Cascading Failure Mitigation via Transmission Switching
IIEEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 1
Reducing the Risk of Cascading Failures viaTransmission Switching
Sayed Abdullah Sadat,
Graduate Student Member, IEEE, and Mostafa Sahraei-Ardakani,
Member, IEEE,
Abstract —After decades of research, cascading blackouts re-main one of the unresolved challenges in the bulk power systems.A new perspective for measuring the susceptibility of the systemto cascading failures is clearly needed. The newly developedconcept of system stress metrics may be able to provide newinsight into this problem. The method employs power engineeringand graph theory to analyze the network structure and electricalproperties of the system, with metrics that measure stress as thesusceptibility to cascading failures. In this paper, we investigatethe effectiveness of transmission switching in reducing the riskof cascading failures, measured in system stress metrics. A casestudy, analyzing different metrics on IEEE 118-bus test system,is presented. The results show that transmission switching can beused as a preventive as well as corrective mechanism to reducethe system’s susceptibility to cascading failures. Contrary to theconventional operation wisdom that switching lines out of servicejeopardizes reliability, our results suggest the opposite; systemoperators can use transmission switching, when the system isunder stress, as a tool to reduce the risk of cascading failures.
Index Terms —Cascading failures, corrective switching, lineoutage distribution factors, network theory, power system secu-rity, preventive operation, stress metrics, transmission switching.
I. I
NTRODUCTION T HERE is an extensive body of academic and industryliterature on analyzing cascading blackouts, seeking waysto eliminate them or at least reduce their frequency andsize, and improve the speed of recovery [1]. Most of theblackouts have been subject to investigations and postmortemanalyses [1]. The largest blackout in the North Americangrid, the Northeast blackout of 2003, was studied for overa year. The results of this extensive analysis was publishedin an illuminating three-volume report [2]. This report alsoprovides useful insight into a number of earlier cascadingfailure events [1]. The North American Electric ReliabilityCorporation (NERC) was established by the US-Canadianpower industry after the 1965 blackout to improve reliability,notably by producing criteria and collecting data. Preventingcascading blackouts has always been central to the objectivesof these criteria [3]. In 1974, state estimation was introducedin power systems, so that system operators have more accurateinputs to real-time procedures for increasing reliability. In thecontext of cascading failures, the purpose of state estimationwas more to make data availability reliable rather than im-proving the data accuracy [4]. Prior to that, a state model wasdeveloped in which necessary considerations for the design
Authors are with the Department of Electrical and Computer Engineer-ing, University of Utah, Salt Lake City, UT, 84112 USA e-mail: (seehttps://ardakani.ece.utah.edu/). of a total control system for reliability improvement of thethe generation and transmission systems were incorporated.In this model, the control system was made of automaticfunctions, human participation, and an information system [5].Much labor has been invested in a host of efforts to solvethe blackout problem. Recently, network theory has beenapplied to blackouts and other problems in power systems,but blackouts continue; the problem has not been solved [1].
A. Cascading Failures
Cascading failures in large systems can be due to at leastone of the following reasons: [1]1) Failure of protection system and control devices;2) Failure of processes and procedures;3) Overly stressed loading conditions;Among these failure causes, the possibilities of forestallingthe first two (i.e., “control and protective devices” and “poli-cies and procedures”) or even testing for these failures areastronomical and individual events are improbable. We simplylack models that would reflect the effects of these two onthe system. In other words, we cannot model protectionand control system failures, and failures in processes andprocedures into our bulk electric system model. However,history shows that cascading also depends critically on how thesystem is loaded, which can be described by the system stressmetrics [1], [6]. This trend can be clearly observed in 2011Western Interconnection post blackout study, shown in Fig. 1.The figure shows the system stress for four different loadingconditions, with three stress metrics. Arizona and SouthernCalifornia are most stressed during the peak in the summer, asthe system is heavily loaded. The system is usually not nearlyas stressed during spring and winter peaks. The Southwestblackout of 2011 occurred on September 8 at around 3:38PM PDT. This time is not usually regarded as a peak hour;however, as shown in Fig. 1, stress metrics reveal that thesystem was indeed atypically stressed prior to the blackout.The blackout was initiated by a technician mistake, whoswitched a 500 kV line between APS’s Hassayampa and NorthGila substations in Arizona [7]. This blackouts could havebeen avoided if stress had been identified and reduced in thevulnerable and critical parts of the system [8].A set of new tools including metrics of stress or susceptibil-ity to cascading failures has been developed and discussed in[1], [6]. They have been built on two very different theoreticbases to develop methods that planners and operators can useto spot stressed operating states and regions, and to plan andoperate the system securely. The tool has been successfully a r X i v : . [ ee ss . SP ] A ug EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 2
137 132 119 1033 2 1 D ay) 2016 (High Spring) 2016 (High Winter) D e g ree ( N u m b er o f B r n a c h e s ) V u l n er a b ili t y R a nk ( % ) Vulnerability Rank Criticality Degree Vulnerability Degree
Fig. 1. Comparison of the stress on Western interconnection for the peak load during different seasons in 2016 and the blackout day in September 2011 [8]. implemented on Peru System, Eastern Interconnection, andWestern Interconnection to explore the susceptibility of thesystem to cascading failures [9]. In every instance of cascadingblackouts, the stress metrics were able to show unusual systemstress before the event [9].
