a new power system transient stability assessment method based

Electrical Power and Energy Systems 64 (2015) 71–87

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

A new power system transient stability assessment method basedon Type-2 fuzzy neural network estimation

http://dx.doi.org/10.1016/j.ijepes.2014.07.0070142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail addresses: [email protected] (A. Sharifian), [email protected]

(S. Sharifian).

Amir Sharifian, Saeed Sharifian ⇑Department of Electrical Engineering, Amirkabir University of Technology, P.O. Box 15914, Tehran, Iran

a r t i c l e i n f o

Article history:Received 10 July 2013Received in revised form 1 July 2014Accepted 8 July 2014Available online 1 August 2014

Keywords:Type-2 fuzzy neural networkTransient stability assessmentCritical clearing timeType-2 fuzzy systemMultilayer perceptron neural networkMLP NN-based sensitivity analysis

a b s t r a c t

Transient stability assessment (TSA) of large power systems by the conventional method is a time con-suming task. For each disturbance many nonlinear equations should be solved that makes the problemtoo complex and will lead to delayed decisions in providing the necessary control signals for controllingthe system. Nowadays new methods which are devise artificial intelligence techniques are frequentlyused for TSA problem instead of traditional methods. Unfortunately these methods are suffering fromuncertainty in input measurements. Therefore, there is a necessity to develop a reliable and fast onlineTSA to analyze the stability status of power systems when exposed to credible disturbances. We proposea direct method based on Type-2 fuzzy neural network for TSA problem. The Type-2 fuzzy logic can prop-erly handle the uncertainty which is exist in the measurement of power system parameters. On the otherhand a multilayer perceptron (MLP) neural network (NN) has expert knowledge and learning capability.The proposed hybrid method combines both of these capabilities to achieve an accurate estimation ofcritical clearing time (CCT). The CCT is an index of TSA in power systems. The Type-2 fuzzy NN is trainedby fast resilient back-propagation algorithm. Also, in order to the proposed approach become scalable in alarge power system, a NN based sensitivity analysis method is employed to select more effective inputdata. Moreover, In order to verify the performance of the proposed Type-2 fuzzy NN based method, ithas been compared with a MLP NN method. Both of the methods are applied to the IEEE standardNew England 10-machine 39-bus test system. The simulation results show the effectiveness of theproposed method in compare to the frequently used MLP NN based method in terms of accuracy andcomputational cost of CCT estimation for sample fault scenarios.

� 2014 Elsevier Ltd. All rights reserved.

Introduction

Nowadays, the continues trend to increase in load demandsalong with economic and environmental constraints for buildingnew power plants and transmission lines, have lead power systemsto operate closer to their limits which increases the occurrenceprobability of transient stability problem [1,2].

The analysis and methods that are used to determine if a systemis safe or unsafe (based on pre-established criteria) is typicallyreferred as power system security assessment. An electric powersystem might have many changes in the system operatingconditions or configuration; therefore, planning phase transientstability studies, would not be reliable for an operational system,so continuous system analysis is necessary for operators to take

proper preventative control actions if insecure system conditionsoccurred.

The primary objective of transient stability analysis (TSA) in apower system is to determine the capability of power system toremain in stable and safe operating condition when a large distur-bance such as severe lightning strike, loss of heavily loaded trans-mission line, loss of generation station, or short circuit on buses [3]influences the system. CCT is a well-known indicator that can beused to measure power system transient stability. The CCT is themaximum time duration by which the disturbance may act onthe power system without losing its capability to recover to asteady-state (stable) operation.

We can broadly classify security analysis depending on model-ing and used technique into static and dynamic category [3,4]. Sta-tic security assessment is related to an equilibrium point of system,where voltage and thermal limits are observed. Generally staticsecurity assessment is done using computational tools based onload flow algorithms. The contingencies events must be considered

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72 A. Sharifian, S. Sharifian / Electrical Power and Energy Systems 64 (2015) 71–87

to ensure an acceptable steady-state condition, even if one elementof the system is lost.

Evaluation of the ability of a power system to withstand a finiteset of contingencies and to survive the transition to an acceptablesteady-state condition is defined as dynamic security assessment(DSA) [4]. As illustrated in Fig. 1, DSA consists of three main cate-gories: rotor angle stability, voltage stability and frequency stabil-ity. Also the rotor angle stability is divided into two sub categorieswhich are small signal stability and transient stability [3,5]. In thispaper we focus on TSA which involves the evaluation of the abilityof a power system to maintain synchronism under severe but cred-ible contingencies. The DSA studies are usually conducted in a timerange between 3 and 5 s for small power systems. For large sys-tems with dominant inter-area swings this time may extend to10 s [5].

Two main categories of TSA methods are time domain simula-tion (or numerical integration) method and direct method. Cur-rently, the widely used method by power utilities and mostaccurate method for TSA is time domain simulation method [5,6].This method is implemented by solving the differential equationsof power network while the direct method involves in calculationof the transient energy margins which shows the system stabilitylimits. This method gives an accurate information about state vari-ables and can be applied to any level of detail of power systemmodels [1,4,7]. In Ref. [37] the concept of lyapunov exponents(LEs) is used to analyze the transient stability of power systems.Also in Ref. [40]; a stochastic-based approach to evaluate the prob-abilistic transient stability index of the power system incorporat-ing the wind farm is proposed.

However, use of such a method requires numerical solution tononlinear equations of system which has high online computationcost and involves intensive and time-consuming numericalintegration efforts. Also, the difficulty of designing good energyfunctions for multi-machine power systems may lead to computa-tional inefficiency and inaccuracy [5,6]. So, it does not provideinformation regarding the degree of stability and the degree ofinstability in a power system.

In addition, TSA of large sized power systems has become a verycomplex process due to the exponential expansion of complexity inpower system topology. For each disturbance many nonlinearequations should be solved that makes the problem too complexand will lead to delayed decisions in providing the necessary con-trol signals for controlling the system. Therefore, there is a neces-sity to develop a reliable and fast online TSA to analyze the stabilitystatus of a power system when exposed to credible disturbances.

On the other hand, direct method techniques require less onlinecomputation efforts and can provide a quantitative measure of thedegree of system stability, but it has some challenges and limita-tions involved in the practical applications for power system TSA

Fig. 1. Taxonomy of power s

[5]. In recent years, machine learning and computational intelli-gence techniques, such as artificial neural networks (ANNs), havebeen proposed as promising approaches to solve some complexpower system protection and control problems instead of simulat-ing the power system equations for TSA in power systems [5,6,8–17]. These approaches can quickly obtain a nonlinear mappingrelationship between the input data and the output and canapproximate solutions of power system’s differential equations[6]. There are two ways in using ANN for power system TSA, oneway is using ANN as a regression function to predict transient sta-bility degree[8–13], such as CCT and system stability margin;another way is using the ANN as a classifier to directly classifythe system into either stable or unstable states [14]. There aremany different types of NN such as MLP NN and radial basis func-tion (RBF) NN which can be used in different applications.

The feed-forward NN, also best known as MLP NN, was the firstand most simple type of NN devised. It was developed in early1970s and is the most popular topology in use today. This NN con-sists of an input layer, an output layer, and one or more hidden lay-ers. In this NN the information only moves in forward direction.Data flows into the NN through the input layer, passes throughthe hidden layer and finally flows out of the NN through the outputlayer. There are no cycles or loops in the network. These networkscan be constructed from different types of units such as binaryMcCulloch-Pitts neurons. But frequently are devised as continuousneurons, with sigmoidal activation function in the context of backpropagation of error. The MLP NN can be considered as simpleinterpolation of input–output model, with NN weights as freeparameters. Such NN configuration can model functions of almostany arbitrary complexity. The function complexity is determinedwith the number of layers and the number of neurons in eachlayer.

