A Novel Partial Discharge Localization Method in Substation Based on a Wireless UHF Sensor Array Zhen Li, Lingen Luo *, Nan Zhou, Gehao Sheng and Xiuchen Jiang Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China; [email protected] (Z.L.); [email protected] (N.Z.); [email protected] (G.S.); [email protected] (X.J.) * Correspondence: [email protected]; Tel.: +86-135-6433-3412 Received: 5 July 2017; Accepted: 13 August 2017; Published: 18 August 2017

Abstract: Effective Partial Discharge (PD) localization can detect the insulation problems of the power equipment in a substation and improve the reliability of power systems. Typical Ultra-High Frequency (UHF) PD localization methods are mainly based on time difference information, which need a high sampling rate system. This paper proposes a novel PD localization method based on a received signal strength indicator (RSSI) fingerprint to quickly locate the power equipment with potential insulation defects. The proposed method consists of two stages. In the offline stage, the RSSI fingerprint data of the detection area is measured by a wireless UHF sensor array and processed by a clustering algorithm to reduce the PD interference and abnormal RSSI values. In the online stage, when PD happens, the RSSI fingerprint of PD is measured via the input of pattern recognition for PD localization. To achieve an accurate localization, the pattern recognition process is divided into two steps: a preliminary localization is implemented by cluster recognition to reduce the localization region, and the compressed sensing algorithm is used for accurate PD localization. A field test in a substation indicates that the mean localization error of the proposed method is 1.25 m, and 89.6% localization errors are less than 3 m. Keywords: partial discharges; wireless UHF sensors; RSSI fingerprint; localization; compressed sensing; substations

1. Introduction Partial Discharge (PD) is the representation of the insulation degradation of the power equipment in a substation, which can give rise to equipment failure and even serious accidents [1,2]. Therefore, PD detection and localization is an effective way to monitor the status of power equipment and avoid accidents. With the development of the smart grid, intelligent Condition Monitoring and Diagnostics (CMD) is one of the key requirement of a substation [3,4]. This paper proposes a novel partial discharge localization system in a substation that can quickly locate the power equipment with potential insulation defects. PD can be detected by the measurement of ultrasonic waves, light, heat, and Ultra-High Frequency (UHF) electromagnetic waves [5]. For PD localization in a substation, the UHF method is one of the most effective ways due to its excellent stability, anti-interference, transmission distance, and transmission speed [6,7]. Typical UHF methods are mainly based on time or angle information of the UHF signals such as time of arrival (TOA) [8], time difference of arrival (TDOA) [9,10], and angle of arrival (AOA) [11,12]. Among them, TDOA has been widely used for PD localization. In this paper [13,14] we proposed a PD localization method in transformers based on TDOA. In the literature, [15] TDOA was used for PD localization in a substation. A traditional TDOA-based PD localization system in a substation is shown in Figure 1. When PD happens, the UHF sensors receive the UHF signals produced by PD. Then, by analyzing the time difference information, the location of Sensors 2017, 17, 1909; doi:10.3390/s17081909

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the the UHF UHF signals signals produced produced by by PD. PD. Then, Then, by by analyzing analyzing the the time time difference difference information, information, the the location location of of PD can be estimated. Since the transmission speed of UHF signals is close to the speed of light, the PD can be estimated. Since the transmission speed of UHF signals is close to the speed of light, the PD can be estimated. Since thesignal’s transmission speed of UHF signals is close to the speed of light, the time time time difference difference of of the the UHF UHF signal’s arrival arrival among among UHF UHF sensors sensors is is on on aa nanosecond nanosecond level, level, which which difference of the UHF signal’s arrival among UHF sensors is on a nanosecond level, which requires a requires requires aa high high sampling sampling frequency frequency and and high-precision high-precision time time synchronization synchronization between between the the UHF UHF high sampling frequency and high-precision time synchronization between the UHF sensors and the sensors sensors and and the the signal signal acquisition acquisition system. system. This This requirement requirement produces produces high high hardware hardware costs costs and and makes makes signal acquisition system. This requirement produces high hardware costs and makes TDOA-based TDOA-based TDOA-based localization localization hard hard to to achieved. achieved. localization hard to achieved.

Figure 1. Traditional time difference of arrival (TDOA)–based Partial Discharge (PD) localization Figure 1. time difference of arrival (TDOA)–based Partial Discharge (PD) localization Figure 1. Traditional system in aTraditional substation.time difference of arrival (TDOA)–based Partial Discharge (PD) localization system in a substation. system in a substation.

