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Power Line Communication Based Smart GridAsset Monitoring Using Time Series Forecasting

Yinjia Huo, Student Member, IEEE, Gautham Prasad, Lutz Lampe, Senior Member, IEEE, andVictor C. M. Leung, Life Fellow, IEEE

Abstract—Monitoring grid assets continuously is critical inensuring the reliable operation of the electricity grid system andimproving its resilience in case of a defect. In light of several assetmonitoring techniques in use, power line communication (PLC)enables a low-cost cable diagnostics solution by re-using smartgrid data communication modems to also infer the cable healthusing the inherently estimated communication channel stateinformation. Traditional PLC-based cable diagnostics solutionsare dependent on prior knowledge of the cable type, networktopology, and/or characteristics of the anomalies. In contrast, wedevelop an asset monitoring technique in this paper that candetect various types of anomalies in the grid without any priordomain knowledge. To this end, we design a solution that firstuses time-series forecasting to predict the PLC channel stateinformation at any given point in time based on its historicaldata. Under the assumption that the prediction error follows aGaussian distribution, we then perform chi-squared statisticaltest to determine the significance level of the resultant Maha-lanobis distance to build our anomaly detector. We demonstratethe effectiveness and universality of our solution via evaluationsconducted using both synthetic and real-world data extractedfrom low- and medium-voltage distribution networks.

Index Terms—Smart gird, System monitoring, Time seriesprediction, Cable diagnostics, Anomaly detection, Power linecommunication systems.

I. INTRODUCTION

ASSET monitoring is critical for the safe and smoothoperation of the electricity grid system [1]. The advent

of smart grid, which allows for bidirectional data exchangebetween the utility and the consumer [2]–[4], unfolds a newparadigm of solutions for grid infrastructure monitoring toimprove the system resilience of the grid. One such techniqueis to re-use power line communication (PLC) modems forcable diagnostics. PLC-based cable diagnostics provides thebenefits of realizing a low-cost solution that can operatein an online, independent, and automatic manner withoutrequiring any new component installations [5]–[9]. It coun-ters the drawbacks of legacy cable diagnostics solutions,e.g., reflectometry-based methods, which require deploymentof specialized equipment and/or personnel to conduct thetests [10], [11], [12, Ch. 6], [13]. Furthermore, several non-PLC solutions that sample the electric signal with a lowerfrequency, such as phasor measurement units, suffer from

The first three authors are with the Department of Electrical and ComputerEngineering, The University of British Columbia, Vancouver, BC, Canada.Victor C.M. Leung is with the College of Computer Science and SoftwareEngineering, Shenzhen University, Shenzhen, Guangdong, China. Email:yortka@ece.ubc.ca, gautham.prasad@alumni.ubc.ca, lampe@ece.ubc.ca, vle-ung@ieee.org.

noisy data impacted by electrical disturbance and are unableto discern precise information about cable defects, e.g., age ofdegradation or accurate location of a fault [11], [14]. PLC-based monitoring techniques, on the other hand, reuse thehigh-frequency broadband communication signals as probingwaves to provide effective cable diagnostics [5], [15].

PLC is a commonly used solution to enable informationand communication technology for the smart grid [16]–[18].Power line modems (PLMs) that transmit and receive smartgrid data constantly estimate the power line channel stateinformation (PLCSI) for adapting their operation. In thiscontext, we refer to PLCSI as any parameter that conveysthe channel behavior, either directly, e.g., channel frequencyresponse (CFR) or access impedance, or indirectly, e.g., signal-to-noise ratio (SNR) or precoder matrix. Prior arts have shownthat this estimated PLCSI also contains information that canbe used to infer cable health conditions [5]–[9].

Many of the proposed PLC-based diagnostics solutionstypically require a reference healthy measurement, i.e., PLCSIof a cable that is not damaged (e.g., [7], [8]). PLCSI estimatedwithin the PLM is then compared against this referencemeasurement to infer the health of the cable. However, such amethod is unreliable since the load conditions are constantlyvarying, which makes it hard to distinguish benign and ma-licious PLCSI changes, e.g., those that are caused due toload variations as opposed to grid anomalies. Alternatively,data-driven methods that were designed to use machine-learning (ML) techniques to intelligently detect and assesscable health are resilient against such challenges [5], [6],[19]. These methods harness ML classification and regressiontechniques to detect, locate, and assess various smart gridnetwork anomalies, such as cable degradation and faults andnetwork intrusions [5], [6], [15], [20]. However, these methodsare not universally applicable since the machines used here aretypically trained under a specific operating network topologyto detect a few known types of characterized anomalies. Whenthe machine is deployed under a different network topology oris applied to detect a type of anomaly it has never encounteredin the process of training, the performance of these solutionssuffer significantly.

