# Network Slicing in 5G Mobile Communication: Architecture, Profit Modeling,
and Challenges

Mohammad Asif Habibi, Bin Han, and Hans D. Schotten M. A. Habibi, B. Han, and
H. D. Schotten are with the Institute for Wireless Communication and
Navigation, Department of Electrical and Computer Engineering, Technische
Universität Kaiserslautern, 67663 Kaiserslautern, Germany. Email: {asif,
binhan<EMAIL_ADDRESS>
###### Abstract

Efficient flexibility and higher system scalability call for enhanced network
performance, better energy consumption, lower infrastructure cost, and
effective resource utilization. To accomplish this, an architectural
optimization and reconstruction of existing cellular network is required.
Network slicing is considered to be one of the key enablers and an
architectural answer of communication system of 2020 and beyond. Traditional
mobile operators provide all types of services to various kinds of customers
through a single network, however, with the deployment of network slicing
operators are now able to divide entire network into different slices each
with its own configuration and specific Quality of Service (QoS) requirements.
In a slice-based network, each slice will be considered as a separate logical
network. In this way, the infrastructure utilization and resource allocation
will be much more energy and cost efficient in comparison to traditional
network. In this paper, we provided a comprehensive discussion on concept and
system architecture of network slicing with particular focus on its business
aspect and profit modeling. We throughly discussed two different dimensions of
profit modeling, so called Own-Slice Implementation and Resource Leasing for
Outsourced Slices. We further addressed open research directions and existing
challenges with the purpose of motivating new advances and adding realistic
solutions to this emerging technology.

##  I Introduction

Fifth Generation (5G) communication system is expected to satisfy services,
consumers, and business demands of beyond 2020. Besides supporting of massive
number of user equipments, increased amount of network traffic, and enhanced
QoS requirements of telephony/data services, 5G system provides support to a
variety of vertical industries such as health-care, manufacturing, automotive,
logistic, energy, environment, construction, and so on. These industries call
for different use-cases and various QoS requirements, therefore, one-size-
fits-all network architectural approach is no longer efficient for the
utilization of 5G and beyond technologies. In order to efficiently accommodate
vertical use-cases along with increased user demands over the same network
infrastructure, 5G system requires architectural optimization and
reconstruction with respect to current deployment. Network slicing can be one
of the appropriate solutions to meet the above mentioned requirements, since
it allows operator to partition network in a structured, elastic, scalable and
automated manner.

Deployment of network slicing enables the operation of multiple logical
networks over a single physical infrastructure in order to reduce total cost,
decrease energy consumption, and simplify network functions in comparison to
one network for different use-cases/business scenarios. In a slice-based
network, each slice should be provided with its own specific characteristics
and will be considered as a single logical network. In this way, the
infrastructure utilization and resource allocation will be much more energy
and cost efficient in comparison to traditional network.

Implementation of network slicing over 5G communication system arises many
technical challenges, which are expected to be solved. There are also some
business and economic issues (e.g. total cost, revenue, etc.) that need for
significant optimization and re-designing in order to cope with new network
architecture. On the other hand, the demand for broadband multimedia services
has been increasing explosively, with this ongoing trend, the revenue of
mobile network operators will soon be exceeded by Capital Expenditure (CAPEX)
and Operating Expenditure (OPEX) required to operate the infrastructure.
Therefore, total cost, expected revenue, and resource allocation in the
context of network slicing are seemed to be very interesting research topics,
which need for further discovery.

In this paper, we provide a comprehensive discussion on concept and system
architecture of network slicing with particular focus on its business aspect
and profit modeling. We throughly discuss two different dimensions of profit
modeling i.e. own-slice implementation and resource leasing for outsourced
slices. We further address challenges and open research directions in order to
add new contributions and provide realistic solutions to existing problems in
the field of network slicing implementation of 5G system. The reminder of this
paper is structured as of following: Sec. II reviews state-of-the art in the
field of network slicing. In Sec. III, we discuss concept and system
architecture of network slicing for 5G mobile communication system. Sec. IV
presents business aspect and two dimensions of profit modeling. Following
that, we provide future research directions in Sec. V. Finally, a summary of
this work is given in Sec. VI.

##  II Related Work

The concept of network slicing has exclusively been studied in literature. For
instance, authors in [1] explained a detailed end-to-end framework of network
slicing implementation in 5G communication system. The paper deals with
deployment of vertical and horizontal slicing over the air-interface, Radio
Access Network (RAN), and Core Network (CN). It further focuses on how to
horizontally slice both computation and communication resources to/from
virtual computation platforms in order to improve scalability, enhance device
capability, and increase end user experience.

Moreover, [2], [3], and [4] focused on deployment of network slicing over the
RAN architecture of mobile networks. Authors in [2] analyzed network slicing
in multi-cell RAN in order to support radio resource splitting among various
slices. This paper further proposed four types of RAN slicing approaches along
with their detailed comparison. However, authors in [3] explained how network
slicing may impact various aspects of design and functions of RAN architecture
of 5G mobile networks. The paper thoroughly covered RAN requirements for
network slicing implementation. In [4], authors provided a comprehensive
discussion on deployment of network slicing in heterogeneous Cloud-RAN (C-RAN)
in order to improve throughput through computation and communication resource
sharing.

Figure 1: Network Slicing System Architecture

Further, authors in [5] addressed network slicing related concepts i.e.
resource allocation, virtualization technologies, orchestration process, and
isolation function. The paper provided a comprehensive discussion on Software
Defined Networking (SDN) and Network Function Virtualization (NFV) along with
a deployment use-case (which considers network slicing using both NFV and SDN
integration). The authors further demonstrated existing challenges and future
research directions of network slicing implementation in 5G communication
system. Moreover, a comprehensive survey on architecture and further research
directions of network slicing is also available in [6].

The Next Generation Mobile Networks (NGMN) introduced Network Virtualization
Substrate (NVS), which allows infrastructure provider to control resource
allocation of each of the virtual instance of an enhanced Node B (eNB) before
customization of scheduling of each virtual operator within allocated
resource. On the other hand, a heuristic-based admission control mechanism is
introduced in [7], which dynamically allocates network resource to various
slices in order to increase end user satisfaction considering specific
requirements of each of the slice.

One of the main objectives of network slicing is to optimize profit modeling
of traditional telecommunication networks. In order to increase overall
revenue and decrease total network expenditure, a comprehensive study of
business and economic dimensions of network slicing is required. Authors in
[8] analyzed profit generated by different slices over the same network
infrastructure and further modeled network resource management. Meanwhile, [9]
dealt with the designing of an algorithm that allocates requests of network
slices, which further maximizes total revenue of network infrastructure
provider. However, in our paper, we first provide a comprehensive discussion
on concept and system architecture of network slicing with particular focus on
its business aspect and profit modeling. We further discuss two different
dimensions of profit modeling i.e. own-slice implementation and resource
leasing for outsourced slices in details. Moreover, we address open research
directions with the purpose of motivating new advances and adding realistic
solutions to this emerging technology.

##  III Network Slicing: Concept and System Architecture

Network slicing, in its simplest description, is to use virtualization
technology i.e. NFV or SDN in order to design, partition, organize and
optimize communication and computation resources of a physical infrastructure
into multi logical networks for the sake of enabling of variety of services
[1]. With deployment of network slicing, a single physical network
infrastructure is sliced/partitioned into multiple virtual networks, which is
called Network Slice. Each slice can have its own architecture, applications,
packet and signal processing capacity, and is responsible for provisioning of
specific applications and services to specific end users. Examples of network
slices can be: a slice to serve remote control function of a factory, a slice
serving for a utility company, a slice dedicated to provide emergency health
services, and so on. A slice is consisted of Virtual Network Functions (VNFs),
which are appropriately composed to support and build up services that are
supposed to be delivered to the end users.

Network slicing deployment includes two main phases: creation and runtime [5].
In the slice creation phase, end user requests a slice from a network slice
catalog, the tenant provides the slice immediately upon request. In the
runtime phase, different functional blocks whiten each slice, which are
already created are now operating and providing service according to the end
user’s request. Each network resource i.e. NFV and functional block within a
specific slice should have its own security mechanisms and must ensure
operation within expected parameters in order to prevent access to
unauthorized entities. This will lead to guarantee that faults or attacks
occurring in one slice are confined to that given slice and will not propagate
across slice boundaries. Slicing helps operator to provide new services and
applications only by deployment of a slice instead of rolling out a new
network, which leads to decrease CAPEX and saves time.

Network slices are operating on a partially shared infrastructure. This
infrastructure is consisted of dedicated hardware i.e. network elements in the
RAN and shared hardware i.e. Network Functions Virtualization Infrastructure
(NFVI) resources. Network functions running on shared resources are usually
instantiated in a customized manner for each slice, however, this approach
cannot be applied to the network functions relying on dedicated hardware.
Therefore, designing and identification of common functions is one of the key
research directions in network slicing.

There are two different concepts and scenarios of using of network slicing in
communication networks [10], slicing for the purpose of QoS and Slicing for
the purpose of infrastructure sharing. Both dimensions of network slicing are
described as of following:

  * •

Slicing for QoS: The basic idea is to create various slices in order to offer
different types of services to the end users, and to assure specific types of
QoS requirements within specific slice. An example of this type of slicing can
be a slice, which is created to provide service to a specific group of devices
considering specific QoS requirements e.g. live video streaming, broadband
connection to medical emergency response operation, and so on.

