arXiv:1807.05347v2 [eess.SP] 6 Feb 2019 nsatgisuigpwrln oesadso h efficiency the show and algorithms. proposed line the s power of of using concept grids the smart validate lo Simu They in above. presented. and listed finally classify anomalies are network detect, results of to kinds algorithms measurem different two the the introduce perform discu then to firstly we We and needed considered, sensors. architectures network bandwidth front-end as wide modems the line the power Given on MHz. rely i several anomalies f to spanning such signals kHz about frequency high information using harvest grids distribution to th how In electri present time. pronounced over we degradation less at cable or also changes more considering impedance faults, to harmless termination from network span some that anomalies work oes al eeto,CbeAging Cable Detection, Fault Modems, meddSse ru,Uiest fKaefr,Klagenfu the Klagenfurt, andrea.tonello}@aau.at. of of {federico.passerini, University mail: aging Group, the System Embedded monitor di a to on relies or work former [4] The [6]. fault [5], a a infrastructure cable det of of to response presence either used frequency the be The can link topology. algorith communication different network point-to-point use the and infer the wiring, estimate to connecting to network the the of handshake in length present the th the modems of of the time-of-flight about all authors the between The measure information [3]. to [2], gain propose modems grid works to the line of power exploited structure two topological been between has connection (PLMs) used a two-way-handshake classical establish The to . reflectometry single or a modems from two between communication medium to-end as networks. networks distribution size voltage small low in or tenths beneficial voltage few is to device up which frequencies single MHz, of a exploitation in the enables communication separate and and need wi sensing and Sensing includes kHz [1]. PLM information few share to to up devices communication frequencies at netw is the work around role which displaced sensors This specific an of grid. (PMUs) kind as units the different measurement only of phasor that by not status sensors absolved (PLMs) the active classically monitor as modems continuously also line but can power ranges. devices, use frequency communication to mere MHz) Narrowband is (2-30 line aim the power The both and of kHz) using analysis (3-500 signals, the from (PLC) (PLN) communication network line power I mr rdMntrn sn oe ieModems: Line Power Using Monitoring Grid Smart eeioPseiiadAde .Tnloaewt h Networ the with are Tonello M. Andrea and Passerini Federico ne Terms Index Abstract L esn a epromdi w as sn end- using ways: two in performed be can sensing PLC oaayewa nomto a ehretdaota about harvested out be carried can been information has what research analyze relevant to years, recent N Temi ujc fti ae stesnigo net- of sensing the is paper this of subject main —The eeioPasserini, Federico SatGi,NtokMntrn,PwrLine Power Monitoring, Network Grid, —Smart nml eeto n Localization and Detection Anomaly .I I. NTRODUCTION tdn ebr IEEE, Member, Student t uti,e- Austria, rt, spaper, is o few rom ensing lation and k ork, cate rect ese ent ect ms cal of th ss n d n nraM Tonello, M. Andrea and oe iecanl 1] eodagrtm hc relies which algorithm, second A characteri that [14]. variance channels ov time between evolution line the their distinguish power account track and into to detect taking and time, we to anomalies, of used Finally, kind is events. different anomal algorithm localize sensing first and detect the A to algorithms thi of i different In take frequency propose that fault. less the techniques brief sensing requires account a different that aging present detecting anomaly we cable than regard, of events tracking kind sensing example, frequent The the For me devices. sought. on different sensing is based establishing as recurrences, of PLC PLM surement consists standard and contribution network signals using input second respectively, test the generate CTF end-to- measure to or the to reflectometric propose and We either impedance are. perform sensing to techniques th end needed what measurement first are establishing and The of that architectures sensing. consists modem end-to-end paper required perform this to of perform PLN contribution termination to the the order at of deployed in nodes is be office, can [13] PLMs central PLM Other networks (IBFD) the reflectometry. Duplex distribution at Full possibly voltage In-Band deployed, low one can least or paper at medium this where in in of proposed applied purpose framework be the The for sho measured monitoring. effect to be grid the and can propagation model quantities signal physical to the which out on carried anomalies Ther been electrical [12]. of has in analysis obtained thorough results a the Th from PLM. a starts in contribution implemented detection be anomaly can the that communica algorithms on the localization rather on but not itself, is technology technolog paper network tion PLC this the of of focus to the location thanks Nevertheless, grids and distribution detection in anomalies autonomous line power the the enables modification i.e. a system, as the anomaly of an behavior medium. to expected refer following We the the examples. of small in to part and application limited the of here to treatment or the problem to an the either detection limited anomaly are to about location close those and developed work implementation, rather aforementioned possible are the identification While topology [11]. be on [10], has [9], location th in infer and to detection addressed ways fault modem. different while transmitting proposed topology, [8] the network and to [7] back of coming analyzing authors echo The by the always of approach, CTF been the reflectometry have a problems off- using same an The tackled assumes before. th and performed algorithm monitors before