Application of Radial Basis Function Network for the Modeling and ...

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JOURNAL OF ADVANCES IN INFORMATION TECHNOLOGY, VOL. 4, NO. 2, MAY 2013

Application of Radial Basis Function Network for the Modeling and Simulation of Turbogenerator Mohsen Hayati 1,2,4,* 1

Electrical Engineering Department, Faculty of Engineering, Razi University, Kermanshah-67149, Iran * Corresponding author: [email protected] 2 Computational Intelligence Research Centre, Faculty of Engineering, Razi University, Kermanshah-67149, Iran

Abbas Rezaei3,4 and Leila Noori4 3

Electrical Engineering Department, Kermanshah University of technology, Kermanshah, Iran Department of biomedical Engineering, Faculty of medicine, Kermanshah University of medical sciences , Kermanshah, Iran [email protected], [email protected]

4

Abstract—In this paper, the applicability of Radial Basis Function (RBF) network for the modeling and simulation of turbogenerators is presented. It is expensive and timeconsuming to do experimental work to predict the behaviour of Turbogenerators with changing all variables. The RBF network is developed with speed and excitation current as inputs and voltage, active power and reactive power as desired outputs. The proposed RBF model is developed and trained with MATLAB 7.8 software. To obtain the optimal RBF model several structures have been constructed and tested. The comparison between experimental and predicted values using the proposed RBF model shows that there is a good agreement between them. Moreover, the RBF model is compared with another model named Multi Layer Perceptron (MLP), which is another important architectures of neural networks. The results obtained show that the proposed RBF model is more accurate and reliable than MLP model. Index Terms— Radial basis function, Modelling, neural network, Turbogenerator.

I.

INTRODUCTION

A turbogenerator is a turbine directly connected to an electric generator for the generation of electric power [1]. Turbo generators are used on steam locomotives as a power source for coach lighting and heating systems [1]. Synchronous generators or alternators are synchronous machines used to convert mechanical power to AC electric power. The term synchronous refers to the fact that the electric frequency of the machine has been locked by a mechanical shaft. Generators are composed of two parts: moving parts, which are called rotor and the fixed part known as the stator. In [2] an artificial neural network (ANN) generalised inversion control strategy for a turbo-generator governor is proposed. The ANN generalised inversion, which can approach the dynamic inversion of the original controlled system, is composed of a single static ANN and several linear components. In [3] the characteristic of neural network to model bulb turbogenerators is presented. The results obtained from

© 2013 ACADEMY PUBLISHER doi:10.4304/jait.4.2.76-79

the nonlinear simulation demonstrate the adaptability and robustness of the control system based on the neural network. In [4] a novel algorithm called particle swarm optimization (PSO-BP) is proposed for ANN learning based on PSO to overcome the flaws of the traditional BP learning algorithm of its low convergence. The modeling and simulation of induction machines using vector computing technique in matlab/simulink is presented in [5], which provides an efficient approach for further research on wind generation system integration and control. A new wind turbine generator system is introduced, and its mathematical model, blade pitch control scheme, and nonlinear simulation software for the performance predication are presented [6]. A variablespeed induction generator, aimed at supplying an autonomous power system is presented [7]. The design of a fuzzy logic supervisor for the control of active and reactive power, which is generated by fixed speed wind energy conversion systems (WECS) is presented [8]. ANN [9] is used for multi-objective optimal reactive compensation of a power system with wind generators and after a training phase, the ANN model has the capacity to provide a good estimation of the voltages, the reactive productions and the losses for actual curves of the load and the wind speed, in real time. However, with regard to complexity and volume of calculations governing generator, the simulation of such a machine is time consuming. In this paper, radial basis function (RBF) network is used for modeling and simulation of turbogenerators. The schematic of the proposed RBF model is shown in Fig.1 where the RBF model is developed with speed and excitation current as inputs and voltage, active power and reactive power as desired outputs.


