Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

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High-impedance Fault Detection Method Based on Feature Extraction and Synchronous Data Divergence Discrimination in Distribution Networks  PDF

  • Yang Liu 1
  • Yanlei Zhao 1
  • Lei Wang 1
  • Chen Fang 2
  • Bangpeng Xie 3
  • Laixi Cui 1
1. School of Electrical and Electronic Technology, Shandong University of Technology, Zibo, China; 2. State Grid Shanghai Electric Power Research Institute, Shanghai, China; 3. State Grid Shanghai Pudong Electric Power Supply Company, Shanghai, China

Updated:2023-07-24

DOI:10.35833/MPCE.2021.000411

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Abstract

High-impedance faults (HIFs) in distribution networks may result in fires or electric shocks. However, considerable difficulties exist in HIF detection due to low-resolution measurements and the considerably weaker time-frequency characteristics. This paper presents a novel HIF detection method using synchronized current information. The method consists of two stages. In the first stage, joint key characteristics of the system are extracted with the minimal system prior knowledge to identify the global optimal micro-phase measurement unit (μPMU) placement. In the second stage, the HIF is detected through a multivariate Jensen-Shannon divergence similarity measurement using high-resolution time-synchronized data in μPMUs in a high-noise environment. l2,1 principal component analysis (PCA), i.e., PCA based on the l2,1 norm, is applied to an extracted system state and fault features derived from different resolution data in both stages. An economic observability index and HIF criteria are employed to evaluate the performance of placement method and to identify HIFs. Simulation results show that the method can reliably detect HIFs with reasonable detection accuracy in noisy environments.

I. Introduction

HIGH-IMPEDANCE faults (HIFs) typically occur in distribution networks (4-34.5 kV) [

1]. Statistically, 5%-10% of distribution network faults [2] and 25% of events caused by a down-conductor [3] are considered as HIFs. Because an HIF current does not manifest sufficient changes for fault detection, and even when the fault point current is less than 10% of the load current based on the medium, it does not pose a severe threat to the system’s regular operation over a long fault duration. However, in addition to degrading power supply quality, HIFs jeopardize human safety and increase fire risk. Severe fire hazards that recently occurred in the United States and Australia originated from HIFs [4]. Therefore, HIFs must be effectively detected and isolated within a reasonable period.

In previous studies, the transient and nonlinear properties of an HIF have generally been applied in detection using different domain analytical methods [

5], [6]. Because measurement accuracy hinders HIF detection performance [7], high-precision measurement data and real-time monitoring performance of a micro-phase measurement unit (μPMU)/PMU enable real-time fault detection and improved fault detection performance [8]-[12]. For example, a semi-supervised learning method [8] has been proposed to detect HIFs in high signal-to-noise ratio (SNR) environments and can achieve fault detection using a combination of labeled and unlabeled data. In [11], a transferred learning-based method is presented to detect HIFs by combining principal component analysis (PCA) with a convolution neural network under a cloud-edge computer framework. However, information communication factors such as channel noise and information coding methods affect HIF detection accuracy. In [12], a synchrophasor-based state estimate is used for fault detection based on synchrophasor data obtained for each bus.

Although a μPMU has very high precision and relatively low cost as compared with a PMU [

13], the full deployment of a μPMU for monitoring purposes is neither realistic nor economical in a distribution network as that in a transmission network. Therefore, HIF detection based on synchronization data from limited μPMUs poses a challenge, particularly under μPMU optimal placement. In [14], synchrophasor-based state estimates are used to detect HIFs under a static framework. An exhaustive search algorithm is applied to achieve the sparse deployment of μPMUs to obtain network observability. In [15], only a few PMUs are used to divide networks into several monitoring fractions, and an artificial neural network (ANN) method is employed to identify an HIF. In [16], a two-level ANN is proposed for detecting HIFs based on synchronized current measurements of different nodes. In [17], the harmonic energy randomness index is integrated with a wave distortion extraction method to detect an HIF. Because fault detection is a time-constrained process, whether the data from measuring devices are sensitive to system state changes is more important in fault detection than in state estimation. Therefore, determining the optimal μPMU/PMU placement for sensitive positions is crucial. However, to the best of our knowledge, most existing HIF detection methods do not consider the optimal μPMU placement [17] or optimal placement essential for state estimation [14] rather than fault monitoring.

