A Novel Method for Single and Simultaneous Fault ... - IEEE Xplore

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IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 30, NO. 6, NOVEMBER 2015

A Novel Method for Single and Simultaneous Fault Location in Distribution Networks M. Majidi, M. Etezadi-Amoli, Life Senior Member, IEEE, and M. Sami Fadali, Senior Member, IEEE

Abstract—This paper introduces a novel method for single and simultaneous fault location in distribution networks by means of a sparse representation (SR) vector, Fuzzy-clustering, and machinelearning. The method requires few smart meters along the primary feeders to measure the pre- and during-fault voltages. The voltage sag values for the measured buses produce a vector whose dimension is less than the number of buses in the system. By concatenating the corresponding rows of the bus impedance matrix, an underdetermined set of equation is formed and is used to recover the fault current vector. Since the current vector ideally contains few nonzero values corresponding to fault currents at the faulted points, it is a sparse vector which can be determined by -norm minimization. Because the number of nonzero values in the estimated current vector often exceeds the number of fault points, we analyze the nonzero values by Fuzzy-c mean to estimate four possible faults. Furthermore, the nonzero values are processed by a new machine learning method based on the k-nearest neighborhood technique to estimate a single fault location. The performance of our algorithms is validated by their implementation on a real distribution network with noisy and noise-free measurement. Index Terms—Compressive sensing, distribution networks, fault and stable location, Fuzzy-c mean, k-nearest neighborhood, -norm minimization, smart meters.

I. INTRODUCTION

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ETERMINATION of fault locations is one of the main challenges in distribution network operation. The outage time, power system reliability, electrical power quality, and customer satisfaction improve if the required time for fault detection, isolation, and restoration (FDIR) decrease. To reach this goal, distribution networks must be equipped with distribution automation (DA) with distribution management system (DMS) functionalities. Fault detection can be realized provided that networks are equipped with smart devices and sufficient communication interfaces. Smart devices measure the necessary signals along the feeders and across the loads and send them to a control center. These data are processed by the Supervisory Control and Data Acquisition System (SCADA) to assess the system condition. Manuscript received July 24, 2014; revised September 29, 2014; accepted November 21, 2014. Date of publication December 18, 2014; date of current version August 03, 2015. This paper is based upon work supported in part by the National Science Foundation under Grant No. IIA-1301726. Paper no. TPWRS01010-2014. The authors are with the Department of Electrical and Biomedical Engineering, University of Nevada, Reno, NV 89557-0260 USA (e-mail: [email protected]; [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2014.2375816

References [1]–[26] propose algorithms to locate faults in distribution networks. These algorithms are based on one or more of seven main techniques: impedance measurement, automated outage mapping (AOM), voltage sag estimation, traveling waves, direct three-phase circuit analysis, superimposed components, and artificial intelligence (AI). In [1]–[9], the apparent impedance calculated from measured voltage and current is used to locate the fault. In [3], the sign of the estimated positive sequence resistance discriminate the fault section. The algorithm in [4] diagnoses the fault before or after the measurement point. The simplicity and cost effectiveness of impedancebased techniques make them desirable, but their performance deteriorates with multiple fault location estimations. AOM improves their performance by limiting the search space for probable faulted points [10]–[13]. AOM can be implemented by monitoring the customers, cutout fuses, and Fault Indicators (FIs). In [13], FIs and directional fault indicators (DFIs) are used to estimate the faulted section. Voltage sags are obtained by capturing the pre- and during-fault voltages for measurement buses. In [3], [10], and [14]–[16], voltage sags are calculated by load flow for all buses using a few measured voltage sags. The differences between the calculated and actual voltage sags are characterized to find the fault location. In [17], [18], some probable faulted points are estimated using the matrix inversion lemma and analyzing the circuit directly. In [17], [19], [20], a combination of direct circuit analysis and superimposition are used to find the fault location. In [21]–[23], the behavior of traveling wave produced due to a fault is evaluated in terms of the time difference between sequential recorded waves. In [24]–[26], extensive scenarios covering all fault conditions are simulated, and some features are extracted from system variables such as voltage and current waveforms. The extracted features are used to train neural networks to locate the fault. As distribution networks always undergo reconfiguration, faults may occur in some circumstances that are not considered in the generated data set. Hence, the trained network does not include sufficient data to estimate the precise fault location. This paper proposes a novel approach for single and simultaneous fault location in distribution networks by fault current vector decoding. A sparse fault current vector is recovered with the voltage sag vector and resized impedance matrix by compressive sensing (CS) and -norm minimization. Since the number of nonzero values in the estimated current vector is not necessarily identical to the number of faults, these values are examined by Fuzzy-c mean clustering to estimate four possible faulted points. It is assumed that no more than three faults can occur in the system simultaneously. Therefore if single,

