A Hybrid Intelligent System for Protection of Transmission

Lines Connected to PV Farms based on Linear Trends

Pallav Kumar Beraa , Samita Rani Panib , Can Isikc , Ramesh C. Bansald
a
Electrical Engineering, Western Kentucky University, Bowling Green, USA
b
School of Electrical Engineering, KIIT University, Bhubaneswar, Odisha, India
c
EECS Department, Syracuse University, Syracuse, NY, USA
d
EE Department, University of Sharjah, Sharjah, UAE
arXiv:2406.13194v1 [eess.SP] 19 Jun 2024

Abstract
Conventional relays face challenges for transmission lines connected to inverter-based
resources (IBRs). In this article, a single-ended intelligent protection of the transmis-
sion line in the zone between the grid and the PV farm is suggested. The method
employs a fuzzy logic and random forest (RF)-based hybrid system to detect faults
based on combined linear trend attributes of the 3-phase currents. The fault location
is determined and the faulty phase is detected. RF feature selection is used to obtain
the optimal linear trend feature. The performance of the methodology is examined for
abnormal events such as faults, capacitor and load-switching operations simulated in
PSCAD/EMTDC on IEEE 9-bus system obtained by varying various fault and switch-
ing parameters. Additionally, when validating the suggested strategy, consideration
is given to the effects of conditions such as the presence of double circuit lines, PV
capacity, sampling rate, data window length, noise, high impedance faults, CT satura-
tion, compensation devices, evolving and cross-country faults, and far-end and near-end
faults. The findings indicate that the suggested strategy can be used to deal with a
variety of system configurations and situations while still safeguarding such complex
power transmission networks.
Keywords: Linear Trend, Inverter-interfaced Renewable Energy Sources, Fault
Detection, High Impedance Faults, Feature Selection, Random Forest, Photovoltaic
Farms, TCSC

1. INTRODUCTION
The generation of electricity using renewable energy sources (RESs) has radically
grown in recent years. This trend is expected to grow as governments, businesses, and
individuals around the world recognize the environmental and economic advantages of
transitioning away from fossil fuels to cleaner energy sources. The predominant portion
of RESs — solar photovoltaic (PV), Type-III wind farm (WF), and Type-IV WF of-
ten integrate into the grid through high-voltage transmission lines (t-lines) to transmit
power generated at remote sites through a power electronic converter. Integration of

Preprint submitted to Elsevier June 21, 2024

RESs has changed the topology of existing power systems having bidirectional power
flow and different fault current levels [1]. The fault ride-through (FRT) requirements
set by modern grid codes and the intermittent nature of these inverter-based resources
(IBRs) control the characteristics of fault currents [2]. Hence, unlike synchronous gen-
erators, the fault current depends on the control approach, inverter control parameters,
and power-system fault conditions. This increased penetration of IBR sources like solar
and wind power into the electrical grid poses challenges to the effectiveness of existing
protection schemes, including distance, differential, and directional protection.
In [3], the study explores how the integration of large-scale PV plants affects the
performance of traditional distance relaying-based t-line protection systems. Distance
relay underreaches due to less contribution of fault current from PV plants with power
electronics [4]. The PV side distance relays may mal-operate due to unique fault char-
acteristics of PV plants [5]. In [6], it is demonstrated how the phase distance elements
in zones 1 and 2 exhibit overreach and underreach, respectively, due to oscillating ap-
parent impedance resulting from currents injected by the IBRs. The integration of
PV systems affecting the reliability of phase and ground distance elements supervised
by negative-sequence directional elements is discussed again in [7]. Haddadi et al. [8]
described the concerns with t-line protection and detailed the use of negative-sequence
values for identifying unbalanced faults. In [9], it is investigated how large-scale grid
connection of PV lowers the dependability of differential protection due to the disparity
in short circuit behavior between PV inverters and conventional synchronous machines.
Yang et al. [10] describes difficulties with sensitivity in t-line differential protection. In
[11], an actual event is examined, and issues with an overcurrent relay’s directionality
are noted. The proficiency of existing protection relays to determine the proper direc-
tion of the fault was impacted by the distortion of the fault signals and the change in
angular disparities between voltages and currents. The altered fault current seen by
overcurrent relays affects fault localization and causes false tripping and blinding of pro-
tection [12]. In [13], the impedance characteristics of IBRs with FRT under European
and North American grid codes are described. It is shown that the impedances seen are
different from the actual fault impedances due to the control strategies implemented.
Moreover, the already challenging task of detecting high impedance faults becomes even
more formidable with the integration of PV [14]. Given that short circuit studies for
these IBRs are not standardized and are instead specific to their designs, it highlights
the need for an alternative and inclusive protection system to support conventional
protective relays.
The intricate fault current properties of IBRs have been the subject of numerous
research studies in the existing literature. In [15], an enhanced scheme utilizing delay
and zero sequence impedance was devised to prevent the malfunctioning of traditional
distance protection for IBRs due to amplitude and phase offset in measured impedance.
In [16], autoregressive coefficients of the 3-phase currents were used for fault detection
and classification for a t-line connected to large scale WF. Saber et al. [17] proposed
a differential protection technique reliant on the phase current samples’ signs on both
ends of the t-line connected to WF. A transient current signal-based current differential

