Transient Instability Prediction Using Decision Tree Technique

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Transient Instability PredictionUsing Decision Tree Technique

Turaj Amraee, Member, IEEE, and Soheil Ranjbar

Abstract—This paper presents a decision tree based methodfor out-of-step prediction of synchronous generators. For distin-guishing between stable and out-of-step conditions, a series ofmeasurements are taken under various fault scenarios includingoperational and topological disturbances. The data of input fea-tures and output target classes are used as the input-output pairsfor decision tree induction anddeduction. Themerit of decision treebased detection of transient instability lies in robust classificationof new unseen samples. The performance of the proposed methodis verified on two test cases including a 9-bus dynamic network andthe practical 1696-bus Iran national grid. The simulation resultsare presented for various input features and learning parameters.

Index Terms—Decision tree, out-of-step, power swing, predic-tion, transient stability.

I. INTRODUCTION

N OWADAYS power systems play an important role inhuman life. Power system performance depends on its

ability to maintain a desired level of stability and securityunder various fault conditions. Transient or large signal rotorangle stability is one of most important types of stability phe-nomena. Transient rotor angle stability is the ability of powersystem to maintain its synchronism under a severe fault suchas three-phase short circuit [1]. Power system stability underdifferent disturbances depends on installed control equipmentto damp electromechanical oscillations. To minimize the spreadof an undesired disturbance and the damage to generators, it isrequired to design appropriate protective schemes.Many techniques have been proposed for out-of-step detec-

tion. The most commonly used out-of-step detection techniqueacts based on the concept of blinders in the relay impedanceplane. This method requires some information about the fastestpower swing, the normal operation region, the possible swingfrequencies, and other system specifications [2]. Another tech-nique for out-of-step detection is based on analytical methodslike equal area criterion (EAC). This technique is suitable fora single machine infinite bus (SMIB) system. For large scalepower systems with many generators and transmission lines, theanalytical methods such as equal area criterion fail to give ef-ficient results. Therefore the time simulations are used for sta-

Manuscript received June 30, 2012; revised October 09, 2012 and November27, 2012; accepted December 31, 2012. Paper no. TPWRS-00747-2012.T. Amraee is with the Department of Electrical Engineering, K.N. Toosi Uni-

versity of Technology, Tehran (14317-14191), Iran (e-mail: [email protected]).S. Ranjbar is with the Science and Research Branch, Islamic Azad University,

Tehran, Iran (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.2013.2238684

bility and security assessment of large scale power systems. Inthis method, the set of differential algebraic equations (DAE) ofpower system are solved using a suitable algorithm.In [3], an out-of-step detection technique has been proposed

based on artificial neural network. In this method, the authorshave used the kinetic energy deviation, mechanical inputpower and average acceleration during fault as input featuresfor neural network training. In [4] a neural network basedhybrid scheme has been proposed for system wide detectionof transient instability. In [5], the application of fuzzy logicusing an adaptive nero-fuzzy inference system (ANFIS) hasbeen suggested for out-of-step detection. In this method theangular frequency deviation and the impedance angle measuredat the machine terminal are used as inputs to the fuzzy logic.The performance of fuzzy logic and neural network methodshighly depends on the user-defined training parameters (e.g.,membership function, parameters of defuzzification algorithm,neuron function, etc.). The concept of energy function is an-other technique has been proposed for out-of-step detection [6],[7]. During unstable power swings, the entire power systemoscillates in two groups. The series elements that connect thesegroups are called cutsets. By evaluating the potential energyof the cutset, the stable and unstable conditions are predicted.This technique needs wide area information. A technique fortransient instability detection has been proposed in [8] basedon the classical equal area criterion (EAC) in the power-angledomain. This technique requires the pre- and post-disturbanceinformation of the system as the inputs to the relay. Also amultivariate polynomial approximation has been presented in[9] for transient stability assessment. In [10], the application ofdecision tree (DT) theory based on R-Rdot strategy has beenproposed for loss of synchronism detection. In this strategythe apparent resistance measured by the relay and its rate ofchange have been used as the input training features. The sametechnique has been used in [11] for wide-area response-basedcontrol using synchronized phasor measurements. In [12] aK-means clustering pattern recognition technique has beenproposed for out-of-step detection. Support vector machine isanother technique that has been proposed for transient stabilityassessment [13], [14]. In this paper a decision tree classifier isproposed to develop an out-of-step predictor. The DT-basedscheme extracts the important features using the informationgain criterion. The required input features are measured at therelay location well before the instant of out-of-step point.The rest of this paper is organized as follows. In Sections II

