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INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL

Volume 2, No 1, 2010

Copyright 2010 All rights reserved Integrated Publishing Association

RESEARCH ARTICLE ISSN - 0976-4259

56

Artificial Neural Network based Hydro Electric Generation Modelling

Deepika Yadav., Naresh.R, Veena Sharma

Electrical Engineering Department, National Institute of Technology, Hamirpur, [email protected]

ABSTRACT

Hydropower generation is a function of discharge of the generating units and the difference

between the fore bay and tailrace levels of the reservoir, and is subject to penstock head

losses and to the generation unit efficiency factor, which in turn is a function of the reservoir

level and reservoir capacity. For this actual plant data from Sewa Hydroelectric Project

Stage-II which is a run-of-the river project having installed capacity of 120 MW situated in

Jammu region has been used.In this paper two hydro electric models such as reservoir level

versus capacity model and head loss versus water discharge rate have been studied which areused for calculating net head and further can be used for online implementation of

Availability Based Tariff in which day ahead scheduling is done. In order to accomplish this

task, data from plant is employed for training, validating and testing the artificial neural

network (ANN) model which provide accurate results. Thereafter with these models, a

comparison is made with multiple regression models in terms of their prediction accuracy,

mean square error and regression R value.

Keywords: Artificial neural network, ANOVA analysis, Levenberg-Marquardt algorithm,

hydroelectric generation models

1. Introduction

In hydro electric Power plants, for calculating energy and online implementation ofavailability based tariff in Indian power industry [Bhushan. 2005 Christensen et al. 1988Geetha et al. 2008 and Deshmukh et al. 2008], there is always a need to develop models for

hydro electric plant as each one is unique to its location and requirement. In most cases, theparameters to be estimated are of non-linear model with respect to control and state variables.

Here data used has been taken from Sewa Hydroelectric Project Stage-II, a run-of-the river project, which fulfills the partial requirements of the irrigation in state of Jammu and

Kashmir. The power house is located in a village called Mashka near the junction of Sewaand Ravi, The project will generate 533.52 million units in a 90% dependable year and also

provide 120 MW peaking capacity in the power system of northern region. This plant has a

small reservoir with maximum storage capacity of 0.9174 million cubic meters (MCM) and

average storage capacity of 0.2234 MCM. Moreover, elevation is taken from above mean sea

level through some level sensors, maximum reservoir level of this plant is 1200 meter andaverage reservoir level measured is 1184 meter.The project envisages 53 meter-high concrete

gravity dam, a 10,020 meter-long head race tunnel and its power house will be equipped with

3*40MW vertical Pelton turbine units with rated net head of 560m. Its geographical

coordinates having latitude 32 36 38 N to 32 41 00 N and longitude 75 48 46 E to

75 55 38 E is shown in figure 1, referred from site (www.nhpcindia.com)

Hydroelectric scheduling of the plants requires a judicious modeling of each of the hydro

electric plant for an improved efficiency, optimum use of water resources and to arrest
http://www.nhpcindia.com/

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Neurons are arranged in layers, an input layer, hidden layer(s), and an output layer. There isno specific rule that dictates the number of hidden layers. The function is largely established

based on the connections between elements of the network. In the input layer each neuron is

designated to one of the input parameters. The network learns by applying a back- propagation algorithm which compares the neural network simulated output values to theactual values and calculates a prediction error. The error is then back propagated through the

network and weights are adjusted as the network attempts to decrease the prediction error by

optimizing the weights that contribute most to the error. The training or learning of the

network occurs through the introduction of cycles of data patterns (epochs or iterations) to the

network. One problem with neural network training is the tendency for the network to

memorize the training data after an extended learning phase. If the network over learns the

training data it is more difficult for the network to generalize to a data set that was not seen

by the network during training. Therefore, it is common practice to divide the data set into a

learning data set that is used to train the network and a validation data set that is used to test

network performance. Figure 2 shows the representation of neural network diagram with

inputs ai, weights wi, hidden layer, and an output z [Beale et al.1996]. In the present study,neural network fitting tool (nftool) of MATLAB7.5 [Beale et al.1996] has been used.

