A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks

Amitkumar V. Jha; Bhargav Appasani; Nicu Bizon; Phatiphat Thounthong

doi:10.3390/asi6010007

Jha, Amitkumar V.;Appasani, Bhargav;Bizon, Nicu;Thounthong, Phatiphat

2023-01-05 00:00:00

Article A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks 1 1 2,3,4, 5,6 Amitkumar V. Jha , Bhargav Appasani , Nicu Bizon * and Phatiphat Thounthong School of Electronics Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar 751024, India Faculty of Electronics, Communication and Computers, University of Pitesti, 110040 Pitesti, Romania Doctoral School, University Politehnica of Bucharest, Splaiul Independentei Street No. 313, 060042 Bucharest, Romania ICSI Energy, National Research and Development Institute for Cryogenic and Isotopic Technologies, 240050 Ramnicu Valcea, Romania Renewable Energy Research Centre (RERC), Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat 1 Road, Wongsawang, Bangsue, Bangkok 10800, Thailand Group of Research in Electrical Engineering of Nancy (GREEN), University of Lorraine-GREEN, F-54000 Nancy, France * Correspondence: nicu.bizon@upit.ro Abstract: In recent years, the Smart Grid (SG) has been conceptualized as a burgeoning technology for improvising power systems. The core of the communication infrastructure in SGs is the Syn- chrophasor Communication Network (SCN). Using the SCN, synchrophasor data communication is facilitated between the Phasor Measurement Unit (PMU) and Phasor Data Concentrator (PDC). However, the SCN is subjected to many challenges. As a result, the components, such as the links, PMUs, PDCs, nodes, etc., of the SCN are subjected to failure. Such failure affects the operation of the SCN and results in the performance degradation of the SG. The performance degradation of the smart grid is observed either temporarily or permanently due to packet loss. To avoid dire consequences, such as a power blackout, the SCN must be resilient to such failures. This paper presents a novel analytical method for the resiliency analysis of SCNs. A graph-theoretic approach was used to model SCN from the resiliency analysis perspective. Furthermore, we proposed a simulation framework Citation: Jha, A.V.; Appasani, B.; for validating the analytical method using the Network Simulator-3 (ns-3) software. The proposed Bizon, N.; Thounthong, P. A non-intrusive simulation framework can also be extended to design and analyse the resiliency of Graph-Theoretic Approach for generic communication networks. Modelling and Resiliency Analysis of Synchrophasor Communication Keywords: smart grid; synchrophasor communication system; resiliency; network simulator Networks. Appl. Syst. Innov. 2023, 6, 7. https://doi.org/10.3390/ asi6010007 Academic Editor: Christos Douligeris 1. Introduction Received: 2 December 2022 Recent studies have revealed the phenomenal growth in energy consumption. Uncon- Revised: 29 December 2022 ventional electricity generation sources, such as wind, solar, etc., must be streamlined to Accepted: 2 January 2023 fulﬁl such a phenomenal rise in the demand for electricity [1]. However, to effectively inte- Published: 5 January 2023 grate these sources, the modernization of existing power grids is required. The Smart Grid (SG) is a modernization of the existing conventional power grid [2]. Moreover, traditional power grids cannot incorporate new technologies and integrate renewable energy sources from individual households [3]. Further, smart metering, dynamic pricing, real-time grid- Copyright: © 2023 by the authors. status monitoring, load balancing, etc. cannot be achieved through conventional power Licensee MDPI, Basel, Switzerland. grids [4]. Consequently, conventional power grids are now being transformed into SGs due This article is an open access article to these several ﬂaws. distributed under the terms and Apart from integrating the multitude of solar sets located at individual households to conditions of the Creative Commons large offshore wind farms with conventional sources for electricity generation, SGs are also Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ useful in monitoring and controlling the health of power grids [5]. Furthermore, the smart 4.0/). grid could also avoid power blackouts to escape from huge economic losses, as observed Appl. Syst. Innov. 2023, 6, 7. https://doi.org/10.3390/asi6010007 https://www.mdpi.com/journal/asi Appl. Syst. Innov. 2023, 6, 7 2 of 20 in the cases of the North American 2003 blackout, the Indian 2012 blackout, the Italian blackout in 2003, the 2011 San Diego blackout, the 2011 Paciﬁc Southwest outage, etc. [6]. Some of the additional beneﬁts of SG technologies in the power system paradigm are their reduced cost, effective operation, operational cost savings, decreased energy losses, improved observability, and controllability of the power grid. Being ﬂexible in design and adaptable to ubiquitous emerging technologies, the SG can cater to the diverse demands of today’s era. The SG components are intertwined through the communication infrastructure. The different sensing and actuating signals are communicated over the communication network. The health of the power grid is monitored on a real-time basis through the Synchrophasor Measurement System (SMS) to ensure its efﬁcient operation [7]. The Phasor Measurement Units (PMUs) act as synchrophasor sensors in the SMS. Some of the electrical buses are equipped with PMUs for the real-time monitoring of the SG. The synchrophasor data from PMUs are sent to the Phasor Data Concentrator (PDC) located on the operator side. The operator analyses the synchrophasor data received at the PDC for the effective monitoring and control of the SG. The synchrophasor data are communicated over the Synchropha- sor Communication Network (SCN), which provides a communication infrastructure for SMS [8]. Thus, the SMS generally consists of several PMUs, PDCs, and the SCN as the prime constituents, which are used for monitoring and controlling the SG in real-time. The monitoring of the SG in real-time is an important paradigm that has been empha- sized in the literature, and a detailed survey of different technologies used in SG real-time monitoring is presented in [9]. In order to monitor and maintain the health of