Decision Tree Assisted Controlled Islanding Pohon keputusan untuk membantu kontrol Islanding Abstrak - pengontrolan islanding mengacu pada kontrol pemisahan dari sistem tenaga interkoneksi ke daerah elektrik yang terisolasi. Tujuan dari makalah ini adalah untuk mengembangkan islanding yang dikendalikan secara adaptif sebagai komponen sistem strategi kontrol daya darurat. Ada dua aspek utama pengontrolan islanding : 1) di mana island dan island dan 2) kapan menjadi island ?. ?. Dibantu oleh pendekatan keputusan pohon (DT), makalah ini berusaha untuk mengatasi aspek "ketika menjadi island ". ". Sebuah alat berbasis pohon keputusan diusulkan untuk mengenali kondisi yang ada dalam sistem yang menjamin kontrol islanding. Sebuah sistem 29-generator, 179-bus 179-bus digunakan untuk mendemonstrasikan mendemonstrasikan tool ini. Data simulasi digunakan untuk melatih DTs, dan kinerja online DTs kemudian dievaluasi sebagai bagian dari strategi kontrol islanding . Indeks istilah - Pengendalian islanding, pohon keputusan, pembelajaran mesin, stabilitas sistem daya R-Rdot daya R-Rdot relay, relay, self healing , sistem perlindungan khusus.
I. PENDAHULUAN Ketersediaan biaya murah dan keandalan listrik dicapai melalui modem sistem tenaga interkoneksi. Misalnya kegagalan Cascading terjadi karena serangkaian peristiwa probabilitas yang rendah. Beberapa relay pelindung konvensional yang dirancang untuk melindungi peralatan lokal dari kerusakan selama gangguan tetapi tidak fokus pada menjaga kelangsungan seluruh sistem pelayanan. Islanding pelayanan. Islanding tidak terkontrol mengacu pada proses dimana sistem listrik interkoneksi dibagi ke dalam island - island yang tidak direncanakan sebagai akibat dari gangguan yang parah [1]. Pemulihan sistem tidak dapat dijamin oleh pembentukan island - island tersebut. Hal ini diinginkan untuk mengontrol
pembentukan island-island ini, dengan memuat dampak gangguan pada wilayah tertentu dari jaringan sedini mungkin Pengendalian islanding disajikan dalam [2], sebagai strategi untuk memisahkan gangguan besat
sistem daya dalam self-
healing island yang ditandai karekteristik dengan minimal ketidakseimbangan beban generator dan generator slowly-coherent. Dalam strategi ini, khusus R-Rdot relay [3] yang terletak di saluran minimum cut-set antara
island’s
yang
direncanakan dan dilengkapi untuk merespon variasi lokal di saluran reisitansi semu. Relay utama R-Rdot, ketika dilengkapi, merespon gangguan pengaturan resistensi saluran semu, dan dengan demikian dapat menciptakan Islands yang direncanakan oleh cross tripping saluran kritis lainnya. Pengendalian islanding seperti yang dijelaskan dalam [2] memiliki dua aspek utama yang akan diteliti: 1) di mana island dan 2) kapan menjadi island ?. Pendekatan [2] dikembangkan lebih lanjut dalam makalah ini dengan mengusulkan pohon keputusan (DT) alat untuk membantu kontrol islanding yang berusaha untuk mengatasi "kapan" aspek pengontrolan islanding . Pengontrolan islanding akan dimulai ketika hanya keputusan ketidakstabilan global didukung oleh indikator stabilitas sistem lokal.
A wide-area measurement system (WAMS) [1] can lead to increased situational awareness, and improved observability and controllability. In the context of WAMS, it is useful to mention the Emergency SIME method [4] that starts acting after the disturbance inception, to prevent loss of synchronism. The system status is 'predicted' by decomposing the multi-machine dynamics into candidate singlemachine-equivalents and further analyzing their power angle curves. Taking a machine learning approach, this paper proposes an online transient stability assessment (TSA) tool to detect when controlled islanding is warranted in a disturbed power system. This tool can arm/inhibit strategically located RRdot/out-of-step relays' response to the local dynamics. The goal of such
controlled islanding is to obtain self-sustaining islands that have potential for swift recovery. This strategy is part of the last line of defense against a potential system blackout. Controlled islanding contains the impact of the disturbance within the islands created. Subsequent restorative control actions (generator run back in generation rich islands and load shedding in load rich islands) are required to improve frequency and voltage stability. Once all the islands have recovered from the initial disturbance, the tie-lines can be brought back into service in a controlled manner, leading to total system recovery. In effect, the proposed approach to intelligent Islanding is a progression from WAMS to WACS (wide area control system, [5]).