Figure 2: Feed-forward neural network model

This research employed supervised learning where the target values for the output are

presented to the network, in order for the network to update its weights. Supervised learning

attempts to match the output of the network to values that have already been defined. After

training network verification is applied in which only the input values are presented to the

network so that the success of the training can be established an algorithm that trains ANN 10to 100 times faster than the usual back propagation algorithm is the Levenberg-Marquardt

algorithm. While back propagation is a steepest descent algorithm, the Levenberg-Marquardt

algorithm is a variation of Newton's method [Hagan et al. 1994]. In this paper, the

Levenberg-Marquardt algorithm has been employed which is an approximation to Newton's

method. Suppose a function V (x), which we want to minimize with respect to the parameter

vector (x), then Newton's method would be

)x(V1

)]x(V2

[)x( --=D (1)

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where, 2 V(X) is the Hessian matrix andV(X) is the gradient. If we assume V (X) is asum of square of errors, given by

=

=N

1i(x)2

ieV(x) (2)

then )x(e)x(T

J2)x(V = (3)

)x(S)x(J)x(TJ2)x(V2 += (4)

where, e(x) is the error vector, J ( x ) is the Jacobian matrix given by

(5)

and S(x) is given by

=

=N

1i)x(ie

2)x(ie)x(S (6)

Neglecting the second-order derivatives of the error vector, i.e., assuming that S(X) 0, theHessian matrix is given by

)x(J)x(T

J)x(V2 = (7)

and substituting (7) and (3) into (1) we obtain the Gauss-Newton update, given by)x(e)x(

TJ

1)]x(J)x(

TJ[x --=D (8)

The advantage of Gauss-Newton over the standard Newton's method is that it does not

require calculation of second-order derivatives. Nevertheless, the matrix JT

(x) J(x) may not be

invertible. This is overcome with the Levenberg-Marquardt algorithm, which consists in

finding the update given by

)x(e)x(T

J1

]I)x(J)x(T

J[x -+-=D m (9)

When the scalar is very small or null, the Levenberg-Marquardt algorithm becomes Gauss-

Newton, which should provide faster convergence, while for higher values, when the first

term within brackets of (9) is negligible with respect to the second term within brackets, the

algorithm becomes steepest descent. Hence, the Levenberg-Marquardt algorithm provides anice compromise between the speed of Gauss-Newton and the guaranteed convergence of

steepest descent [Hagan et al. 1994]. Here, performance function which is the sum of squared

errors between the target outputs and the network's simulated outputs (as is typical in training

feed forward networks) is proportional to .Thus, is decreased after each successful step

(reduction in performance function) and is increased only when a tentative step would

increase the performance function. In this way, the performance function is always reduced at

=

nx

(x)N

e

2x

(x)N

e

1x

(x)N

e

nx

(x)2

e

2x

(x)2

e

1x

(x)2

e

nx

(x)1

e

2x

(x)1

e

1x

(x)1

e

J(x)

K

MOMM

L

L

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each iteration of the algorithm. This algorithm appears to be the fastest method for training

moderate-sized feed forward neural networks.

3. Reservoir Level versus Capacity Model

The modeling of water stored in a reservoir forms a crucial part of any hydroelectric

operational study because it determines the gross head of each plant. This model relates theelevation to the volume of water stored in the reservoir.

3.1 Modelling Using ANN

In this model of reservoir level (m) versus capacity (MCM), the actual river data using

nftool of MATLAB was used to train the neural network model. To use this tool, first

convert the data into MATLAB data file and provide as input to nftool. The system takes60% of data for training, 20% for validation and 20% for testing, so that the same data will

not be used for testing. It requires many runs to converge or to get expected training. Oncethe system was trained then it tests with remaining sample of data for testing. Figure 3 shows

the performance accuracy employing different numbers of hidden nodes.