In recent years, years, the received received signal strength strength indicator (RSSI) (RSSI) localization method method has been been widely In In recent recent years, the the received signal signal strength indicator indicator (RSSI) localization localization method has has been widely widely studied in indoor localization, which uses only the signal strength information and is easily achieved studied in indoor localization, which uses only the signal strength information and is easily achieved studied in indoor localization, which uses only the signal strength information and is easily achieved by a low hardware hardware costsolution solution [16,17].InInthis this paper[18], [18], anRSSI-based RSSI-based PD localization systems by by aa low low hardware cost cost solution [16,17]. [16,17]. In this paper paper [18], an an RSSI-based PD PD localization localization systems systems is is is proposed, which uses the signal propagation model to estimate the distances and then calculates proposed, which uses the signal propagation model to estimate the distances and then calculates proposed, which uses the signal propagation model to estimate the distances and then calculates the the the locationPD. of PD. This methodeasily is easily implemented butsusceptible is susceptiblethe to the complex environment location location of of PD. This This method method is is easily implemented implemented but but is is susceptible to to the complex complex environment environment in in in substation. With the development of wireless UHF sensors,arrangement the arrangement of the sensor UHF sensor substation. substation. With With the the development development of of wireless wireless UHF UHF sensors, sensors, the the arrangement of of the the UHF UHF sensor array array array can be more flexible, which motivates us to use the RSSI fingerprint localizationmethod method for PD PD can can be be more more flexible, flexible, which which motivates motivates us us to to use use the the RSSI RSSI fingerprint fingerprint localization localization method for for PD localization in a substation [19]. The RSSI fingerprint localization method is a scene analysis method localization localization in in aa substation substation [19]. [19]. The The RSSI RSSI fingerprint fingerprint localization localization method method is is aa scene scene analysis analysis method method with excellent excellent environment environment adaptability adaptability and and accuracy. accuracy. The The RSSI RSSI fingerprint fingerprint PD PD localization localization system system with with excellent environment adaptability and accuracy. The RSSI fingerprint PD localization system is shown in Figure 2. First, in the offline stage, a set of test points are arranged in the detection area. is is shown shown in in Figure Figure 2. 2. First, First, in in the the offline offline stage, stage, aa set set of of test test points points are are arranged arranged in in the the detection detection area. area. The RSSI values that are produced by discharging source, which denotes the received UHF signal The The RSSI RSSI values values that that are are produced produced by by discharging discharging source, source, which which denotes denotes the the received received UHF UHF signal signal strength, are are measured measured at at each each test test point. point. The The RSSI RSSI values values are are transmitted transmitted from from wireless wireless UHF UHF sensors sensors strength, strength, are measured at each test point. The RSSI values are transmitted from wireless UHF sensors to the computers computers thougha arouter. router. All the RSSI values and corresponding test points’ coordinates to to the the computers though though a router. All All the the RSSI RSSI values values and and corresponding corresponding test test points’ points’ coordinates coordinates are are are recorded to establish the RSSI fingerprint map ofdetection the detection area. Second, in the online stage, recorded to establish the RSSI fingerprint map of the area. Second, in the online recorded to establish the RSSI fingerprint map of the detection area. Second, in the online stage, stage, when when when PD happens,RSSI the RSSI values of PD are measured by the wireless UHF sensorsarray array andused used to PD PD happens, happens, the the RSSI values values of of PD PD are are measured measured by by the the wireless wireless UHF UHF sensors sensors array and and used to to estimate the location of PD by pattern recognition in the prebuilt RSSI fingerprint map. The purpose estimate the location of PD by pattern recognition in the prebuilt RSSI fingerprint map. The purpose estimate the location of PD by pattern recognition in the prebuilt RSSI fingerprint map. The purpose of our proposed proposed method is is to quickly quickly find the faulty equipment in substations. Due to the the intrinsic of of our our proposed method method is to to quickly find find the the faulty faulty equipment equipment in in substations. substations. Due Due to to the intrinsic intrinsic nature of the measuring process, our method cannot be applied to localize PD sources inside power nature nature of of the the measuring measuring process, process, our our method method cannot cannot be be applied applied to to localize localize PD PD sources sources inside inside power power equipment like transforms or gas-insulated substations. equipment equipment like like transforms transforms or or gas-insulated gas-insulated substations. substations.

Figure 2. signal strength indicator (RSSI)(RSSI) fingerprint PD localization system in substation. Figure 2. The received signal strength indicator fingerprint PD system Figure 2.The Thereceived received signal strength indicator (RSSI) fingerprint PD localization localization system in in substation. substation.

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Typical pattern recognition algorithms such as K Nearest Neighbor (KNN) [20] and neural networks [21] are easy to implement, but the performance in practical application is not satisfactory. In this paper, we use the compressed sensing (CS) algorithm to obtain more accurate PD localization. CS theory indicates that the sparse signal can be reconstructed by solving the l1 -minimization problem [22,23]. For the proposed localization method, a localization result is a specific point in the detecting area. Therefore, the result vectors are sparse in nature. According to the CS theory, the accuracy of the CS localization algorithm decreases with the increase of test points [24]. Therefore, the online stage also consists of two steps. First, the preliminary localization is implemented by cluster recognition, which produces a small RSSI fingerprint map. Second, more accurate localization is obtained by CS algorithm with the use of a small RSSI fingerprint. From practical application point of view, an affinity propagation clustering algorithm is designed and performed in the offline stage to eliminate the influence of interference signals and abnormal RSSI values for the fingerprint map. Furthermore, the built RSSI fingerprint map will also be divided into several clusters by this clustering algorithm for the preliminary localization in the online stage, as described above. A field test is performed in a substation to verify the effectiveness of our proposed PD localization method. The results indicate that the proposed localization method shows satisfactory performance. The mean localization error is 1.25 m, and 89.6% of localization errors are less than 3 m. The remainder of this paper is organized as following: Section 2 introduces the overview of the proposed PD localization method. The data acquisition and processing method and affinity propagation clustering algorithm in the offline stage are proposed in Section 3. Section 4 introduces the preliminary localization by cluster recognition and the accurate localization based on CS algorithm in the online stage. Section 5 introduces the hardware design. A field test and corresponding results are reported and analyzed in Section 6. Section 7 highlights the key contributions of this paper. 2. Overview of the Proposed PD Localization Method The proposed RSSI fingerprint-based PD localization method is divided into two stages. Figure 3 shows the flow chart of the proposed PD localization method using four sensors, AP1 , AP2 , AP3 , and AP4 , as an example. First, in the offline stage, totally N test points are arranged in the detection area, which are denoted by RPj (j = 1, 2, . . . , N). Then, the discharge source is used to produce PD at each test point, and the corresponding RSSI values are measured by L wireless UHF sensors. These wireless UHF sensors are denoted by APi (I = 1, 2, . . . , L). Assuming the RSSI value of the test point RPj measured by the wireless UHF sensor APi is denoted by φi,j , then the RSSI fingerprint of RPj is, r j = [φ1,j , φ2,j , . . . , φL,j ] T

(1)

The RSSI fingerprints of all test points establish the RSSI fingerprint map Ψ of the detection area, which is denoted by, φ1,1 φ1,2 . . . φ1,N φ2,1 φ2,2 . . . φ2,N Ψ= (2) .. .. .. .. . . . . φL,1

φL,2

...

φL,N

There are two clustering processes in the offline stage. The Clustering I process is implemented during the establishment of the RSSI fingerprint map to reduce the influence of PD interference signals and abnormal RSSI values. The Clustering II process is implemented when the RSSI fingerprint map has been established. After the Clustering II process, the RSSI fingerprint map is divided into several clusters, which is the preparation for cluster recognition in the online stage.

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Figure 3. The flow chart of proposed PD localization localization algorithm. algorithm.

