Synchrophasor Data Baselining and Mining for Online Monitoring of ...

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Synchrophasor Data Baselining and Mining for Online Monitoring of Dynamic Security Limits Anissa Kaci, Innocent Kamwa, Fellow, IEEE, Louis-A. Dessaint, Fellow, IEEE, and Sébastien Guillon, Senior Member, IEEE

Abstract—When the system is in normal state, actual SCADA measurements of power transfers across critical interfaces are continuously compared with limits determined offline and stored in look-up tables or nomograms in order to assess whether the network is secure or insecure and inform the dispatcher to take preventive action in the latter case. However, synchrophasors could change this paradigm by enabling new features, the phase-angle differences, which are well-known measures of system stress, with the added potential to increase system visibility. The paper develops a systematic approach to baseline the phase-angles versus actual transfer limits across system interfaces and enable synchrophasor-based situational awareness (SBSA). Statistical methods are first used to determine seasonal exceedance levels of angle shifts that can allow real-time scoring and detection of atypical conditions. Next, key buses suitable for SBSA are identified using correlation and partitioning around medoid (PAM) clustering. It is shown that angle shifts of this subset of 15% of the network backbone buses can be effectively used as features in ensemble decision tree-based forecasting of seasonal security margins across critical interfaces. Index Terms—Baselining, clustering, data mining, dynamic security assessment (DSA), partitioning around medoids (PAM), phasor measurement unit (PMU), random forest (RF), security monitoring, synchrophasor, system reliability.

I. INTRODUCTION

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YSTEM security is the main asset and responsibility [1] of a system operator. Even when everything is in a normal state throughout the grid, the operator should always be able to determine whether the state is secure or insecure, in order to take preventive security control action in the latter case [2]. In practice, many factors can move the system out of its security boundaries [3]–[6] following a normal-state contingency, such as post-contingency voltage or frequency violations, transient rotor angle instability, undamped oscillations, excessive temperature rise, etc. To ensure convenient online supervision,

Manuscript received May 23, 2013; revised September 23, 2013 and January 06, 2014; accepted March 10, 2014. Paper no. TPWRS-00649-2013. A. Kaci and L.-A. Dessaint are with École de Technologie Supérieure (ÉTS), Montréal, QC H3C 1K3, Canada (e-mail: [email protected]; louis. [email protected]). I. Kamwa is with Hydro-Québec/IREQ, Power System and Mathematics, Varennes, QC J3X 1S1, Canada (e-mail: [email protected]). S. Guillon is with the Operational Planning Department of TransEnergie division of Hydro-Québec, Montréal, QC H5B-1H7, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2014.2312418

stability threats are converted into a single stability limit set on the power transfer across key interfaces of the system, which are computed online using DSA packages and offline based on extensive operational planning studies [7]–[11]. Since the introduction of the security control concept in the early seventies and the advent of SCADA shortly afterwards [2], this task has been done by checking in real-time whether 1) the actual power transfer across critical interfaces is below the online or offline pre-determined transfer limits and 2) the voltages of the backbone grid buses and reactive-power reserve remain within prescribed bounds [5], [6]. An automated access to look-up tables containing these threshold values for each likely topology and system status makes it possible to easily compare SCADA measured quantities against the stored limits, compute the security margin and initiate requests for preemptive corrections when the normal state is deemed insecure [3], [4], [7]. As evidenced by the 2003 large-scale blackout in the NorthAmerican Eastern Interconnection [12], this approach has ensured a 5-nine reliability for modern grids for decades but it remains vulnerable to unstudied conditions, especially when the system stress is not properly reflected in the monitored interfaces. One reason is that only static security boundaries are further checked systematically in real time, while dynamic security limits, computed sometimes many years or seasons in advance [3], [8], are not often evaluated again. Another reason is that the notion of transfer limits across interfaces itself may be prone to errors when configurations difficult to forecast and/or contingency combinations occur in sequence. Recently, it has been argued that real-time DSA could resolve this vulnerability by assessing the full static and dynamic conditions of the normal state grid from minute to minute. Though promising, this approach is challenged by the slow progress in DSA made over the last decades [2], [4], [9]. However, with sustained progress in the computational speed using parallel computing, one company claimed [5] that “at least 7 out of 10ISO/RTO in North America have, or are implementing, online DSA systems,” and that “on-line DSA using Powertech’s DSATools™ software has been implemented in 35 control centers around the world”. Although these numbers are encouraging, it is worth mentioning that many of these systems focus on slow voltage stability issues. An emerging approach yet to be fully developed and understood is driven by SBSA using PMU data arriving in the control center at a sub-second rate [7], [13]–[16]. The added value of phase angle information to assess grid reliability (e.g., phase angle separation) became obvious during the analysis of the 2003 Eastern Interconnection blackout and is now well documented [12], [13].

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Fig. 1. Hydro-Québec network with PMU locations and main transfer interfaces where limits are monitored.

However, while significant efforts have been invested in deriving actionable information from synchrophasors following large-scale disturbances and system oscillations [16]–[19], the interpretation of phasor information in the normal state, which is the most common situation addressed by a system operator, has received comparatively less attention [20]–[23]. A straightforward use of angle differences in the control room [16] could consist in comparing measured values from PDC with thresholds derived from operations planning studies and baselining of historical angle differences patterns [22]. In fact, the Planning Implementation Task Team (PITT) and Operational Implementation Task Team (OITT) of the North American Synchro Phasor Initiative (NASPI) identified baselining of phase angles as their highest priority [14]. More generally, baselining includes relating power system measurements (e.g., voltage and phase angles, path flows, and reactive reserves) with the system performance measures for normal operating conditions. Given that the angle shift is a well-known measure of line loadability and system stress [7], [20], [25]–[28], this kind of analysis will facilitate the development of attractive SBSA and online security monitoring tools with a clear migration path to the control room. In this paper, a comprehensive baselining approach [22], [23] is proposed which combines conventional descriptive statistics with predictive data mining to assess the system’s stability state based on the synchrophasor data inflow. This approach takes advantage of Hydro-Quebec’s CILEX and LIMSEL EMS software [3], [10], [11], which together ensure access to a huge data base of real-time power system snapshots (load flow and dynamic data) collected minute by minute and archived over multiple years.