  * •

Slicing for Infrastructure Sharing: The fundamental idea of this scenario of
network slicing is to virtualize RAN domain of a wireless network, and further
share it among various operators. There is a slice owner and a slice tenant.
The owner gives the slice to a tenant based on an agreement. The tenant has
overall control on both functions and infrastructure of that slice. This
concept of network slicing leads to optimize network cost model for increasing
the overall revenue, and meanwhile providing network scalability.

The purpose of network slicing in 5G mobile communication is to allow
operators in order to share infrastructure among each other in flexible and
dynamic manner, and to manage resource efficiently considering increased
number of devices and massive amount of user traffic. However, a detailed
discussion on objectives and motivation of network slicing implementation can
be found in [10]. Network slicing helps mobile operators to simplify creation,
configuration, and operation of network services. In order to efficiently
allocate network resources, two-tier priorities are introduced in [7]. The
first tier is Inter-slice Priority, which refers to different priorities
between various slices of a network. The priority of each of the slice is
defined between owner and tenant of the slice. The second tier is Intra-slice
Priority, which is referred to the priorities between different users of a
single slice. These priorities are defined between users and service provider.

Figure 2: Network Slicing Management Architecture

Slicing can be deployed in two dimensions over 5G communication networks,
Vertical Slicing and Horizontal Slicing. Vertical slicing enables vertical
industries and services, and focuses on CN. However, horizontal slicing
improves system performance and increase end user experience, and mainly deals
with RAN architecture. We define in details what is understood by both types
of slicing as of following [1]:

  * •

Vertical Slicing: The development and deployment of vertical slicing has
already started in late Fourth Generation (4G) and early 5G, and is mostly
focusing on the core domain of mobile networks. Mobile broadband networks are
sliced vertically in order to serve vertical industries and applications in a
more cost efficient manner. It segregates traffic of vertical industries from
the rest of general broadband services of mobile network, which leads to
simplify traditional QoS engineering problems.

  * •

Horizontal Slicing: Increased number of user equipments and massive amount of
traffic generated at the edge of mobile network expand network slicing from
core domain to the RAN and air interface, which is called horizontal slicing.
It is designed to accommodate new trends for scaling of system capacity,
enabling of cloud computing, and offloading of computation devices at the edge
of mobile networks. Horizontal slicing enables resource sharing among nodes
and devices of a network. For example high capable network devices/nodes share
their resources such as communication, computation, and storage with low
capable network devices/nodes, which leads to enhance overall network
performance.

Both vertical and horizontal slicing are independent from each other. End-to-
end traffic flow in a vertical slice is transited between CN and user devices.
While in a horizontal slice, it is usually transited locally between two ends
of a slice e.g. between a portable device and a wearable device [1]. In
vertical slicing, each of the nodes of a network deploys similar functions
among slices, however, in a horizontal slice new functions could be added and
created at a network node.

Fig. 1 shows the concept and system architecture of network slicing. The
architecture consists of CN slices, RAN slices, and radio slices. Each slice
in CN is built from a set of Network Functions (NFs), some NFs can be used
across multiple slices while some are tailored to a specific slice. There are
at least two slice pairing functions, which connect all of these slices
together. The first pairing function is between CN slices and RAN slices, and
the second pairing function is between RAN slices and radio slices. The paring
function routes communication between radio slice and its appropriate CN slice
in order to provide specific services and applications. The pairing function
between RAN and CN slices can be static or semi-dynamic configuration in order
to achieve required network function and communication. The mapping among
radio, RAN and CN slices can be 1:1:1 or 1:M:N, it specifically means that a
radio could use multiple RAN slices, and a RAN slice could connect to multiple
CN slices.

End-to-end slicing architecture shown in Fig. 1 represents logical
decomposition of network slicing, and takes specific network domain functions
i.e. CN and radio network domains into account. From the operational
perspective, NGMN defines that network slicing concept is consisted of three
layers: Service Instance Layer, Network Slice Instance Layer, and Resource
layer. Each of these three layers are described below and shown in Fig. 2.
[11].

  * •

Service Instance Layer: It represents end user and business services, which
are expected to be supported by the network. Each service is represented by a
Service Instance. These services can either be provided by the network
operator or by a third party.

  * •

Network Slice Instance Layer: A network operator uses a Network Slice
Blueprint in order to create a Network Slice Instance. The network slice
instance provides the network characteristics required by a service instance.
The network slice instance may be shared across multiple service instance,
which are provided by a network operator. The network slice instance can be
consisted of none, one or more Sub-network Instances, which may be shared by
another network slice instance. Sub-network Blueprint is used to create a sub-
network instance to form a set of network functions, which runs on the
physical/logical resources.

  * •

Resource Layer: The actual physical and virtual network functions are used to
implement a slice instance. At this layer, network slice management function
is performed by the resource orchestrator, which is composed of NFV
Orchestrator (NFVO), and of application resource configurators.

Network Management and Orchestration (NMO) plane shown in Fig. 2 provides
orchestration and management functions of above mentioned three layers. NMO
functions need to allow for the orchestration and management in a per-slice
level.

##  IV Network Slicing for Profit Modeling

Besides the improved scalability and flexibility provided by network slicing,
it also worths to discuss business dimension of applying of network slicing
from operator’s perspective. In traditional networks, the cost of an operator
in terms of CAPEX and OPEX is high in reference to the total generated
revenue. There are several reasons for such higher costs, where the most
important one is the network resource underutilization.

In traditional network architectures, the network operator provides an
unspecified network resource pool for general utilization of all applications.
However, depending on the performance requirement, various applications can
have highly specified characteristics of resource utilization. Therefore,
under traditional architectures, it is often to reserve excessive amount of
certain network resources for some use-case with only slight demands on them.
A lot of network resources are thus wasted, leading to a low network
utilization rate.

In contrast, with deployment of network slicing, operators are able to
efficiently analyze operational cost and revenue generated from each
individual slice in the entire network. Based on revenue analysis, operators
can allocate specified network resource bundles to different slices, which
makes the resource management much more structured, flexible, and efficient.
It is concluded that the very same network can be utilized to seamlessly
provide more and better services i.e. generate more revenue without any
increase in CAPEX. Therefore, network provider needs new algorithms in order
to cope with new architecture and maximize revenue. To accomplish this, a deep
review of the telecommunication regulatory framework has to be made.
Innovative ways of pricing, new grounds for cost sharing and standardized
solutions, which provide the required support for interoperability in multi-
vendor and multi-technology environments, must be studied as well. Moreover,
inter-operator network sharing and cooperative slicing concepts can be
efficiently implemented by optimizing the network cost model for increasing
the overall revenue, and meanwhile providing network scalability.

Figure 3: Mapping chain that converts properties into profit

Network cost models in traditional networks are typically built based on CAPEX
and OPEX, which are estimated according to the number of base stations (BSs),
the transmission power and the traffic volume. For sliced networks, this
methodology is not appropriate any more. As each resource can be shared by
several network slices, and the slicing scheme varies from one resource to
another. Hence, OPEX cannot be generally estimated for the entire physical
network. A novel slice-oriented cost model is therefore needed. As we already
discussed, every slice is specified for a particular pre-defined service,
which covers a group of use cases with similar demands for the QoS. Therefore,
a slice can be identically defined by a set of KPI requirements.

As 5G networks are supposed to support network slices implemented by both
traditional mobile network operators (MNOs) with own network
infrastructure/resources and virtual MNOs (tenants), which rents
infrastructure and network resources from traditional MNOs to implement and
deliver services, two different business modes are active in 5G networks, and
hence also two different profit models.

  * •

Own-Slice Implementation: When a MNO implements a slice with its own network
infrastructure and resources, it holds the full a priori knowledge about the
slice, including the VNF scaling characteristic, the implementation cost, the
customer demand for the slice service and the service charge rate. Therefore
it can estimate the revenue and expenditure generated by the slice for an
arbitrary certain size, as shown in Fig. 3. By appropriately scaling the sizes
of different slices, the MNO is able to optimize the overall network profit
under the limit of its resource pool, which is an optimization problem in
resource allocation. This business mode and profit model has been discussed in
[8].

  * •

Resource Leasing for Outsourced Slices: Alternatively, a MNO can also make
revenue by leasing its network resources in predefined bundles to tenants for
their slice implementation. Different resource bundles can be provided with
respect to the slice characteristics such as service type and performance
elasticity. In this case, the leases can only be requested by the tenants
while the MNO makes the decision if to accept or to reject the request. Once a
lease is confirmed the MNO cannot flexibly scale or terminate the tenant-
slice. Nevertheless, by setting up an appropriate decision mechanism according
to the statistical knowledge of requests, the MNO can still optimal the long-
term overall revenue under the limit of its resource pool. An example of this
business case an the optimization problem has been reported in [9].

Detailed discussion and comparison of both of these two dimensions of cost
modeling is out of scope of our paper. However, it can further be developed
along with below mentioned research directions in the future.

##  V Open Research Challenges and Future Directions

Network slicing is still at its early stage in terms of development,
therefore, further enhancement and studies are needed to become a mature
technology and thus be adopted over various domains of emerging 5G system.
Despite significant advantages that network slicing brings to 5G system, there
are also some challenges that are arisen. In this section, we are going to
identify main research problems and future directions in the field of network
slicing that are needed to be investigated for its full implementation over
all parts of 5G system [1] [5] [6].

1-Business and Profit: The integration of various slices - each provides
service at different stages and targets specific end users, and partnership
between several operators through infrastructure sharing lead to create new
challenges for total network investment, service level agreement between owner
and tenant, and expected generating revenue. Considering such an integrated
business-oriented approach, new economical strategies and profit modeling
should be extensively analyzed and developed in order to meet 5G network
requirements. To reach this goal, a deep study of existing telecom regulatory
framework has to be conducted. New innovative ways of pricing, cost of
infrastructure sharing, service level agreement between the owner and tenant
of slice, and expected generating revenue should be addressed and furthermore
standardized.

