

Critical value of the normal distribution

(1 − α):

Confidence level

γ ♢ :

Approximated output weights

γ :

Output weights of ELM

\(\hat{\sigma }_{t}^{2}\) :

Variance of the total forecasting error

\(\hat{\sigma }_{L}^{2}\) :

Variance of the model uncertainty

\(\hat{\sigma }_{\varepsilon }^{2}\) :

Variance of the data noise

ρ α t :

Width of PI

\({\text{M}}\) :

Selected wavelet function

w t :

The value of the wind at hour t

DP M rc :

Decomposition coefficient at resolution level r and position c

A r :

Approximation series

D r :

Detail series

\({\mathcal{M}}\) :

Mother wavelet functions

\({\mathcal{F}}\) :

Father wavelet functions

\({\mathcal{X}},{\mathcal{X}}^{best}\) :

Position of ith krill individual, position of best krill individual

\(A_{i} ,A_{w} , A_{b}\) :

Fitness value of ith, worth, best individual

A b i :

Best fitness value of the previously visited position associated with ith krill individual

\({\mathcal{X}}_{i}^{b}\) :

Previous best position of the ith krill individual

ac s :

Accumulation factor of sth strategy

C d :

Cartesian distance to best krill individual

iter :

Iteration counter

iter max :

Maximum number of iterations

\({\mathcal{X}}^{M}\) :

New improved individual based on the mutation operator

\({\mathcal{X}}_{{TS_{i} }}\) :

ith test individual produced in each strategy

N n :

Number of neighbors

N pop :

Krill size

N d :

Number of the decision variables

N im :

Number of krill individuals which choose a strategy

Pr s :

Normalized probability associated with sth strategy

\(d_{z}\) :

Diagnosing zone

UP j :

Upper restriction of jth decision variable

LOW j :

Lower restriction of jth decision variable

\({\mathcal{V}}_{I,i}^{g}\) :

Induced velocity in gth generation

\({\mathcal{V}}_{F,i}^{g}\) :

Foraging velocity in gth generation

\({\mathcal{V}}_{D,i}^{g}\) :

Diffusion velocity in gth generation

\({\mathcal{V}}_{I,i}^{max}\) :

Maximum induced velocity

\({\mathcal{V}}_{i}^{g}\) :

Speed of ith krill individual

ℓ i :

Random variable

\(\partial_{I} , \partial_{F}\) :

Inertia weight of induction velocity, inertia weight of foraging velocity

\(\text{g}_{m}\) :

Mutation level

g :

Generation index

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Authors and Affiliations

  1. Department of Electrical Engineering, Shiraz University of Technology, Shiraz, Iran

    Moseyeb Afshari-Igder, Taher Niknam & Mohammad-Hassan Khooban

Authors
  1. Moseyeb Afshari-Igder
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  2. Taher Niknam
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  3. Mohammad-Hassan Khooban
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Correspondence to Mohammad-Hassan Khooban.

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Afshari-Igder, M., Niknam, T. & Khooban, MH. Probabilistic wind power forecasting using a novel hybrid intelligent method. Neural Comput & Applic 30, 473–485 (2018). https://doi.org/10.1007/s00521-016-2703-z

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  • DOI: https://doi.org/10.1007/s00521-016-2703-z

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