the SG, the SCN is crucial, which is comprehensively highlighted in [10]. It is highly complex and thus believed to be an engineering marvel. The SCN adopts a hybrid communication infrastructure, including wired and wireless interfaces, to facilitate synchrophasor data communication [11]. In fact, under a few scenarios, the only choice is to use wireless technology as there is no scope for Ethernet-based communication. However, like other applications, hybrid solutions may produce promising results in the case of synchropha- sor communication. The different communication technologies offer advantages and are plagued with a few disadvantages. Compared with wired interfaces, the wireless interfaces in SCNs are prone to access failure and stochastic delay. Further, being interdisciplinary, some other challenges exist for these networks [12]. The dynamically changing environmental conditions hinder the operation of SGs. Further, natural calamities, such as earthquakes, tsunamis, and ﬂoods, may disrupt the operation of SCNs. Furthermore, unlike the conventional communication network, the SCNs of SGs must satisfy the minimum delay requirement of the power grid due to the time-critical nature of synchrophasor applications [13]. These dynamic challenges may lead to failure in the communication links of SCNs, which disrupt the operation of SGs. However, the extent of such failure should be minimized as much as possible. To achieve the objective of mitigating the impact of link failure or to evade any dire consequences of it, SCNs are designed to be resilient. Further, a highly resilient synchrophasor communication network can respond to such failures. The paper ’s remainder is organized as follows: The motivation and related work within the paradigm of the present work are discussed in Section 2. The system modelling of the SCN and parameterization for estimating the resiliency are discussed in Section 3. Section 4 proposes a graph-theoretic approach for the resiliency analysis of SCNs. The simulation results and discussion are included in Section 5. Finally, the conclusion of the work with future direction is presented in Section 6. 2. Motivation and Related Work 2.1. Motivation SCNs are subjected to many challenges that may cause abnormal behaviour, resulting in performance degradation of SGs. The taxonomy of threats and attacks that can persist in cyber–physical parts are comprehensively reviewed. Due to link failure of the SCN, some Appl. Syst. Innov. 2023, 6, 7 3 of 20 synchrophasor data can be lost, which would signiﬁcantly affect time-critical monitoring and control applications, such as protection and fault detection [14]. Moreover, since the synchrophasor data are very sensitive to delay, these factors pose additional challenges to the SCN from a design perspective. The challenges are inevitable, and so are the disruptions. Hence, the SCN must be resilient to such challenges. With resilient SCNs, undesirable incidents, such as power outages, blackouts, etc., can be avoided, resulting in huge economic savings. These various motivating incentives encouraged participation in the resiliency paradigm of the SCN. 2.2. Related Work The ability of the system to restore to the original functional state, either from a partially or fully failed state, is known as resiliency [15]. Synchrophasor communication networks have been discussed sufﬁciently in the literature, such as [16–21], to list a few. Being seminal work, however, none of these articles discussed SCNs from the perspective of resiliency analysis. Jha et al., in [16], discussed the impact of routing protocols on the design and analysis of SCNs. K. V. Katsaros et al., in [17], discussed synchrophasor communication infrastructure achieving low communication latency for synchrophasor applications. The SCN was discussed in the risk assessment paradigm in [18]. P. Castello et al., in [19], studied the impact of delay and the approach to minimize it for synchrophasor applications. In this study, the authors computed delay and its minimization corresponding to synchrophasor data at PDCs. S. Das et al., in [20], proposed compressive sampling techniques for the latency analysis of synchrophasor communication systems. In [21], X. Zhu et al. proposed a strategy to optimally place communication links to improve the observability of the synchrophasor communication systems with signiﬁcantly reduced latency. In the analytical paradigm, the reliability analysis of SCNs was comprehensively pre- sented in [22], where the authors considered hardware and data perspectives for the reliability analysis of the SCNs. In [23], the prioritized handover was used in wireless communication infrastructure for SCNs for the reliability analysis and performance improvements of the SCNs. The communication infrastructure was proposed by Appasani et al. in [24] for the operator’s situational awareness, where Monto-Carlo simulations were used. From the cyber–physical perspective, the situational awareness framework for the SCN was proposed in [25]. An approach for the resiliency analysis of SCNs was presented in [26], where a Monte-Carlo-based approach was utilized for the analysis. Resiliency analysis of the SCN from an SG cyber–physical system perspective was proposed in [27], where the authors utilized a simulation-based approach using QualNet 5.2. Recently, an analytical framework for the resiliency analysis of SCNs was presented in [28], in which resiliency analysis with a case study was demonstrated using QualNet 5.2. Despite a resiliency framework being proposed in [26–28], the impact of different TCP/IP protocol suite protocols was not much emphasized. To bridge such gaps in the existing work, a discrete event-based simulation framework must be utilized for network design and implementation. The present work was motivated to bridge such gaps in the literature by proposing a graph-theoretic approach to conceptualize resiliency analysis. The design, implementation, and analysis of the SCN were performed using NS-3, a discrete event-based network simulator. 