Sebuah sistem pengukuran wilayah yang luas (WAMS) [1] dapat menyebabkan peningkatan kesadaran situasional, dan meningkatkan cara pengamatan dan cara pengendalian pengendalian. Dalam konteks WAMS, hal ini berguna untuk menyebutkan metode SIME Darurat [4] yang mulai bertindak setelah awal gangguan, untuk mencegah hilangnya sinkron. Status sistem 'diprediksi' dengan menguraikan dinamika multi-mesin ke calon tunggal-mesin-setara dan selanjutnya melakukan analisis kurva sudut daya mereka.
The paper is divided into eight sections. Section II introduces controlled islanding as an emergency control strategy for severely disturbed power systems. Some of the previous research on the application of DTs in power systems is introduced in Section III Sections IV and V examine the preliminary issues associated with the application of DTs to predict synchronous instability in a system. The islanding tool is demonstrated on a large power system in Sections VI (offline training) and VII (online performance). The intention is to provide a proof of concept only. Actual implementation of this idea on realistic systems is expected to raise other Issues such as communication delays and measurement uncertainty that are beyond the scope of this paper. Section VIII provides the conclusions. II. CONTROLLED ISLANDING USING DECISION TREES Angular stability is a classic power system stability problem, and there exist many effective techniques to assess and insure it. Decentralized control responding to
local variations of system parameters is a first choice for power system protection engineers, for reasons of low associated costs and simplicity of implementation. Additional reliability requirements call for mul-
Uncontrolled islanding is a spontaneous phenomenon and typically starts from the electrical centers in a power system [7]. One of the primary objectives of controlled islanding is to block some electrical centers and initiate islanding at alternative locations. The alternative locations correspond to the minimum cut-set tie lines between the desired islands for a particular scenario. In this paper, slow coherency between generators is used as an aggregation criterion, (along with minimum load-generation unbalance) to form all the possible planned islands. Slowly coherent machine groups are characterized by their tight coupling, while the interconnections between such groups are relatively weaker [2]. If the weaker connections are opened before the perturbation can travel from one part of the system to another, the disturbance may be effectively contained within a limited region. A critical component of any special protection system for adaptive controlled islanding is an online transient stability assessment tool. In this context, it is proposed to evaluate the power system online to predict system separation with the help of machine angle data (Fig. 1). DTs for the system are generated in the form of offline precalculated logical paths. These DTs serve as a statistical alternative to the deterministic system models, If a large number of contingencies are analyzed, and DTs generated offline, these trees can be quickly accessed in real time for prediction. With the help of sensory data, the condition of an evolving system can then be traced on the branches of a DT and rapid response, if warranted, may be initiated [8], HI. DECISION TREES BASED SECURITY ASSESSMENT In this section, the application of DTs to system security assessment is reviewed. Production grade artificial intelligence tools have not been applied to the field of
online TS A [9]. However, considerable research has been done in applying machine learning based classifiers to stability assessment in power systems [10]-[15]. The application of DTs to stability assessment in power systems was given in [11], in which a set of decision rules was built offline for transient stability assessment. The application for an inductive inference method to obtain the set of decision rules for a system is given in [11], [16] and an analytical basis for splitting the nodes of a tree, information measures and attribute selection during training are discussed. Initially, DTs were suggested for preventive transient stability assessment. In other words, given the steady state operating point of the system, the critical clearing time for any fault in the system was to be determined. In [13], a detailed case study on the French EHV system was presented in which randomized training database generation was introduced to stress the need for richness of the training samples, Pre-contingency parameters were employed as attributes, in this study to determine the transient behavior of the system. In [17] and [18], DTs were used for transient stability prediction. Training samples were derived from simulations of disturbed power system. Rotor angles and velocities, obtained from a time window immediately after a fault was cleared, were used to predict the angular stability of the generator. This paper adopts a similar approach of using generator angles and velocities as predictors. However, [17] did not examine the impact of the spacing of the training data points within a simulation on its prediction capability. DTs were also used to predict the loss of synchronism in the Pacific AC Intertie (PACI), given the variation of the apparent line resistance in the center of the line [19]. DTs have also been proposed to set the decision boundaries in the R-Rdot space for loss of synchronism on the PACI [20].