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Fig. 2. Stability-based security monitoring process at Hydro-Québec.

II. SECURITY MONITORING AT HYDRO-QUÉBEC The Hydro-Québec transmission network (Fig. 1) consists mainly of 34 000 km of transmission lines including 11 422 km of 735-kV series-compensated lines. In 2012, the domestic generation mix was 35 829-MW hydro versus 700-MW thermal owned by Hydro-Québec Production, with another 5400-MW hydro from East-North (EN) and 1400 MW of wind power from IPP, for an incredible rate of 98.3% renewable sources in 2012. The main load centers are 1000 km away to the south,1 the network having a characteristic triangular shape (Fig. 1). The peak load was approximately 39 240 MW on January 22, 2014. Today, with series compensation, automatic controls and fast protection systems, the network is very robust. There has been no blackout since 1989 and the limiting factors are not only angle and voltage stability but, increasingly, voltage- and frequency-based service quality criteria. Fig. 2 summarizes the stability-based security monitoring process at Hydro-Québec. The power transfer limits and their corresponding operating strategies are calculated in offline studies, performed months in advance, for a limited number of predefined power network topologies and “umbrella” configurations, selected in accordance with NERC reliability standards [1]. More specifically, the dynamic transfer limit concept considered in this paper is defined in [3]. It is set by transient, oscillatory and voltage stability constraints in addition to post-contingency service quality criteria [6], as usually computed using a comprehensive offline or online DSA system [3]–[5]. They are integrated into LIMSEL and used daily for maintenance planning, operations scheduling and real-time dispatch [10]. 1http://www.hydroquebec.com/publications/en/annual_report/index.html

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Since the severity of the contingencies can be related to power transfers, the operating strategy is based on a set of power limits allowed in the five main corridors of the HQ network (Fig. 1). Each stability transfer limit (i.e., excluding thermal and static limits) is the summation of a base value and other network conditions dependent values which increase or decrease the limit. These conditions include: load dependence on temperature, equipment availability, transfer levels, use of automatic control, and threat of extreme climatic conditions and so on. In real-time operations, LIMSEL (Fig. 2) is used as an efficient look-up table-based DSA system [3], providing nomogram displays to dispatchers while modulating special protection system (SPS) settings to adapt their control schemes to prevailing operating conditions. The CILEX software shown in Fig. 2 is a key interface between the state estimator, which uses the bus-breaker network representation, and the operation planning engineer who seeks bus-branch stability-oriented models for near-real time or post-event investigations. CILEX has had to maintain an archive of power flow cases with matching dynamic files in PSS/E format every minute since 2003. Fig. 3 illustrates sample angle shifts and transfer limit margins (i.e., the difference between the LIMSEL limit and the actual transfer). The demand and actual power transfers come from the EMS SCADA archives. Baselining will allow 1) building phase angle nomograms; 2) setting appropriate values for security monitoring and alarms; 3) establishing predictive models using phase angles to compute precursors to significant operational issues and abnormal behaviors. Using the WAMS illustrated in Fig. 1, Hydro-Québec engineers have confirmed that the angle shifts provided by the state estimator and CILEX interface are in good agreement with PMU data. Similar findings have been reported by PJM [22] and ERCOT [21]. Since the PMU historical data base is generally incomplete, with only few substations metered, it is better to rely on SE filtered phasors. In addition, existing WAMs are based on event records while continuous recording is deemed more appropriate for baselining. III. PHASE ANGLE SHIFTS AS PREDICTORS OF INTERFACE POWER TRANSFERS AND STABILITY LIMITS For all types of network, either meshed or radial, the stability constraints are strongly related to phase angles, which are sound, widely accepted indicators of stability stress. In effect, the power across a lossless line is . If is good enough for dynamic security monitoring why is not good enough for the same purpose? All power grids are operated using the transient-stability criterion, whether they are mostly radial or meshed. But stability stress is not determined by the radial or mesh nature of the grid only; it is also heavily influenced by network dynamics (i.e., generator models, excitation systems, speed governors, reactive compensation, etc.) All this said, radial networks are constrained by stability limits more than mesh networks, which tend to reach thermal limits first (although the voltage stability considered in this paper universally impacts all power grids). To explain the strong coupling between power transfer and phase angles in engineering terms we can refer to St. Clair curves, for predicting line loadability under given operating conditions and

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Fig. 3. Sample minute-to-minute time series form CILEX and EMS archives. (a) Angle shifts at six buses with reference to a slack bus at Boucherville substation. (b) Security margin at five interfaces.2 (Limit(t)-Actual Transfer(t))/Demand(t).

Fig. 4. Equivalent system for St. Clair curves derivation.

line voltage level [25]. The St. Clair curves applied to Thévenin equivalent models (Fig. 4) form the basis for the ideas advanced in this paper. Whereas Thévenin equivalents have previously been used to determine line loadability limits, it has been also proposed recently to use these equivalents to gauge closeness to loadability limits (i.e., loadability) [20], [26]. The theory of St. Clair curves demonstrates that system loadability is limited by stability, i.e., the angle across the line “plus system”. Therefore, when the Thévenin equivalents as seen by both ends of a transmission line in Fig. 4 are known, the angle across the system will indicate a level of loading in the system and this angle should approach 90 degrees at the critical line/ equivalent combination. At 45 degrees, there would be a 30% margin [25]. From Fig. 4, the power transfer on the receiving end is (1) 2In order to better visualize the behavior of angle shifts and security margins on the same plots, angle (D05 and D80) and security margins at interfaces West. South and Center are multiplied by