2
protection approach is explored in [18], which uses correlation focusing on the similarity
of the waveforms and the polarity of transient signals from line ends. A distance
protection system based on positive sequence networks independent of resistance and
plant parameters for the t-lines connected to the PV plants is proposed in [19]. A
directional relaying scheme relying on positive sequence components of the fault and
pre-fault voltages and currents for the t-line connected with the PV plant is proposed
in [20].
The Power System Relaying and Control Committee’s Oct. 2023 report emphasizes
that with increased availability of massive volumes of high-fidelity sampled data in tem-
poral and frequency domains, the development and implementation of machine learning
(ML)-based solutions for challenging protection tasks could be successful [21]. Research
articles have also suggested leveraging machine learning (ML) systems to enhance fault
detection and classification operation. The work presented in [21] introduces an in-
telligent protection technique which utilizes an adaptive neuro-fuzzy inference system
to detect, locate, and classify fault types occurring in large-scale grid-connected wind
farms (WFs). A fault identification method based on positive-sequence currents, cou-
pled with an empirical mode decomposition (EMD) accompanied random forest (RF)
is suggested for a TCSC compensated line in [22]. However, the above articles use very
few features and it’s improbable that a single feature will be able to capture every fault
characteristic concerning PVs. Therefore, before applying any learning technique, it’s
vital to assess different features and utilize a feature selection process. The effect of
PV-fed t-lines in infeed conditions on distance protection is analyzed and an impedance
calculation method using SVM is proposed for transmission systems with PV integra-
tion [23]. An ML technique to detect and classify faults in t-lines connected to PV
and WFs is proposed in [24]. However, various scenarios are not taken into account in
these works, including high impedance faults, double circuit line faults, evolving and
cross-country faults, CT saturation, and so on. Also, protection systems that rely on
communication and synchronized data to detect faults have limitations in the event of
communication failures [25].
In this work, a novel single-ended combined linear trend (CLT) based intelligent
protection technique is developed for the protection of lines connected to PV farms
taking into account multiple power system scenarios and a variety of features. The
study’s originality and main contributions are summed up as follows:

• It proposes a fuzzy logic and RF-based hybrid intelligent method to detect and
locate faults. The technique is tested against various conditions simulated by
taking into account several parameters that may affect the fault currents.

• The CLT-based protection is verified for the instances of noise, near-end and
far-end faults, high impedance faults, double circuit lines, CT saturation, cross-
country and evolving faults, TCSC, different sampling frequencies, window sizes,
and change in PV capacity and test system.

• Phasor estimation and sequence component analysis are not required for the sug-

3
 gested approach.

• Being single-ended, it is fast, without any data loss or synchronization errors, and
there is no need for a communication medium.

• The fault and transient dataset having more than 28000 cases is uploaded to IEEE
Dataport[26].

The remaining portions of the manuscript are arranged as follows: In section II

the modeling of the PV system and simulation of faults, load-switching, and capacitor-
switching events in the IEEE 9-bus test system is performed. The CLT-based hybrid
intelligent protection strategy, feature selection, CLT feature, and RF classifier are
elaborated in section III. Section IV exhibits the findings of fault detection, localization,
and phase selection for the PV in the IEEE 9-bus system. The impact of noise, sampling
rate, window size, CT saturation, number of PV units, double circuit lines, TCSC,
evolving and cross-country faults, high impedance faults, near-end and far-end faults,
and change in test system are explored in section V. Comparative analysis with various
recent articles is provided in Section VI. A summary of the observations can be found
in Section VII.

Figure 1: IEEE 9-bus with PV Plant at bus-9.

Figure 2: 3 phase fault current for lg fault at location f1

4
 Table 1: Specifications of the various system components

Component Parameters Value

capacity (single unit) 0.25MW
number of units 400
PV dc voltage & capacitance 1.16kV,10000µF
LCL filter 5mH, 39.24µF, 5mH
Damper 19.62µF, 10.7Ω, 2.5mH
rated voltage & frequency 0.65kV, 60 Hz
positive seq. impedance 0.95 + 29.90jΩ
t-line zero seq. impedance 32.8 + 109.8jΩ
length & voltage 100km, 230kV
positive seq. impedance 0.18 + 0.23jΩ
collector system cable
zero seq. impedance 0.23 + 0.15jΩ
main rated power 300MVA
transformer (MT) transformation ratio 33kV/230kV
(after cable) connection YNYN
rated power 250kVA
transformer
transformation ratio 33kV/0.65kV
(before cable)
connection YNd

Table 2: Parameters for fault Simulation

Fault Events
Fault location f1, f2, f3, f4, f5, f6, f7, f8 (8)
Fault resistance 0.01, 1, 10 Ω (3)
Fault inception angle 0◦ , 60◦ , 120◦ , 180◦ , 240◦ , 300◦ (6)
Fault type ag, ab, ac, abg, acg, abcg, bg, bcg, bc, cg (10)
Priority P and Q (2)
Total fault cases =8 × 3 × 6 × 10 × 2 = 2880