training learning second line machine (CTF) the a while function using occurrence, CTF fault transfer the channel after and the of comparison h anamo hsppri opooeafaeokthat framework a propose to is paper this of aim main The eirMme,IEEE Member, Senior of s ein, and ies. nto zes en a- er w y. d a e e e e s s 1 - 2 on the knowledge of the network topology, is proposed to Conversion Digital Filters and Amplification automatically localize the detected anomaly by analyzing the V sensed trace in time domain. Different simulation results are TX1 VS presented that elucidate the differences between reflectometric 1 and end-to-end measurements, ant that show the efficiency of EC Algorithms the proposed algorithms. ~ TX: CIRC - DAC VSI The rest of the paper is structured as follows. Section 1 - - Filters - ~ - Power II is dedicated to the description of the required modem V + + L SOI1 amplis architectures and to the introduction of the proposed sensing V Yin RX1 V PE TX2 technique. Detail considerations about the frequency of the V RX: S2 N sensing events and the appropriate sensing algorithms to use - Power EC amplis are given in Section II-D. Section III presents the proposed - Filters ~ Algorithms anomaly detection and location algorithms. Extensive simula- - ADC CIRC VSI tion results are presented in Section IV and conclusions follow ~ 2 - - V + + in Section V. SOI2 V RX2 II. MONITORING WITH PLMS Fig. 1. Proposed architecture of the full duplex PLM. In this section we summarize relevant background infor- mation and present different measurement architectures to perform network sensing with PLMs. yields the best quantity-to-noise ratio (QNR) is the circulator [15]. In this context, the QNR refers to the ratio between the expected value of Yin or ρin and the noise related to A. Background it, similarly to the more commonly used SNR. The circulator Both reflectometric and end-to-end sensing can be used to has also been proposed as hybrid coupler for IBFD PLC [16], monitor a generic PLN. In particular, with the reflectometric [13]. Therefore, the same modem architecture can be used both approach both the input reflection coefficient ρin and the input for communication and sensing purposes. admittance Yin can be measured, while end-to-end monitoring The IBFD PLM architecture needed for the proposed system is based on the measurement of the CTF H. Monitoring is is depicted in Fig. 1. The system consists of a MIMO PLM performed by comparison of the present measurement with with two transmitting and two receiving channels; the trans- a previous one that refers to an unperturbed state of the mitting and receiving ports of each channel are connected to a network. Based on the model used to describe the effect of the circulator, which is also connected to the power line. The dig- anomaly, the comparison is different: it consists of a division, T ital source signal VS = [VS1 , VS2 ] , where the superscript T if the so called chain model is used, or a subtraction, if denotes the transpose operation, is converted to analog domain, the superposition model is used. The resulting trace presents thus becoming the transmitted signal VTX = VS + NTX, peculiar characteristics that allow us to identify the presence where NTX is the noise introduced by the transmission chain. and the type of the anomaly. When the trace is analyzed in The circulators forward the signal to the PLN and the resulting time domain, it also provides information about the location echo is forwarded to the receiver, such that the received signal of the anomaly. As for the quantity to be measured, ρin does VRX is not provide information when used in combination with the chain model, while it is as informative as Yin when used in VRX = VSI + VSOI + NRX + NPL = VSI + VN, (1) combination with the superposition model. Confronting finally where VSI is the echo signal, also called self interference, the reflectometric and end-to-end approaches, with the first −1 approach it is easier to localize an anomaly, while the second VSI = −Y0 ρinY0VTX approach can better detect anomalies that are far away from −1 −1 = −Y0 ρinY0VS − Y0 ρinY0NTX. (2) the receiver PLM. More details on these outcomes and their derivation using multiconductor transmission line theory can Y0 is the input impedance at the channel port of the circulator be found in [12]. and ρin is defined in [12, Eq. 3]. VSOI is the PLC signal coming from a far-end (·FE), also called signal-of-interest, B. Reflectometric sensing VSOI = HVSFE + NTXFE . (3) Full duplex PLMs are needed to sense Yin or ρin, since NRX is the noise introduced by the receiver stage and NPL both the transmitted and the received signal have to be is the network noise. Since ρin is of interest for reflectometric monitored at the same time. The PLM transceiver can be sensing, it has to be estimated based on the measurement of designed to this purpose using different architectures, based VRX. We remark that Yin is directly derived from ρin as on the environment where the modem will be deployed. Such architectures include classical schemes like circulators, −1 Yin = (I + ρin) (I − ρin) Y0 balanced bridges and current-voltage sensors. A recent article −1 showed that, among the mentioned architectures, the one that = Y0 (VTX − VSI) (VTX + VSI) , (4) 3 where I is the identity matrix. D. Considerations on monitoring methods A series of so called Echo Cancellation (EC) techniques When monitoring a network, particular attention has to be can be used either in the analog [16] or in the digital stage payed both to the sensing signals used and the periodicity [13] of the receiver to estimate ρin, with different accuracy of the sensing events. Regarding the sensing signals, they based on the combination and type of algorithms used. We influence the accuracy of the estimation of H, Yin or ρin in point out that these techniques are already used in full-duplex different ways. In the reflectometric case the sensing