Download A Novel Out-of-Step Protection Algorithm Based on Wide Area

The 10th Power Systems Protection & Control Conference
PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
A Novel Out-of-Step Protection Algorithm Based on
Wide Area Measurement System
Bahman Alinezhad
Hossein Kazemi Karegar
Faculty of Electrical and Computer Engineering
Shahid Beheshti University
Tehran, Iran
[email protected]
Faculty of Electrical and Computer Engineering
Shahid Beheshti University
Tehran, Iran
[email protected]
Abstract— This paper proposes a novel Out-of-Step protection
technique based on synchronized phasor measurements and
concept of Equal Area Criterion (EAC). In any disturbance, in
the control center, generators are clustered into safe and risk
groups based on the concept of Boundary of Angle Oscillations.
At the same time, a local stability index also is sent to the control
center from each generator. The latter is obtained by local
phasor measurements based on EAC concept. Generator is
known as unstable if it belongs to the risk cluster at the control
center and its stability index is lower than one. For each
generator, the acceleration area during fault condition is
calculated directly using the generator output power and rotor
angle measured in real-time. As soon as the fault is cleared, the
deceleration area is predicted with the help of post-fault curve
estimated by the least square method. The proposed technique is
verified on the New-England 39-Bus test network.
Keywords- Out-of-step, equal area criterion, boundary of angle
oscillations, least square method, phasor measurement unit (PMU)
S
I.
INTRODUCTION
YNCHRONOUS generators are subjected to various
disturbances such as faults and load variations. When the
balance between mechanical input and electrical output
powers of a generator is disrupted, the generator may lose its
synchronism with the power system and becomes unstable.
This condition is known as Out-of-Step (OOS) [1-2]. The
OOS of a generator not only is a threat for its mechanical
components, but also may affect the stability of the other
generators in the network. Thus, early disconnection of an
unstable generator can prevent other generators from
instability and helps to save the rest of the system from total
instability [3].
Industrial impedance-based OOS relays determine the
generator instability by analysing the impedance trajectory
crossing a predefined characteristic. The main disadvantage of
this technique is its relatively long operation time when the
generator practically loses synchronism with the power
system. In addition, numerous contingency simulations as well
as experimental experiences are required to obtain a reliable
setting which is an expensive and tedious work in a large
power system. Moreover, the settings should be modified by
change of the power system parameters.
The recent advent of Phasor Measurement Units (PMUs)
has made it possible to renew the system states in some
milliseconds and develop more efficient OOS detection
schemes. So far, several research studies have been done in
this subject. A relationship between the rotor angle stability
and maximal Lyapunov exponent is developed in [4] to
determine the rotor angle instability. In [5], a real-time
dynamic stability state estimator based on Lyapunov direct
energy function is proposed. This method uses synchronized
measurements as input and predicts the OOS condition. An
energy function based classification for distinguishing
between stable and unstable states by using synchronized
measurements is presented in [6-7]. A wide area based system
using artificial neural network is introduced in [8] by which an
intelligent technique is proposed to predict and mitigate the
OOS in a large power system. In [9], comparing the postdisturbance voltage trajectories with pre-defined voltage
templates is used to predict the OOS. This algorithm needs
extensive simulations, which should be performed again for
any change in the power system configuration.
Some research studies focus on the Equal Area Criterion
(EAC) to propose a new method. The conventional EAC can
be applied only on the single machine infinite bus (SMIB)
system. The generator stability analysis is performed in offline
mode. The rotor angle is calculated mathematically based on
the system equivalent inertia. In [10], authors present an
adaptive OOS relay based on EAC and synchronized
measurements. An algorithm for mapping the EAC from rotor
angle domain to time domain is proposed in [11-13]. The OOS
is estimated based on the energies obtained from the bounded
area between power curve and time axis under the power-time
curve. This method is simple, but it needs the Unstable
Equilibrium Point (UEP) of each generator. Calculating the
UEP in a large power system is very difficult. In [14], an nthorder autoregressive model is used to predict the post-fault
power-angle
curve. Authors suggest some techniques
to find the appropriate order of autoregressive model. In [15],
an approach based on the EAC and real power swing criterion
The 10th Power Systems Protection & Control Conference
PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
is proposed to detect the unstable state. It shows that the EAC
method can be used even for the OOS protection of small
generators. In [16], a method based on EAC and using
frequency deviations of voltage and discrete Fourier transform
is proposed for estimating the generator rotor angle. However,
the above algorithms are not verified on a multimachine
network.
