A novel approach for harmonic tidal currents constitutions forecasting using hybrid intelligent models based on clustering methodologies

Journal Pre-proof A Novel Approach for Harmonic Tidal Currents Constitutions Forecasting using Hybrid Intelligent Models based on Clustering Methodologies

Hamed H.H. Aly PII:

S0960-1481(19)31445-4

DOI:

https://doi.org/10.1016/j.renene.2019.09.107

Reference:

RENE 12329

To appear in:

Renewable Energy

Received Date:

06 July 2018

Accepted Date:

21 September 2019

Please cite this article as: Hamed H.H. Aly, A Novel Approach for Harmonic Tidal Currents Constitutions Forecasting using Hybrid Intelligent Models based on Clustering Methodologies, Renewable Energy (2019), https://doi.org/10.1016/j.renene.2019.09.107

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A Novel Approach for Harmonic Tidal Currents Constitutions Forecasting using Hybrid Intelligent Models based on Clustering Methodologies Hamed H. H. Aly Electrical and Computer Engineering Department, Dalhousie University and Electrical Power and Machines Engineering, Zagazig University, Mathematics and Statistics Department, Acadia University

Abstract— Forecasting of renewable energy resources and their output power is playing a key role to improve the grid energy efficiency by making some load generation management. Tidal currents output power is depending on the tidal currents constitutions (speed magnitude and direction) forecasting. The accuracy of the tidal currents forecasting models is very important especially when we deal with smart grid and renewable energy integration. Many models are proposed in the literature for tidal currents forecasting but most of the models are not able to control the requirements of the smart grid due to their accuracy. This paper is proposing hybrid approaches for harmonic tidal currents constitutions forecasting based on clustering approaches to improve the system accuracy. These hybrid models involve various combinations of Wavelet and Artificial Neural Network (WNN and ANN) and Fourier Series Based on Least Square Method (FSLSM) techniques. The proposed work is validated by using two different datasets one for tidal currents speed magnitude and the other one for tidal currents direction as well as K-fold cross validation. Simulations results prove the importance of the proposed models to improve the system performance. The proposed models are tested based on actual tidal currents data collected from the Bay of Fundy, Canada in 2008.

Keywords - Tidal currents forecasting; Smart grid; ANN; FSLSM; WNN; Clustering techniques. 1

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1. Introduction Tidal currents energy is playing an important role these days as it is pollution free energy, but its cost is still high compared to other renewable energy resources. Tidal currents energy is promising to be one of the most valuable energies used in the future as it is somewhat predictable energy compared to wind energy. Prediction of tidal currents output power is based on the prediction of tidal currents speed and direction. Forecasting tidal currents using data gathered for short periods of time is predictable to within 98% accuracy. The accuracy of models used for tidal currents forecasting is very important as the integration of the tidal currents power into the grid is depending on its forecasting accuracy. Many works done in the literature for tidal currents forecasting but most of the work done was depending on using an artificial technique for the tidal forecasting and rarely used hybrid models [1-5]. In this paper, we propose hybrid models based on clustering techniques to improve the overall system accuracy; hence improve the integration and increase the overall system stability.

2. Previous Work Done on Tidal Currents Forecasting The idea of representing the tidal currents by a number of simple harmonic constitutions came by Darwin et al. They stated that “The tidal oscillation, of the ocean may be represented as the sum of a number of simple harmonic waves” [6]. Harmonic component theory of tidal currents constitutions is modified by Doodson who suggested to use least squares estimation to estimate the parameters of the series [7-9]. Aly and El-Hawary proposed different models based on ANN and Fourier series based on Least Square method for the tidal currents speed forecasting. They proposed a hybrid model of ANN and FSLSM for improving the system accuracy [1, 2]. Lee and Jeng proposed a model of ANN for tidal forecasting using data from three harbors in Taiwan [10]. 2