Figure 3: Accuracy versus number of trials with different hidden neurons

Table 1: Performance evaluation of Training, Validation and Testing

Number

ofHidden

Neurons

Operation MSE

Best

MSE

Worst

MSE

Average

R

Best

R

Worst

R

Average

Standard

deviationMSE

Standard

deviationR

2 Training 0.15 3.0573 1.21259 0.999 0.985 0.9948 1.36880 0.00582

2 Validatio 0.12 5.5908 1.42512 0.999 0.996 0.9978 0.00154 0.00154

2 Testing 0.02 2.5515 0.96882 0.999 0.989 0.9963 0.00427 0.00427

3 Training 0.03 5.1939 1.72241 0.999 0.967 1.7224 2.36757 0.01391

3 Validatio 0.74 22.247 5.86132 0.999 0.962 0.9907 0.01573 0.01573

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In order to check the sensitivity of neural network performance, initialization of connection

weights, training, validation and testing operations have been performed with five

independent random trials for weight initialization as listed in table 1. The comparison of the

mean squared error values indicates the average squared difference between outputs and

targets, which is used to assess the network performance and is given as

M

))m(d)m(y(MSE

M

1m

2

= -= (10)

where y(m) and d(m) are the network output, and the desired output at any sample m

respectively and M is the length of the investigated data sets. In table1, standard deviation

and correlation coefficient R values provide how well model is close to actual values. In other

words it provides a measure of how well future outcomes are likely to be predicted by the

model, hence it is desired that R square values to be very high i.e., close to 1. The

performance was evaluated in terms of the correlation coefficient R, computed as

=

==

-

---=

M

1m

2

i

M

1m

2

mm

2M

1mm

2

)yy(

)yy()yy(R (11)

where, ym = the observed dependent variable

my = the fitted dependent variable for the independent variable x m

=y mean, =M

yy m

m

xm= the independent variable in the mth

trial

=

-M

1m

2)yy(

m represents total sum of squares, while =-

M

1m

2

mm)yy( represents residual

sum of squares

R Square is a measure of the explanatory power of the model. Here for best model chosen RSquare is 0.999939, 0.999902 and 0.988785 for training, validation and testing respectively

as shown in figure 4(a).

In figure 4 (a) the dashed line is the perfect fit line where outputs and targets are equal to

each other. The circles are the data points and coloured line represents the best fit between

outputs and targets. Here it is important to note that circles gather across the dashed line, so

our outputs are not far from targets. From the graph, it can be realized that the best hidden

unit with 99% accuracy is with 5 neurons with third trial for this model. Figure 4(b) depicts

the training, validation and test mean square errors for Levenberg-Marquardt algorithm with

5 hidden neurons. The training stops when MSE do not change significantly. The comparison

of actual and predicted results by neural network model for reservoir level versus reservoir

3 Testing 0.11 54.645 18.9078 54.64 0.966 0.9857 0.98576 0.01442

4 Training 0.13 1.5519 0.43776 0.999 0.992 0.9977 0.62321 0.00316

4 Validatio 0.18 1.5 0.63667 0.999 0.995 0.9982 0.54863 0.00192

4 Testing 0.10 0.6541 0.44774 0.999 0.995 0.9987 0.21082 0.00196

5 Training 0.01 0.8933 0.26670 0.999 0.996 0.9987 0.36300 0.00155

5 Validatio 0.06 1.3630 0.52426 0.999 0.970 0.5242 0.49348 0.01291

5 Testing 0.13 7.52 1.97857 0.999 0.988 2.4399 3.12214 0.00476

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capacity model has been shown in figure 5(a) which clearly reveals that neural networkmodel has tracked the experimental data closely. Error plot between actual and predicted

results by neural network model has been shown in figure 5(b), which is within quite

acceptable limits.

