a contigency ranking method for voltage stability in real time operation of power systems
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8/16/2019 A Contigency Ranking Method for Voltage Stability in Real Time Operation of Power Systems
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Paper accepted for presentation at 2003 IE EE B ologna PowerT ech Con ference, June 23-.26, Bologna, Italy
A Contingency Ranking Method for Voltage
Stability in Real Time Operation of Power
Systems
M6rio A . Albuquerque and Carlos A . Castro,
Senior Member, IEEE
Abstract- A contingency ranking procedure regarding
voltage
stability
to
be used in a real time operation environment is
proposed in
t h i s
paper.
The
procedure can be added to the
existing ranking pmcednres for
MW
overloads and voltage
violations) with mild modificat ionsand s m a l l extra computational
effort.
A
performance index PI) is computed for each
contingency. The PI is defined in terns of a b rancb-based voltage
stability proximity index. Several simulations show that the most
critical contingencies can be identified correctly.
Index
Terms- Contingency ranking, Performance index,
Voltage stability,
Secnr i ty
anal ysis, Power systems operation.
I.
INTRODUCTION
he operation and control of power systems in real time
in the Control Center. First of all, the current operating
condition of the system (commonly referred to as
base case
is
obtained through state estimation from real time m easurements
and data base information. Once the base case is known, the
security analysis function is carried out. It is well known that
security analysis is a very demanding task
as
far as
computational effort is concerned.
In case violations are detected for the base case, corrective
control actions should be enforced
so
as to eliminate them.
Afterwards, the impact of the ocurrence of contingencies
should be evaluated. This process, usually called
contingency
analysis, aims to detecting post-contingency operational lim its
violations. The usual limits taken into account are
MW
overloads in transmission lines and transformers and bus over
or
under voltages. In case post-contingency violations are
detected, preventive and/or corrective control strategies are
devised to guarantee acceptable post-contingency operating
conditions
[l] .
A conventional practice is
to
perform the analysis of a
contingency list containing all simple and the most probable
multiple contingencies. This analysis corresponds to solving a
load flow for each contingency, for obtaining the post-
contingency operating state. The total number of contingency
cases to be analyzed is very large for real, interconnected
T
equire that a number of supervision functions be executed
M . A . Albuquerque
is with
Furnas Centrais
EICtricas,
Brazil. He
is
currently
an
operation engineer
(email:
C.
A. Casu0 is
with tate
University
of
Campinas, Brazil.
He s currently an
associate
professor
email:[email protected]).
0-7803-7967-5/03/ 17.00 02 00 3 IEEE
power systems. Therefore, this procedure is infeasible in a real
time operation environment.
Some utilities c an y ou t contingency analysis of a reduced list
of critical contingencies, which are defined based on the every
day experience in the system's operation. Some developed
methodologies for automatically defining this list. However,
these methodologies are complex,
lack
a clear physical
meaning and demand consideralile computational effort. The
idea is to define a general, simple, and efficient procedure to
defining those critical contingencies,
so
that they are never
missed even after unpredicted load variations or topology
changes, for example.
A very efficient and well-accepted way to improve the
computational efficiency of the contingency analysis function
consists of adding a
contingency ranking and selection
process
that preceeds the contingency evaluation itself [2]. Each
contingency of the list is first analyzed through a simpler
method. For example, performing on e full iteration of the fast
decoupled load flow is a very well-accepted method
[3].
Then,
contingencies are ranked according to a
performance index
(PI), which is a scalar that reflects the severity degree of a
contingency and it is computed from approximate operating
states. Th e top m ost critical contingencies
are
then analyzed in
detail, by following the conventional approach.
Th e main objectives of this paper are twofold:
(a)
include voltage stability considerations in the contingency
ranking process. This inclusion has already been reported
in the literature, as for example in [41. However, most
methodologies demand more than one load flow per
contingency, which is too time consuming for on-line
applications. In this paper a method is proposed
so
as to
fit as much as possible into the traditional contingency
selection process. The idea is to assure that considering
voltage stability aspects in the contingency selection
process would not result in a prohibitive increase in
computational effort.
(b) propose a PI able to detect the most critical contingencies
as far as voltage stability. Particularly, the id ea is to detect
those contingencies that result in the smallest loading
margin capacities. In this paper the PI will be defined in
terms of branch-based voltage stability proximity indices.
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11.
CONTINGENCY
RANKING
FOR VOLTAGE STABILITl
The post-contingency operational violations usually taken into
account in contingency analysis are MW overload s in
transmission lines and transformers and bus over and under
voltages. However, voltage stability had become a very
important aspect of power systems analysis. The changes in
operating conditions due to load increasing and lack of
corresponding expansion in generation and transmission led
power systems to operate closer to their vo ltage stability limits.
Voltage instabilities and collapse occurs mainly in highly
loaded systems. It is usually associated to inadequate reactive
power support.
Fig. 1 shows a typical PV curve, which is recognized as an
important tool for helping voltage stability analysis. Consider
that a power system operates with a load demand and a voltage
magnitude of respectively P o and v o . n this case, the
maximum load for stable operation is
P
and the loading
margin
is p . A
small load increase beyond
P’
leads the
system to experience voltage stability problems and even to
voltage collapse.
PO P’
P
Fig. I
PV
curve
and
voltage
stability
limit.