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Lee used the ANN backpropagation with descent [11]. Vijay and Govil used radial basis function of ANN and WNN approaches. They found that both ANN and WNN are effective but WNN requires longer time for training [12]. Chen et al. and Adamowski used hybrid model of WNN and ANN. The proposed model improved the accuracy compared to the ANN or WNN alone [13, 14]. An interval-based model constructs the optimal prediction intervals based on support vector regression and a non-parametric method is used for tidal currents forecasting. The fuzzy membership functions are used for that model to provide appropriate balance between the coverage probability and normalized average width [15]. A model based on WNN and support vector regression along with an optimization method based on the bat algorithm is used to train the support vector regression model [16]. Most of the previous used techniques were using the data as it is without any modification or analysis to improve the system accuracy. Due to uncertainties and fluctuation of the data the models were not accurate especially if we are going to use the models to predict the output power for the purpose of integration into the smart grid. In this paper we use clustering techniques to generate different segments of data (we use different number of cluster segments) to improve the overall system accuracy and executable time needed for the training. As well as we use hybrid models of WNN, ANN and FSLSM to add many desired features to the proposed models. Different calibrations methods are used to compare the accuracy of the work to the previous work done. From these methods we use mean absolute error (MAPE). MAPE is defined as the absolute average difference between the actual and predicted values as shown in equation 1[17].

𝑀𝐴𝑃𝐸 =

1 𝑁

∑|

|

𝑁

𝑥𝑖 ― 𝑦𝑖

1

𝑦𝑖

3

(1)

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Another calibration method is the index r which is describing the strength of the relation between the measured and predicted and is defined in equation 2[17].

𝑟=

𝑛(∑𝑥𝑖𝑦𝑖) ― (∑𝑦𝑖)(∑𝑥𝑖)

(𝑛∑𝑥𝑖2 ― (∑𝑥𝑖)2)(𝑛∑𝑦𝑖2 ― (∑𝑦𝑖)2)

(2)

The most commonly used factor also is normalized root mean square error (nRMSE) which is defined in equation 3 [18, 19]. 1 𝑁 ∑1 (𝑥𝑖 ― 𝑦𝑖)2 𝑁 𝑛𝑅𝑀𝑆𝐸 = 𝑦

(3)

where, x is the predicted value, y is the actual value, N is the number of observations and ̅y is mean of the actual data. In this paper we use a clustering technique to discriminate between different shapes for the data and put them in different segments based on their common characteristics. Then we use six different hybrid models of WNN and ANN; ANN and WNN; ANN and FSLSM; FSLSM and ANN; WNN and FSLSM and finally FSLSM and WNN to choose the best one. The clustered data is fed first to the first technique and the error (which is the difference between the actual and the predicted data) is fed to the second technique. Then the output is the summation of the output from the first technique and the output from the second technique. The paper is organized as follows. In Sections 3, 4 and 5 the concept of clustering, ANN, WNN and FSLSM methodologies and the proposed models constructions are introduced. In section 6 we define six different hybrid models proposed as well as the results of the proposed hybrid models along with the simulations for the tidal currents speed and direction forecasting as a way of validation as well as using k-fold for cross validation. The new contribution in this paper is the hybrid models of different techniques 4

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based on Artificial Intelligent as well as the feedback signals from the residuals to improve the overall system accuracy with the help of clustering techniques. Different algorithms with different learning rates, different training functions and epochs are tested based on the clustered data.

3. Clustering Techniques for the Tidal Currents Constitutions Forecasting Model One of the best mathematical methods for improving the forecasting models is to use clustering techniques. K-means is unsupervised learning algorithm used for solving clustering problems. The clustering algorithm could be described by the following steps: 1.The data are clustered into k groups randomly. 2.The k centroid should be defined for each cluster and then take each point near to these centroids. 3. Recalculate new centroids. K centroids are changing their locations repeatedly until no more change takes place. 4.This way is depending on minimizing a certain objective function which is the error as shown in Fig. 1.

x…….. ….. Start m2 …….. x

……..x ….. Start m3 …x…..