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MAJIDI et al.: NOVEL METHOD FOR SINGLE AND SIMULTANEOUS FAULT LOCATION IN DISTRIBUTION NETWORKS

double, or triple faults occur, one, two, or three of the four estimated points, respectively, are closest to the actual faulted point(s). To only locate single faults, a new machine learning technique based on the k-nearest neighbor is proposed. The proposed methodology is implemented on a 13.8-kV, 134-bus distribution network including heterogeneity of overhead lines and validated when all four possible short circuits with various fault resistances occur and noisy measured data. Our model recovers the positive sequence of fault currents in all fault types, and we do not need to know the type of fault. When we need the voltage magnitudes and phases measured by phasor measurement units (PMUs), the voltage data must be synchronized. If we only use the voltage magnitudes captured by smart meters, synchronization is not an issue. We need the impedance matrix of the system as determined by the impedance matrix of each component and the external grid. Therefore, knowledge of system topology and impedance data of the overhead lines and external grid are essential in our methodology. Because we estimate the fault locations using superposition, it is not necessary to consider the loads. It is assumed that, between pre- and during-fault conditions, injected currents to buses do not change significantly except for the faulted buses. Consequently, the voltage changes in all buses between these two steps is due to the injected fault current. The remainder of this paper is organized as follows. Section II describes the proposed fault location methodology, CS concepts, and two approaches for processing the nonzero values in the estimated faults current vector. Section III presents simulation results of the proposed method in numerous scenarios covering most of the single and simultaneous faults conditions. Section IV compares the results with those obtained by previous studies. Our conclusion is presented in Section V.

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where

. Due to the heterogeneity of overhead lines in distribution networks, the zero, positive, and negative sequences equivalent impedances are coupled. As an approximation, we assume diagonal and use the (2,2) entry for the positive sequence impedance of that section. The entries of are calculated by (4) where are zero, positive, and negative sequences of voltage sags at bus , and are three-phase voltage sags at bus . In our approach, three-phase during- and pre-fault voltage magnitudes are measured by smart feeder meters along the primary feeders to form , and corresponding rows of the are chosen and linked together to make for recovering the by (5) As smart feeder meters only record three-phase voltage magnitudes, we assume that they have 120 phase shifts even if the distribution networks are unbalanced. Therefore, angles of 0 120 , and 120 are allocated to voltage sag values in phases a, b, and c, respectively [10]. The voltage sags are calculated by (6)

II. FAULT LOCATION METHODOLOGY For an N-bus distribution system, the voltage sag phasors vector for a fault at bus is calculated by [29] (1) where vector,

is the three-phase voltage sag phasors is the three-phase impedance matrix, is the three-phase fault is the three-phase short circuit current phasor vector, and current phasor at bus . Three-phase fault currents contain the positive sequence values for all possible faults, thus (2)

where is the positive sequence impedance matrix obtained from the positive sequence impedances, is the positive sequence fault curis the positive sequence fault current at rent phasor vector, bus and is the positive sequence voltage sag vector. The zero, positive, and negative sequence impedance matrix of each 3 3 sub matrix of are obtained by (3)

where and are three-phase during- and prefault voltage magnitudes at bus , respectively. The three symmetrical components of the three-phase voltage sag phasors in each bus are calculated by (4), and the average value is obtained by (7) Our extensive simulation proved that results in a better performance than in our proposed fault location algorithm. is substituted for in (5). Subsequently, However, if PMUs are installed along the feeders to measure both magnitude and phase of the voltages, is not re. In addition, absolute values of the entries of placed by both and are used to estimate the absolute value of using (8a) (8b) If the underdetermined (8) is solved for given and using least squares, the solution is inefficient since a sparse vector can be recovered by -norm minimization.

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A. Compressive Sensing Framework CS is an effective method for reconstructing a sparse signal using a basis matrix and relatively few measurements [30], [31]. CS relies on -norm minimization to find the sparse solution [32]. We calculate by (9) is the estimated vector, and is the norm opwhere erator, and use the nonzero values in the sparse solution to estimate the faulted points. Since the data delivered to the control center are noisy, (8) is modified to

Fig. 1. Typical normalized recovered current vector in a double-fault case.