Second, in the online stage, when PD happens, the RSSI fingerprint of PD is measured by Second, in the online stage, when PD happens, the RSSI fingerprint of PD is measured by wireless wireless UHF sensor array and denoted as rPD, UHF sensor array and denoted as rPD , rPD [φ1 , φ2 ,..., φL ]T (3) T r PD = [φ0 1 , φ0 2 , . . . , φ0 L ] (3) where φ′i is the RSSI value of PD measured by APi. Then, recognition is measured performedby to AP find where φ0 i ispattern the RSSI value of PD i . the column in Ψ that is most approximate to rPD. The coordinate of the matched is column is thetolocalization result.inFor better accuracy, Then, pattern recognition performed find the column Ψ that is localization most approximate to rthe PD . pattern recognition consists of two steps. In step, theresult. preliminary localization is implemented The coordinate of the matched column is the first localization For better localization accuracy, by cluster to consists get the small RSSI fingerprint the preliminary second step, localization more accurate the patternrecognition recognition of two steps. In the map first Ψ′. step,In the is 0 localization is got by CS algorithm. implemented by cluster recognition to get the small RSSI fingerprint map Ψ . In the second step, more accurate localization is got by CS algorithm. 3. Offline Stage 3. Offline Stage 3.1. Data Acquisition and Processing 3.1. Data Acquisition and Processing In the offline stage, the RSSI fingerprint map of the detection area is established by site survey. In the stage, athe RSSI fingerprint detection is established sitethe survey. During theoffline site survey, discharge source ismap usedoftothe produce PDarea at each test point,by and RSSI During the site survey, a discharge source is used to produce PD at each test point, and the RSSI fingerprint data is acquired by wireless UHF sensors. fingerprint datastrength is acquired by wireless UHF sensors. Since the of the discharge source is uncertain, the use of the RSSI fingerprint map Since the of the discharge source is uncertain, the use of the RSSI fingerprint map constituted by strength the original RSSI values will produce conspicuous errors in pattern recognition. To constituted by the original RSSI values will produce conspicuous errors in pattern recognition. To solve solve this problem, the original RSSI values should be normalized. this problem, thethe original RSSI values shouldof beRP normalized. Assuming original RSSI fingerprint j is,

ˆ1, j , φ ˆ 2, j ,..., φ ˆ L, j ]T rˆj [φ where φˆ i , j (i = 1, 2, …, L) are the original RSSI values of RPj. Then the normalization process is,

(4)

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Assuming the original RSSI fingerprint of RPj is, Sensors 2017, 17, 1909

T rˆ j = [φˆ 1,j , φˆ 2,j , . . . , φˆ L,j ]

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(4)

ˆofk , j RPj . Then the normalization process is, where φˆ i,j (i = 1, 2, . . . , L) are the original RSSI valuesφ φk , j

φk,j

1 L φˆ φˆ k,j t , j = LLt 1 1 L

(5) (5)

∑ φˆ t,j

where k = 1, 2, …, L. t =1 The normalization process highlights the spatial position relationship between the discharge where = 1,sensors 2, . . . , L. source kand while decreases the influence of PD strength to improve the accuracy of pattern The normalization process highlights the spatial position relationship between the discharge recognition. source and sensors while decreases the influence of PD strength to improve the accuracy of pattern recognition. 3.2. Affinity Propagation Clustering In the offline stage,Clustering two clustering procedures are performed as following. 3.2. Affinity Propagation the offlineI stage, two clustering procedures are performed as following. 3.2.1.In Clustering

object of 3.2.1.The Clustering I Clustering I is to reduce the influence of PD interference in the offline stage as shown in Figure 4. During the measurement of RSSI fingerprint map, there are three PD signals The object of Clustering I is to reduce the influence of PD interference in the offline stage as shown detected by four wireless UHF sensors: AP1, AP2, AP3, and AP4 within about 1500 ns. It is hard to in Figure 4. During the measurement of RSSI fingerprint map, there are three PD signals detected by choose which PD is produced by our discharge source. Since the RSSI fingerprints measured in one four wireless UHF sensors: AP1 , AP2 , AP3 , and AP4 within about 1500 ns. It is hard to choose which test point are similar, we can eliminate the PD interference by following steps: first, producing PD at PD is produced by our discharge source. Since the RSSI fingerprints measured in one test point are one test point for enough times and recording all the RSSI fingerprints. Then, clustering these similar, we can eliminate the PD interference by following steps: first, producing PD at one test point fingerprints by the affinity propagation clustering algorithm. The mean value of the largest cluster is for enough times and recording all the RSSI fingerprints. Then, clustering these fingerprints by the chosen as the RSSI fingerprint of this test point. Clustering I can also eliminate the abnormal RSSI affinity propagation clustering algorithm. The mean value of the largest cluster is chosen as the RSSI values. As shown in Figure 5, these two PD signals are produced by one discharge source at one test fingerprint of this test point. Clustering I can also eliminate the abnormal RSSI values. As shown in point. The waveform received by AP1, AP2, and AP3 are similar, but the waveform received by AP4 Figure 5, these two PD signals are produced by one discharge source at one test point. The waveform contain conspicuous abnormal values. During the Clustering I process, these abnormal values will received by AP1 , AP2 , and AP3 are similar, but the waveform received by AP4 contain conspicuous also be eliminated. abnormal values. During the Clustering I process, these abnormal values will also be eliminated.

Figure 4. The digital envelope detection waveforms, which illustrate the PD interference phenomenon Figure 4. The digital envelope detection waveforms, which illustrate the PD interference phenomenon in the offline stage. in the offline stage.

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Figure The digital digital envelope envelope detection detection waveforms, waveforms, which which show show the the abnormal Figure 5. 5. The abnormal RSSI RSSI values values phenomenon in the offline stage. phenomenon in the offline stage.