……..x ….. Start m1 x……..

x …….. ….. Start mn ……..x

x …….. ….. Start m4 …….. …….. x Final Boundary

Fig. 1 K-mean clustering technique

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The tidal currents constitutions features are varying from location to another and from time to time, so it is a good idea to make some analysis to examine the behaviour of the tidal currents constitutions and create some common segments that has the same characteristics. This is what we call clustering. This could be done using various statistical analysis by different analytical methods and different programs. In this paper we use a clustering technique based on k-mean shown Fig. 1 with the help of R-studio and Matlab softwares. After creating the clustering segments, the data is fed to ANN, WNN and FSLSM for forecasting. This technique is reducing the error profile for the predicted data. The number and size of clusters segments are playing a crucial role for improving the characteristics of the forecasting methods. As the size is increased, the performance is improved but at the same time the number of clusters segments will be decreased, and the overall improvement will be affected. So, this is a nonlinear problem and it is hard to find the best size and segments numbers. By increasing the clustering segment size, the performance will be improved but at the same time will minimize the clusters numbers which has a negative impact on the performance and vise versa. Many clustering sizes and numbers are used in this paper to choose the best one depending on the minimum error. After making some statistical studies we found that the improvement is not recognized if the clusters numbers are above eight and below four, but the best one is when the clusters numbers are eight. In this paper we use different forecasting techniques to predict the tidal currents constitutions after for the clustered data. In the k-mean clusters approach we use z as data with t instances, and S1, S2, . . . ,Sk are the k disjoint clusters of z. The error function is defined by equation 4.

𝑘

Error = ∑𝑖 = 1∑𝑥 ∈ 𝑆𝑖𝐷(𝑦, 𝜇(𝑆𝑖))

6

(4)

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where μ(Si) is the centroid of cluster Si, D(y,μ(Si)) is the distance between y data point and μ(Si), the Euclidean distance for any data points yi = (yi1, yi2, . . . , yin) and yj =(yj1, yj2, . . . , yjn) is defined by equation (4) and shown in Fig. 1 [20, 21]. 𝑛

Deuc(yi, yj) = (∑𝑘 = 1(𝑦𝑖𝑘 ― 𝑦𝑖𝑘) 2)

1/2

(5)

4. Proposed Network Construction

We use hybrid models of WNN, ANN and FSLSM and we aggregate the clustered data into aggregated forecasting hybrid model. Fig. 2 shows the proposed clustering forecasting aggregated model. The data is fed first to the clustering algorithm and the clustered data is fed to different forecasting models to choose the best forecasting model and then data is aggregated to have one model to have an output for each input. Fig. 3 shows the proposed models. The data is fed first to R-studio for creating clustering segments based on the common features. The clustered data is fed to ANN then compare the forecasted data by the actual one to calculate the error data (residuals). The error data is fed to WNN to find the forecasted residuals. The forecasted data is equal to the summation of output from ANN and WNN. In each case the number of neurons, hidden layers and epochs is changed regularly to minimize the error as well as the trained functions. Then we choose the best case for the forecasted data. The forecasted data and the actual data are compared to calculate MAPE and nRMSE. The whole process is repeated for six different approaches (WNN+ANN, ANN+ FSLSM, FSLSM + ANN, WNN + FSLSM, and FSLSM + WNN). The last step is to compare between different approaches and choose the best one that has minimum MAPE, and nRMSE.

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Data input

R-studio for having different clusters numbers and sizes

Cluster 1

Hybrid forecasting model 1

Hybrid forecasting model 4

Cluster 2

Cluster …

Hybrid forecasting model 2

Hybrid forecasting model 5

Cluster n

Hybrid forecasting model 3

Hybrid forecasting model 6

Aggregated forecasting model

Fig. 2 Input output clustered forecasting aggregated model

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Load data file ← two months ahead Use R-studio for creating clustering segments

Feed clustered data to ANN; compare model to actual data to find the error.

Feed clustered data to ANN then compare model to actual data to calculate the error data.

Feed clustered data to WNN; compare the model data to actual data to find the error.

Feed clustered data to FSLSM then compare model data to actual data calculate the error data.

Feed clustered data to WNN then compare the model data to actual data to find the error.

Feed clustered data to FSLSM then compare model data to actual data to calculate the error data.

