IEEE Power and Energy Technology Systems Journal
Received 8 December 2015; revised 8 February 2016; accepted 22 March 2016.
Date of publication 4 May 2016; date of current version 22 June 2016.
Digital Object Identifier 10.1109/JPETS.2016.2546282
A Systematic Approach to n-1-1 Analysis
for Power System Security Assessment
PARAG MITRA1 (Student Member, IEEE), VIJAY VITTAL1 (Fellow, IEEE),
BRIAN KEEL2 (Senior Member, IEEE), AND JENI MISTRY2
1 Arizona State University, Tempe, AZ 85287 USA
2 Salt River Project, Phoenix, AZ 80062 USA
CORRESPONDING AUTHOR: V. VITTAL (vijay.vittal@asu.edu)
Cascading outages can have a catastrophic impact on power systems. One such recent incident
was the September 8, 2011 blackout that affected San Diego and large parts of the southwestern United States.
To prepare for such events, the NERC transmission planning standards require utilities to plan for n-1-1
outages. However, such analyses can be computationally burdensome for any realistic power system owing
to the staggering number of possible n-1-1 contingencies. This paper proposes a systematic approach to
analyze n-1-1 contingencies in a computationally tractable manner for power system security assessment.
The proposed approach addresses both static and dynamic security assessment. The proposed methods have
been tested on the Western Electricity Coordinating Council (WECC) system. The test results show that
a substantial reduction in computational effort is achieved by implementing these methods for an n-1-1
contingency analysis. In addition, the reliability of the proposed methods is evaluated by an exhaustive
contingency analysis.
ABSTRACT
Contingency classification, contingency screening, contingency ranking, dynamic security
assessment, multiple outages, n-1-1 contingency, power system stability, static security assessment.
INDEX TERMS
I. INTRODUCTION
C
ASCADING outages can have a catastrophic impact
on power system operation and planning. Accordingly,
the North American Electric Reliability Corporation (NERC)
transmission planning (TPL) standards requires utilities to
plan for n-1-1 outages [1]. To comply with the NERC TPL
standards, utilities must ensure that the system is able to
maintain stability and operate within acceptable limits following such outages. An n-k contingency analysis involves
studying the impact of simultaneous outage of k components on the system voltages and line flows [2], [3]. For an
n-1-1 contingency analysis, the two contingencies are applied
sequentially rather than simultaneously. System adjustments
if needed are made after the first outage, prior to applying the
second outage [2]. Due to the possible system adjustments
that can be made, the order in which the n-1-1 contingencies occur can be consequential. System adjustments can
include [2]:
1. change in VAr output of generators;
2. adjustments in the settings of tap changer (ULTC),
switchable voltage devices (SVD) and phase adjusting
transformers (PAR); and
3. corrective
measures
like
remedial
action
schemes (RAS), transmission switching and special
protection schemes (SPS).
VOLUME 3, NO. 2, JUNE 2016
Ensuring the safe and reliable operation of a power system requires assessing both the static and the dynamic
security for every n-1-1 contingency [4], [5]. Although
such assessments improve the overall reliability of a
system, it comes with an additional burden of evaluating a vast number of outages. The number of
n-1-1 contingencies can be overwhelming, even for
a small power system. For a system with n elements, the number of possible n-1-1 contingencies is
given by
number of n-1-1 contingencies = n(n − 1).
(1)
Due to the large number of possible n-1-1 outages, a systematic approach to screen n-1-1 contingencies is needed.
It is important to identify the contingencies that are critical from a system security viewpoint in a computationally
efficient manner. The critical contingencies can be consequential, and need to be identified and analyzed prior to the
non-critical cases. To achieve the stated objective this paper
proposes:
1. a method to screen and rank n-1-1 contingencies for
static security assessment (SSA), and
2. a method to screen and classify n-1-1 contingencies for
dynamic security assessment (DSA).
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IEEE Power and Energy Technology Systems Journal
The goal of the paper is to develop screening methods,
which are convenient to implement in practice, at the same
time being highly accurate in detecting critical contingencies.
The proposed methods are intended to be used during the
operations planning phase. In the following section, some of
the existing contingency analysis methods are discussed and
the need for a new approach is highlighted.
The proposed techniques are used to perform contingency
analysis for a utility in the WECC system. The following sections present detailed descriptions of the proposed methods
and the results of the study.
III. CONTINGENCY SCREENING AND RANKING
FOR SSA
power flow solutions capture the effect of an outage on
system voltages and line flows better than dc power flows.
This is particularly significant while analyzing n-1-1 outages.
