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 POWER SYSTEM STABILITY STUDIES USING MATLAB full report
Post: #1

[attachment=2745]

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 - Point-by-Point method, Modified Euler method and Runge-Kutta method.
Â¢ Modern power systems have many interconnected generating stations, each with several generators and many loads. So our study is not limited to one-machine system but we have also studied multi-machine stability.
Â¢ We study the small-signal 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 small-signal 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 high-voltage 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'.
CONCLUSION AND REFERENCES
8.1 CONCLUSION
Thus we see that a two-machine system can be equivalently reduced to a one machine system connected to infinite bus bar. In case of a large multi-machine 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 two-machine or an equivalent one-machine infinite bus system can be easily extended to a multi-machine 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 one-machine 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 speed-governor 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 state-space 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 McGraw-Hill
Publishing Company Limited, l995.
[2] Saadat, Hadi, Power System Analysis, New Delhi, Tata McGraw-Hill Publishing Company
Limited, 2002.
[3] Wadhwa, C.L., Electrical Power Systems, New Delhi, New Age International publishers, 2005. [4] Yo, Yao-nan, 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 McGraw-Hill, 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, McGraw-Hill (UK), l980
[l0] B.Stott, "Power System Dynamic Response Calculations", Proc IEEE, Vol.67, pp.2l0-24l, 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. PAS-l00, pp. 3408-3424, July l98l
Post: #2
can you give me the whole project report of transient stability analysis of single machine system by rungekutta method in matlab
Post: #3
Classical Analysis
Equal Area Criterion
Power System Dynamics and Transients
A generator connected to an infinite bus through a line. Initially Pm=Pe
Stability is governed by the Swing Equation
d2δ/dt2 = (πf/H) (Pm-Pe)

dδ /dt = ω-ωsyn

Swing Equation

Power Angle
Equation

Pe = E’ V sin (δ) /(X+XL)

First swing stability-Equal Area Criterion
Stable Equilibrium—small increase in mechanical power

At D ω is decreasing but > 0
δ increases further say to point E
By now suppose ω is back to zero and decreasing
Thus ω becomes < 0 as the generator continues to slow
Since ω<0 δ decreases towards B First swing stable!

Post: #4
[attachment=6434]
Recent Power Electronics/FACTS Installations to Improve Power System Dynamic Performance

Introduction

Unified Power Flow Controller (UPFC) is used to control the power flow in the
transmission systems by controlling the impedance, voltage magnitude and phase angle.
This controller offers advantages in terms of static and dynamic operation of the power
system. It also brings in new challenges in power electronics and power system design. The
basic structure of the UPFC consists of two voltage source inverter (VSI); where one
converter is connected in parallel to the transmission line while the other is in series with
the transmission line.
Post: #5
POWER SYSTEM STABILITY

Introduction

Since the industrial revolution man's demand for and consumption of energy has increased steadily. The invention of the induction motor by Nikola Tesla in 1888 signaled the growing importance of electrical energy in the industrial world as well as its use for artificial lighting. A major portion of the energy needs of a modern society is supplied in the form of electrical energy. Industrially developed societies need an ever-increasing supply of electrical power, and the demand on the North American continent has been doubling every ten years. Very complex power systems have been built to satisfy this increasing demand. The trend in electric power production is toward an interconnected network of transmission lines linking generators and loads into large integrated systems, some of which span entire continents. Indeed, in the United States and Canada, generators located thousands of miles apart operate in parallel. This vast enterprise of supplying electrical energy presents many engineering problems that provide the engineer with a variety of challenges. The planning, construction, and operation of such systems become exceedingly complex. Some of the problems stimulate the engineer's managerial talents; others tax his knowledge and experience in system design. The entire design must be predicated on automatic control and not on the slow response of human operators. To be able to predict the performance of such complex systems, the engineer is forced to seek ever more powerful tools of analysis and synthesis. This book is concerned with some aspects of the design problem, particularly the dynamic performance, of interconnected power systems. Characteristics of the various components of a power system during normal operating conditions and during disturbances will be examined, and effects on the overall system performance will be analyzed. Emphasis will be given to the transient behavior in which the system is described mathematically by ordinary differential equations.