To counter the aforementioned shortcomings, we developa general purpose cable anomaly detector, which does notrequire any reference measurements from healthy cables andis universally applicable. Our design is fully agnostic to thenature of the anomaly, i.e., its physical or phenomenologicalbehavior, and to the infrastructure configuration, such as cabletype or network topology. To this end, we propose the use of

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historical responses between two PLMs, such as a transmitterand a receiver pair, to train a time-series predictor. By treatingthe time stamped PLCSI as time-series data, we use timeseries forecasting to predict the PLCSI at any given point intime using historical data by exploiting the knowledge that thenetwork topology, cable configuration, and the physical prop-erties of the cable are relatively stable for extended periodsof time. In addition, since the long-term load conditions areclosely related to their historical values, the PLCSI is alsocorrelated in time and can be predicted using historical stateinformation [21]. We then compare the predicted responseagainst the actual response estimated by the PLM to detecta potential anomaly.

The performance of our solution relies heavily on the accu-racy of the predicted PLCSI. With a highly accurate prediction,the detector would be capable of detecting even subtle faults,which might not be discernible if the prediction itself is noisy.To this end, we investigate a range of possible candidates forforecasting, including classical approaches such as the auto-regressive integrated moving-average (ARIMA) model [22,Ch. 4] and feed-forward neural networks (FFNN) [23], andalso relatively recently developed techniques such as long-short-term-memory (LSTM) model [24]. Furthermore, ow-ing to its success in previous PLC-based cable diagnos-tics [5], [15], we also evaluate the use of least-square boosting(L2Boost) [25].

The second factor of consideration toward building oursolution is the design of the cable anomaly detector based onthe predicted and the measured PLCSI values. The challengelies in differentiating between a cable anomaly and an inaccu-rate prediction. For this, we exploit the orthogonal frequency-division multiplexing (OFDM) nature of broadband PLC trans-missions [26]. We first divide all the OFDM subcarriers intoseveral groups and average the value of PLCSI across allsubcarriers within each group. This stabilizes the group PLCSIaverage, which then in turn also makes it more accuratelypredictable. With the working assumption that the predictionerrors across the subcarrier groups follow a multi-variateGaussian distribution, we determine a probable occurrenceof an anomaly event based on the significance level of thesquared Mahalanobis distance (SMD) [27]. The significancelevel can be determined either empirically from the trainingdata or theoretically from a chi-squared test [28].

We verify the feasibility and the effectiveness of ourproposed schemes through numerical evaluations using bothsynthetic data and in-field data. For the former, we use abottom-up PLC channel emulator to generate the PLCSI time-series data, which allows us to investigate the performance ofour proposed solution under various types of cable anomaliesin a customized and a controlled environment. The in-fieldcollected data obtained from [29] further allows us to verifyour proposed schemes in the real-world, which indicates theperformance of our proposed technique in practice.

II. TIME-SERIES FORECASTING

We begin by presenting a brief overview of time seriesprediction by focusing on the pertinent algorithms that we

consider for our proposed method. This helps us in under-standing the performance of the PLCSI forecasting using timeseries data.

A. Time-Series Data for Cable Anomaly Detection

PLMs estimate a range of PLCSI values for adaptingcommunications in a time varying environment. Some of theestimated PLCSIs that shed direct light on the channel andin turn on the cable health are the end-to-end CFR, accessimpedance, precoder matrix, and self-interference channelimpulse response [30]–[32]. However, several existing PLMchip-sets are unable to extract these parameters in their entiretywithout additional firmware modifications [6]. In light of this,we consider the use of SNRs instead, which can be readilyextracted from current-day PLM chip-sets [6] and can beused for processing either locally within the PLM or reportedto a common location by all PLMs, e.g., a sub-station, forcentralized data processing.

The time-stamped SNR between a transmitter-receiver PLMpair is denoted as xj , where j is the integer discrete time index.We formulate our problem as using windowed instances of xj ,where n−w ≤ j < n, to predict xn and obtain the predictedvalue as xj , with w being the window size.