Therefore, an ac power flow based method is proposed here
to develop a reliable n-1-1 contingency screening and ranking method. Reference [22] describes a method for multiple
element contingency screening using line outage distribution
factors (LODF). The method proposed here uses a similar
idea. However, instead of LODFs, it relies on the corresponding ac quantities for the first n-1 outages to screen critical
n-1-1 outages.
AC
II. REVIEW OF CONTINGENCY SCREENING METHODS
For n-1 SSA, performance indices (PIs) based methods have
been widely adopted [6]–[8]. These methods use a first
order estimate of the post-contingency PI value, to measure the severity of a contingency. Contingency screening
methods, which use partial or approximate network solutions to identify voltage and flow violations have also been
proposed [9]–[11]. However, these methods can grossly
underestimate the severity of a contingency [12]. This is
due to the approximations involved and the highly nonlinear impact of the contingencies on the system voltages
and line flows [12]. In recent times, with the advancement
in computational capability, performing a complete ac power
flow for large systems has become computationally feasible.
Analyzing all contingencies, using ac power flow solutions
is far more reliable. The availability of parallel computing
infrastructures further eases this process. Hence, many commercially available power system analysis packages use ac
power flow solutions as a tool to perform n-1 contingency
analysis [13].
For n-1 DSA, it is important to identify contingencies
that may jeopardize the stability of the system before conducting a complete time-domain simulation (TDS) analysis.
Various contingency screening methods for DSA have been
proposed in literature. References [14]–[18] describe contingency screening methods based on the transient energy
function. Filtering of contingencies using sparse transient
energy function is described in [16] and [17]. Extensions
of static security analysis techniques coupled with applications of artificial neural networks have also been explored
for contingency screening and ranking [19]. A coherencybased index for contingency screening is described in [20].
Composite indices based on coherency, transient energy conversion and dot products have been proposed for contingency
screening [21]. Most of these screening methods compute the
required indices by performing short duration TDS only for
a few cycles after the disturbance.
For n-1-1 SSA, performing an ac power flow for all
possible n-1-1 contingencies is computationally prohibitive.
The discussed n-1 contingency screening methods are inadequate due to their dependence on first order estimates
and localized nature of analysis. Similarly, for n-1-1 DSA,
screening n-1-1 contingencies using the traditional screening
methods can also be impractical. This is due to the sheer
number of short duration TDS that need to be performed.
Therefore, there is a need to develop methods, which can
perform n-1-1 contingency analysis in a computationally
tractable manner.
72
A. CONTINGENCY SCREENING FOR n-1-1 ANALYSIS
In an interconnected power system, the outage of a
single component only affects a few branch flows and generator outputs. The majority of branch flows and generator
outputs throughout the system remain practically unchanged.
Substantial changes in branch flows or generator outputs
following an outage indicate that the affected branches and/or
generators compensate for the disconnected component.
Therefore, to account for critical n-1-1 contingencies, candidate branches or generators for the second outage can
be screened by analyzing their pre-contingent and postcontingent state (flows for branches and outputs for generators) following the first outage. To generate a list of
n-1-1 branch-branch contingencies, the following steps are as
follows.
1. Perform a full ac power-flow for all n-1 contingencies,
followed by the system adjustments if any. Store all the
branch MVA flows.
2. For each branch outage, compute the percentages of
the MVA flow in the outaged branch that appears in
all other branches in the system. This percentage is
the ac equivalent of the LODF and is referred to as
ACLODF in the rest of this paper. As an example, the
ACLODF for a hypothetical line A for outage of line B
is computed as follows:
MVAn−1,AB − MVAbase,A
100 (2)
ACLODFAB =
MVAbase,B
where
ACLODFAB is the percentage of the MVA flow on
line B that shows up on line A.
MVAn−1,AB is the MVA flow on line A with line B
disconnected.
MVAbase,A is the MVA flow on line A in the base case
(all lines in service).
MVAbase,B is the MVA flow on line B in the base case
(all lines in service).
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Mitra et al.: Systematic Approach to n-1-1 Analysis for Power System Security Assessment
3. All branches that have an ACLODF more than a set
threshold for an n-1 contingency are screened as candidate branches for the second outage following that
particular n-1 contingency.
4. For every candidate branch screened in step 3, the
MVA flow on that branch due to a combination of any
two n-1 outage is estimated. The change in flow is
linearly approximated by using the already computed
ACLODFs.
5. The n-1-1 contingency list is updated to include all
pairs of the n-1 outage and the corresponding screened
second outages in step 3. Steps 2 to 4 are performed for
all n-1 contingencies.
6. The contingency list is updated to include any combination of two n-1 contingencies, which may cause
the estimated flow on a screened branch computed in
step 5, to be above a set percentage of the emergency
rating of the branch.
7. Finally, all duplicate n-1-1 contingencies are removed
from the list and the final list of n-1-1 contingency is
formed.