Another frequently used NN in the literatures is RBF NN [15,16].RBF NN is powerful method for interpolation in multidimensionalspace. The RBF can be replaced by the sigmoidal hidden layer inMLP NN. The structure of the RBF NN consists of three layersnamely, the input layer, the hidden (or RBF) layer, and the outputlayer. The nodes within each layer are fully connected to the previ-ous layer. The input nodes are directly connected to the hiddenlayer neurons. Usually a Gaussian function is used in each nodein RBF layer to determine distance of inputs with respect to themean of the Gaussian function. A linear combination of hiddenlayer values that represents mean predicted output is generatedin the output layer when RBF NN is used in regression problems.When RBF NN is used in the classification problems, the outputlayer is representing a posterior probability. The output is typicallya sigmoid function of a linear combination of RBF layer values.

In RBF NN each input datum is associated with a RBF kernelfunction such as support vector machine method. In this approach

ystem stability methods.

A. Sharifian, S. Sharifian / Electrical Power and Energy Systems 64 (2015) 71–87 73

a non-linear kernel function is used to project the input data intoanother space. Where in the new space the learning problem canbe solved using a linear model. RBF NN is typically trained by max-imum likelihood framework. RBF NN is outperformed in most clas-sification applications by SVM. But they can be competitive inregression applications when the dimensionality of the input spaceis relatively small [15].

There are many previous papers which are using NN baseddirect methods to predict the CCT. Sobajic and Pao [8] were usedNNs to predict the CCT for a small test power system. Pao and Sob-ajic [9] used both unsupervised and supervised learning for the TSAproblem. In Ref. [10], Aboytes and Ramirez used NNs to predict thestability of generators system. In Ref. [11], Bahbah and Girgis pro-posed a recurrent RBF NN and a MLP NNs to model system dynam-ics and the generators’ angles and angular velocities are predictedto solve TSA problem. In Ref. [17], Sawhney and Jeyasuryaemployed NNs to predict a transient stability index, which wasobtained by the extended equal area criterion method.

In Ref. [18], a procedure has been described for extractingrules from a trained MLP NN for reasoning power systems CCT.In Ref. [19], a generalized regression NNs based classificationmethod has been proposed for transient stability evaluation inpower systems. Also in Refs. [20,21], two methods are introducedTSA which are based on adaptive resonance theory (ART) NNs. Toreduce the number of calculations and online computational timein Ref. [22], the major portion of power system transient stabil-ity’s mathematical calculations has been replaced by an estima-tion procedure. In Ref. [6], a MLP NN and a RBF NN are used toestimate the CCT as an index for power systems TSA accordingto the classical models. In Ref. [12], two MLP NNs are used to esti-mate the CCT and a transient stability time margin. Only a partic-ular fault scenario is considered and the detail models ofsynchronous machines are presented. In Ref. [39] classificationand regression tree (CART) based power system transient stabilitypreventive controls are proposed and the results are comparedwith MLP based method. The finding shows that preventive con-trols developed by both approaches think alike. They are evencomplementary.

Although ANN is the most popular computational intelligencemethod to classify patterns, it requires a complicated design proce-dure and an extensive training process. Moreover, ANN is good ininterpolation but not so good in extrapolation which decreasesits generalization ability [23]. MLP NN is a classic solution forCCT function approximation problem. Its accuracy can be increasedby addition of nodes and hidden layers.

Also RBF NN is shining in the problems that input parameterscan be classified into clusters (input parameters are correlated).Another advantage of RBF NN is that the hidden layer is easier tointerpret than the hidden layer in a MLP NN. Although the RBFNN has fast training capability, when the training is finished andit is being used for testing; it is slower than a MLP NN [6]. So wherespeed is a factor MLP NN may be more appropriate. MLP NN suffer-ing from local minima but RBF NN is not. This is because only thelinear mapping from hidden layer to output layer is adjusted in thelearning process. Linearity ensures that the error surface is qua-dratic, therefore it has a single minimum. The MLP NN requiresan iterative procedure to compute the network weights. But, theRBF NN requires an iterative procedure for clustering the data todetermine the number of nodes in RBF layer. A disadvantage forRBF NN is that the radial basis functions should have a good cover-age of the input space.

Simulation results using the New England test power system inRef. [6] indicates that both of NNs (RBF and MLP) could beemployed to estimate the CCT with a good degree of accuracy.However, better test results were obtained using the MLP NN. Bothof the NNs based solutions (MLP and RBF) can accurately estimate

CCT when the network inputs fallow exactly the training patterns.On the other hand when an input data is noisy or has uncertainvalue; both the MLP NN and the RBF NN failed to estimate anaccurate CCT due to the sensitivity of NN based methods tonetwork inputs. By considering these drawbacks, it becomesnecessary to devise a more robust solution for TSA problem inpower systems.

The Type-2 fuzzy sets have been introduced as an expansion ofthe type-1 fuzzy sets by Zadeh [24]. The Type-2 fuzzy logic systemscan handle uncertainties which are associated to information inthe knowledge base of the process. The Type-2 fuzzy sets have var-ious applications in solving many problems in the power systemarea [25–27]. Recently neuro-fuzzy systems have been used inmany areas of science and engineering [28–33]. A Type-2 fuzzyNN combines the learning capability of NNs and the linguisticinterpretation feature of fuzzy classifier to solve various problemssuch as predication, control and identification [30–35]. A majorproblem in adaptive fuzzy system is that its complexity is expo-nentially increased by the number of inputs to the network. Somany efforts have been done to reduce the number of inputs tothese networks. In Ref. [36], an adaptive fuzzy classification tech-nique is used with normal fuzzy technique to solve the power sys-tems TSA problem. The results are demonstrating the advantagesof using adaptive fuzzy technique. Moreover, a NN and a principalcomponent analysis (PCA) method are employed to reduce thenumber of inputs by sensitivity analysis technique. In Ref. [14], aneuro-fuzzy system is applied for power system DSA focusing onthe transient stability. The power system security state is classifiedby the neuro-fuzzy system into three categories named as‘‘secure’’, ‘‘doubtful security’’ and ‘‘insecure’’. In Ref. [38]; a binarySVM classifier with combinatorial trajectories as inputs wastrained to predict the transient stability status.

None of the previous works did not address the uncertainty andnoisy nature of power system measured data which are used asinputs to TSA system [4–6,8–14,16–22,35–43]. In this paper weproposed a Type-2 fuzzy NN to address the uncertainty which isexist in inputs. The Type-2 fuzzy layer converts uncertain andnoisy inputs to more dependable and reliable linguistic variableswhich are used as inputs to the MLP NN layer. The Type-2 fuzzyNN methodology is used to solve the on-line power system TSAproblem for a set of particular fault scenarios (contingencies)under different system operating conditions.

In the proposed method the Type-2 fuzzy NN is trained to pro-vide the CCT, as a measure of the power system transient stability.The Type-2 fuzzy system is used to cope with uncertainty of thepower system model and measurements of system operatingparameters. In addition, in order to provide a scalable solutionfor a large power system, the proposed approach uses a NN basedsensitivity analysis method [17,43] to reduce the number of inputsto the Type-2 fuzzy NN, so the complexity of system decreased andcalculation time become shorter enough to convert the proposedmethod to a feasible solution. It should be notified that the sensi-tivity analysis and training procedure are conducted offline but theestimation procedure is executed in online manner.

