Cascading Failure Mitigation Via Transmission Switching Sayed Abdullah Sadat, Graduate Student Member, IEEE, and Mostafa Sahraei-Ardakani, Member, IEEE

SUBMITTED FOR REVIEW 1

Cascading Failure Mitigation via Transmission Switching Sayed Abdullah Sadat, Graduate Student Member, IEEE, and Mostafa Sahraei-Ardakani, Member, IEEE,

Abstract—After decades of research, cascading blackouts re- state model was developed in which necessary considerations main one of the unresolved challenges in the bulk power system for designing a total control system for reliability improvement operations. A new perspective for measuring the susceptibility of the generation and transmission systems were incorporated. of the system to cascading failures is clearly needed. The newly developed concept of system stress metrics may be able to provide In this model, the control system was made of automatic new insights into this problem. The method measures stress as functions, human participation, and an information system [5]. susceptibility to cascading failures by analyzing the network Much labor has been invested in a host of efforts to solve the structure and electrical properties. This paper investigates the blackout problem. Recently, network theory has been applied effectiveness of transmission switching in reducing the risk of to blackouts and other power systems issues, but blackouts cascading failures, measured in system stress metrics. Based on line-outage distribution factors, an algorithm is developed continue; the problem has not been solved [1]. to identify and test the switching candidates quickly. A case study analyzing different stress metrics on the IEEE 118-bus A. Cascading Failures test system is presented. The results show that transmission switching identified by our proposed algorithm could be used Cascading failures in large systems can be due to at least in preventive as well as corrective mechanisms to reduce the one of the following reasons: [1] system’s susceptibility to cascading failures. Contrary to the conventional operation wisdom that switching lines out of service 1) Failure of protection system and control devices; jeopardizes reliability, our results suggest the opposite; system 2) Failure of processes and procedures; operators can often use transmission switching, when the system 3) Overly stressed loading scenarios; is under stress, as a tool to reduce the risk of cascading failures. Among these failure causes, the possibilities of forestalling the first two (i.e., “control and protective devices” and “poli- Index Terms—Cascading failures, corrective switching, line cies and procedures”) or even testing for these failures are outage distribution factors, network theory, power system secu- astronomical and individual events are improbable. We simply rity, preventive operation, stress metrics, transmission switching. lack models that would reflect these two’s effects on the system because we do not know if or how a failure will lead to a cascading failure. In other words, we cannot model I.INTRODUCTION protection and control system failures and failures in processes HERE is an extensive body of academic and industry and procedures into our bulk electric system model. However, T literature on analyzing cascading blackouts, seeking ways history shows that cascading also depends critically on how to eliminate them or at least reduce their frequency and the system is loaded, which can be described by the system size, and improve the speed of recovery [1]. Most of the stress metrics [1], [6]. This trend can be observed in the 2011 blackouts have been subject to investigations and postmortem Western Interconnection post blackout study, shown in Fig. 1. analyses [1]. The largest blackout in the North American grid, The figure shows the system stress for four different loading the Northeast blackout of 2003, was studied for over a year. scenarios, with three stress metrics. Arizona and Southern arXiv:1810.00651v2 [eess.SP] 5 Jan 2021 The results of this extensive analysis were published in an California are most stressed during the peak in the summer, as illuminating three-volume report [2]. This report also provides the system is heavily loaded. The system is usually not nearly useful insight into several earlier cascading failure events [1]. as stressed during spring and winter peaks. The Southwest The North American Electric Reliability Corporation (NERC) blackout of 2011 occurred on September 8 at around 3:38 was established by the US-Canadian power industry after the PM PDT. This time is not usually regarded as a peak hour; 1965 blackout to improve reliability, notably by producing however, as shown in Fig. 1, stress metrics reveal that the criteria and collecting data. Preventing cascading blackouts has system was indeed atypically stressed before the blackout. The always been central to the objectives of these criteria [3]. In blackout was initiated by a technician mistake, who switched 1974, state estimation was introduced in power systems to have a 500 kV line between APS’s Hassayampa and North Gila more accurate inputs to real-time procedures for increasing substations in Arizona [7]. This blackout could have been reliability. In the context of cascading failures, the purpose of avoided if the stress was identified and reduced [8]. state estimation was more to make data availability reliable Several metrics have been developed to capture grid oper- rather than improving the data accuracy [4]. Before that, a ation risks [1], [9], [10]. These metrics have their pros and cons. Multiple element contingency consideration provides Authors are with the Department of Electrical and Computer Engi- neering, University of Utah, Salt Lake City, UT, 84112, USA. (e-mail: more levels of visibility of stress on the stress as in [10]. sayed [email protected]; [email protected]). Other metrics take into consideration the voltage profile of the SUBMITTED FOR REVIEW 2