2-Security: Existing and some of proposed open interfaces in network slicing,
which support network programmability lead to bring new potential attacks to
softwarized networks. These concerns are arising major barriers on the way to
deploy 5G networks, and call for an extensive study and development of multi-
level security framework consisted of both policies and mechanisms, dynamic
threat detection, user authentication, accounting management, and remote
attestation.

3-Management: Despite efficient dynamicity and higher scalability that network
slicing brings to 5G system, network management and orchestration in multi-
tenant scenarios are considered to be major concerns. In order to dynamically
assign network resources to different slices, the optimization policy that
manages resource orchestrator should deal with situations where resources
demands are vary. To accomplish this goal, i) an effective cooperation between
slice-specific management functional block and resource orchestrator is
required, ii) all policies are needed to be automatically validated, and iii)
computationally design all resource allocation algorithms and conflict
resolution mechanisms at each abstraction layer.

4-Performance: The 5G communication system is composed of several virtual
networks, different radio access technology, and various QoS requirements over
the same infrastructure. When network slices are deployed, network performance
analysis and QoS measurement can become more challenging and complicated
tasks. Therefore, an intensive study is required to provide solutions for
dynamic performance measurement and network analysis considering both time and
cost.

5-Standardization: Network slicing standardization process is still in its
initial phase and is mostly focused on vertical slicing. There are wide range
of studies being conducted on network slicing by various research projects
including NGMN, 5G NORMA, Co-Funded framework, WWRF, 3GPP, and 5GPPP. In all
these projects, network slicing is considered as one of the most fundamental
requirements of 5G communication system. The current status of network slicing
development is dealing with concept, system architecture, requirements at
different network subsections, and the impact of slicing on network
architecture. Above all these various research directions of network slicing,
a comprehensive global standardization is required to be deployed in emerging
5G system. Full standardization process of network slicing is expected to be
finalized in the context of Release 15 and beyond of 3GPP.

6-Access Network Virtualization: Core network slicing has been already
investigated, and there are numbers of available literature, which focus on
efficient slicing of this particular subdomain. However, one of the main
challenges for further network virtualization lies on the RAN of 5G system. As
5G network is composed of multiple access technologies, therefore, it is vital
for RAN virtualization solutions to be able to accommodate these various
technologies. This presents an additional comprehensive challenge on the RAN,
since it is unclear so far, whether multiple access technologies can be
multiplexed over the same hardware or each will need its own dedicated
hardware. The answers to these questions can further be investigated and
provided by conducting specific studies and various research on this
particular topic.

##  VI Conclusions

In this paper, we have provided a comprehensive discussion on concept and
system architecture of network slicing in 5G mobile communication with
particular focus on its business aspect and profit modeling. We have throughly
discussed two different dimensions of cost modeling, called own-slice
implementation and resource leasing for outsourced slices. We have further
addressed existing challenges and open research directions in the field of
network slicing for the sake of adding new contributions and providing
realistic solutions to the problems.

In future, we intend to extend various dimensions of this paper. In the system
architecture aspect, we are interested to work on the development of
horizontal slicing implementation over RAN architecture and end user devices.
On the profit modeling side, we are interested to design and develop realistic
models of resource cost and service revenue with detailed parameters. Despite
above mentioned two research directions, there are also some other very
important research challenges that are thoroughly described in the previous
section of this paper.

## Acknowledgment

This work has been performed with supports of the H2020-MSCA-ITN-2015 project
5GAuRA. The authors would like to acknowledge the contributions of their
colleagues. This information reflects the consortia’s view, but the consortia
are not liable for any use that may be made of any of the information
contained therein.

## References

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# A Probabilistic Approach to Adaptive Protection in the Smart Grid

Amr S. Mohamed Deepa Kundur
Department of Electrical Engineering
University of Toronto
Toronto, ON M5S 3G4, Canada
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
&Mohsen Khalaf
Department of Electrical Engineering
University of Toronto
Toronto, ON M5S 3G4, Canada
and Assiut University
Assiut, Egypt
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###### Abstract

Smart grids are critical cyber-physical systems that are vital to our energy
future. Smart grids’ fault resilience is dependent on the use of advanced
protection systems that can reliably adapt to changing grid conditions. The
vast amount of operational data generated and collected in smart grids can be
used to develop these protection systems. However, given the safety-
criticality of protection, the algorithms used to analyze this data must be
stable, transparent, and easily interpretable to ensure the reliability of the
protection decisions. Additionally, the protection decisions must be fast,
selective, simple, and reliable. To address these challenges, this paper
proposes a data-driven protection strategy, based on Gaussian Discriminant
Analysis, for fault detection and isolation. This strategy minimizes the
communication requirements for time-inverse relays, facilitates their
coordination, and optimizes their settings. The interpretability of the
protection decisions is a key focus of this paper. The method is demonstrated
by showing how it can protect the medium-voltage CIGRE network as it
transitions between islanded and grid-connected modes, and radial and mesh
topologies.

_Keywords_ Adaptive Protection, Microgrid, Gaussian Discriminant Analysis,
Machine Learning, Inverse-time Protection

##  1 Introduction

The smart grid is a critical cyber-physical system that plays a central role
in modernizing the energy landscape. It stands to enhance energy security,
facilitate the integration of renewable energy sources, and enable significant
improvements in energy efficiency. Enabling the smart grid is dependent on the
development of reliable protection schemes to ensure its resilience against
faults. Smart grid protection is a highly challenging task, particularly at
the distribution level in microgrids, due to factors such as bidirectional
power flow, flexible topology, and the increasing utilization of renewable
energy sources [1, 2]. As microgrids transition between different topology
configurations and between grid-connected mode with a high short-circuit
current capacity and islanded mode with limited and variable capacity, it is
vital for the protection schemes to adapt to changing grid conditions [3, 4].

Adaptive protection is regarded as the most suitable approach to protecting
microgrids [1, 5]. It involves changes in the fault response of protection
relays based on the system operating state and conditions [5, 6]. This is
commonly achieved by extending the functionality of existing traditional
protection devices, such as inverse-time over-current relays, which
constitutes a cost-effectiveness benefit in the absence of specialized
commercial microgrid relays [3] and the desire to easily integrate protection
schemes into existing devices and substations with minimal capital expenditure
[7].

Supported by years of operation in traditional power systems, over-current
relays offer an economical and effective solution to protect the power system
against faults. With the rise of microgrids, there is a growing interest to
extend the capabilities of over-current relays to enable adaptive protection
[8, 9, 10]. This requires the development of methods to update over-current
relay settings in response to changes in the grid, while maintaining both
selectivity and sensitivity [11]. Selectivity refers to the relay’s ability to
precisely locate and classify faults to isolate the smallest possible faulty
section of the power system, while sensitivity refers to the ability to
promptly and accurately detect faults to quickly clear them.

Recent studies have explored the use of data-driven techniques, including
machine learning algorithms, to leverage the growing amount of data generated
in power systems in satisfying these protection requirements. Data-driven
techniques have been applied to detecting faults [12, 2], identifying the
location, type, and phase of faults [13, 14], and adjusting relay settings
[15]. Based on the findings of these studies, it appears that data-driven
techniques can offer several benefits. Firstly, data-driven methods can
enhance the accuracy of protection decisions, improving fault detection and
classification and reducing unnecessary tripping. For example, Mishra et al.
[16] conducted a study where they compared the accuracy of fault detection in
protection schemes based on decision trees and random forests with traditional
over-current relays. Their study showed over 40% improvement in fault
detection accuracy when leveraging the machine learning algorithms. Secondly,
data-driven techniques can offer a scalable solution to adapting relay
settings, significantly reducing the need to manually identify system topology
configurations and compute relay settings. For example, in centralized
communication-based implementations, data-driven techniques have the potential
to replace traditional relays, monitoring the entire power system and directly
controlling circuit breakers [5]. We survey some of the literature applying
data-driven techniques to adaptive protection in Section 2.

Data-driven techniques, however, come with their own set of limitations and
potential threats to protection reliability. Black-box algorithms, such as
neural networks and random forests, while often highly accurate, cannot be
easily verified or validated, making them a significant risk for adoption in
safety-critical applications such as protection. Some other algorithms such as
decision trees, while more interpretable, may suffer from instability:
inconsistent decisions resulting from small changes in input data. This
instability can also make it difficult to validate their decisions, thus
undermining their feasibility for protection. To successfully integrate data-
driven techniques into adaptive protection, it is crucial to ensure that the
interpretability of the protection decisions is preserved. This will enable
protection engineers to verify the decisions while simultaneously reducing
potential threats to reliability.

Additionally, adaptive protection schemes, which rely on real-time
communication infrastructure such as peer-to-peer communication between relays
or communication between a central protection management center and relays,
may face potential threats to reliability due to network failure, latency, and
cyberattacks [17, 11]. Although increased communication can lead to more
accurate and informed protection decisions, the associated risks and threats
must be carefully considered.

To acquire benefits of data-driven techniques and communication-based adaptive
protection while reducing threats to reliability, we propose a novel data-
driven adaptive protection scheme that emphasizes the interpretability of
protection decisions for validation and minimizes reliance on communication.
Our proposed approach is based on Gaussian discriminant analysis and is
designed to: (1) identify the system topology configurations that require a
change in the protection relays’ fault response, (2) specify necessary
communication with relays, (3) locate faults with respect to relays for relay
coordination, and (4) optimize relay settings for fast fault clearing. This
approach is centralized with a central microgrid protection management center
communicating with relays following infrequent major grid changes. To
demonstrate the effectiveness of our proposed strategy, we apply it to
inverse-time protection relays.