To evaluate the efficiency of proposed method, it applied to TSAof sample fault scenarios in the standard New England 10-machine39-bus test system [7]. The simulation results show the effective-ness of the proposed method in terms of accuracy and online com-putation time. In summary, the main contributions of the paper areas follows:

a. We propose a Type-2 fuzzy NN based method to accuratelyestimate the CCT as an index of power system transient sta-bility. The proposed method considers the uncertainty ofpower system model and measurements of system operat-ing parameters.


b. A NN based sensitivity analysis method is employed toreduce the number of inputs. So only the most effectiveinputs are considered and computational costs are reduced.

c. We conduct several simulations with different operatingconditions prior to fault scenario and compare the accuracyof estimated CCT by the proposed Type-2 fuzzy NN methodand other popular relevant method (MLP NN) with actualCCT to demonstrate the effectiveness of the proposedmethod.

The rest of paper is organized as follows: Section ‘Power system’describes power system model and test system. In Section ‘Method-ology for power system transient stability assessment’ theproposed Type-2 fuzzy NN and sensitivity analysis methodologyfor CCT prediction are presented. In Section ‘Results and discussion’we present results and discussion of power system TSA evaluationfor sample fault scenarios by the proposed method and compareit with MLP NN. Finally, conclusions are outlined in Section‘Conclusion’.

Power system

Many transient disturbances can occur in a power system suchas: loss of generation, faults, loss of load, and loss of system com-ponents such as transformers or transmission lines [3]. Assessmentof the rotor swing angles can be used to determine stability orinstability condition of a power system due to transient distur-bance. Following a transient disturbance, if the relative generatorrotor angles in the system remain in synchronism with each other,we conclude that a power system is stable. On the other hand,when the relative generator rotor angles go out of step and lostits synchronism a power system is considered as unstable. In thissection first we give an introduction to the classical model ofpower system and then describe our standard test system.

Power system model

Assume a power system consists of n synchronous generators.The classical model of system and the internal center of inertia(COI) [7,44] can be formulated by Eqs. (1)–(9) as follows:

dhi

dt¼ ~xi i ¼ 1;2; . . . ;n ð1Þ

Mid ~xi

dt¼ Pmi � Pei �

Mi

MTPCOI ð2Þ

Pei ¼Xn

j¼1–i

ðCij sin hij þ Dij cos hijÞ þ E2i Gii ð3Þ

PCOI ¼Xn

i¼1

ðPmi � PeiÞ ð4Þ

MT ¼Xn

i¼1

Mi ð5Þ

Cij ¼ EiEjBij ð6Þ

Dij ¼ EiEjGij ð7Þ

Yij ¼ Gij þ jBij ð8Þ

hij ¼ hi � hj ð9Þ

The notations of parameters in system Eqs. (1)–(9) are providedin Table 1.

Test system

In this paper an IEEE standard New England 10-machine 39-bustest system is used for TSA as shown in Fig. 2. We consider that bus1 in the New England test system is a slack bus whose voltageangle and voltage magnitude values are fixed at known values.The generated active and reactive powers of the slack bus aredenoted by PG1 and QG1. The remaining generator buses (i.e., buses2–10) are assumed as PV buses and their voltage magnitude andgenerated active and reactive powers in the PV buses are denotedby Vi and PGi and QGi (i = 2,3,. . .,10) respectively. In addition theremaining nine PV buses and other slack buses in the test systemhave 29 PQ buses (i.e., buses 11–39) whose active and reactiveloads are denoted by PDj and QDj (j is the bus number), eventhough the loads are acting only on 19 distinct buses. Systemdetails configuration and data are given in Ref. [7].

In this paper we assume the pre-fault system operating condi-tions as applied in Refs. [6,12,13] which is used as input to the pro-pose Type-2 fuzzy NN to estimate the CCT. The inputs areconsidered as follows:

– Voltage magnitudes of all the 9 PV buses (V2�V10).– Generated active powers of all the 9 PV buses (PG2�PG10).– Active load powers of all the 19 loads acting on different buses

(PD1, PD2,. . ., PD37).– Reactive load powers of all the 19 loads acting on different

buses (QD1, QD2,. . ., QD37).

We conduct a sample TSA on the New England standard testsystem with a set of four different fault scenarios. Scenario 1 is athree phases to ground fault injected to bus 32 and is cleared byremoving the line connected between bus 32 and bus 31. Scenario2 is a three phases to ground fault injected to bus 14 and is clearedby removing the line connected between bus 14 and bus 33. Alsoscenario 3 is a three phases to ground fault injected to bus 17and is cleared without removing any line in the post fault systems.And finally scenario 4 is a three phases to ground fault injected tobus 34 and is cleared by removing the line connected between bus34 and bus 35. The faults’ locations are shown in Fig. 2.

Here, its assumed that the occurrence probabilities of the sam-ple fault scenarios are high and these fault scenarios are requiredto have on-line TSA. Although only four fault scenarios are consid-ered for verification, the proposed method is completely generaland it can be used for any fault scenario that applied at any loca-tion of the test system. Also other test systems can be used in sim-ilar way [6,12].

It should be noted that the operating conditions of the test sys-tem are changed here without compelling any limits on maximumand/or minimum generated reactive powers of the all generators(i.e., QG-limits are not taken into account), leading us to use abovementioned independent system operating conditions as inputs tothe Type-2 fuzzy NN. However, other system variables can beapplied as inputs to the Type-2 fuzzy NN. To consider the viola-tions of generated reactive power of system generators, that maytake place in practice, and also to include extra information regard-ing the system total loading conditions, In this paper same as Ref.[12], we have applied the following additional inputs for the Type-2 fuzzy neural network:

– Generated active power of the slack bus (PG1).– Generated reactive power of the slack bus (QG1).– Generated reactive powers of all the 9 PV buses (QG2�QG10).

These operating conditions are obtained by performing an ACload-flow analysis on power system prior to fault. The New Eng-land test system consists of nine PV buses and 19 loads. Hence,

Table 1System equations’ parameter notations.

Parameter Description

hi Rotor angle in reference to the COI~xi Angular velocity of rotor in reference to the COIMi Inertia constant of the ith generatorPmi Mechanical input power of the ith generatorEi Internal generator voltage magnitude for the ith generatorYij The ijth elements of the reduced system admittance matrixGij Conductance of the ijth elements of reduced system admittance

matrixBij Susceptance of the ijth elements of reduced system admittance

matrixPGi Generated active power of the slack busQG1 Generated reactive power of the slack busPGi Generated active power of the ith PV busQGi Generated reactive power of the ith PV busPDj Active load of the jth busQDj Reactive load of the jth busj The bus numberi Index of generatorsn Number of generators in systemPei Electrical output power of the ith generatorPCOI COI accelerating power

Fig. 2. Diagram of the New England standard test system.


for each fault scenarios, the CCT is function of the(9 + 9 + 19 + 19 + 1 + 1 + 9 = 67) operating conditions that are usedas inputs to the Type-2 fuzzy NN.

Methodology for power system transient stability assessment

In this section, we present our proposed Type-2 fuzzy NN basedapproaches to estimate the CCT as an index for power systems TSA.First a general overview of entire system is presented, next we givea short introduction of fuzzy neural systems that finally leads us tothe proposed Type-2 fuzzy NN. In the next sub section training andprediction of CCT procedures are described. Finally MLP NN basedsensitivity analysis methodology is presented.