Steps 1 to 7 described here are used to generate the
n-1-1 contingency list for branch-branch contingencies.
An identical process is used to generate the n-1-1 contingency list for generator-branch and generator-generator contingencies. Instead of the ACLODF, the change in the branch
MVA flows can be used as a criterion to screen generatorbranch contingencies. Similarly, the change in the reactive
power output of generators can be used as a criterion to screen
generator-generator contingencies.
Step 3 to step 6 is the core of the proposed method and
is elaborated here. The ACLODF captures the MVA flow
changes in the system in comparison to the MVA flow on
the disconnected line. This helps to identify the branches that
compensate for the disconnected branch, and hence important
for system operation after the first outage. Lines with higher
ACLODF have a higher influence on the connectivity of the
transmission system and indicate the lower impedance paths
to the loads. For branch-branch outages, if the outage of a
single branch causes the ACLODF for another branch to be
significantly high, it indicates that this second branch is an
important supply route (lower impedance path) to the same
load area. An outage of a branch with a high ACLODF can
lead to considerable weakening of the transmission path to
the load area. The alternate transmission paths to the load,
which have a lower ACLODF, typically have substantially
higher impedance. This can lead to large voltage drops and
possible reactive power problems at the load buses. These
lines may also be overloaded due to the excess power being
routed through them. Close to large generation sources, disconnecting a branch with a high ACLODF can cause significant reduction in the short circuit ratio, leading to voltage
regulation problems. Hence, the outage of such a branch may
be critical following the corresponding n-1 branch outage.
Furthermore, if two separate n-1 branch outages cause the
estimated MVA flow on a branch or branches to increase
VOLUME 3, NO. 2, JUNE 2016
beyond its emergency rating, the sequential combination of
the two n-1 outages can also be critical. Steps 3 to 6 of
the algorithm screen n-1-1 branch-branch outages based on
these ideas. Step 3 was found to be particularly significant in
identifying n-1-1 contingencies that resulted in overloading
of transformers and lines, which were operating near their
emergency ratings in the base case. Similar justifications
can be provided for generator-branch and generator-generator
contingency screening process. Although not all screened
contingencies may be harmful, the screening process substantially reduces the total number of n-1-1 contingencies
that needs to be evaluated in details (by ac power flow).
The remaining non-critical contingencies, if needed, can be
evaluated by faster approximate methods like a dc power
flow.
B. RANKING OF SCREENED n-1-1 CONTINGENCIES
After the screened n-1-1 contingency list is prepared, the
screened contingencies are analyzed by performing ac power
flows. Based on the power flow results, the contingencies can
be ranked according to their impact on the system. Ranking
contingencies based on their severity enables a planner or
an operator to identify the most critical elements in a power
system. Additional measures can then be taken for hardening
such elements to prevent such outages. Among the various
indices proposed in the literature [6]–[8], the voltage-based
index PIV and the flow-based index PIMW as defined [6] are
used in this paper. The indices are as follows:
!2α
sp
nb
X
wbi |Vi | − Vi
PIV =
2α
1Vilim
i=1
!2α
nl
X
wli
Si
PIMW =
.
(3)
2α Silim
i=1
The weighting factors wbi and wli can be chosen by
an operator or a planner based on experience, to assign
higher weights to critical buses or lines in the system. The
parameter α is set to 1 as given in [6].
C. THE n-1-1 CONTINGENCY SCREENING AND THE
RANKING PROCESS
The screening and ranking process described in the preceding subsections are combined to perform the n-1-1 analysis.
Fig. 1 provides a flow chart of the complete n-1-1 contingency
analysis method.
D. n-1-1 CONTINGENCY ANALYSIS RESULTS FOR STATIC
SECURITY ASSESSMENT
For testing the n-1-1 contingency screening and ranking
method, a power flow case representing the WECC system
was used. Contingency screening and ranking was performed
for a selected utility’s service area within the WECC system. The power flow case used is an actual representation
of a large interconnected power system with 20605 buses,
17056 lines, 7836 transformers and 2737 generators.
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IEEE Power and Energy Technology Systems Journal
TABLE 2. Criteria for screening n-1-1 contingencies.
FIGURE 1. Flowchart for the contingency screening and ranking
process.
For n-1 and n-1-1 contingency analysis, elements at all
voltage levels above 100 kV were considered. Including
all transmission lines, transformers and generators within
the selected utility’s service area, the n-1 contingency list
comprises of 403 outage events. For the n-1-1 analysis,
all remedial actions after the n-1 contingencies were limited
to adjustments in voltage control devices (SVD and ULTC),
power control devices (phase adjusting transformers) and VAr
output of generators. The remedial actions were obtained
from the utility supplied data. It was observed that for such
remedial actions, which did not change the system topology
substantially, the order in which the two contingencies were
processed did not have any significant effect on the results.