signal is PLMs in the PLC context. In fact, in communications the known, but its statistics influences the quality of the estimation receiver is only interested in the signal VSOI, while the echo [22]. In the case of end-to-end sensing, the sensing signals VSI generates a self-interference that hinders the reception of ˜ are represented by the pilot symbols used in communication the far-end signal. Therefore, an estimate VSI of VSI is first protocols. The use of pilots intrinsically yields lower perfor- obtained using the EC algorithms and then it is subtracted from mance than knowing the sensing signal at each subcarrier, as VRX, so that the processing stage receives only VSOI plus in the reflectometric case. Hence, a lower performance in the the network and hardware noises, as in classical half-duplex estimation of H w.r.t. Yin and ρin is in general expected. communications. In the context of network sensing, the same Technical solutions and limitations for the reflectometric and ˜ structure is applied, with a slight difference: VSI is not only end-to-end sensing approaches are summarized in Table I. subtracted from VRX for the communication purpose, but can Regarding the periodicity of the sensing events, it depends also be further processed to detect and localize anomalies, as on the convergence time of the estimation methods used and discussed in Section III. is in general a multiple of the symbol rate. The duration Since the PLC channel is intrinsically linear periodic time of an OFDM symbol in PLC is in the order of hundreds variant (LPTV), with periodicity equal to half the mains of microseconds, while the effect of the shortest anomalous cycle, classical EC algorithms such as the Least-Mean-Squares events, like arching faults, lasts for some tenths of millisec- (LMS) would yield poor results on average. An algorithm onds. This means that a convergence time of tenths to hundreds as already been proposed that tracks channel variations in of symbols is enough to capture the shortest anomalies. The the first mains half cycle and saves the respective state (see status of the PLN at high frequency actually varies as often as [13, Algorithm 1]). From the second half cycle onward, a a couple of OFDM symbols (~1 ms) due to the LPTV behavior separate LMS algorithm is run for each one of the channel of the channel. All these variations are tracked as explained in states. The algorithm is also able to track load impedance Section II-B and are not considered as anomalies, since they variations, which are identified by strong mean square error belong to the normal operation of the network. (MSE) registered both at saved or non-saved symbol indexes. Although using every OFDM symbol for sensing enables In Section III, we present a novel algorithm that enables also high resolution, it is actually needed only to sense anomalies the sensing of faults and cable degradations. that have no permanent effect on the system but can still be a threat, like lightning strikes, arching faults, animal or tree C. End-to-end sensing temporary contact with the line and others. On the other end, the anomalies that cause permanent or lasting damage to the In order to sense H, half-duplex PLMs can be used to network do not require to be sensed with such rate. In this acquire VRX and classical estimation techniques can be used. case, H, Yin or ρin can be estimated at time intervals that When the transmitted signal is known, an LMS algorithm can are considerably greater than the length of a communication be used to estimate H the same way as presented in the pre- symbol. In particular, since typical PLC systems are aware of vious section for VSI and ρin. However, transmitting known the mains cycle period [23], we propose the following: signals results in no communication between the two ends. If we want to maintain a communication link between the two • sensing at symbol level is performed using the techniques modems, pilot-based or even blind CTF estimators [17] have presented above in order to identify temporary anomalies. to be used to estimate H. The type of the transmitted signals We call this symbol level sensing (SLS). has therefore to be chosen in order to keep a balance between • at intervals T that are multiples of half the mains period, high-rate communications and CTF estimation accuracy. PLC the channel is sensed using known values of both VS standards [18], [19] already include a number of pilot carriers and VSFE . We call this mains level sensing (MLS). in the OFDM symbols that are used to perform channel estima- We remark that the estimation techniques used for the SLS tion. Pilots can be arranged in different ways: full pilot carriers are anyhow used anytime a PLM wants to communicate with at regular intervals (block-type), constant carrier indexes over other modems, so the overload generated by sensing is just due time (comb-type) or index swapping in consecutive symbols. to the anomaly detection and location algorithm presented in Block type systems have better convergence than the others in Section III. Since both the end-to-end and the reflectometric linear time invariant systems (LTI), while in the case of LPTV SLS can track the periodic channel variations, the unperturbed systems like PLC channels, comb-type or index swapping situation is also periodic time-varying. Hence, the anomaly systems have been shown to yield better performance (see detection algorithm is run on every new sensing instance with [20], [21] and references therein). respect to the unperturbed measurement relative to the specific We finally remark that an algorithm similar to [13, Algo- sensing instant. rithm 1] can be applied to the estimation of H and it can be As for the second sensing approach, it has two main used to track periodic variations of the channel. advantages: first, by sensing every T mains cycles, we elude 4

TABLE I TECHNICALSOLUTIONS, ADVANTAGES AND LIMITATIONS OF SENSING WITH PLMS.