Requirements of a Reliable Electrical Power Service

Post: #6
[attachment=9160]
POWER SYSTEM STABILITY STUDIES USING MATLAB
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 - Point-by-Point method, Modified Euler method and Runge-[censored] method.
Â¢ Modern power systems have many interconnected generating stations, each with several generators and many loads. So our study is not limited to one-machine system but we have also studied multi-machine stability.
Â¢ We study the small-signal 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 small-signal 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 high-voltage 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'.
8.1 CONCLUSION
Thus we see that a two-machine system can be equivalently reduced to a one machine system connected to infinite bus bar. In case of a large multi-machine 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 two-machine or an equivalent one-machine infinite bus system can be easily extended to a multi-machine 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 one-machine 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 speed-governor 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 state-space 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
Post: #7
Post: #8
aoa kindly send me link 0f further iformation and matlab code of power system stability and transiet analysis.
Post: #9
PRESENTED BY
RAHUL VISWAM
SHILPA.K.M
SREEDEVI.K.P

[attachment=14501]
introduction
Stability :

Transient stability:
Ability to remain stable for large disturbance .
Determines whether or not synchronism is maintained.
Disturbances:
Switching of long transmission line
Change in speeds of rotor
Changes in power angle
Need for power flow studies
Involves determination of
1. magnitude and phase angle of voltage at each bus.
2. active and reactive power flow
Necessary for planning, economic scheduling, future expansion and control of existing system
Types of buses
A bus without any generators connected to it.
the real power and reactive power are known.
Generator Bus (PV bus)
a bus with at least one generator connected to it
the real power generated PG and the voltage magnitude |V| is known.
Slack Bus (VQ bus)
one arbitrarily-selected bus that has a generator.
the only bus at which the system reference phase angle is defined
Problem description
Gauss-Seidel method
Iterative algorithm for obtaining load flow solution.
Repeats till the solution converges within the accuracy
Equations used in G-S method:
Magnitude of voltage,
Vp(k+1)=1/Ypp [ (Pp-jQp)/(Vpk) -∑Ypq Vq(k+1)-∑Ypq Vqk ]
Phase angle of voltage,
p(k+1) = tan-1 [Im. Part of Vp(k+1) /Re part of Vp(k+1) ]
Introduction to matlab
Refers to Mathematical Laboratory.
Numerical computing environment.
fourth-generation programming language.
Developed by MathWorks.
Simulink adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems.
Allows interfacing with programs written in other languages, including C, C++, Java, and Fortran.
Program for G-S method is
lfgauss : designed for direct use of load and generation in MW and Mvar, busvoltage in p.u
and angle in degree.
lfybus : converts impedence to admittance
busout : produces bus output result in tabulated form
lineflow : designed to display active and reactive power flow.
eacfault : for obtaining power angle curve before,during ,after the fault clearence.
problem
Design a configuration plan for power system in Happy Island shown in figures below. Run load flow for transmission system that is designed. Using suitable software program conduct the power flow analysis of system. Analyze the transient stability when there is a transient fault in the midpoint of the line between buses 3 and 4.
location
System description
Numbers 1 to 5 represents the load generation points.
The bus data in table 1 list values for P,Q and V at each bus for base case.
Parameters of all power generation and capacitor in table 2.
The transmission lines length from point to point in the system in table 3.
Transmission line parameters in table 4.
Voltage limit of ±5% of normal and thermal limits of 100MVA for all lines.
PROBLEM ANALYSIS
Basemva=100; accuracy=0.001; accel=1.8; maxiter=100;
% 5-BUS TEST SYSTEM (American Electric Power)
% Bus Bus Voltage Angle ---Load---- -------Generator----- Static Mvar
% No code Mag. Degree MW Mvar MW Mvar Qmin Qmax +Qc/-Ql
busdata=
[
1 1 1.04 0.0 65.0 30.0 0.0 0.0 -999 999 40
2 0 1.0 0.0 115.0 65.0 0.0 0.0 -60 150 0
3 2 1.02 0.0 70.0 40.0 180.0 0.0 -20 50 0
4 0 1.0 0.0 85.0 40.0 0.0 0.0 0 0 0
5 0 1.0 0.0 70.0 30.0 0.0 0.0 0 0 0
];