2. System Modeling and Simulation of Transients

The fault and other transient scenarios are simulated using the IEEE 9-bus test
setup (Fig. 1), which has the PV attached to bus-9. Table 1 provides information
about the system implemented in PSCAD/EMTDC. The PV farm consists of a power
plant controller (PPC), PV array, boost converter, DC-AC converter, and scaling com-
ponent. PPC determines the PV farm’s reference active and reactive powers based on
the measured and reference values. Temperature and irradiance both affect how much
power a PV array produces. The boost converter tracks the maximum power point
or regulates the DC voltage. The DC-AC inverter is managed so that the PV farm’s
dynamics can be realized through a variety of control scenarios. Several inverter units
in the PV farm are modeled using the scaling component. Low-frequency oscillations
are dampened using a damper and a filter is used to reduce harmonic effects on the grid
[27]. The t-line 3P V -9 under consideration is 100km in length with positive sequence
impedance of (0.898 + 28.3j)×10−3 pu and zero sequence impedance of (0.031 + 0.103j)
pu. The t-line 4-9 is series compensated to improve its power transfer capabilities and
other operational characteristics. The faults are simulated at eight distinct locations by

5
 Table 3: Simulation parameters & values for other transients.

Non-Fault Events
Switching angle 0◦ to 360◦ in steps of 15◦ (25)
Generator (bus-3) Disconnected/Connected (2)
Location Bus-4, 8, 9 (3)
Load/Capacitor Rating 4
Priority P and Q (2)
Capacitor-switching events = 25 × 2 × 3 × 4 × 2 = 1200
Load-switching events = 25 × 2 × 3 × 4 × 2 = 1200
Total non-fault events = 2400

altering the priority mode, fault resistance, fault type, and fault inception angle. The
generator at bus-3 is turned on and off to examine the effect of infeed in the case of
capacitor and load-switching. Tables 2 and 3 provide the parameters and their values
for simulating faults, load, and capacitor-switching scenarios. A lg fault at location
f1 with fault resistance 0.1 Ω and consisting of the dc decaying and ac components is
shown in Fig. 2.

Figure 3: Framework for proposed hybrid protection system.

3. Proposed Hybrid Protection System

3.1. Protection Scheme
Fig. 3 provides an illustration of the suggested protection mechanism. First, at
the PV side of the t-line under consideration (line 3P V -9) the event detector checks for
any anomalies in the 3-phase currents recorded by the CTP V and captures the data
in case of transients. Linear trend attributes are extracted from the 1-cycle 3-phase
currents that were recorded. Second, the CLT-trained fuzzy inference system and RF

6
are used for fault detection. Third, line 3P V -9 is tripped if the fault locator identifies
the captured transient currents as an internal fault (location f4 & f5). Fourth, the
faulty phase is detected. Preprocessing the data and extracting features are part of the
first step. RF feature selection is used to rank the linear trend features.

3.2. Event Detector

An event detector (ED) is employed to identify any alterations in phase currents.
It calculates the fractional increase by comparing the overall sum of the modulus of
current samples from two consecutive current cycles (equation(1)).
PM PM
x=0 |Iϕ (x)| − |Iϕ (x − M )|
ED(x) = PM x=0 (1)
x=0 |Iϕ (x)|

where M = no. of samples in a cycle, and Iϕ = phase current. The ED filter records
the 3-phase current samples starting from the time instant x that satisfies the equation
(2).
ED(x) ≥ γ = 0.06 ∀ ϕ ∈ a, b, c (2)
The threshold γ is determined by applying grey wolf optimization, a metaheuristic
algorithm that explores for the optimal solution, drawing inspiration from the social
hierarchy and hunting behaviors observed in packs of wolves [28]. Wolves are rep-
resented as candidate solutions, and their positions are updated iteratively based on
fitness evaluations using an objective function. The γ value depends on the maximum
fault resistance considered (here 10 Ω). It decreases with an increase in fault resistance.
Steps for identifying the optimal γ involve:
I: Initializing positions randomly with population size=25, dimension of search space=1,
lower limit=0, upper limit=1, and maximum iteration=200
II: Assessing fitness values employing the objective function:
(1 − disturbances detected in 1 cycle
T otal disturbances detected
)
III: Iterating and updating wolf positions according to dominance hierarchy. Assess the
updated positions’ fitness.
IV: Tracking and returning the best solution and fitness value.

3.3. Random Forest Feature Selection

Random Forest is used to select and rank the features in which multiple decision
trees are trained on a random subset of the data. A random subset of the features at
each node of the decision tree is chosen for splitting. For each feature at a node, the Gini
impurity is calculated before and after the split. The difference in impurity is used to
assess the importance of that feature. The feature importance scores are averaged over
all decision trees. Finally, features are ranked on the average Gini impurity reduction,
with higher values indicating more important features.
C
X
Gini(n) = 1 − (p(i|n))2 (3)
i=1

7
Gini(n) is Gini impurity at node n, C is number of classes, p(i|n) is probability of
class i at node n. RF feature selection chooses the most significant linear trend feature
(Table 4).

3.4. Linear Trends

The 3-phase relay currents can be characterized using pertinent extracted features,
which unveil unconventional insights into the dynamics of the fault currents [29]. Lin-
ear trends are used in various real-world applications across different fields like finance,
climate science, healthcare, engineering, etc. to analyze and predict patterns and rela-
tionships. Linear trends were used to distinguish faults and transients in a 5-bus power
network in [30] and to detect faults during power swings and classify power swings in
[31].
Simple linear trend (SLT): A linear trend, in the context of time series analysis,
refers to a consistent and steady increase or decrease in the values of a variable over
time. It represents a straight line pattern when plotted on a graph, where the data
points follow a linear relationship as time progresses. For the time series values, it
computes the linear least-squares regression, and “p-value”, “correlation coefficient”,
“intercept”, “slope”, and “standard error” are obtained [32]. In this scenario, the three
time series correspond to the 3-phase currents monitored by CTP V .
The linear trend equation is given by:

f = mg + b (4)

where y-intercept is b, slope of the straight line is m, dependent variable is f , and

independent variable is g.
To find the best-fitting values of m and b, “least squares regression” is used. The
purpose is minimizing the sum of squares:
n
X
S= (fi − (mgi + b))2 (5)
i=1

where (gi , fi ) are the data points for i = 1, 2, ..., n.