2.3. Contribution The design of a resilient SCN is the ﬁrst key to the success of SGs. However, the extensive literature survey did not ﬁnd sufﬁcient articles in this direction. Thus, this paper envisions discussing resiliency analysis for the SCNs of SGs. The resiliency estimation of a communication network seems simple at ﬁrst glance. However, in reality, it is not so. Furthermore, despite there being signiﬁcant discussion of resiliency, it is very hard to ﬁnd concrete work where an analytical method was validated using discrete event-based simulation for the resiliency estimation of SCNs. Thus, this paper presents a graph-theoretic approach for the analysis of the resiliency of SCNs. Moreover, a simulation framework for Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 4 of 21 envisions discussing resiliency analysis for the SCNs of SGs. The resiliency estimation of a communication network seems simple at first glance. However, in reality, it is not so. Furthermore, despite there being significant discussion of resiliency, it is very hard to find concrete work where an analytical method was validated using discrete event-based sim- Appl. Syst. Innov. 2023, 6, 7 4 of 20 ulation for the resiliency estimation of SCNs. Thus, this paper presents a graph-theoretic approach for the analysis of the resiliency of SCNs. Moreover, a simulation framework for resiliency estimation was also proposed using discrete event-based Network Simulator resiliency estimation was also proposed using discrete event-based Network Simulator (NS-3) software. (NS-3) software. In a nutshell, the main contributions of the paper are summarized below. In a nutshell, the main contributions of the paper are summarized below. • The concept of resiliency is discussed for the SCNs of SGs; The concept of resiliency is discussed for the SCNs of SGs; • A graph-theoretic approach is presented for the analytical analysis of the resiliency A graph-theoretic approach is presented for the analytical analysis of the resiliency of of the SCNs; the SCNs; • Simple metrics to estimate the resiliency of an SCN have been introduced; Simple metrics to estimate the resiliency of an SCN have been introduced; • State-of-art discrete event-based simulation framework for resiliency analysis of State-of-art discrete event-based simulation framework for resiliency analysis of SCNs SCNs is proposed using the NS-3 simulation tools. is proposed using the NS-3 simulation tools. 3. System Model and Parameterization 3. System Model and Parameterization SCNs have some peculiar characteristics for traffic requirements [29]. We proposed SCNs have some peculiar characteristics for trafﬁc requirements [29]. We proposed a a simplified graph-theoretic approach to model the SCNs of SGs. Particularly, due to ge- simpliﬁed graph-theoretic approach to model the SCNs of SGs. Particularly, due to generic neric considerations, the proposed analysis can be extended to communication networks considerations, the proposed analysis can be extended to communication networks for for other applications. First, the preliminaries of SCN modelling are presented, followed other applications. First, the preliminaries of SCN modelling are presented, followed by by the resiliency estimation metric. the resiliency estimation metric. 3.1. Graph-Theoretic Approach for SCN Modelling 3.1. Graph-Theoretic Approach for SCN Modelling SCNs can be modelled using a graph, where PMU and PDC are represented as the SCNs can be modelled using a graph, where PMU and PDC are represented as the nodes and the communication link between them is represented by an edge in the graph. nodes and the communication link between them is represented by an edge in the graph. Let us consider the SCN as shown in Figure 1, where 12 electrical buses are considered. Let us consider the SCN as shown in Figure 1, where 12 electrical buses are considered. The SCN comprises four PMUs and two PDCs. The buses equipped with a PMU are The SCN comprises four PMUs and two PDCs. The buses equipped with a PMU are shown shown in green, and the buses equipped with a PDC are shown in red. The remaining in green, and the buses equipped with a PDC are shown in red. The remaining buses that buses that are neither equipped with a PMU nor a PDC are shown in black. The electrical are neither equipped with a PMU nor a PDC are shown in black. The electrical buses are buses are electrically connected using Electrical Connections (EC), whereas PMUs and electrically connected using Electrical Connections (EC), whereas PMUs and PDCs are PDCs are communicated using Network Connections (NCs). communicated using Network Connections (NCs). EC Bus PDC NC Bus with PMU Bus with PDC PMU 7 B Figure 1. Illustration of an SCN for graph-theoretical modelling. Figure 1. Illustration of an SCN for graph-theoretical modelling. From the communication network perspective, the PMU, PDC, and their interconnec- tions using NC can be used for analysing SCNs based on a graph-theoretical approach. Let us consider the SCN as a graph G, which is denoted as G(V, E), where V and E denote nodes and edges in the graph G. If the SCN has n PMUs and k PDCs, then the total number of nodes corresponding to PMUs and PDCs in the graph will be N = n + k. Apart from PMUs and PDCs, there will be many intermediate nodes in the SCNs. If U represents the set of intermediate nodes, such that u 2 U = (1, 2, . . . , d), then the total number of nodes Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 5 of 21 From the communication network perspective, the PMU, PDC, and their intercon- nections using NC can be used for analysing SCNs based on a graph-theoretical approach. Let us consider the SCN as a graph G, which is denoted as G (V , E ) , where V and E n k denote nodes and edges in the graph G. If the SCN has PMUs and PDCs, then the total number of nodes corresponding to PMUs and PDCs in the graph will be N=+ n k . Apart from PMUs and PDCs, there will be many intermediate nodes in the SCNs. If U represents the set of intermediate nodes, such that uU= (1, 2, ..., ) , then the total number of nodes in the network would be  =+ N . Hence,  v , v V ; there   ij exists an edge connecting nodes vV  and , such that eE  vV  ij − i j Appl. Syst. Innov. 