3.2.2. 3.2.2. Clustering Clustering II II The The object object of of Clustering Clustering II II is is to to divide divide the the RSSI RSSI fingerprint fingerprint map map into into several several clusters clusters for for the the preparation of cluster recognition in the online stage. The effect of Clustering II can be seen preparation of cluster recognition in the online stage. The effect of Clustering II can be seen in in Section 6.2. section 6.2. The is aa high-efficiency clustering algorithm algorithm [25]. [25]. The affinity affinity propagation propagation clustering clustering algorithm algorithm is high-efficiency clustering Therefore, it is chosen as the clustering algorithm for Clustering I and Clustering II. Affinity propagation Therefore, it is chosen as the clustering algorithm for Clustering I and Clustering II. Affinity clustering useclustering the similarity matrix S to cluster elements, denoted as, denoted as, propagation use the similarity matrixthe S to cluster the elements,

s(1,22) s(1,s(1,1) 1) s(1, ) s(2,1) s(2, 2) s ( 2, 1 ) s ( 2, 2 ) S . S= . . .. . s( D ( D2, )2) s(D, 1),1) s(sD,

. . . ss((1, 1,D D)) . . . s((2, 2, D D)) . ... .. . . . ss(( D D,, D D))

(6)

where D D is is the the number number of of elements, elements, and and s(i, s(i, j) j) is is the the similarity similarity between between the where the element element ii and and element element j,j, which is is denoted denoted as, as, which ( r −2r k2 ∀i, j ∈ (1, 2, . . . , D ), i 6= j ss((i,i, jj)) =−k (7) ri i rj j i, j (1, 2,..., D), i j ∀i, j ∈ (1, 2, . . . , D ), i = j (7) s(i, j) = w

s(i, j) w

i, j (1,2,..., D), i j

where w is the is the control parameter to adjust the number of clusters. The core of affinity propagation algorithm is the iteration process shown where w is theoperation is the control parameter to adjust clustering the number of clusters. in (8)The andcore (9), operation of affinity propagation clustering algorithm is theoiteration process shown in n (8) and (9), res(t+1) (i, j) = s(i, j) − max ava(t) (i, j0 ) + s(i, j0 ) (8) j0 6= j

res (i, j ) s ( i , j ) max ava ( t ) ( i , j ) s( i , j ) (8) 0, res(jt) j( j, j)+ ( t + 1 ) ( t ) 0 ava (i, j) = min (0, res (i , j)) , i 6= j 0 ∑ max (9) (t ) i 6= i,j 0, res ( j, j) ( t + 1 ) ( t ) 0 ( t +1) (i, j) = (i , j)) ,i = j ava ava (i, 0j∑ ) max min (0, res max(0, res(t ) (i, j)) , i j i 6=i,j i i , j (9) where res(i, j) is the responsibility sent from element (tvalue +1) ( t ) i to element j, which reflects how suitably i, j) max(0, res (i, j)) ,i j ava (for the element j serves as the exemplar element i, ava(i, j) is the availability value sent from element i i , j j to element i, which reflects how suitably the element i chooses element j as its exemplar, t is the where res(i, j) is the responsibility from number of iterations, i0 ∈ (1, 2, . . . value , D), i0 sent 6= i or j, j0 element ∈ (1, 2, .i. to . , element D), j0 6= j.j, which reflects how suitably the element j serves as the exemplar for element i, ava(i, j) is the availability value sent from element j to element i, which reflects how suitably the element i chooses element j as its exemplar, t is the number of iterations, i' ∈ (1, 2, …, D), i' ≠ i or j, j' ∈ (1, 2, …, D), j' ≠ j. ( t 1)

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For all elements k (k = 1, 2. . . . , D), the condition of becoming an exemplar is, res(t+1) (k, k) + ava(t+1) (k, k) > 0

(10)

Let E denote the set of exemplars, then for elements, its exemplar is the closest one in E under similarity measurement. When t reaches the maximum number of iterations tmax or the clustering results remain unchanged in consecutive tcon iterations, the iteration is terminated. To solve the convergence problem of iteration, we use the damping factor λ during the updating of res and ava, as shown in (11) and (12), res(t+1) (i, j) = (1 − λ)res(t+1) (i, j) + λres(t) (i, j)

(11)

ava(t+1) (i, j) = (1 − λ) ava(t+1) (i, j) + λava(t) (i, j)

(12)

where the range of λ goes from 0 to 1. The increase of λ will improve the global searching ability of the algorithm and produces better convergence performance but also slow down the convergence rate. Since the clustering processes described here are only implemented in the offline stage, the λ tends to be a big value. 4. Online Stage According to the CS theory, if the number of sensors L is in the order of log (N), the localization result vector can be recovered from the RSSI fingerprint of PD at high probability [26,27]. However, L is hard to reach the order of log (N) in most cases. Therefore, the localization is divided into two steps. First, the preliminary localization is implemented by cluster recognition to determine which cluster the RSSI fingerprint of PD belongs to in the RSSI fingerprint map Ψ. The recognized cluster is regarded as the small RSSI fingerprint map Ψ’. Second, the accurate localization is implemented by CS algorithm with the use of Ψ0 . 4.1. Preliminary Localization by Cluster Recognition To reduce the influence of the boundary problem, we use all the elements in RSSI fingerprint map to implement the cluster recognition rather than only using the exemplars. The cluster recognition finds, minkr PD − r g k2 s.t g ∈ (1, 2, . . . , C ) (13) where C is the number of clusters, and r g is the average value of the RSSI fingerprints in the gth cluster. The RSSI fingerprints in the optimal cluster constitute a small RSSI fingerprint map Ψ0 . The size 0 of Ψ can be adjusted by the parameters in the affinity propagation clustering algorithm. 4.2. Accurate Localization by CS Algorithm Assuming the number of the elements in Ψ0 is N 0 , therefore Ψ0 is a N 0 × L matrix, which is a subset of Ψ. If a PD happens at the test point RPj , the location of PD can be denoted as, F = [0, . . . , 0, 1, 0, . . . , 0] T

(14)

F is a N 0 × 1 vector with all elements are marked as zero, except the element that denotes the position of RPj , which is marked as one. Then we have, r j = Ψ0 F

(15)

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Multiplying both side of (15) by Φ.

Let Y = Φrj , then we have,

Φr j = ΦΨ0 F

(16)

Y = ΦΨ0 F

(17)

As mentioned above, F is a 1-sparse vector. According to the CS theory, (17) is a standard form of CS algorithm [22]. Φ is a m × L measuring matrix where m is the number of measurements and m < N 0 . Let Θ = ΦΨ0 , which is a m × N 0 sensing matrix. Literature [28] indicates that F cannot be well recovered from the measurement Y unless Θ satisfies the Restricted Isometry Property (RIP) condition, which is denoted as, 1−ε ≤

kΘF k2

≤ 1+ε

k F k2

(18)

where ε ∈ (0,1). However, it is hard to use (18) to judge whether the RIP condition is satisfied. Literature [29–31] indicate that if the correlation between Φ and Ψ0 is weak, the RIP condition can be satisfied at high probability. Since the correlation between the Gaussian random matrix and other matrix is weak [32], the measuring matrix Φ is set as the Gaussian random matrix. To satisfying the RIP condition better, we use SVD (Singular Value Decomposition) operation to transform sensing matrix Θ. denoted as, Θ = U∆V T