End-to-end Reflectometry Solutions Pilot-based estimation techniques Adaptive filters based on completely known VS Advantages Use of common half-duplex modems Sensing at symbol level preserving full data rate Limitations Sensing to the detriment of data rate Use of more complex full-duplex modems Not continuous monitoring with block-type pilots Presence of VSOI might hinder estimation accuracy V V Not completely known SFE with comb-type pilots Statistics of S influences the estimation error the time variations of the channel and the resulting system can than the threshold, then an anomaly is detected. Otherwise, be considered LTI. Second, using known signals allows us to A˜ (m,n) is used to update A˜ ref (m,n). reduce the estimation techniques to simple averaging, which When an anomaly is detected, ∂sup(m,t) or ∂ch(m,t) would yield over a significant amount of samples toward null are computed as the inverse Fourier transforms of (5) and estimation error [24]. In fact, all the noise sources, including (6) respectively. Their peaks are detected, either by classical NRX, NTX, VSOI and NPL, can be considered with good peak-detection or super-resolution techniques as presented in Y approximation to have mean zero. Section III-D. The first peak of ∂sup(m,t) tells already the distance of the anomaly from the receiving modem, while H III. ANOMALY DETECTION AND LOCATION an ambiguity remains in the case of ∂sup(m,t). Regarding the type of the fault, a first distinction between localized and In this Section, we present an algorithm that can be used distributed anomalies is made. As shown in [12, Fig. 5,6], to both detect and locate anomalies, as well as distinguish be- a distributed anomaly, conversely from localized anomalies, tween localized faults, load impedance changes and distributed causes a shift in the peaks in frequency domain. Therefore, faults. it is sufficient to test weather the peaks of Yin or Htot are

also present in Yina or Htota respectively to understand if the A. Anomaly detection and classification anomaly is localized or distributed. In the first case, the peak The unperturbed situation is considered to be when, after would be identified in both traces, while in the second case the startup, the estimation algorithms presented in the previous the response will be negative. When the anomaly is identified section converge to a minimum estimation error. It has been as localized, the time domain trace is analyzed. If the position shown in [15], that the noise related to the estimation of ρin of the first peak of ∂sup(m,t) or ∂ch(m,t) coincides with ˜ and Yinis zero mean if VN < VS/10, which is normally the position of a peak of ˜yin or htot respectively, then the the case in PLN. When using adaptive algorithms, subspace anomaly can be a load variation. To confirm this hypotesis, or interpolation techniques with finite impulse response filters we look for the presence of the same peaks after the anomaly ˜ ˜ in presence of noise, the MSE is always lower bounded and in ˜yin or htotand ˜yina or htota . In fact, if the anomaly is a positive. On the other side, the MSE tends to zero when load variation, no new peaks are created in the time domain averaging over a large sample set. response. If this is the case, the anomaly is identified as an In the following, we consider the case of SLS algorithms impedance variation, otherwise it is a fault. The detection and with fixed and finite parameters, such that the MSE converges classification technique is summarized in Algorithm 1. to a minimum MSE∞. For every new estimation step m, we compute the quantity B. Anomaly localization: one sensor ˜ ˜ ∆sup (m,n)= A (m,n) − Aref (m,n) (5) When just one sensor or one sensor pair (in the case of end- or to-end sensing) is available, the distance of an anomaly from −1 the measurement point can be retrieved from the position of ∆ch (m,n)= A˜ (m,n) A˜ ref (m,n) (6) the first peak of ˜ya or h˜a. When the topology of the network depending on weather the chain or the superposition model is known, the relative position of the peaks of ˜ya and h˜a for the anomaly has been chosen [12], where A˜ stands for univocally relates every anomaly to a precise point in the Yin, ρin or H, and A˜ ref (m,n) is a reference value for network, enabling the localization of the anomaly. Consider the unperturbed situation, chosen as a mean of the previous the example of Fig. 2, where a network with a damaged cable estimated values. If at least for one of the n indexes the value section 11.5 km away from the sensing point is considered. of |∆sup| ,|∆ch| is greater than a fixed threshold (we use three The damaged section could be either on branch B2 or B3, but times the standard deviation of A˜ ref (m,n)), then the index we depicted only the B3 case for simplicity. Fig. 2b shows that, nmax of the maximum of (5), (6) is saved. This is because the if the damaged section is in branch B3, then a peak appears value thus found might be caused by impulsive noise, which at 12.4 km, corresponding to the end of the damaged section is common in PLNs. However, if this value is caused by an and another peak appears at 15.95 km, corresponding to the anomaly, in the following iterations a similar value will appear position of the load at the end of the branch. On the other side, at nmax. In order to reduce false positives, few successive if the damaged section is in branch B2, we see a prominent realizations of the increment against the same reference will peak at 12.95 km corresponding to the position of the load be tested. If the value of (5), (6) at nmax is always greater at the end of branch B2. This peak is actually so high that it 5