2023, 6, 7 5 of 20 . We denote the existence of a path between two nodes vV  i, j= 1, 2, 3, ..., | i j and vV  as  which is defined as an unbroken connection through which one can j ij − traverse from node vV  to node vV  . Moreover, path  may consist of one or i j ij − in the network would be h = N + d. Hence, 8 v , v 2 V; there exists an edge e 2 E i j ij more edges. Thus, a path is a set of all nodes connected by edges joining the source and connecting nodes v 2 V and v 2 V, such that fi, jg = f1, 2, 3, . . . , hji 6= jg. We denote the i j destination. In a network with more than one path, the different paths will be represented existence of a path between two nodes v 2 V and v 2 V as g which is deﬁned as an i j ij as unbr a set oken of nod connection es connected thr th ough rough which edges. one Pa can th ‘ltraverse ’ between fr om any node source v 2 a V nd to dnode estina vtio2 n V. i j Moreover, path g may consist of one or more edges. Thus, a path is a set of all nodes ij j can be represented by , where lL = 1, 2, 3..., . Further, the number of paths is given ij − connected by edges joining the source and destination. In a network with more than one  = L by path, cardin the ali dif ty fi.e erent ., paths will . It besh repr ould esented be noas ted a th set atof th nodes e graph connected is assum thr edough undire edges. cted Path to ij − ‘l’ between any source i and destination j can be represented by g , where l = 1, 2, 3 . . . , L. support bidirectional synchrophasor data flow. ij Further, the number of paths is given by cardinality i.e., g = L. It should be noted that For an SCN, it is not necessary to locate the PMUs on all igrid j buses. The entire system the graph is assumed undirected to support bidirectional synchrophasor data ﬂow. can be observable with a few PMUs located at their optimal locations. However, for the For an SCN, it is not necessary to locate the PMUs on all grid buses. The entire system time being, let us assume a simplified diagram where the PMUs, PDCs, and the intercon- can be observable with a few PMUs located at their optimal locations. However, for the time nection between them are as shown in Figure 1. being, let us assume a simpliﬁed diagram where the PMUs, PDCs, and the interconnection As shown in Figure 1, the PMU and PDC are connected with a single edge that may between them are as shown in Figure 1. have many intermediate nodes and edges. For the illustration, the network shown in Fig- As shown in Figure 1, the PMU and PDC are connected with a single edge that may ure 2 was constructed from Figure 1 in such a way that a pair of PMU() v and PDC () v 1 6 have many intermediate nodes and edges. For the illustration, the network shown in is connected through many intermediate nodes and edges. In this, node v and v rep- 1 6 Figure 2 was constructed from Figure 1 in such a way that a pair of PMU (v ) and PDC resent the PMU and the PDC, whereas nodes v ,, v v , and v represent intermediate 2 3 4 5 (v ) is connected through many intermediate nodes and edges. In this, node v and v 6 1 6 nodes on the IP network. Furthermore, node v indicates another device that generates represent the PMU and the PDC, whereas nodes 0 v , v , v , and v represent intermediate 2 3 4 5 nodes on the IP network. Furthermore, node v indicates another device that generates  = 2 background traffic along with the PMU() v traffic. It is worth noting that . 16 − background trafﬁc along with the PMU (v ) trafﬁc. It is worth noting that jg j = 2. 1 16 Figure 2. Simpliﬁed model of an SCN for the graph-theoretic approach. Figure 2. Simplified model of an SCN for the graph-theoretic approach. 3.2. Analysis Metrics 3.2. Analysis Metrics Consider that the synchrophasor data generated at each PMU are r b ps; then, we can Consider that the synchrophasor data generated at each PMU are r bps ; then, we can deﬁne the Packet Delivery Ratio (PDR) as follows. define th Packet e Packet Delivery Deliver Ratio y Ra (PDR tio (P ):DR For ) a an s fSCN, ollows if. A and B represent the source and destina- tion nodes, then PDR at node B corresponding to node A can be deﬁned as: t=t PDR = (1) B A t=t B A where a is the number of packets received by B at time t, b is the number of packets sent t t by A at time t, t is the time at which the ﬁrst packet is sent from A, t is the time at A A 0 ¥ which the last packet is sent from A, t is the time at which the ﬁrst packet is received by B, and t is the time at which the last packet is received by B. ¥ Appl. Syst. Innov. 2023, 6, 7 6 of 20 3.3. Operation Cycle of SCN Under a dynamically varying environment, one or more edges can fail partially or fully. For a resilient system, there should be immediate substitution in the service. The requirement of immediate substitution can be achieved by recovering the failed or partially failed edges. Thus, the overall operation of the SCNs can be analysed in the following three states: normal state, partially failed state, and failed state. 3.3.1. Normal State During the normal operation of the SCN, all edges in the network perform normally. Thus, all the PMUs successfully communicate the synchrophasor data to the corresponding PDC. Consequently, the PDR at the PDC corresponding to the PMU remains equal to 1. As an example, using Equation (1), for the PDR at node B corresponding to node A, we have, B¥ A¥ B A a = b and thus PDR = 1. å å B A t t t=t t=t B0 A0 3.3.2. Partially Failed State In a partially failed state, the SCN fails partially. Thus, the PDR of the corresponding PMUs is affected. Therefore, for the PMUs with partially failed SCNs, the PDR is always less than 1. As an example, for the PDR at node B corresponding to partially failed node A, t t B¥ A¥ B A we have a < b and thus PDR < 1. å å B A t t t=t t=t B0 A0 3.3.3. Failed State In the failed state, the PMU cannot communicate its data to the PDC. Thus, the PDR corresponding to the failed PMUs becomes zero. For example, the PDR at node B t t B¥ A¥ B A corresponding to a failed node A becomes PDR = 0, since å a = 0 å b 6= 0. B A t t t=t t=t B0 A0 3.4. State Representation Using Markov Chain Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 7 of 21 The different states during the operation of the SCN can be modelled using Markov models, as shown in Figure 3. Normal 0.5 Partially failed Failed Operational states as function of time Figure 3. Morkov representation of different states of SCN operation. Figure 3. Morkov representation of different states of SCN operation. With respect to the