1 AbstractFault diagnostics are extremely important to decide proper actions toward fault isolation and system restoration . The

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Abstract—Fault diagnostics are extremely important to decide

proper actions toward fault isolation and system restoration. The

growing integration of inverter-based distributed energy

resources imposes strong influences on fault detection using

traditional overcurrent relays. This paper utilizes emerging

graph learning techniques to build a new temporal recurrent

graph neural network models for fault diagnostics. The temporal

recurrent graph neural network structures can extract the

spatial-temporal features from data of voltage measurement

units installed at the critical buses. From these features, fault

event detection, fault type/phase classification, and fault location

are performed. Compared with previous works, the proposed

temporal recurrent graph neural networks provide a better

generalization for fault diagnostics. Moreover, the proposed

scheme retrieves the voltage signals instead of current signals so

that there is no need to install relays at all lines of the distribution

system. Therefore, the proposed scheme is generalizable and not

limited by the number of relays installed. The effectiveness of the

proposed method is comprehensively evaluated on the Potsdam

microgrid and IEEE 123-node system in comparison with other

neural network structures.

Index Terms—Fault detection, fault location, microgrid

protection, deep neural network, graph learning, temporal.

I. INTRODUCTION

ROTECTION and restoration play critical roles to enhance

the resilient and reliable operation of distribution systems

[1], [2]. Under the increasing integration of distributed energy

resources, the protection of distribution systems becomes

challenging since traditional protective relays are ineffective

due to the smaller fault currents of inverter-based generators

[3]. In parallel with passive relays, fault diagnostics using

measurement data targets provide system operators with fault

types and locations to timely isolate faults and restore normal

operations [4].

Fault diagnostics include fault event detection, fault

type/phase classification, and fault location. There are many

fault diagnostics schemes analyzing data from digital relays or

micro phasor measurement units (µPMU) proposed in

B. L. H. Nguyen and T. V, Vu are with Clarkson University, Potsdam,

NY, USA (e-mail: nguyenbl@clarkson.edu, dassc@clarkson.edu,

hanq@clarkson.edu, tvu@clarkson.edu). T.-T. Nguyen is with New York

Power Authority (e-mail: thaithanh.nguyen@nypa.gov). M. Panwar and R.

Hovsapian are with National Renewable Energy Laboratory. (e-mail:

mayank.panwar@nrel.gov, rob.hovsapian@nrel.gov)

literature [3]–[18]. Loosely, these schemes can be classified

into model-based and data-driven based techniques.

Model-based methods focus on finding the evaluation

metrics that are consistent in accordance with the proposed

fault models. In [19], the pre-fault negative sequence and

positive sequence current are compared for detection.

However, the performance of this method is significantly

affected by the fault current amplitudes. This requires

readjustment and prior information about all possible

microgrid configurations to determine an appropriate

threshold. A transient monitoring function to detect fault is

proposed in [20] by summing the residuals between estimated

and measured current components over one cycle. Although

this differential-based method does not rely on the magnitude

of the fault current, the unbalanced loads and generation

transients can cause a false alarm. In [21], the mathematical

morphology and recursive least square are employed. The

Teager-Kaiser energy operator is proposed in [22] to detect

and classify faults. These methods are strongly dependent on

the configuration of the distribution system and cannot find

the fault location.

Data-driven methods focus on mining measurement data to

diagnose faults. The decision tree [23] and random forest [24],

which are popular statistical classifiers, have been applied in

fault detection. In [25], four machine-learning classifiers i.e.,

decision tree, K-nearest neighbor, support vector machine, and

Naïve Bayes are implemented and compared for fault

diagnostics. The discrete wavelet transform is frequently

employed as a feature extraction technique [26] prior to the

classification process. Advanced machine learning techniques

are also adopted recently i.e., the maximal overlap discrete

wavelet transform and extreme gradient boost algorithm in

[27], Taguchi-based artificial neural networks in [28], and

gated-recurrent-unit deep neural networks in [29] and are

achieved very high accuracy. However, in these works, fault

detection, classification, and location are performed based on

the current measurements from the fault line. There is a

research gap in fault diagnostic in distribution systems with

limited data where the faults may occur in lines without

measurement devices.

Fault diagnostics using PMU data have been investigated in

several papers. In [30], [31], the fault location is determined

based on the discrepancy of the nodal voltages calculated

based on µPMU data and pseudo-measurements. The accuracy

Bang L. H. Nguyen, Student Member, IEEE, Tuyen V. Vu, Member, IEEE, Thai-Thanh Nguyen,

Member, IEEE, Mayank Panwar, Member, IEEE, Rob Hovsapian, Senior Member, IEEE.