Contributions.

  * •

Our work presents a first-of-its-kind application of Gaussian discriminant
analysis (GDA) to adaptive protection. Through our research, we discuss and
demonstrate several benefits of GDA for adaptive protection, including
improved data- and computational-efficiency, interpretability for ease of
validation, adaptability to changing grid conditions, timely response, and
reduced reliance on communication for protection. To showcase the
interpretability of our proposed strategy, we put emphasis on visualizing its
protection decision-making process in this paper.

  * •

We extend the inverse-time protection formula to improve fault distinction by
incorporating voltage drops associated with faults.

  * •

We formulate an optimization problem that enables the coordination and
optimization of relays in a changing system environment.

We validate the strategy on the CIGRE medium voltage benchmark system. The
benchmark system permits many configurations to help validate the proposed
adaptive protection method, including radial and mesh topology, and grid-
connected and islanded modes.

Organization. The rest of the paper is structured as follows: We survey
related work in Section 2. We present background material in Section 3. We
present the problem statement discussing the goals of data-driven adaptive
protection in Section 4. We develop the protection strategy in Section 5.
Next, we illustrate and discuss the results of the protection strategy using
the benchmark system in Section 6. The conclusion is in Section 7.

##  2 Related Work

The literature reviews in [17, 4, 6] provide different perspectives on
adaptive protection. We will summarize the contents of these reviews that are
relevant to our work. Our work proposes an intelligent centralized protection
scheme with pre-set relays, which involves a central microgrid protection
management center issuing instructions to the relays to switch their settings
only after significant topology changes. Next, we will survey some of the
literature that applies data-driven techniques to adaptive protection to
motivate our work.

In their analysis of literature on adaptive protection in the context of
communication, Gutierrez-Rojas et al. [17] categorize their examination
according to communication technology (wireless or wired) and control approach
(centralized or decentralized). Most of the adaptive protection research
proposes centralized control approaches. In centralized control, a central
control center is established to monitor the power system in real-time and
send (either wired or wireless) instructions to relays to switch between relay
settings or directly to circuit breakers to trip. For example, Oudalov et al.
[18] implemented a centralized control approach in which wired communication
is established between the control center and advanced circuit breakers with
integrated over-current relay units. In real-time, data is collected from the
circuit breakers and relay settings are modified. Alternatively, communication
can be limited to notifying relays of infrequent major grid topology changes,
such as network reconfiguration, as in [8], with local measurements used to
detect other changes, such as distributed energy resource status.

Barra et al. [4] organize their review by the methods that rely on
computational intelligence, such as machine learning, fuzzy logic, and
optimization, and methods that do not.

Khalid et al. [6] categorize their review based on papers that propose methods
for fault detection, relay setting adjustment to changes in network
configuration, or relay optimization for coordination, and papers with methods
that require and do not require pre-setting relays.

Recent studies have explored the use of data-driven techniques to make use of
the growing streams of data in power systems for more accurate and reliable
adaptive protection. In these studies, machine learning algorithms are used to
identify (or detect) the presence of a fault, classify the type of fault
(phase-to-ground, phase-to-phase, etc.), and locate the fault in order to
isolate it. Typically, the data collection, pre-processing, and mining, as
well as model training are performed offline. For example, Lin et al. in [12]
trained two artificial neural networks (ANN) models to classify and locate
faults using current measurements. The fault localization ANN was replaced
with a support vector machine (SVM) in [2]. In [2], the fault localization
accuracy of the SVM model was consistently over 99% (when testing the method
using the IEEE 9 bus system). However, the classification accuracy of the ANN
dropped to 77.5% and 80.5% on some lines where fault classification was
challenging. This highlights the challenge of accurately classifying faults in
microgrids.

Similarly, Zayandehroodi et al. in [19] used combinations of radial-basis
function ANNs to locate faults using current measurements. Their results show
that the first ANN was able to locate the fault within 0.01 km error. The
second ANN predicts the faulty line based on the fault location. They propose
a backtracking algorithm to coordinate between relays.

Other studies like James et al. [13] and Tang et al. [15] trained algorithms
on statistical features extracted from wavelet transforms of current
measurements. James et al. used deep recurrent ANNs with to classify and
locate faults. Their method achieved a fault detection, and fault-type and
-phase classification accuracies of over 97%, and over 94% accuracy in fault
localization. Tang et al. used decision trees (DT) local to each relay to
classify faults. Instead of using communication with a central controller,
they proposed a peer-to-peer communication system between relay intelligent
electronic devices (IED). A novelty in Tang et al. was the use of an ANN to
adjust relay settings.

Although neural networks can be highly accurate and valuable for addressing
the complexities of adaptive protection, they pose significant risks for
adoption due to their black-box nature and difficulties in verification and
validation. Alternatively, the authors in [14] and [16] applied interpretable
machine learning algorithms to adaptive protection. Abdelgayed et al. [14]
applied a variety of algorithms to statistical features extracted from wavelet
transforms of current measurements to classify faults type. The accuracy of
the algorithms were as follows: k-nearest neighbors (kNN) with 95.63%, DT with
90.4%, SVM with 93.3%, and naïve Bayes with 94.24%. Mishra et al. used DTs to
detect and classify faults with 97% and 85% accuracy, respectively.

Although their decisions are interpretable, DTs have a drawback of
instability, meaning that small changes in the training data can result in
large changes in the structure of the decision tree, leading to vastly
different hypotheses and undermining their interpretability [20]. The kNN
algorithm is slow in test time as it involves calculating the distance of the
test instance to all training data. This means that as the size and
dimensionality of the training data increases, the computation time for making
a prediction also increases. This can make kNN impractical for real-time
applications with large datasets that require timeliness. Naïve Bayes and GDA
are both probabilistic data-driven techniques that are similar. GDA can learn
more complex features and potentially achieve higher accuracy. We note that
probabilistic data-driven methods are generally stable, intuitive,
interpretable, and computationally- and data-efficient [21, 22]. SVM and GDA
are comparable; we discuss why we apply GDA over SVM in Section 6.

##  3 Background

We apply our adaptive protection method to the optimization and coordination
of inverse-time protection relays. We begin this section by describing the
operation of time-inverse relays. Next, we introduce GDA, which is the
probabilistic data-driven approach that we use to distill fault data into
protection decisions. Lastly, we introduce Conditional Value-at-risk, which we
use in parametrizing the fault data for relay optimization.

###  3.1 Inverse-time Protection

Over-current relays apply the following inverse-time equation [23] to compute
their operation time: the delay before the relay trips.

$t_{op}(I_{M};\text{TMS},\eta,\lambda,L,I_{S})=\text{TMS}\left(\frac{\lambda}{\left(\frac{I_{M}}{I_{S}}\right)^{\eta}-1}+L\right)$
(1)

where $t_{op}>0$ is the relay operation time, $I_{M}$ is the relay current
measurement, and TMS and $I_{S}$ are the time-multiplier and pick-up current
settings of the relay, respectively. Directional over-current relays measure
current in one direction making them useful for protecting mesh and multi-
source grids.

Equation (1) defines a curve that is shaped by characteristic constants
$\lambda$, $\eta$, and $L$. Adaptive protection involves shifting the curve to
cope with changing grid conditions [24].

Inverse-time over-current relays work on the principle that fault currents
decrease with increasing distance to the fault location. As such, shorter
operating times are computed per (1) for nearer faults. This facilitates relay
coordination where relays closer to the fault location trip earlier to isolate
the smallest possible section of the power system.

Anticipating the challenge of coordinating relays only based on fault currents
in distribution systems, such as microgrids, due to limited fault currents, we
extend (1) to consider fault voltage.

$\displaystyle t_{op}$
$\displaystyle(I_{M},V_{M};\text{TMS},\eta_{i},\eta_{v},\lambda_{i},\lambda_{v},L_{i},L_{v},I_{S},V_{S})=$
(2)
$\displaystyle\text{TMS}\left(\frac{\lambda_{i}}{\left(\frac{I_{M}}{I_{S}}\right)^{\eta_{i}}-1}+L_{i}\right)\left(\frac{\lambda_{v}}{\left(\frac{V_{S}}{V_{M}}\right)^{\eta_{v}}-1}+L_{v}\right)$

where $V_{M}$ is the relay voltage measurement and $V_{S}$ is the pick-up
voltage settings of the relay. Setting $\lambda_{v}=0$ and $L_{v}=1$ in (2)
yields (1).

In (2), the trip time is inversely proportional to the current magnitude and
inversely proportional to the voltage magnitude. This means that the
protective device will trip faster for larger currents and voltage drops and
slower for smaller currents and voltage drops.

###  3.2 Gaussian Discriminant Analysis

GDA is a probabilistic data classification algorithm that fits a Gaussian
distribution to each class of data. Let $y\in\\{1,2,...,n\\}$ represent the
classes, and $n$ be the number of classes. The probability of sampling an
observation (or measurement) $\bm{x}$ given class $y=k$ is

$P(\bm{x}|y=k)=\mathcal{N}(\bm{x};\bm{\mu}_{k},\bm{\Sigma}_{k})$ (3)

where $\bm{\mu}_{k}$ and $\bm{\Sigma}_{k}$ are the mean vector and covariance
matrix of the Gaussian distribution fitted to class $k$, respectively. A GDA
classifier infers the observation’s class via Bayes’ theorem:

$P(y=k|\bm{x})=\frac{P(\bm{x}|y=k)P(y=k)}{\sum_{i=1}^{n}P(\bm{x}|y=i)P(y=i)}$
(4)

GDA can also be used for supervised dimensionality reduction to project the
data to a reduced subspace, which maximizes the separation between classes.
Following an assumption that all classes share the same covariance matrix of
$\bm{\Sigma}_{y}=\bm{\Sigma}$ for $y=\\{1,2,...,n\\}$, we can choose this
reduced subspace to be linear, which aids in interpreting the results of GDA.
The resulting algorithm is termed Linear Discriminant Analysis (LDA). Taking
the log-posterior of (4) gives the following equation

$\log P(y=k|\bm{x})=(\bm{\Sigma}^{-1}\bm{\mu}_{k})\bm{x}+C$ (5)

where the coefficients in $\bm{\Sigma}^{-1}\bm{\mu}_{k}$ determine the
importance of the observations’ features in separating the classes ($C$
includes other unimportant terms). Below a certain threshold, unimportant
features can be neglected to reduce the dimensionality of the problem.