Among the available samples of xj , we use xj , where j ≤ntr, to train the time-series predictor, where ntr is the numberof samples used for training the machine. Once the modelis trained, we then use it to predict xj , where j > ntr. Weuse the normalized root mean square error (RMSE), η, as theperformance indicator of our prediction, which is computed as

η =

√N∑

j=ntr+1

(xj − xj)2√N∑

j=ntr+1

(xj − µx)2

, (1)

where µx is the sample mean of the observations of xj forntr + 1 ≤ j ≤ N , and N is the total number of xj samplesused for training and testing.

To compare the performance of our ARIMA and ML basedpredictors against a baseline approach, we consider a simpleextrapolation,

xn = xn−1. (2)

In the following, we discuss the use of different time seriesforecasting methods for predicting xn. We defer to Sec-tion IV-B for the procedure to choose suitable time-seriesprediction models to use for our anomaly detection, dependingon the nature of the data used for our diagnostics scheme.

B. ARIMA

The ARIMA model is a classical time-series predictor thathas successfully been used across various domains of appli-cation, including financial series prediction, demand and loadprediction in the power generation and distribution industry,and customer sales prediction [22, Ch. 1]. An ARIMA modelis specified by its order and its associated parameters. A(p, d, q) ARIMA model is a pth order auto-regressive, qth

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order moving-average linear model with dth order of differ-ence. A (p, d, q) ARIMA model has p auto-regressive termswith p auto-regressive coefficients and q moving-average termswith q moving-average coefficients. A dth order difference isgenerated using d subtraction operations, i.e., ud,j = ud−1,j−ud−1,j−1 for d ≥ 2 with u1,j = xj − xj−1.

The resultant time-series after difference is then assumedto be a (p, q) auto-regressive moving-average model, whichis a linear model with p auto-regressive terms and q moving-average terms, which is specified by

ud,n =

p∑j=1

φjud,n−j + an −q∑j=1

θjan−j , (3)

where φj are coefficients for auto-regressive terms, θj arecoefficients for moving-average terms, and aj is the randomshock terms drawn independently from a Gaussian distributionhaving zero mean and variance σ2

a.

C. Least-Square Boosting

As our second time-series predictor candidate, we inves-tigate L2Boost, which has been shown to be successful inthe past, specifically for cable diagnostics [5], [15]. L2Boostis a popular ML technique used for supervised regressiontasks [25]. It is one of the meta-ML algorithms which works byconsolidating multiple weak learners into a strong learner [33].It applies the weak learners sequentially to weighted versionsof the data, where a higher weight is allocated to examplesthat suffered greater inaccuracy in earlier prediction rounds.These weak learners are typically only marginally better thanrandom guessing but are computationally simple. Boosting isalso known to be robust to over-fitting, and can be efficientlyexecuted since it is a forward stage-wise additive model.

To use the L2Boost for time-series prediction, we orga-nize the SNR time series into a labeled data set for thesupervised learning. For the training data set, i.e., xj , where1 ≤ j ≤ ntr, we prepare each sample with input xj =(xj , xj+1, ..., xj+w−1) and its associated label yj = xj+w,where j + w ≤ ntr. We then prepare the testing samples in asimilar way with input from xj to xj+w−1 and its associatedlabel as xj+w, but with j + w > ntr.

D. Feed-Forward Neural Network and Long-Short-Term-Memory

As our last set of predictor candidates, we investigate the useof two types of artificial neural network (ANN) models, FFNNand LSTM. Despite the absence of feature engineering, ANNscan still explore the inherent structure of the input data, whichcould be hidden and/or complex. The architecture of ANN isflexible with varying number of hidden layers and neuronsin each layer. To use ANNs for time-series prediction, weorganize the PLCSI values into a labeled data set of xj and yjfor the supervised learning the same manner as in Section II-C.