By contrast, HIF transient characteristics and nonlinearities vary with grounding surface features such as material type, humidity, and other factors [

6]. This variation makes it difficult for algorithms to guarantee their validity in practical applications. However, when a fault occurs, the statistical characteristics of the system’s operating state in the fault stages change substantially as compared with the normal state. The divergence method, based on entropy, has recently been shown to be superior in detecting anomalous events. In [18], Kullback-Leibler divergence (KLD) is used to analyze the time-domain characteristics of the current and to discriminate an HIF from switching events and voltage swells/sags. Compared with KLD, the Jensen-Shannon divergence (JSD), because of its upper bound, provides a good, numerically stable, and appropriate measure of the differences between two distributions. Therefore, JSD has been applied to anomaly detection such as incipient faults [19]-[21]. Nevertheless, the efficiency of JSD has never been considered for HIF detection in noisy environments.

In the present work, we propose an improved HIF detection method using μPMU data in distribution networks. The primary purpose of the proposed method is to detect a fault based on the difference between the joint characteristic probability density functions of the system state before and during the fault. l2,1 PCA, i.e., PCA based or the l2,1 norm, is applied to extract the joint characteristics. By comparison, the proposed method requires only a few μPMUs, which are determined by the optimal μPMU placement algorithm. The main contributions of this paper are summarized as follows.

1) HIF detection: fault detection is accomplished by comparing the difference between the joint characteristic probability density functions of the system state before and during the fault. The proposed detection method is based on the difference in the statistical probability distribution of the synchronized data before the fault and fault duration based on the optimized μPMU placement.

2) Optimal placement of μPMU (OPP): the optimal results identified by l2,1 PCA are globally optimal locations from which measurement data are sensitive to state changes. This implies that using the data from these locations for fault detection may satisfy the time constraint of fault detection. The proposed economic observability index can be used to evaluate μPMU placement schemes in practical applications.

3) Challenge of distribution network: combining optimal μPMU placement with HIF detection, the proposed method solves the globally optimal problem of μPMU locations, avoids the difficulty in selecting various configuration schemes in practical applications, and realizes HIF detection based on the data provided by μPMUs at the optimal locations. The proposed method provides a possible implementation for HIF detection using synchronous data probability distribution features.

The remainder of this paper is organized as follows. Section II describes the HIF model and problem formulation. Section III proposes the materials and methods. Section IV presents the case studies. The conclusion is presented in Section V.

II. HIF Model and Problem Formulation

A. HIF Model

The features of HIFs include grounding materials, grounding surface humidity, system operations, and weather conditions, which vary considerably in different situations. Hence, many HIF models have been presented [

22], and various HIF types have been classified [17]. Since most HIFs accompany arcs, which occur in high-inductance circuits [23], and the voltage-current characteristics are similar to field test results [22], the anti-parallel high-impedance model [24] is used in this paper. The model of an HIF includes two inductors, two direct-current (DC) sources, two diodes, and two resistances, as illustrated in Fig. 1, where Rp and Rn are the transition resistances used to represent the resistances of the grounding materials; Vp and Vn are the arcing voltages of air between the grounding materials and the distribution line, respectively; Vf is the fault-point voltage; If is the fault current; and Lp and Ln are two inductors the arcing inductance features. The two variable resistors and inductors change randomly to model the dynamic arcing resistance and inductance.

Fig. 1  HIF model.

The HIF model is formulated as:

Vf=(Rp+jXp)If+Vp    Vf>Vp(Rn+jXn)If-Vn    Vf<Vn0                                VnVfVp (1)

B. Problem Formulation

Considering a distribution feeder with two μPMUs and several buses between the μPMUs, these buses may or may not have laterals. The π model of a distribution feeder is obtained by applying Kirchhoff’s law, as shown in Fig. 2.

Fig. 2  π model of a distribution feeder with two μPMUs.