###  3.3 Conditional Value-at-risk

Figure 1: Illustrating the CVaR of a Gaussian distribution. The red area under
the curve represents the $100\alpha\%$ tail of the Gaussian distribution. The
CVaRα value is the mean of this area and is represented by the vertical line.

Conditional Value-at-risk (CVaR) [25] is a risk measure of the expected value
of a random variable in the lowest $100\alpha\%$ of cases. Let $X$ be the
random variable and $q_{\alpha}$ be the $100\alpha$ percentile value of the
distribution, then the CVaR with a confidence interval of $100\alpha\%$ is

$\text{CVaR}_{\alpha}=E(X|X\leq q_{\alpha})$ (6)

For a Gaussian distribution, CVaR has the following closed-form:

$\text{CVaR}_{\alpha}=\mu-\sigma\frac{\phi(\Phi^{-1}(\alpha))}{\alpha}$ (7)

where $\mu$ and $\sigma$ are the distribution’s mean and standard deviation,
respectively; $\phi$ is the density function; and $\Phi^{-1}$ is the standard
normal quantile. CVaR1 is equivalent to the mean of the random variable

Fig. 1 demonstrates the area representing the $100\alpha\%$ tail of the normal
distribution in red. CVaRα is the mean of this area.

##  4 Problem Statement

Our data-driven adaptive protection method distills data into protection
decisions that address the following goals: (1) fault identification and
classification, (2) relay optimization and coordination, and (3) communication
specification. This section discusses these goals.

When a power system experiences a short-circuit fault, the sudden reduction in
impedance due to the introduction of the short-circuit causes a current rush.
Over-current relays must measure the increased current and isolate the fault
to prevent significant consequences, including power system instability or
equipment damage. Primary relays, closest to the fault, must trip earliest to
isolate the smallest possible section of the power system, with backup relays
coordinated to trip in case the primary fails. In practice, primary relays
should operate following a short delay to allow temporary faults to clear, and
backup relays should operate following a preset minimum coordination time
(MCT) delay to coordinate with the downstream relay.

Hence, in relation to a relay, faults can be classified according to their
distance from the relay. A fault is primary (to a relay) if the relay is the
closest device to the fault location. The next (closest) relay(s) are backup
to the primary relay. A fault can have multiple primary relays and a relay can
have multiple backups in situations of equidistant relays from the fault. In
this paper, we use the terms secondary and tertiary faults to classify faults
that are progressively further from a relay, and ‘other’ to collectively
classify tertiary and further faults. Fault identification and classification
involve enabling relays to accurately identify the existence and class of a
fault from local current and voltage measurements. Identifying the class of
the fault helps relays locate the fault, which enables their coordination.
Relay optimization and coordination involve computing relay settings to ensure
rapid, correct, selective, and coordinated protection.

Variations in power system operating conditions can significantly change the
currents measured by relays, which can cause relay misoperation. Relays must
adjust their operation in response to major grid changes, including the
transition between grid-connected and islanded modes of operation, grid
topology, and generator availability, which can significantly affect fault
current. This involves communicating (typically per the IEC61850 [26]
protocol) these grid changes to the relays and directing them to switch their
relay settings. It is desirable to minimize the reliance on communication to
reduce the infrastructure capital costs and system complexity and prevent
risks associated with communication delays and cyberattacks. Relay
communication specification involves specifying the contents of the
information that will be communicated to the relays, and the communication
channels required to enable reliable protection.

Finally, a comprehensive protection strategy must consider immeasurable,
uncertain factors, including fault impedance, renewable energy intermittency,
and fault distance from relays, which also influence the fault current.

The next section will introduce a GDA-based method that will address these
goals.

##  5 Proposed Adaptive Protection Method

Terminology. We introduce the following terminology before presenting the
method: We use $P(X|Y;Z)$ to denote the probability of a random variable $X$
given $Y$. The distribution parameters are $Z$. We denote directional relays
with R$A$-$B$, where $A$ is the bus it is located at and $B$ is the bus it is
directed to. Each relay stores multiple relay setting groups. A setting group
specifies the TMS, characteristic constants, and pick-up settings used by the
relay to compute its operation time. Each group is for a distinct relay mode
of operation, which is dependent on the state of the system. The superscript
on variable $X^{(r)}$ associates it with a specific relay $r$ and the
uppercase superscript on variable $X^{(Z)}$ additionally associates it with a
specific relay mode $\bm{Z}$. The subscript $\psi$ denotes the fault class
(e.g., primary fault).

Figure 2: Flowchart of the proposed method.

The proposed method consists of the steps shown in Fig. 2, which aim to
address the goals outlined in the Problem Formulation, Section 4. The relay
setting groups are computed via offline steps prior to deployment. The offline
steps consist of running Monte Carlo simulations to generate fault data
representing the various fault scenarios that a protection relay may encounter
following deployment. The fault data consists of local current and voltage
measurements that are locally accessible to the relay and discrete system
states, including switch and generation states, that can be communicated to
the relay from the central Microgrid Protection Management Center (MPMC) when
needed. Next, we apply the dimensionality reduction utility of GDA to identify
the minimal communication requirements of the relay: we fit an LDA classifier
to the fault data and extract the features of most importance to fault
classification. We use these features to specify the grid state (or topology)
changes that the MPMC needs to communicate to the relay to enable adaptive
protection. A stage 2 LDA parametrizes the fault data to statistics that can
be used in an optimization formulation to compute relay settings for relay
selectivity and coordination. The setting groups are stored in the memory of
each relay IED. Depending on the system state, the relay will operate in a
certain mode with an associated setting group. Post-deployment, the MPMC
communicates with the relay to switch its setting group only if the relay
needs to adapt in response to a system change.

In the case of a fault, the relay computes its operating time based on local
measurements and its relay setting group. The steps are explained in detail in
the following subsections. We focus the section on the protection against
3-phase faults as the strategy can be easily generalized to the protection
against other types of faults. We discuss applicability to different fault
types in the Discussions in Section 6.

###  5.1 Offline Steps

This subsection details the steps that are performed using offline simulation
studies prior to deployment.

Generate Fault Data. Monte Carlo simulations [27] are performed to simulate
various fault scenarios by leveraging probability distributions over factors
that affect measured fault currents and voltages, including grid topology and
generator availability and control, and uncertain factors such as fault
impedance, fault distance from the relay, renewable energy intermittency, and
fault class. Power system studies, historical data, or experts’ subjective
judgments should define these distributions.

A fault datum for relay $r$, of the form,

$\\{{\mathcal{X}},\psi,I_{F},V_{F}\\}^{(r)}$

consists of discrete measurements, ${\mathcal{X}}$, that can be infrequently
communicated to relay $r$, including switch states (closed/open) and generator
modes (in-service/out-of-service); the fault current, $I_{F}$, and voltage,
$V_{F}$, measured by the relay; and the fault class, $\psi$. In this work, we
consider three classes for $\psi$ grouped in the set
$\Psi=\\{\text{primary},\text{backup},\text{other}\\}$; but these classes can
be extended.

Specify Relay Communication. In the proposed method, each relay is an agent
making decisions based on its local current and voltage measurement and a
subset of the measurements ${\mathcal{X}}$ communicated to the relay from the
MPMC. It is desirable to reduce this subset to minimize the reliance (in terms
of communication frequency and bandwidth) on communication infrastructure for
protection decisions. To address this communication requirement, we use the
feature importance, as determined by LDA, to specify which measurements need
to be communicated to the relay to adapt its settings. A (stage-1) LDA
classifier fits Gaussian distributions to each class of $\psi$ over the space
(${\mathcal{X}}$, $I_{F}$, $V_{F}$). i.e.,

$(I_{F},V_{F})|\psi\sim\mathcal{N}(\bm{\mu}^{(r)}_{\psi},\bm{\Sigma}^{(r)}),\quad\psi\in\Psi$
(8)

after which the subset of ${\mathcal{X}}$ with significant coefficients in
$\\{\left(\bm{\Sigma}^{(r)}\right)^{-1}\bm{\mu}^{(r)}_{\psi}\\}^{(\psi\in\Psi)}$
is considered. We denote the reduced set
$\mathcal{X}^{(r)}_{S}\subseteq\mathcal{X}$.

Each of the elements in $\mathcal{X}^{(r)}_{S}$ is an equipment status, which
when changed will require the relay to use a different relay setting group.
Hence, $\mathcal{X}^{(r)}_{S}$ contains information of the minimal distinct
modes of operation of the relay. Grid changes that are not in
$\mathcal{X}^{(r)}_{S}$ would not significantly affect the protection
decisions of relay $r$, and hence, are not communicated to the relay.