Therefore, the total number of n-1-1 contingencies is 81003,
ignoring the duplicate contingencies. In this sense, the proposed method could be extended to screen n-2 contingencies
as well. However, for n-2 contingencies the ACLODFs are
computed without performing any system adjustments.
Table 1 lists the voltage and flow thresholds used for n-1
and n-1-1 contingency analysis. Any contingency violating
TABLE 1. Voltage and flow thresholds.
these thresholds is considered as critical. GE-PSLF [14] was
used to perform the power flow calculations. From the power
flow analysis of the n-1 contingencies, 6 contingencies were
found to violate the thresholds listed in Table 1. Table 2 lists
the criteria used for screening the n-1-1 contingencies.
Table 3 presents the results of the screening process. From
Table 3, it is observed that the screening process substantially reduces the number of cases that need to be analyzed
in detail. It is worthwhile to mention that even with the
moderate screening thresholds (see Table 2) used in this
study, a significant reduction in the number of cases to be
74
TABLE 3. Results of the screening process.
examined in detail, was achieved. As a recommendation,
moderate screening thresholds should be chosen to begin with
and these thresholds should be tightened/tuned over time to
achieve better efficiency. ac power flows were performed
for the 5549 screened cases to identify the contingencies
that resulted in violations. The power flow study indicated
that 3115 contingencies resulted in violations of voltage or
flow or both thresholds. To check whether the contingency
screening process is reliable, an exhaustive ac power flow
based study was conducted for the 81003 contingencies.
The exhaustive study identified the same 3115 contingencies
reported in Table 3 as critical. It should be noted that the
screening method captures a considerable number of noncritical contingences due to the moderate screening thresholds used in this work. The number of screened cases could
be further reduced by tightening the screening thresholds
mentioned in Table 2. Although, using tight thresholds could
result in possible omission of some critical contingencies.
However, even moderate screening thresholds reduce the total
number of contingencies to be analyzed to a manageable
level. Table 3 also lists the number contingencies that lead
to only voltage or only flow violations. It can be seen that for
38 contingencies no flow violations were observed although
these outages led to severe voltage violations in parts of the
system. The voltage violations were due to large voltage
drops on lines, which served as the alternate transmission
paths to the load area. However, the flows on these lines were
well below their emergency ratings. This further illustrates
VOLUME 3, NO. 2, JUNE 2016
Mitra et al.: Systematic Approach to n-1-1 Analysis for Power System Security Assessment
that contingency screening based on ACLODF is able to
identify cases where voltage violations may be an issue rather
than flow violations. dc power flow based screening methods
typically focus on detecting possible flow violations in the
system.
Once the n-1-1 contingencies are screened and ac power
flows are conducted for the screened cases, the bus voltages
and the line flows are recorded. The contingencies are then
ranked based on the indices given by (3) and (4) in [6].
Table 4 lists the choice of weights used for ranking the
contingencies. As mentioned earlier a different weighting
As an example, consider the outage of lines 1159-1232
and 1217-1133. Fig. 2 shows a schematic one-line diagram
of the area of interest. The disconnected branches 1159-1232
TABLE 4. Weights used for contingency ranking process.
FIGURE 2. Schematic one-line diagram of the load area supplied
by lines 1159-1232 and 1217-1133.
scheme can be used based on the operator/planner’s experience. Table 5 lists the first three contingencies based on
voltage based ranking and flow based ranking respectively.
TABLE 5. Voltage and flow based ranking of n-1-1 contingencies.
and 1217-1133 are marked with cross. When these two lines
are disconnected, the loads in the region are supplied through
1143-1218-1121/1122 (marked with dotted line), which has a
considerably higher impedance. The large voltage drop on the
higher impedance path and lack of reactive power resources
in the region leads to depressed voltages at the load buses.
Fig. 3 shows the voltage at selected load buses in the region
when the branches are disconnected. The power flow fails
Ranking the contingencies enables an operator or a planner
to identify the most severe outages in the system. Based on
the information whether voltage violations or flow limit violation are of concern for these contingencies, corresponding
measures can be taken to mitigate such violations.
FIGURE 3. Voltages at selected load buses in the area supplied
E. ANALYSIS OF n-1-1 CONTINGENCIES WHERE
POWER FLOW FAILS TO SOLVE
by lines 1159-1232 and 1217-1133.
Since n-1-1 contingencies result in loss of two system components, such contingencies may lead to cases where the postcontingent power flow fails to solve. For the WECC case used
here, the power flow fails to solve for 17 n-1-1 contingency
cases. These contingencies can be examined by performing a dynamic study simulating the opening of the second
line. Such a time domain simulation can be performed as
follows.