B. Transmission Switching
Transmission switching (TS) refers to changing the topologyof the transmission network by opening or closing transmis-sion lines. The concept, which was first introduced in 1968by the German mathematician Dietrich Braess, is counter-intuitive but a well-known fact that removing edges from anetwork with selfish routing can decrease the latency incurredby traffic in an equilibrium flow. Since then, a large body ofacademic literature has been dedicated to study this paradox ininfrastructure networks [10]. This concept was first proposedin power system in the 1980s; in the following years, a numberof studies adopted transmission switching as a correctivemechanism [11]. Later, the concept of optimal transmissionswitching was proposed to minimize the operation cost [12].Recently, this technique has been integrated within differentpower system operation models, such as security-constrainedeconomic dispatch, security-constrained unit commitment, aswell as real-time contingency analysis. TS has been provento be able to significantly reduce the operational costs andimprove the system reliability [12]–[15].Due to computational complexity, as well as other concernssuch as dynamic stability, industry adoption of TS has beenvery limited. Some system operators use TS as a correctivemechanism for improving voltage profiles and mitigating lineoverloads [16], [17]. TS is also being employed during plannedoutages, to make the transition smooth, and also as a post-contingency corrective action [18]. California ISO (CAISO)is reported to perform TS on a seasonal basis and to relievecongestion in the system [14], [19]. PJM has posted a listof potential switching solutions that may reduce or eliminateviolations for normal and post-contingency situations [20], [21]. However, these switching actions are not guaranteed toalways provide benefit because they are identified offline.The use of transmission switching has been extensivelystudied for different purposes in power systems, but no studyyet explicitly looked into the impact of transmission switchingon reducing the susceptibility of the system to cascadingfailures.This paper, first, aims to quantify the system susceptibilityto cascading failures in terms of the system’s stress. Thepaper, then, studies the impacts of transmission switching onreducing the system stress, and thereby lowering the system’ssusceptibility to cascading failures. The contributions of thispaper can be summarized as follows:1) Further development of statistical metrics to measuresystem stress by introducing two new metrics;2) Examination of the impacts of preventive transmissionswitching on reducing stress during unusually stressedor poorly forecasted loading conditions;3) Investigation of the benefits of corrective transmissionswitching in reducing the system stress, after N-1 con-tingencies.The rest of the paper is organized as follows. In Section II,we introduce stress metrics to measure the susceptibility of thesystem to cascading failures. Section III presents preventiveand corrective transmission switching. Section IV demon-strates the effectiveness of the method via simulation studieson IEEE 118-bus test system. Finally, Section V concludesthis paper. II. M
EASURE OF S TRESS
To measure the stress on the system, elements from net-work theory and traditional power system analysis have beencombined. Consequently, indices are developed, which candescribe how a failure would propagate through a system [1],[6].To calculate the stress metrics, flow violations on all thelines after every potential contingency are needed. Such infor-mation is readily available from the contingency analysis tool,
EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 3 which is a part of energy management systems [18], [22]. Evenwithout access to such information, post-contingency flowscan be approximately calculated via line outage distributionfactor (LODF), which colloquially are also referred to asDFAX [1], [6]. These sensitivities can be calculated usingconventional power flow software with DC approximation, orusing the current-based generalized injection shift factors [23].An