While the FFNN has a plain architecture, where the outputof the previous layer is fed as the input to the current layer,i.e. feed-forward from the input layer to the output layer, theLSTM has a feed-back mechanism, where the output of the

current layer at the last time stamp together with the output ofthe previous layer at the current time stamp are fed as the inputto the current layer at the current time stamp. For the LSTMmodel, the feed-back of the current layer from the last timestamp is controlled by a forgetting gate and the output of theprevious layer at the current time stamp is controlled by aninput gate. The forgetting gate controls how much previousinformation memorized by the LSTM machine is forgottenand the input gate controls how much new information fromthe input layer is passed through the LSTM machine. Such afeed-back mechanism is capable of capturing long term timedependence relationship and suitable for a variety of timeseries prediction tasks. When such long term time dependencerelationship is not present, using FFNN in place of an LSTMmachine can reduce the risk of over-fitting.

III. CABLE ANOMALY DETECTION

In this section, we present the design of a cable anomalydetector based on the difference between the actual SNR andits forecast, with the goal of maximizing the detection ratewhen simultaneously also minimizing false alarms.

A. Data Preparation

PLC channels are frequency selective in nature. For theoverwhelming majority of broadband PLC transceivers thatuse OFDM transmission [26], the frequency selective nature ofPLC channels results in different SNRs at different sub-carriersmeasured by the PLM. This renders the time series predictionof individual SNRs hard. Therefore, we divide all the OFDMsubcarriers into multiple groups called stabilizer batches. Wethen average the SNR across all individual subcarriers withineach stabilizer batch. This procedure of averaging within astabilizer batch ensures that the time series SNR data ismore stable and predictable when compared to using SNRs ofindividual sub-carriers. In this regard, it is essentially to havethe subcarriers within a batch be contiguous. This ensures thatthe variation in individual SNR values are only gradual and theimpact of cable anomalies on the individual subcarrier SNRsare similar in nature.

This process results in several stabilizer batches, and thetime-stamped average SNR values in each individual stabilizerbatch are treated as a set of time-series data. We denote zi =zi,j, 1 ≤ i ≤ nSB to denote the time series of the averageSNR of the ith stabilizer batch, where nSB is the number ofsuch stabilizer batches. For every ith stabilizer batch, we usethe candidate forecasting models described in Section II todevelop a time-series predictor Fi to predict the average timeseries SNR, γi,j . The input to the predictor is the windowedtime series

vi,j = [zi,j , zi,j+1, ..., zi,j+w−1]T, (4)

with the samples corresponding to j + w ≤ ntr used duringtraining and those corresponding to j + w > ntr used whiletesting. Hence, the prediction is γi,j = Fi(vi,j) while the truelabel is γi,j = zi,j+w.

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B. Detection Using Squared Mahalanobis Distance

To detect an anomaly we consider the difference in thepredicted SNR to the one measured by the PLM,

δi,j = γi,j − γi,j . (5)

Several aspects in the grid that are typically random innature (e.g., randomly varying power line noise) contributeto the prediction error. Therefore, we assume that δi,j fol-lows a multi-variate Gaussian distribution, which is stationaryover j, with mean µ and covariance matrix Σ. With δj =[δ1,j , δ2,j , ..., δnSB,j ]

T, we compute the SMD as

D2MA = (δj − µ)TΣ(δj − µ). (6)

D2MA follows a chi-squared distribution with a degree of

freedom of κ = nSB. Then, following the theory of chi-squaredstatistical test [28], for a significance level of α, we define thequantile function of the chi-squared distribution with a degreeof freedom κ, as χ2

κ(·), i.e.,

Pr(D2MA ≤ χ2

κ(1− α)) = 1− α, (7)

where Pr(·) is the probability function. Finally, for a chosentarget false alarm (FA) rate of pFA, our anomaly detectordeclares a warning of a potential cable anomaly when

D2MA > Tr(pFA), (8)

where the threshold Tr(pFA) is determined according to thecorresponding significance level by

Tr(pFA) = χ2κ(1− pFA). (9)

IV. DESIGN AND CASE STUDIES

We now highlight the performance of our proposed cableanomaly detection by applying it to two different types ofdata sets, one generated synthetically and the other collectedin-field, and we describe the design details involved.

A. Data Sets

1) In-field Data: We acquire in-field measurements fromthe data made available to us by the author of [29]. Thedata were measured using 24 BB-PLC modems installed inthe low-voltage (LV) sector of a distribution network and 12BB-PLC modems in the medium-voltage (MV) grid. Theseform 22 transmitter-receiver pairs with 44 bidirectional datatransmission links in the LV network and 6 pairs with 12links in the MV portion. The SNR data are measured by thePLMs every 15 minutes over 917 OFDM sub-carriers spaced24.414 kHz apart. This data collection spans an overall timeperiod of 17 to 21 months.