(10) is a measurement noise vector with energy . Stable -norm minimization is used to reconstruct the via the noisy data where

(11) where is the norm operator. A primal-dual linear programming algorithm is used to solve the -problems [33]. B. Nonzero Values Processing Since there are fewer faults than nonzero values in both the and solutions, we cannot assign the bus numbers of all nonzero values to faulted points. We propose two approaches to analyze nonzero values. First, we assume that no more than three faults occur simultaneously and normalize coefficients of the estimated current vector by their maximum. Entries greater than 0.3 are labeled as dominant values because our simulations show that they contain enough information to appropriately estimate faulted points. Each of the dominant values corresponds to one bus whose distance to the main substation is calculated as the sum of all connecting spans. The corresponding distances to all dominant values are categorized in four groups via Fuzzy-c mean clustering [34] and the four estimated centers are assigned as the four possible faulted points in the network. Note that each estimated center may be associated with more than one point in the distribution networks due to the presence of laterals. However, the buses corresponding to dominant values in the estimated sparse current vector limit the search space for fault location and cancel the multiple fault location estimation. If the number of dominant values is not more than four, the four largest values in the current vector are selected, and their corresponding buses are defined as the four possible faulted points. In this method, if one, two, and three faults occur in the system simultaneously, then one, two, and three of the four estimated points are nearest to actual points, respectively. For example, suppose that two-phase to ground faults with 77- and 85- resistances occur at buses 85 and 65 simultaneously. The normalized recovered current vector is shown in Fig. 1. Ten dominant values

more than 0.3 are found in the vector whose corresponding distances to substation are 2200, 2300, 2320, 2340, 2500, 2550, 2580, 2630, 2650, and 2600 m. The distances are categorized in four groups by Fuzzy-c mean. The centers of the groups are 2531.5, 2320.3, 2200.3, and 2622.5 m from the substation. Since the distances of actual faulted points to substation are 2580 and 2250 m, the nearest estimated distances to these two actual distances are 2622.5 and 2250 m. Therefore, the estimation errors are 42.5 and 49.7 m. In the second approach, since simultaneous faults are not common in power systems, all dominant values in the normalized current vector are used to estimate one single point by the k-nearest neighborhood technique [35]. If there are dominant values in the normalized current vector whose row numbers are , the estimated distance of the faulted point to substation is calculated using [40] (12) denotes the normalized current vector, and is where the distance of the bus associated with the th dominant value to the substation. This method estimates the faulted point distance to the substation. Although a given distance may correspond to more than one point in the distribution networks, the faulted zone is restricted by the associated buses with dominant values, and only one bus is assigned as faulty. For example, suppose that a singlephase-to-ground fault with 0.5- resistance occurs at bus 91. Based on the normalized recovered current vector shown in Fig. 2, four dominant values are greater than 0.3. The corresponding distances of the buses associated with them are 2400, 2580, 2600, and 2670 m. Using (12), we obtain the equation shown at the bottom of this page. The actual fault point distance is 2580 m, and the error is 17.9 m. The steps for the fault location algorithm are as follows. Step 1) Assume that fault occurs at bus .

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Step 2) If smart feeder meters are used, measure the voltage magnitude for buses, calculate using (6), and allocate phase angles 0, 120 , and 120 to voltage sag values in phases a, b, and c, respectively. Then, calculate using (4) and (7). If PMUs are used, measure the magnitude and phase of the voltages for buses, calculate and then using (4). Step 3) Select corresponding rows of and link them together to form . Step 4) Solve (9) for noise-free and (11) for noisy voltage sag measurements for recovery. Step 5) Normalize the estimated current vector by its maximum value. Step 6) Select entries greater than 0.3 in the normalized current vector as dominant values. Step 7) Find the buses corresponding to dominant values and calculate their distances to the substation. Step 8) For simultaneous faults, if there are more than four dominant values, categorize the distances in four main groups by Fuzzy-c means and use the group center and bus number of the dominant values to determine the four possible faulted points. Otherwise, select the buses associated with the four largest entries in the current vector as four possible faulted points. For a single fault, estimate the distance of the fault to the substation using (12) and assign a point in the faulted area distinguished by buses associated to dominant values.