LODF ij of 0.5 indicates that 50% of the pre-outageflow on line j would be added to the flow on line i , shouldline j go out of service. Post-outage flow on line i after theoutage of line j is calculated in (1), where f indicates thepre-outage flow. f i ∼ = f i + LODF ij × f j (1)This relationship is approximate, because the power systemis only approximately linear. However, the accuracy of (1) isacceptable and power system planners and operators exten-sively use LODFs in contingency analysis [1]. The experienceshows that for real power analysis, which is believed tobe the key issue, the nonlinearity is rarely troublesome [1],[24]. It can be argued that nonlinear and dynamic issues,as well as voltage problems, which are not reflected in thelinearized LODF, are part of cascading failures. We, of course,agree that such effects occur, for example in the two famousblackouts we described above. However, cascading failuresalways begin with the linearizable real-power stresses that ourmodel captures.The LODF matrix is not symmetrical. However, for a largenetwork, most of its values are rather small. Small valuesbeyond a threshold can be ignored to generate a sparse matrix.The sparsity can, then, be exploited for enhancement of thecomputation. In a passive linear network, the value of eachLODF is between -1.0 and + 1.0. Large positive or negativevalues of LODF make cascading failure more likely. Tightercoupling is more likely to overload line i and force it out ofthe service if line j experiences and outage, all else beingequal. With an LODF of zero, the outage of line j by itselfwill not cause an overload or outage of line i [1], [6].Network theory suggests analyzing a network with metrics.The metrics we describe below are variants of metrics usedcommonly in network analysis. The stress metrics proposedin [1], [6] reflect the pre-contingency and post-contingencyflows. This pre-contingency loading is determined by thedemand and the generation dispatch. These values are hy-pothetical in planning models; however, in operation, thepre-contingency loading is obtained from real-time metering,which is processed by the state estimator [1], [6].The definition of some of the metrics developed previously,and those proposed in this paper to measure the stress orsusceptibility of the bulk electric power systems to cascadingblackouts are given below. A. Vulnerability
Vulnerability deals with the post-outage flow on a moni-tored line or transformer after the outage of another line ortransformer in the system. This is a reasonable measure ofstress, because cascading failures always begin with an outage, overloading one or more other line or transformer. Conse-quently, the protection relays will isolate the newly overloadedlines, which will further weaken the system. Two metrics wereproposed in [1], [6] to quantify the vulnerability: the rank andthe degree of vulnerability. In addition, we introduce a newmetric for indexing the entire system’s vulnerability.
1) Rank of Vulnerability ( V ranki ): The rank of vulnerabilityis the maximum absolute value of flow on a line or transformerin per unit of its rating after the outage of another line ortransformer. The rank of vulnerability matrix is a × m matrix, where m is the number of monitored lines andtransformers. The i th rank of vulnerability is the maximumpost-outage flow on line or transformer i after the outage ofall m lines and transformers, taken out one at a time, where m is the number of lines and transformers, whose outageis monitored. Note that, the i th rank of vulnerability may begreater than, less than, or equal to the pre-contingency flowon the line or transformer [1], [6]. This metric is expressedas a percentage of the post-contingency flow compared to theline/transformer rating. V ranki = max( | f i | f ratedi ) (2)
2) Degree of Vulnerability ( V degreei ): The degree of vul-nerability is the number of single outages for which a moni-tored line or transformer will be loaded over some thresholdvalue. The line’s rating is used to compute the degree ofvulnerability in this paper. The degree of vulnerability matrixis a × m matrix, where m is the number of monitoredlines and transformers. The i th element of this matrix is thenumber of lines and transformers, among all the m lines andtransformers, whose outage leads to a power flow beyond thespecified threshold for the i th line or transformer. This metricis calculated and shown in (3). V degreei = count if ( | f i | f ratedi > T hreshold i ) (3)
3) System Vulnerability Degree ( V System ): The systemvulnerability degree, proposed in this paper, is the number ofnon-radial monitored branches that will have a vulnerabilityrank beyond some threshold value. The lines’ ratings wereused, here, to compute the number of vulnerability in thisstudy. The system vulnerability degree is a scalar, which ismeasured as an index for the entire system, rather than aspecific line or transformer.