In Fig. 2, Zmn and Ymn are the equivalent impedance and earth admittance, respectively. Obviously, the relationship between the measurements of the two µPMUs contains the characteristics of a distribution feeder. The ith µPMU records the samples of the three-phase voltage phasor viC3×1 and three-phase current phasor iiC3×1 at the jth sample. For a distribution network with µPMUs, the µPMU dataset X^ is formulated as:

X^=(x^i,j)n×M (2)

where x^i,j=(v,i)i,j represents the phasor value of the ith µPMU in the jth sample; n is the number of µPMUs; and M is the number of continuous samples. The phasor value x^i,j is obtained as:

x^i,j=x^i,jRe+jx^i,jIm (3)

where x^i,jRe and x^i,jIm are the real and imaginary parts of the x^i,j, respectively. The µPMU dataset can be rewritten as:

X^=[x^i,jRe    x^i,jIm]N×M (4)

where N=4×3n denotes the number of recorded variables.

In this paper, synchronized data are used for the HIF detection procedure. As previously mentioned, the fault detection problem is a time-constraint problem. This means that the data for fault detection are sensitive to abrupt fluctuations in the system states. However, finding a benchmark system with μPMUs to meet data sensitivity requirements is difficult because most proposed benchmark systems are not designed to detect a fault but rather to estimate the system state [

14]. Therefore, in this paper, the HIF detection problem is divided into two subproblems: determining the source locations of synchronized data and detecting an HIF based on synchronized data features.

Because a data-driven method is used to detect an HIF in this study, the following assumptions are made regarding the used data.

Assumption 1: the maximum percentage measurement errors involve assumptions similar to those found in [

25].

1) Substation measurements: 1%. Measurements include the voltage magnitude, current magnitude, and active and reactive power flows at the substation. Although substation measurements have different accuracies according to different time references, the measurements are considered to be highly accurate if a time reference is precise in the substation. Therefore, a 1% error is chosen for the substation measurement.

2) Real measurements: 10%. Measurements include active and reactive power in lines from the intelligent electronic device (IED). Due to the uncertainty of the instrument and the influence of possible signal dynamics, the error of real measurements is set to be 10%.

3) Pseudo-measurements: 50%. Measurements are obtained from historical load data.

4) µPMU measurements: a total error vector of 1% is compliant with the IEEE synchro-phasor standard [

26].

Assumption 2: since a zero-injection bus rarely appears in a distribution grid [

25], it is not included in the test cases.

III. Materials and Methods

This section proposes two steps for implementing two sub-procedures: ① feature extraction, and ② feature analysis and discrimination, which consist of HIF detection and optimal allocation of µPMUs.

A. l2,1 PCA

Events, e.g., switching, fault, and contingent, in the system cause data fluctuations in the monitored variables such as voltage and current amplitudes. These data fluctuations are often similar to the step changes at the beginning of an event. Because PCA is quite sensitive to step change, it is increasingly used in power systems, e.g., fault detection [

11], [27]-[31]. However, PCA neglects PCs, which contain critical information about fault characteristics [32], and PCA cannot achieve a unique solution if the measurement matrix is not full rank [33]. Therefore, we introduce the l2,1 norm into PCA and the regulation penalty for forming l2,1 PCA, as proposed in our previous work [34].

P=argminPJ(P) (5)

where J(P)=Y-XP2,1-λP2,1 is the objective function, and λ>0 is an adjustment coefficient, Y is the PCs obtained by PCA, X is the measurement data matrix, P is the loading matrix; and 2,1 is the l2,1 norm of the matrix.

Differentiating J(P) with regard to P and setting the result to be zero, we can obtain:

δJ(P)δP=2XTΞ(Y-XP)+2λΘP=0 (6)

where E=Y-XP; and Ξ and Θ are the diagonal matrices, with the ith diagonal element given as:

Ξii=12Ei2 (7)
Θii=12Pi2 (8)

Thus, P can be obtained as:

P=(XTΞX-λΘ)-1XTΞY (9)

Note that P is dependent on Ξ and Θ and is thus an unknown variable. An iterative algorithm to solve (9) can then be designed as follows. The l2,1 PCA algorithm is given in Algorithm 1 [

34].

Algorithm 1  : l2,1 PCA

Input: the measurement data matrix X

Output: the component analysis PsRm×q

  Set t=0, and initialize Ξ=Im, Θ=In

  Calculate SVD of X for obtaining Y and E

Repeat

   Calculate Pt+1=(XTΞtX-λΘt)-1XTΞtY

   Update Ξt+1 and Θt+1

   t=t+1

Until convergence.

   Ps=P/P2

Remark 1: a sample size of 30 is sufficiently large to enable the probability density function (PDF) of samples to approach a Gaussian distribution [

9]. The μPMU data may be considered a Gaussian distribution because of the large sample set.