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Fig. 2. Typical normalized recovered current vector in a single-fault case.

Fig. 3. Single-line diagram of the case study [10], [14].

TABLE I SIMULATION RESULTS FOR LOCATING SINGLE FAULTS USING 22 SMART METERS

III. SIMULATIONS RESULTS AND ALGORITHM VALIDATION Our algorithm is implemented on the simulation model of a 13.8-kV, 134-bus distribution network whose single line diagram is shown in Fig. 3 [10]. The 22 smart feeder meters are randomly installed along the primary feeder buses: 3, 4, 14, 20, 30, 34, 39, 43, 45, 51, 55, 57, 68, 83, 93, 96, 101, 111, 118, 127, 129, and 134. DIgSILENT is used to model the network and simulate pre- and during-fault conditions [36]. The voltage sag values are imported to our MATLAB algorithm to estimate the faulted points. Using DIgSILENT, many scenarios including single and multiple faults are considered to assess the performance of our algorithm. Three variables that define the different scenarios are fault types, faulted buses, and fault resistances. Bus # 1 is protected by a circuit breaker at the substation and is not considered. Each of the four fault types in each of the 133 buses is simulated with 0.5- and 10- fault resistances to provide single fault scenarios. To compare our results with [10], we only investigate the two fault resistances they used in single-fault location. In addition, 2000 scenarios are randomly produced for each of the double and triple simultaneous faults. For two simultaneous faults, two buses and two fault types are randomly selected 2000 times with random fault resistances between 0 and 100 . The procedure is repeated for three buses to produce triple simultaneous faults. The error in estimating the faulted location is evaluated as (13)

Regardless of the number of faults in the system, four possible faulted points are estimated. The error index is presented for the minimum distance between four estimated and one, two, or three actual faulted points. In each scenario, the errors between simulated and estimated faulted buses are categorized in 100-m steps. The numbers of buses estimated between 0 and 100 m, 100 and 200 m, 200 and 300 m, 300 and 400 m, and higher than 400 m are enumerated individually and demonstrated in results. A. Simulations Results for Single Faults Location Table I presents our results for locating single faults using the data of 22 smart feeder meters. Method 1 uses Fuzzy-c means to estimate four possible faulted points, and Method 2 uses k-nearest neighborhood to find a single faulted point. Since most fault location errors are less than 100 m, the performance of our algorithms to locate single faults is excellent. The number of faulted buses with less than 200-m

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TABLE II SIMULATION RESULTS FOR LOCATING SINGLE FAULTS BY 22 SMART METERS WITH NOISE GENERATED FROM (0,0.5%)

TABLE III SIMULATION RESULTS FOR LOCATING SINGLE FAULTS BY 22 SMART METERS WITH NOISE GENERATED FROM (0,1%)

Fig. 4. Histogram graph of error distributions for locating single faults.

estimation error is not notably influenced by changing the fault resistance or fault type. However, both methods recognize single-phase, double-phase-to-ground, and double-phase short circuits slightly better than three phase faults which are less common in distribution networks. Method 1 gives a lower total error and more fault locations with error less than 100 m compared with Method 2. It requires crew groups to inspect four possible faulted points to find the fault. Method 2 finds only one fault point, and one crew group can restore the network. Thus, there is a tradeoff between human resources and fault location accuracy. The error distributions are exponential, as shown in Fig. 4. 1) Performance With Noisy Measured Data: Smart feeder meters measure the pre- and during-fault voltages with between 0.1 to 0.5% accuracy [37], [39]. Load and temperature fluctuations significantly affect smart meter accuracy [38]. To examine the performance of our algorithm with noisy input data, each measured line to ground voltage is multiplied by normally distributed random numbers with zero mean and 0.5%, 1%, and 2% standard deviation. The simulation results with noisy input data are presented in Tables II–IV. In addition, we assess the performance of our algorithm with measurement calibration errors. We assume that all measurements include 0.5% noise and the measured voltage drops at buses 20 and 101 are multiplied by 1.15. Table II shows that the numbers of faulted buses estimated with less than 200-m errors in Method 2 are close to the noisefree results in Table I. This is not the case for faulted buses with more than 400-m estimation errors where, except for the 0.5double-phase short circuits, the total errors increase with noisy data. The total error of Method 1 decreases in all cases, except for 10- single-phase and double-phase-to-ground cases. Thus, the combination of Fuzzy-c mean and reconstructing the