Feed the error data to WNN

Feed the error data to FSLSM

Feed the error data to ANN

Feed the error data to FSLSM

Feed the error data to ANN

Feed the error data to WNN

ANN+ WNN

ANN+ FSLSM

WNN+ FSLSM

WNN+ ANN

FSLSM +ANN

FSLSM +WNN

Calculate MAPE, and 𝑛𝑅𝑀𝑆𝐸 for each model and choose the best one.

Stop

Fig. 3 Tidal currents forecasting proposed models

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Algorithm 1. Load data file. 2. Use R-studio for creating clustering segments. 3. Feed the clustered data to ANN then compare the forecasted data by the actual one to calculate the error data. 4. Feed the error data to WNN and find the forecasted error. 5. The forecasted data is equal to the summation of output from ANN and WNN. 6. Compare between the forecasted data and the actual data and calculate MAPE and 𝑛𝑅𝑀𝑆𝐸. 7. Repeat from 3 to 6 by using different approaches (WNN+ANN, ANN+ FSLSM, FSLSM + ANN, WNN + FSLSM, and FSLSM + WNN). 8. Compare between different models and choose the best one that has minimum MAPE, and 𝑛𝑅𝑀𝑆𝐸.

5. ANN, WNN and FSLM Approaches Back propagation ANN is a supervised training approach and is used to improve the error derivative of the weights and biases. The training is done in two modes, the online and the batch modes. The Radial Basis Function network is practical application model. Linear transfer functions are used for layers and nonlinear transfer functions are used for hidden layers. It requires more neurons compared to BP but it needs less time for the training. FSLSM model can be described by equation (6).

𝑁

Zestimated(k) = DC + ∑𝑛 = 1𝑎𝑖sin (𝑤𝑖𝑘 + 𝜃𝑖)

10

(6)

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where DC is the constant value and is depending on the data; k is discrete time; a is amplitude; i is the number of harmonics in the wave; and θi is the phase shift. The actual data is defined by: Z = DC + HX + Ɛ(k)

(6.a)

where Ɛ(k) is the error, and then we apply the least squares model, as shown in the equations (711), to estimate the Fourier series parameters Xhat = (HTH)-1HTZ

(7)

Zsetimate = DC + HXhat

(8)

Zerror = Z - Zsetimate

(9)

[

H=

𝑠𝑖𝑛𝑤1 𝑐𝑜𝑠𝑤1 ………………. 𝑠𝑖𝑛𝑤𝑖 𝑐𝑜𝑠𝑤𝑖

]

𝑠𝑖𝑛2𝑤1 𝑐𝑜𝑠2𝑤1……………….……….𝑐𝑜𝑠2𝑤𝑖 ………… ……………. ………..……….………..…………. 𝑠𝑖𝑛𝑛𝑤1 ……………..……….. …….. ………. 𝑐𝑜𝑠𝑛𝑤𝑖

[ ]

(10)

𝑎1𝑐𝑜𝑠𝜃1

X=

………. …….. 𝑎𝑖𝑐𝑜𝑠𝜃𝑖

(11)

6. Harmonics Tidal Currents Constitutions Forecasting Models 6.1. Tidal Currents Hybrid Model of ANN and WNN In this model we use ANN feed forward back propagation function to train the un-clustered (row data) and clustered data. The input to the model is the time for each ten minutes for two months and the output is the tidal currents speed in meters per second. The forecasted data for the unclustered data is compared to the actual data and we calculate the residuals which is the forecasted minus the actual. We do the same with the clustered data, but the data is aggregated before 11

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calculating the residuals. The residuals are then fed to WNN for both cases (clustered and unclustered data). The model is validated by using different set of data which is the tidal currents direction forecasting. The MAPE and nRMS are calculated for that model for tidal currents speed and direction forecasting as shown in table 1 and 2. As we see from table 1 the MAPE for unclustered data is 1.55791 and for clustered data is 1.1578 and nRMS is 0.0406 for un-clustered data and is 0.0202 for clustered data. Fig. 4 shows the relationship between the actual and forecasted data with and without clustering for tidal currents speed forecasting and the time. Fig. 5 shows the same relationship for the tidal currents direction as a way of validation of the proposed model. As we see the clustering technique is improving the performance of the forecasting model.