Overview of Type-2 fuzzy NN for CCT prediction

In this section we are going to describe a general overview ofpower system TSA infrastructure as shown in Fig. 3. With thedevelopment of wide area measurement system, the operationalcondition of a power system can be directly measured bygeographically distributed phasor measurement units (PMUs)before and following a disturbance. All the power system operatingconditions are transferred to an energy control center (ECC). The

aggregated operating conditions are easily accessible in ECC. Alsothis historical data are stored in log data base for further offlinepower system analysis. These measured operating conditions con-tain all the real time information of the system, such as models,arguments and disturbance. How to predict the transient stabilitystatus post-disturbance using these measured operational condi-tion is an important research topic in power system stabilityassessment that is the focus of this paper.

According to the Ref. [12], different fault scenario causes to dif-ferent CCT value. Moreover, the system’s operating conditionsprior to the fault and also the power system network topologiesboth have significant effect on the CCT. Hence, the CCT is a nonlin-ear and complex function of the system configuration after andbefore fault occurrence, system operating conditions prior to faultand also fault type and its location in the network.

Many different source of fault can be considered in a power sys-tem such as loss of load, loss of generation and loss of system com-ponents such as transformers or transmission lines. These sourceshave different level of importance and different probability ofoccurrence. So we should calculate CCT for each fault scenario sep-arately. The anomaly detection block (Fig. 3) is an online systemthat inspects the measured operational conditions to find anomalypatterns related to each fault scenario. After detection of a fault,the anomaly detection block reports fault scenario index to sce-nario selection block.

Two different NNs are associated with each fault scenario indexwhich are activated by the scenario selection block. One of them isa Type-2 fuzzy NN that online approximates the CCT nonlinearfunction instead of solving power system differential equations.Since the CCT is only the function of system operating conditionsprior to fault [6,8], the proposed Type-2 fuzzy NN is used toapproximate this complex function. The proposed Type-2 neurofuzzy method can estimate CCT for each fault with an acceptableaccuracy. Different sets of training patterns are required to trainthe CCTs for each fault scenario. Once the training phase of theType-2 fuzzy NN is completed; the CCT for each fault scenariocan be quickly computed.

Another NN that associated with each fault scenario index is aMLP NN that used for sensitivity analysis of input parameters inoffline manner. For each fault scenario we run a MLP NN based sen-sitivity analysis to determine more effective operating conditionsthat influences CCT estimation accuracy for each fault. The MLPNN uses offline log database to determine more effective inputoperating conditions in calculation of CCT and extract them as avector associated with each fault scenario. It reduces the trainingtime and the effort of measuring features online while declinesthe complexity of Type-2 fuzzy neural network. When the scenarioselection block reports the index of fault scenario; the selectorblock, filters input operating conditions according to the mostimportant feature vectors which is provided by MLP NN in the sen-sitivity analysis procedure. More details about sensitivity analysisare presented later.

Generally; we should consider a separate Type-2 fuzzy NN foreach fault scenario in the power system TSA; like works done inpapers [6,12,13]. When we have limited computing capability,we can only consider more important faults. On the other handsome fault scenarios have similar effects on power system vari-ables (e.g., voltage, active and reactive power). In working systems,the combination of dependent faults instead of using separate faultcan be used to reduce the number of Type-2 neuro fuzzy modelsand in consequence reduction of computation cost of the proposedmodel. In this paper we consider a sample combination of faultscenarios which is consist of 4 different uncorrelated and indepen-dents faults (the worst case scenario) and shows the proposedType-2 neuro fuzzy method can estimate CCT for each fault withan acceptable accuracy. The capability of proposed method can

Fig. 3. Block diagram of the proposed fuzzy NN based TSA.


be expanded by considering a set of Type-2 fuzzy NNs for eachprobable fault scenario in the power system. It is obvious thatthe expansion capability of the proposed Type-2 fuzzy NNs dependon the applied data in the training process.

As mentioned before, the CCT of a particular fault scenario inthe New England test system is a function of 67 power systemoperating conditions. The neural networks-based sensitivity analy-sis method is used to select 15 top most effective operating condi-tions in order to reduce the number of inputs to the Type-2 fuzzyneural network.

Fuzzy Interface

Linguisticstatements

Neural NetworkPerception as neural inputs

Decisions

Learningalgorithm

Neuraloutputs

Fig. 4. The first model of fuzzy neural system.

Fuzzy neural systems

NNs are good at recognizing input patterns, but are weak toexplaining how they reach their decisions. On the other hand,fuzzy logic systems can reason with imprecise information andnicely explain their decisions but they are incapable of automati-cally acquiring the rules they use to make those decisions. Theselimitations are cause for combination of two or more techniquesinto intelligent hybrid systems. This combination overcomes thelimitations of individual techniques. Also hybrid systems areimportant when dealing with different application domains.

The intelligent hybrid systems are used successfully in manyapplications including process control, cognitive simulation, finan-cial trading, medical diagnosis, and engineering design. In theintelligent hybrid systems an inference mechanism under cogni-tive uncertainty is provided by fuzzy logic and advantages, suchas learning, generalization, adaptation, parallelism and fault-toler-ance are offered by computational NNs. The concept of NNs isincorporated into the fuzzy logic in order to achieve humans likecapability for the system to deal with cognitive uncertainties. Usu-ally fuzzy neural systems are used in two different configurationsas follows [23]:

In the first configuration as illustrated in Fig. 4 the fuzzy inter-face block accepts linguistic statements and provides the percep-tion as an input vector to a NN. After the training phase of NN, itis adapted to yield desired command outputs or decisions.

Second configuration as illustrated in Fig. 5 use different struc-ture. In this configuration a NN drives the fuzzy inference mecha-nism. The NNs have the roll of tuning membership functions offuzzy systems. In this configuration fuzzy systems are employedas decision-maker for controlling equipment.

Fuzzy logic can use rules with linguistic labels which aredirectly encoded by expert knowledge, but designing and tuning

of the membership functions which quantitatively define these lin-guistic labels is a time consuming task. By using the learning capa-bility of NN we can automate designing and tuning of themembership functions and substantially reduce development timeand cost while improving performance.

In this paper we used the first configuration of fuzzy neural sys-tem. The Type-2 fuzzy layer converts uncertain and noisy inputs tomore dependable and reliable linguistic variables which are usedas inputs to the MLP NN layer.

Type-2 fuzzy NN

The concept of the Type-2 fuzzy set was introduced by Zadeh[24] as an extension to the type-1 fuzzy set. It can handle theuncertainties associated with process and input variables. The ideaof the Type-2 fuzzy logic is shown in Fig. 6. Type-2 fuzzy logic con-sists of three main components named as: fuzzification (Type-2fuzzifier), inference (rule base and inference engine) and outputprocessing (type-reducer and difuzzifier) [45]. The Type-2 fuzzifiertransforms an input crisp variable into a Type-2 fuzzy set it uses incircumstances where it is difficult to determine an exact member-ship function of input variables. Hence it is very useful for incorpo-rating uncertainties.

The rule base block in Type-2 fuzzy logic consists of a set offuzzy If–Then rules which can handle rule uncertainties. The fuzzyinference engine gives a mapping from the input Type-2 sets to theoutput Type-2 sets. The type-reduction block converts the Type-2output sets of inference engine to a type-1 set that is called ‘‘thetype-reduced set’’. These type-reduced sets are then defuzzifiedto obtain crisp outputs. As a result, Type-2 fuzzy logic systemsare very powerful paradigm to handle uncertainty in the real world

Neural Network Fuzzy Interface

NeuralInputs Decisions

Learningalgorithm

Neuraloutputs

Neuraloutputs

Knowledge-base

Fig. 5. The second model of fuzzy neural system.