140 10 137 132 9 130 8 120 119 7 5 110 6 5 103 100 5

4 90 2 3 3

3 Degree (Number of Brnaches) Vulnerability Rank (%) 80 2 2 1 1 70 1

60 0 2016 (High Summer) 2011 (Blackout Day) 2016 (High Spring) 2016 (High Winter) 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]. system and the probability of the failures of transmission ele- implemented on Peru System, Eastern Interconnection, and ments [9]. We believe that it has to be computationally efficient Western Interconnection to explore the system’s susceptibility and inexpensive for metrics to offer real-time stress visibility, to cascading failures [12]. In every instance of cascading preferably employing the existing Energy Management System blackouts, the stress metrics were able to show unusual system (EMS) tools. Considering multiple-element contingencies are stress before the event [12]. computationally very expensive. The majority of the computationally less expensive algorithms for metrics often capture less than one-third of the sever contingencies, which are B. Transmission Switching more likely to be followed by a cascading failure, thereby making these metrics less effective [10]. Besides, cascading Transmission switching (TS) refers to changing the trans- failures that began with N-2 (i.e., simultaneous independent mission network’s topology by opening or closing transmis- contingencies instead of causal N-1-1 contingencies, where a sion lines. The concept, which was first introduced in 1968 first contingency caused a second to occur) are rarely heard by the German mathematician Dietrich Braess, is counter- of. We believe that considering the voltage factor in the intuitive but a well-known fact that removing edges from metrics, which brings in significant additional computational a network with “selfish routing” can decrease the latency expense are less helpful. Ignoring the voltage impact does incurred by traffic in an equilibrium flow. Since then, a large not impact the viability of our method. It can be verified by body of academic literature has been dedicated to studying this another work [11], which analyzed transmission switching in paradox in infrastructure networks [13]. This concept was first the PJM network, one of the largest transmission network proposed in the power systems in the 1980s; in the following operators globally, has shown that more than 99% of the years, several studies adopted transmission switching as a switching transmission elements provide a stable solution as corrective mechanism [14]. Later, the concept of optimal expected by the NERC standards. Additionally, the response to transmission switching was proposed to minimize the oper- voltage disturbances by the protection system is usually slow ation cost [15]. This technique has recently been integrated compared to its response to overload, which is instantaneous. within different power systems operation models, such as The slow response to voltage change provides enough time security-constrained economic dispatch, security-constrained for the operator to mitigate the impact and take corrective unit commitment, and real-time contingency analysis. TS has actions. We also prefer to avoid probabilistic methods of been proven to significantly reduce the operational costs and approach to produce metrics simply because of the varieties of improve system reliability [15]–[18]. Due to computational factors that can contribute to the probability of a contingency complexity and other concerns such as dynamic stability, and, consequently, the computational burden of it versus the industry adoption of TS has been very limited. Some system benefit it can offer to an operator in real-time. A set of new operators use TS as a corrective mechanism for improving tools, including metrics of stress or susceptibility to cascading voltage profiles and mitigating line overloading [19], [20]. TS failures, which were introduced and discussed in [1], [6], is also being employed during planned outages to make the have been adopted and further extended. We found these transition smooth, and also as a post-contingency corrective tools more appropriate for determining the potential elements action [11]. California ISO (CAISO) is reported to perform TS for transmission switching in real-time operations. They have on a seasonal basis and relieve congestion in the system [17], been built on two very different theoretic bases to develop [21]. PJM has posted a list of potential switching solutions methods that planners and operators can use to spot stressed that may reduce or eliminate violations for normal and post- areas in different operating states and subsequently plan and contingency situations [22], [23]. However, these switching operate the system securely. The tool has been successfully actions are not always guaranteed to provide benefits because they are identified offline. SUBMITTED FOR REVIEW 3

The use of transmission switching has been extensively as well as voltage problems, which are not reflected in the studied for different purposes in power systems. Still, no study linearized LODF, are part of cascading failures. Of course, we yet explicitly looked into the impact of transmission switching agree that such effects occur, for example, in the two famous on reducing the system’s susceptibility to cascading failures. blackouts we described above. However, cascading failures First, this paper aims to quantify the system’s susceptibility always begin with the linearizable real-power stresses that our to cascading failures in terms of the system’s stress. The paper model captures. then studies the impacts of transmission switching on reducing The LODF matrix is not symmetrical. However, for a large the system stress, and as a result, lowering the system’s network, most of its values are rather small. Small values susceptibility to cascading failures. The contributions of this beyond a threshold can be ignored to generate a sparse matrix. paper can be summarized as follows: The sparsity can, then, be exploited for enhancement of the 1) Further development of statistical metrics to measure computation. In a passive linear network, the value of each system stress by introducing four new metrics, including LODF is between -1.0 and + 1.0. Large positive or negative indices for potential candidates for transmission switch- values of LODF make cascading failure more likely. Tighter ing; coupling is more likely to overload line i and force it out of 2) Examination of the impacts of preventive transmission the service if line j experiences an outage, all else being equal. switching on reducing stress during unusually stressed With an LODF of zero, the outage of the line j by itself will or poorly forecasted loading scenarios; not cause an overload or outage of the line i [1], [6]. 3) Investigation of the benefits of corrective transmission Network theory suggests analyzing a network with metrics. switching in lowering the system stress, after N-1 con- The metrics we describe below are variants of metrics used tingencies. commonly in network analysis. The stress metrics proposed The rest of the paper is organized as follows. In Section in [1], [6] reflect the pre-contingency and post-contingency II, we introduce stress metrics to measure the susceptibility flows. The demand and the generation dispatch determine of the system to cascading failures. Section III presents this pre-contingency loading. These values are hypothetical in preventive and corrective transmission switching. Section IV planning models; however, in operation, the pre-contingency demonstrates the effectiveness of the method via simulation loading is obtained from real-time metering, which is pro- studies on the IEEE 118-bus test system. Finally, Section V cessed by the state estimator [1], [6]. The definition of some concludes this paper. of the metrics developed previously and those proposed in this paper are given below.