To find the optimal values of m and b, the partial derivatives of S with respect to
m and b is taken and set to zero:
∂S
=0 (6)
∂m
∂S
=0 (7)
∂b
Solving these equations simultaneously gives the values of m and b minimizing the
sum of squares:
P P P
n (fi hi ) − gi fi
m= (8)
n (fi2 ) − ( gi )2
P P

8
 P P
fi − m gi
b= (9)
n
Once these values are obtained the linear equation f = mg + b is used to predict
the values of f for any given g. The linear trend line will represent the “best fit” line
through the data points, minimizing the overall distance between the actual values and
the expected values.
Pearson’s correlation coefficient (Pearson’s r) can then be obtained for the data
points using: P
(gi − g)(fi − f )
r = qP P (10)
(gi − g)2 (fi − f )2

where gi and fi are the individual data points , g and f are the means of the variables
g and f , respectively. The summation is over all data points in the dataset.

Table 4: List of linear trend features extracted

F eature Description P arameters

Simple ‘p-value’, ‘Pearson’s r’,
calculates least-squares
Linear Trend ‘intercept’, ‘slope’, ‘error’
regression for time series values
(1-5) total = 5
‘p-value’, ‘Pearson’s r’,
Combined calculates least-squares ‘intercept’, ‘slope’, ‘error’
Linear Trend regression for time series Segment size = 5, 10, 50
(6-65) values combined over segments f =mean, variance, max, min
total = 5 × 3 × 4 = 60

Figure 4: Feature importance of Figure 5: Steps for calculation of combined

SLT and CLT linear trend (CLT)

Combined linear trend (CLT): In addition to SLT attributes, the CLT attributes
are also evaluated. For time series values aggregated across segments, CLT performs

9
a linear least-squares regression. The same attributes: “p-value”, “correlation coeffi-
cient”, “intercept”, “slope”, and “standard error” are extracted with the segment size
varied between 5, 10, and 50. The number of time series values in each segment is
determined by the segment size. For a segment size of 10, the number of segments is
12.8 ≈ 13 (1 cycle = 128 data points), thus reducing the data points from 128 to 13.
Maximum, minimum, mean, or variance of time series values in a segment is used to
get the combined value.
The list of SLT and CLT features evaluated using RF feature selection is listed in
Table 4. CLTs with attribute: ‘Pearson’s r’, segment size: 50, and f : mean for the
3-phase currents are thus chosen after feature selection. The importance of SLT and
CLT are shown in Fig. 4. In determining the feature importance of (say SLT phase a)
from a tree, the process involves first computing the importance specifically for nodes
where the split occurred due to feature SLT phase a, then dividing it by the total
feature importance of all nodes. The RF feature importance is derived by averaging
the importances across all trees. It is apparent from the figure that the CLT is a more
effective feature for identifying faults in t-lines connecting PV farms.
The feature calculation steps for CLT are displayed in Fig. 5. First, the one-cycle
phase currents are split into N = 50 segments. Second, the data of each segment is
aggregated over the mean in a single data point per segment to reduce the number of
measurement points to the number of segments. Third, the acquired data points are
then used to create a linear least-squares regression line. Fourth, the Pearson correlation
coefficient is utilized to describe the data points. Here, the feature is named correlation
coefficient r which is dimensionless.

3.5. Random Forest

Once the input features (CLT) are selected, they are used to train Decision Tree
(DT), Random forest (RF), Naive Bayes (NB), Support-vector machines (SVM), and
k-nearest neighbors (kNN) classifiers.
RF is a classification algorithm that uses ensemble learning. It creates multiple
decision trees through bootstrapping (random subsets of data) and random feature
selection. Every tree makes a class label prediction; the ultimate prediction is decided
by a majority vote of all the trees. This approach improves accuracy and reduces
overfitting, making RF a powerful and widely used classifier. The predicted class for a
given input sample p is depicted as:
NT
X
q̂ = argmaxi I (Tj (p) = i) (11)
j=1

where q̂ is predicted class label for the input sample p, NT is total number of decision
trees, Tj (p) is predicted class label by the j-th decision tree. The indicator function
I returns 1 in the case that the condition included in parenthesis is true and 0 in the
other case.