In multimachine networks due to interactions between
generators, the conventional EAC cannot be used directly. The
major problem of this technique is determining the post-fault
curve. In [17], EAC and critical clearing time
estimation is used for calculation of transient stability margin
index for predefined areas of the power network. A fast online
coherency identification technique is developed in [18-19] to
identify the coherent generators. In [20], an extended EAC and
real-time swing curves are used to detect the OOS condition.
This method reduces the power system to one machine infinite
bus system and analyses the stability of the reduced system
based on the EAC concept. In [21], a special protection
scheme is developed based on the one machine infinite bus
and EAC to prevent the power system from blackout during
the power swing. The post-fault
curves are estimated
using the least square method.
In this paper, an online predictive OOS detection
technique is developed based on the EAC concept. The main
idea is clustering the generators in safe and risk groups. A new
algorithm is proposed for estimating the post-fault curve
parameters based on local measurements. Results show that
the proposed technique is able to predict the OOS of each
generator just in a few cycles after the disturbance, which is
considerably earlier than the time at which the generator rotor
angle meets the UEP. In addition, the proposed technique is
independent of changes in power system configurations, no
special setting is required and no extra measurements are
required except local ones.
The rest of the paper is organized as follows. In sections 2
and 3 the concepts of impedance-based OOS relays and the
proposed method are discussed. Simulations are presented and
discussed in sections 4.
I. IMPEDANCE-BASED OOS RELAYS
Step 1) Suppose all generators are equipped with a PMU to
measure the generator voltage and current phasors as well as
their active and reactive powers. The generator Rate of
Change of Frequency (ROCOF) also is available from PMU
output. Generator rotor angle can be easily calculated from its
internal voltage, as:
(1)
Fig. 1 Impedance-based OOS relay
and are generator per-phase terminal voltage
where,
and current.
is the generator sub-transient reactance. This
value can be either calculated locally or in the control center.
Step 2) As seen in Fig. 2, the PMUs send the measured
phasors to the control center, where the equivalent twomachine model of the network is established as shown in Fig.
3. In this model, the total network generators are replaced with
an equivalent generator , which is connected to a dummy
infinite bus via an equivalent impedance
which simulates
the transmission system effect.
and
, are
The area active and reactive powers
and
where
calculated from
and
are
is the number of generators in the system. The
calculated and transmitted to the control center by PMUs.
However, the difference between and infinite bus voltage is
is more
important, but the value of phase difference
important. Without losing the generality, we can assume that
the equal to 1P.U. the problem is calculating the and .
Fig. 1 shows a typical characteristic of an impedance-based
OOS relay [22]. Generator is disconnected when the
impedance trajectory passes the borders of characteristic 1 or
characteristic 2 at the left side. For preventing the mechanical
damages, the generator is disconnected as soon as the
impedance trajectory crosses the left border of characteristic 1.
For remote faults, where impedance trajectory passes of
characteristic 2, generally more than one crossing is allowed
before disconnecting. In this case, more time is given to the
generator in order to return to the stable condition [23-24].
The values of , , , and determine the relay borders
and may change when the network configuration is changed.
This method often require numerous and time-consuming
simulations to find a reliable settings [25].
II. THE PROPOSED APPROACH
The algorithm procedure is summarized as below:
Fig. 2 The communication between PMUs and control center
The 10th Power Systems Protection & Control Conference
PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
?=@
A
9
C:
9:
B
(10)
In (10), 1D is the equivalent rotor angle immediately
before the disturbance. The value of ?=@ defines the “Safe”
and “Risk” boundary for the generators rotor angles. For each
generator in the network, if its rotor angle is greater than ?=@
during the disturbance, it categorized in the “Risk” cluster,
otherwise it belongs to the “Safe” cluster.
Step 3) The swing equation of a single generator E is
defined as:
,3 97
7 9:
Fig. 3 Two-machine equivalent model
For this, the power-angle equations are considered as:
!"#
%
which is simplified to (
(2)
&'(
(3)
)$ * + :
)
)
(4)
&'(
(5)
C
FG
(11)
In (11), 3 is the E :H generator inertia constant in seconds, 7
is the frequency of EIJ generator at its terminal, 7 is the system
nominal frequency, 0 and are mechanical input and output
power respectively. The system equivalent inertia constant 3454
is defined from:
)
K L%
, 4
M
3454
!"#
FG
0
M 3
M
(12)
Where, M is the generator apparent power and K is its
inertia. Substituting the 3 from (11) in (12) will be resulted in:
FG
and
The value of
M N
are obtained from (4) and (5) as:
,
%
!"#- .