II.MEASUREOF STRESS A. Vulnerability Elements from network theory and traditional power system analysis have been combined to measure the system’s stress. Vulnerability deals with the post-outage flow on a mon- Consequently, indices are developed, describing how a failure itored line or transformer after the outage of another line would propagate through a system [1], [6]. or transformer in the system. This is a reasonable measure Flow violations on all the lines after every potential con- of stress because cascading failures always begin with an tingency are needed to calculate the stress metrics. Such outage, overloading one or more other line or transformer. information is readily available from the contingency analysis Consequently, the protection relays will isolate the newly tool, which is a part of the EMS [11], [24]. Even without overloaded lines, which will further weaken the system. Two access to such information, post-contingency flows can be metrics were proposed in [1], [6] to quantify the vulnerability: approximately calculated via line outage distribution factor the rank and the degree of vulnerability. In addition, we (LODF), which colloquially is also referred to as DFAX [1], also introduce a new metric for indexing the entire system’s [6]. These sensitivities can be computed using conventional vulnerability. rank power flow software with DC approximation or using the 1) Rank of Vulnerability (Vi ): The rank of vulnerability current-based generalized injection shift factors [25]. is the maximum absolute value of flow on a line or transformer An LODFij of 0.5 indicates that 50% of the pre-outage per unit of its rating after the outage of another line or flow on line j would be added to the flow on line i, should transformer. The vulnerability matrix’s rank is a 1×m1 matrix, line j go out of service. Post-outage flow on line i after the where m1 is the number of monitored lines and transformers. outage of line j is calculated in (1), where f 0 indicates the The ith rank of vulnerability is the maximum post-outage flow pre-outage flow. in the line or transformer i after the outage of all m2 lines and transformers, taken out one at a time, where m is the ∼ 0 0 2 fi = fi + LODFij × fj (1) number of lines and transformers, whose outage is monitored. th This relationship is approximate because the power system Note that the i rank of vulnerability may be greater than, is only approximately linear. However, the accuracy of (1) is less than, or equal to the pre-contingency flow on the line or acceptable, and power system planners and operators exten- transformer [1], [6]. This metric is expressed as a percentage sively use LODFs in contingency analysis [1]. The experience of the post-contingency flow compared to the line/transformer shows that for real-time power analysis, which is believed to rating. be the key issue, the nonlinearity is rarely troublesome [1], |f | V rank = max( i ) [26]. It can be argued that nonlinear and dynamic issues, i rated (2) fi SUBMITTED FOR REVIEW 4