Due to limitations in generating flexible observations andanomalies in practical grids, the in-field data consists of onlytwo recorded instances of network anomalies. Furthermore,although information of the cable type, length, and the bio-logical age of the cables are provided in [29], there is limitedinformation available on the operation condition during thefield test. Therefore, for a comprehensive evaluation, togetherwith using the in-field data, we also use synthetic data setsobtained from constructing a PLC network and generatingPLCSI using the bottom-up approach.

PLM-1 PLM-2

PLM-3

BP

500m 500m

100m

Fig. 1. PLC network topology for synthetic data generation.

2) Synthetic Data: For consistency between the two typesof data sets, we borrow several network settings for generatingthe synthetic data from the in-field measurement campaign. Wegenerate PLCSI between a pair of PLMs for every 15 minutesover a period of 664 days. We construct the PLC network asa T -topology as shown in Fig. 1. We use multi-core N2XSEYHELUKABEL cables with cross-linked polyethylene (XLPE)insulation, whose configuration and parameters can be foundin [34, Table 2].

To generate the synthetic data, we consider three types oftime-series load models to emulate the temporal dependenceof electrical loads, motivated by seasonal and auto-regressiveproperties of loads in the mains frequency [21]. We denotethe load value at discrete time index j of the load model k,k ∈ 1, 2, 3, as Lk,j . For k = 1, 2, we apply a second-orderauto-regressive model and a cyclic model with one day percycle, respectively. We then set the third model to be

L3,j =1

2(L1,j + L2,j) (10)

as a hybrid of both the auto-regression and the cyclic behav-iors. Furthermore, we add random shocks, rk,j , to the modelsto introduce a degree of randomness in the load variations. Asa result, our load models are

L1,j =

r1,1, for j = 1

0.8L1,1 + r1,2, for j = 2

0.6L1,j−1 + 0.3L1,j−2 + 0.1r1,j , for j ≥ 3

(11)

where rk,j ∼ (U [0, 50] + jU [−50, 50]), with j =√−1 and

U [a, b] denoting a uniform random distribution from a to b.For the second model, we set

L2,j = 0.9L′2,j + 0.1r2,j , (12)

where L′2,j is a summation of a set of sine and cosine terms,each with its frequencies being harmonics of a set fundamentalfrequencies. We set the cycle corresponding to the fundamentalfrequency to be one day.

B. Time Series Prediction for Studied Data Sets

In this part, we develop the time-series prediction solutionsfor our studied data sets using the candidate models describedin Section II.

1) ARIMA: We consider ARIMA models for all combina-tions of p, d, q, where 0 ≤ p, d, q ≤ 2, which is known to besufficient for most practical time-series prediction tasks [22,Ch. 6]. Discarding the case of p = q = 0, we investigate atotal of 24 candidate ARIMA models.

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2) L2Boost: We choose the hyper-parameter, ktotal, whichrepresents the total number of iterations as ktotal =50, 100, 200. We make the choice considering that for smallervalues of ktotal, the resultant trained model has a lesser repre-sentation power but also a lower risk of over-fitting.

3) ANN: Given the small input size to the NN, i.e., thewindow size w, we consider a simple architecture with onehidden layer with eight neurons for the FFNN and the LSTMmodels. For the FFNN and LSTM, we use the sigmoidfunction and hyperbolic tangent as the activation functions forthe hidden layer, respectively. The purpose of the activationfunction for the hidden layer is to implement a non-lineartransform so that non-linear relationship between the outputand the input can be learned by the ANN.

Our aim is to develop a time-series predictor that can predictfuture values as accurately as possible when the system isoperated under normal conditions, i.e., without anomalies.Thereby, an anomaly produces a pronounced deviation be-tween the actual value and the predicted one. Therefore, inthis part of the study, the training and testing data for thesynthetic data sets only contain the SNR values when the cableis under normal operating conditions. For the in-field data, westipulate that most of the data were collected when the cableswere operated under the normal condition with only occasionalvalues corresponding to anomalous conditions.