IV. DECISION TREES
APPLICATION ISSUES
—
A complete description of the theory of DTs appears in [16], [21 ]-[24], The goal in any supervised machine learning problem is the following: Given a set of learning examples consisting of input-output pairs, is there an underlying cause-effect relationship? Can this relationship be used further to predict the output(s) in the presence of unseen inputs? The inputs to the problem are called predictors, while
the output in the case of a DT classifier is symbolic. The DTs used in this study are applied as a special protection system for dynamic security. Angular instability manifests itself in the electromechanical states of the system. It was also found from simulations that the transient stability behavior of a power system was best characterized by generator angles and velocities. Generator angles and velocities were also found to be sufficient to understand the degree to which a stable machine is disturbed. Therefore, the DT predictors were selected to be the generator angles and rotor velocities of a severely disturbed power system, and the output is the decision whether the system is potentially stable or unstable. A DT is a classifier in high dimensions. Each internal node in the tree tests the value of a predictor while each branch of the tree represents the outcome of a test. The terminating nodes, also referred to as leaf nodes, represent a classification. The number of predictors, used in the classification problem, indicates the dimension of the problem. Associated with each decision (leaf) of the tree is the confidence of the decision. This is simply a measure of the ratio of the particular class to all the classes present in the dataset for that node. The main strength of a DT is its readability, as shown in Fig. 2. Such a tree may be interpreted as a series of if-then statements that use the values of the predictors to arrive at a classification. This indicates the relevant predictors for a particular class of the output. To classify the training data (into potentially stable and unstable cases), it is necessary to apply a sequence of rules to split the dataset. One splitting
criterion, referred to as the chi-square automatic interaction detector (CHAID) algorithm [25], utilizes the chi-square test to evaluate all possible ways of splitting a dataset. An alternative tree building algorithm is the CART algorithm (classification and regression trees) [26]. In the application of the DT to predict the final state of an evolving power system in real time, the measures of success are slightly different. It is expected that a DT will ultimately recognize (classify) an unstable generator swing curve as unstable.
How soon it performs the classification, is a measure of its success. It is stressed here that the DT by itself does not physically island the system. Strategically located RRdot/out-of-step relays are armed by the DT, to trip independently in response to local sensory signals. The relay locations correspond to the weak links connecting groups of coherent machines. A disturbance takes time to reach these cut-set lines, and the DT must arm/disarm the relay within this time window. A late recognition of potentially unstable swing curves is referred to as & false dismissal. A false alarm means that a stable swing curve is mis-classified as unstable. An exacerbation of the critical state of a dynamically evolving system can occur only if a false alarm of the DT is followed by a false tripping of the corresponding R-Rdot/out-of-step relay, V. DECISION TREES
TRANSIENT I NSTABILITY PREDICTION
—
In experiments on a sample six-machine system, key issues about the training of DTs were determined. The objective of these experiments was to examine the importance of the composition of the training data on the online performance of the DTs. The absolute angles of all six machines and their angular velocities were used as predictors. The transient stability simulations on the system were carried out using the PowerTech software TSAT 5.0 [27]. All the DTs in this paper were built using the Enterprise Miner 5.2 module contained in the statistical analysis software, statistical analysis system (SAS) [28], The splitting criterion used by the SAS Enterprise Miner is the chi-square test. Three-phase bolted faults (of different clearing times) were simulated on all the buses of the power system. Once a simulation was complete, it was classified as stable or unstable. From each simulation, n data points are selected for training. The distribution of the data points within the time window of simulation was found to be critical, affecting the predictability of the DT. Two options were considered for the distribution of the points spacing. In exponential spacing, the points
exponential and equal
—