Remark 2: in this paper, the sensitivity of l2,1 PCA to data changes and the global optimality of the solution are used to identify the nodes sensitive to system state changes to obtain a benchmark system with optimal μPMU placement for HIF detection.

Remark 3: since l2,1 PCA can extract joint features from data, making it more sensitive to data fluctuations caused by system state changes as compared with standard PCA, the l2,1 PCA method is also used to extract data features from synchronized measurements to detect the HIF.

B. HIF Detection

For Gaussian data such as the X^ recorded by µPMUs, the principal scores obtained by l2,1 PCA obey a Gaussian distribution with respect to central limit theorem. Then, the PDF of the principal scores satisfies:

fi~N(μ1,σ12)hi~N(μ2,σ22) (10)

where fi and hi are the PDFs of the principal scores for the ith µPMU measurement under normal and faulty conditions, respectively; μ1 and σ1 are the mean and standard deviations of fi, respectively; and μ2 and σ2 are the mean and standard deviations of data hi, respectively. Consequently, the JSD for a single variable DJS is calculated as:

DJS=12DKL(fi||M)+12DKL(hi||M) (11)

where DJS and DKL are the JSD and KLD values, respectively; and M=(fi+hi)/2 satisfies a mixture distribution.

For n µPMUs, the historical data matrix is structured according to (4). Without loss of generality, the online data matrix structure is consistent with the historical data matrix structure. Suppose p~N(μp,Σp) and q~N(μq,Σq) are denoted as the PDFs of the first principal scores obtained under the normal and faulty conditions, respectively. μp and μq are the n-dimensional mean vectors of p and q, respectively; and Σp and Σq are the covariance matrix of p and q, respectively. The univariate JSD value in (11) can be rewritten as:

DJS=12DKL(f ||M)+12DKL(h||M) (12)

where M is the mixture distribution. The covariance matrix is a symmetric position definite matrix. DJS can be rewritten as:

DJS=14tr(ΣM-1(Σp+Σq))+lgΣM2ΣpΣq-n+(μM-μp)TΣM-1(μM-μp)+(μM-μq)TΣM-1(μM-μq) (13)

where tr(·) is the trace of the matrix. Since the mean of the distribution is assumed to be unchanged (zero) after the occurrence of an HIF, an HIF will not move the center of the l2,1 PCA model.

μp=μq (14)

Equation (14) and the mixture distribution M are unimodal because of the two Gaussian distributions with the same mean. It is also assumed that M remains a Gaussian distribution, i.e., M~N(μM,ΣM). The mean and variance of M are calculated using (14) as:

μM=12(μp+μq)ΣM=12(Σp+Σq) (15)

Equation (12) is then rewritten as:

DJS=14tr(ΣM-1(Σp+Σq))+lgΣM2ΣpΣq-2 (16)

When the divergence value is theoretically equal to zero, the two considered PDFs are identical. The references and tested functions are both obtained under normal operational conditions. In practical cases, a low nonzero divergence is always caused by the factors such as random noise/fluctuations, normal switching operations, or data acquisition devices.

In a noisy environment, the variances of the first principal scores Σ¯p and Σ¯q consist of the variance of the principal score without noises and the noise variance, respectively.

Σ¯p=Σp+Iσn2Σ¯q=Σq+Iσn2 (17)

where Σ¯p and Σ¯q are the variances of the first PC under the fault-free and faulty states, respectively; σn2 is the noise variance; and I is a unit matrix of the same size as Σ¯p. Faults result in a change in the distribution network, and the variance changes considerably in the fault direction [

35]. In other words, variances with faulty states can be rewritten by considering the variance bias as:

Σq=Σp+ΔΣ (18)

where ΔΣ is the variance bias due to the occurrence of an HIF. Based on (11), (13), and (15), the variances in M are obtained as:

ΣM=12(2Σp+ΔΣ+2σn2I) (19)

Thereby, (12) can be further rewritten as:

DJS=14lgΣ¯M2Σ¯pΣ¯q=14lg(2Σp+ΔΣ+2σn2I)24(Σp+σn2I)(Σp+ΔΣ+σn2I) (20)

where DJS has a clear relationship with the variance deviation caused by the fault and random noise. Therefore, a threshold must be used to determine whether the system enters an abnormal operating state. Because the threshold selection affects the method performance, the threshold may be set by evaluating the JSD on the PDFs of the first principal scores calculated from the μPMU data in this paper. We use a sliding window of a fixed size L, and the first principal score is partitioned into sections using a sliding window. However, a large window size decreases the detection delay and accuracy and causes some essential fault information to be neglected. Thus, a trade-off between accuracy and delay detection is required. During regular operation, the current waveforms in the two subsequent sections are similar. In other words, the first principal scores in the two subsequent sections are also similar. Therefore, we use the average value of the distribution with the first principal score with fault-free states:

η=1Ki=1NDJS(fi-1,fi) (21)

where K is the total number of partitioned sections. Since the zero-section f0 does not exist, f0 is generally represented by initializing the section. Since the switching event time is usually approximately 2-3 cycles and the duration of the HIF often lasts for 8-10 cycles or more [

18], [36], [37], when the JSD with fault states abruptly changes, DJS exceeds a threshold for more than the continuous time τ [18]. Consequently, the HIF criteria are defined as:

DJS>η (22)
tJSD>τ (23)

where tJSD is the duration. The time criterion is used to avoid false detections derived from normal operations such as switching events. Figure 3 presents the HIF detection procedure.

Fig. 3  HIF detection procedure.

Figure 3 shows that the detection process is divided into offline and online stages. We derive a representation of the system state probability distribution under normal operating conditions from historical data and determine the detection threshold in the offline stage. We use the multivariable JSD method to detect the system state in the online stage. If DJS exceeds the detection threshold and the continuous over-limit time exceeds the set value, it is determined that an HIF has taken place.

Remark 4: it is evident that the proposed method can also be applied to the detection of low-impedance faults (LIFs). LIFs are easily detected and can trigger the protection device. The fault detection procedure presented in Fig. 3 assumes that the fault has been detected without applying the proposed method if an LIF occurs.

C. Optimal Allocation of μPMUs

Some operation state changes are often mistaken as disturbances at the early stage, thereby increasing the chance of false identification of sensitive locations. The monitored variable is reconstructed in the state change direction to determine sensitive locations, i.e.,

zi=x-ςiri (24)

where zi is the reconstructed variable; x is the measurement vector of variable xi; ςi is the direction of the state change and the ith column of the identity matrix; and ri is the estimated fault magnitude such that zi is closest to the normal region. According to [

35], the contribution of variable xi to state changes is calculated using the following combined index (CI):

CIi=(xTΦςi)2/ϕii (25)

where ϕii is the ith diagonal entry in Φ. The threshold of CIi is:

CIlimi=ςiTΦTSΦςiςiTΦςiχα2 (26)

where S is the covariance matrix of x; and χα2 is the chi-square distribution with α degree of freedom.

For the jth bus, N variables can be monitored. Therefore, the joint contribution index JCIj and threshold JCIlimj of the jth variable are defined, respectively, as:

JCIj=i=1MviCIi,jJCIlimj=i=1MviCIlimi,j (27)

where vi is the weight coefficient corresponding to the significance of the monitored variables and i=1vi=1; and CIi,j and CIlimi,j are the combined index and threshold for the ith variable in the jth bus, respectively. The JCIj reflects the comprehensive sensitivity of the jth bus to the state change. The more significant the joint contribution, the more sensitive the bus corresponding to the monitored variables will be to state changes.

To facilitate a comparison of the comprehensive sensitivity of each node, the relative contribution index (RCI) is defined as:

RCI=JCIj/JCIUCLj (28)

where JCIUCLj is the upper control limit of each bus, given in the following form:

JCIUCLj=m(JCIlimj) (29)

where m(JCIlimj) is the mean of JCIlimj. If the relative contribution is more than one, we can select it as the bus responsible for placing the μPMU. The optimal placement identification procedure is illustrated in Fig. 4.

Fig. 4  Optimal placement identification procedure.

Remark 5: the l2,1 PCA method is applied in fault detection and μPMU deployment, but the processed data sources are different. The data analyzed by fault detection derive from the μPMU measurement data, and the data for μPMU deployment derive from the IED or other measuring devices.