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 Table 5: Fault Detection perfor-
mance with chosen five traditional
ML algorithms

Figure 6: GA tuned Mamdani fuzzy system Classifier

SVM RF DT kNN NB
having 3 inputs and 1 output with trape- Accuracy(η̄)
zoidal membership functions for fault de- without SMOTE (%) 93.3 98.0 96.2 96.5 70.3
tection with SMOTE (%) 92.6 98.2 97.0 97.0 70.1

4. Findings of Detection, Location, and Phase Selection of Faults

This section examines the outcomes of fault detection, fault location, and phase
selection stages on the IEEE 9-bus system. For evaluation of ML algorithms the fault
and transient dataset is divided into two separate subsets: training set and test set in
a 4:1 split ratio to strike a balance between training and evaluation, ensuring models
do not overfit and are proficient in handling new, unseen data. Stratified 10-fold cross-
validation is used which combines stratification and cross-validation, providing a robust
means to thoroughly assess model performance. Stratification groups data by class la-
bels to maintain class distribution and 10-Fold Cross-Validation divides data into 10
subsets. Iterates 10 times, training on 9 subsets and testing on 1, then averages per-
formance for reliable metrics. Grid search is applied for hyperparameter optimization
which explores exhaustively all possible combinations of the hyperparameter values in
a specified range to determine the combination that yields the best performance. The
common metric used to assess the classifiers’ performance is accuracy. However, it
is skewed toward data imbalance. Hence, balanced accuracy η̄ is used to gauge the
model’s performance where η̄ = 12 [ (T PT+F
P
N)
+ (T NT+F
N
P)
] for a binary class problem in
which the terms true positive (TP), false negative (FN), false positive (FP), and true
negative (TN) are used. Further, SMOTE (synthetic minority over-sampling technique)
[33], which aims to alleviate the issue of unbalanced datasets by generating synthetic
samples of the minority class, is also applied.

4.1. Fault Detection

The fault detector is a hybrid intelligent system consisting of a fuzzy system sup-
ported by ML. The fuzzy logic system provides a framework for handling uncertainty
and imprecision in the decision-making process. The a,b,c,d parameters of the trape-
zoidal membership function define it’s shape and the fuzzy rules determine how the

11
 (14,400)
(14,2)

0.96 0.96

0.94 0.94

0.92 0.92
Accuracy

Accuracy
0.9 0.90

0.88 0.88

0.86 0.86

0.84

0.98
(400,2)

0.98

0.95 0.95

0.92

Accuracy
0.92
0.89

0.86
0.89

0.86

Figure 8: Scatter plot showing

Figure 7: Surface plots showing hyperparam- CLTs of faults, load-switching, and
eter search for RF capacitor-switching cases

fuzzy sets interact to produce outputs. Genetic Algorithm is used to fine-tune these pa-
rameters of the trapezoidal membership functions of inputs (CLTs of 3-phase currents)
and output for optimal performance (Fig. 6). The fuzzy inference system customized
using a data-driven methodology is used to find the faults.
In research articles on power system protection, RF, SVM, DT, kNN, and NB have
shown promising outcomes. The classifiers take as inputs the 3-phase CLTs that were
chosen using RF feature selection. Table 5 shows the η̄ for different classifiers with
SMOTE and without SMOTE analysis for fault detection. RF outperforms the SVM,
DT, kNN, and NB. The hyperparameters for these classifiers are optimized using grid
search. It is observed that the use of SMOTE didn’t influence the results considerably.
RF classifier gives the best η̄ of 98.0% without SMOTE (2880 faults and 2400 non-
faults) and η̄ of 98.2% with SMOTE (2880 faults and 2880 non-faults). The optimal
hyperparameters of RF are obtained with grid search on n estimators = [400, 800, 1200,
1600, 2000, 2400, 2800, 3200, 3600, 4000], min splits = [2, 3, 4, 5, 6, 7, 8, 9, 10], and
max depth =[2, 4, 6, 8, 10, 12, 14, 16]. The best hyperparameter (n estimators = 400,
min splits = 2, max depth = 14) obtained is depicted in the 3D surface plot in Fig.
7. The 3D surface plots help understand the relationship between any two out of the
three RF hyperparameters and model performance in the hyperparameter optimiza-
tion. The higher accuracy of RF compared to other algorithms can be attributed to
ensemble learning, feature importance, robustness to overfitting, and ability to handle
high-dimensional and non-linear data.
t-SNE [34] plot is used to visualize the high-dimensional data in a lower-dimensional
space while preserving the local structure and relationships between data points (cor-
relation coefficient of CLTs) of faults, load-switching, and capacitor-switching events
(Fig. 8). It reveals clusters of capacitor and load-switching transients with scattered
clusters of fault data having higher variability. The separation of fault and switching
transient clusters visible in the plot makes it easier for the ML classifiers to differentiate

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Figure 9: Spread of CLT features for 0.1 Ω and 10 Ω fault resistances at location f4
on 60 fault cases each considering different fault types and fault times

them.
It’s essential that the suggested algorithm works well for various fault resistances.
Box plots offer a clear and detailed depiction of a dataset’s distribution encapsulating
key data points – the minimum, first quartile, median, third quartile, and maximum –
providing a comprehensive view of the data’s spread, central tendency, skewness, and
potential outliers. The side by side comparisons of each feature for 0.1Ω and 10Ω using
Violin plots which provide the shape of the distribution in addition to the information
from boxplots are shown in Fig. 9. It is evident that the faults with 0.1Ω resistance
have slightly more variability or spread (width of IQR and length of whiskers) than
10Ω. However, the density plots are similar. This overall similarity in density and box
plots for all three features suggests that a classifier would be effective in distinguishing
fault cases with different resistances from switching transients.