4 Forecasted with clustering Actual data Forecasted without clustering

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Fig. 4 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents speed forecasting and the time in minutes based on ANNWNN Hybrid model. 12

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Fig. 5 The relationship between the actual data, forecasted data with and without clustering for tidal currents direction forecasting and the time based on ANNWNN Hybrid model. 2.6

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Fig. 6 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents speed forecasting and the time in minutes based on based on WNNANN Hybrid model.

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Fig. 7 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents direction forecasting and the time based on WNNANN Hybrid model. 6.2. Tidal Currents Hybrid Model of WNN and ANN In this model we use WNN to train the un-clustered (row) and clustered data. The input to that model is the time for each ten minutes for two months and the output is the tidal currents speed in meter per second. The forecasted data for the un-clustered data model is compared to the actual data and we calculate the residuals which is the forecasted minus the actual. We do the same with the clustered data, but the data is aggregated before calculating the residuals. The residuals are then fed to ANN for both cases (clustered and un-clustered data). The model is validated by using different set of data from which is the tidal currents direction forecasting. The MAPE and nRMS are calculated for that model for tidal currents speed and direction forecasting and it is shown in table 1 and 2. As we see from table 1 the MAPE for un-clustered data is 1.2522 and for clustered 14

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data is 1.0322 and nRMS is 0.0176 and for un-clustered data and is 0.0091 for clustered data. As we see the clustering technique is improving the performance of the forecasting model. Fig. 6 shows the relationship between the actual and forecasted data with and without clustering for tidal currents speed forecasting and the time. Fig. 7 shows the same relationship for the tidal currents direction as a way of validation of the proposed model.

This model is considered as the best

model for both tidal currents speed magnitude and direction forecasting. 6.3. Tidal Currents Hybrid Model of ANN and FSLSM In this model we use ANN to train the un-clustered (row) and clustered data. The forecasted data for the un-clustered data is compared to the actual data and we calculate the residuals. We do the same with the clustered data, but the data is aggregated before calculating the error. The residuals are fed then to FSLSM for both cases (clustered and un-clustered data). 4 Forecasted with clustering Actual data Forecasted without clustering

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Fig. 8 The relationship between the actual data, forecasted data with and without clustering for tidal speed forecasting and the time in minutes based on based on ANNFSLSM Hybrid model. The model is validated by using different set of data from which is the tidal currents direction forecasting. The MAPE and nRMS are calculated for that model for tidal currents speed and

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direction forecasting and it is shown in table 1 and 2. As we see from table 1 the MAPE for unclustered data is 1.4945 and for clustered data is 1.1945 and nRMS is 0.0421 for un-clustered data and is 0.0292 for clustered data. Fig. 8 shows the relationship between the actual and forecasted data with and without clustering for tidal currents speed forecasting and the time. Fig. 9 shows the same relationship for the tidal currents direction as a way of validation of the proposed model.

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Fig. 9 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents direction forecasting and the time based on FSLSMANN Hybrid model.

6.4. Tidal Currents Hybrid Model of FSLSM and ANN In this model we use FSLSM to train the un-clustered (row) and clustered data. The forecasted data for the un-clustered data is compared to the actual data and we calculate the error. We do the same with the clustered data, but the data is aggregated before calculating the error. The error 16

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is fed then to ANN for both cases (clustered and un-clustered data). The model is validated by using different set of data from which is the tidal currents direction forecasting.

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Fig. 10 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents speed forecasting and the time in minutes based on FSLSMANN Hybrid model. The MAPE and nRMS are calculated for that model for tidal currents speed and direction forecasting and it is shown in table 1 and 2. As we see from table 1 the MAPE for un-clustered data is 1.686 and for clustered data is 1.306 and nRMS is 0.0361 for un-clustered data and is 0.0212 for clustered data. As we see the clustering technique is improving the performance of the forecasting model. Fig. 10 shows the relationship between the actual data, forecasted data with and without clustering technique for the tidal currents speed and the time. Fig. 11 shows the same relationship between tidal currents direction and the time.