Spatial-Temporal Recurrent Graph Neural

Networks for Fault Diagnostics in Power

Distribution Systems

of this method depends on the load model and the reliability of

pseudo measurements. With a larger scope, data from two

µPMUs are analyzed to locate and classify events in the

distribution grid using SVM, k-NN, and DT algorithms [32].

However, the investigated system is radial with small nodes,

and the number of events is small. The faulted line location

using µPMU data via convolutional neural networks is

proposed in [33], [34]. The semi-supervised learning is

performed on µPMU data to detect and locate high-impedance

faults [35]. None of the mentioned works demonstrated fault

diagnostics on mesh-topology networks and their scheme lack

fault type/phase classification.

This paper proposes a unified fault diagnostic scheme

including detection, classification, and location based on

voltage measurement data, which can be collected from

µPMU, advanced metering infrastructure (AMI), and

consumer-side smart meters. The proposed scheme leverages

transfer learning and fine-tuning with the combination of

recurrent neural networks (RNN) and graph neural networks

for the diagnostic models. Although there are existing fault

detection schemes using graph neural networks (GNN) or

graph convolutional networks (GCN), those works contain

limits or focus on different objects as follows. [34] only focus

on the fault location and lack of comprehensive analysis of the

results. [36] applies the GNN for fault diagnosis of

transformers. Moreover, none of the existing works have

considered the temporal correlation in graph learning on time-

series data of fault diagnostic problems.

The unique contributions are outlined as follows

• The combination of RNN and GNN structures is

proposed for fault diagnostics with voltage

measurement data as inputs.

• Both spatial and temporal correlations in the graph-

based time-series data are intrinsically considered by

the temporal recurrent graph neural network (R-GNN).

• The proposed fault diagnostic scheme can detect fault

events, classify the fault type and phase, and identify

the fault location.

• The transfer learning and fine-tuning approaches are

implemented for multiple learning tasks in the

proposed fault diagnostic scheme.

• Comprehensive case studies and comparisons with

other machine learning techniques and NN structures

such as general artificial NN (ANN), RNN,

convolutional NN (CNN), and GCN are also provided.

Notably, the proposed deep NN structure is capable of

incorporating current measurements as edge-feature inputs for

fault detection; however, this is not investigated in this paper

but future work. The remaining parts are organized as follows.

In Section II, the Potsdam microgrids and IEEE 123-node

feeder systems under investigation are described. Section III

introduces the deep graph neural network model considering

spatial-temporal µPMU data. Section IV describes the data

collection, pre-processing, and series of case studies to

demonstrate the effectiveness of the proposed scheme. The

results are compared and discussed in Section V. Section IV

concludes the paper.

[X1]

[X2]

[X3][XN-1]

[XN]

Inputs

12N

3N-1

R-GCN

layers

12N

3N-1

[H1]

[H2]

[H3][HN-1]

[HN]

Node classification

Fault location

[y1]

[y2]

[y3][yN-1]

[yN]

3N-1

[yphase][ytype]

Graph classification

Fault phase Fault type

Dense

Pool

Dense

Fig. 1. Block diagram of the proposed fault diagnostic scheme.

II. PROPOSED FAULT DIAGNOSTICS SCHEME USING TEMPORAL

RECURRENT GRAPH NEURAL NETWORKS

A. Preliminaries

The distribution network is defined as an undirected graph

, where  denotes the set of vertices,



each vertex in the graph represents a node (bus) in the

distribution network,  is the tuple of node

features,  denotes the set of edges,

, each edge

represents a line (branch) connecting two buses, 

 is the tuple of edge feature, and 

denotes the adjacency matrix of the distribution network. The

input data for graph learning are the node features , and

the edge features . Some applications also contain the

attributes for each graph data ( [37].

The learning goal is to generalize the mapping model

between the inputs of node and/or edge attributes and the

outputs. The outputs of graph learning can be the classification

or regression task at node or graph levels. The input-output

model  of the GCN can be expressed as

 ()

where  is the trainable weights,  is the inferred output.

The trainable weights are updated iteratively via

backpropagation over minimizing the loss function ,

where  is the output labels. The loss function can be a mean

squared error (MSE) or mean absolute error (MAE) in a

regression problem or cross-entropy in a classification

problem [38].

The main difference between the traditional and graph

neural networks structures is that graph learning includes the

graph structure via the adjacency matrix  of the undirected

graph . In case of that, the set of edges  and the

adjacency matrix  do not change, we have a static graph.

Otherwise, there is a dynamic graph [39].

B. Fault Diagnostic Scheme via Recurrent-Graph Neural

Networks

This paper focuses on fault diagnosis via graph neural

network models by voltage measurements. Herein, only the

bus voltage measurements are considered as input node

features for consistency. The incorporation of current

measurement as the edge features would be extended in future

work. Each bus have three-phase voltages , ,  in

time series, where  is the time index. Therefore, the node

feature in node  is shown in the form of

   

   

    ()

where  is the length of the evaluation period. The learning

performance is investigated under different values of . It is

worth noting that the nodal admittance matrix ( of the

distribution network can be the weighted adjacency matrix.