Figure 4 (a): Regression plots for actual and predicted results by feed-forward neural

network model for training, validation, testing samples and all data set (b): shows training,

validation and testing mean square errors for Levenberg-Marquardt algorithm with 5 neurons.

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Figure 5 (a): Plot of actual and predicted results for Reservoir level versus Capacity model

using Levenberg-Marquardt algorithm (b): shows Error Plot between Actual and Predicted

Results by neural network model

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3.2 Modelling Using ANOVAAnalysis of variance [Draper et al. 1998 and Myers et al. 1993] is a parametric procedure

Figure 6: ANOVA results obtained for Reservoir level versus Capacity

used to determine the statistical significance of the difference between the means of two ormore groups of values. ANOVA techniques are applied on the polynomial of different

degrees by fitting them on to data for reservoir level and reservoir capacity.

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Figure 7: Plot for R Value, Standard error and Accuracy

The graphical curves of fit obtained are shown in figure 6(a). In figure 6(b) the residuals

using ANOVA model for different polynomials have been plotted. From the analysis of the

above graphical results it is evident that the higher order polynomial provides better fit in this

case. Further analysis to regression R Value, Standard error and Accuracy has been plotted in

figure 7 for different degrees of polynomials. The details of ANOVA analysis approach can

be referred in [Naresh et al. 2009].

4. Head Loss versus Water Discharge Rate Model

When determining head (falling water), gross or static head and net or dynamic head must beconsidered. Gross head is the vertical distance between the top of the penstock and the point

where the water hits the turbine. Net head is gross head minus the pressure or head losses dueto friction and turbulence in the penstock. These head losses depend on the type, diameter,

and length of the penstock piping, and the number of bends or elbows. Gross head can be

used to estimate power availability and determine general feasibility, but net head is used to

calculate the actual power available. In addition, electricity demand and generation

scheduling depend on water released during the next day through generators and/or gates.

The amount is determined by the water level of the reservoir of the preceding day and the

water arriving from runoff. Here in this section the head loss (m) versus water discharge rate(m

3s

-1) model analysis has been outlined.

4.1 Modelling Using ANN

To evaluate neural network performance, initialization of connection weights, training,

validation and testing has been performed with five independent random trials for weight

initialization as listed in table 2. Figure 8 shows the performance plot employing different

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numbers of hidden units. It can be noted from the graph that with increase in number ofneurons in the hidden layer, accuracy also increases. From the graph, it can be realized that

the best hidden unit with good accuracy is achieved with 5 neurons units on third trial.

Figure 8: Accuracy versus number of trials with different hidden neurons

Table 2: Performance evaluation of Training, Validation and Testing

Numberof

Hidden

Neurons

Operation MSE

Best

MSE

Worst

MSEAvera

ge

R

Best

R

Worst

R

Average

Standarddeviation

MSE

Standarddeviation

R

2 Training 0.00590 0.039 0.022 0.999 0.9999 0.99995 0.01296 2.91E-

2 Validatio 0.00495 0.187 0.063 0.999 0.9988 0.99960 0.07951 0.00048

2 Testing 0.00607 0.704 0.156 0.999 0.9997 0.99991 0.30692 0.00012

3 Training 9.85E- 0.008 0.003 0.999 0.9999 0.99998 0.00440 7.80E-

3 Validatio 1.74E- 0.012 0.003 0.999 0.9999 0.99999 0.00516 1.22E-

3 Testing 1.83E- 0.073 0.016 0.073 1.83E- 0.01624 0.03209 0.03209

4 Training 1.11E- 0.000 0.000 0.999 0.9999 0.99999 0.00027 4.47E-

4 Validatio 0.00036 0.007 0.003 0.999 0.9999 0.99998 0.00351 0.00351

4 Testing 2.12E- 0.000 0.000 0.999 0.9999 0.99999 0.00016 0.00016

5 Training 2.41E- 5.485 1.218 0.999 0.9906 0.99781 2.39617 0.00407

5 Validatio 0.00300 1.299 0.307 0.999 0.9980 0.99952 0.56078 0.00082

5 Testing 0.00182 18.86 5.436 0.999 0.9999 0.99548 8.23760 0.00564

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In this network, training is provided for 100 epochs, minimum MSE for best model in case oftraining is 2.41E-08 as shown in figure 9 (b). The training stops when MSE do not change