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Fig. 11 The relationship between the actual data, forecasted data with and without clustering for tidal currents direction forecasting and the time based on FSLSMANN Hybrid model. 6.5. Tidal Currents Hybrid Model of WNN and FSLSM WNN is used first to train the un-clustered (row) and clustered data. The input to that model is the time for each ten minutes for two months and the output is the tidal currents speed in meter per second. We do the same with the clustered data. The error is then fed to FSLSM for both cases (clustered and un-clustered data). The model is validated by using the tidal currents direction data. The MAPE and nRMS are calculated for that model for tidal currents speed and direction forecasting and it is shown in table 1 and 2. As we see from table 1 the MAPE for un-clustered data is 1.5212 and for clustered data is 1.2212 and nRMS is 0.0298 for un-clustered data and is 0.0102 for clustered data. As we see the clustering technique is improving the performance of the forecasting model. Fig. 12 shows the relationship between the actual data, forecasted data with and without clustering technique for tidal currents speed and the time while Fig. 13 shows the same relationship for the tidal currents direction forecasting.

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Fig. 12 The relationship between the actual data, forecasted data with and without clustering for tidal currents speed forecasting and the time in minutes based on for WNNFSLSM Hybrid model.

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Fig. 13 The relationship between the actual data, forecasted data with and without clustering for tidal currents direction forecasting and the time based on WNNFSLSM Hybrid model. 6.6. Tidal Currents Hybrid Model of FSLSM and WNN In this model we feed the un-clustered data to FSLSM first. We do the same with the clustered data, but the data is aggregated before calculating the error. The error is fed then to WNN for both

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cases. The model is validated by using different set of data which is the tidal currents direction forecasting. The MAPE and nRMS are calculated for that model for tidal currents speed and direction forecasting and it is shown in table 1 and 2. As we see from table 1 the MAPE for unclustered data is 1.7069 and for clustered data is 1.4068 and nRMS is 0.0421 for un-clustered data and is 0.0299 for clustered data. As we see the clustering technique is improving the performance of the forecasting model. Fig. 14 shows the relationship between the actual and forecasted data with and without clustering for tidal currents speed forecasting and the time a certain period. Fig. 15 shows the same relationship for the tidal currents direction forecasting.

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Fig. 14 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents speed forecasting and the time in minutes based on based on FSLSMWNN Hybrid model.

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Fig. 15 The relationship between the actual data, forecasted data with and without clustering technique for tidal currents direction forecasting and the time based on WNNFSLSM Hybrid model. Another way of validation is to use K-fold cross validation. In k-fold cross validation the data is first partitioned into k approximately equally sized segments. Data is commonly stratified prior to being split which means rearranging the data to ensure each fold is a good representative of the whole. Table 3 shows a comparison between 8-fold 6-fold and 4-fold cross validation. Table 1. MAPE and nRMS for different models with and without clustering technique for tidal current speed magnitude forecasting Different techniques for direction forecasting ANN+WNN ANN+FSLSM WNN+ANN WNN+FSLSM FSLSM+ANN FSLSM+WNN

Models without clustering MAPE nRMSE 1.55791 0.0406 1.4945 0.0421 1.2522 0.0176 1.686 0.0361 1.5212 0.0298 1.7069 0.0421

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Models with clustering MAPE nRMSE 1.1578 0.0202 1.1945 0.0292 1.0322 0.0091 1.306 0.0212 1.2212 0.0102 1.4068 0.0299

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Table 2. MAPE and nRMS for different models with and without clustering technique for tidal currents direction forecasting Different techniques for direction forecasting

Models without clustering MAPE 1.6793 1.5452 1.322 1.605 1.705 1.823

ANN+WNN ANN+FSLSM WNN+ANN WNN+FSLSM FSLSM+ANN FSLSM+WNN

nRMSE 0.0505 0.0501 0.0215 0.0320 0.0467 0.0542

Models with clustering MAPE nRMSE 1.191 0.0321 1.245 0.0395 1.0413 0.0102 1.321 0.0205 1.306 0.0322 1.376 0.0375

