Data-Driven Incident Detection in Power Distribution Systems
Nayara Aguiar, Vijay Gupta, Rodrigo D. Trevizan, Babu R. Chalamala, Raymond H. Byrne
DData-Driven Incident Detection in PowerDistribution Systems
Nayara Aguiar, Vijay Gupta
Department of Electrical EngineeringUniversity of Notre Dame
Notre Dame, IN, USA { ngomesde,vgupta2 } @nd.edu Rodrigo D. Trevizan, Babu R. Chalamala
Energy Storage Technology & SystemsSandia National Laboratories
Albuquerque, NM, USA { rdtrevi,bchalam } @sandia.gov Raymond H. Byrne
Electric Power Systems ResearchSandia National Laboratories
Albuquerque, NM, [email protected]
Abstract —In a power distribution network with energy storagesystems (ESS) and advanced controls, traditional monitoring andprotection schemes are not well suited for detecting anomaliessuch as malfunction of controllable devices. In this work, wepropose a data-driven technique for the detection of incidentsrelevant to the operation of ESS in distribution grids. Thisapproach leverages the causal relationship observed amongsensor data streams, and does not require prior knowledge of thesystem model or parameters. Our methodology includes a dataaugmentation step which allows for the detection of incidentseven when sensing is scarce. The effectiveness of our techniqueis illustrated through case studies which consider active powerdispatch and reactive power control of ESS.
Index Terms —Energy storage systems, incident detection,power distribution systems.
I. I
NTRODUCTION
Power Distribution Systems (PDS) have been historicallydesigned to transport power from the bulk transmission systemto end consumers of electricity. However, the recent increasein the adoption of Distributed Energy Resources (DERs) hasstarted to shift this paradigm, with consumers and utilitiesleveraging these resources at increasing rates. This highpenetration of DERs in PDS will create multiple technicalchallenges associated with new operating characteristics suchas bidirectional power flows and voltage fluctuations due to thevolatility of renewable power generation. Specifically, in a dis-tribution system with Energy Storage Systems (ESS), renew-able generation and advanced controls, traditional monitoringand protection schemes are not well suited for detecting faults,changes in topology, and malfunction of controllable devices.Furthermore, the methods that rely on accurate measurementsand knowledge of parameters currently used in transmissionsystems, such as traditional power system state estimation,are inadequate for monitoring in PDS. Thus, it is essential todevelop new methodologies to detect abnormities in PDS dueto critical events (e.g., natural disasters, physical and cyber-attacks) and to mitigate the consequences of these abnormities.Classical approaches for incident detection in the transmis-sion grid rely on some knowledge of the system model. Forexample, the integer programming approach in [1], compres-sive sensing based approach in [2], quickest change detection
SANDXXXXX2020 method in [3], and the Gauss-Markov graphical model in [4]all rely on some knowledge of grid parameters and of theassets connected to the grid. As compared to works that studythe transmission system, the body of literature that considersincident detection in the distribution grid is not as large.Despite the differences between both grids, such as the factthat distribution grid models are little known and sensing isscarce, studies that aim to detect events in the distribution gridstarted by also assuming knowledge of the network topology,such as in graph-based techniques and methods based ontraveling waves (see [5] for a review of methods for faultand outage area detection in distribution grids). With theintroduction of PMUs, data-driven techniques started receivingmore attention, as in the case with SVD-based approaches [6].However, most of the focus has still been on the transmissiongrid, where sensing is more abundant and uniform. When itcomes to distribution grids, an increase in the use of microPMUs and AMIs has been observed, but the existence ofheterogeneous sources of data has also posed challenges.Our proposed approach draws on Koopman operator theory,which accounts