We use ntr = 0.8N and the remaining samples for testingthe performance of the time series predictor. The performanceof our chosen set of time-series predictors are shown inTable I, where the results are presented for the SNR of thefirst subcarrier group. For brevity, we only present selectiveresults for ARIMA models. From Table I, we can observe thatFFNN, LSTM, L2Boost and some ARIMA models match orimprove the performance over the baseline setting. Moreover,the LSTM model shows the best performance across the datasets that we have investigated, supporting its suitability totime-series prediction tasks. Similar results were obtained forother subcarrier groups.

We also note from Table I that the performance of thebaseline model is often fairly close to those from other timeseries prediction models. Therefore, since the baseline predic-tor does not require any training and presents no additionalcomputational complexity (see (2)), the anomaly detector canbegin prediction with this technique until sufficient samplesare collected over the operation to use other predictors thatrequire a meaningful set of training data. In the subsequentSection IV-C, we show that the improvement in MSE of time-series prediction can also translate into an enhancement ofanomaly detection.

C. Anomaly Detection for Studied Data Sets

In this section, we develop and test our anomaly detectorfor the studied data sets. According to the discussion inSection III-B, we assume the prediction errors for the averageSNR values follow a multivariate Gaussian distribution, witha dimension of nine since we have nine stabilizer batches intotal. We then calculate D2

MA using (6) and use (9) for theanomaly detection with varying pFA and κ = nSB = 9.

TABLE INORMALIZED RMSE PERFORMANCE OF TIME SERIES PREDICTION FOR

THE FIRST SUBCARRIER GROUP AVERAGE SNR

Data Set MV2 LV45 Syn1 Syn2 Syn3

ARIMA(2, 0, 1) 43.7% 38.5% 52.2% 61.4% 20.1%

ARIMA(2, 0, 2) 42.9% 38.5% 52.2% 89.9% 25.2%

ARIMA(0, 1, 1) 42.9% 38.9% 53.1% 63.1% 20.4%

ARIMA(0, 1, 2) 42.9% 38.9% 53.1% 62.6% 20.1%

L2Boost(100) 40.2% 40.5% 52.2% 54.8% 19.2%

L2Boost(50) 42.0% 41.7% 53.1% 55.6% 20.5%

FFNN 39.4% 39.3% 52.5% 53.5% 18.0%

LSTM 39.4% 38.0% 52.5% 51.8% 17.7%

Baseline 43.7% 40.5% 56.7% 70.5% 20.2%

(a) Data Set MV2 (b) Data Set LV45

Fig. 2. SMD for the in-field collected data using ARIMA(2, 1, 1).

(a) Data Set MV2 (b) Data Set LV45

Fig. 3. SNR color map for the in-field collected data.

The only available recorded anomaly events for the in-fielddata in [29], are the switching operations at the 20th dayin the data set MV2 and the fuse failure at the 156th dayin the data set LV45. For each stabilizer batch, we computethe average SNR data and calculate the SMDs based on theprediction errors. The results for data set MV2 and data setLV45 are shown in Fig. 2a and Fig. 2b, respectively. The twodocumented events are clearly seen in these two figures asnotable spikes. To relate this result with the observed rawdata, we present the SNR color maps for the two data setsin Fig. 3a and Fig. 3b. It is also clearly noticeable from thefigures that there are multiple (undocumented) anomalies inthe LV data in Fig. 3b, which are rightly represented as notablespikes in the SMD plot of Fig. 2b. The higher rate of theindicated abnormal events in LV networks in comparison withMV networks can be attributed to the increased presence ofinterference and higher disturbance levels in an LV network.

While the two documented events in the in-field dataprovided us the opportunity to test the performance of oursolution using real-world data, the exercise does not provide

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(a) Concentrated Fault (b) Termination ImpedanceChange

Fig. 4. Average SNR for the batch i = 1.

a comprehensive evaluation of our method, especially fordifferent types of cable anomalies and operation under variousload types and load changes. To this end, we use synthetictraining and testing data sets obtained from the network andload models constructed as explained in Section IV-A. Thisprovides us the flexibility to choose a variety of load andanomaly types to investigate the robustness of our method.