Fig. 6. The idea of a Type-2 fuzzy logic system.

Fig. 7. Overview block diagram of Type-2 fuzzy NN.


applications and environments where there are uncertainties thatare difficult to predict.

Structure design of inference and the output processing algo-rithms in Type-2 fuzzy systems is difficult. Therefore, we use aNN to model operation inference (rule base and inference engine)and output processing (type-reducer and difuzzifier) in Type-2fuzzy system. Such a system which is named Type-2 fuzzy NNcombines the learning capability of NNs with the linguistic inter-pretation ability of fuzzy classifiers. Overview block diagram ofthe proposed Type-2 fuzzy NN system is illustrated in Fig. 7.

The block diagram is composed of two parts; a Type-2 fuzzifier(Type-2 fuzzy sets) and a neural network. The Type-2 fuzzifierenables efficient modeling of the linguistic and numerical uncer-tainties in the inputs and expert knowledge. Inputs to Type-2 fuzz-ifier is crisp values while output vector consists of the fuzzifiedinputs values which are called linguistic variable [23].

The NNs are designed in an attempt to mimic the human brainand inspired from the biological world. These networks can betrained and used for different types of problems such as functionapproximation, mapping (pattern association and pattern classifi-cation) and clustering. In this paper we use a MLP NN trained bythe back-propagation algorithm [15] in the proposed Type-2 fuzzyNN where inputs to the MLP NN is linguistic variable. In fact, theMLP NN uses fuzzified inputs instead of crisp values that embeduncertainty of measurement in input parameters. The componentsof the proposed Type-2 fuzzy NN is given in Fig. 8. Referring toFig. 8, for each input variable xi, i = 1, 2, . . ., n, a set of Ki Type-2fuzzy member ship functions are defined as Ali

i ; li ¼ 1;2; . . . ;Ki.Here, we use Type-2 Gaussian membership functions for theType-2 fuzzy set. Fuzzifying inputs by a non-linear Type-2 fuzzymembership function enables modeling the uncertainty of inputs.

As shown in Fig. 9. Each Type-2 membership function Ai is rep-resented by an upper membership function (UMF) and a lowermembership function (LMF) that are denoted as AðxÞ and AðxÞ[21]. As it can be seen in Fig. 9; �lAi

ðxiÞ and lAiðxiÞ are the member-

ship degree of input variable xi to the upper membership functionAi and the lower membership function Ai respectively. The detailsof data processing method in the proposed Type-2 fuzzy NNs aredescribed in the following steps:

Step 1: Fig. 10 illustrates the degrees of membership to Alii and

Alii which are obtained for each of the input variable xi that is an

input to Type-2 fuzzy neural network. Where Alii and Ali

i are thelith UMF and LMF of ith input variable respectively.Step 2: after the degree of membership for total input variablesare obtained, vector Z and V that represents degree of member-ship set can be written as:

Vi ¼ �lA1iðxiÞ; lA1

iðxiÞ; . . . ; �l

Alii

ðxiÞ; lA

lii

ðxiÞ; . . . ; �lA

Kii

ðxiÞ; lA

Kii

ðxiÞ� �t

ð10Þ

Z ¼ ½V1; V2; . . . ; Vi; . . . ; Vn�t ð11Þ

Z ¼ �lA11ðx1Þ; lA1

1ðx1Þ; . . . ; �l

AK11ðx1Þ; l

AK11ðx1Þ; �lA1

2ðx2Þ;

�

lA12ðx2Þ; . . . ; �l

AK22ðx2Þ; l

AK22ðx2Þ; . . . ; �lA1

iðxiÞ; lA1

iðxiÞ; . . . ; �l

AKii

ðxiÞ;

lA

Kii

ðxiÞ; . . . ; �lA1nðxnÞ; lA1

nðxnÞ; . . . ; �lAKn

nðxnÞ; lAKn

nðxnÞ

�t

ð12Þ

where �lA

lii

ðxiÞ and lA

lii

ðxiÞ are respectively the membership degree of

input variable xi to the UMF Alii and the LMF Ali

i .The L is size of Z and can be obtained by the following equation:

L ¼ 2�Xn

i¼1

Ki ð13Þ

Step 3: the fuzzified input vector Z is considered as input to NN.A MLP consists of an input layer, an output layer and one ormore hidden layers. L represents the size of the input layerwhere size of the output layer is determined by number ofNN outputs. Number of the hidden layer and the size of hiddenneurons at each hidden layer are carefully selected to providebest results in training phase of system. One of the populartraining algorithms for MLP NN is error back propagation algo-rithm [15], which is based on the gradient descent technique.The standard back propagation method is too slow in MLP NNtraining [46], so it is superseded by fast resilient back-propaga-tion technique for training the MLP NN.

Training and testing of Type-2 fuzzy NN to predict CCT

In this section, we give a general overview of training procedureof Type-2 fuzzy NN which is designed in previous section. As men-tioned before the structure of Type-2 fuzzy NN is composed of twoparts, a Type-2 fuzzifier and a NN. In order to Type-2 fuzzy NN canbe used in estimation of CCT, it should first be trained. The traininginputs should be carefully selected in a range related to possiblevariation of input parameters. According to Section ‘Test system’,the CCT for a particular fault scenario in New England 39-bus testsystem is function of 67 (19 + 19 + 9 + 9 + 1 + 1 + 9 = 67) powersystems operating parameters. This configuration can be applied

Fig. 8. The components of the proposed Type-2 fuzzy neural network.

Fig. 9. Upper and a lower membership functions in Type-2 Gaussian membershipfunction.

Fig. 10. The structure of the Type-2 fuzzifier for input variable xi.


to estimate the CCT for every valid fault scenario in a given powersystem. As described in Refs. [6,12,13], and illustrated in Fig. 11,the training and testing patterns of Type-2 fuzzy NN can beobtained from the following procedures:

1. It is assumed that the following operating conditions can varyrandomly over some specified ranges of their nominal values:� Voltage magnitudes of all the nine PV buses are bounded

between 0.9 and 1.1 times their corresponding nominal values.� Active and reactive powers of all the 19 loads are varied in the

range 0.6–1.1 times their corresponding nominal values.

2. A random value with uniform distribution is assigned indepen-dently to each of the variables mentioned in step 1as turbu-lence. The random turbulence described by the followingequations:

PDjðkÞ ¼ PDj0 0:6þ 0:5ejPDðkÞ

� �ð14Þ

QDjðkÞ ¼ QDj0 0:6þ 0:5ejQDðkÞ

� �ð15Þ

ViðkÞ ¼ Vi0 0:9þ 0:2eiV ðkÞ

� �ð16Þ

where PDj(k) and QDj(k) are, the active power and the reactivepower of load at the jth load bus, respectively. And PDj0 and QDj0

are their nominal load at the jth load bus. Also Vi(k) is the voltagemagnitude at the ith PV bus for the kth training pattern and Vi0 isthe nominal voltage magnitude at the ith PV bus. Also e denotes auniformly distributed random number within range [0, 1].3. In the next step, a load-flow analysis is performed on the above

mentioned training data to make sure that each of the scenariosis a feasible power flow solution. Moreover, other operatingconditions including generated active and reactive power ofthe slack buses and generated reactive powers of all the ninePV buses which are assumed as input to Type-2 fuzzy NN areobtained from the results of the load-flow program.

