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Transcript of Ashraf Ali C24
King Fahd University of Petroleum and Minerals Electrical Engineering Department
2011-12 (111)
IDENTIFIER C-24
APPLICATION OF EQUAL AREA CRITERION IN THE TIME-DOMAIN
FOR OUT OF STEP PROTECTION
Advisor:
Dr. M. A. ABIDO
Professor, EE Department
Submitted by:
Mohammad Ashraf Ali
Student ID: g201102010
January 31, 2012
Application of Equal Area Criterion in the Time-Domain for
Out-of-Step Protection Mohammad Ashraf Ali, ID: g201102010
Abstract- Power system stability refer to the ability of
synchronous machines to move from steady-state operating
point following a disturbance to another steady-state
operating point, without losing synchronism. An Algorithm
to predict the out-of-step protection by mapping the Equal-
Area-Criterion in the time-domain is proposed in the paper.
The criterion is applied to SMIB system on
MATLAB/SIMULINK environment and the classification
between the stable and out-of-step swings is done using the
accelerating and decelerating energies, which represents
the area under the power-time curve. This algorithm is
based only on the local electrical quantities available at the
relay location and does not depend on the network
configuration and parameters. Simulations have been
carried out extensively to test the effectiveness of the
proposed algorithm.
Index Terms –Power system transient stability, Out-of-
Step Protection, Equal area criterion, Power swings.
I. INTRODUCTION
The electric power system is a highly dynamic and
non-linear system. The dynamics are due to changes
such as the load and generation changes, due to
switching phenomena, due to faults such as short
circuits and may be due to lightning surges. 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.
In other words it is the ability of various machine in the
system to remain in synchronism (stay in step), with
each other following a disturbance. The stability
studies may be classified upon the nature of
disturbance as Steady state stability, Dynamic stability,
and the Transient stability. The representation of
synchronous machine in the stability studies differ
from one kind of study to the other. As stated earlier,
the electric power being a non-linear and dynamic
system is subjected to electromechanical oscillations
whenever a disturbance occurs in the system. The
transient stability may be defined of as the ability of a
synchronous machine to maintain synchronism with
respect to other machines following a sudden large
disturbance. Transient stability studies are needed to
ensure that the system can withstand the transient
condition following a sudden major disturbance.
Typically these major disturbances happen when the
power systems are heavily loaded and a number of
multiple outages occur within a short period of time,
causing power oscillations between neighboring utility
systems. Also due to the power mismatch between
generation and load demands these disturbances occur.
These electromechanical oscillations cause variation in
phase and amplitude of voltage and current signals
throughout the power system and consequently it
causes variation in power flow between two areas
known as power swing. A power swing can be
classified as a stable power swing in which the
oscillations are damped and stable operation of the
system is achieved. The other case which leads to loss
of synchronism between generator groups located in
the different areas of a power system is referred to as
Pole Slip or Out-Of-Step (OOS) conditions or loss of
synchronism conditions. When an Out-of-Step
condition occurs in a power system the healthy section
must be islanded from the faulty section. It necessitates
the use of Out-of-Step relays which sense such
conditions and isolate the section where stability is
restored from the faulty section.
There are several techniques available in literature and
in practice to detect Out-of-Step conditions. The
conventional method uses a distance relay with
blinders in the impedance plane and a timer. The
settings of blinder and timer requires the knowledge of
the fastest power swing, the normal operating region
and the possible swing frequencies and is therefore
system specific. These are used in offline stability
studies for obtaining the settings and their complexity
increases for multi-machines.
Another technique proposed out-of-step detection
based on a neural network and application of fuzzy
logic using an adaptive network-based fuzzy interface
(ANFIS). The mechanical input power, generator
kinetic energy deviation and average kinetic energy
deviation are selected as inputs to the neural network.
Another method based on fuzzy logic uses machine
angular frequency deviation and impedance angle
measured at the machine terminals as inputs. The
above two techniques are able to make decisions
quickly for a new case, which has close resemblance to
a known predefined case for which the algorithm is
trained. It requires enormous training effort to train all
2
possible swing cases. This makes the training process
tedious and also the complexity increases as system
interconnections increase.