and III, the fundamentals of out-of-step conditions and its cri-teria are described. The details and structure of the proposed de-cision tree based scheme are presented in Section IV. The simu-lation results of applying the proposed method over a 9-bus dy-namic test system and the practical 1696-bus Iran national grid

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Fig. 1. Equal area criterion (EAC) for transient stability assessment.

are given in Section IV. Finally, the conclusions are provided inSection V.

II. OUT-OF-STEP FUNDAMENTALS

Referring to Fig. 1 based on the equal area criterion, the oc-currence of a disturbance makes an imbalance between mechan-ical input power, i.e., , and electrical output power, i.e., .When the disturbance severity is weak, the accelerating area,i.e., , is smaller than the decelerating area, i.e., . There-fore the oscillations die out quickly and the power system willremain stable. When the disturbance is severe, the acceleratingarea is greater than decelerating area and the oscillations donot damp out and the machine experience an unstable conditionwhich is called out-of-step or loss-of synchronism conditions.The concept of out-of-step conditions is described using an

SMIB as shown in Fig. 2. The data of SMIB system are givenin the Appendix. Considering Fig. 2, the current at generatorterminal is expressed as follows:

(1)

(2)

where stands for the voltage magnitude behind the transientreactance, i.e., , of the generator. The angle by whichleads is named . Based on (1), the impedance measuredat the relay location is

(3)

where . By assuming , the measuredimpedance at the relay location, i.e., , can be written as afunction of as follows:

(4)

Fig. 2. Single machine infinite bus system (SMIB).

Fig. 3. Impedance trajectories at the relay location during a power swing as afunction of , when .

The impedance trajectory measured at the relay location isshown in Fig. 3. During a power swing, the angle is changingand the measured impedance by the relay changes too.When thevoltagemagnitudes, i.e., and , are equal (i.e., ), thetrajectory of the apparent impedance during a power swing cor-responds to the straight line that goes through the impedance tra-jectory at its middle point. The point at which the voltagemagnitude is zero and is called electrical center of theswing. In situation where is not equal to (i.e., ),the impedance trajectory corresponds to circles that centers onextensions of the impedance trajectory [1], [15]. Fig. 3shows the measured impedance at the relay location, i.e., asa function of in plane for .The trajectories of the rotor angle and the R-Rdot character-

istic are illustrated in Figs. 4 and 5 for two stable and unstablescenarios for the single machine infinite bus system shown inFig. 3. The R-Rdot acts based on the detection of the locus ofoperating points in and plane. In this paper, five dif-ferent input features are used to predict out-of-step conditionswhich are described in the next section.

III. OUT-OF-STEP DETECTION

Traditionally the out-of-step detection is carried out usingblinders as shown in Fig. 3. These blinders are placed inway-in (i.e., entrance) and way-out (i.e., departure) path ofthe impedance trajectory according to the maximum allowablevalue of rotor angle. Based on the measurement of the rateof change of impedance, i.e., , which is dominatedapproximately by the rate of change of resistance, these blin-ders detect the out-of-step conditions. Also the out-of-stepconditions could be identified using strategy as described


AMRAEE AND RANJBAR: TRANSIENT INSTABILITY PREDICTION USING DECISION TREE TECHNIQUE 3

Fig. 4. Rotor angle trajectories of the machine for two stable and unstablescenarios.