TABLE IV SIMULATION RESULTS FOR LOCATING SINGLE FAULTS BY 22 SMART METERS WITH NOISE GENERATED FROM (0,2%)

fault current vector from noisy measurements by minimization performs better than Fuzzy-c mean clustering and recovering the current vector from noise free data by minimization. Therefore, the main feature of the proposed algorithm is robustness to noise. Tables II–IV show the performance deterioration of both Method 1 and 2 as the noise levels increase. From Tables IV and V, for data corrupted by 2% noise or with meter calibration errors, the performance of Method 1 remains acceptable, but Method 2 is unsatisfactory. 2) Performance With Different Number of Measurements: We investigate sensitivity to the number of measurements in three cases with fewer smart meters than the base case. Case 1) Seventeen smart meters are placed at buses 3, 4, 14, 20, 34, 39, 45, 51, 57, 73, 83, 96, 101, 111, 116, 127, and 134. Case 2) Thirteen smart meters are placed at buses 3, 20, 30, 45, 51, 60, 100, 111, 118, 121, 127, 129, and 134.


TABLE V SIMULATION RESULTS FOR LOCATING SINGLE FAULTS BY 22 SMART METERS WITH (0,0.5%) NOISE AND BAD CALIBRATION IN METERS 20 AND 101

TABLE VI RESULTS FOR LOCATING SINGLE FAULTS USING 17 SMART METERS

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TABLE VIII RESULTS FOR LOCATING SINGLE FAULTS USING NINE SMART METERS

TABLE IX SIMULATION RESULTS FOR DOUBLE FAULT LOCATIONS

TABLE VII RESULTS FOR LOCATING SINGLE FAULTS USING 13 SMART METERS

Case 3) Nine smart meters are placed at buses 3, 30, 45, 60, 100, 118, 127, 129, and 134. The simulation results with 17, 13, and nine smart feeder meters are given in Tables VI–VIII, respectively. When more measurements are used, the number of faulted buses with estimation error less than 200 m does not change significantly in both methods but the total errors decrease. Simulation results for Method 2 to identify 0.5- two-phase faults show that acceptable performance in both methods requires 9 or more measurements. Both our methods and those of [10] give the best performance when meters are placed at branch terminations. B. Simulation Results for Multiple Fault Locations Results for double and triple simultaneous faults location are presented in Tables IX and X, respectively. For multiple fault location, nonzero values in the calculated fault current vector contain more information about two or three faults location and more detailed input data is needed. Therefore, application of PMUs in distribution networks to enhance the accuracy of multiple fault location is investigated.

To incorporate 0.5% noise into the measured PMUs’ raw data, two Gaussian N(0,0.5%) random numbers k1 and k2 are generated, then the magnitude of each line to ground measured voltage is multiplied by , and k2 degrees are added to its phase. 1) Simulation Results for Double Fault Locations: Table IX presents the performance of the multiple fault location algorithm with 22 and 25 smart meters and PMUs. Most estimation errors are less than 100 m, and the performance of our algorithm for double fault location is acceptable. The algorithm performs better for noise-free conditions if PMUs rather than smart meters are used to measure the voltage sags. However, the results with noisy measurements are better using smart meters than PMUs. This is because PMU voltage magnitude and phase are noisy while only voltage magnitudes are noisy for smart meters.

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2) Simulation Results for Triple Fault Locations: Based on Table X, although our algorithm is slightly worse at identifying triple fault locations than double fault locations, the number of faulted buses with less than 200 m estimation error does not fall below 83.6% in noise free conditions, which is still satisfactory. A comparison between Tables IX and X shows that the PMUs are more effective in improving the performance of triple fault location than double fault location. In addition, the performance of the fault location algorithm in triple fault location is more sensitive to measurement noise.