% Line code
% Bus bus R X 1/2 B 1 for lines
% nl nr p.u. p.u. p.u. > 1 or < 1 tr. tap at bus nl
linedata=
[ 1 2 0.042 0.167 0.0 1
1 3 0.026 0.104 0.0 1
1 4 0.133 0.531 0.0 1
1 5 0.013 0.125 0.0 1
2 3 0.013 0.125 0.0 1
2 4 0.115 0.4602 0.0 1
2 5 0.08397 0.335 0.0 1
3 4 0.08391 0.3346 0.0 1
3 5 0.0525 0.209 0.0 1
4 5 0.0629 0.2509 0.0 1
];

lfybus % form the bus admittance matrix
lfgauss % Load flow solution by Gauss-Seidel method
busout % Prints the power flow solution on the screen
lineflow % Computes and displays the line flow and losses
RESULT
Line Flow and Losses
--Line-- Power at bus & line flow --Line loss-- Transformer
from to MW Mvar MVA MW Mvar tap

1 167.888 167.248 236.977
2 60.463 46.521 76.289 2.260 8.986
3 17.262 45.673 48.827 0.573 2.292
4 26.015 18.816 32.106 1.268 5.061
5 64.128 56.450 85.435 0.877 8.436
2 -115.000 -65.000 132.098
1 -58.203 -37.534 69.256 2.260 8.986
3 -60.339 -26.166 65.768 0.631 6.066
4 7.677 3.741 8.540 0.094 0.377
5 -4.194 -5.286 6.748 0.043 0.171
--Line-- Power at bus & line flow --Line loss-- Transformer
from to MW Mvar MVA MW Mvar tap
3 110.000 7.553 110.259
1 -16.689 - 43.381 46.481 0.573 2.292
2 60.969 32.232 68.965 0.631 6.066
4 34.277 14.702 37.297 1.191 4.749
5 31.517 4.161 31.791 0.541 2.155
4 -85.000 - 40.000 93.941
1 -24.747 -13.755 28.313 1.268 5.061
2 -7.583 -3.365 8.296 0.094 0.377
3 -33.086 -9.953 34.551 1.191 4.749
5 -19.593 -12.817 23.412 0.410 1.635
--Line-- Power at bus & line flow --Line loss-- Transformer
from to MW Mvar MVA MW Mvar tap
5 -70.000 -30.000 76.158
1 -63.251 -48.015 79.411 0.877 8.436
2 4.237 5.457 6.909 0.043 0.171
3 -30.976 -2.006 31.041 0.541 2.155
4 20.002 14.452 24.677 0.410 1.635

Total loss 7.888 39.926
Calculation of transient stability
EI Xt=0.2 1 XL1 =0.515 2 V=1.0
З  Xid =0.3 XL2 =0.335
PROGRAM:
Pm =0.8; E=1.17; V=1.0;
X1=0.76; X2=1.8; X3=0.76;
eacfault(Pm ,E ,V, X1, X2, X3)
RESULT
To find tc enter Inertia Constant H, (or 0 to skip) H = 5
Initial power angle = 31.309
Maximum angle swing = 148.691
Critical clearing angle = 77.863
Critical clearing time = 0.232 sec.
Post: #10

Post: #11
http://www.seminarprojects.org/t-power-s...ull-report

http://www.seminarprojects.org/t-power-s...9#pid54319
Post: #12
I learned a lot from reading this!
Post: #13
sir can u pls mail me this whole project with synopsis and matlab coding of it,i need it urgently sir
sir can u pls mail me this whole project along with the matlab coding of it,ineed it urgently.my mail id is shobhitgarg58[at]yahoo.com
Post: #14
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http://seminarprojects.org/t-power-syste...ort?page=2

Post: #15
to get information about the topic"power system projects" full report ppt and related topic refer the link bellow

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