degree 2) Degree of Vulnerability (Vi ): The degree of vul- after the outage of the ith line or transformer. This metric can nerability is the number of single outages for which a moni- be calculated, as shown in (5). tored line or transformer will be loaded over some threshold degree |fk| value. The line’s rating is used to compute the degree of C = count if( > T hresholdk) (5) i f rated vulnerability in this paper. The degree of vulnerability matrix k is a 1 × m1 matrix, where m1 is the number of monitored 3) System Criticality (CSystem): The system criticality lines and transformers. The ith element of this matrix is the rank and degree proposed in this paper are the maximum rank number of lines and transformers, among all the m2 lines and of criticality and the maximum degree of criticality of non- transformers, whose outage leads to a power flow beyond the radial critical elements, respectively. Nominal line ratings were specified threshold for the ith line or transformer. This metric used to compute the number of criticality in this study. Like is calculated and shown in (3). the system vulnerability metrics, system criticality metrics are also a scalar measured for the entire system. |f | V degree = count if( i > T hreshold ) (3) i f rated i i C. Switching Stress Relief Index (SSR) i 3) System Vulnerability Degree (VSystem): The system The SSR is a metric intended for non-critical lines i to vulnerability rank and degree, proposed in this paper, are represent their impact on the system if switched. Like other respectively the maximum rank of vulnerability and maximum metrics, these metrics are of two types: Switching Stress Relief i i degree of vulnerability of non-radial monitored vulnerable Rank SSRr and Switching Stress Relief Degree SSRd, and elements. Here, the lines’ normal ratings were used to compute are calculated as shown in the algorithm 1. the vulnerability number in this study. The system vulnerability metrics are scalar, measured as indices for the entire for c in Critical List do system, rather than a specific line or transformer. for nc in Noncritical List do 0 nc o if (Fc < 0 & LODFi × Fnc > 0) k 0 nc o (Fc > 0 & LODFi × Fnc < 0) then nc nc B. Criticality SSRd ← SSRd + 1 ; nc nc 0 100 SSRr ← SSRr + (|Fc | − |Fc|) × max ; Criticality measures how the outage of a line or transformer Fc affects other lines and transformers in the system. Rank and end degree of criticality are used to define criticality [1], [6], [8]. end In addition, this paper introduces a new metric for measuring end Algorithm 1: Calculating SSRnc and SSRnc indices for the entire system’s criticality level. d r rank noncritical lines. 1) Rank of Criticality (Ci ): The rank of the criticality of a line or transformer i is the maximum absolute value of The higher the value of SSR of any element, the more flow through all other lines and transformers, per unit of their preferred candidate is the element for transmission switching capacity, after the outage of line or transformer i. The rank of to reduce the system’s stress. criticality matrix is a 1 × m2 matrix, where m2 is the number of lines and transformers whose outage is monitored. The ith III.TRANSMISSION SWITCHING rank of criticality is the maximum absolute value of all the post-outage flows divided by the ratings of the m1 monitored The electric transmission network is built redundantly to lines and transformers after the outage of line or transformer ensure mandatory reliability standards, requiring protection i [8]. This metric is expressed as a percentage of the monitored against worst-case scenarios. Due to loop flows in this re- lines or transformers’ rating, as shown in (4). dundant meshed network, transmission switching may lead to improved economic efficiency and reliability [17]. This rank |fk| phenomenon is widely acknowledged; however, finding appro- Ci = max( ) (4) k rated fk priate switching candidates within the available computational time for power system operation remains challenging. degree 2) Degree of Criticality (Ci ): The degree of criticality Although transmission switching has many applications, it of a line or transformer i is the number of monitored lines can be solely performed to enhance the system reliability [11], and transformers that will be loaded above some threshold [23], [24], [27]. Reliability-motivated switching is perhaps the after the outage of line or transformer i. The lines’ nominal first application of transmission switching that is used by the rating was used here for calculating the degree of criticality, industry [22]. References [11], [23], [24] employ transmission similar to the degree of vulnerability. However, the operator switching to reduce the post-contingency network violations. can pick any desirable threshold, and the method does not limit The method proposed in this paper also aims to enhance relia- this choice. The degree of criticality matrix is also a 1 × m2 bility. We focus on reducing the system stress measured via the matrix, where m2 is the number of lines and transformers metrics Section II, rather than the post-contingency violation whose outage is monitored. The ith degree of criticality is the reduction. As mentioned before, transmission switching is con- number of lines and transformers among all the m1 monitored sidered to be a computationally challenging problem. A recent lines and transformers whose flows will exceed the threshold method, which achieved tractability for reliability-motivated SUBMITTED FOR REVIEW 5

switching, handled this challenge by only allowing a minimal LODF set of switching candidates [11], [23], [24]. The switchable Start (Contingency elements were picked either from a small vicinity of the topology) Base case contingency or the violation. The extensive analysis showed EMS (State estimation) L=1 Stress metrics that this small subset includes almost all quality solutions [11], [23], [24]. In this paper, we use a similar approach by only Stress Select top n switching L=L+1 metrics solutions No relying on a small subset of switchable lines; however, rather Stress reduced with TS? than searching within the vicinity of contingency or violation, LODF Generate switching (Base case we employ the LODF matrix to choose the most effective candidates rank list topology) switching candidates. The potential candidates can be selected based on SSR values Yes by looking at the overloaded line column corresponding to No a contingency. A high negative LODF value is one of the indications of the likely line for switching. Thus, the LODF Is stress level matrix will provide us with a smart and fast method to select acceptable? the switching candidates. Switching is generally classiﬁed into two categories, de- Yes End pending on its timeline: preventive and corrective transmission switching. We consider both of these categories in the next two Fig. 2. The algorithm, proposed in this paper, to reduce the system stress subsections, in the context of system stress reduction. using transmission switching.