Table 6: Results for Fault Location

and Phase Selection

Classifier
SVM RF DT kNN NB
Accuracy(η̄)
Fault location (%) 80.5 92.3 88.3 89.2 69.5 Figure 10: Confusion/Error Matrix for
Phase selection (%) 97.0 97.2 85.3 88.5 68.4 phase selection

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4.2. Fault location
Once a transient is identified as a fault, the proposed method ascertains the region
of fault. Eight places are used to simulate these faults, with internal faults at f4 and
f5. Faults at locations f1, f2, f3 are considered as backward external faults, and f6, f7,
and f8 as forward external faults. Table 6 shows the η̄ for different classifiers with RF
outperforming the others with a η̄ of 92.3% on 2880 (see Table 2) fault cases.

4.3. Phase selection

Post fault detection and identification of the fault as internal, the faulty phase is
determined. The faulty phase/phases among phase a, phase b, phase c, phases ab,
phases bc, phases ca, or phases abc are identified. Again, RF gives η̄ of 97.2% on 720
faults at f4 and f5 locations (Table 6). The phase selection confusion/error matrix is
displayed in Fig. 10.

5. Validity of Proposed Scheme in Different Scenarios

The next paragraphs discuss the probable scenarios that could create challenges for
the suggested CLT-based approach. The capability of RF to detect faults and switching
transients is assessed for these unique circumstances.

Figure 11: 3D tSNE plot showing the CLT coefficients for faults with CT saturation
and switching transients

14
 Figure 12: Pair plot for the 3-phase CLT features

5.1. Effect of Faults with CT Saturation and CVT Transients

During severe faults, the CT cores may get saturated, which could negatively impact
how well protection algorithms perform. A fault with CT saturation has no effect on
the CLT-based fault detection. To show this the secondary burden is increased to 20
ohms, which will cause the CTs to become saturated. The faults are identified with η̄ of
97.3% on 1760 faults simulated in P and Q priority for fault resistances (0.01, 1, 2, & 10
ohms), fault types (10), and fault inception angles (11) at fault locations (f5 & f6); and
2400 switching transients cases. For the fault and switching transients, representing two
distinct classes, the 3D t-SNE plot illustrates how effectively the classes are separated
in the reduced space, showcasing the feature’s discriminative power. The clusters do
not overlap, indicating that the selected features can distinguish between the classes
(Fig.11). Additionally, in Fig.12, the diagonal elements display the distribution of each
individual feature. For example, the cell at row phase a and column phase a shows the
density plot of the phase a CLT feature. The off-diagonals present pairwise scatter plots
of the features. For instance, the cell at phase a row and phase b column is a scatter
plot comparing phase a with phase b CLT feature. CVT transients, which typically
cause overreach for zone 1 distance relays with no intentional delay [35], have no effect
on the proposed method because only phase currents are taken into account here for
feature extraction.

15
5.2. Effect of Change in Farm Capacity
By changing the PV units from 400 (base value) to 300 and 500, the PV system’s
capacity is altered, and the suggested method is evaluated. The technique recognized
the faults and switching transients with η̄ of 96.0% and 96.4% on 300 and 500 units
respectively using 2400 no-fault transients and 2160 faults simulated by changing pri-
ority (P and Q), fault resistances (0.01, 1, and 10 ohms), fault types (10), and fault
inception angles (6) at locations f2, f5, and f6.
Table 7: Effect of noise in the 3- Table 8: Effect of sampling rate of
phase currents the 3-phase currents

Noise(dB) Accuracy(%) Sampling(kHz) Accuracy(%)

∞ 98.0 7.68 98.0
40 96.3 5.76 (3/4) 96.5
30 95.8 5.12 (2/3) 74.1
20 94.3 3.84 (1/2) 70.2

Figure 13: Spread of CLT features for different noise levels

5.3. Performance in Presence of Noise

Measurement noise can significantly impact the performance of protection methods
in power systems by leading to false tripping, missed fault detection, coordination issues,
and more. Electromagnetic interference from nearby equipment, power lines, and other
sources can cause noise in current waveforms. A 220 kV t-line normally has a 25 dB
noise level. CLTs from 3-phase currents with SNRs of 20 dB, 30 dB, and 40 dB are
used to test the anti-noise capability of the suggested method. The 3-phase currents
obtained at CTP V have Gaussian white noise added to them. The η̄ decreases from 98%
for no noise to 94.3% for 20 dB noise (Table 7). CLT features for 2880 fault and 2400
switching transients without noise and with 20dB noise show that switching transient
have more spread and skewness (unequal whiskers or median line closer to Q1 or Q2)
than the fault data. However, the boxplots at 20db are very similar to the ones for no
noise (Fig. 13).

16
5.4. Effect of Sampling Frequency and Window Length
The relay’s ability to operate quickly and reliably can be impacted by the frequency
of data sampling and length of the data window. High sampling frequencies capture
more detailed information about the power system’s behavior, including fast transients
and high-frequency disturbances. Low sampling frequencies may miss critical events
and nuances in the system’s behavior, potentially leading to false alarms or delayed
responses. However, a high sampling rate generates larger volumes of data, which
can be challenging to store, process, and transmit in real time. Therefore, a trade-off
between data processing and accuracy is necessary. Multiple kilohertz (kHz) are used to
sample the 3-phase relay currents in order to assess the effects of sampling frequency.
The quantity of samples utilized to train the RF classifier influences the suggested
method. It is observed that the CLT-based scheme suffers when the sampling rate is
reduced below 5.76 kHz (Table 8).
The optimal data window size depends on the characteristics of transients and the
desired trade-offs between temporal resolution and computational efficiency. The im-
pact of the data window is examined using window sizes of half, one, and two cycles.
η̄s of 98.0%, 98.0%, and 97.2% are obtained correspondingly, showing the scheme’s
resilience to change in window size.