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After simple algebraic manipulations, it can be shown that [28]

and (2) Therefore, the power transfer between the two ends is a direct function of the angle shift across the line, while the maximum transfer is determined by the sending-end voltage. If the equivalent systems at both ends are very strong, is independent from but, when the Thévenin impedances are nonzero, there is coupling between the two variables. In fact, the Thévenin equivalent parameters are functions of the external network topology and, especially, the reactive power control devices. Hence, while the relation between the transfer and angle shift is direct, the relation between and is strongly coupled with the Thévenin equivalents at the two ends of the interface. Moreover, in real power networks, it is only under peak load conditions that most equipment is in service (providing the grid’s lowest impedance). Over the year, different power lines are out of service (increasing the grid impedance), changing the matrix ABCD’s parameters accordingly. However, as far as we know, empirical studies proving beyond all doubt the correctness of such a conjecture on largescale power systems are scarce, even though it is well acknowledged that a stressed system is characterized by high values of phase- angle shifts across the corridors or cut-set interfaces [27]. Using actual 2010 Hydro-Québec time series, let us consider first the correlation between all 735-kV buses and the five-interface power transfer and margins. The results in Fig. 5 show that many buses have over 95% positive correlation with interface power transfers. Likewise, the negative correlation between phase angle and transfer margin is higher than 90% except one interface whose correlation is limited to 50%. It is important to note that this interface is a tie-line operated most of the year under a fixed long-term contract, which makes its behavior atypical but usually predictable. To confirm these high correlations between angles and security margins, at least in the Hydro-Québec system, in Fig. 6 we have plotted side by side the seasonal patterns of the security margin at two interfaces [CENTER (CE) and ES] versus phase angle patterns of two medoid buses. We see that, when the north-south angles are high, the security margin of the two transfers is low and vice versa. According to (1)–(2) and the related discussion, the correlations between phase angles and power transfers through interfaces are not due to the radial nature of the grid. They are better explained with the St. Clair curves of the Thévenin equivalent of the lines constituting the interface. The transfer limit margins have lower correlations with the phase angle compared to the power transfer because transfer limits are not easily predictable, given that they are complicated functions of contingency location, network topology, reactive compensation, load model, power plant and control system models, etc. In other words,

Fig. 5. Correlations between bus angle and (a) power transfers and (b) security margin (Limit(t)-ActualTransfer(t))/Demand(t).

Fig. 6. Diurnal cycles and phase angles (top, in degrees) versus transfer margins (bottom, in % of actual demand).

although the Hydro-Québec network has few clearly identified corridors, determination of its stability limits is a far from easy task. It requires a huge volume of dynamic studies and covers a wide range of events and operating conditions. In addition, the WECC procedures (dictated by NERC) [6] for determining stability limits on major interfaces are exactly the same as in Québec and do not seem to depend on whether the network is radial or meshed.

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Fig. 7. Proposed framework for synchrophasor data baselining. The bottom layer on “Operations planning with synchrophasor data” is further described in Fig. 18.

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• Investigating all 37 phase angles of the network’s 735-kV buses for missing data and spikes (sanity check). • Assessing properties and patterns of typical behavior of these phase angles in terms of statistical characteristics (using box plots, cumulative curves). • Identifying groups of buses with similar phase angle patterns and associating a medoid with each group. • Profiling of medoid phase angles in terms of the seasons, and peak and off-peak periods of the day. • Investigating transfer powers and stability margins according to different medoid phase-angle profiles. • Random-forest modeling of transfers and stability margins with 37 angles on the one hand and according to medoids on the other hand. • Recommending suitable limits on phase angles, reliability margins and phase-plane nomograms for secure operation of the network under normal conditions. • Comparing data-mining results with reality (Section VI-B). In the following sections, we will navigate through the various steps in Fig. 7 while illustrating each step based on actual EMS data from Hydro-Québec.

A. Data Filtering and Decimation However, we recognize that measuring the angle has been historically very challenging using a SCADA. Still, the angle is the state variable of the synchronous generator which dictates rotor stability conditions and, using PMU data, it is likely that in the future we will be able to measure the rotor angle with enough accuracy [29], [30] to legitimize its use in online prediction of the stability margin as well as facilitating the measurement of power transfer variables. Ultimately, we could envision using rotor-angle differences instead of bus phase-angle differences. IV. FRAMEWORK FOR PMU DATA BASELINING PMU measurements give us current system states. However, to be aware of the true situation we need to know where the edge is and how close to the edge we can safely (reliably) operate [3]–[7], [26]. Enabling PMU data to answer these questions, at least partially, requires offline baselining studies of phasor angles that can rely on EMS state-estimator data or on mid- to long- term stability simulations, even though the ultimate goal remains to rely on synchrophasor data in actual implementation. The approach adopted is based on an extensive EMS database, combining a 1-min interval state estimator and 1-min SCADA information, as illustrated in Fig. 7. This data was acquired during the development of a new power grid control simulator for wind-integration studies [24]. It contains, for five civil years, 37 phasors at all 735-kV buses, seven interface limits and corresponding active and reactive power transfers, balancing area load and its real-time forecast. Up to 30 other SCADA variables such as operating reserves, AGC, reactive-power compensator production, etc. were available in the data set but were left out for future investigations. The main steps of data mining for baselining studies will now be described:

