Sep 2014. Vol. 5, No.5
ISSN 2305-1493
International Journal of Scientific Knowledge
Computing and Information Technology
© 2012 - 2014 IJSK & K.A.J. All rights reserved
www.ijsk.org/ijsk
EFFECTS OF MACHINE CONSTANT TO ROTOR ANGLE
STABILITY IN SINGLE MACHINE INFINITE BUS POWER
SYSTEMS
1
Bilgehan TOZLU, 2Fatin SONMEZ
1
2
Osmancık Omer Derindere Vocational School, Hitit University, Corum, TURKEY
Artvin Vocational School, Artvin Coruh University, Artvin, TURKEY
E-mail:
1
bilgehantozlu@hitit.edu.tr, 2 fatinsonmez@atvin.edu.tr
ABSTRACT
This paper treats the effect of inertia constant of machine (machine constant) which is synchronous
generator in single machine infinite bus power systems, to rotor angle stability. The system is modeled by
an equation named swing equation and it is simulated in computer by using Matlab/Simulink. It is observed
that how the rotor angle stability is affected by changing machine constant when all values of the system
except for machine constant were assumed to be permanent. In this study, it is investigated that how the
rotor angle stability changes with synchronous machine constant in SMIB power systems.
Keywords: Rotor angle stability, machine inertia constant, SMIB.
work power systems more closest points in stability
limit and so reduction in limits of stability and
voltage stability has become a critical issue [2,3].
1. INTRODUCTION
Especially since the beginning of the 1990s,
environmentally friendly energy production has
been a promoted area on technological researchdevelopment and making investment in parallel
with it by many international institutions
throughout the World.
A large nonlinear interconnected power
system shows some complex acts when operating
point moves away from a continuous state. Power
systems become more and more multi-loaded for
that economic and environmental pressures narrow
the raise of new transmission and production
capabilities.
However, most of this new generation
electricity production facilities that defined as
renewable energy technologies are doing variable
production, so integration between the existing
electricity network and this type of power stations
is very difficult.
Under these stressed conditions, a power
system can exhibit a new type of dynamic unstable
behaviors such as slow voltage drops or even
voltage collapse. Therefore, requirements for
dynamic analysis of power system has grown
significantly in recent years [4,5].
Renewable energy power stations usually
land regions where network is not strong, and it
requires that these power stations usually connect
to the electricity system from the end points of
network. This situation significantly modifies the
network's existing energy flux and especially
flexible energy production characteristics of wind
power stations affect negatively the voltage and
frequency values of the system [1].
Committees of the IEEE and CIGRE have
defined power system stability as an ability of an
electric power system, for a given initial operating
condition, to regain a state of operating equilibrium
after being subjected to a physical disturbance,
with most system variables bounded so that
practically the entire system remains intact [6].
Another negative effect in the power system
stability is overload. Economic-environmental
pressures and continuous load increment forced to
Transient instability has been the dominant
stability problem on many systems. As power
1
Sep 2014. Vol. 5, No.5
ISSN 2305-1493
International Journal of Scientific Knowledge
Computing and Information Technology
© 2012 - 2014 IJSK & K.A.J. All rights reserved
www.ijsk.org/ijsk
systems have evolved through continuing growth in
interconnections, using of new technologies and
controls, and the increased operation in highly
stressed conditions, different forms of system
instability have emerged. For example, voltage
stability, frequency stability and inner oscillations
have become greater concerns than in the past
[7,8].
power system known as a grid. When a
synchronous generator connects to the grid, its rotor
speed and terminal voltage are fixed by the grid
and it is said to be operating on infinite bus. A
change in field excitation results in a change in
the operating power factor while a change in
mechanical power input causes a corresponding
change in the electrical power output [13].
Disturbing effect may be small or large.
Small distortions such as load change are
continuously and the system adapts to changing
conditions. The power system should be ready to
short-circuited transmission line, a large generatorload loss or deterioration of various types, such as
disconnection of the line between two bars.
Voltage stability is defined as the ability to be
within acceptable limits, of voltage magnitude on
all bars, after a disturbance on a power system
[9,10].
Figure 2. A SMIB Power System
The equation called as swing equation of a
conventional SMIB power system that is shown in
figure 2, is as follows:
2 H d 2
 Pm  Pe
0 dt 2
It is expressed that, frequency is controlled
by balancing the load with generation [11].
(1)
Where;
Frequency instability results from unbalance
of active power between the load and generation.