1. A power-flow is solved for the first outage. The powerflow solution is taken as the initial condition for the
time domain simulation.
2. A time domain simulation is run and the second branch
is opened at t=1 sec.
to solve for this case due of the abnormally low voltages in
this area, resulting from the outage. Contingencies, that cause
divergence in power flow solutions, lead to very high or very
low voltages in parts of the system. Hence, these cases are
critical from a static security perspective.
VOLUME 3, NO. 2, JUNE 2016
IV. n-1-1 CONTINGENCY SCREENING AND
CLASSIFICATION FOR DSA
The contingency events referred to in this section are
three-phase faults on lines followed by removal of the faulted
lines from service by appropriate protection devices. Faults
are large disturbances on the system and have significant
impact on transient stability. DSA for n-1-1 contingencies
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IEEE Power and Energy Technology Systems Journal
is done in two steps. The first step is to simulate the initial
contingency and check whether it is stable. If the system is
stable and reaches an acceptable equilibrium after all automatic controls have acted, the second contingency is simulated. If the second contingency is stable and an acceptable
steady state is reached, the n-1-1 contingency is labeled as
secure. Otherwise, the n-1-1 contingency is labeled as insecure. As discussed earlier, one of the main challenges for
n-1-1 contingency screening and classification is the large
number of cases that need to be evaluated. As such, performing simplified fast calculations can become computationally
prohibitive for realistic power systems. To alleviate the computational burden associated with n-1-1 contingency analysis,
a two-stage approach is proposed here. In stage I, a subset
of n-1-1 contingencies is screened for further classification.
The screening process is based on the power flow results
of the n-1 analysis. In stage II, the screened contingencies
are classified based on kinetic energy gained due to a fault
and the change in Thévenin’s impedance (Zth ) at the point
of interconnection (POI) of the affected generators in the
post-fault network. Once the contingencies are screened and
classified accordingly, detailed TDSs are conducted to check
whether the contingencies may lead to dynamic security
issues.
A. STAGE I: SCREENING OF n-1-1 CONTINGENCIES
The screening process is based on the power flow results
of n-1 contingency analysis. The power flow solution after
a contingency describes the post-disturbance equilibrium of
the system, once all fast control actions have taken place.
The impact of the second contingency on the system is
dependent on this equilibrium point and hence the n-1 power
flow solution is the starting point for the n-1-1 screening
process. It should be noted that only stable n-1 contingencies
are considered as the contingencies for the n-1-1 screening.
This is a valid consideration as it is meaningless to analyze a
successive contingency if the initial contingency is not stable.
The screening process is similar to the screening process proposed for SSA in section III A. However, instead of ACLODF
a new quantity MWLODF is used. The MWLODF is the
percentage of MW flow in the outaged branch that shows
up in all other branches in the system. As an example, the
MWLODF in a hypothetical line A for outage of line B is
computed as follows:
MWn−1,AB − MWbase,A
100.
(4)
MWLODFAB =
MWbase,B
To generate the list of screened n-1-1 contingencies
involving branch-branch outages, steps 1 to 7 excluding
steps 3 and 6 as given in section III A are performed.
Steps 3 and 6 are excluded in this screening process as
overloading of lines is a steady state issue and does not
impact dynamic security assessment. Since system stability
is of concern, change in the MW flow is a suitable screening
parameter as it influences the rotor angles of the generators
in a system. A higher value of MWLODF indicates that only
76
a few branches compensate for the lost flow on the disconnected branch. This implies that the branch may be closer
to a generation source or a load center where the network
is vulnerable. A fault on a line with a high MWLODF can
be critical as the disturbance may be close to a generator or
group of generators. Subsequent disconnection of the line to
clear the fault can result in a weak post-disturbance network
due to loss of a main transmission path. A lower value of the
MWLODF indicates that only a small fraction of the lost flow
on the disconnected line shows up in other lines. Faults at
such locations followed by removal of the line do not weaken
the transmission system significantly. It is worthwhile to
mention that a higher value of the MWLODF does imply that
a fault on the corresponding line will be more severe than
on others. However, it is a good measure to identify critical
lines where faults could be possibly severe. The screening
process is conservative in the sense that not all screened cases
are unstable. It should be noted that stability assessment is
not an issue here. The screening and classification process
aims to prioritize the analysis of cases, which are critical from
a stability assessment viewpoint. The n-1-1 contingencies
eliminated by the screening process are categorized as least
critical (LCR) for stability assessment.