A. Preventive Transmission Switching B. Corrective Transmission Switching (CTS) Preventive action in power system operation is taken to As transmission switching can be implemented instan- avoid the adverse consequences of a potential disturbance. The taneously, unlike generation redispatch, which is relatively disturbance may never happen, but the preventative measure slow, more studies have focused on corrective transmission will protect the system against it, should it actually occur. In switching than preventive transmission switching. Corrective this paper, we use preventive transmission switching to reduce transmission switching solutions are identified beforehand, the system’s susceptibility to cascading failures. History shows within the contingency analysis tool, and are ready for imple- that cascading failures depend critically on how the system is mentation [11], [24]. Only after the contingency occurs does loaded, which can be described by the system stress metrics. the operator need to implement the solution. Post-blackout investigations show that, in most cases, the This paper aims to study how corrective transmission system was atypically stressed before the blackout [1]. Had switching can reduce post-contingency stress rather than the the stress of the system been taken care of, the blackout could post-contingency violations. The two are related but are not have been prevented. This can be seen in [8], where the stress the same. This paper examines two hypotheses regarding in the San Diego area was analyzed over different seasons of corrective transmission switching. First, we analyze the post the year and found that on September 8, 2011, and before contingency system stress imposed on the system by the the blackout that happened later on the same day, the system possibility of an N-1-1 event for the system that is already in was atypically stressed. The blackout could have been avoided the N-1 state. The second point of interest for us is to monitor through appropriate preventive actions that reduce the system the ongoing stress level in the system, which is measured stress. in terms of the lines that have already exceeded their con- This paper proposes that preventive transmission switching tingency limits. These overflows should be addressed within should be looked at whenever the system is under atypical a short period, defined by the emergency limit’s maximum stress, beyond a predefined level, to reduce the stress on duration; otherwise, the overloaded lines may trip and initiate the system. We hypothesize that transmission switching may a cascading failure. Thus, transmission switching can either offer a cheap and fast solution, relieve the system stress, be considered corrective concerning the current post-N-1 state and avoid potential cascading failures. Once the system stress or preventive concerning the possibility of an N-1-1 event. has been reduced due to a change in the loading, the line can be switched back if it provides economic benefits. Other alternatives can be implemented as preventive actions, such IV. CASE STUDIES as generation redispatch. However, transmission switching The case studies are conducted on the IEEE 118-bus test can be implemented much faster and is often the cheapest system. We use different loading scenarios at 97%, 105%, option, as it only involves the operation of a circuit breaker. 106%, and 110% of the system’s peak load to generate various Moreover, generation redispatch is often depleted during the stress levels. The nodal loads are uniformly adjusted for all stressed operating scenarios and not available anymore to the the cases, except for the 106% loaded case, where the demand operator. Fig. 2 shows the proposed algorithm for transmission is increased only on select buses (16% in West End (40) and switching in response to atypical stress on the system. An 105% in S. Tiffin (41)). Then, we run an AC optimal power example of an atypically stressed system was shown in Fig. 1, flow for each loading scenario to obtain AC feasible base which led to the Southwest blackout of 2011. case solutions for the analysis. These solutions are fed to the SUBMITTED FOR REVIEW 6

TABLE I THECRITICALITYANDVULNERABILITYSTRESSMETRICSFORTHE IEEE 118 BUS TEST CASE AT 97%, 105%, 110% OFPEAKLOADING.

97% Loading 105% Loading 110% Loading Line or No. Criticality Vulnerability Criticality Vulnerability Criticality Vulnerability Transformer Rank (%) Degree Rank (%) Degree Rank (%) Degree Rank (%) DegreeRank (%) Degree Rank (%) Degree 1 L_26-30 222.94 5 34.2 0 231.31 5 34.18 0 234.28 5 34.19 0 2 L_8-9 155.73 2 32.47 0 190.11 3 32.46 0 192.43 4 32.46 0 3 L_25-27 128.69 1 103.38 2 136.47 1 105.77 2 140.69 1 105.61 1 4 T_30-17 127.94 1 88.13 0 134.95 1 91.44 0 138.38 1 90.2 0 5 T_8-5 116.33 1 60.14 0 119.76 1 62.2 0 121.6 3 61.62 0 6 L_5-11 102.22 1 67.68 0 107.52 1 71.25 0 109.59 1 72.41 0 12 L_5-6 67.68 0 67.68 0 101.76 1 52.17 0 102.74 1 50.75 0 7 L_23-25 100.46 1 114.5 1 100.34 1 112.58 1 99.66 0 112.71 1 8 L_15-17 80.9 0 116.33 1 85.07 0 119.76 1 86.73 0 121.6 1 9 L_32-113 77.38 0 222.94 4 81.51 0 231.31 4 83.29 0 234.28 5 10 L_23-24 77.37 0 155.78 4 77.87 0 190.16 4 77.17 0 192.48 4 11 L_4-5 67.68 0 102.22 1 73.32 0 107.52 2 73.11 0 109.59 2 12 L_12-14 67.68 0 67.68 0 67.68 0 67.68 0 72.58 0 100.25 1