Fig. 5. R-Rdot strategy (a) for a stable scenario, (b) for an unstable scenario.

previously. Many criteria have been used in literatures fortransient instability prediction[3]. Here five parameters areconsidered as input features for loss of synchronism detectionas follows.• Mechanical input power: the mechanical input power (Pm)is equal to the electrical output power (Pe) before faultinitiation. In other words, this parameter is equal to theinitial generator loading

• Kinetic energy deviation: the kinetic Energy deviation, i.e.,, is calculated as follows:

(5)

where stands for the moment of inertia of the machine.For calculating , the signal of speed, , is measuredat the moment of the fault occurrence, i.e., , and at themoment of the fault clearing, i.e., . Here the out-of-

step detection is carried out for each synchronous generatorseparately. Therefore the constant parameters add no gainto the learning process and are ignored. Therefore the newfeature is redefined as follows:

(6)

• Average acceleration: the average acceleration duringfault is written as follows:

(7)

where and denotes the electrical poweroutput of the generator at and , respec-tively. The constant parameters add no gain to the learningprocess and are ignored. Therefore the new acceleratingpower is defined as follows:

(8)

• Electrical output power: the fourth feature is the electricaloutput power at the moment of the fault clearing, i.e.,

.• The fault duration is an important feature in transient sta-bility assessment. Therefore the clearing time, i.e., , isdefined as follows:

(9)

IV. DECISION TREE THEORY

Decision tree (DT) is one of the most commonly usedmethods for inductive inference or prediction. Decision treehas been successfully applied in various applications. Manytechniques have been introduced for construction of DT suchas Inductive Decision Tree (ID3), CART and C4.5 [16]. In thispaper the C4.5 algorithm is used for DT construction. Thisalgorithm could handle discrete target classes easily. Also thisalgorithm is robust against noisy data [17].

A. Decision Tree Learning

Decision tree is constructed using a set of training samplesand is then applied to classify a set of unseen samples that arecalled test samples. DT is constructed using a top-down searchperformance for data classification. It starts from a root nodeand samples are then classified by posing a series of questionsabout the features associated with the data. A node is dividedinto two sub branches according to the possible answers for itsquestion. As shown in Fig. 6, DT starts with a question in rootnode. To answer each question, it uses a set of statistical criteriafor data classification. The two commonly used measures areEntropy and the Gini indexes. For a typical two-class data setwith negative and positive target classes, the entropy of the dataas the purity degree of the data set is defined as follows:

(10)



Fig. 6. Major parts of a typical decision tree.

where(11)

(12)

where is the number of input samples with positive target classand is the number of input samples with negative target class.The entropy is lowest when all the samples have the same targetclasses (i.e., either or ), whereas it is maximumwhen the number of samples with positive class equals to thenumber of data with negative class (i.e., ). The Gini index

at a node , is defined as

(13)

where is conditional probability of category in nodeand it is defined via (14) to (16):

(14)

(15)

(16)

where is the prior probability value for category ,is the number of records in category of node , and isthe number of records of category in the root node. TheGini index is zero when all the samples in set have the sametarget class. Decision tree is grown by adding questions overremaining training samples. A good question will split a largecollection of data with different target classes into subsets withnearly of the same kind labels so that there is little variance ineach branch. If a question has possible answers, entropy ofinto subsets is defined as

(17)

Based on (18), if is the entropy function, then thedifference between the entropy of the distribution of the classesin the root node and the weighted average of the internal nodeentropy is named the information gain. The information gain atnode is expressed as

(18)

where is the data having been split in node . Information gainhas always a positive value because is the entropy of allsamples on a node and is the entropy of various classes of thenode. Therefore is always greater than . Informationgain is computed at each non-leaf node, and the feature with thehighest information gain will be selected as input feature for thatnode. This process will be repeated recursively to classify datainto smaller subsets in tree space until all of data are classified.