Algorithm 1 Anomaly detection and classification algorithm Algorithm 2 Anomaly localization algorithm ˜ ˜ Y Require: Yina , Yin Require: peaks[∂sup], type, topology Ensure: Presence of an anomaly, Type of the anomaly Ensure: Position of the anomaly Y Y 1: while maxn ∆sup < thr1 do 1: dan = peaks[∂sup](1) 2: update A˜ ref 2: Compute d 3: transmit a new OFDM symbol 3: if type == impedance variation then Y 4: a = find{d - d < thr} 4: compute maxn ∆sup an 5: end while 5: the impedance variation is on node a 6: an anomaly has been detected 6: else Y 7: find the M branches where the anomaly might be 7: compute ∂sup, ˜yina and ˜yin Y 8: for i=1toM do 8: compute peaks[∂ ], peaks[˜yina ] and peaks[˜yin] sup m m ˜ ˜ 9: compute b = |dˆa − [N1 ,N2 ]| 9: compute peaks[Yina ] and peaks[Yin] ˜ ˜ 10: compute c = min{peaks[∂Y ]- b + dˆ } 10: if max{peaks[Yin]- peaks[Yina ]} > thr2 then sup  a 11: the anomaly is a distributed fault 11: end for Y 12: else if min{peaks[∂sup](1) - peaks[˜yin]} < thr3 then 12: the anomaly is located on the branch with lowest c

13: if max{peaks[˜yin]- peaks[˜yina ]} < thr4 then 13: end if 14: the anomaly is an impedance variation 15: else if the anomaly is a localized fault then 16: end if branch ending might refer to the ending towards the receiver or 17: else the transmitter, while in the reflectometric case it always refers 18: the anomaly is a localized fault to the farther branch ending. All of this would add significant 19: end if complexity to an anomaly localization algorithm. For these reason, the anomaly localization is not treated in this work for the case of end-to-end monitoring. The following algorithm (see Algorithm 2) can be derived to automatically locate an anomaly after it has been detected. When analyzing ˜ya, its first peak provides an estimate dˆa of the distance of the anomaly from the sensing point. If the anomaly is identified as a load impedance change, then the branch is directly identified in the hypothesis that the network is asymmetric and there are no nodes equally distant from the (a) sensing point, which is common in PLN. If the anomaly is identified as a lumped fault or a distributed anomaly, then in a 0.15 Damaged cable in branch 3 X: 1.295e+04 first step all the M possible branches where the anomaly can Y: 0.1552 Damaged cable in branch 2 be located are identified. The distance d between all the nodes X: 1.595e+04 0.1 Y: 0.0888 and the receiver is also computed. Subsequently, for each of the M possible branches, the difference b between dˆa and 0.05 the nodes N m and N m at the extremities of the mth branch X: 1.15e+04 X: 1.24e+04 1 2 Y: 0.01931 Y: 0.01676 is computed. This step allows to identify the distance of the 0 first few peaks after dˆa is the fault is in branch m. The result 0 0.5 1 1.5 2 a distance [m] 104 is subtracted from ˜y , to check weather the guessed peaks (b) correspond to the measurement. Finally, the branch with the lowest result is selected as the estimated anomaly branch. Fig. 2. Example of a simple network with a damaged section: a) sketch and b) estimated admittance variation when the damaged section is on branch 2 or 3. C. Anomaly localization: multiple sensors In the case of multiple sensors, different techniques can be hides the peak at 12.4 km generated by the end of the damaged applied. The simplest one is based on geometric considera- section. Besides, we notice that the peaks corresponding to tions: the information about the position of the first peak of the network loads are located nearer to the sensing point as Y˜ a or H˜ a coming from multiple sensors is fused to select the expected in an unperturbed situation. As explained in Section point that has the expected distance from each sensor. If the III, this is a clear sign that the detected anomaly is a distributed network is not symmetric, two sensing points are, in the case fault. This example shows that, in the reflectometric case, it is of reflectometry, enough to univocally determine the branch sufficient to analyze few peaks after the first to understand in where the anomaly has occurred. In the case of end-to-end which branch an anomaly is located. The end-to-end sensing sensing, the presence of multiple modems also removes the case is more complex, as explained in [12]. In fact, the first intrinsic ambiguity of the estimated distance from the receiver. peak of h˜a cannot tell weather the corresponding distance is We point out that two-way end-to-end sensing (i.e. a signal is from the transmitter or the receiver; the first peak caused by a transmitted from one modem to the other and a response is 6

immediately sent back to the first one) is not sufficient to solve TABLE II the position ambiguity; at least a third modem is needed. PARAMETERS USED FOR THE SIMULATION Geometric considerations are reliable in the case of MLS, Parameter Value but when it comes to SLS, the anomaly needs to be localized Frequency 4.3 kHz - 500 kHz span, 4.3 kHz sampling [18] in a short time frame, therefore all the sensors might need to Network noise According to [18, Annex D.3] perform the measurement at the same time. In this case, there Transmitter noise -50 dBc (10 bit DAC, OFDM [29]) Receiver noise -60 dBc (12 bit ADC, OFDM [29]) is a problem of interference between the sensors, which can Transmitted power According to [18, Ch. 7] be alleviated by using sensing signals that are orthogonal to Number of nodes 20 each other [25]. Average branch length 900 m [30] Other approaches implementable with PLMs are based on Load value According to [18, Annex D] the decomposition of the time reversal operator (DORT) [26]. These approaches are specifically designed to detect and localize very weak faults along the network, but they need 0 0 a simulator with a complete topological and electrical model -2 of the network in order to work. The scattering matrix of the -5 -4 network is measured before and after the fault. The DORT is -10 afterwards applied to find an optimum set of signals, whose -6 transmission is then simulated on the test network. The energy [dB] [dB] -15