B. Criticality
Criticality measures how the outage of a line or transformeraffects other lines and transformers in the system. Rank anddegree of criticality are used to define criticality [1], [6], [8].In addition, this paper introduces a new metric for measuringthe entire system’s criticality level.
1) Rank of Criticality ( C ranki ): The rank of criticality ofa line or transformer i is the maximum absolute value offlow through all other lines and transformers, per unit of theircapacity, after the outage of line or transformer i . The rank ofcriticality matrix is a × m matrix, where m is the number EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 4 of lines and transformers whose outage is monitored. The i th rank of criticality is the maximum absolute value of all thepost-outage flows divided by the ratings of the m monitoredlines and transformers, after the outage of line or transformer i [8]. This metric is expressed as a percentage of the rating ofthe monitored lines or transformers, as shown in (4). C ranki = max k ( | f k | f ratedk ) (4)
2) Degree of Criticality ( C degreei ): The degree of criticalityof a line or transformer i is the number of monitored lines andtransformers that will be loaded above some threshold after theoutage of line or transformer i . The nominal rating of the lineswas used, here, for calculating the degree of criticality, similarto the degree of vulnerability. However, any desirable thresholdcan be picked by the operator, and the method does not limitthis choice. The degree of criticality matrix is also a × m matrix, where m is the number of lines and transformerswhose outage is monitored. The i th degree of criticality is thenumber of lines and transformers among all the m monitoredlines and transformers whose flows will exceed the thresholdafter the outage of the i th line or transformer. This metric canbe calculated as shown in (5). C degreei = count if ( | f k | f ratedk > T hreshold k ) (5)
3) System Criticality Degree ( C System ): The system crit-icality degree is the number of non-radial contingencies thatwill result in a criticality rank beyond some threshold value.Nominal line ratings were used to compute the number ofcriticality in this study. Similar to the system vulnerabilitydegree, system criticality degree is also a scalar, which ismeasured for the entire system.III. T
RANSMISSION S WITCHING
The electric transmission network is built redundant, inorder to ensure mandatory reliability standards, which requireprotection against worst case scenarios. Due to the existenceof loop flows in this redundant meshed network, transmissionswitching may lead to improved economic efficiency andreliability [14]. This phenomenon is widely acknowledged;however, finding appropriate switching candidates within theavailable computational time for power system operation re-mains to be a challenge.Although transmission switching has many applications, itcan be solely performed to enhance the system reliability [18],[21], [22], [25]. Reliability-motivated switching is perhapsthe first application of transmission switching that is usedby the industry [20]. References [18], [21], [22] employtransmission switching to reduce the post-contingency networkviolations. The method proposed in this paper also aims toenhance reliability, but rather than post-contingency violationreduction, we focus on reducing the system stress, which ismeasured via the metrics, introduced in Section II.As mentioned before, transmission switching is consideredto be a computationally challenging problem. A recent method,which achieved tractability for reliability-motivated switching, handled this challenge by only allowing a very limited set ofswitching candidates [18], [21], [22]. The switchable elementswere picked either from a small vicinity of the contingencyor the violation. Extensive analysis showed that this smallsubset includes almost all of the quality solutions [18], [21],[22]. In this paper, we use a similar approach by only relyingon a small subset of switchable lines; however, rather thansearching within the vicinity of contingency or violation,we employ the LODF matrix to choose the most effectiveswitching candidates. The potential candidates can be selectedby looking at the column of the overloaded line correspondingto a contingency. A high negative LODF value is one of theindications of the potential line for switching. Thus, LODFmatrix will provide us with a smart and fast method to selectthe switching candidates.Switching is generally classified into two categories, de-pending on its timeline: preventive and corrective transmissionswitching. We consider both of these categories in the next twosubsections, in the context of system stress reduction.