This scenario justifies the need of adding voltage stability
aspects into the Contingency analysis function. Particularly,
detecting the critical contingencies
as
far as their impact on the
system’s loading margin is
of
paramount importance. The
maximum loading point and consequently
the
loading margin
can he precisely computed by continuation methods
[ 5 ]
However, they demand intensive computational effort. The
challenge here is to develop a ranking criterion
(a
PI) that
reflects appropriately the post-contingency situation. It must be
simple, efficient from the computational standpoint, and
present a clear physical meaning. On the other hand, the
voltage stability problem is very complex and results from a
strongly nonlinear behavior of the system.
So
there is a clear
trade-off between precision and efficiency to be overcom e.
111.VOLTAGE
STABILITY
INDICES
Consider a load fed by a generator through a transmission line
as shown in Fig. 2.
Rg.2.
Examplepawer system
The real power delivered to the load at the receiving end bus
R
of the transmission line is
v,’ cos q ZR
P
=-
z, 1+
z,
z , y 2 z, Z , ) C O S 8 - q z ,
I )
It can be shown that the point
of
maximum power transfer
occurs for
Z,
/ z ,
=
1. Substituting
this
value in ( I ) , one
gets
The branch-based voltage stability proximity indicator
proposed in
[ 6 ]
s given by
PR
L,,
=-
p-
3)
A
similar index can be obtained for reactive power. In
this
paper, a new apparent power-based index is proposed.
The
idea is to consider both real and reactive power flows
simultaneously. The apparent power flow is given by
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and the m aximum power transfer is
IV. PROPOSED METHOD
FOR
CONTINGENCY RANKING
The method proposed in this paper consists of ranking
contingencies according to
a
performance index that reflects
the post-contingency loading margin. Contingencies with large
PI present a small post-contingency loading margin, and are
considered severe from the vo ltage stability standpoint. A very
important constraint that has been imposed is that the
computation of PI for volta,se stability should require
approximately the sam e computational effort as the equivalent
computation for branch overloads and voltage magnitude
violations. The idea
is
to perform
all
three rankings using the
same framework.
5 )
6) The performance index for a certain contingency k is
computed as follows.
Th e new voltage stability index is
1.
2.
Perform one load flow iteration.
In case one or more generation units have reached their
he indices given by (3) and (6) approach unity as the system
load appr oaches the maximum loading point. Fig. 3 show s an
example power system used to evaluate the behavior of the
voltage stability indicator.
Bus
1 0 s 6
BUS 5
Rg.3. Six bus test system
BUS 2
Rg.3. Six bus test system
S
Fig. 4 shows that the voltage stability index LsRfor branch
6 increases as the load of bus 3 increases, approaching unity ai
the maximum loading point,
q .....
O
35 45 55 65 75 85 95 105
Real power at bus 3
Rg.4.
Behaviorof
the
voltage stability proximity indicator
-
respective reactive power generation limits, perform
another load flow iteration. In this case, generation buses
with violated generation lintits are treated as load buses,
as it is usually done in conventional load flow
calculations.
Compute the voltage stability proximity indices for all
branches according to (6).
3.
4.
Compute the performance index for contingency
k
according to
where and Lc re respectively the base case and post-
contingency indices for branch i L,,,, is the largest index
after contingency k and n r comesponds to the number of
branches. PI takes into account the index variation from pre- to
post-contingency operating conditions. This variation is
multiplied by a weight (&/L: , tm) . The
PI
for a certain
branch will he
small
even if there is a large index variation,
provided that the index for
this
branch is
sinall
if compared to
the largest index.
k
The addition of step 2 was necwary since voltage stability
problems and reactive power support are tightly related.
Therefore, violations of reactive power generation limits
strongly influence the final result;. Performing step 2 results in
a computational time overhead. However, it will not he
performed for all contingencies. Actually, this step is
necessary for the most severe contingencies only. In practice,
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VIII. BIOGRAPHIES
ABLE Iv
CAFTLlrtE RATIOS
FOR
THE 904 BUS SYSIEM
Mririo deALmeida
e
Albuquerquewas born
in N i td i , Bras il , on November
11,1956.
He obtained the BS degree
f rom the
Federal University from Ria de
Janeiro
in 1980.
He is with Fumas Csntais
El6uicas. Brazil,
where he is
responsible
for
supervising the operation of
part
of the southeast
area
of the
brazilian power system. He is pursuing i s MS egree at the State University
of
Campinas (UNICAMP).
Carlos A. Castro S’1990, M1994 , ;M2000) btained his BS and MS
degrees from UNICAM P in
1982
and
1985,
respectively. H e also obtained the
PhD
degree from A rizona State University,
USA,
in
1993. He is
currently an
associateprofessorat~ICAMP.
n the particular case of the
904
bus system, there were no
advantages in using the second PI.
VI.
CONCLUSIONS
The objective of
this
paper was to propose a contingency
ranking procedure for selecting the most critical contingencies
for voltage stability. Additionally, the ranking process should
take
the smallest extra computational effort possible with
respect to the current screeening practices (for
MW
overload
and vo ltage violation analyses). In other words, only one load
flow iteration should be computed for each contingency. This
constitutes an important constraint if compared to other
selection procedures proposed in the literature. Results have
shown that a second iteration is necessary in case of reactive
power generation limit violations at generation buses.
Therefore, the conventional contingency selection procedure
was preserved with mild modifications.
The
proposed
procedure requires in average less than two load flow
iterations per contingency. A very simple, easy to und erstand,
and easy to compute voltage stability proximity index was
used.
This
index was incorporated into a performance index
for ranking the contingencies. Results showed that the
proposed method can correctly identify the critical
contingencies for voltage stability.
VII.
REFERENCES
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