are exponentially spaced, with most of the points located at the start of the window (Fig. 3). Thus, majority of the training data consists of rotor angles and velocities of small magnitude. The alternative is to space the points equally within the simulation time window. Some conclusions were drawn from the tree building exercises using a sample sixmachine test system. When the training data were obtained by simulating three-phase faults uniformly on all the buses of the system, the DTs obtained can be considered unbiased with respect to any particular bus/region of the system. Such a globally trained DT, while a good indicator of the overall stability of the complete system did not respond satisfactorily to events in a sensitive portion of the system. DTs focused on a particular area/bus or kind of event in the power system would better complement the response of such a globally trained unbiased tree. Further, it was confirmed that the more the training data, the higher is the general confidence level of the tree. Enriching the training data by including disturbed (yet stable) machine angles also decreased the occurrence of false alarms. The distribution of the training data within the simulation time window also has a significant effect on the response of the tree. A DT trained on data that is exponentially chosen towards the start of the simulation window gives an earlier prediction than a tree trained on data spaced equally within the simulation time window. This is because the trained tree classifies an evolving power system, while its individual machine angles are small in magnitude. Finally, the criteria for controlled islanding must be defined clearly. Controlled islanding is not proposed as the answer to all instability problems in the system. For instance, controlled islanding need not be initiated for plant mode instability. From numerous simulations on the test beds, it was observed that slow coherent generators tended to separate from the rest of the system in well defined and consistent groups. Each critical group of machines separating from the system corresponds to a particular mode of instability. The DT must be trained accordingly to recognize only those modes of instabilities that are likely to result in uncontrolled system separation. VL DECISION TREE TRAINING DEMONSTRATION
A 29-machine, 179-bus test system is employed to demonstrate the DT based controlled islanding strategy. There are two aspects of the illustration. •
Offline processing of simulation data for training the DT.
•
Online performance of the trained DT.
The test bed system, shown in Fig. 4, consists of 29 machines modeled in detail along with their turbines and exciters, 179 buses and three HVDC lines, modeled as load injections at the appropriate buses. The system is loosely based and inspired by the WECC system in the western United States. Possible island boundaries (shown in Fig, 4) were calculated using slow coherency information along with the minimum load generation unbalance obtained from the base case. Some of the relevant buses and test cases are indicated in Fig. 4, for clarity of the demonstration. The objective is to create DTs for this system, which can detect an impending loss of synchronism among generators with the potential to cause systemwide failure. The 179-bus system at base case loading was subjected to three phase bolted faults at all 179 buses (one at a time), with the fault clearing time ranging from 0.05 to 0.29 s (total 4550 simulations). The disturbed system was simulated for 5 s, at the end of which angular stability in the system was investigated. Conventional protection was not represented within the simulations, and the possibility of outages dependent on initiating disturbances was not examined. The simulation was labeled as stable if all the machines remain in synchronism (3986 simulations). The 3986 stable simulations were further examined and classified into "disturbed stable" simulations and "extremely stable" simulations. The definition of "extremely stable" is a case in which at least 80% of the generators remain (qualitatively) relatively undisturbed. This is a fuzzy definition based on numerous tests using the test system. A relatively
undisturbed dynamic response of a generator rotor angle is of the order of
approximately 5° or less. The term "disturbed stable" refers qualitatively to the stable cases that do not qualify as "extremely stable". There are 2743 "extremely stable" simulations. In the remaining 1243 "disturbed" simulations, the majority of the machines exhibit oscillations, while remaining in synchronism. The objective is to train the tree on a wide variety of stable simulations. Fig. 5 contrasts "disturbed stable" and "extremely stable" cases. If isolated groups of machines exhibited loss of synchronism (i.e., plant mode instability), the simulation was discarded (475 simulations). If the system spontaneously separated into clearly distinguishable groups of generators which have previously been identified as coherent, it was labeled as unstable, i.e., fit for islanding (89 simulations). All training data points obtained from these 89 simulations were labeled as unstable when a global DT was being trained The 89 unstable