Markov representation of SCN states, let us consider the probabil- With respect to the Markov representation of SCN states, let us consider the proba- ities of being in the normal, partially failed, and failed states be denoted as p , p , and p f bilities of being in the normal, partially failed, and failed states be denoted as p , p , p respectively. The state transition probabilities are p , p , p p , pn , pf and f n f n p f p fn p f f fn anp d for respec normal tively. to failed, The stnormal ate tranto siti partially on proba failed, bilities partially are failed , to normal, , partially , p p p p p f p f f nf − n− pf pf − n pf − f failed to failed, failed to normal, and failed to partially failed states, respectively. As the , and for normal to failed, normal to partially failed, partially failed to normal, p p fn − f − pf partially failed to failed, failed to normal, and failed to partially failed states, respectively. As the current state decides the next state and the next state does not depend upon the initial state, the system model satisfies the Markov properties. The resiliency of the syn- chrophasor communication network can also be described using the Markov chain. 4. Graph Theoretic Resiliency Framework 4.1. Preliminaries of the Resiliency Estimation Framework PDR The can be calculated at the PDC corresponding to each PMU. Based on the PDR PDR= 1 , the overall performance of the SCN can be evaluated. This is because for the normal state, PDR is less than one for a partially failed state, and PDR = 0 for the fully failed state. Thus, we considered the PDR as a Figure of Merit (FoM) for resiliency esti- mation. Moreover, the average PDR value was considered for the overall system perfor- mance, as more than one PMU communicates synchrophasor data to a particular PDC. Thus, the average PDR at the PDC due to the corresponding PMUs can be determined as th PDR follows. If there are n PMUs connected to j PDC (say, PDC ), then the average at PDC is: nn  PDR  i (2) i=1 PDR = PDC A resiliency curve using the average PDR as a figure of merit is shown in Figure 4 for different instances of time. PDR Partially Failed Normal failed Appl. Syst. Innov. 2023, 6, 7 7 of 20 current state decides the next state and the next state does not depend upon the initial state, the system model satisﬁes the Markov properties. The resiliency of the synchrophasor communication network can also be described using the Markov chain. 4. Graph Theoretic Resiliency Framework 4.1. Preliminaries of the Resiliency Estimation Framework The PDR can be calculated at the PDC corresponding to each PMU. Based on the PDR, the overall performance of the SCN can be evaluated. This is because PDR = 1 for the normal state, PDR is less than one for a partially failed state, and PDR = 0 for the fully failed state. Thus, we considered the PDR as a Figure of Merit (FoM) for resiliency estimation. Moreover, the average PDR value was considered for the overall system performance, as more than one PMU communicates synchrophasor data to a particular PDC. Thus, the average PDR at the PDC due to the corresponding PMUs can be determined as follows. If th there are n PMUs connected to j PDC (say, PDC ), then the average PDR at PDC is: j j n n å PDR i=1 PDR = (2) PDC Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 8 of 21 A resiliency curve using the average PDR as a ﬁgure of merit is shown in Figure 4 for different instances of time. PDR PDR th t t 5 t t 3 4 1 2 time Figure 4. Resiliency curve. Figure 4. Resiliency curve. As shown in Figure 4, the SCN is said to be in a normal state when all of its components As shown in Figure 4, the SCN is said to be in a normal state when all of its compo- work normally, resulting in an average PDR of 1. This can be observed up to time t . Due nents work normally, resulting in an average PDR of 1. This can be observed up to time to some external/internal factors, some components may fail, which will decrease the t . Due to some external/internal factors, some components may fail, which will decrease average PDR, as shown beyond time t . An SCN can tolerate a certain level of reduction the average PDR , as shown beyond time . An SCN can tolerate a certain level of re- in PDR, but in order to perform satisfactorily, it must maintain a minimum value of PDR, PDR which duction is in r eferred , but to as in o the rder thr to eshold perfovalue rm satis denoted factorily, asit Pm Du Rst .mEven aintain during a minim the um interval value th t t the PDR remains equal to or greater than the threshold value and, thus, the system of PDR , which is referred to as the threshold value denoted as PDR . Even during the 2 4 th performs satisfactorily. However, if the PDR becomes less than the threshold value, then PDR interval tt − the remains equal to or greater than the threshold value and, thus, the system disrupts and it enters the out-of-service state, i.e., the failed state. This is the system performs satisfactorily. However, if the PDR becomes less than the threshold represented by the decaying exponential (in red colour) beyond time t in Figure 4. When value, then the system disrupts and it enters the out-of-service state, i.e., the failed state. the failed components of the system come back to the normal state, then the average PDR This is represented by the decaying exponential (in red colour) beyond time t in Figure will improve, as depicted during t t . For time t > t , all components recover to their 4 5 5 4. When the failed components of the system come back to the normal state, then the av- original working state; thus, PDR again reaches the unity value. erage PDR will improve, as depicted during tt − . For time tt  , all components recover The overall operation of the SCN can be45 studied through 5the following phases: (1) to degradation their origin phase, al worki (2)nthr g st eshold-operated ate; thus, PDR aphase, gain reand ache(3) s th re ecovery unity va phase. lue. The overall operation of the SCN can be studied through the following phases: (1) (1) Degradation phase: The phase during which the components of the SCN start failing degradation phase, (2) threshold-operated phase, and (3) recovery phase. partially, resulting in the degradation of the PDR. However, the SCN is considered