We identify three main categories of anomalies, similarto those in [35], which are, concentrated faults, distributedfaults (DFs), and abnormal termination impedance changes.We emulate a concentrated fault by inserting a fault resistancerf between a pair of conductors at the fault point. Such aline-line fault is the most common among all types of hardfaults [36]. This process can also be extended by placing afault impedance rf between each pair of conductors to emulatea symmetrical fault. To emulate a DF, we increase the per-unit-length (PUL) resistance of the conductor and the PULconductance of the insulation materials over a section of thecable that is affected by this degradation. For many typesof DF, the conductors have a deteriorated conductance andthe insulation material has degraded insulation property [37],which we emulate by this process. Finally, to emulate theabnormal termination impedance changes, for our syntheticgenerators, we change from one load model to another, amongthe three that we use, over a period of time, e.g., one hour forfour samples.

We first present the results of the change in SNR valueswith the introduction of a concentrated fault. We introduce afault impedance rf = 100 Ω between a pair of conductorsat a location that is 100 m from a PLM transmitter, e.g.,PLM-1 in Fig. 1. We show the impact of this in Fig. 4 bycontrasting the average SNR change of one stabilizer batch forthe condition of concentrated fault in Fig. 4a and a terminationimpedance change in Fig. 4b. It is clearly visible that thesechanges cause a significant, noticeable, and distinctive changesin the measured SNR values. As a result, we focus on the morechallenging case of DF in the following.

We introduce three different types of DFs, a slight DF, amild DF, and a medium DF. We emulate each of these threeconditions by increasing the PUL serial resistance and shuntconductance of the cable by 10%, 20%, and 60%, respectively,to emulate different extents of cable degradation [38]. Weintroduce the DF over a 300 m section of the cable with thestarting point of the faulty section being at a distance of 100 maway from a PLM transmitter.

The average SNR values of the first stabilizer batch over

(a) Mild DF (b) Medium DF

Fig. 5. Average SNR with mild and medium DFs for the stabilizer batchi = 1.

(a) Mild DF (b) Medium DF

Fig. 6. SMD for mild and medium DFs whose SNRs are presented in Fig. 5.

Fig. 7. ROC for the generated test cases with slight DF.

time, as shown in Fig. 5a and Fig. 5b, signifies that detectinga DF is more challenging than a hard fault. We employ ouranomaly detection procedure, and accordingly compute theSMDs, as illustrated in Fig. 6, where the faulty events areindicated as distinctive spikes in the middle. We then deter-mine the anomaly detection thresholds with a false alarm ratepFA either theoretically using (9) or empirically through thetraining data. For the empirical determination, we sort |D2

MA|for the training data prediction difference in the descendingorder as di from d1 to dmax. We then compute the thresholdas

Tr(pFA) = dbpFA(ntr−w)c, (13)

where b·c is the floor function.Choosing the threshold involves a trade-off between the

detection rate pDT, i.e., the probability that an anomaly canbe successfully detected, and pFA, i.e., the probability thata normal condition is identified as an anomaly. An increasein detection rate is typically accompanied by higher falsealarm rates. We show this behavior in the receiver operatingcharacteristic (ROC) curve for our anomaly detection solutionin Fig. 7. Since the performance of our method for the casesof mild and medium DFs are nearly ideal for all candidateforecasting choices, we only present ROC behaviors for themore challenging case of slight DF. We generate 100 different

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(a) Trained Using MV4 (b) Trained Using Synthetic Data

Fig. 8. SMD for the in-field collected SNRs from the data set MV2.

test cases, where in each case, we introduce a slight DF in themiddle of the time series. The blue single-step (SS) curve inFig. 7 is the baseline prediction method in (2), and AVG is analternative trivial prediction scheme that uses the average ofthe training data as the predicted value at all times. We observefrom Fig. 7 that ARIMA and baseline predictors provide thebest detection performance, as also evidenced in Table I forprediction performance. However, anomaly detectors usingLSTM or other data driven time-series predictors have worseperformance than even the AVG predictor for the case ofslight DF. We observe that data driven time-series predictors,including LSTM, FFNN and L2Boost, have good predictionperformance both before and after the slight DF is introduced.This shows that they adapt better to the case of faulty cablecondition. Such generalization ability to unobserved data witha slight difference from the training data is a detriment toanomaly detection as it does not produce a distinct change ofthe prediction error after the slight DF is introduced. For moredistinct DFs however, e.g., mild and medium DFs, anomalypredictors using data driven time-series predictors and thoseusing the classical ARIMA models have matched performance.