The full civil year 2010 was selected for this study. All variables were initially aligned with a convergent load flow which was further matched to minute-by-minute aggregate demand from the EMS SCADA [24]. When a convergent load is missing for a specific minute, all variables are assigned a NA and treated as missing values (about 10% of the data). When a statistical method used in the sequel cannot deal intrinsically with NAs, these are replaced by spline-interpolated values or, more simply, the median value of the corresponding time-series. To reduce the data volume, these filtered data were down-sampled to a 3-min sampling rate, resulting in 175 000 samples over one year. The box plot in Fig. 8 provides a glimpse of the complexity of a brute-force statistical analysis of all system phasors. It shows how variations depend on geographic location and electrical strength. Phase angles increase when the substation’s distance from the load increases. Substations in close locations have similar angle shifts. For one specific distance, substations with a weaker link to the main grid have larger angle shifts. Even for this small set of 37 phasors, it would be rather impractical to set thresholds for each of them in view of the security monitoring, given that, as shown in Fig. 1, the current approach relies on five interface limits only. To keep with this parsimonious practice, we have to streamline the large raw PMU data set into a few primary phasors angles conveying the same information about system security. This small subset of phasors will be treated essentially the same way as power transfers at critical interfaces for the sake of designing security nomograms or determining security margins in degrees or MW. To check if the bus ensemble lends itself to such grouping, we can use correlation analysis [31], [32]. The symmetrical correlation matrix is shown in Fig. 9 for all 37 candidate phase angles and 175 000 samples per variable. We

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Fig. 10. Visualization of the Manhattan distance-based dissimilarity matrix using the iVAT method [34].

Fig. 8. Box plot of the 735-kV phase angle shifts (175 000 samples).

titioning Around Medoids) clustering, a classic algorithm for k-medoid clustering, which is widely available in statistical software packages [33]. It is similar to k-means, the major difference between them being that, while a cluster is represented with its center in the k-means algorithm, it is represented with the object closest to the cluster’s center in the k-medoids clustering. However, PAM requires the user to specify the number of clusters k, which can be conveniently estimated using the Improved Visual Assessment of Cluster Tendency (iVAT) algorithm. The results of iVAT [34] presented in Fig. 10 show two plots: on the left, the 37-bus dissimilarity pattern is presented with its initial sequential ordering. On the right is the iVAT grouping where similar buses are contiguous. We easily recognize three dominant groups but, focusing on the blue cells, we could further identify about seven to 10 cells. Therefore, we could reasonably pick in this case. The medoid substations for a three-cluster PAM grouping are LG3 (22), MICOUA (06) and CARIGNAN (30). Given that the slack bus, which is also the phase-angle reference, is located near Montréal (shown as a yellow box in Fig. 1), the most important feature describing the cluster seems to be its electrical distance to the load center. In the sequel, we will further assess these medoids in terms of their capability to predict security margins. C. Baselining Using the Exceedance Levels

Fig. 9. Auto-correlations matrix of the bus angle shifts: 37 [32]].

37 matrix [cf.

can understand the degree of any correlation between two variables by both the shape and the color of the graphic elements. Any variable is, of course, perfectly correlated with itself, as reflected by the straight lines on the diagonal of the plot. A perfect circle, on the other hand, indicates that there is no (or very little) correlation between the variables. In this context, we can visually locate patterns of buses clustered around the following: 22, 83, 60, 19, 3, 90, 15, 30, 8, and 1. However, though useful in assessing the existence of clusters in bus phase angles, a visual approach like this is unable to objectively identify the cluster centers and, furthermore, can hardly be generalized to a large system. B. PAM Clustering The subset of so-called medoid phasors (which are the centers of phasor clusters) can be determined through PAM (Par-

Once the medoids are known, the next simplest step is to mine the historical data and identify appropriate settings for alarm purposes. In Fig. 11, the daily max-min phase angles of two typical medoid buses are illustrated. The range of variations by day of the year can be used to trigger alarms. However, this approach is sensitive to noise and abnormal values in the historical data. A more robust approach is to use a box plot, as shown in Fig. 12. Each box describes the inter-quartile range of the data for each month, for on-peak and off-peak hours separately. The point in the middle of the box represents the median value, while the dotted lines highlight the variability of the extreme values, which can therefore be spotted and analyzed to remove abnormal values. Finally, the most sophisticated approach would be to build exceedance curves as in Fig. 13, where the 2010 time-series is considered in full and the data is grouped by on- and off-peak hours for winter and summer seasons separately [39]. It appears that the tails of the curves for offand on-peak hours are very close to each other, though winter and summer shapes are quite different. A 10 to 15 gap is noted between them. We can also see that during the winter, the 0.01% (or 99.99%) monitoring threshold is 71 , 61 and 43

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Fig. 11. Daily trends of medoids bus phase angles over one year.

for medoids 64, 60, and 6, respectively, while in summer we have 58 , 48 , and 30 . Therefore, the seasonal variations are far greater than the diurnal. Other descriptive statistics shown in Table I broadly support the same conclusions. We admit that designing a synchrophasor-based security monitoring tool using state estimator (SE) data derived from SCADA measurements can be confusing at times. In fact, we are forced to use EMS-SCADA historical data to baseline the new application because PMU data has a very limited history at a limited number of buses and, when past data exists, it contains gaps due to communications, clock and other young-technology issues. In addition, it is difficult to synchronize historical PMU data from a Phasor Data Concentrator (PDC) with historical transfer limits and SCADA data from the EMS. Furthermore, the baselining studies recently performed on the Eastern Interconnection with PJM data and DOE funding relied on state-estimator derived angles in the design stage, keeping in mind that in actual deployment the settings obtained through baselining will be integrated with actual PMU measurements [15], [16], [22], [30]. This viewpoint is further supported by NERC [13] and FERC policies [37] which recommend PMU-based WASA developed and implemented separately from the SCADA, for several reasons: 1) PMUs are able to measure the angle accurately thanks

Fig. 12. Monthly trends of margin (top) versus of phase angle (bottom) in 2010.

to GPS time synchronization (in contrast to SCADA, which provides an estimate sensitive to timing, RTU and topology issues); 2) PMU data is refreshed 30 to 60 times per second compared to only three to four times every second for SCADA data, and every 1 to 5 min for SE data; 3) and finally, PMU data provides an alternative, measurement-based, path to the SCADA in case of a major disturbance disrupting the SCADA process momentarily as during the 2003 Eastern blackout [10]. V. PREDICTIVE BASELINING USING RANDOM FOREST MODELS The last stage of the baselining framework proposed in Fig. 7 consists in forecasting the stability margins once the angle-shifts are known from measurements. If online analysis of phase angles can provide the operator with a tool for real-time security monitoring of the system according to (1), it does not inform him accurately about the maximum loading (what-if analysis), especially in complex systems with multiple voltage-control means and power line conditions. To circumvent this limitation, we will now develop a predictive model able to map measured phase angles to actual limits, computed in offline or

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Fig. 14. Summary of random-forest algorithm.