4. A time-domain simulation technique is employed to computethe CCT for all the sample fault scenarios by solving power sys-tem differential equations. The solving method is 4th orderRunge–Kutta with time scale resolution of Dt = 0.001 s.

5. As shown in Fig. 11, in parallel to the time-domain simulation,the MLP NN based sensitivity analysis is used to reduce numberof input operating conditions and chooses more effective onesin order to simplify the design and training procedure ofType-2 fuzzy NN.

Fig. 11. Block diagram of the proposed Type-2 fuzzy NN based approach.


6. Results of CCT from the time-domain simulation block is usedas the desired output of Type-2 fuzzy NN that is associated withselected input operating conditions which are used in trainingprocedure of Type-2 fuzzy neural network.

It should be noted that in this paper the MATPOWER software[47] is applied for load-flow analysis. The presented pattern gener-ation procedure produces 2000 random data patterns for samplefault scenarios. Among them 1500 patterns (about 75% of the totalproduced patterns) were chosen for training and the remaining500 patterns (25% of the total produced patterns) were appliedto test the Type-2 fuzzy neural network.

MLP NN based sensitivity analysis method

Sensitivity analysis is the study of how the variation in the out-put of a model can be allocated, qualitatively or quantitatively todifferent sources of variation [17,43]. The main idea behind thesensitivity analysis method is that it reduces the number of inputfeatures from original set of features without losing the importantinformation. According to Section ‘Test system’, we have 67 sys-tem’s operating parameters as input to the Type-2 fuzzy neuralnetwork. These operating parameters have direct impacts in calcu-lation of CCT. However some of these operating parameters havemore information and higher influence in final CCT than others.Therefore, we are going to rank the operating parameters in orderof their importance and determine those operating parameters(inputs) for each fault scenario that have higher impact on the finalvalue of CCT. So we use a MLP NN based sensitivity analysismethod as proposed in Refs. [12,17,43], to find the operatingparameters (Type-2 fuzzy NN inputs) those have more impact onCCT. The benefit of reduction in inputs of Type-2 fuzzy NN is thatit reduces the training time and effort of on-line measurement offeatures while declines in complexity of Type-2 fuzzy NN.

As illustrated in Fig. 12, in this analysis, one input parameter ata time is selected and varied by a fixed percentage while rest of theinputs remains constant. Then input data is fed to the NN and themean absolute error (MAE) is calculated. These steps are repeatedfor all the input parameters and MAE is calculated. After all theinputs have been examined, ranking decision is made based onthe change in MAE. Those inputs whose change in value makes anoticeable change in the value of output MAE are selected as favor-ite candidate as input parameters. Remaining parameters which

did not have noticeable change in error are omitted from Type-2fuzzy NN inputs.

Results and discussion

In this section, we evaluate the accuracy of proposed Type-2fuzzy NN in CCT estimation for sample fault scenarios in New Eng-land 39-bus test system. Also, a MLP NNs based sensitivity analysisis used to reduce the number of input parameters to Type-2 fuzzyNN as illustrated in the block diagram of Fig. 13. So the total num-ber of inputs is reduced from 67 operating conditions to only 15more effective operating conditions for New England 39-bus testsystem. Then the design is trained by 15 inputs to estimate CCTfor four sample fault scenarios.

Application of Type-2 fuzzy NN to predict the CCT

In this section, first we design a Type-2 fuzzy NN then thedesign is trained by 15 more effective operating conditions to esti-mate CCT for four sample fault scenarios. Here, we select 15 oper-ating conditions among of total 67 inputs that have more effect onCCT of four sample fault scenarios. These 15 selected operatingconditions are: VG2, PG5, VG9, VG3, VG10, PG2, VG5, PD1, PG7,VG8, PG4, PG6, VG7, VG4, and PG1. The details of sensitivity anal-ysis based parameter selection method is presented in the nextsection. Design and train procedures of the proposed Type-2 fuzzyNN are described in the following steps:

Step 1: the maximum and minimum variation of 15 input oper-ating conditions are extracted from 1500 training patterns asshown in Table 2.Step 2: for each of the 15 inputs, three sets of Type-2 fuzzy aredefined as ‘‘S’’, ‘‘M’’ and ‘‘L’’. Here, Gaussian membership func-tions are chosen for inputs as shown in Fig. 14. Moreover thenumber of membership functions and UMF and LMF variancesare determined by an expert knowledge.Step 3: after Type-2 fuzzifier is designed, we are going to designNN. Here, we use a single layer perceptron NN and train it bythe resilient back-propagation method. The number of inputneurons is obtained by the following equation:

L ¼ 2�Xn

i¼1

Ki ¼ 2� ð15� 3Þ ¼ 90 ð17Þ

Fig. 12. Block diagram of the MLP NN based sensitivity analysis.

Fig. 13. Block diagram of the proposed Type-2 fuzzy NN based approach.

Fig. 14. Membership functions of the input xi.

Table 3The RMSE and MAPE for 500 total testing patterns for each fault scenario.

Fault scenario1

Fault scenario2

Fault scenario3

Fault scenario4

RMSE 0.0102 0.0061 0.009 0.0061MAPE 2.49% 1.69% 2.41% 2.11%


The perceptron NN has 90 neurons in input layer and four neu-rons in output layer without any hidden layer. A linear transferfunction is applied for the neurons in output layer. The MSE thresh-old to stop the training procedure was set to 0.005 s. It took about8 s with 1159 epochs on average to train the proposed Type-2fuzzy NN.

In order to evaluate how well the trained Type-2 fuzzy NNreacts on the sample fault scenarios; it was tested by 500 test pat-terns. Performance of the proposed Type-2 fuzzy NN is evaluatedby Root Mean-Squared Error (RMSE) and Mean Absolute Percent-age Error (MAPE) between real and estimated values. The defini-tion is given by Eqs. (18) and (19) as follows:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1N

XN

p¼1

ðactual CCTðpÞ � estimated CCTðpÞÞ2vuut ð18Þ

MAPE ¼ 100� 1N

XN

p¼1

actual CCTðpÞ � estimated CCTðpÞactual CCTðpÞ

ð19Þ

Table 2The maximum and minimum value for each 15 input.

Input Minimum value Maximum value Input Minimum value Maximum value Input Minimum value Maximum value

VG2 0.8838 pu 1.0802 pu PG2 4.6651 pu 6.3680 pu PG4 4.6548 pu 6.3540 puPG5 3.7415 pu 5.1073 pu VG5 0.9112 pu 1.1134 pu PG6 4.7874 pu 6.5350 puVG9 0.9239 pu 1.1291 pu PD1 6.6246 pu 12.1439 pu VG7 0.9572 pu 1.1698 puVG3 0.8848 pu 1.0814 pu PG7 4.1245 pu 5.6301 pu VG4 0.8975 pu 1.0969 puVG10 0.9428 pu 1.1522 pu VG8 0.9250 pu 1.1306 pu PG1 6.3707 pu 8.9442 pu

Fig. 15. Comparison between the estimated output and the actual output for selected fault scenarios of New England 39-bus test system.

Fig. 16. Distribution of errors between the actual CCT and the estimated CCT in percent (Ep) for all sample fault scenarios.


Table 4Specification of MLP NNs which are used in sensitivity analysis.

Fault scenarionumber

Number of NNinputs

Number of NN hiddenneurons

Average NN trainingtime (s)

Average trainingepochs

Fault scenario 1 67 9 9 891Fault scenario 2 67 9 7 749Fault scenario 3 67 12 8 689Fault scenario 4 67 10 6 526

Table 5The RMSE and MAPE for total 500 testing patterns of four fault scenarios.

