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Intelligent Hybrid Wavelet Models for Short-term Load

Forecasting

Ajay Shekhar PandeyDevender Singh

Sunil Kumar Sinha

IEEE transactions on POWER SYSTEMS, Aug 2010

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Outline Introduction Wavelet decomposition &

reconstruction Proposed methods

Intelligent hybrid models Forecasting process

Results

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Introduction Electricity load at particular time is usually assumed to be a

linear combination of different components. From signals point of view, load can also be considered as a linear combination of different frequents.

Wavelet is a tool can be effectively utilized for the prediction of short-term loads, and can be integrated with the neural network.

Approaches in earlier literature used wavelet coefficients of the time series as input data to the network. The present approach use the wavelet pre-processed time series after removing the higher frequency component, can use on both traditional methods(time series) and nontraditional methods(neural networks or fuzzy).

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Wavelet The discrete wavelet transform(DWT) is capable of

producing coefficients of fine scale for capturing high frequency information and coefficient of coarse scales for capturing low frequency information. For a mother wavelet function and a given signal :

where is the dilation or level index, is translation or scaling index, is a scaling function or coarse scale coefficients, are the scaling function of detail(fine scale) coefficient

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Wavelet decomposition Wavelet decomposition break a signal into many

lower resolution components, known as wavelet decomposition tree

Wavelet decomposition can yield a signal to get valuable information. And a suitable number of levels based on the nature of the signal can be selected for having an optimum solution

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Wavelet Reconstruction Wavelet decomposed units can be assembled into

the original signal without loss of information, this process called reconstruction or synthesis

Original signal S is reconstructed after deleting the high frequency detail coefficients D1 for smoothening of the data S = A1 + D1 = A2 + D2 + D1 = A3 + D3 + D2 + D1

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Proposed methods Intelligent Hybrid Models Forecasting process

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Intelligent Hybrid Models Wavelet decomposition based RBF neural

networks Radial basis function neural network(RBFNN) is one of

the basic feedforward neural networks. The neurons in the hidden layer contain Gaussian

transfer functions whose outputs are inversely proportional to the distance from the center of the neuron(radial basis function).

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Intelligent Hybrid Models Wavelet decomposition based time series model

The Time Series Forecast uses linear regression to calculate a best fit line over a designated time period; this line is then plotted forward a user-defined time period.

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Intelligent Hybrid Models Wavelet decomposition based FINN model

The fuzzy inference neural network (FINN) is a hybrid model of fuzzy inference engine and RBFNN

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Forecast Process Wavelet decomposition

The actual time series, load and temperature data are first decomposed in to a number of wavelet coefficients signal and one approximation signal.

The approximations are high scale and low frequency componentThe details are low scale and high frequency component

A three resolution with Daubechies wavelet(db2) is used

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Forecast Process Smoothening and reconstruction

After decomposition, smoothening of data is required for having a fast and smooth training of the network

Smoothening is to delete the higher frequency components of the decomposed data

The high frequency component does not change from reference day to the forecast day, and thus do not show any causality => delete

The signal is reconstructed after deleting the higher frequency components of detail coefficients

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Results Settings

Training by four weeks load and temperature historical data

To reflect the behavior of network during season changes, the results are reported for three weeks, one each for winter, spring and summer

Three comparison performed WNN in two different leading time (24h & 168h

ahead) WNN against conventional(MLR1, MLR2, TS) and

nonconventional models(FFNN, RBFNN, clustering, FINN)

Three methods with/without wavelet pre-processing

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Results Lead time comparison

Forecast day ahead and week ahead on an hourly basis

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Results Comparison with other forecast models

With multiple linear regression , time series, feed forwarding neural network(FFNN), RBFNN, clustering and FINN

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Results

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Results Comparison with/without wavelet

Non wavelet forecasting models are compared with the wavelet based forecasting models of the same method.

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Results