(19)

where U is a m × m orthogonal matrix, V is a N 0 × N 0 orthogonal matrix. ∆ is denoted by (20) and (21), ∆=[ P (

P = diag(δ1 , δ2 , . . . , δm ) δ1 ≥ δ2 ≥ . . . ≥ δm

Let

" ∆∗ = (

0 ]

P∗ 0

(20) (21)

#

P∗ = diag( δ1 , δ12 , . . . , δ1m ) 1 δ1 ≥ δ2 ≥ . . . ≥ δm

(22)

(23)

Combining with (17), we have, ∆∗ U T Y = ∆∗ U T ΘF h i P∗ U T Y = Im 0 V T F

(24)

Y 0 = P∗ U T Y h i Q = Im 0 V T

(26) (27)

Y 0 = QF

(28)

(25)

Let

We have,

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where Y0 is a transformed RSSI fingerprint of PD and Q is the transformed sensing matrix. From (27), we know that Q is a nearly orthogonal matrix. According to the literature [24], Q satisfies the RIP condition. Sensors 2017, 18 CS Since Q is17,a1909 m × N 0 matrix and m < N 0 , (28) cannot be solved directly. According 9toof the theory, by solving l1 -minimization model F can be well recovered from the measurement Y0 [32,33]. Since Q is a m × N′ matrix and m < N′, (28) cannot be solved directly. According to the CS theory, As shown in (29), by solving l1-minimization model 0F can be well recovered from the measurement Y′ [32,33]. As shown F = argmink F k1 s.t. Y 0 = QF (29) in (29),

where F0 is the recovered location vector. F arg min F 1 s.t . Y QF (29) We use the greedy algorithm to solve (29) due to its fast computation speed and small where F′ is the recovered location vector. algorithm complexity [34]. Typical greedy algorithm includes the orthogonal matching pursuit We use the greedy algorithm to solve (29) due to its fast computation speed and small algorithm (OMP) algorithm [35], the compressed sampling pursuit matching (CoSaMP) algorithm [36], subspace complexity [34]. Typical greedy algorithm includes the orthogonal matching pursuit (OMP) pursuit (SP) algorithm [37], and the generalized orthogonal matching pursuit (GOMP) algorithm [38]. algorithm [35], the compressed sampling pursuit matching (CoSaMP) algorithm [36], subspace We will use (SP) these four algorithms forgeneralized comparison in experiment. pursuit algorithm [37], and the orthogonal matching pursuit (GOMP) algorithm [38]. Since PD happen at afor test point exactly, F0 is a vector with several nonzero elements We will usemay thesenot four algorithms comparison in experiment. rather than 1-sparse vector in theory. paper, the F′ location of PD is several decidednonzero as the coordinate of Since PD may not happen at a In testthis point exactly, is a vector with elements rather than 1-sparse biggest element in F0 . vector in theory. In this paper, the location of PD is decided as the coordinate of biggest element in F′.

5. Hardware Design 5. Hardware Design

5.1. Wireless UHF Sensors 5.1. Wireless UHF Sensors

The wireless UHF sensor used in the proposed PD localization method is shown in Figure 6. The wireless UHF sensor used in the proposed PD localization method is shown in Figure 6. The The antenna, bandpass filter, amplifier, detector, MCU, Wi-Fi module, and battery are concentrated antenna, bandpass filter, amplifier, detector, MCU, Wi-Fi module, and battery are concentrated in a in a metal shell. As shown in Figure 6b, the PD signal processing module (including filter, low noise metal shell. As shown in Figure 6b, the PD signal processing module (including filter, low noise amplifier, detector) is masked by copper foil for better anti-interference performance. amplifier, detector) is masked by copper foil for better anti-interference performance.

(a)

(b)

Figure 6. The picture of wireless Ultra-High Frequency (UHF) sensor. (a) Outside; (b) Inside.

Figure 6. The picture of wireless Ultra-High Frequency (UHF) sensor. (a) Outside; (b) Inside.

There are many kinds of antenna used in UHF sensors. Among them, the dipole antenna has the

There are of many of antenna UHF sensors. Among them, the dipole antenna has advantage high kinds sensitivity and smallused size. in Therefore, we designed an PCB elliptical dipole antenna with a double low cost. and The panel the elliptical dipole is shown in Figure 7. The the advantage of feed highand sensitivity smallofsize. Therefore, weantenna designed an PCB elliptical dipole measured sensitivity curve is shown in Figure 8. The average effective height of our designed antenna antenna with a double feed and low cost. The panel of the elliptical dipole antenna is shown in is approximately 11.77sensitivity mm. The effective height denotes the ability of the antenna to transform the Figure 7. The measured curve is shown in Figure 8. The average effective height of our electromagnetic wave to voltage. Higher effective height will produce higher voltage. designed antenna is approximately 11.77 mm. The effective height denotes the ability of the antenna to transform the electromagnetic wave to voltage. Higher effective height will produce higher voltage.

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Figure 7. Elliptical dipole dipole printed antenna panel. Figure 7. Elliptical Elliptical printed antenna panel. Figure 7. dipole printed antenna panel.

Figure 8. Sensitivity curve of the elliptical dipole printed antenna.

The process of the data acquisition by wireless UHF sensors is shown in Figure 9. First, the UHF electromagneticFigure wave is received by the antenna. Second, the detection waveform is obtained after Figure 8. 8. Sensitivity Sensitivity curve curve of of the the elliptical elliptical dipole dipole printed printed antenna. antenna. signal conditioning by the bandpass filter, amplifier, and detector. Finally, via A/D sampling, the digital data are generated and transmitted to computer through a Wi-Fi module controlled by MCU. The process of the the data acquisition by wireless wireless UHFissensors sensors shown inFigure Figure 9.than First, the UHF UHF The of acquisition by UHF isiswhich shown in First, the It process is worthwhile todata denoted that the sampling frequency 2.7 MHz, is much lower9. that electromagnetic wave is by the the the detection waveform is obtained after electromagnetic is received received by theantenna. antenna. detection waveform obtained in TDOA because the goal of our method is to get Second, theSecond, amplitude of waveforms rather than getisthe time difference information. peak value of the detection waveform isFinally, theFinally, original value. A signalsignal conditioning by the filter, amplifier, andand detector. via RSSI A/DA/D sampling, the after conditioning bybandpass the The bandpass filter, amplifier, detector. via sampling, peak detector (AD8318) together with the peak holding circuit are designed to obtain the peak value digital data are generated and transmitted to computer through a Wi-Fi module controlled by MCU. the digital data are generated and transmitted to computer through a Wi-Fi module controlled by of PD signals. Figure 10 shows the peak detection waveform of a PD signal generated by PD emitter. It is worthwhile to denoted that the sampling frequency is 2.7isMHz, which is much lower thanthan that MCU. It is worthwhile to denoted that the sampling frequency 2.7 MHz, which is much lower The waveform lasts about 15 us. Since the A/D sampling frequency is 2.7 MHz, there are about 40 in TDOA because the goal of our method is to get the amplitude of waveforms rather than get the that in TDOA because the goal of our method is to get the amplitude of waveforms rather than get sampling points, which can ensure that we obtain the peak value.