simulations were further examined to see which islands were separating. Accordingly, they were labeled with respect to the island separating from the system. It was seen that in 42 (out of 89) simulations, the system separated into three islands (East, South, North). In 44 (out of 89) simulations, only the East island separated from the rest of the system. The South island was observed to separate in only simulation, while in the remaining two simulations, the North island separates. The structure of the training data set is given in Fig. 6. When a DT for a particular island was being trained, the unstable training data were obtained from simulations where the particular island was observed to separate. For instance, when a DT for the South island was being trained, data points labeled unstable are obtained from 43 simulations (42 4-1). During each simulation, the absolute rotor angles for the 29 machines present in the system were collected. The rotor angle
velocity for each machine was then approximated using a backward difference approximation
where UJ is rotor angle velocity of the generator, 6 is absolute angle of the generator, and At is sampling time interval. The sampling interval was chosen to be one cycle (i.e., 1/60 s in a 60-Hz system). The larger the sampling time interval, At, the greater will be the error in approximating the rotor angle velocity of the generator. The absolute rotor angles along with the velocities of the machines were used as predictors of a "target" variable, which can hold binary values of stable and unstable. Thus, there were 58 predictors available to classify one target variable. While this seemingly increases the dimension of the classification problem to 58, it is advisable to supply the tree with a maximum number of predictors during the training process. A trained DT relies on a relatively small number of predictors to accomplish the task of classification effectively. Hence, the DT achieves economy of measurement in the sense that it filters out the irrelevant predictors (measurements). Table I summarizes the ten DTs trained for this network, There were three DTs trained for each island {North, South, East), in addition to a global DT, that predicts the formation of any/all of the three islands as a result the disturbance. The training data composition for each tree is given by the ratio of stable data points to unstable ones. Reducing the amount of unstable training data results in delayed prediction of truly unstable contingencies. The stable points in the training data for all trees, except E9(Lsld2, N9(Lsld2, and S90_sld2 were derived from the 'disturbed stable' simulations. For E90_sld2, N9G_s1d2, and S90_sld2 trees, the stable data points are obtained from both "extremely stable" and "disturbed stable" simulations. Each DT was thus trained with a different composition of data, to compare their classification performance. It was observed that the DTs relied on angular velocities more than the absolute angles, to accomplish early prediction of the system tendency to spontaneous islanding. The predictors used by the trained tree to classify new observations are also tabulated in Table I. VII. O NLINE PERFORMANCE AND R OBUSTNESS In this section, the online performance of DTs for the 29 generator test system is
presented. The test system was subjected to various contingencies, and the ability of the DTs to predict the need for controlled islanding with accuracy (minimum fa he alarms) and foresight (minimum false dismissals) was examined. The DTs were trained from simulations carried out on the test system at base case loading. Further, the pre-fauk s; topology was not changed during the training period. To determine the robustness of the trained DT, the test system wa jected to a wide variety of disturbances, not "seen" by the DT during training. When the DT based islanding warning mechanism declared a particular contingency7 unstable and in need for "islanding in a particular configuration", the R-Rdot/out-of-step relays on relevant tie lines were armed. Local variations of the apparent line resistance caused the RRdot/out-of-step relays to trip, creating the desired islands. The relevant tie lines to create the desired islands (and hence the locations of the relays) are lines 99-84 and 7-28 for the East island, lines 99-84, 119-132 and 119-134 for the North island, and lines 119-132, 119-134 and 7-28 for the South island. The setting of the R-Rdot/outof-step relays is not the focus of this paper; hence the physical tripping of tie lines to create the islands was done arbitrarily. Conventional protection was not considered in the simulations, and outages dependent on an initiating event were not studied. Additionally, transfer tripping was been modeled, and all the tie-line tripping was done in response to variations in the apparent line resistance. A wide variety of contingencies (not seen by the DT during its training) was simulated on the indicated test system. Two cases are selected as illustrations of the robustness of the DT. •
Case I: Single circuit from bus 7 to bus 28 tripped.