Fig. 13. Seasonal exceedance curves of typical medoids of phase angles sorted by on- - - - and off-peak (____) hours.

TABLE I TYPICAL SEASONAL DESCRIPTIVE STATISTICS OF MEDOID BUS PHASE ANGLES (IN DEG.)

online operations planning with full awareness of grid topologies, taking into account load models, power source locations, flow patterns, etc. Applying these limits is similar to developing accurate Thévenin equivalents in Fig. 4 from phasor data [15] and then using the simplified model for a line-loadability assessment and gauging closeness to loadability limits (i.e., loadbility) [26]. We have proven in Section III that, albeit complicated, a nonlinear relation exists between measured phase angles and power transfers and, to a certain extent, transfer limits. To derive this nonlinear function, we opted for a random-forest (RF) model,

recently established as the best approach to achieve the high accuracy required by power system analytics for reliability and security control purposes [32]. The RF is a regression method based on the aggregation of a large number of regression trees [35], [40]. Specifically, it is an ensemble of trees constructed from a training data set and internally validated to yield a prediction of the response given new predictors. A. Background [35], [40] Let us suppose that we have a set of examples describing the general concept of a dynamic security margin, , where is a real number measuring the distance to the edge, with a large positive margin meaning a safe operating condition while or negative means poor dynamic security margins. To each time sample in Fig. 3, a set of attributes (A) corresponding to phase angles of all or a subset of system buses is stored along with the security margin found in EMS SCADA at the same instant. The basic idea of most procedures for ensemble tree growing is that for the kth tree ( , the number of trees in the ensemble) a random vector is generated, independent but with the same of the past random vectors distribution, and a single tree is grown using the training set S and the set of attributes in , resulting in an inducer where is an input vector. In a random split selection, consists of a number of independent random integers where , the number of attributes in . A random forest consists of a collection of tree-structured inducers , where are independent, identically distributed, random vectors. Each tree casts a single estimate of security margin M, giving an input . An algorithmic view of the RF growing process is summarized in Fig. 14.

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B. Prediction From Ensemble Trees A random-forest prediction is the combination of all individual tree predictions. Assuming that the error estimates from individual trees are random variables, each with a variance , [35], which the variance of the average prediction is confirms that the random forest leads seamlessly to improved prediction accuracy. In addition to the ordinary prediction, random forests have a so-called out-of-bag (OOB) prediction: according to Fig. 14, each tree is built on a bootstrap sample which serves as a learning set for this particular tree; this contains only two-thirds of the observations [31], data set [35], i.e., the third of samples not participating in the training of a given tree can serve as a “built-in” test sample for computing the prediction accuracy of that tree. The advantage of an out-of-bag error is that a more realistic estimate of the error rate can be obtained. The training data is generated in the RF algorithm by randomly picking 70% of the supplied dataset, consisting of bus phase angles and corresponding limit in a given corridor. The remaining 30% is used for external RF testing. However, if we feed the RF inducer with a data set S containing only 70% of the original data and keep the rest for testing, given that each of the 100 trees was trained on two-thirds of the data only, it turns out that, at the learning stage, only 50% of the data is actually seen by a given tree in the random forest. When the resulting predictor still worked well on the external test set, we had to admit that it is a robust and general model of the underlying process. C. Results of RF-Based Predictive Baselining We applied the random forest as a regression tool to model power transfers and security margins across the five main interfaces of the system, using, respectively, a) all 37 phase angles in the data set and b) phase angles of the 8-medoid bus identified as green boxes in Fig. 1. Each interface variable was modeled individually using time-series predictors consisting of 175 000 filtered samples (3-min interval for a year), with a typical split of 70% for training and 30% for testing. We used 100 trees in order to save time, although in some cases the OOB error was still decreasing at a slower rate, with 37- and 8-variable model configurations a) and b), respectively. To illustrate the good quality of RF models, Fig. 15 presents the linear fit of prediction versus actual variable for margins (in %, relative to corresponding demand) and power transfers (in MW) across some interfaces. A full data set is shown in the plot. It clearly appears that random-forest regression models are highly accurate based on the R-squares measure, especially for predicting power transfer even if only 8 medoids are used. Table II provides a comprehensive assessment of the RF model accuracy. As expected, the margin predictions are less accurate, although the R-square value is higher than 99, meaning a statistically consistent and robust model. Figs. 16 and 17 illustrate the prediction errors of RF models as time-series over a full year. Again the errors are unbiased, as in Fig. 15, but tend to be large when the margins or transfers are large. VI. PMU-BASED STABILITY MARGIN MONITORING IN EMS

Fig. 15. (a) Assessing the RF goodness of fit: dynamic security margin at two interfaces in two model configurations (a) and (b). (b) Assessing the RF goodness of fit of two interface-power. Transfers using 8-medoid phase angles as inputs.

A. Why Use PMU-Based Phase Angles and How? Although SCADA data are used in the design stage of the security monitoring system, the implementation of SSBA illustrated in Fig. 18 needs PMU data for its intrinsic accuracy and

responsiveness. Whereas a state estimator determines the angles indirectly, PMUs measure them directly. In the same way, measured line flows are used to check the transfer limit in the ex-

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TABLE II RANDOM FOREST MODEL PERFORMANCE ASSESSMENT (MAE MEAN OF ABSOLUTE ERRORS)

Fig. 16. RF prediction errors of the south interface margin over one year. Top: 37 predictors; bottom: 8 predictors.

Fig. 17. RF prediction errors of power transfer over one year. Top: West-North; bottom: East-South.