The other method based on the Liapunov energy
function criterion for loss-of-synchronism detection for
a complex power system. During unstable swings, the
entire power system oscillates in two groups, and series
elements called cutset connect them. It requires
measurements all across series elements to find the
cutset. It is difficult to implement a protection
algorithm by this technique because of wide area
information involved in the protection systems.
Another method monitors the rate of change of swing
center voltage (SCV) and compares it with a threshold
value to differentiate between a stable and unstable
swing. The SCV is obtained locally from the voltage at
the relay location. It is independent of power sysem
parameters but this technique requires offline stability
studies to set the threshold value making it system
specific.
Reference [8] proposed an out-of-step detection
technique based on classical equal area criterion (EAC)
in the power angle (δ) domain. This technique requires
pre-and post- disturbance power angle (Pe-δ) curves of
the system to be known to the relay. Many
measurement devices are required at various locations
to acquire the current system information as the Pe-
delta curves are dependent on system configuration.
In this paper, we modify the concept of equal area
criterion EAC to the time-domain to detect the loss of
synchronism condition. We have devised an algorithm
to detect out-of-step swing using the time-domain
concept of EAC. We have obtained the power-time
(Pe-t) curves for the system instead of the conventional
Pe-δ curves. This algorithm does not require any power
system parameters information and only requires
measurements of local quantities available at the relay
location. The transient energy areas under the Pe-t
curve are calculated and the swing may be identified as
stable or out-of-step swing. This algorithm is
successfully tested on SMIB (single machine infinite
system) using the SIM POWER SYSTEMS toolbox of
SIMULINK.
In the first part of this paper some introduction about
the power system oscillation is presented. In the second
part, equal area criterion for out-of-step protection is
described and modified to the time-domain. In section
IV a brief description about the dynamic model used in
the simulation studies is discussed. In section V
simulation results for Single Machine Infinite Bus
(SMIB) model are presented.
II. POWER SYSTEM OSCILLATION
A simple power system consisting of one generator
connected through a transmission grid to an infinite bus
is shown in Fig.1. This model can be used to describe
the oscillating parts of a power system.
It can be shown that the maximum power, that can
be transmitted through the line, depends on the
difference of the voltages at the two terminals. This
angle may be expressed as .
The power flow from the synchronous machine to the
infinite bus is given by the equations as follow:
Where,
The amplitudes of E‟ and can be different but the
phase difference of voltages is more important. Fig. 2
shows a typical example of current, voltage and active
power flow due to variation of angle difference
between the two EMF‟s during loss of synchronism.
When the phase voltages are maximum and the
currents are at a minimum the two areas are in phase.
Conversely, the two areas are out of phase or 180ο the
voltages are at minimum and the currents are at a
maximum.
3
Fig.2 Typical examples of voltage, current and power
flow during loss of synchronism
The frequencies of oscillation are inherent to the
system and are about few Hz (0.2Hz-3Hz). The sizes of
oscillations depend upon the system inertia and
impedance between different machines in the system.
The Swing Equation corresponding to SMIB system is
as follow:
Where
Pm = mechanical power input p.u.
Pmax= maximum electrical power output p.u.
H = inertia constant in MW-s/MVA
δ = rotor angle in elec. Radians
t = time in s
The curve drawn between Power P and δ is known as
power angle curve and it is shown in fig.3 below.
III. EQUAL AREA CRITERION
Figure 1 shows a SMIB system; we have the sending
end voltage ES leading the receiving end voltage ER by
delta. This angle delta is referred is to as power angle.
The steady state output power of the generator is Pe
and is equal to the mechanical power input Pm to the
generator. This system has two parallel lines with
impedances equal to X1 and X2 respectively.
A three phase fault at the middle of the line TL-II is
applied and this fault is cleared after some delay by
opening the two breakers „A‟ and „B‟. The transient
response following a disturbance in the SMIB
configuration is obtained by solving the swing
equation.