•
Case II: HVDC tie line from bus 60 to bus 71 tripped. Case I: In this case, the
test system at base case loading was subjected to a line tripping between bus 7 and bus 28. The system was simulated, and it was observed that this event caused global instability and the East island starts to separate from the system after 2.2 s. The ability of the DTs to predict this separation was investigated. From Table I it can be seen that three DTs focus on predicting the separation of the East island
E50, E90, and E90_sld2. In addition,
—
A50 focuses on the potential separation of the system into any islanding
configuration. For this event all the four abovementioned trees predicted islanding by giving a trip = 1 signal. The remaining trees expectedly gave a trip = 0 signal for this event. In Fig. 7, the response of four DTs is shown. Further information about the response of these DTs can be obtained from their confidence levels. Every
tirne the DT is given inputs, it gives a decision with a corresponding confidence level The earliest islanding warning (at 0.4 s) came from E9G_sld2 tree and it remained high for the whole duration of the simulation (i.e. up to 2.29 s) with a confidence of 98.7% throughout. The latest warning came from the tree A50 at 0.66 s with a confidence of 53.5%. At 0.66 s, all four DTs gave a trip = 1 decision, and the decision to arm the R-Rdot/out-of-step relays was taken at this juncture. An interesting feature of the tree A50 was that although it gave a trip = 1 signal at 0.66 s, the confidence of 'trip = 0' decision fell from 95.5% to 58.5% at 0.51 s. It may be concluded that the tree A50 recognizes the formation of the East island with low confidence. Tree E50 gave a trip = 1 decision at 0.5 s with 97.6%. The false dismissal by tree E50 from 1.88 s to 2.20 s, was given with a confidence of 75%. Tree E90 gave a trip = 1 decision at 0.41 s with 88.6%, which improved to 99.5% at 0.51 s. The false dismissal by this tree from 1.86 to 2.20 s was given with a confidence of 52.9%. From the above discussion, it is clear that the confidence of a particular decision must also be monitored to interpret the decision correctly. A localized DT must give its decisions with high confidence, to be acknowledged by the islanding warning mechanism. A global DT, on the contrary, may show persistent low confidence while recognizing localized events. The R-Rdot/out-of-step relays placed on the relevant cut-set lines (line 99-84 in this case) were armed at 0.66 s. The remaining R-Rdot/out-of-step relays on other lines were disarmed to prevent the formation of the North and South islands. It was observed that there is a clear change in line resistance between 1.5 and 2 s. The RRdot/out-of-step relay is expected to interpret this change as an unstable swing in line resistance, and accordingly, the line 99-84 was tripped at 1.8 s. This results in the formation of East island, electrically isolated from the rest of the system. The intention
of islanding is to confine the disturbance to a particular island, as well as to prevent the spread of the disturbances. From Fig. 8, it can be observed that the generators 70, 43, and 118 (all outside the East island) remain in synchronism as a result of the formation of East island. A significant improvement in the voltage profile was observed on bus 39 (Fig. 9). Bus 39 is located in the southwest region of test system (see Fig. 4). The thicker lines correspond to the voltage of the bus, when the tie-lines were tripped to form the islands. The thinner lines correspond to the voltage of the bus if controlled islanding had not been initiated.