Figure 14: Configuration of TCSC

5.5. Performance in Presence of TCSC

The performance of traditional distance relays may be impacted by TCSCs which
are used to improve system stability, increase power transfer capability, and regulate
voltage levels in presence of IBR [22]. In the 9-bus test system, a TCSC with a capacitor,
an inductor, and a metal oxide varistor which handles overvoltages is installed between
bus-9 and 4 i.e. at location f6 to provide a maximum compensation of 50% (Fig. 14).
By altering the priority (P and Q), fault locations (f2, f5, and f6), fault resistances
(0.01, 1, and 10 ohms), fault types (10), and fault inception angles (6) 1080 faults and

17
 Figure 15: Spread of CLT features for different compensating devices

2400 switching transients are simulated. The proposed method correctly recognized the
transients and faults with a η̄ of 96%. Distribution of CLTs for cases with compensation
with series capacitor, no compensation, and compensation with TCSC are shown in Fig.
15. 180 fault cases for each of these 3 scenarios at location f6 are considered. The series
capacitor and TCSC boxplots are more skewed than the no compensator boxplots.

Figure 16: HIF model

5.6. Performance in Presence of High Impedance Faults

Due to relay sensitivity concerns with extremely low-level fault currents and relay
design constraints, high impedance faults (HIFs) can be hard to recognize with tradi-
tional distance or overcurrent relays [36]. There are three main approaches to modeling
HIFs [37]. In this work, the circuit-based configuration that uses two diodes and two

18
 Figure 17: 2D tSNE plots of CLT features for different scenarios

variable resistors to connect two anti-parallel DC sources is used. The model for HIF
employed is illustrated in Fig. 16. The dynamic arc is modeled by the two variable re-
sistors, the diodes control the current direction, and the asymmetry in the fault currents
is modeled by the varying DC sources. V ph > V n in positive half cycle, V ph < V n
in negative half cycle, and when V n < V ph < V p current is zero. For the purpose of
simulating the 370 HIFs at fault locations f4, f5, f6, f7, and f8 with P and Q priority for
37 fault inception angles, the lg fault in phase-a with fault resistances between 50 ohms
and 300 ohms obtained arbitrarily every two milliseconds is taken into consideration.
The suggested method successfully distinguished HIFs from other switching transients,
achieving a η̄ of 96%. The t-SNE plot for the 3 CLT features plotted on a 2D plane
shows clusters of similar data points, with the distances between these points reflecting
their relationships in the original 3-dimensional space. The overlaps in 2D t-SNE plot
happens due to the inherent loss of information when reducing dimensions from 3 to 2
(Fig. 17a).

5.7. Performance in presence of Double Circuit Line

The reliability of ground distance relays is threatened by the mutual coupling of
double circuit t-lines, demanding additional consideration [38]. So, between buses 3P V
and 9, a 100 km long double-circuit t-line working at 230 kV and 60 Hz is connected.
The suggested scheme recognized the faults from switching transients with a η̄ of 99.4%
on 2400 transients and 1260 faults generated in the middle of this t-line in P and

19
Q priority modes for fault resistances (0.01, 1, and 10 ohms), fault types (10), and
fault inception angles (21). Fig. 17b shows the CLT features for faults and switching
transients.

Figure 18: Cross-country faults:(a) bg at f7 and cg at f5 at 9.0s, (b) cg (circuit 1) and bg

(circuit 2) at f5 at 9.0s, (c) evolving fault: ag at 9.0s transformed into abg at 9.008s at f5.

5.8. Effect of Cross-country Faults and Evolving Faults

The effectiveness of the distance relaying scheme is adversely affected by cross-
country faults encompassing faults occurring at two separate locations with different
or same fault inception time (Fig. 18a,b), and evolving faults, which have primary and
secondary faults that start at different times but happen at the same place (Fig. 18c)
[39].
The method is assessed across 1188 instances of cross-country faults acquired at P
and Q priority by varying fault inception angles (11) and fault resistances (0.01, 1, and
10 ohms). Simultaneous lg faults at location f7 and location f5 (e.g. bg at f7 and ag,
bg, cg at f5)(see Fig. 18a) are simulated. Also, simultaneous lg faults in circuit 1 and
circuit 2 (e.g. cg in circuit 1 and ag, bg, cg in circuit 2) at location f5 (Fig. 18b) are
simulated. The proposed CLT-based method identified the faults with η̄ of 96.6%.
The method is also assessed across 396 instances of evolving faults acquired by
varying fault inception angles (11), fault resistances (0.01, 1, and 10 ohms), and P and
Q priority. lg faults in one phase get transformed into llg faults involving two phases
(e.g. ag to abg, acg; bg to abg, bcg; cg to bcg, acg) at same location f5 (Fig. 18c). The
faults are found with η̄ of 96.5% by the proposed method. Fig. 17c and 17d shows the
CLT features for these faults and switching transients.