Fig. 18. Evaluation and visualization of PMU-based reliability margins. The tasks on the far left can be repeated from seasonally to daily. The tasks on the far right are refreshed at PMU reporting rates.

isting SCADA, not the line flows derived from state estimation. It is important to rely on actual (not processed) measurements for assessing the security condition of the system. Why are PMUs needed? We would rather ask why should we not use PMUs if phase angles are deemed necessary or suitable for monitoring stability limits? Manifold projects sponsored by utilities and government agencies throughout the world are deploying PMUs massively for EMS applications. In the United States alone, the number of PMUs will increase from 166 networked devices in 2010 to 1043 in 2014 [15]. According to the DOE, these PMUs are being installed to “evaluate and visualize reliability margins (which describes how close the system is to the edge of its stability boundary).” These devices measure the phase angles more accurately than any SCADA can do, with a refresh rate 100 to 200 times higher and without some of the

problems inherent in a SCADA-based state estimator, such as RTU and topology errors, which make the SE phase angle estimates less reliable than when directly measured with a modern PMU-based WASA. In addition, for redundancy purposes, we want the system to be independent and physically decoupled from the SCADA in case of a major EMS failure. This said, although digital filtering-based PMUs complying with IEEE Std C37.118.1-2011 have a vastly improved accuracy compared to rms-based analog transducers feeding the SCADA through substation RTUs, both systems ultimately use the same PTs and CTs as primary metering devices. Raw PMU data can therefore have errors for a variety of reasons including PT and CT miss-calibration or communication issues. The quality of raw data can also degrade over time even if it was perfect at the PMU commissioning. Blind use of such non-verified raw data

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Fig. 20. Matching of phase-angle events associated with the 99.5% exceedance level of medoid 06 with other variables. The margin in % refers to global demand.

Fig. 19. Yearly phase angle-based nomograms at the CE interface. Top: power transfer; bottom: transfer margin.

could be dangerous. Just as for SCADA data, PMU data should always go through some processing or quality verification before being used for any purpose. PMU devices should also be periodically checked for accuracy, as required by NERC reliability standards, to make sure that their data fully complies with the accuracy class specified in the commissioning documentation. According to Fig. 18, the first way that PMU data can be used in our framework consists in implementing a phase-plane-based nomogram, as suggested by NE-ISO in [7]. One such nomogram is introduced in Fig. 19 for illustration. In real time, PMU data is simply positioned on the phase-plane and, when the measured data point drifts close to the boundary computed offline or online (from seasonally to a daily to hourly time interval), we know that the system condition is unsafe. The second approach consists in using the random-forest approach in order to map the phase angles on the stability (or reliability) margin. When the latter is too small, we can conclude that the current operating condition is no longer safe. A last approach, illustrated in Fig. 18, could be to compare measured phase-angle values against historical baselines directly and generate alerts to operators when the 99.5% exceedance value is met. Although such an event occurring in a normal or post-event condition is not necessarily a sign of an unsafe operating point, it certainly points to an atypical situation and requires special attention on the part of the operator [23]. B. Preliminary Application Results From SCADA-Based Phase Angles The results of the angle-shift analysis in previous sections using correlation, PAM and RF models give the medoids the

necessary legitimacy to represent the behavior of other network buses in the same cluster. As illustrated in Fig. 19, it is possible to use phase angles of well-chosen buses for drawing level plots that can realistically mimic nomogram patterns of critical-path margins and transfers. We observe that, as the angle shift increases, the transfer increases (yellow to red) while the margin decreases (magenta). To further assess the feasibility of security-monitoring based on 99.5% exceedance levels of the phase-angle features, we performed a minute-to-minute analysis of the 8-medoid angle shifts over a full year to detect atypical events experienced in the five corridors over the same period. Fig. 20 illustrates all instances of the phase angle of medoid D06 exceeding the 99.5% threshold. They all occurred during the winter season. It appears that such events closely match occurrences of low dynamic security margins. For more clarity, two consecutive specific events on the same day are further depicted in Fig. 21. In the first incident the violation was brief, with stressed conditions appearing in corridor ES where the margin dropped to less than 1% before the situation was quickly remedied. This recovery was properly reflected in the behavior of the medoid phase angle which was back to normal. An incident then occurred again at 18 h, with a longer duration of the phase angle exceeding the 99.5% threshold, and we observed a greater variation of the corridor ES margin. In this case, the corridor EAST-NORTH (EN) margin also dropped below the critical 1% threshold but, when all margins were restored, the angle was back in the normal 99.5% range. Comparing these two events lasting about 12 min with the recorded archive of network events, we were able to confirm that their detection from angle shifts did indeed coincide with real phenomena on the grid, such as losing a line due to icing when the load was high. Other atypical confirmed events were equally detected from medoid phase angles exceeding the 99.5% level. In fact, after an overall inspection of the results over one year, we found that each medoid phase angle exceeding this limit corresponded to at least one corridor in an insecure state, i.e., operating near or below the normal limits.

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Therefore, even though no solid theory exists yet to back explicit use of the phase angle as a dynamic security predictor, there is much indirect evidence to motivate further investigations in this direction. It is also worth adding that pre-contingency phase angles are used in combination with many other features such as active- and reactive-power injections and, more importantly, the contingency type and location in order to simplify the structure and training of the model. In this paper, we show that, with sufficiently complex models, such as random forests with hundreds of regression trees, pre-contingency phase angles alone can achieve a significant level of accuracy and robustness in predicting dynamic security limits. B. Generalization and Real-Time Extension

Fig. 21. Detection of two events based on medoid phase-angle exceedance levels. Margins in % refer to limit values.