IV. Case Studies

A. Simulation Conditions

The proposed method is tested on an IEEE 34-node system, which is a three-phase unbalanced test system [

38]. Different fault types are simulated in the system where the μPMU is deployed based on the proposed placement method. Figure 5 shows the μPMU and DG placements in the test system with 12 μPMUs and two DGs installed, and the red dots indicate the representative buses. The location and capacity of DGs are listed in Table I.

Fig. 5  Single-line illustration of IEEE 34-node system.

Bus No.Active power (MW)Reactive power (Mvar)
890 0.235 0.127
840 0.124 0.021

The maximum error of the DG outputs is 3%. It is assumed that the measurement noise obeys Gaussian distributions. In the detection cases, μPMUs obtain voltage and current phasor measurements for HIF detection. In most HIF detection results, the ground resistances are between 100 Ω and 2 kΩ [

5], [6], [39]. The grounding resistance of many HIFs in the initial fault stage is often greater than 1 kΩ or 3 kΩ. Therefore, the grounding resistances are set from 500 Ω to 5 kΩ in the HIF simulation. Table II lists the parameters of the HIF model.

Component (Ω)Value range
Rp, Rn 500-5000
Lp, Ln 20-80

PSCAD/EMTDC is used to obtain the magnitude and phase angle of the voltage and current, active and reactive power flows, and injected active and reactive power on each bus, and MATLAB 2016(a) is applied to analyze the measurement data.

B. Optimal μPMU Placement

Compared with the improved PCA (IPCA) [

40], the explained variances (var.) and cumulative variances (cum var.) of the first five PCs are presented in Table III.

No. of PCl2,1 PCAIPCA
Var. (%)Cum var. (%)Var. (%)Cum var. (%)
1 94.56 94.56 88.08 88.08
2 3.62 98.18 7.70 95.78
3 1.34 99.52 3.52 99.30
4 0.35 99.87 0.51 99.81
5 0.12 99.99 0.08 99.89

Table III shows that the sum of the first two explained variances is higher than that of the IPCA (98.18% versus 95.78%), and the cumulative variances of the five PCs are 6.48%, 2.4%, 0.22%, 0.06%, and 0.1% higher than those of the IPCA, respectively. The information in the first PCs is more than that in the IPCA. This is why the proposed method has joint feature extraction characteristics that are more sensitive to an operation state change resulting from DG access. To achieve a trade-off between system observability and device cost, the economic observability index (EOI) is defined as:

κ=100×γ/ς (30)

where κ is the system observability redundancy for every $100; ς is the cost of μPMUs, which is approximately $3500 for every μPMU [

41]; and γ is the system observability redundancy index (SORI) proposed by [42], that is, γ=iβi, where βi is the number of μPMUs that can observe the given bus i. In the present study, the costs of other related devices such as communication apparatuses are not considered. The results are compared with those of [40], [43], [44], in which the number of identified nodes is similar to those in this study. The comparison between results of proposed and other methods is given in Table IV.

MethodNo. of PMUSORIEOI
Proposed method 12 42 1.000
Reference [40] 14 38 0.776
Reference [43] 12 42 1.000
Reference [44] 13 40 0.879

Table IV shows that 12 μPMUs are acquired by the proposed method, which are fewer than the numbers reported in [

40] and [44]. Compared with [40] and [44], the cost of the proposed method is reduced by $7000 and $3500, respectively. However, the EOI is increased by 0.237 and 0.121, respectively. Although the method is identical to that of [43] in terms of the number of μPMUs, SORI, and EOI, the proposed method determines the globally optimal placement. Therefore, determining the final placement result from multiple optimal placement schemes, as in [43], is not necessary.

C. Performance Evaluation

This subsection uses the IEEE 34-node system as a case to show fault detection using measurements from μPMUs on the representative buses, as shown in Table V and by the red dots in Fig. 5.

μPMU No.Bus No.μPMU No.Bus No.μPMU No.Bus No.
1 800 5 820 9 890
2 802 6 824 10 858
3 808 7 854 11 844
4 850 8 888 12 836

Fault detection performance is evaluated for transition impedances of 2 kΩ and 5 kΩ for a single-phase-to-ground fault. The measurement noise is assumed to follow a Gaussian distribution. The SNRs are 60 dB, 30 dB, and 10 dB, respectively. In this paper, the size of window L is 6, that is, one bin for every six sampling points, which is an empirical value. The total vector error of the μPMU is 1% [

25]. All events occur at t=0.5 s.