Parametrize Fault Data. Next, to parametrize the fault data into statistics
that we can use for relay optimization and coordination, a (stage-2) LDA fits
Gaussian distributions to each class of $\psi$ over $(I_{F},V_{F})$ for each
grid topology identified in the reduced space $\mathcal{X}^{(r)}_{S}$. For
each relay mode $\bm{Z}$, the distributions fitted to the data are:

$\displaystyle P(I_{F},V_{F}|\psi,\bm{Z})$
$\displaystyle=\mathcal{N}\left(I_{F},V_{F};\bm{\mu}^{(Z)}_{\psi},\bm{\Sigma}^{(Z)}_{\psi}\right),$
(9) $\displaystyle\psi\in\Psi,\bm{Z}\in\mathcal{X}^{(r)}_{S}$

where

$\bm{\mu}^{(Z)}_{\psi}=\begin{bmatrix}{\mu}\\{I_{F}\\}^{(Z)}_{\psi},{\mu}\\{V_{F}\\}^{(Z)}_{\psi}\end{bmatrix}$
$\bm{\Sigma}^{(Z)}_{\psi}=\begin{bmatrix}{\sigma}^{2}\\{I_{F}\\}^{(Z)}_{\psi}&{\sigma}\\{I_{F},V_{F}\\}^{(Z)}_{\psi}\\\
{\sigma}\\{I_{F},V_{F}\\}^{(Z)}_{\psi}&{\sigma}^{2}\\{V_{F}\\}^{(Z)}_{\psi}\end{bmatrix}$

denote the mode’s fault statistics: ${\mu}\\{I_{F}\\}^{(Z)}_{\psi}$ and
${\mu}\\{V_{F}\\}^{(Z)}_{\psi}$ are the means of the fault current and
voltage, respectively, and ${\sigma}^{2}\\{I_{F}\\}^{(Z)}_{\psi}$ and
${\sigma}^{2}\\{V_{F}\\}^{(Z)}_{\psi}$ are the variances of the fault current
and voltage, respectively, in mode $\bm{Z}$.

Compute Relay Settings. Next, relay settings are optimized, using the above
fault statistics, to achieve speed and selectivity of protection, and
facilitate relay coordination. We will describe the parameters of the
optimization problem before formulating it. To simplify relay optimization, we
assume $L_{i}=L_{v}=0$ in (1) and introduce the variable
$\zeta=\text{TMS}\times\lambda_{i}\lambda_{v}$ to derive the following
equation for relay operating time:

$\displaystyle t_{op}$
$\displaystyle(I_{M},V_{M};\zeta,\eta_{i},\eta_{v},I_{S})=$ (10)
$\displaystyle\frac{\zeta}{\left(\left(\frac{I_{M}}{I_{S}}\right)^{\eta_{i}}-1\right)\left(\left(\frac{V_{S}}{V_{M}}\right)^{\eta_{v}}-1\right)}$

The objective is to optimize the parameters $\zeta$, $\eta_{i}$, and
$\eta_{v}$.

To include information about both the mean and variance of the current and
voltage fault data in the optimization problem, we replace $I_{M}$ and $V_{M}$
in (10) with

$I_{M}=\text{CVaR}_{\alpha_{i}}(I_{F})=\mu\\{I_{F}\\}^{(Z)}_{\psi}-\sigma\\{I_{F}\\}^{(Z)}_{\psi}\frac{\phi(\Phi^{-1}(\alpha))}{\alpha}$
(11)
$V_{M}=\text{CVaR}_{\alpha_{v}}(V_{F})=\mu\\{V_{F}\\}^{(Z)}_{\psi}-\sigma\\{V_{F}\\}^{(Z)}_{\psi}\frac{\phi(\Phi^{-1}(\alpha))}{\alpha}$
(12)

Using the CVaR enables more control over the parametrization of the fault
statistics, as we will illustrate in Section 6.

We use the following notation in the optimization problem formulation:
$\mathcal{R}$ is the set of all relays in the system, $\mathcal{B}$ is the set
of all buses in the system, $\mathcal{P}_{B}\subset\mathcal{R}$ is the set of
all primary relays to bus $B$, and $\mathcal{S}_{p}\subset\mathcal{R}$ is the
set of all backup relays to relay $p$. $\bm{\zeta}$ is the vector of all
settings $\zeta^{(r)},r\in\mathcal{R}$. $\eta_{i},\eta_{v}$ are the same for
all relays in the system for a specified topology. Primary relays should
operate following a short delay $\text{D}_{\text{min}}$, and backup relays
should operate following an MCT delay.

For all grid topology configurations, we solve the following:

$\displaystyle\min_{\bm{\zeta},\eta}\quad$
$\displaystyle\sum_{B\in\mathcal{B}}\bigg{(}\sum_{p\in\mathcal{P}_{B}}\Big{(}t_{op}\big{(}\text{CVaR}^{(p)}_{\alpha_{i}},\text{CVaR}^{(p)}_{\alpha_{v}};\zeta^{(p)}\big{)}$
$\displaystyle+\sum_{b\in\mathcal{S}_{p}}t_{op}\big{(}\text{CVaR}^{(b)}_{\alpha_{i}},\text{CVaR}^{(b)}_{\alpha_{v}};\zeta^{(b)}\big{)}\Big{)}\bigg{)}$
(13) subject to
$\displaystyle\eta_{i,\text{min}}\leq\eta_{i}\leq\eta_{i,\text{max}}$ (14)
$\displaystyle\eta_{v,\text{min}}\leq\eta_{v}\leq\eta_{v,\text{max}}$ (15)
$\displaystyle\zeta_{\text{min}}\leq\zeta^{(r)}\leq\zeta_{\text{max}},\quad
r\in\mathcal{R}$ (16) $\displaystyle
t_{op}\big{(}\text{CVaR}_{\alpha_{1}};\zeta^{(p)}\big{)}\geq\text{D}_{\text{min}}$
(17) $\displaystyle
t_{op}\big{(}\text{CVaR}_{\alpha_{2}};\zeta^{(b)}\big{)}-t_{op}\big{(}\text{CVaR}_{\alpha_{1}};\zeta^{(p)}\big{)}\geq\text{MCT},$
(18) $\displaystyle\quad\quad\quad\quad
B\in\mathcal{B},p\in\mathcal{R}_{B},b\in\mathcal{S}_{p}$

Next, relay settings $\\{{\zeta}^{(r)},\eta_{i},\eta_{v}\\}$ are stored in-
memory on relay $r$ if the grid topology is identified in
$\mathcal{X}^{(r)}_{S}$.

This optimization problem over $\\{\bm{\zeta},\eta_{i},\eta_{v}\\}$ is not
convex. However, pre-setting $\eta_{i},\eta_{v}$ yields a linear program over
$\bm{\zeta}$. We optimize $\eta_{i},\eta_{v}$ via gradient descent by re-
running the linear program for different values of $\eta_{i},\eta_{v}$. While
not convex, in practice we have found that starting from very small
$\eta_{i}=\eta_{v}=0.01$ yields good optimization results.

The pickup settings $I_{S},V_{S}$ are preset before optimization. $I_{S}$
should exceed the maximum full-load line currents, and $V_{S}$ should be less
than bus voltages seen during normal operation. We compute $I_{S}$ separately
for each relay depending on its line’s maximum load, and preset $V_{S}$ to
$0.9$ pu for all relays.

###  5.2 Online Operation

During operation, each relay will operate in a specific relay mode with a
relay setting group, based on the current state of the system. If the system
state changes, and the relay’s fault response needs to be switched
accordingly, the MPMC will communicate with the relay to instruct it to switch
to a different relay setting group. The communication between the MPMC and the
relay should be developed to ensure that the MPMC message has been delivered
successfully to the relay (e.g., acknowledgments); else, the message should be
redelivered.

In the event of a fault, the relay detects the fault by checking whether its
local current and voltage drop measurements exceed its pickup settings.
Applying (10), the relay will calculate its operating time. If the fault is
not cleared before the relay’s operating time is reached, the relay will trip
its circuit breaker. If the relay fails to trip, backup relays will have
computed a longer operating time and will trip their circuit breakers
following an MCT delay. After tripping its circuit breaker, the relay will
communicate to the MPMC the open status of its circuit breaker.

##  6 Simulation Results, Validation and Discussion

Figure 3: CIGRE medium voltage distribution network [28, 3]. It consists of
two microgrids (MG). S denotes a switch, PC a point-of-common coupling, and DG
a distributed generator.

In this section, we will illustrate the proposed method and discuss its
benefits. The benchmark system we use to demonstrate the results is the CIGRE
medium voltage distribution network, shown in Fig. 3. The system is composed
of two radial microgrids (or feeders), but meshed topology can be obtained by
closing switches S1, S2, and S3. The system-rated voltage and frequency are
12.47 kV and 60 Hz. For the purpose of studying fault current contributions
from distributed generation, we add, as in [3], three DG units:

  1. 1.

DG1 is a 4 MW rated full-scale VSC-interfaced DG. A 5 MVA, 4.16/12.47 kV,
$X=0.07$ pu dYG transformer connects the DG to bus 6.

  2. 2.

DG2 is composed of two 4.3 MVA synchronous generators. A 10 MVA, 4.16/12.47
kV, $X=0.07$ pu dYG transformer connects the DGs to bus 8.

  3. 3.

DG3 is a 4.3 MVA synchronous generator. A 5 MVA, 4.16/12.47 kV, $X=0.07$ pu
dYG transformer connects the DG to bus 12.