TABLE X SIMULATION RESULTS FOR TRIPLE FAULT LOCATIONS

IV. DISCUSSION AND COMPARISON We propose a practical feasible and cost-effective fault location algorithm that can be implemented with measurement devices along the primary feeders. A similar method [10]needs the meters to measure the pre- and during- fault voltages along the primary feeder and requires polling several smart load meters to update the impedance matrix by load data and detect the faulted area. The simulations results in [10] using 13 smart feeder meters and 100 smart load meters are presented in Table XI. Only single-phase and three-phase short circuits were analyzed in [10] to evaluate their fault location algorithm. However, all four probable faults are simulated for our algorithm using 22 smart feeder meters. Importantly, the performance of [10] significantly deteriorates with noisy measurements while our method is robust to noise. Since the performance of our algorithm with smart meters is comparable or better than the performance of [10] with PMUs, only single fault locations are estimated using smart meters. In other words, our single fault location algorithm can, with voltage sag magnitudes measured by smart feeder meters, estimate the fault locations with the same accuracy as [10], when the latter requires both voltage sag magnitudes and phases measured by PMUs. In addition, the performance of our algorithm is less dependent on fault resistance than [10]. The numbers of faulted buses estimated with less than 100-m error drop below 100 buses in [10] for 0.5- fault resistance. However, for both Methods 1 and 2, the numbers of estimation errors less than 100 m do not significantly change with fault resistance. Simultaneous faults are rarely addressed in the literature, but the work in [13] presents an algorithm to find line-sections for single or simultaneous faults. Their algorithm cannot recognize fault sections for overlapping fault current paths while ours can. Reference [3] uses the sign of the positive sequence resistance at each measurement point to detect a downstream or upstream fault. Power quality meters are needed to measure the voltage and current phasors at some buses along the primary feeder to identify the sag source direction. Reference [14] only finds single-phase to ground fault locations with no measurement noise. In addition, load uncertainties have impacts on the performance of their proposed method. We propose a fault location algorithm which is robust to measurement noises and load uncertainties and usable for all fault types. Although [14] requires fewer measurements than our approach, its computational load is higher due to its load flow calculations and large number of iterations. Reference [15] estimates fault location using a similarity measure between calculated and captured during-fault noise-free voltage phasors. Unlike our approach,

TABLE XI SIMULATION RESULTS IN [10]

it requires knowledge of the faulted phases and fault types as well as time-consuming power flow calculations. The run time of [15] is about 14 s, as compared with about 0.05 s in our algorithm when the simulations are performed on a computer with a 2.4-GHz Intel Core i3-2370 M CPU and 4.00-GB memory. In [16], the states of voltage sags along the primary feeder are estimated by least squares to locate the fault. They do not investigate the sensitivity of their method to measurement noise or calibration errors. V. CONCLUSION This paper proposes a method to exploit the potential of compressive sensing to reconstruct the sparse faults current vector with impedance matrix and voltage sag values captured


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Mehrdad Majidi received the B.Sc. and M.Sc. degrees in electrical engineering (with honors) from the Power and Water University of Technology (PWUT), Tehran, Iran, in 2009 and 2011, respectively. He is currently working toward the Ph.D. degree at University of Nevada, Reno, NV, USA. His research interests include smart grids, power system automation, fault location, machine learning methods, and applications of signal processing in power system.

Mehdi Etezadi-Amoli (LSM’11) received the Ph.D. degree from New Mexico State University, Las Cruces, NM, USA, in 1974. From 1975 to 1979, he was an Assistant Professor of electrical engineering with New Mexico State and the University of New Mexico, Las Cruces, NM, USA. From 1979 to 1983, he was a Senior Protection Engineer with Arizona Public Service Company, Phoenix, AZ, USA. In 1983, he joined the faculty of the Electrical Engineering Department, University of Nevada, Reno, NV, USA. His current interest is in large-scale systems, power system distribution and protection, distributed generation, and renewable energy. Dr. Etezadi is a registered Professional Engineer in Nevada.

Mohammed Sami Fadali (SM’91) received the B.S. degree in electrical engineering from Cairo University, Cairo, Egypt, in 1974, the M.S. degree from the Control Systems Center, UMIST, Manchester, U.K., in 1977, and the Ph.D. degree from the University of Wyoming, Laramie, WY, USA, in 1980. He was an Assistant Professor of electrical engineering with the University of King Abdul Aziz, Jeddah, Saudi Arabia, from 1981 to 1983. From 1983 to 1985, he was a Post-Doctoral Fellow with Colorado State University. In 1985, he joined the Electrical Engineering Department, University of Nevada, Reno, NV, USA, where he is currently a Professor of electrical engineering. In 1994, he was a Visiting Professor with Oakland University and GM Research and Development Labs. He spent the summer of 2000 as a Senior Engineer with TRW, San Bernardino, CA, USA. His research interests are in the areas of fuzzy logic stability and control, state estimation and fault detection.