Fig 3 Pe-δ a curves illustrating stable case.
Fig 4 Pe-delta curves illustrating unstable case.
The swing equation can be solved graphically using the
equal area criterion. This method is based on the
graphical interpretation of the energy stored in the
rotating mass as aid to predict the condition for
stability. This method is only applicable to SMIB
system or a two-machine system.
4
In Pe-t domain we do not need to solve the swing
equation and prediction of out-of-step condition is
quite easy as the complete data is available through
relays. Hence this method is used in the paper. Fig 3,
Fig 4 shows the Pe- curves for the stable and unstable
swings. The Pe-t curves corresponding to these cases
are shown in figures 5&6. We use these curves to
describe the proposed algorithm.
Fig 5 Pe-t curve illustrating stable case
Fig 6 Pe-t curve illustrating unstable case.
Consider the figure 5, the areas A1 and A2 represents
the accelerating and decelerating areas under the Pe-t
curves. The area A1 is positive as for t= t0 to
t1. Similarly the areaA2 is obtained by integrating the
Pe-t curve from t1. to tmax. The time t0correspond to the
fault initiation time. The time t1correspond to the case
when . The time tmaxis the time at which
.
The areas A1 & A2 are given by the following
equation:
∫ ( ( ))
[ ]
∫ ( ( ))
[ ]
For stable condition,
∫ ( ( ))
For out of step condition or unstable power swing we
have,
∫ ( ( ))
This shows that for a stable condition the rotor
oscillations and the rotor will attain a new stable
operating point and for unstable power swing the rotor
speed increases indefinitely and the machine may go
out-of-step or it may synchronism with the infinite bus.
Thus the areas obtained by the above equations form
the basis of the proposed algorithm to detect out-of-
step condition. As per the proposed algorithm the
system will be stable if the decelerating area is more
than or equal to the accelerating area. And an unstable
condition occurs if the accelerating area is more than
the decelerating area.
IV. SOFTWARE SIMULATIONS
The proposed algorithm is applied to a SMIB (Single
Machine Infinite Bus) system in order to test the
effectiveness of the algorithm in detecting the stable
and unstable power swing.
Figure bellows shows the block diagram of the SMIB
system implemented on SIMULINK.
5
A) PROCEDURE:
A power system shown in Fig 1 is used to test the
proposed algorithm. This system is simulated in
SIMULINK environment of MATLAB R 2010b. The
simulation steps are given below.
1. The mechanical power input is kept at Pm=0.8
p.u keeping simulation time 10 seconds.
2. The initial power angle 0 is determined.
3. The time corresponding to the initial power angle
t0 is computed, the time t1, and tmax corresponding
to = max.
4. The critical clearing time(200 msec)) and critical
angle is calculated.
5. The fault clear time(130msec & 220 msec) is
varied over critical clearing time and the Pe-t
curve is obtained.
6. The accelerating and decelerating areas A1 & A2
under the Pe-t curve are calculated.
7. The areas A1 & A2 are compared to test for out-
of-step condition.
Next the following cases are tested.
1. The mechanical power input is raised to Pm =0.9
p.u keeping simulation time 10 seconds.
2. The initial power angle 0 is determined.
3. The time corresponding to the initial power angle
t0 is computed; the time t1 and tmax are also
calculated.
4. The critical clearing time (170 msec) and critical
angle is calculated.
5. The fault clear time(170 msec & 180 msec) is
varied over critical clearing time and the Pe-t
curve is obtained.
6. The accelerating and decelerating areas A1 & A2
under the Pe-t curve are calculated.
7. The areas A1 & A2 are compared to test for out-
of-step condition.
B) EXCITATION SYSTEM:
In the transient stability studies, the excitation systems
play an important role. AVR (Automatic Voltage
Regulator) improves the first swing stability but
reduces stability in following swings.
