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Presented By
PRANAMITA BASU
AISWARYA HARICHANDAN
National Institute of Technology Rourkela
Under the guidance of PROF. P.C. PANDA
ABSTRACT
The stability of an interconnected power system is its ability to return to normal or stable operation after having been subjected to some form of disturbance. With interconnected systems continually growing in size and extending over vast geographical regions, it is becoming increasingly more difficult to maintain synchronism between various parts of the power system.
Â¢ In our project we have studied the various types of stability steady state stability, transient state stability and the swing equation and its solution using numerical methods using MATLAB and Simulink .
Â¢ We have presented the solution of swing equation for transient stability analysis using three different methods  PointbyPoint method, Modified Euler method and RungeKutta method.
Â¢ Modern power systems have many interconnected generating stations, each with several generators and many loads. So our study is not limited to onemachine system but we have also studied multimachine stability.
Â¢ We study the smallsignal performance of a machine connected to a large system through transmission lines. We gradually increase the model detail by accounting for the effects of the dynamics of the field circuit. We have analysed the smallsignal performance using eigen value analysis.
Â¢ Further a more detailed transient stability analysis is done whereby the classical model is slightly improved upon by taking into account the effect of damping towards transient stability response. Characteristics of the various components of a power system during normal operating conditions and during disturbances have been examined, and effects on the overall system performance are analyzed.
INTRODUCTION
Successful operation of a power system depends largely on the engineer's ability to provide reliable and uninterrupted service to the loads. The reliability of the power supply implies much more than merely being available. Ideally, the loads must be fed at constant voltage and frequency at all times. The first requirement of reliable service is to keep the synchronous generators running in parallel and with adequate capacity to meet the load demand. Synchronous machines do not easily fall out of step under normal conditions. If a machine tends to speed up or slow down, synchronizing forces tend to keep it in step. Conditions do arise, however, such as a fault on the network, failure in a piece of equipment, sudden application of a major load such as a steel mill, or loss of a line or generating unit., in which operation is such that the synchronizing forces for one or more machines may not be adequate, and small impacts in the system may cause these machines to lose synchronism.
A second requirement of reliable electrical service is to maintain the integrity of the power network. The highvoltage transmisssion system connects the generating stations and the load centers. Interruptions in this network may hinder the flow of power to the load. This usually requires a study of large geographical areas since almost all power systems are interconnected with neighboring systems.
Random changes in load are taking place at all times, with subsequent adjustments of generation. We may look at any of these as a change from one equilibrium state to another. Synchronism frequently may be lost in that transition period, or growing oscillations may occur over a transmission line, eventually leading to its tripping. These problems must be studied by the power system engineer and fall under the heading "power system stability".
Chapter 2
STUDY OF SWING EQUATION
2.1 STABILITY
The tendency of a power system to develop restoring forces equal to or greater than the disturbing forces to maintain the state of equilibrium is known as "STABILITY'.
The problem of interest is one where a power system operating under a steady load condition is perturbed, causing the readjustment of the voltage angles of the synchronous machines. If such an occurrence creates an unbalance between the system generation and load, it results in the establishment of a new steadystate operating condition, with the subsequent adjustment of the voltage angles. The perturbation could be a major disturbance such as the loss of a generator, a fault or the loss of a line, or a combination of such events. It could also be a small load or random load changes occurring under normal operating conditions. Adjustment to the new operating condition is called the transient period. The system behavior during this time is called the dynamic system performance, which is of concern in defining system stability. The main criterion for stability is that the synchronous machines maintain synchronism at the end of the transient period. So we can say that if the oscillatory response of a power system during the transient period following a disturbance is damped and the system settles in a finite time to a new steady operating condition, we say the system is stable. If the system is not stable, it is considered unstable. This primitive definition of stability requires that the system oscillations be damped. This condition is sometimes called asymptotic stability and means that the system contains inherent forces that tend to reduce oscillations. This is a desirable feature in many systems and is considered necessary for power systems. The definition also excludes continuous oscillation from the family of stable systems, although oscillators are stable in a mathematical sense. The reason is practical since a continually oscillating system would be undesirable for both the supplier and the user of electric power. Hence the definition describes a practical specification for an acceptable operating condition. The stability problem is concerned with the behavior of the synchronous machines after a disturbance. For convenience of analysis, stability problems are generally divided into two major categoriessteady state stability and transient state stability and transient state stability.