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The output of the mth neuron in the output layer is given by: k

ym ( x) = ∑ w jm z j ( x)

m = 1,2,.., M

(2)

j =1

where w jm is the weighting factor. III. RESULT AND DISCUSSION

Figure 1. A simplified overview of RBF model.

II. RADIAL BASIS FUNCTION A RBF network is an ANN that uses RBFs as activation functions. RBFs can fit erratic data [10, 11]. They are used in function approximation, time series prediction, and control due to their good approximation capabilities, faster learning algorithms and simpler network structures. The RBF has a feed forward structure and typically has three layers: an input layer, a hidden layer with a non-linear RBF activation function and a linear output layer as shown in Fig. 2. Hidden unit implements a radial activated function. The input layer is made up of source nodes that connect the network to its environment. The hidden layer consists of a set basis function unit that carry out a nonlinear transformation from the input space to the hidden space. The transformation from input to hidden layer is nonlinear and from hidden to output layer is linear. The output from jth neurons of the hidden layer is given by: ⎛ x−μj Z j = K⎜ ⎜ σ 2j ⎝

⎞ ⎟ ⎟ ⎠

j = 1,2,.., k

(1)

where K is a strictly positive radially symmetric function (kernel) with a unique maximum at its center ( μ j ), which drops off rapidly to zero away from the

For developing the proposed RBF model about 440 data were used. Total data are divided into two sets: training and testing. About 70% of the data were selected for training and 30% for testing the proposed RBF model. The best RBF network is obtained with 452 neurons in hidden layer. The comparisons between experimental and predicted values using the proposed RBF model are shown in Figs. 3-6. These figures compare the predicted values (RBF) and experimental values of voltage, active power and reactive power. From these figures, it is clear that the predicted values using the proposed RBF model are in good agreement with experimental data with least error. Also we have compared the proposed RBF model with MLP model [12] as shown in Table 1, where the mean relative error percentage ( MRE% ) is evaluated as: ⎛1 MRE% = ⎜ ⎜N ⎝

N

∑ i =1

X Exp − X Pred ⎞⎟ × 100 ⎟ X Exp i⎠

Where N is the number of data and ‘XExp’ and ‘XPred’ stand for experimental and predicted values, respectively. It is observed from Figs. 3-6 and Table I that there is a good agreement between experimental and predicted values using RBF network and also the proposed RBF model is more accuracy in comparison with the MLP model [12].

center. The number of neurons in the hidden layer is k, and σj is the width of the receptive field in the input space from unit j. This indirectly indicate that

z j has a

desired value only when the distance x − μ j is smaller than the σj .

Figure 3 Comparisons between the experimental and the RBF model results for testing data.

Figure 2. RBF structure.

© 2013 ACADEMY PUBLISHER

(3)

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Test

Voltage Active power Reactive power

0.07921 0.51162

0.0623 0.441

0.4868

0.385

IV. CONCLUSIONS

Figure 4 Voltage-excitation current characteristics curve for predicted (RBF model) and experimental testing values.

In this paper, an accurate RBF model is developed for the modeling and simulation of turbogenerator. The network is developed based on the experimental data. The comparison between experimental values and predicted values shows that there is a good agreement between them with MRE% less than 0.52%. Also the proposed RBF model is compared with the MLP model. The results obtained clearly demonstrate that RBF is more accurate in comparison with MLP model. With this ability, we can use our model as a tool in order to obtain turbogenerator outputs with different conditions with high computation speed and accuracy. REFERENCES

Figure 5 Active power-excitation current characteristics curve for predicted (RBF model) and experimental testing values.

