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18th Power Systems Computation Conference Wroclaw, Poland – August 18-22, 2014

EVOLUTION STRATEGIES-TUNED SUPPORT VECTOR MACHINE-BASED CLASSIFICATION OF INTER-AREA OSCILLATIONS

Adamantios Marinakis ABB Corporate Research

Baden-Dättwil, Switzerland [email protected]

Carsten Franke ABB Corporate Research


Mats Larsson ABB Corporate Research


Abstract – Tools for real-time monitoring of inter-area

oscillations are now commercially available. These tools have been validated in many power systems with different characteristics and are in operation in some control rooms. Yet missing, however, are tools that can assist an operator to identify the root cause of poorly damped oscillations and propose appropriate countermeasures. As a step towards this direction, this paper describes the construction of a support vector machine model trained to classify potential operating points according to their corresponding oscilla-tion damping ratios. Evolution strategies are used to tune the SVM hyperparameters, including the selection of its kernel function, such that the accuracy of the resulting model is as high as possible.

Keywords: inter-area oscillations, support vector machines, evolution strategies, wide-area monitoring systems

1 INTRODUCTION Low-frequency inter-area oscillations are typically

observed in interconnections where large power systems are connected via weak ties. These oscillations are a result of swings between groups of machines in one area against groups of machines in another area, interacting via the transmission system [1]. Poor damping of such oscillations is an indicator of power system stress, which in turn implies decreased capability of the system to withstand component outages.

Phasor measurement units (PMUs) [2] make identi-fication and monitoring of such oscillations in real-time possible. A vast amount of literature is available, where various methods from signal processing and system identification are employed in order to estimate the frequencies, damping ratios and shape of each oscilla-tion mode [3]-[6]. In this way, oscillations that are poor-ly damped, and could thus develop to dangerous insta-bilities, are identified.

The methods and tools are now mature and in daily use by several power system operators around the world. Just from ambient system measurements, an operator can know in real-time, at any moment, what is the oscillatory behavior of its system. The next step should be to develop decision-support tools that can help identify the root causes of poorly damped oscillato-ry modes and propose operator actions to improve the characteristics of those modes. A potential first step towards this direction would be to associate system operating points with expected oscillatory behavior. This paper tackles exactly this issue.

Presently, system operators usually associate the presence of a poorly damped oscillation with that of an

“excessive” power flow over a specified cut (typically representative of some wide-area power transaction, like east-west, north-south etc.). However, in a meshed grid, such interpretations may be overly simplifying and may lead to a conservative use of the network. Objective of this work is to develop more fine-tuned techniques to associate the system operating status with the existence of poorly damped oscillatory modes. To this purpose, we derive a support vector machine (SVM) model to classify candidate operating points as secure or insecure according to the corresponding anticipated oscillation damping ratio.

In its essence, the proposed SVM is capable of re-ceiving, as input, a candidate operating point and pre-dicting whether its corresponding damping ratio is ex-pected to be above an acceptable threshold or not. In other words, the SVM results in a secure/insecure clas-sification of an operating point according to its antic-ipated damping ratio.

The problem can be viewed as a special case of the generic dynamic security assessment (DSA) problem. After pioneering work done in the late ’80s and ’90s, the application of various automatic learning techniques to enhance the real-time applicability of classical DSA is again receiving increasing attention in the last years [7]-[10]. These approaches use data created offline, by dynamic simulations of many scenarios, to train a ma-chine learning model, which is in turn deployed in real-time to check online the security status of the system. In post-fault (or corrective) DSA the model predicts the future security status under an ongoing disturbance, while in pre-fault (or preventive) DSA the model eva-luates the present security status with respect to a set of possible disturbances. Typically, steady-state variables are used as input features in pre-fault DSA.

Although conceptually similar to pre-fault DSA, the here-proposed approach differs in the following aspects: 1) The security status of an operating point is defined solely by its corresponding damping ratio. It is assumed that the system operator has already defined an unac-ceptable value for this ratio. 2) It is not the objective of our approach to estimate this ratio (hence, the security status) in real-time, since this is exactly what is done by the wide-area monitoring system (WAMS), but rather to foresee whether a candidate system dispatch / configu-ration is expected to turn out insecure in actual opera-tion.