for the causal relationship among multiplesensor data streams without prior knowledge of the dynamicmodel. The major feature of the proposed approach lies on thedetection of events which produce sharp changes in the causalmap of the system dynamics, while being robust to smallvariations such as measurement noise and load fluctuation.Koopman operators have been explored in the power systemsliterature for the identification of system dynamics, stabilityassessment, and other topics [7]–[11]. In this work, we proposean algorithmic approach that provides evidence of the effec-tiveness of this operator in incident detection tasks relevantto distribution systems. We also tackle the issue of sensoravailability by proposing a way to augment the dataset througha transformation that computes the relationship between datastreams. Our case studies explore the detection of incidents inESS operation that relates both to active power dispatch andreactive power control, while accounting for the presence ofmeasurement noise and load fluctuations.The remainder of this paper is organized as follows. Weintroduce the Koopman operator theory in Section II, presentthe proposed algorithm for incident detection in Section III,and detail the steps in the methodology for incident detection a r X i v : . [ ee ss . SP ] F e b n Section IV. Section V presents two representative casestudies which exemplify the use of the proposed algorithm,and concluding remarks are presented in Section VI.II. K OOPMAN O PERATOR T HEORY P RELIMINARIES
Consider a nonlinear system with states x t ∈ R n whosedynamics can be characterized by x t +1 = F ( x t ) . (1)The Koopman operator K is a linear infinite-dimensionaloperator that acts on the space of observables g ( x ) : R n → R ,i.e. the space of scalar-valued functions of the states of thesystem, as follows: K g ( x ) = g ( x ) ◦ F . (2)The map F can be described as a linear combination of theeigenfunctions of the linear infinite-dimensional operator K .Then, the evolution of the state becomes a linear combinationof independent dynamics along each eigenfunction. Assumethat the dominant eigenfunctions are roughly in the span ofthe D dictionary functions Ψ = (Ψ , ..., Ψ D ) T . (3)Then, the dynamics of F becomes roughly linear if liftedto a space in which the functions in Ψ are roughly takenas coordinates. This linear description is characterized by K ∈ R D × R D , which is a finite-dimensional approximationof the Koopman operator. An observable g ( x ) in the spanof dictionary functions identified by weights b is given by g ( x ) = Ψ ( x ) T b . Under the action of the Koopman operator,this observable can be approximated as g ( F ( x )) ≈ Ψ ( x ) T K b. (4)Techniques such as the Extended Dynamic Mode Decom-position (EDMD) algorithm proposed in [12] provide a wayto calculate an approximation of the Koopman operator byminimizing || Ψ ( F ( x )) T b − Ψ ( x ) T K b || for an arbitrary b .Let ( x , x ) , ..., ( x M , x M +1 ) be a time-series data. The mini-mization problem of interest is equivalent to min K∈ R D × R D || A − G K|| F , (5)where || . || F is the Frobenius norm, and A and G are defined as A := 1 M M (cid:88) j =1 Ψ ( x j ) Ψ ( x j +1 ) T , G := 1 M M (cid:88) j =1 Ψ ( x j ) Ψ ( x j ) T . (6)III. A LGORITHM FOR I NCIDENT D ETECTION
In this work, we leverage a sparsity-promoting variant ofthe EDMD algorithm [13] for the detection of incidents in thedistribution grid, given by min K∈ R D × R D || A − G K|| F + λ || vec ( K ) || . (7) For our algorithm, we consider the following notation. Fortime-series data x and t ≤ t , define x [ t : t ] := ( x t x t +1 , ..., x t ) . (8)At time t , let A [ t − T : t ] and G [ t − T : t ] be computedwith T + 1 observations and their one-step propagation in theobserved data series x [ t − T : t ] .Our goal is to maintain a sparse representation of thedynamic system, and detect incidents by detecting changesin this sparsity pattern. For that, we build on (7) to define ouralgorithm for incident detection as follows: • At time t = T + 1 , compute K t by solving min K t ∈ R D × R D || A [1 : T +1] − G [1 : T +1] K t || F + α || vec ( K t ) || . (9) • From t = T + 2 onward, compute K t by