VII. INHERENT LIMITATIONS OF THE PROPOSED METHOD AND IDEAS FOR FURTHER IMPROVEMENT A. Bus Phase-Angle Separation as Dynamic Security Predictor A major limitation in this work remains the lack of a rigorous formal demonstration of the link between the pre-contingency phase-angle separation and the security status of the system. The St. Clair curves are based on a physical representation of the transfer paths as actual transmission lines, which is not true. It also relies on Thévenin equivalents of the sending and receiving ends of the interfaces, which are hard to determine in addition to being configuration-dependent. More importantly, phase angles are not currently used in the control room for actual real-time system operation, which makes it difficult to assess their merit as security-limit predictors based on hard and undisputable facts. All this being said, we should point to the large body of empirical evidence from the existing literature which highlights the technical potential of the phase angle as a feature for monitoring dynamic security limits in real time. For instance: • In [42, Sec. 2], a brief explanation of the angle behavior when the power system is operated under large angle separation is presented. It is concluded that voltage stability can be monitored based on the voltage magnitude and angle contour plot. • Similarly, Sauer et al. proposed computing the margins to power system loadability limits from phasor measurements in [20] and [26], while emphasizing the instrumental role of the phase angle in their algorithms. • In [43] and [44], pre-contingency phase angles are successfully used along with other relevant variables to predict the dynamic-voltage stability status and stability margins, respectively. • In [45], pre-contingency phase-angle separation is used as a feature in a list of 20 attributes for transient-stability status prediction using neural networks.

Another clear limitation of the predictive baselining method as outlined in this paper is the requirement that a large data base of operating conditions should be available to enable training using known offline calculated transfer limits. It is well known that calculated offline limits to be used in real-time dispatch must be quite conservative to cover all possible types of actual system conditions, particularly at high penetration of renewables. However, to remove any conservativeness in the limits and calculate reasonably accurate limits on the increasing variability of parameters and market conditions, a general tendency to calculate limits online using online DSA systems is observed [5], even though most power systems in North America and worldwide are still operated on the basis of dynamic limits computed offline. By contrast, static security limits are determined online almost everywhere. To increase the real-time readiness under variable conditions, it is proposed in [2] and [46] to re-train the model in the operations time-frames using stored results of online DSA systems, which are becoming widespread. Fig. 22 recapitulates how this model updating can be performed in the present framework. The structure shows the offline training and online assessment for the system stability’s decision-making process. It also allows for continuous updating of the knowledge base for better performance using DSA system output. It is also worth mentioning that a random-forest model inherently has a very good generalization capability [32], [40], as a result of how it is constructed (cf. Section V.) To demonstrate this built-in robustness against unseen network conditions, we extended the EMS time-series of phasor and dynamic-security limit data to 4 years, i.e., from 2009 to 2012, instead of the single year (2010) considered in the previous sections. Interestingly, Hydro-Québec’s net exports changed wildly over this period: 18.5, 12.6, 20.8, and 30.2 TWh in 2009, 2010, 2011, and 2012, respectively. This implies a huge variation in flow patterns and network conditions by season and by hour of the day to match variable inter-tie flows driven largely by activity on real-time electricity markets in the neighboring ISOs. Again, only 70% of the data is used in the training so that the model is not aware of 30% of the network conditions available. In the end, we have a model where are the parameters resulting from training and are the phase-angle attributes for training and validation, respectively. Table III shows that this model is quite accurate in predicting the

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Fig. 23. Assessing the RF prediction residuals for power transfer (top) and security margin (bottom). Single model developed with 70% EMS data covering 4 years of minute-to-minute operation.

Fig. 22. Approach to improve model-based phase-angle baselining using online DSA.

TABLE III PREDICTIVE BASELINING PERFORMANCE OF A SINGLE RANDOM-FOREST MODEL OVER A 4-YEAR PERIOD WITH 37 BUS ANGLES AS INPUTS

30% of data corresponding to network conditions never seen by the random-forest model during training. For instance, considering the transfer path CE, the R-squares coefficient measured on the 4-year validation data is 99.73% compared to 99.93% for 2010 alone. The R-squares of the CE dynamic stability margin between the 4-year validation and the year 2010 alone is similarly close (i.e., 99.78% versus 99.85%). Finally, Fig. 23 illustrates the prediction errors of RF models as time-series over a full 3-year period. We note that the errors are unbiased (zero mean) with a relatively small variance compared to actual values. Again, this multi-year performance of a single model compares favorably with the 2010 performance in Fig. 17, confirming the good generalization property of phase angles as predictors of the dynamic transfers and margins of the actual power system considered. C. Discussion and Future Prospects Since, to the best of our knowledge, this is the first paper where dynamic-security margins are derived entirely from phase angles, we have no reference method to make a comparison. Instead, we compared the dynamic transfer limits

forecasted by our random-forest system with the true limits established by the EMS’s table look-up software (end of Section V-C of this paper). The comparisons are made in terms of the accuracy achieved in % with respect to the load, or in terms of the mean absolute value of MW errors. Our results compare very favorably with those proposed by the actual system LIMSEL for new cases never used in the random-forest training. Alternatively, if the security limits are considered to be the phase thresholds, at 95 or 99.9% exceedance levels, we compare our results with LIMSEL’s limits in terms of the detected events. In other words, when our defined phase-angle limit is exceeded, does that correspond to an actual security event that occurred in the system and was detected in the EMS? The answer is yes, as illustrated in Figs. 20 and 21, with low EMS security margins closely matching phase-angle violations. Therefore, PMU-based stability-limit monitoring can be a degraded backup to SCADA in its early deployment stage. It may later evolve in a more active role when its accuracy and reliability have been demonstrated. Any decision based on line flows (as done today in EMS-SCADA) can potentially (yet to be confirmed) be made on the basis of phase angles, provided these are measured with as much accuracy as possible now with PMUs, compliant with IEEE Std C37.118.1-2011 [41]. Although the random forest model can cope with unseen operating conditions, its real-time awareness and accuracy can be improved as suggested in [2] by taking full advantage of online DSA systems to perform a periodic or on-demand retraining near the operations time frames. This challenging extension might be mandatory for systems with high penetration of intermittent renewables and markets dynamics, as it would reduce the conservativeness inherent in offline calculated limits and enable a smarter operation of such systems with higher parametric variability. Another way of improving the proposed approach, especially in the context of highly meshed systems would be to use in addition to phase angles other useful features popular in the literature, such as generators active and reactive reserves, active and reactive power injections and critical buses, bus magnitudes, etc., as input to the random forest model of dynamic transfers. VIII. CONCLUSION This paper has proposed a systematic data-mining approach for developing synchrophasor-based security-monitoring