(6)
%
/
%
%
(7)
%
1*2*
3454 9
678 9: %
(8)
is the total mechanical input power equal to the
where 0
electrical output powers before the disturbance. 78 is the
nominal frequency and the value of 3454 is the equal inertia
time constant of the whole network which should be
calculated. All P.U parameters should be calculated the same
reference, e.g. );;;< =. If (8) is available, then,
9
9:
678
>
3454
(13)
P
,
In case of disturbance, the value of
is changed
abnormally based on the system equal inertia time constant
and power unbalanced. In this situation, the dynamic behavior
of the whole system should be considered. For this, first
consider the well-known swing equation as:
0
3454
7C
O
97
,
9:
M
0
9:
(9)
The value of Boundary of Angle Oscillation ?=@ in each
sample can be updated as:
In (13), the value of Q is the Rate of Change of Frequency
I
(ROCOF) value which is available at PMU output. Therefore,
the 3454 can be evaluated from:
3454
)
7
,
C
U
S@T@B
M
R
(14)
The value of 3(V( from (14) which is participated in (9)
should be calculated immediately after disturbance before
generator control systems such as exciters or governors will be
operated. During this condition, the value of 0 will be equal to
its previous values before disturbance. The disturbance can be
either load switching or fault depending on the system type.
Step 4) A local stability index (SI) Based on the EAC
concept is calculated for each generator in the network. As
shown in Fig. 4, three operation conditions may be possible,
which are pre-fault B , fault B and post-fault M . In B
and the rotor angle is 8 . During the fault,
condition, 0
the acceleration area = is obtained and the rotor angle is
increased up to WX . When the fault is cleared, the M operation
is started and deceleration area =%% is appeared. In real, if
=%% Y = Z =% , then the generator is stable, otherwise it is
unstable. The UEP is the intersection of 0 and M
curve. For calculating these areas and assessing the generator
stability, both the generator rotor angle and
curves for
B and M are required.
The 10th Power Systems Protection & Control Conference
PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
h
1\
i
1\
0 ]
8
!"#
i &'(^
fg!
i (E
^
In a matrix form,
) !"#
fg!
8
h
h k p q 01\] &'(^ r
jh
1\
) mm
!"#
fg!
lm
mmmnm
mm
mmmo
^
i
i
lm
mmnm
mo
0
] (Em
1\
q h r
1\
i
lno
s
(19)
W
The unknown matrix, ? can be obtained from pseudo
inverse transformation,
Fig. 4 Equal Area Criterion (EAC)
?
= =
-
= T
(20)
The number of measurement samples, d has a great effect
on the estimation procedure. The more sample result in better
estimation but increase the instability detection time. A tradeoff is required for choosing the best sample numbers. In this
paper, a value of four samples is suggested which based on the
PMU reporting rate of ,;t(, the local instability detection
time is approximately equal to 80ms.
Fig. 5 Impedance trajectory in case of fault and post-fault
As seen in Fig. 5, which shows the positive sequence
trajectory from a generator terminal, the system swing during
the fault is negligible. Therefore, the fault curve in Fig.4 can
be evaluated by a sine shape and = can be calculated from:
)
[ ,
,
=
Z
0
C
(15)
Signal (SI<1) is
received from
a generator
Generator
is in the
Risk Cluster
Fig. 6 Instability criterion in the control center
1\
0 ] !"#
8
^
(16)
The simulation studies are carried out on the New England
39-Bus test network shown in Fig. 7 [8]. The power system
frequency is 50Hz and nominal voltage of transmission system
is 345kV. All simulations are performed in time domain with a
step size of 100Hs based on the initial conditions obtained
from power flow results. The instantaneous values of terminal
voltage and phase current of all generators are sampled and
saved with the frequency of 2kHz during the simulation.
In (16), 8 is the DC offset of the curve, 01\ ] is its
maximum value and ^ is the phase. If (16) is available, then
the =% Z =%% area can be calculated continuously from:
2_1
>
=%
8
`ab
=%
1\
0 ]
=%%
!"#
^
0
9
(17)
=%
c= . The target is
to estimate the values of 8 , 01\ ] , and ^ as depicted in Fig. 4.
To this, a solution based on least square method is proposed in
this paper. Suppose, there is d measurement pairs of 1\ e
are available as:
Finally, the M value is equal to, M
1\
1\
%
Send trip
to the
generator
III. SIMULATION AND RESULTS
In (15), 0 is assumed to be constant and equal to before
the disturbance, E ) and E
are referred to 8 and X
positions, respectively.
The
M curve is influenced from inter-machine
oscillations in the network and cannot be estimated directly.