B. Decision Tree Pruning

In a top-down search performance, DT is grown fully to depthuntil all of the training samples are classified. Full growth of DTleads to the data over-fitting. Therefore DT should be prunedto avoid over-fitting of the training data. Several pruning tech-niques have been introduced in the literature, including cost-complexity pruning, reduced error pruning, pessimistic pruning,error-based pruning, penalty pruning andMDL pruning. The de-tails of these methods can be found in [18]. One pruning tech-nique is the full growing of tree and then pruning it back with thegoal of identifying the tree with lowest error and lowest com-plexity. In this paper the decision tree pruning is carried out byerror reduction technique. Based on this method, the error rateof each leaf node is written as follows:

(19)

where , , and denote the number of samples in node ,the number of target classes, and the number of samples withmajority class in node respectively. For a non-leaf node thebacked up error (BE) is

(20)



where is the node number and is the conditional probabilityof each leaf node in node . Finally based on (19) and (20), theerror rate of each node is determined as follows:

(21)

This method starts with a complete tree. For node , (i.e.,error in each node) is computed. Then for each leaf node in nodethe (i.e., error in each leaf belonging to node ) is computedand multiplied by its conditional probability. The computed er-rors at leafs are summed and the new is computed that calledbacked up error of the th node. If the backed-up error estimateis greater than in node , all sub-branches of node are re-moved and will be replaced with a new leaf. This process will berepeated in each node of tree until further pruning increases themisclassification rate (i.e., is greater than backed-up error).This method creates the smallest and the most accurate possibletree.

V. CLASSIFICATION ALGORITHM

The proposed scheme has two major parts: the first part isgenerating input training samples and the second part includesthe process of decision tree construction. In the first part, variousfault scenarios are created. Each scenario is then simulated usinga transient stability simulator and the required data with theirtarget classes (i.e., stable or unstable) are recorded.The proposed out-of-step prediction algorithm is imple-

mented via the following steps.Step 1) Create the simulation scenarios, , regarding var-

ious fault conditions.Step 2) Set scenario counter .Step 3) Simulate the th scenario using transient stability

simulator.Step 4) For the th scenario at , measure

and at , measure and.

Step 5) Construct the th input-output pair using (6), (8), and(9) as:

(Input Features, Target Class)Input Features:Target Class: [Stable, Unstable].

Step 6) If , then go to Step 3; else continueStep 7) Define basic adjustments of decision tree.Step 8) Construct Root node: Compute and

over all samples.Step 9) Grow decision tree.Step 10) If based on settings in Step 7, the best decision tree

is found, then continue; else go to Step 8.Step 11) Prune DT using the technique described in

Section IV-A.Step 12) Classify new samples using best decision tree and

send or signal.Step 13) End.

VI. SIMULATION RESULTS

In this section, the proposed DT-based out-of-step scheme issimulated over two test cases including a 9-bus dynamic 230-kV

Fig. 7. Single line diagram of 9-bus dynamic network.

network and the practical 1696-bus Iran national grid. The sim-ulations are carried out for a comprehensive list of scenarios anddifferent combinations of input features. The input scenariosshould cover all the credible contingencies. For incredible con-tingencies (e.g., loss of a major transmission corridor or loss ofall units in a specific power plant), it is required to update theexisting decision tree. From part A to part D, the major aspectsof the proposed scheme are verified over the 9-bus test system.The application of the proposed method over the practical Irannational grid is presented in part E.

A. Generation of Input Samples

The proposed DT-based out-of-step protection scheme issimulated over a 9-bus dynamic 230 kV network [15] shown inFig. 7. The generator G1 is selected as the reference generatorand the generator is equipped with an out-of-step relay atbus 2. The required inputs are measured at bus 2 or generatorterminal and the input features are then calculated. In thisstudy the samples are generated at 15 different fault locationsincluding end and middle points of transmission lines, and LVside of step up transformers. Two fault types including singlephase and three phase short circuit faults are applied. Fiveloading scenarios are defined as 50%, 75%, 100%, 125%, and150% of base case loading. Also three different critical clearingtimes including 10 ms, 50 ms and 150 ms clearing times areconsidered. The faults at transmission side are followed bytransmission line outage. Based on the simulation scenarios,there are a total number of 513 events or 513 input-output pairs.Each input event has been simulated by the transient stabilitysimulator and the system response has been monitored duringa 6-s simulation. If the system experiences the pole slippingpoint (i.e., ), then the event is named an out-of-stepcondition. For this test case, there are 410 stable samples and103 unstable samples.