PowerWorld Simulator to calculate stress metrics and examine TABLE II transmission switching impacts. THECRITICALITYSTRESSMETRICSFORTHE 106% LOADED IEEE 118 TESTCASEBEFOREANDAFTERTHEIMPLEMENTATIONOFASINGLE We assume that all lines have their contingency limits at PREVENTIVESWITCHINGACTION (17 SORENSON - 113 DEER CRK). 120% of the normal limits, which can be used for a limited duration of 4 hours. We further assume the emergency limits Criticality Before Criticality After to be at 135% of the normal line limits, which can be used up Line or Switching Switching (L_17-113) No. Transformer to 15 minutes [28]. We acknowledge that the contingency and Rank (%) Degree Rank (%) Degree emergency limits are not necessarily always scaled uniformly 1 L_26-30 239.06 4 120.01 3 2 L_8-9 206.49 5 199.73 2 to the normal limits; however, we make this assumption to 3 T_30-17 139.72 2 71.8 0 simplify the paper’s analysis. We further acknowledge that 4 L_25-27 139.33 1 146.92 1 these limits may change depending on the weather or loading 5 L_38-65 134.44 1 129.86 1 6 L_37-40 129.91 1 129.64 1 scenarios; again, we have neglected such details to simplify 7 T_8-5 121.2 2 119.92 1 the analysis. 8 L_5-11 107.68 1 107.84 1 Table I presents the stress analysis with different loading 9 L_5-6 101.89 1 102.03 1 10 L_23-25 99.64 0 99.09 0 scenarios, as described earlier. The purpose of these stress 11 L_23-24 85.69 0 85.71 0 tables is to demonstrate how loading with different patterns can 12 L_15-17 85.27 0 85.31 0 affect the system stress metrics. Generally, the stress increases 13 L_23-32 84.52 0 87.34 0 14 L_4-5 75.87 0 72.37 0 with the loading; however, the 106% loaded case, with the 15 L_37-39 61 0 98.17 0 non-uniform increase in the nodal loads, is atypically stressed, even beyond the 110% loaded case. This demonstrates that the distribution of the load has a significant impact on system different stress metrics parameters are tabulated in Table III. stress. We pick this atypically stressed case to demonstrate the The results clearly show that a single transmission switching benefits of preventive transmission switching. action can substantially reduce the system stress and avoid a potential cascading failure event. A. Preventive Transmission Switching Figure 3 shows the various stress metrics, comparing the B. Corrective Transmission Switching stress on the IEEE 118-bus case system in terms of maximum One of the highly critical non-radial contingencies, identi- criticality rank, maximum degree, and system degree under fied by PowerWorld Simulator, is 8 Olive - 5 Olive transformer. different loading scenarios. As can be seen, the stress for the For this contingency, the system’s stress is such that at least case with 106% loading is atypically high. Table II shows one of the in-service lines exceeds the contingency limit. the stress on the same case before and after a preventive Therefore, the operator has about 15 minutes to address this switching action is implemented, where 17 Sorenson - 113 issue, or another line will be tripped. The algorithm developed Deer Crk line is opened, but the generation dispatch is not in this paper suggests switching of 15 FtWayne - 17 Sorenson changed. Full stress analysis is performed for pre- and post- line as a corrective action to reduce the system stress to an transmission switching, and the stress comparison for this acceptable level. case is shown in Fig. 5. The Switching Stress Relief indices Fig. 4 compares the stress on the system in terms of 17−113 calculated for this loading condition as SSRd = 6 and criticality rank and degree under different loading scenarios 17−113 SSRr = 199.86. The plot, comparing the number of for the base case, contingency (8 Olive - 5 Olive transformer), lines loaded above both emergency and contingency limits, and corrective transmission switching of 15 FtWayne - 17 under different loading patterns, including after preventive Sorenson line for the IEEE 118-bus test case. The results transmission switching, is shown in Fig. 6. The results of confirm the effectiveness of corrective transmission switching SUBMITTED FOR REVIEW 7 Comparing overall system stress using different stress metrics under two different loading conditions 20 239.6 240 18 231.31 234.28 222.94 230 16 14 220 11 12 8 7 210 9 9 10 8 200 7 7 8 5 5 5 5 6

Criticality Rank (%) 190 4 180 2 170 0

97% 105% 106%* 110% Degree and Number (Number of Brnaches) Loading as a Percentage of Peak Demand * The load is increased only in select buses Criticality Rank Criticality Degree System Criticality Degree System Vulnerability Degree

Fig. 3. Comparison of the stress on the IEEE 118-bus test system in terms of criticality rank, degree, and system degree under different loading scenarios.

TABLE III VARIOUS STRESS MEASUREMENTS FOR THE SYSTEM UNDER DIFFERENT LOADING SCENARIOS, INCLUDINGTHE 106% LOADEDCASEAFTER IMPLEMENTATIONOFONEPREVENTIVETRANSMISSIONSWITCHINGACTION.