time difference information. TheThe peak value of the detection waveform is the original RSSI value. A the time difference information. peak value of the detection waveform is the original RSSI value. peak detector (AD8318) together with the the peak holding circuit are designed to obtain the peak A peak detector (AD8318) together with peak holding circuit are designed to obtain the value peak of PD of signals. FigureFigure 10 shows the peak waveform of a PDof signal by PD emitter. value PD signals. 10 shows thedetection peak detection waveform a PDgenerated signal generated by PD The waveform lasts about 15about us. Since theSince A/D the sampling frequencyfrequency is 2.7 MHz, there are there aboutare 40 emitter. The waveform lasts 15 us. A/D sampling is 2.7 MHz, sampling points, which can ensure we obtain peakthe value. about 40 sampling points, which canthat ensure that wethe obtain peak value.

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The diagram diagram of wireless UHF sensor. Figure 9. The Figure 9. The diagram of wireless UHF sensor.

Figure Figure 10. 10. The The detection detection waveform waveform of of aa PD PD signal signal generated generated by by PD PD emitter. emitter. Figure 10. The detection waveform of a PD signal generated by PD emitter.

5.2. PD Source 5.2. 5.2. PD PD Source Source In the offline stage, stage, the the discharge discharge source source we we used used is a a standard standard PD PD simulator simulator named “EM TEST In the named “EM In that the offline offline stage, the discharge pulse sourceaccording we used is is aEN/IEC standard PD simulator named “EM TEST TEST DITO” can produce air discharge to 61000-4-2, as shown in Figure 11. DITO” 61000-4-2, as as shown DITO” that that can can produce produce air air discharge discharge pulse pulse according accordingto toEN/IEC EN/IEC 61000-4-2, shown in in Figure Figure 11. 11.

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Figure 11. The PD simulator “EM TEST DITO”.

6. Experimental Verification Verification 6.1. Experimental Scheme To of proposed PD localization method, we chose test sitea intest a substation To verify verifythe theperformance performance of proposed PD localization method, wea chose site in a to perform a field experiment in a 24 × 24 m’ square area. Our PD localization system consists of a substation to perform a field experiment in a 24 × 24 m’ square area. Our PD localization system computer, andafour wireless UHF sensors, AP1sensors, , AP2 , AP shown consists of a router, computer, router, and four wireless UHF AP , AP2AP , AP , and AP4, in as Figure shown12. in 3 , 1and 4 ,3as From 8 we can see thatcan these UHF sensors have a signal bandwidth of 300 MHz– FigureFigure 12. From Figure 8 we see wireless that these wireless UHF sensors have a signal bandwidth of 1500 MHz and MHz can transmit envelope detectiondetection data of PD a computer through Wi-Fi. 300 MHz–1500 and can the transmit the envelope datasignal of PDto signal to a computer through To measure the RSSIthe fingerprint map of map the test site,test a total 625 test points arranged in the test Wi-Fi. To measure RSSI fingerprint of the site,of a total of 625 testwere points were arranged in site and site distributed evenly with the adjacent 1 m. The of sensors of and test points the test and distributed evenly with the distance adjacentof distance ofplacement 1 m. The placement sensors and is shown test pointsinisFigure shown13. in Figure 13. The test two stages. First, in the stage, the RSSI fingerprint map Ψ was measured. testconsists consistsofof two stages. First, inoffline the offline stage, the RSSI fingerprint map Ψ was A PD source was used to produce PD for 50 times at each test point. The RSSI fingerprint data was measured. A PD source was used to produce PD for 50 times at each test point. The RSSI fingerprint measured by wireless sensor array andarray transmitted to a computer. By Clustering I processI data was measured byUHF wireless UHF sensor and transmitted to a computer. By Clustering the RSSIthe fingerprint of each test pointtest waspoint obtained and theseand fingerprints constituted Ψ. Then the process RSSI fingerprint of each was obtained these fingerprints constituted Ψ. Clustering II process was implemented to divide Ψ into several clusters, which is the preparation for Then the Clustering II process was implemented to divide Ψ into several clusters, which is the cluster recognition in therecognition online stage.inThe settings the affinitysettings propagation clustering preparation for cluster theparameters online stage. The of parameters of the affinity algorithm areclustering shown in algorithm Table 1. are shown in Table 1. propagation Second, in used thethe standard discharge source to produce PD atPD oneattest point, inthe theonline onlinestage, stage,wewe used standard discharge source to produce one test and theand RSSIthe fingerprint of PD wasofobtained. the preliminary implemented point, RSSI fingerprint PD wasThen, obtained. Then, the localization preliminarywas localization was by cluster recognition, the smalland RSSIthe fingerprint Ψ0 was generated. the accurate implemented by clusterand recognition, small RSSImap fingerprint map Ψ′ wasFinally, generated. Finally, localization implemented by CS algorithm. This process was repeated all the test points to the accurate was localization was implemented by CS algorithm. This process wasatrepeated at all the test verify effectiveness of the proposed PD localization method. method. points the to verify the effectiveness of the proposed PD localization

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(a)

(c)

(b)

(a)

(b)

(c)

(d)

(d)

Figure 12. The picture of test site. (a) Picture 1; (b) Picture 2; (c) Picture 3; (d) Picture 4.