Figure 1 shows one of the latest critical inter-area os-cillation occurred in the ENTSO-E continental Euro-pean network on Feb. 19th 2011 [11] when during an early Sunday morning the Italian power system mainly


oscillated against the rest of the systeminutes. This large oscillation was succby both the WAMS power oscillation installed at Swissgrid, which providedwarning and an alarm about 30 secondsly, 2 minutes after the onset of the osciduring the time of the oscillation the Ewas operating with a large import to same time a significant infeed from Southern Italy. Due to these two factorsshare of thermal generation, which tstabilization of oscillations through tonline. The result was a negatively dathat became visible following the redithe new market clearing at 8 in the mthermal generation was taken offline anan oscillation that grew to a magnitudsouthern Italy over a period of 8 minutcontinue growing, it is not unlikely thwould have caused loss of synchronismof the ENTSO-E grid. However the timoperators to redispatch with the objectthe import to Italy prevented this.

This event highlights the importanceagement of power oscillations in the This paper contributes to a frameworkindicators from WAMS can be correlatedispatch operation from SCADA and fotially propose preventive actions befothreatening to power system security. that the cross-border flows as well as tment are important factors to consider low modal damping.

Figure 1: Frequency recording from Swissg02-19 where a large oscillation in the Norwas detected by the power oscillation monoutside envelop is the frequency measuredwhile the inside envelop is the frequency mDenmark.

The remaining of the paper is organSections 2 and 3 provide, respectivelysupport vector machines and evolutionThe latter are used to tune the SVM hypexplained in the sequel. In Section SVM-based classifier is presented as a by an illustrative realistic example inpaper closes with concluding remarks.

em for about 15 cessfully detected monitoring tools

d a low damping s and, respective-llation. Prior and

ENTSO-E system Italy and at the solar power in

s a relatively low typically support their PSSs, was

amped oscillation ispatch based on morning. Further nd the result was de of 120mHz in tes. If allowed to at the oscillation

m and a break-up mely decisions by tive of lowering

e of proper man-ENTSO-E grid.

k where stability ed by operational oresee and poten-ore they become

It also suggests the unit commit-when predicting

grid WAMS 2011-rth-South direction nitoring tools. The d in Brindisi Italy,

measured in Kassoe

nized as follows. , an overview of

n strategies (ES). perparameters, as 4 the ES-tuned whole, followed

n Section 5. The

2 SUPPORT VEThe “building block” of an

of an optimal separating hyptwo classes by maximizing tpoint from either class [12]. that choosing the maximum plane (among all possible senimizes the classifier’s genedata [12]. This choice is an isuccess in classification taskSVMs can be found in many[13]). We only present a short

Let us from now on refer this is the problem that we wtions classification implemenvector of input features and lethe two respective classes. Eaup of a pair , , with separating hyperplane is defin

such that 1 when samand 1 when sample

Typically, interclass margfor some points to be on the waccommodate non-linearly sediscard outliers.

Finding parameters andsolving the quadratic program

min, 12where is the number , , … , are slack variab(or regularization, as typically

Problem (2) is typically dual problem, eventually lead

max 120,where , with tconstraint 0 in (2). From(3), weights of (1) are eveing use of the Karush-Kuhn-T

which gives the following bou

( is easily computed from th

ECTOR MACHINES n SVM is the construction

yperplane, which separates the distance to the closest In fact, it has been shown margin separating hyper-

eparating hyperplanes) mi-eralization error on unseen mportant aspect of SVM’s s. Detailed descriptions of y reference textbooks (e.g. t refresher to the reader. to a two-class problem, as

will deal with in the oscilla-ntation. Let denote the et us label by ‘+1’ and ‘-1’ ach sample , thus, is made denoting the class label. A

ned as a linear boundary 0 1

mple belongs to class ‘+1’ belongs to class ‘-1’.

gin is maximized allowing wrong side of the margin to eparable cases but also to

d of translates into mming (QP) problem

1 , 0 2

of training samples and bles. Constant is a tuning y called) parameter. solved by resorting to its

ding to

, 0 , 3

the Lagrange multiplier of m the solution of problem entually computed by mak-Tucker conditions of (2)

, 4

undary function

5

e training examples).


In order to capture nonlinear patteSVMs generalize over the just describeclassifier by mapping the original feathigher dimension one, where classes arable. This would normally require that replaced by a new input vector problem (3) is solved over the new trainInstead, a so-called kernel function ,that corresponds to inner products in space, is used, alleviating the dimensioputational burden associated with explall terms. The user chooses thewithout need to actually ever define thtion. Terms in (3) are substi, and then the QP problem is puts are classified according to (5) bykernel function.