H
w
θ
Pm
Pe
The rotor angle stability is the ability to stay
in synchronized of all synchronous machines in a
power system [6]. This stability problem is
concerned with the electromechanical oscillations
in a power system. For understanding the stability
problems, it needs to classify the stability to parts
[12]. The classification of power system stabilities
is shown as in Figure 1.
is the inertia constant,
is the angular velocity of machine,
is rotor angle,
is the mechanical power,
is electrical power
Inertia constant of synchronous machine
changes depending on size of machine which is
huge or small. Even the inertia constant could
change depending on type of material used.
The inertia constant (H) is obtained as:
H
0,5  J  m2 0
S
(2)
Where;
Figure 1. Classification of power system
stability.
J
is total inertia of rotor and turbine,
m 0
is mechanical angular velocity,
S
is total power (MVA) of machine
Inertia constants of different types of
synchronous machines are given in Table1 [12].
2. SINGLE
MACHINE-INFINITE
BUS
(SMIB) POWER SYSTEM AND ROTOR
ANGLE STABILITY
Synchronous generators seldom operate in
the isolated mode, most of all are usually connected
in parallel to supply the loads, forming a large
2
Sep 2014. Vol. 5, No.5
ISSN 2305-1493
International Journal of Scientific Knowledge
Computing and Information Technology
© 2012 - 2014 IJSK & K.A.J. All rights reserved
www.ijsk.org/ijsk
Table 1 –Typical values of H for different types
of synchronous machines
Type of Synchronous
MachineThermal Power
- Steam Turbine
- Gas Turbine
Hydro Power
- Slow (<200 min-1)
- Fast (>200 min-1)
Synchronous Compensators
Synchronous Motors
Inertia Constnant
H(s)
4-9
7-10
2-3
2-4
1-1,5
≈2
Figure 4. Rotor angle-Time graph of H=3
Rotor angle is unstable for H=3. Rotor angle
doesn’t come to a fixed value, it flies after 130º.
3. SIMULATION RESULTS
Holding fixed all parameters of synchronous
generator, the rotor angle stability has been seen by
the change of the machine constant value at the
MATLAB/SIMULINK simulation which has been
composed to view the effect of inertia constant (H)
of synchronous machine to rotor angle stability in a
single- machine infinite-bus power system.
for H=3,2
At the simulation;
Constant of damping winding is 0.02,
electrical power before error is 1.86 pu, electrical
power after error is 1.26 pu, cleaning error time
is 6 cycles and reclosing time is 1000 ms.
Figure 5. Rotor angle-Angular velocity graph for
H=3,2
for H=3
Figure 3. Rotor angle-Angular velocity graph for
H=3
Figure 6. Rotor angle-Time graph of H=3,2
The system starts coming to stability for
H=3,2. The rotor angle makes the first oscillation
at 2,5 seconds. Rotor angle starts to recover after
125º.
for H=4
3
Sep 2014. Vol. 5, No.5
ISSN 2305-1493
International Journal of Scientific Knowledge
Computing and Information Technology
© 2012 - 2014 IJSK & K.A.J. All rights reserved
www.ijsk.org/ijsk
Figure 10. Rotor angle-Time graph of
H=10
The system is more stable than H=4. Rotor
angle starts to recover after 90º.
Figure 7. Rotor angle-Angular velocity graph for
H=4
4. CONCLUSION
In the SMIB system given above, it is
changed the inertia constant of the machine by
holding fixed all parameters of the synchronous
generator, and it is examined the effect of the inertia
constant of the synchronous generator to rotor angle
stability. Figure-3 and Figure-4 are showing that
the rotor angle stability hasn’t been provided for
machine constant is 3 (H=3).
It is seen that; the rotor angle stability has
been very difficult provided after 125º for machine
constant is 3,2 (H=3,2) in figure5-6, however the
rotor angle stability has been more easily and more
quickly provided when the value of machine
constant grew in figure7-8 and figure9-10. In this
study, it is determined by the simulations that after
repairing an error in a single-machine infinite-bus
power system, the rotor angle stability improves
when the inertia constant of synchronous machine
grows.
Fıgure 8. Rotor angle-Time graph of H=4
The system is more stable for H=4. The
rotor angle oscillates the first oscillation at 1,5
seconds. Rotor angle starts to recover after 110º.
for H=10
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Sep 2014. Vol. 5, No.5
ISSN 2305-1493
International Journal of Scientific Knowledge
Computing and Information Technology
© 2012 - 2014 IJSK & K.A.J. All rights reserved
www.ijsk.org/ijsk
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