For estimation the
M curve, this paper suggests the
following equation as:
1\
Step 5) In control center, the generator is unstable and will be
tripped if the following criterion will be satisfied,
8
1\
0 ]
!"# &'(^
fg! (E ^
8
1\
0 ]
!"# % &'(^
fg! % (E ^
(18)
Fig. 7 New-England 39-Bus test network
The 10th Power Systems Protection & Control Conference
PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
A software PMU based on IEEE C.37.118 standard is coded
in MATLAB to calculate the phasor values [26]. The PMU
reporting rate is equal to one frame per cycle.
Although in a real network, fault can occur on any of the
transmission lines, here, the first three lines of higher loading
listed in Table I are selected for the purpose of stability
studies. Two alternatives are available for choosing the
duration of a short circuit fault. The first alternative is load
switching which is a minor disturbance in the system. The
next alternative is three-phase faults in which the faulted line
is disconnected after 400~800ms.
Table I. Lines with heavy loading in NE-39 test system
Case
No.
From
Bus
To
Bus
Length of
Line (km)
1
2
3
B5
B6
B21
B6
B7
B22
6
10
17
Line
Fault
Loading (%) Location (%)
84
123
104
50
50
50
A. Load disturbance
The load connected to the B3, is switched on at 0.5s.
Simulations show that all of the generators remain stable after
the disturbance. Fig. 8Error! Reference source not found.
depicts the ?=@ and generator rotor angles in this case. In Fig.
9 also the values of M is depicted for this case. As all
generators are belong to the stable cluster (their rotor angle is
lower than the ?=@) and all M values are greater than one,
then all generators are stable.
0
G2
G3
G4
G5
G6
G7
G8
G9
G10
Fig. 9 The value of SI in case of load disturbance
B. System Faults
In this case, some three-phase faults are simulated in
transmission lines listed in Table I. The results of the
simulation studies for this case are presented here for the
following scenarios:
Scenario 1: Case 1 of Table I, fault duration = 390ms
Scenario 2: Case 2 of Table I, fault duration = 480ms
Scenario 3: Case 3 of Table I, fault duration = 320ms
0.45
0.91
0.45
2
2.33
4
3.67
5.25
7.23
5.34
6
0.86
50
8
Stability Index (SI)
100
91
98
113
139
137
123
115
101
Stability Index (SI)
150
112
Fig. 8 The value of BAO and generators rotor angles in case of load disturbance
0
G2 G3 G4 G5 G6 G7 G8 G9 G10
Fig. 10 The value of SI obtained using proposed algorithm for scenario 1
Scenario 1: In this case, according to Fig. 10, the local
OOS detection says that generators G5, G7, G8, and G9 are
unstable, because their SI values are lower than one. In this
scenario, the ?=@ and generators rotor angles are shown in
Fig. 11. As seen, the rotor angle of G4, G5, G6, G7, and G9
are greater than the ?=@ and are clustered in “Risk” group.
From Fig. 6, two conditions are required to assess a generator
as unstable. Therefore, G5, G7, and G9 are unstable and others
are stable. A trip command is sending to theses generators to
The 10th Power Systems Protection & Control Conference
PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
disconnect them from the power system.
Fig. 11 The value of BAO and generators rotor angles in case of fault (Scenario 1)
is cleared. The algorithm performance was tested on the NewEngland 39-Bus test network. The major advantage of the
proposed technique is fast detection of unstable generators
before their rotor angle meet the UEP. For a complete
verification, a field test procedure on industrial generators is
required.
V. REFERENCES
7.77
[1]
3.91
5.28
8.04
2
1.45
4
1.41
6
3.15
8
0.24
Stability Index (SI)
10
8.85
Scenario 2: Fig. 12 shows the values of M for this scenario.
Since M is greater than one for all generators except % and it
belongs to the Risk cluster, the proposed technique predicts
that only % will become unstable and therefore it is
disconnected from the network. This guarantees the stability
of remaining generators in the system.
[2]
0
G2
G3
G4
G5
G6
G7
G8
G9 G10
Fig. 12 The value of SI obtained using proposed algorithm for scenario 2
[3]
[4]
[5]
[6]
[7]
1.34
2.89
6.90
5.88
9.11
5.71
0.11
5
1.50
Stability Index (SI)
10
7.51
Scenario 3: Fig. 13 shows the values of M for this scenario.
As can be seen, the proposed algorithm predicts the instability
of u because it its SI is lower than one and it is a member of
“Risk” group.
0
[8]
G2 G3 G4 G5 G6 G7 G8 G9 G10
Fig. 13 The value of SI obtained using proposed algorithm for scenario 3
IV. CONCLUSION
This paper proposes a novel technique for prediction of
OOS of generators in control center. It is based on EAC and
network boundary of angle oscillations immediately after fault
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PSPC, January 19, 20th 2016, Tehran, Iran
School of Electrical & Computer Engineering, University of Tehran
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