29-06-2013, 03:44 PM
Simulation of Synchronous Machine in Stability Study for Power System
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Abstract
This paper presents a linear mathematical model of
the synchronous generator with excitation system for power system
stability. For large systems the state space model has been used more
frequently in connection with system described by linear differential
equations. The flux linkage of each circuit in the machine depends
upon the exciter output voltage. The excitation system models
described use a pu system. The complete system is mainly included
synchronous machine, exciter and transmission line. The system is
whether stable or unstable is determined by eigen-values of the
system coefficient matrix A. These eigen-values are identified with
the parameters of the machine and are not depend on the exciter
parameters. Complete state equations are obtained first order
differential equation from the system model by identifying
appropriate state variables.
INTRODUCTION
ONTROL system design and analysis technologies are
very useful to be applied in real time development. A
stable power system is one in which the synchronous
machines, when perturbed will either return to their original
state if there is no net change of power or will acquire a new
state without losing synchronism. If the system equations are
linear (have been linearized ), the techniques of linear system
analysis are used to study dynamic behavior. The most
common method is to simulate each component by its transfer
function. The system performance may then be analyzed by
such methods as root-locus plots, frequency domain analysis
(Nyquist criterion), and Routh-Hurwitz criterion. These
methods have been frequently used in studies pertaining to
small systems or a small number of machines.
STATE-SPACE DESCRIPTION OF OVERALL SYSTEM
The excitation system controls the generated EMF of the
generator and therefore controls not only the output voltage
but also the power factor and current magnitude as well. The
following equations (13) through (17) of the excitation control
system transformed into S plane are given below. The
corresponding model block diagram is shown in Fig. 3.
MODELING AND SIMULATION
MATLAB/SIMULINK program was used in testing of the
stability condition of the synchronous machine infinite bus
system. The M-file and SIMULINK model can be combined
by the commands [num, den]=ss2tf(A, B,C, D, 1);c=step(num,
den, t); plot(t, c); title; x label and y label. The parameters for
35 MVA, 11kV generator, exciter and transmission line are
listed in Table I and II. This input parameters are used to
simulation program. The simulation results are shown in Fig.5
to Fig. 9. The out put field current of synchronous machine is
shown in Fig. 5. The d axis stator current and damper winding
current of the machine is shown in Fig. 6 and 7. The response
is highly oscillatory, with a very large overshoot and a long
settling time. It cannot have a small steady state error and a
satisfactory transient response at the same time. The system is
whether stable or unstable is determined not only eigen-values
of overall system matrix A but also root locus plot. In Fig. 8,
all the poles of the system transfer function have negative real
part. Therefore, the system is stable. Fig. 9 is terminal voltage
step response (with (or) without feed back stabilizer).
CONCLUSION
The aim of this paper is to introduce Technicians to the
Modeling of Synchronous machine with excitation system on
stability studies and to use computer simulation as a tool for
conducting transient and control studies. Next to having an
actual system to experiment on, simulation is often chosen by
engineers to study transient and control performance or to test
conceptual designs. MATLAB/SIMULINK is used because of
the short learning curve that most students require to start
using it, its wide distribution, and its general-purpose nature.
This will demonstrate the advantages of using MATLAB
for analyzing steady state power system stability and its
capabilities for simulating transients in power systems,
including control behavior.