failure -8 failure p p of this optimum signals will focus on the position of the Y Y 1-1 sup sup -20 1-1 anomaly. -10 sup sup H H 1-1 sup sup Y Y 1-2 -25 sup -12 ch 1-2 ch sup H H 1-2 D. Spectral analysis ch sup -14 -30 5 10 15 5 10 15 As we explained in the previous section, locating an distance from the receiver [km] distance from the receiver [km] anomaly basically turns into finding a series of peaks in the (a) (b) time domain response. Due to band limitations in communi- Fig. 3. pfailure when measuring Yin, ρin and Htot. a) Comparison of the cation systems, especially in PLC, the resolution might not be superposition and chain models, b) comparison of SISO and MIMO sensing. sufficient to separate close peaks or might provide a too loose estimation of a peak position. However, when the transfer function of a system can be represented as a sum of weighted we tune the simulator to displace the nodes with average exponentials, subspace methods can be applied. This is the distance of 900 m, which mimics the average displacement case of H, Yin or ρin, as explained in [12, Eq. 17, 18, 27]. in a low voltage distribution network, or a medium voltage Such methods are used to better detect and locate the presence underground distribution network. of peaks, since they can achieve super-resolution [27]. In this An anomaly in the form of a lumped impedance or a cable research work, we applied different subspace algorithms [27], branch with modified parameters can be inserted in any point [28] to the anomaly localization problem. Among all, the root- of the network. The simulator computes Yin, Yin ,ρin, ρin Music method [28] provided the best performance. However, a a at every node and Htot, Htot between every node pair. As when many peaks have to be detected, their amplitude varies a for the PLM impedance, we consider the optimum conditions greatly, and the signal bandwidth is sufficiently wide, we found for reflectometry and end-to-end transmission. In the first case, that peak-location algorithms can identify more peaks than Y0 is equal to YC of the cable to which the PLM is branched. subspace methods, even though the resolution is lower. In the second case, the output impedance of the transmitter is In the anomaly detection and localization problem it is fixed to 1Ω and the input impedance of the receiver is fixed more important to identify a peak than to precisely localize it. to 100 kΩ as typical in half-duplex PLMs. Therefore, peak-location algorithms are preferred in this paper As for the noise and signal powers, we use standard levels over subspace algorithms. for PLC as specified in [15] if not otherwise stated. We finally assume the noise introduced by the PLM coupler (hybrid and IV. RESULTS transformer) to be negligible with respect to the other noise In this Section, we present some results obtained by sim- sources. ulation that show the performance in detecting and locating Finally, in the following we do not make use of a specific EC anomalies of the discussed algorithms. algorithm in the reflectometric case or a specific interpolation filter in the end-to-end case, but we rather model the effect of the overall error when estimating ρin or Htot on the A. Simulation Setup performance of the anomaly detection and location algorithms. We developed an MTL PLN simulator using the equations presented in [12, Sec. 1]. Such simulator randomly displacesa given number of nodes on a given surface and connects them B. Comparison of models and measurement types taking into account a maximum node degree (i.e. the number As explained in Section III, there are different ways to of branches connected to a node). If not otherwise specified, detect the presence of an anomaly with PLMs. It is possible 7

to estimate Y˜ in, ρ˜in or H˜ tot, using either the superposition or the chain models, which lead to the computation of |∆sup| 1 1 or |∆ch| respectively. We simulated the presence of a fault 0.9 0.9 in 2000 random networks and computed in each case the 0.8 0.8 noise distributions of |∆sup|and |∆ch| for the three considered 0.7 0.7 physical quantities, both in the presence and absence of 0.6 0.6 the anomaly. By integrating over the overlapping areas of 0.5 0.5 success success p p the distributions, we computed the probability pfailure of 0.4 0.4 not detecting the anomaly and, vice-versa, of detecting a 0.3 0.3 normal measurement as anomalous. We remark that the values 0.2 Unperturbed 0.2 Unperturbed Load impedance change Load impedance change Concentrated fault Concentrated fault 0.1 0.1 of pfailure are not important per-se, since they depend on Distributed fault Distributed fault Generic anomaly Generic anomaly multiple factors. Herein, we focus on the relation of the values 0 0 5 10 15 20 25 -80 -60 -40 -20 of pfailure obtained with different methods. nodes QNR [dB] The results of Fig. 3 show pfailure as function of dˆa in (a) Noise fixed (see Table II) (b) 10 nodes all the aforementioned cases. Fig. 3a shows that the lowest Fig. 4. Probability of correctly detecting and identifying an anomaly. values of pfailure are reached when estimating H˜ tot, followed by ρ˜in and then Y˜ in, independently of the model used. This is related to the fact that the presence of anomalies yields a greater variation in H˜ tot than in Y˜ in, while ρ˜inis statistically 1 1 more scattered (cfr. [12, Fig. 7]). Regarding the reliability of 0.9 0.9 0.8 0.8 the models, Fig. 3a shows that the difference in pfailure when 0.7 0.7 using |∆sup| or |∆ch|is not very pronounced. However, the chain model constantly yields slightly better results than the 0.6 0.6 0.5 0.5 superposition model. success success p p Fig. 3b shows the performance