1) Case 1: HIF

A single-phase-to-ground occurs in phase B between the 824th bin and 850th bin when the SNR is 60 dB and the transition impedance is 2 kΩ. The fault phase current is shown in Fig. 6.

Fig. 6  Fault phase current.

The fault current exhibits distinct HIF characteristics, and the fault current magnitude is 1% of the load current, as shown in Fig. 6. In this case, conventional overcurrent protection devices cannot detect the fault. Because this small current mutation will not cause saturation of the current transformer, using the current for HIF detection is feasible. The detection results using the proposed method when the fault grounding impedance is 2 kΩ and the SNR is 60 dB are shown in Fig. 7.

Fig. 7  Fault detection results for SNR=60 dB and R=2 kΩ.

Figure 7 shows that the JSD of μPMU4 (the 850th bin), μPMU5 (the 824th bin), and μPMU6 (the 824th bin) exceeds the limit. In addition, the continuous time cumulatively exceeds the set discrimination time. This allows us to determine that an HIF occurred, and the location may be near the 824th bin. The SNR remains unchanged, but the transition resistance changes from 2 kΩ to 5 kΩ.

Figure 8 shows the detection results when the fault grounding impedance is 5 kΩ. As shown in Fig. 8, the monitoring curve starts to exceed the threshold in the 848th bin. Compared with the results shown in Fig. 7, the data distribution characteristics become smaller before and during the fault because the transition resistance increases. Besides, the over-limit time at 5 kΩ lags behind that at 2 kΩ (the 831st bin). Due to the increase in the number of power electronic equipments and electric vehicle charging and discharging, the system may operate under low SNR conditions during fault monitoring. Therefore, the scenarios with the fault grounding impedance of 2 kΩ and 5 kΩ are monitored at 30 dB and 10 dB of SNR, respectively. The results are presented in Figs. 9 and 10.

Fig. 8  Fault detection results for SNR=60 dB when R=5 kΩ.

Fig. 9  Fault detection results for SNR=30  dB. (a) R=2  kΩ. (b) R=5 kΩ.

Fig. 10  Fault detection results for SNR=10 dB. (a) R=2  kΩ. (b) R=5 kΩ.

The proposed method can detect HIFs in both scenarios, as shown in Fig. 9. When the grounding impedance is 2 kΩ, the monitoring JSD curve of μPMU6 initially exceeds the threshold in the 826th bin, and the monitoring JSD curves of μPMU4, μPMU5, and others in turn exceed and remain above the threshold. The JSD of the 824th bin falls in the 846th bin because of the noise in the scenario with the fault grounding impedance of 5 kΩ. The curve then rises quickly, recrossing the limit and remaining in the over-limit state.

Figure 10 shows the monitoring JSD curve of the 850th bin first crossed the limit. However, fluctuations are apparent. Although the monitoring curve fluctuates because of noise, the monitoring results of the 824th bin and 820th bin continuously exceed the limit. Both the monitoring results and cumulative time of continuous limit violation exceed the limit in each monitoring range. With the fault grounding impedance of 5 kΩ, the variations in the monitoring curve are similar to those in the 2 kΩ scenario, but the result of the 850th bin exceeds the threshold in the 828th bin. For most of the time, the fluctuations appear to remain in the over-limit state, and the continuous cumulative over-limit time exceeds the time constraint. Therefore, it could be preliminarily determined that an HIF occurs. Figure 10(a) and (b) shows that the over-limit time under SNR=10 dB is earlier than that of the other SNRs. Although the detection results in this process do not exceed the limit, the process of initial establishment of the fault is also evident.

The fault inception angle (FIA) affects the fault voltage/current magnitude, which in turn affects the fault detection results. When the most severe situation, i.e., FIA=0 is considered, Fig. 11 shows the detection results of the transition resistance of 5 kΩ for SNR=10 dB and SNR=60 dB, respectively.

Fig. 11  Fault detection results for FIA=0 and R=5  kΩ. (a) SNR=60  dB. (b) SNR=10 dB.

Figure 11(a) shows that the JSD curves of the 824th bin exceeds the threshold in the 861st bin. Subsequently, the JSD curves of the 850th bin and 820th bin violate the limits in the 862nd bin and 863rd bin, respectively.