B. Feature Selection

Decision trees are adaptive in different aspects such as:1) DTs automatically adapt to favorable conditions near de-cision boundary, 2) DTs focus on data distributed on lower



TABLE IRESULTS OF DT ACCURACIES FOR DIFFERENT

COMBINATIONS OF INPUT FEATURES

dimensional manifolds and 3) DTs reject irrelevant features bythe concept of information gain. Many parameters could beconsidered as input features for decision tree learning. Theseparameters were described before. In this paper five parametersincluding mechanical input power (Pm), the kinetic energydeviation, i.e., KE, the average acceleration, i.e., , theelectrical output power at the moment of the fault clearing ,i.e., , and the fault duration, i.e., CT, are consideredas input features. For each scenario, a 6-s simulation is carriedout and the input features with their related target classes aredetermined.Based on the proposed method, for each combination of input

features, the best decision tree is found. The results of the com-prehensive DT construction are given in Table I for pruning de-gree of 45%. For each combination, the classification accuracyand total number of misclassified samples are presented. A mis-classified sample is a stable sample classified as unstable, or anunstable sample classified as stable.Based on Table I it can be seen that for 1-dimension input fea-

ture, the is the most important attribute with the accuracy of95.52%. Also for 2-dimension input features, thecombination is the most important attribute with accuracy of97.66%. For 3-dimension input features, the two combinationsincluding andare themost important attributes with accuracy of 95.22%. It canbe seen that by selecting four input features (i.e., combinations21 and 25 in Table I), the classification is perfect, i.e., the accu-racy is 100%. By selecting all input features, the best accuracyis 99.61%. For better explanation, the distributions of total 513samples have been illustrated in Figs. 8 and 9 in and

planes, respectively. The sensitivity of the bestaccuracy versus the pruning degree is depicted in Fig. 10. By

Fig. 8. Distribution of input samples in and plane.

Fig. 9. Distribution of input samples in , , and plane.

Fig. 10. Accuracy of best tree versus pruning degree.

increasing the pruning severity, the best accuracy is decreased.The obtained DTs for 21st combination are illustrated in Figs. 11and 12 for 80% and 45% pruning degree, respectively.

C. Misclassification Cost

In a power system, the cost of a false trip is much more thanthe cost of a failure to trip. A false trip is a stable scenario whichhas been classified as an unstable scenario. In the previous case,the misclassification cost for both failure to trip and false trip



TABLE IIRESULTS OF DT ACCURACIES FOR DIFFERENT VALUES OF MISCLASSIFICATION COST

Fig. 11. Best decision tree under 80% pruning degree.

was assumed equal. In this section, the cost of a false trip isassumed 5 times of the cost of a failure to trip. The results ofdecision tree construction are given in Table II.Based on the results given in Table II, it can be deduced that

the constructed decision tree goes in favor of failure to trip in-stead of false trip.

D. Comparison

Two previously proposed methods, i.e., artificial neural net-work and support vector machine, are selected to make a clearcomparison. The ANN technique is a multilayer perceptron feedforward neural network while the training process is achievedvia the back-propagation algorithm. The parameters of ANNscheme are determined using gradient descent algorithm withminimizing the output mean squared error. The hidden layer has10 neurons. Training is carried out for 300 epochs over inputdata. The network parameters including weight vector, , biasterm, , and the learning rate, , are optimized to obtain the min-imum error. and are assumed as 0.1 and 0.9. The input dataare normalized with a zero mean and unit variance. To make abetter comparison, the SVM technique has the same structure asthe one proposed in [13]. The radial basis function kernel withstandard deviation of 0.1 is used. Different values for the regu-lating parameter including 0.1,10, and 1000 are tested and thebest accuracy is selected. The accuracies of classification usingDT-based scheme, ANN and SVM are given in Table III. Thedimension of input features is changed from 1 to 5 and the bestaccuracy found in each case is reported. It can be seen that theDT-based scheme presents lower number of misclassified sam-ples in all combinations.

