Proceedings of 2014 1st International Conference on Non Conventional Energy (ICONCE 2014)

Application of An Artificial Neural Network to Study The Transient Stability of An Alternator

Connected to Infinite Bus

Priyaranjan MandaI Department of Applied Physics

University of Calcutta Kolkata, India

priyaranjan _ 44@yahoo.co.in

Abstract-This paper uses the neural network theory to study the transient stability. The MATLAB simulink model of an alternator is considered to be connected to an infinite bus. The transient stability of this alternator is studied after a phase fault. The relative rotor angle is taken as the measuring parameter. A neural network based approach is applied to study the transient stability of the same system. This approach gives expected results.

Keywords-power system stability; transient stability; neural

network; training of neural network.

I. INTRODUCTION

This paper deals with the study of transient stability of a power system. The nature of variation of the rotor relative

torque angle in the transient state is studied here. A state space model of the alternator connected to an infinite bus is

considered assuming a fault occurred to it. The post fault analysis shows that transient state of rotor torque angle suffers with sustained oscillations predicting a complete uncertainty about the steady state stability of the system.

For stable operation variation of torque angle will be within a prescribed limit. The system is provided with a small amount of negative feedback which provides the damping to the system. Thus the sustained oscillation of the transient state of the relative rotor torque angle is reduced to zero and ultimately

the steady state stability of the torque angle is attained gradually. Different methods are there to analyze the transient stabilities.

Here, we apply neural network theory to analyze the

system. A neural network block is configured by method of training (trainlm). Using this block the model of the machine is simulated. Transient stability of the neural network based machine is studied. The results are very much close to the time­domain analysis of the simulink model of the machine.

II. TRANSIENT STABILITY OF POWER SYSTEM

Power system stability may be defined as the property of the system which enables the synchronous machines of the

system to respond to a disturbance from a normal operating condition so as to return to a condition where their operation is again normal. Stability studies are usually classified into three

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types depending upon the nature and order of magnitude of the

disturbance. These are transient, dynamic and steady-state studies.

Transient state starts just after clearing the fault time.

Transient stability studies are aimed to determine whether the system remain in synchronism, just after clearing the major disturbances such as transmission system faults, sudden load changes, loss of generating units, or line switching. In all the stability studies, the objective is to determine whether or not the rotors of the machines being perturbed return to constant speed operation.

III. SIMULINK MODEL OF AN ALTERNATOR CONNECTED To AN INFINITE BuS WHEN NO DAMPING IS ADDED TO THE

SYSTEM

A single alternator is considered to be connected with an

infinite bus. State space model of the alternator is configured via MATLAB simulink toolbox -7.2. The variation of relative rotor torque angle with respect to time is observed through 'Scope1'. The workspace 'priya212' is provided to draw different characteristics as shown in Fig. nos. 2, 4, 14, 16.

Fig. I. Simulink configuration based on swing equation of an Alternator connected to an infinite bus when no damping is provided.

A switch is used to change the state from sustained fault

condition to post fault condition. The clock is used to change

the fault clearing time. Actually this shows the duration of fault sustained in the system. The blocks 'constant3' and 'constant4' are provided to give reactance values to the system. The system

ICONCE 2014

January 16 - 17, 2014, Kalyani, WB, India.

Proceedings of 2014 1st International Conference on Non Conventional Energy (ICONCE 2014)

is introduced with a phase fault. Let the fault clearing time be assumed to 7 milliseconds. As the fault is cleared the system will enter in the region of transient's state.

Fig. 2 shows the characteristic which starts just after the

fault is cleared. It shows the transient state. This clearly shows that the zone of transient stability is affected with a sustained oscillation. Thus the attaining of steady state stability by this system is quite uncertain and it may never attain steady state stability. To overcome the situation an arrangement is provided to offer damping to this system as considered in Fig. 3.

f\ \

Fig. 2. Transient response of rotor torque angle for an alternator connected to infinite bus, when no damping is added to the system.

IV. SIMULINK MODEL OF AN AL TERNA TOR CONNECTED To AN INFINITE BUS WHEN DAMPING IS ADDED TO THE

SYSTEM

Fig. 3 shows the system of Fig. 1 with only a change made by providing a negative feedback to it. The magnitude of the

feedback is very small. This small amount of

f-l-----,.I priy.212 I ToWoikspa(e

Fig. 3. Simulink configuration based on swing equation of an Alternator connected to an infinite bus system, subjected to damping.

Negative feedback will change the nature of transient

stability completely. The characteristic of transient stability zone is shown in Fig. 4.

" (\

I I

.J

\ \ �

\

Fig. 4. Transient response of rotor torque angle, for an alternator connected to infinite bus, with damping added to the system.

It is likely to follow an under damping nature of transient

response. Thus ultimately the machine will reach to the area of steady state stability. Thus the application of such small

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amount of negative feedback damped the sustained oscillation state to a steady state condition.

It is seen from Fig. 4 that the values of transients are reduced to zero within two-three cycles of operation. It is also

observed that the reduction of the transients to a zero value will be governed by the amount negative feedback applied to the system. Less is the amount of negative feedback; less is the lifetime of the transients.

V. ABOUT THE NEURAL NETWORK

An artificial neural network may be compared with human brain. The brain is enriched with set of densely configured neuron cells. An artificial neural network consists of simple

processing units. These units are also called 'neurons'. These are analogous to the actual biological neurons of human brain.