B. STAGE II: CLASSIFICATION OF SCREENED
n-1-1 CONTINGENCIES
Stage II deals with classifying the screened n-1-1 contingencies obtained from stage I. The screened contingencies are
classified based on two factors:
1. total kinetic energy gained by the machines due to the
applied fault, and
2. the maximum change in Zth seen at the POI of
a generator or a group of generators affected by
the fault due to removal of the faulted line from
service
It is assumed that a fault applied on the system will be
cleared in 5 cycles, which is a standard clearing time for
modern circuit breakers rated for 100kV and above [23].
This clearing time can be suitably adjusted for specific
cases without loss of generality. Based on the two measurements the screened contingencies are categorized as critical (CR), possibly critical (PCR) and non-critical (NCR).
The following steps are followed to classify the screened
contingencies.
1. Solve the power flow by removing the first line considered in the n-1 contingency.
2. Perform a time domain simulation and apply a 5-cycle
three-phase fault on the screened second line considered in the n-1-1 case. The time domain simulation is
run only until the fault is cleared.
3. Record the angular speed of generators in the area of
study at the end of the fault and compute the total
kinetic energy gained by the system with respect to
the center of inertia (COI) [25] of the area of interest. The total kinetic energy gained during the fault is
VOLUME 3, NO. 2, JUNE 2016
Mitra et al.: Systematic Approach to n-1-1 Analysis for Power System Security Assessment
given by

ωcoi
 

X
X
Mi ω i  
Mi 
=
allgens
1ωi = ωi − ωcoi
X 1
KE =
Ji (1ωi )2
2
(5)
allgens
(6)
(7)
allgens
where
ωcoi is the angular velocity of the center of inertia
ωi is the angular velocity of the ith generator
Mi is the inertia constant of the ith generator
KE is the kinetic energy gained by the system
Ji is the moment of inertia of the ith generator
4. Remove the faulted line from service and compute the
change in Zth as seen at the POIs of all generators/group
of generators in the region of interest.
5. Record the maximum change in Zth and the corresponding bus number of the POI where it occurs. The
maximum change in Zth will be referred to as 1Zthmax .
The stability of a power system during a fault depends on
the kinetic energy gained by the system due to the fault and
the robustness of the post-disturbance network to absorb [24].
This can be understood by examining the equal area criterion
for a one-machine infinite bus system. The idea has been
extended to multi-machine systems as well [25]. During a
fault, the ability of the network to export electrical power is
severely restricted causing the machine to accelerate. Once
the fault is cleared by opening the faulted line, the machine is
able to export electrical power and it decelerates. The stability
of the machine is dependent on its ability to decelerate in the
post-disturbance condition and reach a steady state.
The kinetic energy gained by the system during a fault
is computed by performing a short time domain simulation
with a three-phase fault applied on the concerned branch.
To estimate the ability of the system to decelerate, the change
in Zth seen into the system at the POI of the generator due to
opening of the faulted line is computed. The buses, which
are the POI of generating stations, are typically known to
planners beforehand. The change in Zth can be computed by
using sparsity oriented compensation methods [26]. A review
of the swing equation [24] indicates that a large change in
Zth results in a substantial reduction in the peak of the postfault swing curve as compared to the pre-faulted condition.
A reduction in the peak of the post-fault swing curve limits
the ability of the generator to decelerate, thereby making it
prone to instability. Hence, these two factors are chosen to
categorize contingencies based on their impact on stability.
Based on the computed quantities the contingencies are
categorized into three distinct categories. Brief descriptions
of the three different categories are as follows
I. Critical (CR): A Contingency is categorized as CR if
both the kinetic energy and the 1Zthmax due to the
contingency are high. A critical contingency implies
that the fault is electrically close to a generator and
VOLUME 3, NO. 2, JUNE 2016
opening of the faulted line weakens the transmission
system. Such cases are likely to have stability issues
and warrant detailed time domain analysis.
II. Possibly Critical (PCR): A Contingency that results in
large kinetic energy and small 1Zthmax or small kinetic
energy and large 1Zthmax is categorized as PCR.
A large kinetic energy and small 1Zthmax implies that
although the fault is close to generation units, the post
disturbance network is strong. On the other hand, a
large 1Zthmax and small kinetic energy indicates that
although the post-fault network is weak, the fault is
electrically distant from large generation units. Contingencies categorized as PCR may not be unstable under
a given operating condition, but can become critical as
the operating conditions change.
III. Non Critical (NCR): Contingencies that result in both
small kinetic energy and small 1Zthmax are categorized
as NCR. No detailed time domain analysis is required
for these contingencies.