5.9. Near-end and Far-end faults

Traditional relays might experience malfunctions when facing near-end faults, pri-
marily owing to low voltage and high current magnitudes leading to CT saturation.
Additionally, it can be difficult to detect far-end faults since the voltage and current
values are both within the usual range. By altering the fault inception angles, fault
resistances, priority, and fault types, 720 faults were produced at locations f5 and f3,
which were used as the far-end and near-end faults, respectively. RF distinguishes these
faults with η̄ of 99.3%.

20
 Figure 19: IEEE 39-bus with PV at bus-9

5.10. Effect of change in system

The IEEE 39-bus system is also used to assess the viability of the proposed scheme
(Fig.19). The 39-bus system is also served by the CLT-based fault detection, which has
a η̄ of 98.0% on 1080 faults and 2400 non-fault cases. The priority (P and Q), fault
locations (f2, f5, and f6), fault resistances (0.01, 1, and 10 ohms), fault types (10), and
fault inception angles (6) are all altered to simulate the faults.

6. Comparative Evaluation
This section illustrates the conduct of the conventional distance relay connected to
a PV farm, while also highlighting the lack of comprehensiveness of results from recent
works to establish the effectiveness of the proposed algorithm in this article.
The impedance plane associated with traditional distance relay 3P V 9, near bus 3P V ,
demonstrates the fault behavior. It’s evident that the distance relay exhibits unreliable
responses (Fig. 20). For instance, during an ag fault occurring at location f5 (refer
Fig. 1) within zone 1, the relay remains inactive in case 1 (PV units = 300, Rf = 10Ω,
priority = P) but it triggers in case 2 (PV units = 500, Rf = 1Ω, priority = P). It
remains dormant for a high impedance ag fault at location f4 (zone 1) in case 3 (PV
units = 400, priority = Q). Also, it stays inactive for an ab fault at location f5 in case 4

21
 Figure 20: Impedance trajectories for AG and AB components of the distance relay at
CTP V for faults in zone 1

(PV units = 300, Rf = 10Ω, priority = P). The procedure for obtaining the impedance
trajectory is described in [16].
Additionally, Table 9 compares current publications concentrating on criteria, with
particular emphasis on the impact of different transient conditions on the proposed
techniques. This evaluation aims to assess the comprehensiveness of these proposed
techniques. While the methodologies have produced favorable results under some par-
ticular scenarios, performance analysis in many significant situations appears to be
lacking. The aforementioned publications also touch on the proposed algorithms’ exe-
cution times. For double-ended protection, the communication paths between the two
terminals can introduce a time delay of up to 6.87ms, according to IEEE standard
[40]. The proposed technique being single-ended is free from this delay. The intelligent
protection system based on CLT depends on data preparation and inference time. The
event detector takes 0.001ms and the calculation of CLT takes 0.01ms. The fuzzy and
the ML systems work in parallel taking 1.8ms and 0.5ms respectively to test new in-
puts. Hence, net running time considering 1-cycle data = 16.67ms + 1.8ms + 0.01ms
+ 0.001ms = 18.5ms.

7. CONCLUSION
The attributes of dependability, security, selectivity, robustness, and speed should
be present in a protective system. However, the dependability for internal faults and
security for external faults and other transients may get challenged in the case of trans-
mission lines connected to bulk PV farms. The suggested combined linear trend-based
hybrid intelligent protection method is dependable for internal faults, cross-country

22
 Table 9: Comparison of recently published articles.

Proposed
Reference [17] [20] [19] [22]
method
signed +tive seq. CLT,
Technique used impedance EMD,RF
correlation network Fuzzy,RF
Signals used i v&i v&i i i
Single or double end double single single single single
System freq.(Hz), Samp. freq.(kHz) 60,1.2 60,1 60,1.2 50,1 60,7.84
Model includes WF PV PV WF PV
FACTS used - - - TCSC TCSC
Time delay (ms) ˜16 16.67 - 8 18.5
Effect of HIF - - yes yes yes
Effect of Noise yes yes yes yes yes
Effect of Double ckt. lines - - - - yes
Effect of farm capacity yes - - - yes
Effect of cross-country faults - - - - yes
Effect of evolving faults - yes yes - yes
Effect of Sampling freq. - - - - yes
Effect of data window - - - yes yes
Effect of CT saturation - yes yes yes yes
Effect of load switching yes yes - yes yes
Effect of capacitor switching yes - - yes yes
Effect of near-end faults - yes - yes yes

faults, evolving faults, double circuit line faults; and responsive to low current levels in
high impedance faults. It provides security for capacitor and load-switching, and exter-
nal fault with CT saturation events. It locates the faults correctly and is selective. It
is resilient to changes in data window size, capacity of the PV, noise in measurements,
change in the test system, and the presence of TCSC. However, the performance of the
model is impacted by the sampling rate of the phase currents. The combined linear
trend-based intelligent approach has been successfully evaluated in the IEEE-9 bus sys-
tem across a wide range of fault parameters and operating scenario variations. It has
been found that the linear combined trend-based decision-making system provides a
thorough protection for transmission lines connected to bulk photovoltaic farms while
being dependable, secure, accurate, and quick. Furthermore, it solely utilizes locally
measured data, eliminating the requirement for a remote-end communication device.
The proposed method can be applied in real time using edge computing for power
system protection with careful planning, cybersecurity measures, and integration with
existing infrastructure, thereby enhancing the speed, reliability, and scalability of pro-
tection functions.

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