VI. TRAINING OF A NEURAL NETWORK

An artificial neural network is developed here to predict the transient stability of the alternator at post fault condition. This optimizes a criterion, generally, known as process of learning. After learning the existing system, it executes the process of training to fit the network with the existing system model. The

weights are assigned very randomly. Then this is updated to achieve the target. The process of 'TRAINING' applied to neural network is a process of small adjustment in the weights to enable the neural network to reduce the difference between the actual and the target value.

10 <toc--;;,o 1:;--O;;'":',.......,O�6--,O�8-'�-;" ,;;--:'",,;--;';, 6:--:':';:8 � 2 EIItIdI.�

Fig. 5. Best perfonnance of training obtained after two nos. of epochs or iterations.

Fig. 5 shows the performance of training of the initially

assigned neural network. It is seen that the best 'goal' is attained only after two iterations or 'epochs'.

Neural Network

Algorithms

Training: Levenberg-Marquardt (traanm) PerfOfffiance: Mean SqlJ.1lred Error (rnse)

Progress

Epoch: 0 I 2itero!ltions

Time: I 0:00:02

Performarxe: 9.81 I 0.000242

Gradient: 1.00 I 0.0105 =:::J Mu: 0.00100 I I.DOe-OS

Vahdd::ionChecl<s: 0 I

I 500

I I 0.00100

I LOOe-1O

I 1.00e+IO

I 6

Fig. 6. A detailed report of training (trainlm) the neural network.

ICONCE 2014

January 16 - 17, 2014, Kalyani, WB, India.

Proceedings of 2014 1st International Conference on Non Conventional Energy (ICONCE 2014)

A detailed report of the procedure of 'training' is shown in fig. 6. Fig. 7 shows the visualization of variation of different data related to training of the network.

11 • • ':'."'"�:�'�'�'.' • • 1 o 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2 Epochs

Fig. 7. Visualization of different data related to training (train/m) of the neural network.

Fig. 8 shows the neural network block produced after execution of the process of training.

Fig. 8. The neural network block configuration after the process of training (trainlm).

Fig. 9 shows the layers embedded in the neural network block as shown in Fig. 8.

� .�.�--��,-��--------�:) X{l} Pmce_lnput 1 Layer 1 a{l} �").m

Layer2

� a{l} Process Output 1 y{l}

Fig. 9. Different layers embedded within the neural network block.

Fig. 10 shows the embedded configuration of layer 1 of the

trained neural network block.

Fig. 10. The embedded configuration of layer 1 of the neural network block.

Fig. I I. Detailed configuration of the weight block as shown in layer I of the neural network.

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Fig. 11 shows the detailed configuration of the weight block as shown in Fig. 10. Fig. 12 shows the 'constant value' parameter. The concerned constant value is 5.2038011632254264.

� , Constant

Output the constant specified by the 'Constant value' parameter. If

'Constant value' is a vector and 'Interpret vector parameters as 1-D' is

on, treat the constant value as a I-D array. Otherwise, output a matrix

with the same dimensions as the constant value.

Main I Signal Attributes I Constant value:

15.2038011632254264

Fig. 12. The constant value parameter.

VII. NEURAL NETWORK BASED MODEL OF THE MACHINE

WITHOUT PROVIDING DAMPING TO THE SYSTEM

Fig. 13 shows the neural network based simulink model of the alternator connected to the infinite bus. The simulink model of the alternator of Fig. 1 is now configured by the trained (trainlm) neural network block as shown in Fig. 8.

Fig. 14 shows the state of transient stability of the neural network based model of the alternator. This is comparable with the characteristic as shown in Fig. 2. Both the figures signifie

for sustained oscillations at post fault condition to show the transient stabil ity.

8�K' IT] Constan

_ Gain2 Integratol1

Product

Divide

�-------r.1 priya212 I ToWoJkspace

Fig. 13. Simulink configuration of neural network based Alternator, connected to an infinite bus system, when no damping is added to it.

Fig. 14. Transient state of the rotor torque angle of the neural network based machine, connected to infinite bus, when no damping is added to the

system

VIII. CONCLUSION

In this section of the paper, we shall discuss about the feasibility of application of the neural network. The transient

ICONCE 2014

January 16 - 17, 2014, Kalyani, WB, India.

Proceedings of 2014 1st International Conference on Non Conventional Energy (ICONCE 2014)

stability predicted by the neural network based model of the machine as shown in Fig. 14 is very much close to that of the Fig.2.

In the same way, if we analyze the result of the model

furnished in the Fig. 15, it clearly observed that the transient stability predicted by the neural network based model of the machine, with negative feedback provided to it, is very much close to that of the Fig.4.

REFERENCES

[I] O. L. Elgerd, Electric energy systems theory- an introduction, 2nd ed., TMH publishing co. Ltd: New Delhi, 1988.

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[2] W. D. Stevenson, Jr, Elements of Power System Analysis, 4-th Edition, McGRA W HILL Book Company, 1982.

[3] N. Amjady, M. Ehsan, 'Transient stability assessment of power systems by a new estimating neural network,' Can. J. Electrical

and Computer Engg., vol. 22, no.3, pp.131-137, July, 1997.

[4] K. K. Sanyal, 'Transient stability assessment using neural

network,' IEEE international Conference on Electric Utility Deregulation, Restructuring and Power Technologies, Hong Cong, 633-637,2004.

ICONCE 2014

January 16 - 17, 2014, Kalyani, WB, India.