increment obtained when 0.4 0.4 0.3 Load impedance change 0.3 Load impedance change using MIMO instead of SISO measurements. We consider Concentrated fault Concentrated fault 0.2 Distributed fault 0.2 Distributed fault a fault placed between a couple of conductors in a three- Generic anomaly Generic anomaly Concentrated fault - 1 node 0.1 0.1 Concentrated fault - 1 node Distributed fault - 1 node Distributed fault - 1 node wire network. The 1 − 1 symbol stands for a signal that Generic anomaly - 1 node Generic anomaly - 1 node 0 0 has been sent on two non-faulted conductors and received 5 10 15 20 25 -80 -60 -40 -20 nodes QNR [dB] on the same pair. The 1 − 2 symbol stands for a signal that has been injected on the pair of conductors interested by the (a) Noise fixed (see Table II) (b) 10 nodes fault and received on the other. The figure shows that, if the Fig. 5. Probability of correctly locating a detected anomaly. anomaly is detected using a SISO modem placed between the non-faulted conductors, pfailure is greater than analyzing the cross-coupling transfer function with a MIMO modem. This is Fig. 4 shows the performance of Algorithm 1 for varying particularly true when considering admittance measurements, network size and QNR, respectively. We considered the prob- while almost no performance increment is obtained when ability of correctly detecting and classifying the unperturbed estimating H˜ tot. This result highlights the importance of using situation and the three considered anomalies. We also consid- MIMO PLC modems when sensing power line networks. ered the probability of detecting a generic anomaly without classifying it. The results show that the proposed algorithm C. Performance of the proposed algorithms yields high values of psuccess for every kind of anomaly when the network is very small. With increasing size of the In this section, we evaluate the performance of Algorithm 1 network, the performance of the concentrated fault case does and 2, focusing on the estimation of Y˜ in. To this purpose, not significantly change while it decreases considerably in the we simulate the presence of different kind of anomalies case of distributed faults. Fig. 4b shows that the algorithm is in networks of different sizes and compute the probability rather resilient to noise up to values of QNR of -30 dB, with p of correctly detecting, classifying or locating an success the exception of the concentrated fault case. Low values of anomaly. Moreover, in order to simulate the effect of a generic QNR tend not to increase the performance of the algorithm estimation algorithm, we also run a simulation where the noise either. This suggests two observations: on one side, it is not parameters of Table II are no longer used. Instead, we directly needed to implement estimation algorithms that yield very set the estimation error by modifying the QNR, defined as [15] low values of QNR; on the other side, most of the error 2 |X0| is due to the topological structure of the network and how QNR = , (7) 2 the detection algorithm copes with it. Therefore, better results E |X | h N i can be achieved by improving the detection and classification where E [· ] is the expectation operator, X = X0 + XN can algorithm. be either Yin, ρin, or Htot, and the subscripts 0 and N stand Coming to the performance of Algorithm 2 regarding the for the mean value and the noisy component of the estimated location of anomalies, Fig. 5 shows the probability of correctly quantity. identifying the branch where an anomaly has occurred, when 8

it has been correctly identified. In this case, both the size of the [7] M. Ahmed and L. Lampe, “Power line network topology inference using network and the QNR have a significant impact on the results. frequency domain reflectometry,” in Communications (ICC), 2012 IEEE International Conference on, June 2012, pp. 3419–3423. In fact, psuccess almost linearly decreases with the number of [8] F. Passerini and A. M. Tonello, “On the exploitation of admittance mea- nodes and is resilient to noise only up to a QNR of around -50 surements for wired network topology derivation,” IEEE Transactions on dBm. The distributed fault case is more flat than the others, Instrumentation and Measurement, vol. 66, no. 3, pp. 374–382, March 2017. but this is due to the fact that the detection probability already [9] ——, “Power line fault detection and localization using high frequency decreases significantly with the size of the network. In Fig. 5 impedance measurement,” in 2017 International Symposium on Power we also plotted the probability of identifying the first node of Line Communications and its Applications (ISPLC), April 2017. [10] A. Milioudis, G. Andreou, and D. Labridis, “Detection and location the branch where the anomaly has occurred (there might be of high impedance faults in multiconductor overhead distribution lines more ramifications). The results are in this case significantly using power line communication devices,” IEEE Transactions on Smart better, especially for the distributed fault case. This means that, Grid, vol. 6, no. 2, pp. 894–902, March 2015. [11] A. M. Pasdar, Y. Sozer, and I. Husain, “Detecting and locating faulty even though the exact branch might not be identified, the set nodes in smart grids based on high frequency signal injection,” IEEE of possible faulted branches is significantly reduced. Transactions on , vol. 4, no. 2, pp. 1067–1075, June 2013. Finally, we remark that the results presented in this paper [12] F. Passerini and A. M. Tonello, “Smart grid network sensing using power line modems: Effect of anomalies on signal propagation,” Submitted to refer to Algorithms 1 and 2 applied to networks with random IEEE Transactions on Smat Grids, 2018, available on arXiv. topologies. If the algorithms