Figure12. 12.The Thepicture pictureofoftest testsite. site.(a) (a)Picture Picture1;1;(b) (b)Picture Picture2;2;(c) (c)Picture Picture3;3;(d) (d)Picture Picture4.4. Figure Table 1. Parameters settings for affinity propagation clustering algorithm.

Table1.1.Parameters Parameterssettings settingsfor foraffinity affinitypropagation propagationclustering clusteringalgorithm. algorithm. Table Parameters

w

Values Parameters Parameters

Values

Values

λ

tmax

tcon

−1.56 w w

λ tmax λ 0.9

1000 tmax con

100 tcon

−1.56 −1.56

0.9 0.9 1000

1000 100

100

Figure 13. The plan of test site.

Figure Figure13. 13.The Theplan planofoftest testsite. site.

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6.2. Performance Evaluation of Offline Stage 6.2. Performance Evaluation Offline Stage 6.2. Performance Evaluation of of Offline Stage The RSSI fingerprint map Ψ of ofof the test test site measured in the the offline stage is shown shown inin Figure 14. The RSSI fingerprint map test site measured the offline stage shownin Figure14. 14. The RSSI fingerprint map ΨΨ thethe site measured inin offline stage is is Figure Together with the plan ofofthe test site ininFigure 13, we find that the RSSI fingerprint map measured Together with the plan the test site Figure 13, we find that the RSSI fingerprint map measured Together with the plan of the test site in Figure 13, we find that the RSSI fingerprint map measured by bybyeach isisreasonable. The ofofthe values obeys eachsensor sensor reasonable. Thedistribution distribution theRSSI RSSI values obeysthe thesignal signaltransmission transmission each sensor is reasonable. The distribution of the RSSI values obeys the signal transmission properties properties and can reflect the spatial information ofofthe test site. The irregular points ininΨΨ are properties and can reflect the spatial information the test site. The irregular points arecaused and can reflect the spatial information of the test site. The irregular points in Ψ are caused bycaused the bybythe influence ofofthe complex electromagnetic and spatial environment ininthe substation. the influence the complex electromagnetic and spatial environment the substation. influence of the complex electromagnetic and spatial environment in the substation.

Figure 14. The RSSI fingerprint map measured by four sensors in the offline stage. Figure 14.14. The RSSI fingerprint map measured byby four sensors inin the offline stage. Figure The RSSI fingerprint map measured four sensors the offline stage.

ByBy the Clustering II II process, ΨΨ into several clusters asas shown inin Figure 15. The RSSI By the Clustering II process, Ψ isisdivided into several clusters as shown in Figure 15. The RSSI the Clustering process, isdivided divided into several clusters shown Figure 15. The RSSI fingerprints inin ΨΨ are divided into 2121 clusters. Therefore, the average number ofof fingerprints included fingerprints in Ψ are divided into 21 clusters. Therefore, the average number of fingerprints included fingerprints are divided into clusters. Therefore, the average number fingerprints included inin Ψ′0Ψ′ isis clustering isissatisfactory because most ofofclusters are in Ψ is about (625/21). Theperformance of clustering issatisfactory satisfactory because most ofclusters clusters about3030(625/21). (625/21).The performanceofof clustering because most are compact. This compactness indicates that if ifsome test RSSI are compact. This compactness indicates that if some some testpoints are close to each RSSI compact. This compactness indicates that test pointsare areclose closeto toeach eachother, other,their their RSSI fingerprints are also similar. This property indicates that the distribution ofof RSSI fingerprints can fingerprints are also similar. property indicates that the distribution of RSSI fingerprints can fingerprints are also similar.This This property indicates that the distribution RSSI fingerprints can reflect the spatial information ofof test site precisely. reflect the spatial information of test site precisely. reflect the spatial information test site precisely.

Figure 15.15. The clustering ofof Ψ.Ψ. Figure The clustering Figure 15. The clustering of Ψ.

InInFigure Figure15, 15,we wecan canalso alsofind findsome someelements elementsininΨΨthat thatare arefarfarfrom fromitsitsexemplar. exemplar.Most Mostofofthis this In Figure 15, we can also find some elements in Ψ that are far from its exemplar. Most of this phenomenon appears at the boundary of clusters. Therefore, this phenomenon is mainly caused by phenomenon appears at the boundary of clusters. Therefore, this phenomenon is mainly caused by phenomenon appears at the boundary of clusters. Therefore, this phenomenon is mainly caused measurement measurementerrors errorsand andthe thecomplex complexelectromagnetic electromagneticand andspatial spatialenvironment environmentofofthe thesubstation. substation. by measurement errors and the complex electromagnetic and spatial environment of the substation. Obviously, Obviously,if ifPD PDhappens happensatatthese thesetest testpoints, points,the thelocalization localizationerror errorwould wouldbebelarge. large. Obviously, if PD happens at these test points, the localization error would be large.