solving min K t ∈ R D × R D || A [ t − T : t ] − G [ t − T : t ] K t || F + α || vec ( K t ) || + β ||K t − − K t || F . (10) • If the sparsity pattern of K t differs significantly fromthat of K t − , flag the occurrence of an incident that hasaltered the causal map between a state and its one-steppropagation.The sparsity pattern of each K encodes the causal relation-ship among observables, and the level of sparsity is adjustedby the choice of the hyper-parameter α . Small values of α define more complete networks, while large values promotesparsity. The hyper-parameter β is related to the smoothnessof transitions. Thus, larger values of β tend to stabilize K alonga trajectory, making its less prone to change due to smallervariations which do not lead to major structural changes.IV. M ETHODOLOGY FOR I NCIDENT D ETECTION
Our methodology can be divided into two distinct parts, asillustrated in Fig. 1. The first part consists of a data collectionstep, followed by a data transformation. The transformed datais then used to compute the K matrices using the slidingwindow approach introduced in Section III. The second part isa post-processing clustering task which performs a clusteringanalysis with the goal of grouping the K matrices calculatedinto clusters that are uniquely identified by one of the scenariossimulated in the data collection step. Each part of this approachis discussed in more detail in the next sections. A. Part 1: Koopman Operator1) Data Collection:
We begin by selecting suitable simu-lation scenarios from which our data will be gathered. Sinceour focus is on incidents related to the operation of ESS inthe distribution grid, the following two broad types of eventswere considered:1) Changes in ESS charging/discharging rate: In distribu-tion systems, ESS can be used for peak-shaving opera-tions, absorption of excess local renewable production,and other tasks which involve a coordinated charg-ing/discharging schedule. We aim to analyze whether ig. 1. Two-part methodology developed for the detection of incidents indistribution grids. changes in the charging/discharging rates of ESS canbe identified with our proposed framework. Detectingsuch changes would allow us to recognize, for example,when a battery fleet is no longer following the commandissued for their power supply/absorption operation.2) Changes in ESS controller parameters: Voltage regula-tion is an important task in power distribution systems,especially with the increasing adoption of DERs. Byconsidering a scenario in which batteries offer voltageregulation services, we model Volt/VAR curves to con-trol the reactive power output of these devices. Thegoal is to detect changes in controller parameters, whichcould have been caused by attacks that aim to destabilizethe grid.We assume the data collected comes from PMUs, and thuswe use voltage magnitude and phase measurements. The datawas collected with a 0.25s sampling time. Because sensormeasurements are typically noisy, Gaussian noise was added tothe voltage magnitude ( ± . ) and voltage angle ( ± . °)measurements. Further, considering that sensing capabilitywould be limited in the distribution grid, we assumed thatonly nodes with an ESS had PMUs. These scenarios weresimulated using OpenDSS.
2) Data Transformation:
We hypothesize that the relation-ship between different time-series data carries more informa-tion than individual data streams. In [14], this dependenceamong observations is explored in a data-driven spectralanalysis using the Koopman operator with the objective ofunderstanding complex biological network dynamics. For thispurpose, using a ballgame as an example, the authors trans-formed the data using the Gaussian kernel g ( x i , x j ) = exp (cid:18) − || x i − x j || σ (cid:19) , (11)where each x i is a stream of raw data, || . || is the Euclideannorm, and σ is an adjustment parameter.We apply (11) to the distribution grid data to be used inour analysis. This nonlinear transformation lifts the data intoa higher dimensional space by giving a measure of similaritybetween states, thus augmenting our dataset. The transformed data is then used to compute a sequence of K matrices througha sliding window.