Figure 6 Reactive power-excitation current characteristics for predicted (RBF model) and experimental testing values. TABLE I. OBTAINED MRE% FOR THE PROPOSED RBF MODEL IN COMPARISON WITH MLP MODEL [12]. Data Train

Output Voltage Active power Reactive power


MLP [12] 0.0492 0.2116

RBF 0.0421 0.193

0.186

0.169

[1] C. Ginet, R. Joho, M. Verrier, “the Turbogenerator - A Continuous Engineering Challenge”, Power Tech, IEEE Lausanne, pp. 1055-1060, 2007. [2] X. Dai, “ANN generalised inversion control of turbogenerator governor”, Generation, Transmission and Distribution, IEE Proceedings, pp. 327-333, Vol. 151, 2004. [3] H. Song, “Neural network control for bulb turbogenerators, Geoscience and Remote Sensing (IITAGRS) International Conference on, pp. 612 - 614, Vol. 2, 2010. [4] Y. zhang, H. su, “Turbo-Generator Vibration Fault Diagnosis Based on PSO-BP Neural Networks”, WSEAS TRANSACTIONS on SYSTEMS and CONTROL, pp. 3747, Vol. 5, 2010. [5] Z. Mia, Lingling Fan, “The art of modeling and simulation of induction generatorin wind generation applications using high-order model”, Simulation Modelling Practice and Theory, pp. 1239-1253, Vol. 16, 2008. [6] T.S. N, J-E. Kim, J.H. Moon, S.J. Kim, “Modeling ,control,and simulation of dual rotor wind turbine generator system”, Renewable Energy, pp. 2124– 2132 , Vol. 34, 2009. [7] Y.W. Liao, E. Levi, “Modeling and simulation of a standalone induction generator with rotor flux oriented control”, Electric power systems research, pp. 141-152, Vol. 46, 1998. [8] L. Krichen, B. Francois, A. Ouali, “A fuzzy logic supervisor for active and reactive powercontrol of a fixed speed wind energy conversion system”, Electric Power Systems Research, pp. 418–424, Vol. 78, 2008. [9] L. Krichen, H. B. Aribia, H. Abdallah, A. Ouali, “ANN for multi-objective optimal reactive compensation of a power System with wind generators”, Electric Power Systems Research, pp. 1511–1519, Vol. 78, 2008. [10] S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks", IEEE Transactions on Neural Networks, Vol 2, No 2, 1991. [11] M. D. Buhmann, “Radial Basis Functions: Theory and Implementations”, Cambridge University, ISBN 0-52163338-9, 2003. [12] M. Hayati, K. Darabi, “Modeling and Simulation of Turbogenerator Using Computational Intelligence”, Applied Mechanics and Materials, pp. 5211-5215, Vols. 110 – 116, 2012.


Mohsen Hayati received the BE in electronics and communication engineering from Nagarjuna University, India, in 1985, and the ME and PhD in electronics engineering from Delhi University, Delhi, India, in 1987 and 1992, respectively. He joined the Electrical Engineering Department, Razi University, Kermanshah, Iran, as an assistant professor in 1993. At present, he is an associate professor with the Electrical Engineering Department, Razi University. He has published more than 110 papers in international and domestic journals and conferences. His current research interests include application of computational intelligence, artificial neural networks, fuzzy systems, neuro-fuzzy systems, and electronics circuit synthesis, modeling, and simulations and design of microwave circuits. Abbas Rezaei received the BS and MS in electronics engineering from Razi University, Kermanshah, Iran, in 2005 and 2009, respectively. He was with the Computational Intelligence Research Center, Faculty of Engineering, Razi University during 2007 to 2009. He is currently working towards the Ph.D. degree in electrical engineering at Razi University, Kermanshah, Iran. His current research interests include nanotechnology, QCA, artificial intelligence, neural networks, fuzzy systems and neuro-fuzzy systems.

Leila Noori received the BS and MS in electronics engineering from Razi University, Kermanshah, Iran, in 2006 and 2010, respectively. She was with the Computational Intelligence Research Center, Faculty of Engineering, Razi University during 2008 to 2010 and she is currently working towards the Ph.D degree in electrical engineering at the Shiraz University of technology, Shiraz, Iran. Her research interest includes the low-power and low-size integrated circuit design, and Passive RF component.


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