Once the contingencies are categorized as CR, PCR and
NCR, they can be displayed on a kinetic energy vs. 1Zthmax
plot for ease of visualization. The visualization approach is
helpful as it enables a planner/operator to estimate the relative
severity of the contingencies. Fig. 4 shows the three regions
on the kinetic energy vs. 1Zthmax plot. It should be noted
FIGURE 4. CR, PCR, and NCR, regions on the kinetic energy
versus 1Zthmax .
that the boundaries of the three different regions are system
dependent and hence, not defined explicitly. These boundaries can be defined ad hoc for a particular system and
subsequently tuned over time to increase the efficiency of the
classification process. The lack of an explicit definition of
the boundaries does not negate the classification process, as
this process does not judge whether a contingency is unstable.
Rather, the classification process categorizes the contingencies based on their relative severity. A comprehensive stability assessment is performed via TDS, which is a more reliable
method. The cases marked as CR and PCR should be assessed
by detailed TDS. Cases marked as NCR and LCR can be
assessed by early termination TDS [27], which is faster. The
contingencies should be assessed in the order CR and PCR
followed by NCR and LCR.
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IEEE Power and Energy Technology Systems Journal
C. n-1-1 CONTINGENCY ANALYSIS RESULTS FOR
DYNAMIC SECURITY ASSESSMENT
MATLAB and GE PSLF [13] were used to perform the
n-1-1 contingency classification. As mentioned in
Section III-B, a 5-cycle three-phase fault was considered as
the disturbance on the system. An n-1 contingency analysis
was performed for DSA before proceeding to the
n-1-1 analysis. 13 n-1 contingencies lead to islanding of
generation units and all other contingencies were stable. The
13 contingencies were excluded as the first contingency for
the n-1-1 analysis.
The screening process described in stage I of the proposed
method was used to screen candidate lines for simulating
the second outage. The MWLODF threshold for screening
candidate lines for second outage was set to 40%. Lowering
the MWLODF threshold did not result in screening of any
additional unstable contingency. Hence, the set threshold was
considered sufficient for the screening process. After the
second set of candidate lines are screened, a list of n-1-1
contingencies is created. The screened n-1-1 contingencies
are then classified appropriately by the classification process
described in stage II of the proposed method. Table 6 lists the
number of all possible n-1-1 contingencies and the number of
screened contingencies. The screening process substantially
TABLE 6. Metrics for the screening process in stage I.
reduces the number of cases to be classified. As indicated
earlier the screening process of stage I is a conservative
in nature. Not all screened contingencies are likely to have
dynamic issues. However, the screening process eliminates
all the n-1-1 contingencies that are least critical from a transient stability perspective.
Fig. 5 shows the location of the screened n-1-1 contingencies on the kinetic energy vs. 1Zthmax plot. The three different
TABLE 7. Number of contingencies in different categories.
four different categories. TDS were performed for the 204
screened n-1-1 contingencies. All the contingencies in the
categories PCR and NCR were found to be stable. The 3 contingencies categorized as CR were found to cause instability.
Table 8 presents the results of TDS for 8 selected contingencies in categories CR and PCR. The 8 selected contingencies
TABLE 8. Stability status of selected contingencies after
performing TDS.
(otg1-otg8) are marked in Fig. 5. The 8 contingencies were
chosen the cover the CR cases and the PCR cases, which
resulted in high kinetic energy or high 1Zthmax . The contingencies in the region PCR are stable at this operating condition. This is because in these cases either the fault is far from
large generation or the post-disturbance network is strong
enough to provide adequate deceleration to the accelerating
generators.
It is worthwhile to examine the contingencies categorized
as PCR in further detail. As mentioned earlier, these contingencies could become critical due change in operating
conditions. An example to illustrate such a case is as follows:
Case: otg8 - outage of the lines 1518–1519 and 1211-1212
Outage of line 1518–1519 is considered as the n-1 outage.
A 5-cycle three-phase fault on line 1211-1212 and the ensuing outage is considered as the n-1-1 event. Fig. 6 shows
a schematic one-line diagram of the area of interest. From
Fig. 5, it can be seen that the contingency otg8 results in
FIGURE 5. n-1-1 contingencies on a kinetic energy versus Zthmax
plot.
categories of contingencies are marked distinctly on the
plot. Table 7 lists the number of n-1-1 contingencies in the
78
FIGURE 6. Schematic one-line diagram of region close to
bus 1212.
VOLUME 3, NO. 2, JUNE 2016
Mitra et al.: Systematic Approach to n-1-1 Analysis for Power System Security Assessment
a large 1Zthmax , though the kinetic energy gained is comparatively less. 1Zthmax for this contingency was recorded
at bus 1212, which is the POI of 12 generators CTG1 to
CTG 12, each rated at 44 MW. In the present scenario, only
4 generators are switched on producing 140 MW. Since the
machines are smaller and have low inertia, the total kinetic
energy gained by the machines is not significantly high.