Loading % of Emergency limit Contingency limit V rank V degree V Crank Cdegree C peak demand N N Violation Violation 97% 222.94% 5 8 222.94% 4 6 2 4 105% Load 231.31%Base Case 5 Contingency8 231.31%Tranmission4 Swtiching 6 3 4 Rank Degree Rank Degree Rank Degree 106% 90%239.06%96.7 0.25 121.99 239.06%7.2 99.55 0.2 9 100 4 7 106% (PTS) 95%199.73%92.5 0.23 120.88 199.73%6 95.94 0.2 7 100 2 4 100% 88.4 0.2 120.8 8 93.4 0.2 100 110% 105%234.28%88.5 0.25 131.87 234.28%8 93.75 0.2 7 100 3 4 110% 88.2 0.2 126.6 8 92.7 0.2 100

150 9 8 140 135 % 7 130 120.8 121.9 131.8 126.6 6 120 % 120.8 120 5

110 4 100 % 99.5 3 100 CriticalityDegree

Criticality Rank (%)CriticalityRank 95.9 93.4 93.7 2 96.7 92.7 90 92.5 1 88.4 88.5 88.2 80 0 90% 95% 100% 105% 110% The percent of average peak demand (MW)

Base Case Degree Contingency Degree Transmission Swtiching Degree Base Case Rank Contingency Rank Transmission Switching Rank

Fig. 4. Comparison of system stress in terms of criticality rank and degree under different loading scenarios for the base case, contingency case (an outage of 8 Olive - 5 Olive Transformer), and post corrective transmission switching of 15 Ft. Wayne - 17 Sorenson. in reducing the post-contingency system stress, close to the preventive and corrective measure, to reduce the system stress. normal operation levels. LODF sensitivities were used to generate a relatively small subset of quality switching candidates and achieve compu- V. CONCLUSION tational tractability for the transmission switching algorithm. Those candidates were then tested for effectiveness until a System stress metrics are recently developed to provide practical solution was found or the list was depleted. The insights into the susceptibility of the system to cascading simulation studies on the IEEE 118-bus system conﬁrmed the failures. The metrics include measures of the criticality of efﬁcacy of the method. A single transmission switching action contingencies and vulnerability of the transmission elements was able to reduce the system stress to the normal levels to overloads after contingencies. Building upon those metrics, substantially. This implies that system operators should look at this paper introduced two new metrics to measure the system’s transmission switching as a potentially useful tool to prevent criticality and vulnerability. All of these metrics can be quickly cascading failures when the system is atypically stressed. calculated via the outputs of the contingency analysis tool Other alternative actions, such as generation redispatch, are or through LODFs. Furthermore, the paper investigated the substantially more expensive and may also not be available possibility of employing transmission switching, both as a SUBMITTED FOR REVIEW 8 Comparing the pre and post preventative transmission switching system stress for fixed load demad 239.6 20 240 [9] Ming Ni, J. D. McCalley, V. Vittal, and T. Tayyib, “Online risk-based IEEE Transactions on Power Systems 230 security assessment,” , vol. 18, 15 no. 1, pp. 258–265, Feb 2003. 220 11 199.78 [10] C. M. Davis and T. J. Overbye, “Multiple element contingency screen- 210 10 9 ing,” IEEE Transactions on Power Systems, vol. 26, no. 3, pp. 1294– 200 10 7 1301, Aug 2011. 190 5 [11] X. Li, P. Balasubramanian, M. Sahraei-Ardakani, M. Abdi-Khorsand, 180 3 5

Criticality Rank (%) K. W. Hedman, and R. Podmore, “Real-time contingency analysis 170 with corrective transmission switching,” IEEE Transactions on Power 160 0 106%* 106%* after Preventative TS Systems, vol. 32, no. 4, pp. 2604–2617, July 2017. Loading as a Percentage of Peak Demand [12] H. M. Merrill. ”Private Conversation”, ”2018”. * The load is increased only in select buses [13] G. Valiant and T. Roughgarden, “Braess’s paradox in large random graphs,” Random Struct. Algorithms, vol. 37, no. 4, pp. 495–515, Dec. Criticality Rank Criticality Degree