Fault scenario 1 Fault scenario 2 Fault scenario 3 Fault scenario 4

RMSE 0.0067 0.0055 0.0049 0.0052MAPE 1.61% 1.59% 1.69% 1.82%


where N is the total number of patterns in test set and p representsthe pattern index. The RMSE and MAPE for 500 total test patternsare shown in Table 3 for each sample fault scenario.

The results are proving generalization accuracy of trained Type-2 fuzzy NN for all sample fault scenarios. Comparison between theactual CCT and the estimated CCT by using 30 test patterns out oftotal 500 test patterns is shown in Fig. 15.

Also, distribution of errors in percent for sample fault scenariosare shown in Fig. 16 and calculated by the following equation:

Ep ¼ 100� actual TargetðpÞ � estimated TargetðpÞactual TargetðpÞ ð20Þ

Fig. 17. Comparison between MLP NN CCT estimation and the actual C

where p represents index of test pattern. As it can be seen in Fig. 16,occurrence frequency of error in percent (Ep) for all fault scenariosfollows the Gaussian distribution. In the first fault scenario about30.4% of total test patterns have Ep between �1% and 1%. Moreover,only 0.2% of total 500 test patterns have Ep between �12% and�11% which is worse case error.

In the second fault scenario about 40.6% of total test patternshave Ep between �1% and 1%. Moreover, only 0.2% of total 500 testpatterns have Ep between �12% and �11% which is worse caseerror. Also in the third fault scenario about 27.6% of total test pat-terns have Ep between �1% and 1%. Moreover, only 0.2% of total500 test patterns have Ep between �9% and �8% which is worsecase error. Finally in the fourth fault scenario about 34.4% of totaltest patterns have Ep between �1% and 1%. Moreover, only 0.2% oftotal 500 test patterns have Ep between 10% and 11% which isworse case error.

As shown in Fig. 16 we can conclude that for all the sample sce-narios, small |EP|s (less than 5%) are more frequent (about 90%)than large |EP|s. on the other hand if a Gaussian probability func-tion is fitted to the EP distribution, it will be have small varianceand mean value near to zero. So in 90% of conditions the estimation

CT for sample fault scenarios of New England 39-bus test system.

Table 615 Most important inputs and their MAE for each fault scenario.

Fault scenario 1 Fault scenario 2 Fault scenario 3 Fault scenario 4

Operating conditions Value of MAE Operating conditions Value of MAE Operating conditions Value of MAE Operating conditions Value of MAE

VG2 0.1682 PG10 0.053 VG9 0.1167 VG2 0.1636VG9 0.0885 VG2 0.052 VG10 0.0596 VG3 0.0589VG10 0.0576 PD1 0.0516 PD1 0.0525 PG7 0.0526PD1 0.0548 PG8 0.0439 VG2 0.0432 PG4 0.0481VG5 0.0528 VG6 0.0434 PG10 0.0424 VG7 0.046PG7 0.0509 PG9 0.0421 PG8 0.0411 VG9 0.0439VG8 0.0409 VG10 0.0418 PG4 0.0399 PG9 0.037PG1 0.0329 VG3 0.0414 PG2 0.0396 PG10 0.0359PG6 0.0245 VG9 0.0302 VG8 0.0331 PG6 0.0277PG10 0.0236 VG4 0.0287 PG1 0.0306 VG6 0.0254PG3 0.0222 PG5 0.0279 VG4 0.0275 PD1 0.0242PG9 0.0196 PG6 0.0216 PG7 0.0151 VG10 0.0209PG4 0.0189 VG5 0.0197 PG9 0.0147 PG3 0.0153PG2 0.0187 VG8 0.0182 PD19 0.0143 VG4 0.0145VG6 0.0164 VG7 0.0146 PG3 0.0136 PG2 0.0139

Table 7Comparison between MLP NN and Type-2 fuzzy NN in training phase.

Type-2 fuzzy neuralnetwork

MLP NN

Training algorithms Resilient back-propagation

Resilient back-propagation

Training time 8 s 16 sAverage training

epochs1159 1842

Training MSE 0.005 0.035Number of inputs 15 20


error is less than 5%. It can be observed that the trained Type-2fuzzy NN estimates actual CCT for all sample fault scenarios withan acceptable accuracy. The experimental results show that pro-posed Type-2 fuzzy NN which is only considered higher impactinputs give satisfactory CCT estimation for all sample faultscenarios.

Sensitivity analysis

As described in Section ‘MLP NN based sensitivity analysismethod’ a MLP NNs based sensitivity analysis is used to reducenumber of input parameters to the Type-2 fuzzy NN. This reduc-tion can affect estimation accuracy. In this section we are goingto analyze the effect of MLP NNs based sensitivity analysis on esti-mation accuracy. The MLP NN is first trained with 67 operatingconditions in each training pattern. Then the trained NN is appliedto perform sensitivity analysis. We use four MLP NNs to performsensitivity analysis for each fault scenario separately. Details offour trained MLP NNs are shown in Table 4.

Here, number of neurons in hidden layer are tuned after run-ning several experiments. Also for all the MLP NNs tangent sigmoidtransfer function and linear transfer function are applied to the

Table 8The RMSE and MAPE of MLP NN and Type-2 fuzzy NN for each fault scenario in testing p

Type-2 fuzzy neural network

Faultscenario 1

Faultscenario 2

Faultscenario 3

RMSE 0.0102 0.0061 0.009MAPE 2.49% 1.69% 2.41%Response time for 500 test patterns 0.1020 s

hidden layer neurons and the output layer neurons respectively.MSE between actual and estimated values of CCT in the trainingphase was set to 0.001 s. The training method for MLP NN is resil-ient back-propagation method. Total computations are performedon a personal computer with 2 GB of RAM and 2.93 GHz PentiumDual-Core Processor.

In order to see how well the trained MLP NNs acts in simulatedfault scenarios, the NN was tested by 500 test patterns. The perfor-mance of trained MLP NN in evaluation of CCT is determined byRMSE and MAPE between actual and estimated CCT. The RMSEand MAPE for 500 total test patterns and sample fault scenariosare shown in Table 5.

The results of Table 5 are proving the generalization accuracy oftrained MLP NN for all sample fault scenarios. Comparisonbetween the actual CCT and the estimated CCT for 30 out of 500test patterns are shown in Fig. 17 for sample fault scenarios. Itcan be observed that the trained MLP NNs estimates actual CCTwith an acceptable accuracy in sample fault scenarios.

When MLP NNs was trained by 67 inputs, it is used to performsensitivity analysis. The sensitivity of NNs output (CCT) respect tothe each input are calculated. Each time, one MLP NN input is cho-sen to train and perturbed by a fixed percentage of its value (e.g.,10%), where the other inputs remains constant. In the same timeinputs are fed to the MLP NNs and output (CCT) is calculated.The mean absolute error (MAE) between outputs which are esti-mated by NN before and after each variation to the input is com-puted. These steps are repeated for all the NN’s inputs and finallyMAE is computed.

After all the 67 inputs have been examined, those inputs whosechange leads to a big variation in the MAE are chosen as best can-didates for input to the Type-2 fuzzy NN. The rest of inputs withsmall MAE, does not considered for Type-2 fuzzy NN. As a matterof fact, a big value for MAE means that the corresponding per-turbed variable greatly influences the system output. MAE is com-puted by the following equation:

hase.