A. Preventive Transmission Switching
A preventive action in power system operation is taken toavoid the adverse consequences of a potential disturbance. Thedisturbance may never happen, but the preventive action willprotect the system against it, should it actually occur. In thispaper, we use preventive transmission switching to reduce thesystem’s susceptibility to cascading failures. History showsthat cascading failures depend critically on how the system isloaded, which can be described by the system stress metrics.Post-blackout investigations show that in most cases the sys-tem was atypically stressed before the blackout [1]. Had thestress of the system been taken care of, the blackout couldhave been prevented. This can be seen in [8], where the stresson San Diego area was analyzed over different seasons ofthe year and found that on September 8, 2011, and beforethe blackout that happened later on the same day, the systemwas atypically stressed. The blackout could have been avoidedthrough appropriate preventive actions that reduce the systemstress.In this paper, we propose that preventive transmissionswitching should be looked at, whenever the system is underatypical stress, beyond a predefined level, in order to reducethe stress on the system. We hypothesize that transmissionswitching may be able to offer a cheap and fast solution, re-lieve the system stress, and avoid potential cascading failures.The line can be switched back, once the system stress hasbeen reduced due to change in the loading, if the line provideseconomic benefits. There are other alternatives that can be im-plemented as preventive actions, such as generation redispatch.However, transmission switching can be implemented muchfaster and is often the cheapest option, as it only involves theoperation of a circuit breaker. Moreover, it is often the case thatduring the stressed operating conditions, generation redispatchis depleted and not available anymore to the operator. Fig. 2shows the proposed algorithm for transmission switching inresponse to atypical stress on the system. An example of anatypically stressed system was shown in Fig. 1, which led tothe Southwest blackout of 2011.
EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 5
StartBase caseEMS ( s tate estimation)LODF( b ase case topology) Stress metrics Is stress level acceptable?EndNoYesGenerate switching candidates & rank list using LODF matrix for highly stressed linesSelect top n switching candidates L=1 L=L+1Stress reduced with TS?Stress metricsLODF( after switching ) NoYes
Fig. 2. The algorithm, proposed in this paper, to reduce the system stressusing transmission switching.
B. Corrective Transmission Switching (CTS)
As transmission switching can be implemented instan-taneously, unlike generation redispatch, which is relativelyslow, more studies have focused on corrective transmissionswitching than preventive transmission switching. Correctivetransmission switching solutions are identified beforehand,within the contingency analysis tool, and are ready for im-plementation [18], [22]. Only after the contingency occurs,does the operator need to implement the solution.Our interest in this paper is to study how correctivetransmission switching can contribute to reducing a post-contingency stress rather than the post-contingency violations.The two are related, but are not the same. This paper examinestwo hypotheses regarding corrective transmission switching.First, we analyze the post contingency system stress that isimposed on the system by the possibility of an N-1-1 event,for the system that is already in the N-1 state. The second pointof interest for us is to monitor the ongoing level of stress inthe system, which is measured in terms of the lines that havealready exceeded their contingency limits. These overflowsshould be addressed within a short period of time, definedby the emergency limit’s maximum duration; otherwise, theoverloaded lines may trip and initiate a cascading failure. Thus,transmission switching can either be considered corrective,with respect to the current post N-1 state, or preventive, withrespect to the possibility of an N-1-1 event.IV. C
ASE S TUDIES
The case studies are conducted on IEEE 118-bus testsystem. To generate a variety of stress levels, we use differentloading conditions at 97%, 105%, 106%, and 110% of thesystem’s peak load. The nodal loads are uniformly adjustedfor all the cases, except for the 106% loaded case, wherethe demand is increased only on select buses (16% in WestEnd (40) and 105% in S. Tiffin (41)). We, then, run an AC
TABLE IT
HE CRITICALITY AND VULNERABILITY STRESS METRICS FOR THE
IEEE118
BUS TEST CASE AT
OF PEAK LOADING . Rank (% ) Degree Rank (% ) Degree N o . Line or Transformer Criticality Vulnerability optimal power flow for each loading, to obtain AC feasiblebase case solutions for the analysis. These solutions are fedto PowerWorld for to assist with calculation of stress metricsand examination of transmission switching impacts.We assume that all lines have their contingency limits at120% of the normal limits, which can be used for a limitedduration of 4 hours. We further assume the emergency limitsto be at 135% of the normal line limits, which can be used upto 15 minutes [26]. We acknowledge that the contingency andemergency limits are not necessarily always scaled uniformlyto the normal limits; however, we make this assumptionto simplify the analysis presented in this paper. We furtheracknowledge that such limits may change depending on theweather or loading conditions; again, we have neglected suchdetails to simplify the analysis.Tables I-IV present the stress analysis with different loadingconditions as described earlier. The purpose of these stresstables is to demonstrate how loading with different patterns canaffect the system stress metrics. Generally, the stress increaseswith the loading; however, the 106% loaded case, with non-uniform increase in the nodal loads, is atypically stressed,even beyond the 110% loaded case. This demonstrates that thedistribution of the load has a significant impact on the systemstress. We pick this atypically stressed case to demonstrate thebenefits of preventive transmission switching.