to (1) Degradation phase: The phase during which the components of the SCN start failing still be operational, since PDR PDR . The degradation rate (x ) can be defined as th deg partially, resulting in the degradation of the PDR . However, the SCN is considered PDR PDR t t to still be operational, since PDR  PDR . The 1 degradation rate ( ) can be defined x = th deg (3) deg t t 1 2 as PDR − PDR tt  = (3) deg tt− where and 𝐷𝑃𝑅 are the PDR received at times 𝑡 and 𝑡 respectively. Thus, if 𝑡 𝑡 1 2 1 2 −1 a node degrades at a rate of 0.075 s , then it takes 13.34 s to degrade the 𝐷𝑃𝑅 from 1 to 0. (2) Threshold-operated phase: This is the state corresponding to the PDR value being close to the threshold value PDR = PDR . During this phase, the SCN operates with min- th imum performance, since some packets may be lost. (3) Recovery phase: When a partially failed component recovers from the partially failed state to the normal state, or even when a failed component is substituted by normal components, the 𝐷𝑃𝑅 value increases such that max PDR = 1 and PDR  PDR .   th The recovery rate  can be determined during the recovery phase 𝑡 to 𝑡 us- ( ) rec 4 5 ing Equation (4), such that . tt ,  recovery phase   PDR − PDR tt  = (4) rec tt− PDR where and 𝐷𝑃𝑅 are the received at times 𝑡 and 𝑡 , respectively. Thus, if 𝑡 𝑡 4 5 4 5 −1 a node recovers at a rate of 0.075 s , then it takes 13.34 s to restore the from 0 to 1. The following vital observation can be noted: 𝑃𝐷𝑅 𝑃𝐷𝑅 𝑃𝐷𝑅 Appl. Syst. Innov. 2023, 6, 7 8 of 20 where PDR and PDR are the PDR received at times t and t respectively. Thus, if t t 1 2 1 2 a node degrades at a rate of 0.075 s , then it takes 13.34 s to degrade the PDR from 1 to 0. (2) Threshold-operated phase: This is the state corresponding to the PDR value being close to the threshold value PDR = PDR . During this phase, the SCN operates with th minimum performance, since some packets may be lost. (3) Recovery phase: When a partially failed component recovers from the partially failed state to the normal state, or even when a failed component is substituted by normal components, the PDR value increases such that maxfPDRg = 1 and PDR > PDR . th The recovery rate (x ) can be determined during the recovery phase t to t using rec 4 5 Equation (4), such that ft , t g 2 recovery phase. 4 5 PDR PDR t t 4 5 x = (4) rec t t 4 5 where PDR and PDR are the PDR received at times t and t , respectively. Thus, if a t t 4 5 node recovers at a rate of 0.075 s , then it takes 13.34 s to restore the PDR from 0 to 1. The following vital observation can be noted: A resilient SCN must follow the resiliency curve shown in Figure 4. However, a highly resilient SCN should preferably have a shorter recovery phase (i.e., minx ) and a longer rec degradation phase (i.e., maxx ). It is worth noting that a higher slope for the recovery deg phase and lower slope for the degradation phase are desirable. 4.2. Resiliency Estimation Framework Let us consider the network model using the graph approach as described earlier. Now, we consider the representation of the network by an undirected graph, as shown in Figure 2. We assume that there are two paths between the PMU and PDC such that the paths are not distinct, as a node is observed to be common in two paths. To be noted, except for the source and destination nodes, the other nodes between the PMUs and PDCs are not common. Thus, the paths between the PMU and PDC are distinct if the source and destination nodes are ignored. At the beginning, all the nodes in v 2 V are in their normal states. Furthermore, all links e 2 E connecting nodes v 2 V and v 2 V, such that fi, jg = f1, 2, 3, . . . , hji 6= jg, ij i j are operational. Consequently, the PMU and PDC will be able to exchange the data as the network is operational. Now, consider at time t , link e 2 E partially fails. The failure of 1 16 this node results in the necessity to reroute the data through another possible path. There will be degradation in the PDR beyond time t , and this degradation depends upon the route recovery time (RRT). As node v is a shared node having more background trafﬁc than the previous path, the PDR is always less than 1 but greater than threshold value of this path. The PDR can be improved such that PDR becomes close to 1 if, and only if, the failed link e 2 E is restored to its normal state. This can be seen beyond time t in 16 4 Figure 4. If the background trafﬁc over link e 2 E is assumed to be large enough, then the 23 PDR degrades in such a way that PDR becomes less than the threshold value. This results in the disruption of service. The main cause of the disrupted service is the failed state of the link e 2 E with no backup path, such as through e 2 E. 16 23 Initially, we considered all nodes to be operational. Thus, they participated in the data exchange, resulting in PDR = 1. For simplicity, all nodes and links are assumed to be of equal capacity. Link e 2 E works as a shared link between the v v and 23 1 6 v v source–destination pairs. Thus, for equal sharing, half of the link capacity will 0 6 be used for each of the source–destination pairs, whereas the remaining half will be considered as the background trafﬁc. Thus, for each source–sink pair, there exist two paths: 1 2 g = f v , v g and g = f v , v , v , v , v , v g . Here, the dominant path for the v v 1 6 1 2 3 4 5 6 1 6 16 16 source–destination pair becomes g = f v , v g . We assume that the dominant path 16 Appl. Syst. Innov. 2023, 6, 7 9 of 20 carries 80% of the PDR data and the other paths carry 20%. It is worth mentioning that the choice of data carried by the dominant path is optional and subject to the researcher ’s choice. The exact path between the PMU and PDC for the routing of the data can be estimated by any of the suitable network layer-routing techniques, which is not part of this work. In fact, the routing protocol will be used for the simulation of the network using ns-3. which will be discussed in the later section of proposed work. Next, the network’s resiliency will be estimated under four cases: normal state, partially failed state, restoration state, and fully failed state. 