Case II: In this case an HVDC de-line was tripped. One HVDC tie line in the test system is modeled as load injections at the appropriate buses i.e. negative load at Bus 60 and corresponding positive load at Bus 71. The total dc power flow (negative load at Bus 60) is 2771 MW. The effect of tripping this line is to create a severe contingency situation that can potentially lead to spontaneous loss of synchronism between the machines in the system. It was observed that all the machines in the system start to lose synchronism 1.5 s, after the HVDC tripping. From Fig. 10, the earliest islanding warning (trip = 1) was obtained from E90_sld2 (at 0.699 s) followed by N90_sld2 (at 0.719 s) and S90_sld2 (at 0.759 s). A50, which was trained to predict any kind of islanding in the system, gave a trip = 1 decision at 1.23 s. The confidence level of E90_sld2 fell from 99.5% to 98.4% when it gave its trip = 1 decision at 0.699 s. The confidence level of N90_sld2 fell from 100% to 98% when it gave a trip = 1 decision at 0.719 s. The confidence level of S90_sld2 fell from 99.8% to 99.6% when it gave a trip = 1
decision at 0.75 s. The confidence of A50 for a trip
—
1 decision at 1.23 s was
97.7%. In general, all the DTs had a high confidence level for whatever decision they gave, for this contingency. The lowest confidence level was shown by the E50 tree (99.3% to 92% when it changed decision from trip = 0 to trip = 1 at 1.159 s), and E90 tree (98.8% to 92.8% when it changed decision from trip = 0 to trip = 1 at
1.21 s). Once the islanding warning was obtained from all the DTs, islanding was initiated by arming the R-Rdot/out-of-step relays placed at the strategic tie lines: 99-84, 7-28,119-132, and 119-134. The first major disturbances were seen on line 99-84 at 1.5 s, followed by lines 119-132 and 119-134 at 2 s. Line 99-84 was tripped at 1.5 s and lines 119-132 and 119-134 were tripped at 2.0 s. Line 7-28 was tripped at 2.5 s. As a result of the controlled islanding the effect of the disturbance was restricted, and distant generators and buses were less affected. The effect of controlled islanding may be observed from the voltage magnitude profile of bus 156 (located in the East island) in Fig. 11. The thicker lines correspond to the voltage of the bus, when controlled islanding was initiated. The thinner lines correspond to the voltage of the bus in the absence of controlled islanding. Without the tripping of line 99-84 and 728 to form the East island, the voltage on Bus 156 would have sagged to 0.5 p.u. after 1.8 s as a result of the HVDC tripping. In Fig. 12, it is evident that machines 148,40 and 144 located in the South island remain in synchronism as a result of controlled islanding. The tripping of the HVDC line was, thus, prevented from affecting the synchronous stability of generators located in the East and South islands. An important point to be noted here is that due to the HVDC tripping, 2700 MW of incoming power to the South island was disrupted. Therefore, South
island is expected to be load rich, and further load-shedding programs, beyond the scope of this paper, must be initiated [2], Vm. CONCLUSIONS The contribution of this paper is the application of a tool to detect cascading degradation of power system security at an early stage using machine learning via DTs. The training process to obtain various kinds of DTs for a large interconnected power system has been demonstrated. A 29-generator, 179-bus test system was used to simulate various kinds of contingencies that lead to stable and unstable scenarios. The training data extracted from each simulation were exponentially distributed in
time within the time horizon of the simulation. While each DT was supplied with the rotor angles and velocities of all the 29 generators in the system as predictors, it was found that the final trained DT was able to filter out many predictors as irrelevant to its task of classification. Thus, a trained DT was able to discriminate between relevant and irrelevant measurements. The DT relied primarily on rotor angle velocities rather than the absolute rotor angles, for the task of early prediction of impending instability. The simulation data were used to train ten differem kinds of DTs offline. Some of the DTs were trained to predict pessimistically, by training with "extremely stable*' simulation data. The result is early detection of truly unstable contingencies and increased possibility of false alarms. Other DTs. in contrast, were trained to be cautious and hence, their decisions were more "reliable". A combination of a cautious global DT and a 'pessimistic* localized DT was used to rninimize the possibility of false alarms as well as effectuate early and accurate islanding decisions. Such a controlled islanding algorithm appears to exhibit robustness [29] in the sense that all contingencies, seen and unseen during training were correctly classified. The DTs developed in this paper, were trained on simulations on a particular pre-fault operating point. As the operating point changes, a new set of DTs may be required for robust security assessment. The rate of "refreshing" DTs would ultimately depend on the sensitivity of the DTs to changes in operating conditions. This kind of a special protection system is effective in particular interconnected systems that show consistent slow coherency between groups of machines. The islands formed as a result of this mechanism and approach, are expected to be selfhealing and healthy. This is desirable in the face of an alternative scenario of large scale failure. The DT-based islanding tool, if implemented, would rely heavily on wide-area phasor measurements, A key feature of the DT training process is the resultant
selectivity
and
discrimination
between
relevant
and
irrelevant
measurements. Thus, only important generator angles and rotor velocities are required by the islanding tool to predict the need for controlled islanding. The readability of DTs sheds more light on the contribution of different machines to spontaneous system-wide separation. Discrimination between a global DT and a localized DT is also especially relevant in the context of implementing this idea in a
large power system.