A. Preventive Transmission Switching
Figure 3 shows the various stress metrics, comparing thestress on IEEE 118-bus case system, in terms of maximumcriticality rank, maximum degree, and system degree underdifferent loading conditions. As can be seen, the stress for thecase with 106% loading is atypically high. Table V shows thestress on the same case after a preventive switching actionis implemented, where 17 Sorenson - 113 Deer Crk line isopened, but the generation dispatch is not changed. A fullstress analysis is performed for pre- and post- transmissionswitching and the stress comparison for this case is shown inFig. 4. The plot, comparing the number of lines, loaded aboveboth emergency and contingency limits, under different load-ing patterns including after preventive transmission switching
EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 6
97% 110% D e g ree a nd N u m b er ( N u m b er o f B r n a c h e s ) C r i t i c a li t y R a nk ( % ) Loading as a P ercentage of Peak Demand* The load is increased only in select buses
Comparing overall system stress using different stress metrics under two different loading conditions
Criticality Rank Criticality Degree System Criticality Degree System Vulnerability Degree
Fig. 3. Comparison of the stress on IEEE 118-bus test system in terms of criticality rank, degree, and system degree under different loading conditions.TABLE IIT
HE CRITICALITY AND VULNERABILITY STRESS METRICS FOR THE
IEEE118
BUS TEST CASE AT
OF PEAK LOADING . Rank (%) Degree Rank (%) Degree N o . Line or Transformer Criticality Vulnerability
TABLE IIIT
HE CRITICALITY AND VULNERABILITY STRESS METRICS FOR THE
IEEE118
BUS TEST CASE AT
OF PEAK LOADING . Rank (%) Degree Rank (%) Degree N o . Line or Transformer Criticality Vulnerability
TABLE IVT
HE CRITICALITY AND VULNERABILITY STRESS METRICS FOR THE
IEEE118
BUS TEST CASE AT
OF PEAK LOADING . Rank (% ) Degree Rank (% ) Degree N o . Line or Transformer Criticality Vulnerability
TABLE VT
HE CRITICALITY AND VULNERABILITY STRESS METRICS FOR THE
LOADED
IEEE 118
TEST CASE AFTER THE IMPLEMENTATION OF A SINGLEPREVENTIVE SWITCHING ACTION (17 S
ORENSON - 113 D
EER C RK ). Rank (% ) Degree Rank (% ) Degree N o . Line or Transformer Criticality Vulnerability
EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 7
TABLE VIV
ARIOUS STRESS MEASUREMENTS FOR THE SYSTEM UNDER DIFFERENT LOADING CONDITIONS , INCLUDING THE
LOADED CASE AFTERIMPLEMENTATION OF ONE PREVENTIVE TRANSMISSION SWITCHING ACTION .Loading *Limit **Limitas a % of V rank V degree V N C rank C degree C N (Emergency) (Contingency)peak demand Violation Violation97% 222.94% 5 8 222.94% 4 6 2 4105% 231.31% 5 8 231.31% 4 6 3 4 + % 239.06% 5 9 239.06% 5 9 4 7 ++ % (PTS) 199.73% 3 8 199.73% 4 7 2 4110% 234.28% 5 7 234.28% 5 7 3 4* This column represents the number of lines that violate at least one of the lines’ Emergency Limit* This column represents the number of lines that violate at least one of the lines’ Contingency Limit+ load is increased only at select buses.++ The stress of + loading is measured post preventive transmission switching of 17 Sorenson - 113 Deer Crk line is shown in Fig. 5. The results of different stress metricsparameters is tabulated in Table VI. The results clearly showthat a single transmission switching action can substantiallyreduce the system stress, and avoid a potential cascadingfailure event.