Opening the considered lines (marked crosses in Fig. 6) due to
the sequential outages, results in a large 1Zthmax . This is due
to the high impedance of the path 1212-1518-1160 (marked
with dotted line), through which the generation is connected
to the rest of the system in the post-fault condition. As
listed in Table 8, the contingency is stable for this operating
scenario.
The total generation capability at bus 1212 is 528 MW
(12 units, 44 MW each). As such, the generation level may
be increased under heavy load periods or due to the loss of
generation at some other location in the system. Fig. 7 shows
the trace of the otg8 on the kinetic energy vs. 1Zthmax plot as
the generation at 1212 is increased.
FIGURE 7. Trace of otg8 on the kinetic energy versus Zthmax plot.
Fig. 7 shows that as the generation increases, the contingency leaves the PCR region and moves towards the
CR region. This is because the added generators contribute to
the kinetic energy. At a total output of 510 MW at bus 1212,
with 12 units online, otg8 results in both high kinetic energy
and 1Zthmax. At this operating condition, otg8 is in the CR
region and needs to be analyzed by detailed TDS. Table 9 list
the results of the TDS performed for otg8 for five different
generation levels at 1212.
From Table 9 it can be seen that otg8 leads to instability
when the generation at 1212 is increased.
TABLE 9. Results of TDS for changing generation levels at
bus 1212.
VOLUME 3, NO. 2, JUNE 2016
V. PROCESSING TIME
The processing time for the proposed n-1-1 analysis for both
SSA and DSA is presented in Table 10. The methods were
TABLE 10. Processing time of different subroutines for the
proposed methods.
implemented on an Intel Core i7-3770 @ 3.40 GHz processor
with a 16 GB RAM.
The following comments are in order.
1. Step 1 needs to be performed first before proceeding
to the other steps. Step 1 is parallelizable if parallel
computing capability is available.
2. Step 2 is performed to generate the contingency list for
both SSA and DSA.
3. Step 3 and Step 4 are independent of each other and can
be done separately in any order.
4. Step 3 is parallelizable if parallel computing capability
is available.
5. Step 4a and Step 4b are independent of each other and
can be done separately in any order. Both step 4a and 4b
are parallelizable.
The timings presented in Table 10 are considering sequential processing due to the unavailability of parallel computing.
However, using the newer versions of PSLF [28], which have
high performance computing (HPC) module [28] a substantial reduction in the processing time is possible. It should
be noted that the methods discussed here are proposed for
n-1-1 analysis in the operations planning phase. Hence, the
timings achieved in the presented report were sufficient for
the intended purpose.
VI. CONCLUSION
This paper presents a systematic approach to n-1-1 contingency analysis for a realistic large power system.
An n-1-1 contingency screening and ranking method was
proposed for SSA and an n-1-1 contingency screening and
classification method was proposed for DSA. The main merit
of these methods lies in the ease of implementation and the
ability to screen critical contingencies reliably with reduced
computational effort. The screening methods limit the number of contingencies for which detailed analysis needs to be
performed. Ranking of the screened contingencies allows the
operator/planner to identify the most severe contingencies
and devise corresponding corrective measures from a steady
state perspective. Classification of contingencies from a stability viewpoint enables an operator to identify contingencies,
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IEEE Power and Energy Technology Systems Journal
which are unstable or may become unstable under changing
grid conditions. The accuracy of the proposed methods was
verified by a comparing the results with an exhaustive n-1-1
power flow analysis and n-1-1 TDS results.
The methods presented in this paper provide an approach
to identify the potentially harmful contingencies quickly and
reliably from the large number of possible contingencies.
In future work, the methods need to be implemented using
parallel computing infrastructure to identify the potential savings in processing time. Furthermore, the proposed methods
need to be tested on more actual power system cases, which
will evaluate the efficiency of the methods.
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PARAG MITRA (S’13) is currently working toward the Ph.D. degree in
electrical engineering at Arizona State University, Tempe, AZ, USA.
VIJAY VITTAL (S’78–M’79–SM’87–F’97) received the Ph.D. degree from
Iowa State University, Ames, IA, USA, in 1982.
He is currently the Director of the Power Systems Engineering Research
Center with Arizona State University, Tempe, AZ, USA.
BRIAN KEEL (M’07–SM’08) received the B.Sc. and M.Sc. degrees in
electrical engineering from the University of Illinois, Champaign, IL, USA,
in 1988 and 1989, respectively.
He is currently the Manager of Transmission System Planning with the
Salt River Project, Phoenix, AZ, USA.
JENI MISTRY received the B.Sc. degree from Arizona State University,
Tempe, AZ, USA.
She is currently a Senior Engineer of Transmission Planning with the Salt
River Project, Phoenix, AZ, USA.
VOLUME 3, NO. 2, JUNE 2016