Two widely used kernels are the

• radial basis (Gaussian): ,• th degree polynomial: ,

which are the two kernels that we conslations predictor application presented i

The role of the regularization parameven more pronounced in an enlargewhere perfect separation can typicalOverly large value of will lead tocurvy” boundary. Overly small will lsmooth boundary, with big training erro

One can see that training the “optisifier, i.e. with an as small as possibleexamples, for one’s application is a taskchoices that need to be made before actSVM optimization problem. Namely, thfunction, its parameters (e.g. the degreeal), as well as the regularization paramproperly selected (let us from now on choices together as “hyperparameters”the same training data, different hyperplead, in general, to different test accuracing SVMs.

One typical approach to this “hyperpproblem is to try different combinationa grid search over the space defined byly choose those that led to the SVM witaccuracy. Clearly, grid search is a which may miss promising solutions. follow a more systematic approach fortuning, as explained in the following sec

3 EVOLUTION STRATEGIHYPERPARAMETER

Formally, we are facing the problemnon-analytical objective function, over and discrete variables. Precisely, the riables are the SVM hyperparameters1,

1 the choice of kernel been seen as a d

erns in the data, ed support vector ture space into a re linearly separ-each vector is

and then ning examples .

, 6

the transformed onality and com-licitly computing e kernel function he mapping func-ituted by terms solved. New in-

y resorting to the

1

sider in the oscil-n this paper.

meter becomes ed feature space, lly be achieved. an overfit “too lead to an overly

or. mal” SVM clas-

e error on unseen k that depends on tually solving the he type of kernel e of a polynomi-meter must be refer to all those

”). Using exactly parameter choices cies of the result-

parameter tuning” ns of them (doing them) and final-

th the highest test rough approach, In this work we

r hyperparameter ction.

ES FOR SVM R TUNING m of optimizing a

both continuous optimization va-while the objec-

discrete variable

tive function is computed by choice of hyperparameters) anThe latter can be computed eiable dataset into training anding procedure, or by cross-vdataset into equal sets andusing 1 sets for training ing. The accuracy in this casecomputed accuracy vales.

We search for the hyperpahighest accuracy (for our give

In the remainder of the papdiscrete, variable of choosingcontinuous variable which dpolynomial and the Gaussianin this application, we limit onels), resulting into the follow, with 0 1.

Equation (7) is a valid kerof two valid kernels.

Choosing 10-fold (i.e. our accuracy measure, Figurewe are solving. Let us recall in formulating and solving a in Section 2.

Figure 2: Optimization problem

Global optimization problsuccessfully tackled with proas heuristic) methods like swarm intelligence methods, search and others [14]. In thistion strategies (ES) [15], dueciency and their resistance inContrary to genetic algorithmreal continuous variables, as

Figure 3 delineates the barithm. Each evolutionary oriented selection operator ininto promising regions in the evolution a direction. Selectthe variation operators (mutwhich are responsible for ex

training an SVM (given a nd calculating its accuracy. ither by dividing our avail-d test sets before the train-validation, i.e. separate the d train SVMs, each time and the remaining for test-e is the average over the

arameters that result in the en initial set of data). per, we relax the, originally g the kernel function to a defines a share between the

n kernels (let us recall that, ourselves into this two ker-wing mixed kernel: 1 1 7

rnel, as linear combination 10) cross-validation as 2 summarizes the problem that train an SVM consists QP problem, as illustrated

for hyperparameter selection.

ems of this type are often obabilistic (also referred to

evolutionary algorithms, simulated annealing, tabu

s work, we resort to evolu-e to their high search effi-

n falling into local minima. ms, ES are most suited for , , and are. asic cycle of the ES algo-algorithm needs a goal

n order to guide the search variables space, giving the

tion is the “antagonist” to tation and recombination), xploring the search space.


Variation should not use any fitness inthe search information indicated by the tion. There is no preference of any of ents in ES, since the variation operatoduce no bias.

A 5/ 2, 1, 35notation) has been used in this work.

Figure 3: The basic cycle of the ES algorith

4 IMPLEMENTATION OF IOSCILLATION CLA

The here-proposed application starability of today’s WAMS to compute, oscillatory modes in the system they mPMUs are properly located. Over tim(expected to be) created, containing, amhas the oscillatory modes’ damping besystem configurations (i.e. operating paper, we train an ES-tuned SVM cscribed in Sections 2 and 3, that is abacceptability, in terms of oscillationspotential operating point.