311 109 7 D e g ree a nd N u m b er ( N u m b er o f B r n a c h e s ) C r i t i c a li t y R a nk ( % ) Loading as a Percentage of Peak Demand * The load is increased only in select buses
Comparing the pre and post preventative transmission switching system stress for fixed load demad
Criticality Rank Criticality DegreeSystem Criticality Degree System Vulnerability Degree
Fig. 4. The stress comparison of pre and post transmission switching forthe 106% loaded IEEE 118 bus test case. The rank and degree in this chartrepresent the single highest value for the system.
97% 110% N u m b er o f L i n e s % Loading as a Percentage of Peak Demand * The load is increased only in select buses
PTS: Preventative Transmission Sw i tching Number of Lines Violating Various Line
Limits
Violating Line Contingency Limits Vi o lating Line Emergency Limits (PTS) Fig. 5. The plot compares the number of lines, violating both emergencyand contingency limits under different loading conditions, including the postpreventive transmission switching.
B. Corrective Transmission Switching
One of the highly critical non-radial contingencies, identi-fied by PowerWorld Simulator, is 8 Olive - 5 Olive transformer.For this contingency, the stress on the system is such that atleast one of the in-service lines exceeds the contingency limit, and therefore, the operator has about 15 minutes to address thisissue or another line will be tripped. The algorithm developedin this paper suggests switching of 15 FtWayne - 17 Sorensonline, as a corrective action, to reduce the system stress to anacceptable level.Fig. 6 compares the stress on system in terms of critical-ity rank and degree under different loading conditions forthe base case, contingency (8 Olive - 5 Olive transformer),and corrective transmission switching of 15 FtWayne - 17Sorenson line for the IEEE 118-bus test case. The resultsconfirm the effectiveness of corrective transmission switchingin reducing the post-contingency system stress, close to thenormal operation levels.V. C
ONCLUSION
System stress metrics are recently developed to provideinsight into the susceptibility of the system to cascadingfailures. The metrics include measures of the criticality ofcontingencies and vulnerability of the transmission elementsto overloads after contingencies. Building upon those metrics,this paper introduced two new metrics to measure the system’scriticality and vulnerability. All of these metrics can be quicklycalculated via the outputs of the contingency analysis tool,or through LODFs. Furthermore, the paper investigated thepossibility of employing transmission switching, both as apreventive and corrective measure, to reduce the system stress.In order to achieve computational tractability for the trans-mission switching algorithm, LODF sensitivities were used togenerate a rather small subset of quality switching candidates.Those candidates were, then, tested for effectiveness, until aneffective solution was found or the list was depleted. Thesimulation studies on IEEE 118-bus system confirmed theeffectiveness of the method. A single transmission switchingaction was able to substantially reduce the system stress tothe normal levels. This implies that system operators shouldlook at transmission switching as an effective tool to preventcascading failures, when the system is atypically stressed.Other alternative actions, such as generation redispatch, aresubstantially more expensive and may also not be availablewhen the system is highly stressed.