The two microgrids can each operate in islanded mode as DG2 and DG3 can supply
entire loads of their respective microgrids, form an islanded mesogrid, or
operate in grid-connected mode. Hence, the benchmark system permits many
configurations to help validate the proposed adaptive protection method. We
generate short circuit data using Pandapower [29]. Pandapower is an open-
source software library for power system analysis and optimization in Python,
which we use for the ease of integration with Python’s data analysis and
machine learning libraries. Pandapower’s short circuit calculations are based
on IEC60909 [30] and tested against DigSilent. We also verify our results
using a PSCAD time-domain fault simulation. The probability distributions used
to generate Monte Carlo simulations for faults with different grid topology
and fault impedance are outlined in Table LABEL:table:monte-carlo-vars in the
Appendix.

The studied cases focus on relay R12-13 and the protection of bus 8 for the
insights that can be gained from their analysis. The study of R12-13 validates
the method for adjusting relay settings in response to variations in fault
current resulting from transitioning from an isolated to a grid-connected mode
of operation, as well as modifications in network structure from radial to
mesh configuration. The study of Bus 8 faults validates the method for
coordinating relays in a mesh topology. In optimizing the relay settings, we
set $\text{D}_{\text{min}}=3$ cycles, $\text{MCT}=0.15$ seconds, and
$\alpha_{i}=\alpha_{v}=1$.

###  6.1 Computing offline relay settings of R12-13

|
---|---
(a) | (b)

---
(c)

Figure 4: Kernel density estimation plots of (a) current multiples, (b)
voltage inverse multiples, and (c) current multiples and voltage inverse
multiples measured by relay R12-13 during 3-phase faults.

Fig. 4 illustrates kernel density estimations (KDE) of the fault current and
voltage data of relay R12-13. The independent variables in Fig. 4 (a) and (b)
represent the fault currents and voltages measured by R12-13 during the
primary, secondary, and other classes of faults. Fig. 4 (c) combines the
currents and voltages into a single KDE plot. Note that the current (voltage)
is expressed in terms of multiples (inverse multiples) of the current
(voltage) pickup setting. The significant overlap between the different fault
classes hinders the ability to classify faults based on the fault current
and/or voltage magnitude. In order to address this issue, the stage-1 LDA
separates the relay operation into modes that better distinguish the fault
classes based on current and/or voltage measurement to enable a local
measurements-based approach for protection.

Fig. 5 displays the feature importance coefficients as determined by the
stage-1 LDA. From Fig. 5, it is observed that the features with the most
significant importance coefficients are the voltage and current magnitudes,
and the status of the downstream switch S1. This is further confirmed in Fig.
6 by evaluating the LDA’s classification accuracy as the number of features it
has access to is increased (in accordance with the order of feature importance
in Fig. 5). The blue bars in Fig. 6 indicate the accuracy when classifying
faults into 3 classes (primary, secondary, or other), and the orange bars
indicate the accuracy when classifying faults into 2 classes
(primary/secondary or other). The classifier’s accuracy (in blue) reaches a
plateau of $77\%$ after being provided with a small subset of the measurements
comprising the voltage and current magnitudes, and the states of S1 and PC2.
As such, we compartmentalize the R12-13’s operation into $2^{2}=4$ modes of
operation corresponding to permutations of each of S1 and PC2 being open or
closed. Hence, the MPMC needs only to communicate the status of S1 and PC2 to
relay R12-13.

Figure 5: Feature importance coefficients of the GDA classifier trained on
R12-13 fault data. The voltage (V) and current (I) are the only two local
measurements. The rest are states of switches (S), points-of-common coupling
(PC), or distributed generators (DG) that can be communicated to the relay
from the MPMC. Figure 6: GDA fault classification accuracy. The classes are
primary (P), backup (B), and other (O). Each bar represents the classification
accuracy when the GDA is trained on its feature, in addition to all features
to the left of the bar. The right-most bar is the GDA accuracy when trained on
all features. The accuracy plateaus after the first 4 features.

In Fig. 7 (a) to (d), we divide R12-13’s operation into these 4 modes and plot
the KDEs of the fault current and voltage data in each mode. Fig. 7 (a) and
(b) correspond to the modes with S1 open; hence, R12-13 only measures primary
and secondary faults. Fig. 7 (b) and (d) correspond to the modes with PC2
closed; hence, R12-13 experiences higher fault current magnitudes due to the
increased contribution from upstream sources, including the main grid.

It can be observed that by compartmentalizing the relay operation into modes,
the overlap between the different fault classes is significantly reduced,
facilitating the distinction of fault classes based on voltage and current
magnitude. The fault current (voltage) magnitude decreases (increases) as the
distance from the fault increases. This enables the use of inverse-time
protection to coordinate relays. The objective of the stage-2 LDA is to
parametrize the fault data so that their distribution statistics can be
utilized for relay coordination.

To the right of each KDE plot in Fig. 7, we plot the corresponding inverse-
time operation curves against the fault current (measured as multiples of
pickup current setting). While the relay operation time is a function of both
the fault current and voltage, we only plot the operation curves against the
fault current for the purposes of demonstrating relay coordination, as it is
hard to observe the coordination in a 3-dimensional plot. We illustrate the
full 3-dimensional inverse-time operation curve of R12-13 against both fault
current and voltage (measured as inverse multiples of pickup voltage setting)
for mode (c) in Fig. 8.

(a) |  |
---|---|---
(b) |  |
(c) |  |
(d) |  |
Figure 7: (left) Kernel density estimation plots of current multiples and
voltage inverse multiples measured by relay R12-13 and (right) relay operating
curves against current multiples for each of its four modes. Modes (a): S1,
PC2 open, (b): S1 open, PC2 closed, (c): S1 closed, PC2 open, (d): S1, PC2
closed.

To demonstrate relay coordination:

  * •

We plot vertical dashed lines in Fig. 7 to illustrate the CVaR of primary
fault currents measured by R13-14 (blue), i.e.,
$\text{CVaR}_{\alpha_{i}}(I_{F})^{13-14}$.

  * •

Since the current multiple measurements by the backup relay R12-13 might be
different than that measured by R13-14 due to different $I_{S}$ settings or
line branching, we shift the operation curve of R12-13 so that the vertical
line also matches how R12-13 measures the fault current.

  * •

The voltage value of each of the operation curves of R13-14 and R12-13
corresponds to the voltage values each measures during the fault characterized
by the vertical line.

The intersection of the relay curve with the dashed line marks the relay
operation time; hence, the higher curve trips later. Relay coordination can be
easily evaluated by looking at the relay operation curves. R12-13 serves as a
backup for R13-14, which can be observed from R12-13’s curve being higher than
R13-14’s curve in all modes.

Fig. 7 illustrates how the relays adjust to changes in the grid operation,
including going from connected to islanded modes and switching between radial
and meshed topologies. The 4 relay group settings for R12-13 and its
downstream relay R13-14 are included in Table LABEL:table:m2settings in the
Appendix. These settings groups must be stored in their memories to enable
them to adapt to changing conditions.

Figure 8: Relay operating curve of relay R12-13 against current multiples and
voltage inverse multiples for mode (c): S1 closed, PC2 open.

Remarks: In modes (a) and (b) when S1 is open, the optimization results in a
TMS of 0 for R13-14, which means it is sufficient to operate R13-14 as an
instantaneous over-current relay. The increase in operation time for the
relays when S1 is closed allows for coordination with relays further
downstream.

In Fig. 7 (c), an important insight is the distinctive ‘crescent’ shape
observed in the KDE plot. This shape indicates that voltage drops increase
more significantly than fault current increases for nearer faults. A factor
contributing to this is the limited fault current of distributed generation.
As a result, incorporating voltage measurements enhances the ability to
distinguish fault classes in this mode. This finding supports our decision to
include voltage drops in the inverse-time relay operation.

Lastly, we discuss how the use of CVaR is beneficial in the relay optimization
process. Fig. 9 shows how different value pairs of CVaR for current and
voltage can be used to better control how the data is parametrized before it
is used in the optimization. Lowering the CVaR values allows for greater
emphasis on the lower tails of the fault current and voltage distributions.
This is useful because inverse-time protection is faster at clearing faults
with high current and low voltage magnitudes (top-right corner of the figure).
Lowering (raising) the CVaR values shifts the focus of the optimization and
allows for faster (slower) clearing of faults.

Figure 9: Illustrating the benefits of CVaR in optimization. Each point
represents
$(\text{CVaR}_{\alpha_{i}}(I_{F})^{12-13},\text{CVaR}_{\alpha_{v}}(V_{F})^{12-13})$.
The values of $(\alpha_{i},\alpha_{v})$ are annotated.

###  6.2 Relay coordination at Bus 8 with topology change

|
---|---
(a) | (b)
|
(c) | (d)
Figure 10:  Relay operation curves against current multiples for relays (a)
R14-8, R13-14, and R12-13, (b) R7-8 and R6-7, and (c) R3-8, R2-3, and R1-2 for
a fault at bus 8 when S3 is open and S1, S2, PC1 and PC2 are closed. (d) Relay
operation curves against current multiples for relays R3-8, R2-3, and R1-2 for
a fault at bus 8 when S1, S2, and S3 are open and PC1 is closed. Figure 11:
PSCAD simulation of the (a) instantaneous current measured by R1-2, (b)
voltages, and (c) tripping signals of R3-8, R2-3, and R1-2 for a $1\Omega$
fault at bus 8 with PC1 closed, and switches S1, S2, and S3 open.

To validate the method for coordinating relays in a mesh topology, we consider
faults at bus 8. When S1 and S2 are closed, a fault at bus 8 is isolated by
three primary relays: R14-8, R7-8, and R3-8. Each primary relay has one or
more backup.