Table 3: Comparison between 8-fold 6-fold and 4-fold Cross Validation WNN+ANN techniques for 8-fold 6-fold and 4fold 4-fold 6-fold 8-fold

Models with clustering MAPE nRMSE 1.191 1.160 1.0413

0.0221 0.0215 0.0102

Conclusions Harmonic tidal currents constituents forecasting is considered as one of the highest important topics to be discussed these days and in the near future. Many models are proposed in the literature but most of them were focusing on either using one forecasting technique or two as a hybrid model. In this paper we use clustering techniques to modify the shape of the wave that will be forecasted to improve the accuracy of the forecasted model. As well as six different hybrid models are proposed based on different techniques. Due to fluctuation and nonlinearity of the forecasting data and the crucial requirements of new generation of renewable energy; forecasting of the renewable energy generated became very important key for load management and system coordination. This paper is not recommended to use only one technique for forecasting, but it is better to use hybrid

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techniques to take the advantages of each one. Also, it is recommended to use clustering techniques to have common segments for improving the system variance and as a result improving the overall system performance and accuracy. In this paper six different hybrid models based on clustering techniques are proposed. The procedure of clustering along with the hybrid models are repeatedly adjusts the network, so as to minimize the measure of the difference between the actual and the forecasted data. All proposed models are accurate compared to the previous conventional models without using clustering techniques, but the best model is the hybrid model of WNN and ANN with MAPE of 1.0322 compared to 1.2522 without clustering. The work is validated by applying the proposed models on two different datasets; one for tidal current speed magnitude and the other one is for tidal currents direction. Also, we use K-fold cross validation. From table 3 we conclude that the best size is 8 as it has the smallest (MAPE and nRMSE) error compared to 6-fold and 4fold cross validation. The simulation results prove the effectiveness of the proposed hybrid models based on clustering techniques compared to conventional models used without clustering techniques. The system accuracy is improved when the clustering techniques with hybrid models are used as the advantages of all techniques are added together in one model.

References [1] Hamed Aly, “Forecasting, Modeling and Control of Tidal Currents Electrical Energy Systems” Ph.D dissertation, Dept. Elect. Eng., Dalhousie Univ., Halifax, N.S., 2012. [2] Hamed H. H. Aly, M. E. El-Hawary, “A Proposed ANN and FLSM Hybrid Model for Tidal Current Magnitude and Direction Forecasting” IEEE Journal of Oceanic Engineering, Volume: 39, Issue: 1, Jan. 2014. [3] Hamed H. H. Aly, M. E. El-Hawary, A Proposed Algorithms for Tidal in-Stream Speed Model, American Journal of Energy Engineering. Vol. 1, No. 1, 2013, pp. 1-10. 23

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[4] Hamed H. H. Aly, M. E. El-Hawary, The Current Status of Wind and Tidal in-Stream Electric Energy Resources, American Journal of Electrical Power and Energy Systems. Vol. 2, No. 2, 2013, pp. 23-40. [5] Hamed H. H. Aly, and M. E. El-Hawary "State of the Art for Tidal Currents Electrical Energy Resources", 24th Annual Canadian IEEE Conference on Electrical and Computer En-gineering, Niagara Falls, Ontario, Canada, 2011. [6] G. H. Darwin, “On an apparatus for facilitating the reduction of tidal observations,” Proc. Roy. Soc. A, vol. 52, pp. 345–376, 1892. [7] A. T. Doodson, “The harmonic development of the tide-generating potential,” Proc. Roy. Soc. Lond., vol. 100, pp. 305–329, 1923. [8] A. T. Doodson, “The analysis and predictions of tides in shallow water,” Int. Hydrographic Rev., vol. 33, pp. 85–126, 1958. [9] V. John, “Harmonic tidal current constituents of the Western Arabian Gulf from moored current measurements,” Coastal Eng., vol. 17, pp. 145–151, 1992. [10] T. L. Lee and D. S. Jeng, “Application of artificial neural networks in tide forecasting,” Ocean Eng., vol. 29, no. 9, pp. 1003–1022, Aug. 2002. [11] T.-L. Lee, “Back-propagation neural network for long-term tidal predictions,” Ocean Eng., vol. 31, no. 2, pp. 225–238, Feb. 2004. [12] R. Vijay and R. Govil, “Tidal data analysis using ANN,” Journal of World Academic Science Engineering Technology, no. 24, pp. 872–875, 2006. [13] B.-F. Chen, H.-D. Wang, and C.-C. Chu, “Wavelet and artificial neural network analyses of tide forecasting and supplement of tides around Taiwan and South China Sea,” Ocean Eng., vol. 34, no. 16, pp. 2161–2175, Nov. 2007.