4.2.1. Case-I: Normal State In the normal state, the SCN is modelled in a way that all nodes, edges, and, thus, paths are operating under their normal state. In this case, the dominant path g = f v , v g is 1 6 16 considered to carry 80% of the PDR data for v v , whereas the redundant shared path 1 6 g = f v , v , v , v , v , v g is modelled to carry 20% of the PDR data, as the dominant 1 2 3 4 5 6 16 path carries more PDR data. Thus, the overall PDR at destination v , corresponding m=g 16 to source v , is PDR = PDR . The PDR at v , corresponding to v for the 1 61 6 1 61 m=g 16 dominant path, is 6¥ å a t=t g 6 16 PDR = (5) 61 t=t ( ) t t t t t 6 2 3 4 5 ¥ ¥ ¥ ¥ ¥ 6 2 3 4 5 1 where a = min a , a , a , a , such that fv , v , v , v g 2 g , å å å å å 2 3 4 5 t t t t t 16 t=t t=t t=t t=t t=t 6 2 3 4 5 0 0 0 0 0 as the nodes are under their normal condition, i.e., no data loss and the dominant path g carries 80% of the total trafﬁc generated by the source. Thus, 111 t t 6 1 ¥ ¥ 6 1 a = 0.8 b (6) å å t t=t t=t 6 1 0 0 This implies that 1 t=t g 6 16 PDR = = 0.8 (7) 61 t=t t t 6 1 ¥ ¥ 2 6 1 Similarly, for path g carrying 20% of the data, a = 0.2 b . This implies that å å 16 t t t=t t=t 6 1 0 0 t=t 16 PDR = = 0.2 (8) 61 1¥ å b t=t Therefore, from Equations (7) and (8), m=g 16 PDR = PDR 61 61 (9) m=g 16 1 2 g g 16 16 = PDR + PDR 61 61 Appl. Syst. Innov. 2023, 6, 7 10 of 20 t t 1 1 ¥ ¥ 1 1 0.8 b + 0.2 b å å t t t=t t=t 1 1 0 0 PDR = = 1 (10) 61 Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 11 of 21 t=t The corresponding resiliency curve corresponding to Case-I is shown in Figure 5. PDR PDR th time Figure 5. Resiliency curve of the SCN model for Case-I. Figure 5. Resiliency curve of the SCN model for Case-I. 4.2.2. Case-II: Partially Failed State 4.2.2. Case-II: Partially Failed State It is likely that some of the nodes in the network may not operate normally. As It is likely that some of the nodes in the network may not operate normally. As few few nodes are subjected to partial failure, the partially failed state is inevitable, which is nodes are subjected to partial failure, the partially failed state is inevitable, which is con- considered in this section. In this case, we consider that the direct link e 2 E fails at time 16 sidered in this section. In this case, we consider that the direct link fails at time eE  16 − t . The failure of this node decreases the PDR, as can be deduced from Equation (11). t . The failure of this node decreases the PDR, as can be deduced from Equation (11). ( ) t t t t t 6 2 3 4 5 ¥ ¥ ¥ ¥ ¥ t t t t t 6 6 2 2 3 3 4 4 5 5       a = min a , a , a , a å å å å å  t 6 2 t 3 t 4 t 5 t 1  = min  ,  ,  ,  t=t  t=t t=t t=t t=t 6 t  2 t  3 t  t  t 5 g 4 0 0 0 0 16 1 t= t t= t t= t t= t t= t PDR = 6  2 3 4 5 (11) 0  0 0 0 0 61 16 − PDR = 1 (11) 61 − t 1 1 t =t tt= 16 In this case, PDR 16 − < 0.8 due to the partially failed state of a node in dominant PDR 61 0.8 In this case, due to the partially failed state of a node in dominant path 61− path g . Thus, all of the trafﬁc generated at node v is re-routed to the alternative path 16 . Thus, all of the traffic generated at node v is re-routed to the alternative path if if16 −available, such as g . Hence, the PDR at the destination node corresponding to path 16 2 2 16 2  available, such as . Hence, the PDR at the destination node corresponding to path g becomes PDR > 0.2. However, there will be some time for the re-routing of the 16 − 16 61 traf 2 ﬁc over path g  . During this time, the PDR will continue to decrease. Once the new 16 − 16 becomes PDR  0.2 . However, there will be some time for the re-routing of the 61 − 16 − optimum path is detected, then the PDR either increases or maintains the present level. This is shown in the resiliency curve in Figure 6 for the time period t to t . Moreover, as 1 2 traffic over path . During this time, the PDR will continue to decrease. Once the new 16 − edge e is shared, the PDR corresponding to this path can never reach 1. Hence, the 23 optimum path is detected, then the PDR either increases or maintains the present level. following inequality holds: This is shown in the resiliency curve in Figure 6 for the time period t to t . Moreover, 1 2 16 0.2 < PDR < 1 (12) 61 PDR as edge e is shared, the corresponding to this path can never reach 1. Hence, 23 − the following inequality holds: 16 Particularly if 0.2 < PDR < PDR < 1, the overall PDR at destination v th 6 61 corresponding to source v can be produced by, 16 − (12) 0.2 PDR 1 61 − m=g 16 16 − PDR = PDR (13) 0.2 PDR  PDR  1 PDR Particularly if 61 , å the overall at destination v corre- 61 th 61 − 6 m=g 16 sponding to source v can be produced by, 1 2 g g m= 16 16 16 − PDR = PDR + PDR (14) 61 m 61 61 PDR = PDR (13) 6−− 1  6 1 m= 16 −  1−− 6 1 6 (14) PDR =PDR + PDR 6−1 6−1 6−1 Therefore, the following inequality holds: PDR PDR 1 (15) th 61 − The corresponding resiliency curve is shown in Figure 6. As PDR  PDR , the net- 61 − th work is considered to be functional in this case. It is worth noting that, for a network Ɲ, Appl. Syst. Innov. 2023, 6, 7 11 of 20 Therefore, the following inequality holds: Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 12 of 21 PDR PDR < 1 (15) 61 th The corresponding resiliency curve is shown in Figure 6. As PDR PDR , the 61 th network is considered to be functional in this case. It is worth noting that, for a network   1 PDR  0 if . Thus, for non-zero PDR , there must exist an alternative path be- ij − N , PDR 6= 0 if g > 1. Thus, for non-zero PDR, there must exist an alternative path ij tween source–destination pairs. between source–destination pairs. PDR PDR th t t 1 2 time Figure 6. Resiliency curve of the SCN model for Case-II. Figure 6. Resiliency curve of the SCN model for Case-II. 4.2.3. Case-III: Restoration State 4.2.3. Case-III: Restoration State In this case, we consider that the failed edge in the previous case e 2 E starts to repair In this case, we consider that the failed edge in the previous case 1 eE 6  starts to 16 − itself either by substitution or recovery at time t . Upon recovery, the failed edge e 2 E 3 16 repair itself either by substitution or recovery at time t . Upon recovery, the failed edge restores the path g , which increases the PDR, as can be deduced from Equation (16). 16 1 restores the path , which increases the PDR , as can be deduced from Equa- eE  16 − 16 − ( ) t t t t t 6 2 3 4 5 ¥ ¥ ¥ ¥ ¥ tion (16). 