CONCLUSION AND REFERENCES
8.1 CONCLUSION
Thus we see that a twomachine system can be equivalently reduced to a one machine system connected to infinite bus bar. In case of a large multimachine system, to limit the computer memory and time requirements, the system is divided into a study subsystem and an external subsystem. The study subsystem is modeled in details whereas approximate modeling is carried out for the rest of the subsystem. The qualitative conclusions regarding system stability drawn from a twomachine or an equivalent onemachine infinite bus system can be easily extended to a multimachine system.
It can be seen that transient stability is greatly affected by the type and location of a fault so that a power system analyst must at the very outset of a stability study decide on these two factors. For the case of onemachine system connected to infinite bus it can be seen that an increase in the inertia constant M of the machine reduces the angle through which it swings in a given time interval offering a method of improving stability. But this can not be employed in practice because of economic reasons and for the reason of slowing down of the response of the speedgovernor loop apart from an excessive rotor weight.
For a given clearing angle, as the maximum power limit of the various power angles is raised, it adds to the transient stability limit of the system. The maximum steady power of a system can be increased by raising the voltage profile of a system and by reducing the transfer reactance. Thus we see that by considering the effect of rotor circuit dynamics we study the model in greater details. We have developed the expressions for the elements of the state matrix as explicit functions of system parameters. In addition to the statespace representation, we also use the block diagram representation to analyse the system stability characteristics.
While this approach is not suited for a detailed study of large systems, it is useful in gaining a physical insight into the effects of field circuit dynamics and in establishing the basis for methods of enhancing stability through excitation control.
We have explored a more detailed model for transient stability analysis taking into account the effect of damping which is clearly visible from the dynamic response of the system. We have included a damping factor in the original swing equation which accounts for the damping taking place at various points within the system.
Our aim should be to improvise methods to increase transient stability. A stage has been reached in technology whereby the methods of improving stability have been pushed to their limits. With the trend to reduce machine inertias there is a constant need to determine availability, feasibility and applicability of new methods for maintaining and improving stability.
8.2 REFERENCES
[I] Nagrath, I.J., and Kothari, D.P., Power System Engineering, New Delhi, Tata McGrawHill
Publishing Company Limited, l995.
[2] Saadat, Hadi, Power System Analysis, New Delhi, Tata McGrawHill Publishing Company
Limited, 2002.
[3] Wadhwa, C.L., Electrical Power Systems, New Delhi, New Age International publishers, 2005. [4] Yo, Yaonan, Electrical Power Systems Dynamics, Academic Press, New York, l983. [5] Anderson P.M., Analysis of Faulted Power Systems, IEEE Press, New York,l973. [6] ] Kundur Prabha, Power System Stability and Control, Tata McGrawHill, 2007.
[7] W.D. Stevenson, Elements of Power System Analysis, 3rd Edition, McGrawHill,l975 [8] R.T. Byerly and E.W.Kimbark, Stability of Large Electric Power Systems, IEEE Press,l974 [9] E.R. Laithwaite and L.L.Freris, Electric Energy: Its Generation, Transmission and Use, McGrawHill (UK), l980
[l0] B.Stott, "Power System Dynamic Response Calculations", Proc IEEE, Vol.67, pp.2l024l, February l979
[II] N.Kakimoto, Y.Ohsawa, and M. Hayashi, "Transient Stability Analysis of Electric Power
System Via Lure, Type Lyapunov Functions, Parts I and II," Trans. IEE of Japan, Vol.98, No.5l6,
May/June l978
[l2] A.A. Fouad and S.E. Stanton, "Transient Stability of Multi machine Power System, Parts I and II," IEEE Trans., Vol. PASl00, pp. 34083424, July l98l 