significantly.Validation vectors are used to stop training early if the network performance on

the validation vectors fails to improve or remains the same for max fail epochs in a row, forthis model in MSE noted for validation is 3.01E-03 as in figure 9(b).Test vectors are used asa further check that the network is generalizing well, but do not have any effect on training

Neural Network Toolbox, minimum MSE for this model in case of testing is 2.14E-03 as

shown in figure 9(b). Here for best model chosen R Square is 0.999999, 0.999997 and

0.999997 for training, validation and testing as shown in figure 9 (b). As per the model 99%

of variation in dependent variable has been explained by independent variable.

Figure 9 (a): Regression plots for actual and predicted results by feed-forward neural

network model for training, validation, testing samples and all data set (b): shows training,

validation and testing mean square errors for Levenberg-Marquardt algorithm with 5 neurons.

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Figure 10 (a): Plot of actual and predicted results for head loss versus water discharge rate

model using Levenberg-Marquardt algorithm Figure 10 (b): Error plot between actual andpredicted results by NN Model

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The comparison between actual and predicted results by neural network model is shownabove in figure 10 (a). From figure 10 (b) it can be seen that small amount of errors are

present in the beginning of the predicted results and afterwards the neural network model is

predicting quite well.

4.2 Modelling Using ANOVA

Figure 11: ANOVA results obtained for head loss versus water discharge rate

It can be noted from figure 11(a) that although difference between the cubic,4th

,5th

and 6th

degree Polynomials were small and predicted data gets converged with the actual data for all.

The best fitting was obtained for 3rd

order model with 99.9893% accuracy with minimum

standard error obtained among all as shown in figure 12. Also, this model provides good

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significant fit with regression R value 0.99. More details regarding this model can be found in[Naresh et al. 2009].

Figure 12: Plot for R Value, Standard error and Accuracy

5. Conclusion

In this paper two hydro electric models, reservoir level versus capacity model and head loss

versus water discharge rate model have been developed using artificial neural network.

During modelling process 60% of the available data is used for training, 20% is used for

cross validation and 20% is used for testing. The data for each class are chosen randomly

from the data set. Further, the developed models are compared with ANOVA approach.

Predicted results by ANN and ANOVA analysis are quite cohesive to the actual results of

Sewa river. However, ANN proved to be a useful tool to predict and estimate non-linear

relationship between the variables because of its adaptive capability. These models in a way

help in effective utilization of available water that can help us to fight against uncertainty,especially for the optimal generation, scheduling of the run-of- river project in a multipurpose

context and also can be used as an effective input to the decision support system for real-time

operation of reservoir systems that results in increased power production and enhancedrevenue earnings in the process of planning and management of a water resources project.

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6. Acknowledgment

The authors are grateful for the kind support rendered by the Electronics division of BHEL

Bangalore, India for carrying out this work.

7. References

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Boston, Massachusetts, U.S.A.

2. Bhushan et al., 2004: The Indian medicine, In IEEE Power Engineering Society

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3. Buizza and Taylor, 2002: Neural network load forecasting with weather ensemble

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power systems with a variable head. In Journal of Optimization Theory andApplications, Springer Netherlands, 58(2), pp.301-317.

5. Deshmukh et al., 2008: Optimal Generation Scheduling under ABT using Forecasted

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13. Naresh et al., 2009: Hydro Electric Generation Models for Hydro Power StationStudies. In Proceedings of National Conference-TACT-09, NIT-Hamirpur, India, 16-

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EIJAER2006