Operating points are assumed to be cure or insecure by the system operatorshold damping ratio (or any other criterdifference to the followed methodologytraining, a dataset is available; each entrset of input variables’ values (i.e. thooperating point, as discussed in the binary (i.e. secure/insecure) output.

The most straightforward applicatiooped classifier is to be used in order to planned operating point is acceptable preventive check mode. Another potentto use the classifier in an offline analysto identify patterns of insecure operatimost influential input variables. Lascould be used, as module in a decisirithm, in a corrective mode, i.e. to actinsecure operating point, either in reaactually implementing the operating poi

Keeping these applications in mind,operating point is represented by SCADtion like the dispatch of generators antings of FACTS devices and the status power system stabilizers (PSS). The status as input variable is to be explainein Section 5.

The reasoning behind this choice of ithe SVM is twofold. On one hand, the

nformation, only parental popula-the selected par-ors should intro-

(see [16] for

hm.

INTER-AREA ASSIFIER rts out from the

in real-time, the monitor, provided me, a database is mong others, what

en under various points). In this

classifier, as de-ble to predict the s damping, of a

classified as se-r based on a thre-rion; it makes no y). Hence, before ry consisting of a ose defining the sequel) and one

on of the devel-check whether a or not, i.e. in a

tial application is is mode, in order ing points and/or st, the classifier on-making algo-tively modify an

al-time or before int. , in this paper an

DA-type informa-nd loads, the set-of the generators

choice of PSS ed in the example

input variables to ese are variables

that are expected to be availabIn Europe, for instance, the various regional electricity msuch type of information comators. The classifier can, thusa planned dispatch. On the riables should contain the conagainst the insecurity. If poteoperating point are identified counter-measures should be im

Two important practical issto actual implementation of thto be ensured that all usedsynchronized. Typically, WAbe available with a higher timdata. One solution could be damping ratios over the timSCADA data, while anotheSCADA instance with the instance and discard the rema

A second important issue variables should be used as iing the whole set of SCADvariables may not be approprMuch of this information maylem. b) There is a lot of reduntraining may become compPoints a, b and c may lead tosifier. e) The operator may wto what is under its control. f)check out the influence of spnations of them (e.g. power fleration at specific area etc.).

The last two points suggesput variables by the user. Onrequire rather an automatic dimension reduction) procedeither be done before trainingthe training. Filter methods classifying features based oncorrelation with the output wrapper methods follow the ly adding/subtracting features

Figure 4: Linking WAMS and classifier.

ble on a system-wide level. increasing coupling of the

markets makes exchange of mmon practice among oper-

, check the acceptability of other hand, the input va-

ntrol means of the operators ential causes of an insecure

by the classifier, proposed mplementable. sues emerge when it comes he approach. First, it needs d data are properly time-AMS data are expected to me-resolution that SCADA

to average the oscillation me period covered by the er would be to link each

closest available WAMS ining WAMS data. is to properly select which nputs to the classifier. Us-A data instances as input

riate for several reasons: a) y be irrelevant to the prob-ndancy in the data. c) SVM putationally intractable. d) a less accurate SVM clas-

want to limit the input only ) The operator may want to pecific variables or combi-flows in specific lines, gen-

st an explicit choice of in-n the other hand, points a-d

feature selection (and/or dure. This procedure may g the classifier or be part of

follow the first approach, n some information gain or

type of criterion, while second approach, iterative-

s and training the classifier.

SCADA systems with SVM


Down to here, for the simplicity of thhave been referring to an “oscillationsfrom which the security/insecurity ouClearly, each oscillation mode has itratio. The approach followed in this paan operating point based on the leastAnother possibility could be to train oexisting oscillatory mode.

Figure 4 illustrates the described app

5 TEST CASE – RESWe tested the proposed approach on

Nordic32 system, modified to be more tions. 12978 different scenarios have classified according to their minimumOscillation modes have been computedof the system. Generations are repreorder models. The various scenarios starting from a base-case one and progrand/or decrease (under constant powergenerations and loads towards specifiethe construction of each scenario, Gabeen added individually to each generatadditional aspect that has been investigaeffect of dispatching of units not equipFor example, when conditions for phoproduction are favorable, conventionaroutinely equipped with PSS may be shtest cases, this has been represented byPSS of a generation. Hence, each inigiven rise to actually 21 scenarios, obeing on and 20 scenarios each correspbeing off (there are 20 generators in outhreshold of 2% has been chosen for tceptable damping ratio, i.e. an operaticure if at least one of its correspodamped by less than 2%.