Figure below depicts the general structure of a detailed
excitation system model having a one-to-one
correspondence with the physical equipment. While
this model structure has the advantage of retaining a
direct relationship between the model parameters and
physical parameters, such detail is considered too great
for general system studies.
IEEE Type I DC excitation system is used in the
stability studies.
V. ANALYSIS OF RESULTS
Table below shows some of the simulation results for
the SMIB system. In each case, calculated accelerating
(A1) and decelerating (A2) areas from the Power-time
(Pe-t) curve are presented in the Table.
In the case 1, the mechanical power input Pm = 0.8 p.u.
is fixed constant. The fault time is kept at 130 msec
well above the Critical clearing time (200msec) thereby
calculating the areas A1 = 0.0592 & A2 = 0.0973. And
by keeping fault operation time at 220 msec, above the
critical clearing time and calculated areas A1 = 0.1297
& A2 = 0.1155.
Case 1 2 3 4
Pm(p.u.) 0.8 0.8 0.9 0.9
Critical time(ms)
200 200 170 170
Fault clear time(ms)
130 220 140 180
Area A1 (pu-s)
0.0592 0.1297 0.074 0.1572
Area A2 (pu-s)
0.0973 0.1155 0.3902 0.1100
Decision Stable Out-of-step
Stable Out-of-step
6
Pm=0.8 p.u. and t(op) =130msec
Pm=0.8 p.u. and t(op) =220 msec
Pm=0.9 p.u. and t(op) =140 msec
Pm=0.9 p.u. and t(op) =180 msec
VII. COMPARISON WITH THE REFERENCE PAPER
Case 1 2 3 4
Pm(p.u.) 0.8 0.8 0.8 0.8
Critical time(ms)
200 200 200 200
Fault clear time(ms)
167 200 233 267
Area A1 (pu-s)
0.0993 0.1144 0.1270 0.1451
Area A2 (pu-s)
0.4530 0.1406 0.0717 0.0367
Decision Stable Stable Out-of-step
Out-of-step
Pm=0.8 p.u. and t(op) =167msec
Pm=0.8 p.u. and t(op) =200msec
7
Pm=0.8 p.u. and t(op) =233msec
Pm=0.8 p.u. and t(op) =267msec
VII. CONCLUSION
An algorithm for out-of-step detection in the time-domain has
been proposed by modifying the classical equal area criterion
condition. The effectiveness of this technique has been tested
for SMIB system. The proposed algorithm perfectly
discriminated between stable and out-of-step swings based on
the local voltage and current information available at the relay
location. This algorithm does not require the line parameter
information and also do not require any off-line system
studies. The proposed technique also does not need the inertia
constant „M‟ and is therefore more accurate than the classical
equal area criterion.
VIII. REFERENCES
[1] D. Tziouvaras and D. Hou, “Out-of-Step Protection
Fundamentals and Advancements,” Proc.30th Annual
Western Protective Relay Conference, Spokane, WA,
October 21–23, 2003.
[2] E. W. Kimbark, Power System Stability, vol. 2, John
Wiley and Sons, Inc., New York, 1950.
[3] IEEE Recommended Practice for Excitation System
Models for Power System Stability Studies, IEEE Std.
421.5, 1992.
[4] IEEE Guide for Synchronous Generator Modeling
Practices and Applications in Power System Stability
Analyses, IEEE Std. 1110, 2002.
[5] “Out of step relaying using phasor measurement unit
and equal area criterion”, M chehreghani Bozchalui and
M Sanaye Pasand.
[6] P. Kundur, Power System Stability Control. New York:
McGraw-Hill1994.
[7] V.Centeno, A.G.Phadke and A.Edris, “Adaptive Out-of-
step relaywith phasor measurements”, IEEE Conf Pub
No.434 1997, pp. 210-213.
[8] “Out of Step Protection using Equal Area Criterion”,
Shengli Cheng, Mohindar S. Sachdev.
[9] “Application of Equal Area Criterion Condition in Time
Domain for Out of Step Protection”, Sumit Paudyal,
Gokaraju Ramakrishna, Mohindar S. Sachdev.