In Fig. 10, we plot the relay operation curves of relays (a) R14-8, (b) R7-8,
and (c) R3-8 and their backup relays when PC1, PC2, S1 and S2 are closed. The
dashed vertical lines show the CVaR of fault currents measured by the primary
relays for faults at bus 8. The figure demonstrates the successful isolation
of the fault from all generation sources and relay coordination in case of
relay failure.

If S1 and S2 are open, the topology of the microgrids becomes radial with R3-8
offering primary protection to bus 8 and R2-3 and R1-2 its backups. The fault
current is supplied by the main grid. The relay operation curves of these
relays in this case are shown in Fig. 10(d). PSCAD simulations validate the
coordination results of this case study. In Fig. 11, a $1\Omega$ fault occurs
at bus 8 at the 0.2 seconds mark. We suppress the operation of the primary
(R3-8) and its backup (R2-3) relays, and let R1-2 isolate the fault. The
operation times of the relays closely match the coordination curves in Fig.
10(d).

The relay settings for these two case studies are listed in Table
LABEL:table:m1settings in the Appendix.

###  6.3 Discussion

The proposed method has the following merits:

Figure 12: Comparing LDA classification accuracy with other algorithms.

####  6.3.1 Evaluating LDA accuracy

The significant overlap of different fault classes observed in Fig. 4 shows
that it is infeasible to classify a fault based only on local current and
voltage measurements. In Fig. 12, we compare the classification accuracy of
multiple machine learning algorithms in classifying the faults measured by
R12-13 when limiting the training data to discrete grid states and local
measurements – to avoid the reliance on real-time communication. On the left
side of Fig. 12, we include algorithms that yield interpretable results,
including SVM, DT, LDA, and kNN. On the right, we include algorithms that
generally have lower learning bias and higher accuracy, but do not yield
interpretable results, including random forest (RF) and multi-layer
perceptrons (MLP). Hyperparameter optimization for these algorithms is listed
in Table LABEL:table:hyperparameters in the Appendix. We observe that MLPs
achieve the highest classification accuracy, as expected; but, highlighting
the difficulty of the classification task, the maximum accuracy is only
$84\%$.

Note that these algorithms have been shown to yield higher performance in
centralized real-time communication-based protection strategies in the
literature, when not constrained to local measurements and discrete system
states. But this exposes the protection to reliability threats related to the
communication infrastructure.

While LDAs accuracy is lower, the interpretability of the LDA results enabled
us to augment it with an optimization-based approach that facilitates relay
coordination, preventing miscoordination between relays and their backups. The
interpretability of LDA enabled easy visualization of the fault data
statistics, protection decisions, and relay coordination. Hence, the results
of the method can be easily interpreted and validated by system operators and
protection engineers, facilitating its use for adaptive protection and
reducing associated implementation risks and reliability threats.

Despite its lower accuracy, we prefer LDA over DT due to its stability.
Further, we prefer LDA over SVM since LDA enables fitting Gaussian
distributions to fault classes, which we use to reduce problem dimensionality
and parametrize the fault data for optimization. As observed by the results,
Gaussian distributions fit well to the fault data.

####  6.3.2 Communication Network Delays and Cyberattacks

The proposed protection strategy requires communication of the grid topology
to the relays. Generally, this reliance on communication infrastructure can
expose the protection relay operation to potential risks, such as network
delays or cyberattacks. To address this issue, our method minimizes
communication to the relays by communicating only a subset of the infrequent
major changes to the grid topology. The necessary settings to operate the
relays in real-time are stored locally in memory on the relays. This provides
an advantage over centralized protection strategies that require a constantly
active communication channel with the relay. Due to the infrequent
communication, temporary network delays will not significantly impact the
protection. Further, the infrequency permits the use of encryption algorithms
to authenticate and protect the communication to relays. This approach ensures
that the proposed protection strategy is more secure against potential
cyberattacks and/or network delays.

####  6.3.3 Achieving Protection Relay Characteristics

The strategy extends the operation of inverse-time protection relays by
adapting protection decisions to changing grid conditions and considering
voltages for an improved distinction of faults in systems with limited fault
currents. Below, we evaluate the proposed strategy against the characteristics
of effective protection strategies.

  * •

Reliability: The proposed protection strategy detects and clears faults in a
timely and accurate manner. The optimization problem minimizes the operation
time of relays to expedite isolating faults.

To prevent false alarms or misoperations, the relays in the proposed strategy,
similar to existing inverse-time over-current relays, do not trigger unless
the fault current exceeds a preset pick-up current setting.

Uncontrolled variables, including fault impedance, inception angles, pre-fault
power system conditions, and relay measurement errors, can be modeled into the
Monte-Carlo simulations. Further considerations, including in-rush currents
due to switching of loads, distributed generation, filter capacitors, or
transformers and transformer saturation, can be addressed as is currently with
over-current relays or included as constraints in the optimization (5.1).

  * •

Selectivity: As illustrated in the KDE plots, the proposed protection strategy
compartmentalizes relay operation into modes, in which it is more feasible for
the relay to discriminate between different types of faults based on local
measurements.

  * •

Coordination: As demonstrated by relay curves in multiple case studies in the
paper, the protection strategy is able to coordinate relays to isolate minimal
sections of the system during faults.

Non-adjustable devices, such as fuses, should be coordinated with the relays,
or further constraints can be considered in the optimization (5.1) to
coordinate with any devices.

  * •

Adaptability: Cases have demonstrated the ability of the relays to adapt to
transitions from isolated to a grid-connected mode of operation with higher
short-circuit capacities, as well as modifications to network topology from
radial to mesh configuration.

  * •

Simplicity: Modern IEDs used for protection can readily process the proposed
protection strategy. The strategy minimizes the reliance on the communication
infrastructure and memory use of the IEDs.

In addition, the method yields interpretable decisions that can be easily
validated by protection engineers.

  * •

Communication: The strategy relies on a communication infrastructure between
the MPMC and relays. Commands can be established from the MPMC to switch the
relay setting group by means of the IEC61850 protocol.

The method minimizes the communication bandwidth and frequency, only relying
on infrequent updates due to changes in a grid topology.

####  6.3.4 Applicability to Different Protection Relays and Fault Types

The proposed method specifies the communication requirements and optimizes
relay settings. While we demonstrated our method on inverse-time protection
relays, the method can be extended to other protection devices, such as
distance relays, to adapt their operation to changing grid conditions. We
emphasize that the main contribution of the paper is the data-driven
component: applying GDA to the adaptive protection of power systems.

We demonstrated the strategy for 3-phase faults. The proposed strategy is
applicable to other fault types. In the same way that relay settings were
computed for 3 phase faults in the paper, data can be generated and relay
settings can be computed for other fault types. The relay settings will be
stored on the relay IED memory. During a fault, the relay will use the current
and voltage measurement to distinguish the fault type. The relay settings for
the fault type and relay mode will be used to compute an operation time and
isolate the faulted phases.

##  7 Conclusion

In recent years, there has been a growing interest in utilizing machine
learning for adaptive protection in power systems, leveraging the increasing
amount of power system data. However, safety-critical applications such as
power system protection require methods that are transparent, interpretable,
and easily validated. Deep learning methods, although highly accurate, are
difficult to validate – presenting a significant risk to their utilization for
power system protection.

To address this issue, we propose a novel adaptive protection strategy for
inverse-time relays based on probabilistic machine learning, specifically
Gaussian discriminant analysis. We apply the strategy to distill power system
data to inverse-time relay settings, generating operation curves that can be
used to verify and validate protection decisions. We demonstrate the use of
our strategy for fault detection and localization, relay coordination and
optimization, and protection management by specifying minimal communication
requirements for adapting relays. To demonstrate the effectiveness of our
method, we apply it to the protection of the CIGRE medium voltage grid, as it
switches between islanded and grid-connected modes of operation, as well as
radial and mesh topology in the presence of distributed generation.

Table 1: Monte Carlo Simulation Variations Random variable | Values
---|---
Fault resistance | $\text{Unif}(0,3)\Omega$
Fault reactance | $\text{Unif}(0,3)\Omega$
Main grid short-circuit capacity |  $20-22$ MVA
DG1 short-circuit to nominal current ratio | $1.1-1.3$
Switch status | On/Off
PC states | On/Off
Generator in-service | True/False
Table 2: Relay Settings for relays R12-13 and R13-14 Mode | $\eta_{i}$ | $\eta_{v}$ | $\zeta^{13-14}$ | $\zeta^{12-13}$
---|---|---|---|---
S1 Open, PC2 Open | 1 | 1 | 0 | 0.81
S1 Open, PC2 Closed | 1 | 1 | 0 | 0.62
S1 Closed, PC2 Open | 1.24 | 0.9 | 2.03 | 2.52
S1 Closed, PC2 Closed | 1.2 | 1.01 | 3.17 | 2.27
Table 3: Settings of relays protecting bus 8 Mode | $\eta_{i}$ | $\eta_{v}$ | Primary | Backup
---|---|---|---|---
Open: S1, S2, S3 | 0.1 | 2.89 | $\zeta^{3-8}=5.07$ | $\zeta^{2-3}=0.66$
Closed: PC1, PC2 |  |  |  |
Closed: S1, S2 | 0.1 | 4.75 | $\zeta^{3-8}=7.03$ | $\zeta^{2-3}=2.26$
PC1, PC2 |  |  | $\zeta^{14-8}=3.25$ | $\zeta^{13-14}=1.85$
Open: S3 |  |  | $\zeta^{7-8}=6.75$ | $\zeta^{6-7}=14.91$
Table 4: Hyperparameter optimization Algorithm | Hyperparameters | Range | Optimal
---|---|---|---
RF | Number of DTs | 5-40 | 30
kNN | Number of neighbors | 2-10 | 8
MLP | Hidden layers | 5-80 | 40

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