MLP NN

Faultscenario 4

Faultscenario 1

Faultscenario 2

Faultscenario 3

Faultscenario 4

0.0061 0.0265 0.0208 0.0208 0.02482.11% 8.01% 6.44% 7.13% 9.09%

0.1015 s

Fig. 18. Estimated CCT by Type-2 fuzzy NN and MLP NN are compared with actual CCT for each fault scenario in the New England 39-bus test system.


MAE ¼ 1N

XN

p¼1

tcrðpÞ � t0crðpÞtcrðpÞ

ð21Þ

where tcrðpÞ is estimated CCT before any variation to the input andt0crðpÞ is estimated CCT after variation of input. N is the total numberof testing patterns and p represents pattern index. After conducting

Fig. 19. Distribution of error in percent between the actual CCT and the

sensitivity analysis for each fault scenario, 15 out of total 67 inputparameters that have higher impact on MAE are chosen. The 15most important inputs and their MAE for each fault scenario areshown in Table 6.

As illustrated in Table 6, most of the chosen input operatingconditions are voltage magnitudes and the active generated

estimated CCT for all the sample fault scenarios using the MLP NN.

Table 9Different value of Ep, variances of Ep and means of Ep corresponding to the MLP NN and the Type-2 fuzzy NN for sample fault scenarios.

Fault scenario index Type-2 fuzzy NN MLP NN

1 2 3 4 1 2 3 4

Maximum value of Ep �12%, �11% �12%, �11% �9%, �8% 10%, 11% 29%, 30% �24%, �23% �28%, �27% �32%, �31%Percentage of worst case error in Ep distribution 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.2% 0.6%Distribution percentage Ep between �1% and 1% 30.4% 40.6% 27.6% 34.4% 8.2% 9% 7.4% 7.2%Variance of Ep 8.1099 4.7271 6.8101 7.7759 94.1163 61.2167 72.2927 127.4749Mean of Ep �0.1044% �0.1988% �0.0398% �0.0993% �0.7957% �1.7208% �1.169% �0.6521%

Fig. 20. Comparison of absolute error (AE) between actual CCT and the estimated CCT (by Type-2 fuzzy NN and MLP NN) for sample fault scenarios.


powers of those generators that are in proximity of the faultscenario in test system.

Comparison between Type-2 fuzzy NN and MLP NN for CCI prediction

In order to compare the performance of proposed Type-2 fuzzyNN with other relevant methods, we implement a MLP NN like theapproach which is used in papers [6,12,13]. In order to better con-vergence of MLP NN, we used 20 inputs which are including theType-2 fuzzy neural inputs and extra five inputs (next ranks inthe sensitivity analysis). Five additional inputs are as follows:PG9, PG3, PG10, VG6 and PG8. Also the same number of train(1500) and test (500) patterns as we applied to the Type-2 fuzzyNN are used for the MLP NN.

The MLP NN has 20 neurons in input layer and one hidden layerthat includes 12 neurons. A tangent sigmoid transfer function isapplied to the hidden layer neurons. Also a linear transfer functionis applied to the output layer neurons. MSE threshold in the train-ing phase of NN was set to 0.035 s. The MLP NN is trained by resil-ient back-propagation method. It took about 16 s with average of

1842 epochs to train the MLP NN. The trained MLP NN was testedby using 500 test patterns. The response time for 500 test patternsand the RMSE and MAPE values for 500 total test patterns are com-puted for each scenario. The result of experiments for comparisonbetween the MLP NN and Type-2 fuzzy NN are illustrated in Tables7 and 8.

It can be seen in Tables 7 and 8, that in the training phase, MLPNN consumes more training time and takes more epochs to con-verge in compare with the Type-2 fuzzy NN. Also in testing phaseof the system RMSE and MAPE of MLP NN is higher than the Type-2fuzzy NN results, that indicates higher rate of estimation error. Theestimated CCT results that obtained by Type-2 fuzzy NN and MLPNN are compared with actual CCT for first 30 test patterns out of500 total test patterns are shown in Fig. 18. The results are pre-sented for each fault scenario separately. Also, the distribution oferrors in percent are shown in Fig. 19 for sample fault scenarios.

As it can be seen in Fig. 19, the distribution of Ep follows aGaussian distribution. For first fault scenario about 8.2% of totaltest patterns have Ep between �1% and 1%. Also, only 0.2% of500 total test patterns have Ep between 29% and 30% which is


worse case error. In the second fault scenario about 9% of total testpatterns have Ep between �1% and 1%. Moreover, only 0.2% of total500 test patterns have Ep between �24% and �23% which is also aworse case error. In third fault scenario about 7.4% of the total testpatterns have Ep between �1% and 1%. Where, only 0.2% of the 500total test patterns have Ep between �28% and �27% which isworse case error. Finally in the fourth fault scenario about 7.2%of total test patterns have Ep between �1% and 1%. Moreover, only0.6% of total 500 test patterns have Ep between �32% and �31%which is worse case error.

As shown in Fig. 19 we can conclude that for all sample scenar-ios, small |EP|s (less than 5%) are about half of samples (about 50%)and large |EP|s are more frequent than Type-2 fuzzy NN results(Fig. 16). On the other hand if a Gaussian probability distributionfunction is fitted to the EP distribution, it will be have large vari-ance and negative mean value near to zero. So in 50% of conditionsthe MLP NN estimation error is less than 5%. Different values of Ep,variances of Ep and the means of Ep corresponding to two differentmethods are compared in Table 9 for sample fault scenarios.

Also absolute error (AE) between the actual CCT and the esti-mated CCT by Type-2 fuzzy NN and MLP NN for first 30 out of500 test patterns are shown in Fig. 20. The results are presentedfor each fault scenario separately. It can be concluded that theType-2 fuzzy NN could estimate CCT with higher degree of accu-racy than MLP NN for sample fault scenarios. Also the proposedmethod requires less computational cost in compare to the MLPNN method.

Conclusion

In this paper we propose a new direct method for online TSAproblem in power systems. A hybrid Type-2 fuzzy NN system isdesigned to estimate the CCT of sample contingency (fault scenar-ios). Also, MLP NN based sensitivity analysis is used to reduce thenumber of inputs to Type-2 fuzzy NN about four times. That resultsto less complex and faster Type-2 fuzzy NN system with negligibledecrease in estimation accuracy. By using Type-2 fuzzy sets asType-2 fuzzifier, we can handle the uncertainties which are associ-ated to measurements of operating conditions and device parame-ters in a power system and complexity of power networkseffectively. Type-2 fuzzy layer converts uncertain and noisy inputsto more dependable and reliable linguistic variables which areused as inputs to the MLP NN layer. Moreover, heavy computa-tional burden is avoided in online applications. The outputs ofType-2 fuzzifier are injected to a single layer perceptron NN to esti-mate CCT. We applied resilient back-propagation method for fastoffline training of Type-2 fuzzy NN system.

New England 10-machine 39-bus standard test power systemwas applied as an example to demonstrate the efficiency of pro-posed method. Simulation results show that the proposed Type-2fuzzy NN could estimate the CCT for sample fault scenarios withreasonable accuracy at different system operating conditions incompare to widely used MLP NN method. The proposed Type-2fuzzy NN reduces RMSE and MAPE of CCT estimation about fourtimes in compare to MLP NN method. In addition, the proposedmethod has very simple structure and consumes low computa-tional power for training and in online systems; therefore the solu-tion is feasible and can be employed for fast assessment of thetransient stability in a power system control center.

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