3) Approximate Koopman Operator:
In this step, the finite-dimensional approximation of the Koopman operator for thetransformed data was performed numerically following thesteps detailed in Section III. Significant changes in K indicatesaltered causality in states (i.e., occurrence of incidents). Radialbasis functions of the form Ψ i ( x ) = || x − c i || log e ( || x − c i || ) , (12)where c i are unique center points, have shown to be effectivefor our application. We face the following trade-off whenchoosing the amount of dictionary functions to be used:too few dictionary functions Ψ i ( x ) may lead to poorer dis-tinguishability of the sparsity pattern of K ’s from differentincidents; increasing the amount of functions, however, alsoincreases computational time. B. Part 2: Offline Clustering
The previous step was aimed at generating data for differentcase studies, transform the data collected, and compute theapproximate Koopman operator for multiple time windows.The offline clustering task performs a clustering analysis inthe K matrices calculated. Since the sparsity pattern of thesematrices is expected to be similar if the system dynamics re-mains the same, this analysis is expected to cluster together the K ’s coming from the same simulated scenario. For example,the matrices calculated from a scenario in which a battery fleetis discharging at 25% rate should be clustered together, while K ’s from a scenario where these batteries are discharging at100% should be together but in a different cluster.We used the k-means clustering algorithm for this analysis.The idea behind k-means is that observations within a clusterare close to each other, while observations in different clustersare far apart. This method takes as inputs a distance measure,the number of clusters, the data to be clustered, and a randomseed that is used to initialize the algorithm. For our application,the correlation distance was shown to perform better than othermetrics. Further, prior to the clustering analysis, the K matriceswere transformed into binary matrices, i.e. values below acertain threshold were set to zero and all others were set toone. The purpose behind this transformation is that we areonly concerned with the sparsity pattern of these matrices,and not with the actual values of their elements. This stepalso avoids numerical issues that may arise when workingwith small numbers. Since the approximate Koopman operatoris a representation of our original data in a high-dimensionalspace, it is common to see elements of K which have a reallysmall order of magnitude. The effectiveness of our results isevaluated based on the misclassification rate achieved in thisclustering analysis. V. C ASE S TUDIES
We considered the IEEE 8500-node test feeder with 7 bat-tery energy storage systems (BESS) added, implemented usingOpenDSS. This feeder is an unbalanced radial network, whichre typical characteristics of distribution grids. These BESScan take real power dispatch commands and perform Volt/VARcontrol. The data was collected with a 0.25s sampling time,and Gaussian noise was added to the voltage magnitude( ± . ) and voltage angle ( ± . °) measurements. Besidesnoise, fluctuations in real and reactive load were consideredin the feeder model. Our aim is to evaluate the robustness ofour algorithm when these variations are accounted for.As previously discussed, changes in the sparsity pattern ofthe K matrices indicated the occurrence of an incident. Toconfirm the K matrices had unique sparsity patterns for eachscenario in which the causality of the model was maintained,an offline analysis was performed using k-means clusteringto cluster these matrices. For both case studies, the centersfor the radial basis functions c i in (12) were chosen in thecomputation of the first K matrix, and then kept constantthroughout the experiment. The center points were selectedusing a randomly generated perturbation, so that they were ofthe same order of magnitude as the data itself. Further, we used D = 400 dictionary functions, a time window of T = 100 s ,and a new K was estimated every s . We also assumedvoltage magnitude and phase measurements from PMUs wereavailable at the nodes of 3 of these BESS. A. Detecting changes in discharging rates
We first consider a scenario in which the battery fleet isinitially idle. After 5min, all the batteries start dischargingat 50% of their discharging rate, maintaining this rate for5min. Fig. 2 shows the results for this case. For the Koopmanoperator approximation step, we let α = 0 . and β = 0 . . Fig. 2. Results for case study which aims to detect changes in the rate atwhich the battery fleet supplies active power to the grid.
The red numbers in Fig. 2 mark the time instants at whicha new K matrix was estimated. The plots on top show arepresentative sparsity pattern for each of the two situationsconsidered, and we can clearly observe that this patternchanges after the incident happens, allowing us to successfullydetect its occurrence. To corroborate that the two patterns areindeed distinct, all the 20 K matrices computed were subjectedto a clustering analysis using k-means. For this case study, wehave two different clusters: the first representing our networkdynamics when the batteries are idle, and the second related to the case in which the battery fleet discharges at 50% oftheir rate. As a result, we found that 3 of these matriceswere misclassified, i.e. they were classified to the cluster thatdoes not correspond to the scenario they actually refer to.We note that the misclassified matrices, highlighted in Fig. 2,were computed immediately after the event occurred. Dueto the sliding window approach, their computation used datafrom both the first and the second scenarios, which impactstheir sparsity pattern. However, the matrices after those werecorrectly classified. Thus, we can state that some time may beneeded after the event for the new sparsity pattern to stabilize.We remark that the results were robust to measurement noise,as well as load variations, since these fluctuations did notlead our algorithm to erroneously identify the occurrence ofnonexistent incidents. B. Detecting changes in controller parameters
In this case study, we considered the battery fleet providesvoltage regulation services. For this purpose, the hierarchicalVolt/VAR (VV) control strategy proposed in [15] is used tocontrol the reactive power supply/absorption of these devicesso that the voltage magnitudes are maintained close to theirnominal value. Each battery is assigned a VV curve, which isdesigned to adjust the reactive power of the device accordingto measured local voltage levels. An example of this curveis shown in Fig. 3 [15]. The VV curve has a deadbandcorresponding to acceptable voltage levels which do not triggercontrol action for correction. When voltage levels becomehigh, the battery absorbs reactive power to lower the voltageback to acceptable levels. The opposite happens when voltagelevels are low, with the batteries injecting reactive power intothe grid. This control layer is local, as each device does nothave information about the overall system condition, and onlyresponds to their local condition.