A dataset has been eventually creconsisting of all generators’ active poweloads’ active consumption, all lines’ actall PSS status and a label denoting seoperating point.

Figure 5 shows the five less damped es for each of the considered scenariopearing at around 0.35-0.5 Hz is an basically between generators in the norrators located in the southern ends of thout to be the only “unstable” one (less ing ratio) in our dataset.

2 e.g. increase north to south powe

various combinations of generation anes/decreases, increase total system loimport to / export from specific system

he discussion, we damping ratio”, utput is derived. ts own damping aper is to classify t damped mode. one classifier per

proach.

SULTS n a version of the

prone to oscilla-been solved and

m damping ratio. d by linearization esented by sixth have been built

ressively increase r factor) relevant ed directions2. In ussian noise has tion and load. An ated concerns the pped with a PSS. otovoltaic power al units that are hut down. In our y turning off the tial scenario has

one with all PSS ponding to a PSS ur test system). A the minimum ac-ng point is inse-

onding modes is

ated, each entry er production, all tive power flows, ecure or insecure

oscillatory mod-s. The mode ap-inter-area mode, rtheast and gene-e system. It turns than 0.02 damp-

er transaction by nd load increas-oading, increase areas and more

Figure 5: Damping ratios of “firs

Figure 6: Damping ratio vs. inte12978 samples have a dampingsamples with intertie flow > 38 Mdamping ratio < 2%, while thereflow > 40.5 MW, 780 out of whic

As inter-area modes’ lowehigher inter-area power transwe plot in Figure 6 all dataseing ratio (i.e. the damping mode) versus the active poweby four tie-lines (which we caing the northern with the souThe correlation between intdamping is obvious. Howevethis inter-area flow seems notry factor for low damping. A this information would have tive or to allow considerable ing points. For example, if used as a classification thresples are correctly classified. 92.2% if a 40.5 MW threshopense of missing half of the in

The effect of the lack of athis figure. For each intertie f(precisely 21) operating pointvarious generators’ PSS beinof the PSS in some particularorates the system oscillatory p

Table 1 shows the accuraclassifier for different selectdifferent selection of kernelsthe polynomial or radial basiachieved by ignoring the respsmall improvement in the claachieved by resorting to the m

st 5” oscillatory modes.

ertie power flow. 1643 out of

g ratio < 2%. There are 4851 MW, 1271 out of which have a e are 924 samples with intertie ch have a < 2% damping.

er damping and presence of saction typically correlate, et operating points’ damp-ratio of the least damped

er flow over the cut defined all “intertie flow”) connect-uthern area of the system. tertie flow and oscillation er, it should be noted that t being the only explanato-security rule based only on either to be too conserva-amount of insecure operat-a 38 MW intertie flow is

shold, only 69.5% of sam-This accuracy is risen to

old is used, but at the ex-nsecure operating points. a PSS is, as well, visible in flow value there are several ts. These correspond to the

ng one-by-one off. Missing r locations severely deteri-performance. acy (in %) of the resulting tion of input features and . The results presented for is kernels alone have been pective term of Eq. (7). A assifier’s accuracy may be

mixed kernel.


In the input features column of Table 1, “PSS status” stands for whether the on/off status of each particular generator PSS is considered as input variable. 20 va-riables have been created, each taking value “1” if the corresponding generator PSS is off and “0” otherwise. Since SVMs accept only continuous inputs, they have been treated as continuous variables. Feature “dispatch” in the table contains all generators and loads respective active power production and consumption (41 va-riables). “Power flows” contains the active power flows in all lines (37 variables). The term “synthetic features” stands for a set of higher level features that a system operator may wish to use. It contains 16 variables, each representing total generation or total load in a specific area of the system (e.g. total “North Generation”).

Input features kernel

mixed radial basis

poly-nomial

Only intertie flow 92.7 92.7 92.0Intertie flow & PSS status

93.4 94.0 92.8

Dispatch 95.6 95.6 95.6Intertie flow, PSS status & synthetic features

98.3 97.8 98.2

Dispatch & PSS status 98.6 97.8 98.3Dispatch, power flows, PSS status & synthetic features

99.2 98.6 99.1

Table 1: Resulting accuracy, computed by 10-fold cross-validation, for various input features and kernels. All ES are solved with 5, 35, with a maximum 320 evaluations termination limit.