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6.3. Performance Evaluation of the Online Stage 6.3. Performance Evaluation of the Online Stage First, for the preliminary localization, the performance of cluster recognition is satisfactory. First, for the preliminary localization, the performance of cluster About 81.9% of cluster recognition can recognize the correct cluster.recognition is satisfactory. About 81.9%Second, of cluster recognition can recognize the correct cluster. for the CS algorithm, in order to choose the best solution for l1-minimization model, Second, for the and CS algorithm, in implemented order to choose best solution l1 -minimization OMP, CoSaMP, SP, GOMP were for the comparison. The for results are shown inmodel, Figure OMP, CoSaMP, SP, and GOMP were implemented for comparison. The results are shown in Figure 16. 16. We can see that when m > 3, the localization errors are stable. The performance of OMP, SP, and We can see that when m > 3, the localization errors are stable. The performance of OMP, SP, and GOMP GOMP are almost the same. Since the algorithm complexity of OMP is minimum, it is chosen as the are almost same. Since the algorithm complexity of OMP is minimum, it is chosen as the solution solution forthe l1-minimization model finally. for l1 -minimization model finally. Third, we compared three different pattern recognition algorithms: BP neural network, KNN, Third, we compared three different pattern results recognition algorithms: BP2,neural KNN, and the proposed CS algorithm. The localization are shown in Table and thenetwork, corresponding and the proposed CS algorithm. The(CDF) localization results shown17. in Table 2, and the corresponding cumulative distribution function is shown inare Figure The results indicate that the cumulative distribution function (CDF) is shown in Figure 17. The results indicate that the performance performance of BP neural network and KNN is almost the same, while our proposed CS algorithm of BP neural network and KNNThe is almost the same, our proposed algorithm exhibits the best exhibits the best performance. tendency of the while CDF curve indicatesCS that if the cluster recognition performance. The tendency of the CDF curve indicates that if the cluster recognition can recognize can recognize the correct cluster and generate a suitable Ψ′, the localization by CS algorithm would the correct cluster and generate a suitable Ψ0 , the localization CSalgorithms. algorithm would be accurate. We be accurate. We also investigated the execution times of these by three The average execution also investigated the execution timesour of these three algorithms. The execution ones times of one PD localization is that: CS algorithm needs 11.38 s; average BP neural networktimes needsof3.39 PD localization is that: our CS algorithm needs 11.38 s; BP neural network needs 3.39 s and KNN and KNN needs 0.68 s. needsFinally, 0.68 s. we investigated the performance of the Clustering I process. Table 3 gives the Finally, we investigated the Clustering performanceI of the Clustering I process. 3 gives the localization localization errors under the process and without theTable Clustering I process. The errors under the Clustering I process and without the Clustering I process. The corresponding CDF corresponding CDF is shown in Figure 18. The Clustering I process can reduce 39.6% of the mean is shown in errors, Figure which 18. The Clustering process can of reduce 39.6% of the mean localization errors, localization illustrates thatIthe accuracy RSSI fingerprint map is one of the key factors which illustrates that the accuracy of RSSI fingerprint map is one of the key factors that determine the that determine the localization performance. The clustering I process will add extra execution times localization performance. The clustering I process will add extra execution times which rely on the which rely on the actual situation of the site survey in the offline stage. actual situation of the site survey in the offline stage.

Figure 16. Relationship between localization error and the number of measurements m for OMP, Figure 16. Relationship between localization error and the number of measurements m for OMP, CoSaMP, SP, and GOMP. CoSaMP, SP, and GOMP. Table 2. Localization results for different pattern recognition algorithm. Table 2. Localization results for different pattern recognition algorithm. Parameters Parameters Average errorerror (m) (m) Average The proportion of the within 1m 1m The proportion of errors the errors within The proportion of the errors within 3 m The proportion of errors the errors within The proportion of the within 5m 3m The maximum error (m) within 5 m The proportion of the errors

The maximum error (m)

CS CS

BPBP

1.25 1.25 2.51 2.51 68.3%68.3% 24.2% 24.2% 89.6% 70.2% 70.2% 95.2%89.6% 85.0% 8.4995.2% 10.57 85.0%

8.49

10.57

KNN KNN 2.63 2.63 27.0% 27.0% 68.1% 68.1% 80.2% 11.89 80.2%

11.89

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Figure 17. CDF of the localization errors under different pattern recognition algorithms. Figure 17. CDF of the localization errors under different pattern recognition algorithms. 17. CDF of the localization errors under different pattern recognition Table Figure 3. Localization results under a different Clustering I process and withoutalgorithms. the Clustering I process. Table 3. Localization results under a different Clustering I process and without the Clustering I process. Table 3. Localization results under a different Clustering I process and without the Clustering I Parameters Under Clustering I Process Without Clustering I Process process. Parameters Under Clustering Without Clustering I Process Average error (m) 1.25 I Process 2.07 Parameters The proportion of error the errors 68.3% 37.3% Average (m) within 1 m Under Clustering 1.25 I Process Without Clustering 2.07 I Process Average error (m) 1.25 2.07 The ofofthe errors within 68.3% 37.3% Theproportion proportion the errors within1 3mm 89.6% 77.9% The proportion the errors within 68.3% 37.3% The 89.6% 77.9% Theproportion proportionofof ofthe theerrors errorswithin within315mm m 95.2% 88.8% The of the errors within 5 m 95.2% 88.8% Theproportion proportion of the errors within 3 m 89.6% 77.9% The maximum error (m) 8.49 10.25 The maximum 8.49 10.25 The proportion of the error errors(m) within 5 m 95.2% 88.8% The maximum error (m) 8.49 10.25

Figure 18. CDF of localization the localization errors under the Clustering I process and without the Clustering Figure 18. CDF of the errors under the Clustering I process and without the Clustering I process. I process. 18. CDF of the localization errors under the Clustering I process and without the Clustering I process. 7.Figure Conclusions

7. Conclusions This paper proposes a novel PD localization method based on wireless UHF sensor array. The 7. Conclusions This paper proposes method a novel shows PD localization based on wireless sensor array. proposed PD localization satisfactorymethod accuracy through field test.UHF Together with its This paper proposes a novel PD localization method based on wireless UHF sensor array. The The proposed PD localization method shows satisfactory accuracy through field test. Together with low hardware cost, the proposed method is worthy to be widely applied in substations to find power proposed PD localization shows satisfactory accuracy through field test. Together with its its low hardware cost, themethod proposed method is worthy to be widely in in substations find equipment with potential insulation defects quickly. Considering theapplied workload the offlinetostage, low hardware cost,with the proposed method is worthy to be widely applied inthe substations toinfind power power equipment potential insulation defects quickly. Considering workload the offline the proposed method is more suitable in small and medium voltage level substations. In our future equipment with potential insulation defects quickly. Considering the workload the offline In stage, stage, method is more suitable in small and medium voltage level in substations. work, the we proposed plan to use the sub-regional monitoring strategy for larger substation and investigate our the the proposed method more in small and medium voltage level substation substations. In investigate our future future work, we plan toisuse thesuitable sub-regional monitoring strategy for larger and work, we plan to use the sub-regional monitoring strategy for larger substation and investigate the

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the methodology to reduce the workload of fingerprint mapping. The weather conditions can also influence our proposed method. For example, in humid conditions, the PD interference will increase. Therefore, to guarantee the effectiveness of the clustering I process, the number of PDs produced by our discharge source in the offline stage should also be increased. However, according to the normalization process as addressed in Equation (5), the influence to the localization accuracy caused by weather conditions could be reduced to an acceptable level. Acknowledgments: This work was supported by the National Natural Science Foundation of China (514070116) and the State Grid science and technology project. Author Contributions: The idea of this work was proposed by Zhen Li, Lingen Luo, Gehao Sheng, and Xiuchen Jiang. Zhen Li Lingen Luo and Nan Zhou performed the experiments and analyzed the results. Zhen Li and Lingen Luo wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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