Fig. 3. Example of VV curve and shifting logic [15].
To overcome this limitation and expand the control strategyto regulate voltage levels throughout the network, a centralizedcontrol layer is added. This layer has full information aboutthe voltages over the entire feeder, and is able to dispatchnew VV curves to the devices with the goal of regulating theoverall voltage in the system, even when the device’s localvoltage magnitude is within acceptable ranges. Fig. 3 showsan example of how the initial VV curve assigned to a batterycan be shifted using the proposed centralized strategy. We notehat shifting the curve to the left induces an increase in reactivepower absorption, which helps decreasing voltage levels moresignificantly across the network. The reverse holds for rightshifts in the curve.Using this hierarchical VV control, we modeled two eventsfor this case study, leading to a total amount of three dif-ferent scenarios. For each event, the controller parametersare changed by adjusting the set-points for the VV curvesassigned to the batteries. The dead band of the controllerchanges from 0.95 to 0.98 and then 0.99 pu, with saturationpoint shifting right accordingly at t = 200 s and t = 400 ,respectively. The results for this case study are presented inFig. 4, in which we observe three distinct sparsity patternsfor the K matrices in each scenario. These patterns wereachieved by using α = 0 . and β = 0 in the Koopmanoperator approximation. Similarly to the first case study, thedifferences in the K matrices were sufficient for us to identifythe occurrence of the events considered. Further, in the offlineclassification task, 3 out of the 32 matrices were misclassified,all of which were computed in time instants immediatelyfollowing an event. Fig. 4. Results for the detection of changes in the controller parameters ofbatteries providing voltage regulation through Volt/VAR control.
VI. C
ONCLUSIONS
We proposed a data-driven method that requires no priorknowledge of the network dynamic model for the detectionof incidents in power distribution systems. Our case studiesconsidered the occurrence of changes in BESS operations thatrefer both to active power dispatch and reactive power con-trol of these devices. The successful detection of the eventsmodeled allows for proper mitigation strategies to be set forth,if needed. Our methodology introduces a data transformationstep which augments the dataset while maintaining meaningfulinformation of the system states. This strategy is particularlyuseful in situations with restricted sensor availability, whichcan be common in distribution grids. Further, the algorithmproposed was shown to be robust to measurement noise andload fluctuations, and thus such variations do not trigger a falsedetection. Future work includes designing a more systematicway to choose the hyper-parameters for the Koopman operatorapproximation, and evaluating our methodology in the pres-ence of data loss or data streams with different sampling time. A
CKNOWLEDGMENT
This research was funded by the energy storage programat the U.S. Department of Energy under the guidance of Dr.Imre Gyuk. Sandia National Laboratories is a multi-missionlaboratory managed and operated by National Technologyand Engineering Solutions of Sandia, LLC., a wholly ownedsubsidiary of Honeywell International, Inc., for the U.S. De-partment of Energy National Nuclear Security Administrationunder contract DE-NA-0003525. This paper describes objec-tive technical results and analysis. Any subjective views oropinions that might be expressed in the paper do not neces-sarily represent the views of the U.S. Department of Energy orthe United States Government. Jamal Al Hourani helped withsome numerical experiments. Hyungjin Choi helped with theinitial code and explanation of Koopman operator calculations.The work of the first two authors was supported in part bySandia National Lab under the grant PO 2079716.R
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