Degree Degree and Number (Number of Brnaches) 2010. [Online]. Available: http://dx.doi.org/10.1002/rsa.v37:4 System Criticality Degree System Vulnerability Degree [14] J. G. Rolim and L. J. B. Machado, “A study of the use of corrective switching in transmission systems,” IEEE Transactions on Power Sys- Fig. 5. The stress comparison of pre and post transmission switching for tems, vol. 14, no. 1, pp. 336–341, Feb 1999. the 106% loaded IEEE 118 bus test case. The rank and degree in this chart [15] Y. Sang and M. Sahraei-Ardakani, “The Interdependence between Trans- represent theNumber single highest of Lines value forViolating the system. Various Line mission Switching and Variable-Impedance Series FACTS Devices,” Limits IEEE Transactions on Power Systems, vol. PP, no. 99, pp. 1–1, 2017. [16] P. A. Ruiz, A. Rudkevich, M. C. Caramanis, E. Goldis, E. Ntakou, and Violating Line Contingency Limits Violating Line Emergency Limits C. R. Philbrick, “Reduced MIP formulation for transmission topology control,” in 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Oct 2012, pp. 1073–1079. 4 [17] K. W. Hedman, S. S. Oren, and R. P. O’Neill, “A review of transmission switching and network topology optimization,” in 2011 IEEE Power and 2 3 2 3 Energy Society General Meeting, July 2011, pp. 1–7. 7 [18] M. Abdi-Khorsand, M. Sahraei-Ardakani, and Y. Al-Abdullah, “Correc- Number Number Lines of 4 4 4 4 tive transmission switching for N-1-1 contingency analysis,” in 2017 IEEE Power Energy Society General Meeting, July 2017, pp. 1–1. 97% 105% 106%* 106% (PTS) 110% [19] California ISO, “Minimum effective threshold report,” March, 2010. Loading as a Percentage of Peak Demand * The load is increased only in select buses [Online]. Available: http://www.caiso.com/274c/274ce77df630.pdf PTS: Preventative Transmission Switching [20] ISO-NE, “ISO New England operating procedure No. 19: transmission operations,” June, 2016. [Online]. Avail- Fig. 6. The plot compares the number of lines, violating both emergency able: https://www.iso-ne.com/static-as-sets/documents/rules proceds/ and contingency limits under different loading scenarios, including the post operating/isone/op19/op19 rto final.pd preventive transmission switching. [21] ——, “Transmission constraint relaxation parameter revision,” October, 2012. [Online]. Available: https://www.caiso.com/Documents/ StrawProposal-TransmissionConstraintRelaxationParameterChange.pdf [22] PJM, “Switching solutions,” October, 2016. [Online]. when the system is highly stressed. Available: http://www.pjm.com/markets-and-operations/etools/oasis/ system-information/switching-solutions.aspx [23] P. Balasubramanian, M. Sahraei-Ardakani, X. Li, and K. W. Hedman, ACKNOWLEDGMENT “Towards smart corrective switching: analysis and advancement of PJM’s switching solutions,” IET Generation, Transmission Distribution, The authors would like to thank Dr. Hyde Merrill for vol. 10, no. 8, pp. 1984–1992, 2016. his careful review and detailed feedback. We also thank Dr. [24] M. Sahraei-Ardakani, X. Li, P. Balasubramanian, K. W. Hedman, and M. Abdi-Khorsand, “Real-time contingency analysis with transmission Marc Bodson for providing us with the PowerWorld Simulator switching on real power system data,” IEEE Transactions on Power license. Systems, vol. 31, no. 3, pp. 2501–2502, 2016. [25] Y. C. Chen, S. V. Dhople, A. D. Dom´ınguez-Garc´ıa, and P. W. Sauer, “Generalized injection shift factors,” IEEE Transactions on Smart Grid, REFERENCES vol. 8, no. 5, pp. 2071–2080, Sept 2017. [26] S. A. Sadat, D. Haralson, and M. Sahraei-Ardakani, “Evaluation of vari- [1] H. M. Merrill and J. W. Feltes, “Cascading blackouts: Stress, vulnera- ous techniques to warm-start a successive linear programming algorithm bility, and criticality,” 2016. for solving the IV ACOPF,” in IEEE Power & Energy Society General [2] U.S.-Canada Power System Outage Task Force, “Final report on the Meeting (PESGM). In Proceedings, 2018, pp. 1–5. august 14, 2003 blackout in the United States and Canada,” April, 2004. [27] P. Balasubramanian and K. W. Hedman, “Real-time corrective switching [3] NERC, “Standard TPL-001-4 - transmission system planning perfor- in response to simultaneous contingencies,” Journal of Energy Engineer- mance requirements”, in “reliability standards for the bulk electric ing, vol. 141, no. 1, p. B4014003, 2015. systems of North America,” 17 August 2016. [28] North American Electric Reliability Corporation (NERC), “System [4] F. C. Schweppe and E. J. Handschin, “Static state estimation in electric operating limit definition and exceedance clarification,” 2014, pp. 1–10. power systems,” Proceedings of the IEEE, vol. 62, no. 7, pp. 972–982, July 1974. [5] T. E. Dy Liacco, “The adaptive reliability control system,” IEEE Transactions 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 versus computation time in IV-ACOPF with socp initialization,” in IEEE International Conference on Probabilistic Methods Applied to Power Systems (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 of susceptibility to cascading blackouts,” in 2017 IEEE Power and Energy Conference at Illinois (PECI), Feb 2017, pp. 1–5.