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[14] J. F. Adamowski, “River flow forecasting using wavelet and cross wavelet transform models,” J. Hydrol. Processes, vol. 22, no. 25, pp. 4877–4891, 2008. [15] Abdollah Kavousi-Fard “Modeling Uncertainty in Tidal Current Forecast Using Prediction Interval-Based SVR” IEEE Transaction on Sustainable Energy, vol. 8, no. 2, April 2017. [16] Abdollah Kavousi-Fard and Wencong Su “A Combined Prognostic Model Based on Machine Learning for Tidal Current Prediction” IEEE Transactions on Geoscience and Remote Sensing, vol. 55, no. 6, June 2017. [17] Y. Jie, Z. Mingzhan, and W. Qinglin. "Correlative analysis of measured data between anemometer tower and WTG," 8th International Conference on Computing and Networking Technology (ICCNT), Gueongju, 2012. [18] T. Senjyu, H. Takara, K. Uezato, and T. Funabashi, “One-Hour-Ahead load forecasting using neural network,” IEEE Trans. Power Syst., vol. 17, pp. 113–118, February 2002. [19] Tri Kurniawan Wijaya, Matteo Vasirani, Samuel Humeau, Karl Aberer, “Cluster-based Aggregate Forecasting for Residential Electricity Demand using Smart Meter Data”, IEEE International Conference on Big Data, Santa Clara, CA, USA, 2015. [20] J. B. MacQueen "Some Methods for classification and Analysis of Multivariate Observations, Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability", Berkeley, University of California Press, 1976. [21] Franklin L. Quilumba, Wei-Jen Lee, Heng Huang, David Y. Wang, Robert L. Szabados “Using Smart Meter Data to Improve the Accuracy of Intraday Load Forecasting Considering Customer Behavior Similarities”, IEEE Transactions on Smart grid, vol. 6, no. 2, March 2015.

Biography

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Hamed H. Aly received the B.Eng. and M.ASc. degrees in electrical engineering with distinction, in 1999 and 2005, respectively, from Zagazig University, Egypt and the Ph.D. degree from Dalhousie University, Canada, in 2013. He was working as Postdoctoral Research Associate for one year and as a lecturer for four years at Dalhousie University. He worked as a lecturer at Zagazig University for eight years. His research interests include: Power System Dynamics and Stability; Power Electronics; Electric Machines, Power Quality Issues; Applications of Artificial Intelligence in Power Systems; Smart Grid; and the Integration of Renewable Energy into the Electrical Grid. He taught in different universities in Canada. He pioneered many computational and artificial intelligence solutions to problems in economic/environmental operation of power systems. He has written one textbook, three chapters books and more than 50 refereed journal and conference articles. He has consulted and taught for more than 16 years. He is a senior member of the Institute of Electrical and Electronics Engineers (IEEE). Dr. Aly is a faculty member at Acadia University since 2013. Dr. Aly is currently an Assistant Professor at Faculty of Engineering, Zagazig University and an adjunct Assistant Professor at Dalhousie University.

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Highlights •Six different hybrid models are proposed for harmonic tidal currents forecasting. •The hybrid approaches are combinations of Wavelet, ANN and Least Square Method. •The most accurate hybrid model is the model of WNN and ANN with MAPE of 1.0322. •Two different datasets used (speed magnitude and direction) for work validation. •The proposed models are tested using data collected from the Bay of Fundy in 2008.