E. Application to Iran National Grid

The proposed scheme is tested on the practical large scalegrid of the Iran. Iranian power system has 63 384 MW installedcapacity including 24.3% steam units, 37.3% gas turbine units,22.7% combined cycle units, 13.4% hydro units, and 2.3% fromother resources. There are about 444 synchronous machines[19]. The dynamic model of the all elements and their controldevices are inserted in the Transient Stability Simulator. Thesingle line diagram of the Mazandaran electric region and itsneighbors is illustrated in Fig. 13. One of the synchronousmachines in NEKA power station is selected for out-of-stepdetection. Many scenarios including 75%, 100%, 125% loadingscenarios, topological changes including single line outages,



Fig. 12. Best decision tree under 45% pruning degree.

TABLE IIICOMPARISON OF OUT-OF-STEP CLASSIFICATION USING DIFFERENT METHODS, 9-BUS TEST SYSTEM

TABLE IVCOMPARISON OF OUT-OF-STEP CLASSIFICATION USING DIFFERENT METHODS, IRAN NATIONAL GRID

double lines outages, 3-phase short circuits, fault locationsincluding end points and middle points of transmission lines,and clearing times including 50 ms, 100 ms, 150 ms, 200 ms,and 250 ms. These scenarios have been simulated for two con-figurations with and without one of the synchronous generatorsat NEKA power station. There are a total of 1080 input eventsor training samples. Half of total samples, i.e., 540 events, are

for normal configuration, (i.e., all generation units in NEKApower station are in service) and the other 540 remaining eventsare for configuration when one of the generation units in NEKApower station is out of service. Therefore the constructed DT isa single DT with 1080 input training samples including topo-logical changes. Each input event has been simulated by thetransient stability simulator and the system response has been



Fig. 13. Single line diagram of Iran national grid, Mazandaran electric region.

Fig. 14. Best DT of Iran grid, ( , , ) features.

monitored during a 6-s simulation. If the system experiencesthe pole slipping point (i.e., ), then the event is namedan out-of-step condition. The results of comparison betweentwo previously proposed methods, i.e., artificial neural networkand support vector machine with the DT-based scheme, aregiven in Table IV. The ANN and SVM algorithms have thesame structures as used in the previous case. It can be seen thatunder topological changes (i.e., the outage of a synchronousunit at the NEKA station), the DT-based scheme presents betterresults. Also the obtained decision tree for 3-dimension inputfeatures including , , and has been illustrated inFig. 14.

VII. CONCLUSION

In this paper an approach for out-of-step detection in syn-chronous generators was proposed based on the decision treetheory. The obtained results indicated that the proposed methodis an effective technique for OS detection after fault clearing.Different combinations of input features were considered for de-cision tree construction. The proposed scheme was applied overa 9-bus dynamic network and the practical 1696-bus Iran na-tional grid. Also the results were compared with two previouslyproposed techniques. It was shown that the DT-based techniquecould reach the perfect classification for the small test systemand a accuracy for a large scale system. The merit ofthe proposed scheme lies in robust classification while speci-fying different cost for false trip and failure to trip cases. Theproposed decision tree is an effective technique which keeps itsperformance under topological changes.

APPENDIXDATA OF TWO-BUS TEST SYSTEM

Transformer: , ,Machine: , ,

,

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[19] [Online]. Available: http://www2.tavanir.org.ir/info/stat90/tafsili/tolid/tolid.pdf.

Turaj Amraee (M’12) was born in Loristan. He received the Ph.D. degree inpower system engineering from Sharif University of Technology, Tehran, Iran,and Grenoble Institute of Technology, Grenoble, France, in 2011.He is with the Electrical Engineering Department of K.N. Toosi University

of Technology, Tehran, Iran. His research interest is power system dynamic.

Soheil Ranjbar received the M.Sc. degree in power system engineering fromScience and Research Branch University, Tehran, Iran, in 2012.His research interest is power system dynamic.

Transient Instability Prediction Using Decision Tree Technique

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