For a false alarm rate of pFA = 1%, we obtain the thresholdas Tr(pFA) = 21.67 theoretically using (9), or empiricallyusing the training data and (13) as Tr(pFA) = 23.91 asan alternative. For the generated test cases, the threshold toachieve a false alarm rate of pFA = 1% is Tr(pFA) = 23.75,which is very close to the threshold determined theoreticallyusing (9) or empirically using the training data. This showsthat both theoretical and empirical approaches are viablemethodologies to determine the threshold Tr(pFA).

V. SUPPLEMENTARY EVALUATION

In this section, we further investigate the suitability ofour proposed solution in practical scenarios. In particular, weaddress two challenges faced in practice, which are the lackof available data for training and the identification of cableanomalies that are gradual in nature, such as an incipient fault.

A. Robustness Test

Our evaluation campaign in Section IV involved using his-torical SNR time series data for training and prediction. Thistype of data collection is suitable in fixed asset monitoring.However, we investigate the suitability of using our solution asa dynamic diagnostics technique, where a machine is trainedto detect anomalies on one type of a network and requiredto function on another type. This expands the scope of our

Fig. 9. SMD for detecting an incipient fault.

proposed solution to make it more universally applicable,where, e.g., the SNR data from one pair of transmitter andreceiver can be used to detect anomalies in networks operatingin a different portion of the grid. A likely more beneficial use-case is to train the machine using synthetic data extracted froma best-guess estimate of the network-under-test and to use it inthe real-world network to detect cable anomalies. We conductboth these investigations and present the performance resultsin Fig. 8a and in Fig. 8b.

In the first evaluation, we train the machine using SNR dataextracted from the dataset MV4 of the in-field data from [29],and test it over the data set collected in a different portionof the MV network, i.e., dataset MV2. The result in Fig. 8ashows a clearly discernible spike in the SMD plot, which iseasily detectable by our anomaly detector with little/no falsealarm. The adjacent Fig. 8b demonstrates that training thenetwork with synthetic data, which was generated using L3

according to the procedure explained in Section IV-A, andtesting it with the in-field collected data set MV2 is also ableto detect network anomalies. The results from Fig. 8a andFig. 8b indicate the robustness of our solution to variationsbetween training and application data.

B. Incipient Fault

Our investigations in Section IV considered faults that areabrupt, i.e., occurring to their full extent at one instant of time.However, the cable may also be susceptible to an incipientfault, which is introduced gradually over time. We emulatesuch a condition by generating a 132-day time sequence,where the incipient fault begins to develop on the 66th day.We quantify the severity of the fault by γ(t) ∝ t, where tis time in seconds. We scale the PUL serial resistance andPUL shunt conductance by a factor of γ(t) between 0 onthe 66th day to 2 on the 132nd day. We place the incipientfault on a cable section of 300 m whose starting point is100 m from the transmitter PLC modem and use L1 togenerate our synthetic SNR data. We train the predictor usingnormal operating conditions, i.e., without the incipient fault,and then use ARIMA(2, 1, 1) for time series forecasting. Theresultant SMD for the generated incipient fault case is shownin Fig. 9. The SMD plot shows spikes indicating a fault fromthe 66th day onward and whose magnitude increases as timeprogresses. Naturally, the choice of the threshold determineshow quickly an incipient fault can be detected and what is thefalse alarm rate that is sacrificed in the process. This decisionwould be made based on the operating scenario.

SUBMISSION TO AN IEEE JOURNAL 8

VI. CONCLUSIONS

We have designed a first-of-its-kind PLC-based universalcable anomaly detector using time series forecasting and statis-tical test of prediction errors. Our low-cost solution repurposedPLC modems to also enable monitoring the grid system toensure its smooth operation and improve its resilience byreusing the channel state information inherently estimated bythe modems. Our method, which combines forecasting withthe post-processing of prediction errors based on Mahalanobisdistance, produces a robust cable anomaly detection perfor-mance. Our solution is also applicable across various networkconditions and can operate without prior domain knowledgeof the anomaly, network topology, type of the cable, or loadconditions.

ACKNOWLEDGMENT

This work was supported by funding from the Natural Sci-ences and Engineering Research Council of Canada (NSERC).The authors would also like to thank Dr. Nikolai Hopferfrom the University of Wuppertal, Germany, and Power PlusCommunications AG (PPC), Germany, for making the experi-mental data available and assisting with the data analysis. Theexperimental data was collected in a research project supportedby the German Federal Ministry of Education and Research[grant number 03EK3540B].

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