EEE TRANSACTIONS ON POWER SYSTEMS, SUBMITTED FOR PUBLICATION, MAY 2018 8 C r i t i c a li t y D e g ree C r i t i c a li t y R a nk System loading as the percentage of the peak load
Base Case Degree Contingency Degree
Post-
Swtiching Degree
Base Case Rank Contingency Rank
Post-
Switching Rank
Line Limit (Normal) 100%Line Limit (Contingency) 120%Line Limit (Emergency) 135%
Fig. 6. Comparison of system stress in terms of criticality rank and degree under different loading conditions for the base case, contingency case (outage of8 Olive - 5 Olive Transformer), and post corrective transmission switching of 15 Ft. Wayne - 17 Sorenson. A CKNOWLEDGMENT
The authors would like to thank Dr. Hyde Merrill forhis careful review and detailed feedback. We also thank Dr.Marc Bodson for providing us with the PowerWorld Simulatorlicense. R
EFERENCES[1] H. M. Merrill and J. W. Feltes, “Cascading blackouts: Stress, vulnera-bility, and criticality,” 2016.[2] U.S.-Canada Power System Outage Task Force, “Final report on theaugust 14, 2003 blackout in the United States and Canada,” April, 2004.[3] NERC, “Standard TPL-001-4 - transmission system planning perfor-mance requirements”, in “reliability standards for the bulk electricsystems of North America,” 17 August 2016.[4] F. C. Schweppe and E. J. Handschin, “Static state estimation in electricpower systems,”
Proceedings of the IEEE , vol. 62, no. 7, pp. 972–982,July 1974.[5] T. E. Dy Liacco, “The adaptive reliability control system,”
IEEETransactions on Power Apparatus and Systems , vol. PAS-86, no. 5, pp.517–531, May 1967.[6] S. A. Sadat, D. Haralson, and M. Sahraei-Ardakani, “Security versuscomputation time in IV-ACOPF with socp initialization,” in
IEEEInternational Conference on Probabilistic Methods Applied to PowerSystems (PMAPS) . In Proceedings, 2018, pp. 1–5.[7] Federal Energy Regulatory Commission and the North American Elec-tric Reliability Corporation Report, “Arizona Southern California Out-ages on September 8, 2011, Causes and Recommendations,” April, 2012.[8] M. A. Hossain, H. M. Merrill, and M. Bodson, “Evaluation of metrics ofsusceptibility to cascading blackouts,” in , Feb 2017, pp. 1–5.[9] H. M. Merrill. ”Private Conversation”, ”2018”.[10] G. Valiant and T. Roughgarden, “Braess’s paradox in large randomgraphs,”
Random Struct. Algorithms , vol. 37, no. 4, pp. 495–515, Dec.2010. [Online]. Available: http://dx.doi.org/10.1002/rsa.v37:4[11] J. G. Rolim and L. J. B. Machado, “A study of the use of correctiveswitching in transmission systems,”
IEEE Transactions on Power Sys-tems , vol. 14, no. 1, pp. 336–341, Feb 1999.[12] Y. Sang and M. Sahraei-Ardakani, “The Interdependence between Trans-mission Switching and Variable-Impedance Series FACTS Devices,”
IEEE Transactions on Power Systems , vol. PP, no. 99, pp. 1–1, 2017.[13] P. A. Ruiz, A. Rudkevich, M. C. Caramanis, E. Goldis, E. Ntakou, andC. R. Philbrick, “Reduced MIP formulation for transmission topologycontrol,” in , Oct 2012, pp. 1073–1079. [14] K. W. Hedman, S. S. Oren, and R. P. O’Neill, “A review of transmissionswitching and network topology optimization,” in , July 2011, pp. 1–7.[15] M. Abdi-Khorsand, M. Sahraei-Ardakani, and Y. Al-Abdullah, “Correc-tive transmission switching for N-1-1 contingency analysis,” in
IEEE Transactions on PowerSystems
IET Generation, Transmission Distribution ,vol. 10, no. 8, pp. 1984–1992, 2016.[22] M. Sahraei-Ardakani, X. Li, P. Balasubramanian, K. W. Hedman, andM. Abdi-Khorsand, “Real-time contingency analysis with transmissionswitching on real power system data,”
IEEE Transactions on PowerSystems , vol. 31, no. 3, pp. 2501–2502, 2016.[23] Y. C. Chen, S. V. Dhople, A. D. Domnguez-Garca, and P. W. Sauer,“Generalized injection shift factors,”
IEEE Transactions on Smart Grid ,vol. 8, no. 5, pp. 2071–2080, Sept 2017.[24] S. A. Sadat, D. Haralson, and M. Sahraei-Ardakani, “Evaluation of vari-ous techniques to warm-start a successive linear programming algorithmfor solving the IV ACOPF,” in
IEEE Power & Energy Society GeneralMeeting (PESGM) . In Proceedings, 2018, pp. 1–5.[25] P. Balasubramanian and K. W. Hedman, “Real-time corrective switchingin response to simultaneous contingencies,”