had to be applied to specific [13] G. Prasad, L. Lampe, and S. Shekhar, “In-band full duplex broadband topologies or topological classes, then they could be better power line communications,” IEEE Transactions on Communications, vol. 64, no. 9, pp. 3915–3931, Sept 2016. tailored to the specific situation an yield better results. [14] L. Lampe, A. M. Tonello, and T. G. Swart, Eds., Power Line Commu- nications: Principles, Standards and Applications from Multimedia to Smart Grid. Wiley, 2016. V. CONCLUSIONS [15] F. Passerini and A. M. Tonello, “Analysis of high-frequency impedance measurement techniques for power line network sensing,” IEEE Sensors In this paper, we presented a framework to deploy power Journal, vol. 17, no. 23, pp. 7630–7640, Dec 2017. line communication modems as power grid sensors, exploiting [16] ——, “Adaptive hybrid circuit for enhanced echo cancellation in full their ability to transmit sensing signals and to acquire them. duplex PLC,” in 2018 IEEE International Symposium on Power Line Communications and its Applications (ISPLC), April 2018. We described the modem architectures needed for sensing [17] A. Musolino, M. Raugi, and M. Tucci, “Cyclic short-time varying chan- and evaluated different options to estimate H, Yin and ρin. nel estimation in OFDM power-line communication,” IEEE Transactions We proposed two monitoring techniques, namely the symbol on Power Delivery, vol. 23, no. 1, pp. 157–163, Jan 2008. [18] IEEE Standard for Low-Frequency (less than 500 kHz) Narrowband level sensing and mains level sensing, that allow to monitor Power Line Communications for Smart Grid Applications. IEEE different types of anomalies. In this regard, we proposed two 1901.2-2013, 2013. algorithms that start from the estimated channel response at [19] IEEE Standard for Broadband over Power Line Networks: and Physical Layer Specifications. IEEE 1901-2010, different time instants and are able to detect, classify and locate 2010. an anomaly. The results show that correctly identifying and [20] A. A. M. Picorone, T. R. Oliveira, and M. V. Ribeiro, “PLC channel locating an anomaly does not depend much on the size of estimation based on pilots signal for ofdm modulation: A review,” IEEE Latin America Transactions, vol. 12, no. 4, pp. 580–589, June 2014. the network or on the noise, but rather on the topology of [21] S. Coleri, M. Ergen, A. Puri, and A. Bahai, “Channel estimation tech- the network and how it is taken into account by the detection niques based on pilot arrangement in ofdm systems,” IEEE Transactions and localization algorithms. The performance of the proposed on Broadcasting, vol. 48, no. 3, pp. 223–229, Sep 2002. [22] S. Haykin, Adaptive Filter Theory (3rd Ed.). Upper Saddle River, NJ, algorithms encourages further endeavors in the area of grid USA: Prentice-Hall, Inc., 1996. monitoring with power line communications. [23] H. A. Latchman, S. Katar, L. W. Yonge, and S. Gavette, Homeplug AV and IEEE 1901: A Handbook for PLC Designers and Users. John Wiley & Sons, Inc., 2013. [Online]. Available: REFERENCES http://dx.doi.org/10.1002/9781118527535 [24] S. Kay, Fundamentals of Statistical Signal Processing - Estimation [1] A. von Meier, E. Stewart, A. McEachern, M. Andersen, and Theory. Prentice-Hall, 1993. L. Mehrmanesh, “Precision micro-synchrophasors for distribution sys- [25] A. Lelong, L. Sommervogel, N. Ravot, and M. O. Carrion, “Distributed tems: A summary of applications,” IEEE Transactions on Smart Grid, reflectometry method for wire fault location using selective average,” vol. 8, no. 6, pp. 2926–2936, Nov 2017. IEEE Sensors Journal, vol. 10, no. 2, pp. 300–310, Feb 2010. [2] T. Erseghe, S. Tomasin, and A. Vigato, “Topology estimation for smart [26] M. Kafal, A. Cozza, and L. Pichon, “Locating multiple soft faults in wire micro grids via powerline communications,” Signal Processing, IEEE networks using an alternative dort implementation,” IEEE Transactions Transactions on, vol. 61, no. 13, pp. 3368–3377, July 2013. on Instrumentation and Measurement, vol. 65, no. 2, pp. 399–406, Feb [3] M. O. Ahmed and L. Lampe, “Power line communications for low- 2016. voltage power grid tomography,” IEEE Transactions on Communica- [27] P. Stoica and R. Moses, Spectral Analysis of Sig- tions, vol. 61, no. 12, pp. 5163–5175, Dec. 2013. nals. Pearson Prentice Hall, 2005. [Online]. Available: [4] A. M. Lehmann, K. Raab, F. Gruber, E. Fischer, R. Müller, and J. B. https://books.google.at/books?id=h78ZAQAAIAAJ Huber, “A diagnostic method for power line networks by channel [28] A. Barabell, “Improving the resolution performance of eigenstructure- estimation of plc devices,” in 2016 IEEE International Conference on based direction-finding algorithms,” in ICASSP ’83. IEEE International Smart Grid Communications (SmartGridComm), Nov 2016, pp. 320– Conference on Acoustics, Speech, and Signal Processing, vol. 8, Apr 325. 1983, pp. 336–339. [5] L. Förstel and L. Lampe, “Grid diagnostics: Monitoring cable aging [29] C. R. Berger, Y. Benlachtar, R. I. Killey, and P. A. using power line transmission,” in 2017 IEEE International Symposium Milder, “Theoretical and experimental evaluation of clipping and on Power Line Communications and its Applications (ISPLC), April quantization noise for optical ofdm,” Opt. Express, vol. 19, 2017. no. 18, pp. 17 713–17 728, Aug 2011. [Online]. Available: [6] F. Yang, W. Ding, and J. Song, “Non-intrusive power line quality http://www.opticsexpress.org/abstract.cfm?URI=oe-19-18-17713 monitoring based on power line communications,” in 2013 IEEE 17th [30] G. A. Pagani and M. Aiello, “Power grid network International Symposium on Power Line Communications and Its Ap- evolutions for local energy trading,” 2012. [Online]. Available: plications, March 2013, pp. 191–196. https://arxiv.org/abs/1201.0962