The graph data  includes the

voltage measurement of nodes in the distribution system and

the adjacency matrix  representing the connection of the

graph.

Outputs  of the GCN models  are the fault categories

and fault location, where the graph classification task is for

classifying the fault categories and the node classification is

for determining the fault location. The fault categories have

two labels: fault types and fault phases. The fault types are

classified into six types included 1) no-fault (NF), 2) single-

phase-to-ground (LG), 3) two-phase (LL), 4) two-phase-to-

ground (LLG), 5) three-phase (3L), and 6) three-phase-to-

ground (3LG). Therefore,   with the -th element

of :  indicates the -th fault category

occurred while all other . The fault phases are

determined by  , where  indicating

the fault occurs in phase  or  when the fault

types are asymmetrical i.e. LG, LL, and LLG, respectively.

The fault location is indicated by , where 

 if the fault occurs in the -th bus, otherwise 

. The fault location detection is performed at node-level

classification.

The block diagram of the proposed fault diagnostic scheme

using recurrent graph learning is shown in Fig. 1. From the

node features , the hidden features

 are extracted through the R-GCN layers. From

these distinct hidden features, on one hand, the fault location

outputs  can be captured using the dense layers in a node

classification task. On the other hand, the pooling operation is

performed to achieve the unified graph features, then via the

dense layers, the fault type and fault phase is determined. The

fault type is detected first, and in cases of asymmetrical faults

detected, the fault phase is identified thereafter. The R-GCN

layers are designed in detail in the next section II. C. The

transfer learning and fine-tuning techniques are described in

section II. D is applied to reduce the training time for multi-

tasks in this fault diagnostic scheme.

C. Temporal Recurrent-GCN layers

Existing works adopted the gated recurrent unit (GRU) or

graph convolutional network (GCN) structures for fault

diagnostic in the distribution system in [29] and [34],

respectively. However, these structures can only extract either

the temporal or spatial dependencies. This paper implements

the temporal recurrent GCN layers of the graph-learning-based

models for fault diagnosis. Temporal R-GCN layers can

capture both temporal and spatial correlation in the input data.

The fault diagnostic models are represented by a classification

function

RNN

cells

RNN

cells

RNN

cells

GCN

layers

Global pooling

Dense

layers

Dense

layers

Dense

layers Fault

location

Fault

event

Fault

type/

phase

Fig. 2. Proposed temporal R-GCN structure for fault diagnostic.

 mapping the input time sires  over the

graph  to the fault labels as follows.

 ()

Where the node feature  and so on with

the under script denoting the node index and the superscript

denoting the time index. The structure of the graph  is

reflected through the adjacency matrix .

The proposed temporal R-GCN framework for fault

diagnosis is illustrated in Fig. 2. The proposed R-GCN

structure includes RNN cells and GCN layers for feature

extraction. Firstly, the RNN cells are employed to extract the

temporal feature from the voltage in the time series of each

node. Thereafter, the GCN layers are used to identify the

spatial correlation between the bus voltages over the

distribution system. The global pooling operation

concentrates all hidden features from nodes and finally, the

dense layers are trained to classify the fault type and fault

phase. The fault location is performed based on all hidden

features from all the nodes. The formulation of GCN and RNN

layers is presented as follows.

Graph Convolutional Network Layers:

The node feature at each time index is processed by the

GCN layers [40], which can be expressed as













 ()

where  is the adjacent matrix with self-connection,

 is the identity matrix, 

 is the agree to matrix from  with



  and 

 , 

 is the output of layer , 



,  is the weight matrix of layer ,  is a nonlinear

activation function. This graph propagation formula can be

derived as a first-order approximation of localized spectral

filers [37].

Outputs of GCN layers at each time index are the inputs of

a recurrent neural network (RNN), where the RNN cells can

be GRU or long-short-term memory (LSTM) [41]. GRU

structure is simpler than LSTM, thus it is computationally

more efficient. However, LSTM can remember longer

sequences and achieve better performance in temporal long-

distance tasks [42].

Long-Short-Term Memory Cell:

One LSTM cell computes for each time step the hidden

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1Abstract—Faultdiagnosticsareextremelyimportanttodecideproperactionstowardfaultisolationandsystemrestoration.Thegrowingintegrationofinverter-baseddistributedenergyresourcesimposesstronginfluencesonfaultdetectionusingtraditionalovercurrentrelays.Thispaperutilizesemerginggraphlearningtechniquestobuild...

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