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schemes with a clear migration path to the control room. Taking advantage of the actual 2009–2012 minute-to-minute state-estimator load-flow data from Hydro-Québec’s EMS, combined with time-synchronized actual operating limits across the main interfaces, seasonal exceedance levels of angle shifts are first determined over the full grid to improve operator understanding of historical synchrophasor data trends. The crossing of the 99.5% thresholds determined separately for onand off-peak hours was positively correlated with outages or weather-related incidents on the grid. Next, correlation analysis and partitioning around medoid clustering were used to select a concise set of phasor data on which to base online security monitoring. The actual stability-based, secure transfer limits across the various interfaces [3] were then forecast using ensemble decision trees [32], [35], [40] with medoid-bus phase shifts as predictive features. The accuracy of such predictive models as measured by the R-squares coefficient and MAE criterion was very high for both power transfers and security margins. Lastly, a chronological playback of the state-estimator phasors over a full year, performed while checking the phase-angle exceedance levels and corresponding model-based security margins confirmed that the new approach is quite realistic and could be readily extended to actual PMU data from Hydro-Quebec’s PDC [30], [37] for potential migration to the control room. The synchrophasor-based security monitoring of stability limits therefore appears to be a promising approach faithfully complementing the usual practice of critical transfer-path monitoring based on a novel independent set of accurate and responsive data capable of surviving an outage of the state estimator during a blackout. The proposed approach is applicable to any power grid with stability constraints that seeks to use a synchrophasor-based WASA [15] for improved tracking of time-varying changes in the network-stability condition. Although our current implementation focuses on power systems operated with offline dynamic security limits [3], it can (and would) be definitely improved to achieve a better real-time responsiveness and adequacy, through a continuous or conditional re-training in the operations time-frame using dynamic transfer limits updates form online DSA systems [5]. We hope that this paper will encourage other utilities with characteristics different from Hydro-Québec’s to evaluate SBSA with their own data. REFERENCES [1] Reliability Standards for Quebec Interconnection, May 28, 2009 [Online]. Available: http://www.regie-energie.qc.ca/audiences/3699-09/ Demande_3699-09/B-1_HQCME-2Doc1_3699_02juin09.pdf [2] T. E. Dy-Liacco, “Enhancing power system security control,” IEEE Comput. Applicat. Power, vol. 10, no. 3, pp. 38–41, Jul. 1997. [3] A. Valette, J. Huang, S. Guillon, L. Loud, G. Vanier, F. Lévesque, L. Riverin, J.-C. Rizzi, and F. Guillemette, “An integrated approach for optimizing dynamic transfer limits at Hydro-Quebec,” IEEE Trans. Power Syst., vol. 24, pp. 1310–1317, 2009. [4] P. W. Sauer, K. Tomsovic, J. Dagle, S. Widergren, T. Nguyen, and L. Schienbein, Integrated Security Analysis, CERTS rep., 2004, p. 72 [Online]. Available: http://certs.lbl.gov/pdf/certs-isa-final.pdf [5] L. Wang, On-Line Dynamic Security Assessment: Its Role and Challenges for Smart Control Centers, Dec. 2012 [Online]. Available: http://mydocs.epri.com/docs/PublicMeetingMaterials/ 1202/MVNQQ2YVLLT/Lei_Wang.pdf

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Anissa Kaci received the B.Eng. degree in electrical engineering from Béjaia University, Algeria, and the M.Eng. degree in electrical engineering from Jijel University, Algeria. She is currently pursuing the Ph.D. degree in electrical engineering at the École de Technologie Supérieure, Université du Québec, Montréal, QC, Canada.

Innocent Kamwa (S’83–M’88–SM’98–F’05) received the Ph.D. from Laval University, Québec City, QC, Canada, in 1988. He then joined Hydro-Québec’s research institute (IREQ), where he is currently Manager of Power Systems and Mathematics. He is also the chief scientist for Hydro-Québec’s smart grid. He is a P.Eng. and Adjunct Professor of Power Systems Engineering at McGill University and Laval University. Dr. Kamwa is an Editor of the IEEE TRANSACTIONS ON POWER SYSTEMS and Co-Editor-in-Chief of IET Generation, Transmission and Distribution. He was awarded the IEEE PES Prize Paper Award in 1998, 2003, 2009, and 2012. He serves on many IEEE/PES technical committees as member and officer, including the Fellow Evaluation, Electric Machinery, and Power System Stability committees.

Louis-A. Dessaint (M’88–SM’91–F’13) received the B.Ing., M.Sc.A., and Ph.D. degrees from the École Polytechnique de Montréal, Montréal, QC, Canada, in 1978, 1980, and 1985, respectively, all in electrical engineering. He is currently a Professor at the École de Technologie Supérieure, Université du Québec in Montréal. He holds the Hydro-Quebec/TransEnergie Chair on Simulation and Control of Power Systems. He is an author of The MathWorks “SimPowerSystems” (SPS) Blockset. Dr. Dessaint is a Fellow of the Canadian Academy of Engineering and a member of the Cercle d’excellence de l’Université du Québec. He was an associate editor of the IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY from 2009 to 2013.

Sébastien Guillon (M’03–SM’07) received the engineering physics degree from École Polytechnique de Montréal, Montréal, QC, Canada, and the M.Sc. degree in theoretical physics from Concordia University in Montréal. He joined Hydro-Québec TransÉnergie in 2000. His experience is mainly with the Operational Planning Department.