One can clearly observe that alone the intertie flow is too poor an indicator for proper classification. Classifi-cation based on the dispatching increased accuracy by 3%. In addition, considering the type of generation in operation (represented here by the “PSS status” fea-tures) is very relevant (compare results obtained with and without the “PSS status” feature). Interestingly, substituting the detailed dispatch with the “synthetic features” very little affected the accuracy. Finally, it is worth commenting that, despite the clear data redundan-cy, our classifier consistently achieved the highest accu-racy levels when all available features were used as input variables.

The improvement on the accuracy of the final clas-sifier (obtained at the end of the ES algorithm execu-tion) compared with the best of the 5 classifiers making up the initial population (obtained via randomly choos-ing the SVM hyperparameters) has been, in all cases in Table 1, ranging from 1% to 3%; tuning of the SVM hyperparameters pays off.

Figure 7 shows the evolution of the best candidate before each selection step. The plot is drawn for the mixed kernel case. Similar results have been obtained for the radial basis and the polynomial kernels. Each line in the plot corresponds to a scenario where different input features have been used, as already illustrated in Table 1. The “dispatch” scenario has been omitted, to avoid overloading the figure.

Figure 7: Best accuracy at each selection step during the execution of the ES optimization (the mixed kernel is used).

Figure 8: Hyperparameter values of the best selected individ-ual for the “all features” ES execution.

One can see that when less input features are availa-ble, higher accuracy increase is achieved during the ES optimization, suggesting that proper selection of SVM hyperparameters is more critical in the lack of high feature redundancy. In the “only intertie” and “intertie & PSS” cases, it is clear that the ES should be left to run further. A 320 fitness evaluations termination limit has been used in all our tests to allow us to produce enough results with limited computational and time resources. In practice, the user should of course let the ES con-verge. This has been the case for the three cases with more input features. There the algorithm converged at a point where no further improvement in accuracy can be achieved.

As a matter of fact, a maybe useful property of the approach is that the operator can use the best “up to now” available classifier in its decision-making tools, while letting the ES optimization run and possibly fur-ther improve the classifier.

Figure 8 shows the hyperparameter values of the best selected individual after each selection step for the “all features” mixed kernel ES optimization. It is interesting to notice that, although from iteration 4 and on the best individual’s fitness is almost constant (see “all features” line in Fig. 7), the corresponding hyperparameter values vary quite significantly. This behavior reflects the tra-deoff between model complexity (expressed by and ) and the regularization parameter , discussed in Section

90

92

94

96

98

100

1 2 3 4 5 6 7 8 9 10

Acc

urac

y of

bes

t so

luti

on

Iteration of ES algorithmall features

only intertie

intertie and PSS

dispatch and PSS

intertie, synthetic and PSS

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9 10

Hyp

erpa

ram

eter

val

ue

Iteration of ES algorithm

C

d

λ

γ


2. It also unveils the fact that different hyperparameter choices may result in practically equally good models. With the number of offsprings sufficiently large, many such “equivalent hyperparameter clusters” survive over iterations.

Last, it is worth commenting on the robustness of the proposed approach with respect to the starting popula-tion of the ES algorithm. For instance, Table 2 summa-rizes the resulted best, worse, mean accuracy and stan-dard deviation, achieved after 13 executions of the pro-cedure (for a specific choice of kernel and input fea-tures), each starting from different, randomly selected, initial population.

The algorithm stably converges to a very close to op-timal solution. It should be noted however, that there are many different combinations of the SVM hyperparame-ters that may yield an almost optimal SVM (as illu-strated in Fig. 8).

best worse mean std

98.23 98.17 98.19 0.024Table 2: Statistics from 13 executions of the procedure

6 CONCLUSION An ES-tuned SVM classifying operating points (de-

fined by SCADA type of input features) according to the damping ratio of the corresponding inter-area oscil-lation modes has been presented in this paper. The clas-sifier links WAMS with SCADA system data and aims at being an additional tool supporting system operators’ decisions. The presented results show that the metho-dology can model the underlying physical system with considerably high accuracy, making a step of improve-ment from present common practice.

Ongoing work is focusing on allowing for an auto-matic feature selection process inside the ES optimiza-tion and on incorporating the developed SVM model into online procedures that would properly modify the operating point in case an insecure one is observed. Although not in this paper’s focus, the proposed metho-dology should be also tested on instabilities not defined by the mode damping ratios.

ACKNOWLEDGEMENT

The financial support from the Marie Curie FP7-IAPP project “Using real-time measurements for moni-toring and management of power transmission dynam-ics for the Smart Grid – REAL-SMART”, Contract No: PIAP-GA-2009-251304 is gratefully acknowledged.

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