In addition, the cumulative time of the continuous limit violation exceeds the time limit. Although the monitoring result of the 854th bin exceeds the threshold before the 861st bin, it quickly falls and the duration does not meet the time limit. Compared with the results shown in Fig. 8, the over-limit time of the monitoring curves lags by many bins; for example, the over-limit time of the 824th bin lags by 13 bins. However, the steepness of the monitoring curve is more obvious. The same results can be observed in Fig. 11(b). Figure 11 shows that the fault inception angle causes a delay in fault identification. However, the fault inception angle does not affect the HIF detection results because the HIFs could last for a long period. The fault inception angle does not affect the difference in the probability distribution before and during the fault.

Nevertheless, the monitoring results fluctuate near the threshold under the influence of noise. An HIF can be determined by calculating the cumulative time of the continuous limit violation. Figure 12 presents the detection probabilities against different SNRs with different grounding impedances.

Fig. 12  Detection probability against different SNRs and different earthing impedances.

Figure 12 shows that the detection probability of the proposed method reveals high detection efficiency at low noise levels (SNR>30  dB). It also shows a very low false detection probability (<0.9). However, the lower the detection probability, the higher the grounding impedance. The noise affects the detection probability of the proposed method at high noise levels (SNR<30  dB). However, the lower the grounding impedance, the higher the detection probability; for example, the detection probabilities are 0.2649 (5 kΩ), 0.2822 (2 kΩ), and 0.3787 (500 Ω) for SNR=10 dB, respectively. The detection performance of the proposed method distinctly increases with SNR under the same grounding impedance. In addition, the detection performance decreases as the grounding impedance increases under the same SNR.

2) Case 2: Load and Capacitor Switching

Because the switching of loads and capacitor banks produces features similar to those from high-impedance waveforms, the performance of the proposed method is tested during capacitor switching (CS) and load switching (LS). The first scenario is to switch on the one-phase capacitor bank installed at the 802nd bin, and the second scenario is to switch on the one-phase linear and nonlinear loads installed in the 808th bin and 854th bin, respectively. Both scenarios occur at t=0.5 s. One capacitor and two load models are shown in Fig. 13.

Fig. 13  Capacitor and load models. (a) Capacitor model. (b) Linear load model. (c) Nonlinear load model.

The capacitor bank and two load models are similar to those in [

37] and [45]. The proposed detection method detects both capacitor and load switching, as shown in Fig. 14, with results obtained when the SNR is 60 dB.

Fig. 14  Detection results of CS and LS. (a) CS. (b) Linear LS. (c) Nonlinear LS.

Figure 14 shows that the JSD results of CS exceed the limit at the 861st bin, and the JSD curves of LS also simultaneously cross the threshold. However, regardless of either the CS and LS detection results, the continuous over-limit time does not exceed the set time threshold. Therefore, according to the high-impedance fault criteria, the process shown in Fig. 14 does not indicate a high-resistance fault.

V. Conclusion

This paper proposes an HIF detection method using synchronized data divergence based on globally optimal μPMU placement. The proposed method consists of optimal μPMU placement and HIF detection. First, an optimal μPMU placement algorithm is proposed to obtain the globally optimal location for fulfilling fault detection time constraints. Second, HIF detection is presented based on the probability distribution divergence of the synchronous data before and during a fault. The performance of the proposed method is validated using simulated data from an IEEE 34-node test feeder system. The results reveal that, through feature extraction and synchronous data divergence discrimination, sensitive nodes could be captured to determine the optimal μPMU location and accurately detect HIFs using multivariate JSD combined with l2,1 PCA in high-noise environments. The probabilities of fault detection are 92.12% (500 Ω), 83.28% (2 kΩ), and 73.93% (5 kΩ) for SNR=20 dB, respectively, and are greater than 99% under SNR=30 dB. The method can accurately detect faults in high-noise environments and is robust to transient resistance, the fault inception angle, and noise.

Renewable energy sources with different access locations, access capacities, and capacity ratios affect fault detection. Suppose that the effect of renewable energy on fault detection is the noise. As shown in the simulation verification, the noise may play a supporting role in enhancing HIF detection. Therefore, in future research, we intend to use the noise-assisted method to increase the sensitivity of HIF detection under reliability constraints. Another main task is to identify fault lines and phrases and locate the fault based on data probabilistic statistics.

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