6 2 3 4 5 a = min a , a , a , a å å å å å t t t t t t=t t=t t=t t=t t=t 6 2 3 4 5 t 0 t 0 t 0 t 0 t 0 16 6 2 3 4 5       PDR = (16)  6 2 3 4 5 61  = min  ,  ,  ,   ¥  t  t  t  t  t 1 t= t t= t tå = t b t= t t= t 6  2 3 4 5  0  0 0 0 0 16 − PDR = (16) t=t 61 − t 1 1 0  t tt= In this case, the PDR corresponding to1 the dominant path increases such that 16 max PDR = 0.8. The restoration will be achieved over a certain time span, such In this ca 6se, 1 the PDR corresponding to the dominant path increases such that 16 − t t 4 4 max PDR = 0.8 . The restoration will be achieved over a certain time span, such as t   3 61 − 6 1 as t to t such that, at t = t , a 0.8 b . å å 3 4 4 t t tt t=t t=t 3 3 to t such that, at tt = , .   0.8 1 2 4 4  tt Further, with the restoration of dominant path g , the trafﬁc from path g will 16 16 t== t t t be off-loaded and diverted to dominant path g . This is because the dominant path 1 2 16   Further, with the restoration of dominant path , the traffic from path will 16 − 16 − is considered to be dedicated, whereas the g path is shared. Hence, the PDR at the 16 be off-loaded and diverted to dominant path2 . This is beca 1use 6 the dominant path is destination node corresponding to path g becomes 16 − PDR 0.2, such that, at t = t , 61 16 16 1 considered to be dedicated, whereas the path is shared. Hence, the PDR at the des- PDR = 0.2. There will be some time for the re-routing of the trafﬁc over path g . 16 − 61 111 During this time span, the PDR will continue increasing. 2 16 − tination node corresponding to path becomes PDR  0.2 , such that, at tt = , 61 − 4 The overall PDR at destination v 16 −corresponding to source v can be given by  1 16 − PDR = 0.2 L . There will be some time for the re-routing of the traffic over path . 61 − m=g 1−11 16 PDR = PDR (17) PDR 61 å During this time span, the will continue increasing.6 1 m=g 16 The overall PDR at destination v corresponding to source v can be given by 6 1 1 2 g g m= 16 − 16 16 PDR = PDR + PDR (18) 61 61 61 PDR = PDR (17) 6−− 1  6 1 m= 16 −  1−− 6 1 6 (18) PDR =+ PDR PDR 6−1 6−1 6−1 Thus, at tt = ,  PDR 1 . Therefore, the following inequality holds: 4 61 − Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 13 of 21 Appl. Syst. Innov. 2023, 6, 7 12 of 20 Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 13 of 21 PDR PDR 1 (19) th 61 − Thus, at t = t , ) PDR 1. Therefore, the following inequality holds: 4 61 The corresponding resiliency curve is shown in Figure 7, where the restoration phase PDR PDR 1 is shown through the interval t to t . Nevertheless, as PDR  PDR , the network (19 is) th 61 − 3 4 61 − th PDR PDR 1 (19) 61 th considered to be functional in this case. The corresponding resiliency curve is shown in Figure 7, where the restoration phase The corresponding resiliency curve is shown in Figure 7, where the restoration phase is shown through the interval t to t . Nevertheless, as PDR  PDR , the network is 3 4 61 − th is shown through the interval t to t . Nevertheless, as PDR PDR , the network is PDR 3 4 61 th considered to be functional in this case. considered to be functional in this case. PDR PDR th PDR th t 4 t t 3 1 2 time Figure 7. Resiliency curve of the SCN model for Case-III. t 4 t t 3 1 2 time 4.2.4. Case-IV: Failed State Figure 7. Resiliency curve of the SCN model for Case-III. Figure 7. Resiliency curve of the SCN model for Case-III. In this state, we consider that node v fails permanently at time t . The failure of 4 1 4.2.4. Case-IV: Failed State this node decreases the PDR, as can be deduced from Equation (20). 4.2.4. Case-IV: Failed State In this state, we consider that node v fails permanently at time t . The failure of this 4 1 t t t t t In this state, we consider that node v fails permanently at time t . The failure of 6 2 3 4 5       4 1  6 2 3 4 5 node decreases the PDR, as can be deduced from Equation (20).  = min  ,  ,  ,   t   t  t  t  t this node decreases the PDR, as can be deduced from Equation (20). 1 t= t t= t t= t t= t t= t ( ) 6 2 3 4 5  0  0 0 0 0 16 − PDR = (20) t t t t t 61 − 6¥ 2¥ 3¥ 4¥ 5¥ t t t t t t 6 2  3 4 5      6  2 3 4 5 a = min a , 1 a , a , a å 6 å 2 å 3 å 4 å 5 t t t t t  = min  ,  ,  ,       t   1 t t t t t t=t t=t t=t t=t t=t g 6 2 3 4 5 0 0 0 0 0 16 t= t t= t tt= t= t t= t t= t 1  1 6 2 0 3 4 5  0  0 0 0 0 PDR = (20) 16 − 61 PDR = t (20) 61 − 1 t ¥  å 16 − t  t PDR  0 In this case, due to the fully fail t= ed t state of a node in the dominant path 61− 1 tt= 1 2   . Thus, all of the traffic generated at node v must be re-routed to path . If there 1 1 16 − 16 −  16 16 − In this case, PDR 0 due to the fully failed state of a node in the dominant path PDR  0 In this case, due to the fully failed state of a node in the dominant path 61 61− exists no such path, i.e., for an SCN Ɲ with   2 , then it can be clearly seen that the 1 2 ij − g . Thus, all of the trafﬁc generated at node v must be re-routed to path g . If there 1 2 16 16   . Thus, all of the traffic generated at node must be re-routed to path . If there 16 − 16 − Pexists DR no such path, i.e., for an SCN N with g < 2, then it can be clearly seen that the decreases, such that PDR  0 at tt = Moreover, even though there exists such ij 61 − 5 PDR decreases, such that PDR 0 at t = t Moreover, even though there exists such a  5  2 exists no such path, i.e., for an 6S CN 1 Ɲ with , then it can be clearly seen that the 16 − ij − PDR2  PDR a path with , the systems loses its functionality. For an instance, PDR 61 − th 61 − 16 path with PDR < PDR , the systems loses its functionality. For an instance, PDR th 61 PDR decreases,6 such 1 that PDR  0 at tt = Moreover, even though there exists such 61 − 5 decreases beyond tt = and PDR  0 at tt = . This is shown in Figure 8 for time span 1 61 − 5 decreases beyond t = t and PDR 0 at t = t . This is shown in Figure 8 for time span 1 61 5 16 − t to t . a 1path wi 5 th PDR  PDR , the systems loses its functionality. For an instance, PDR t to t . 1 5 61 − th 61 − decreases beyond tt = and PDR  0 at tt = . This is shown in Figure 8 for time span 1 61 − 5 PDR t to t . 1 5 PDR PDR th PDR th t t t t t 1 2 5 3 4 time Fig Figure ure 8.8. Res Resiliency iliency curv curve e of of th the e SCN SCN m model odel for for Ca Case-IV se-IV. . t t t t t 1 2 5 3 4 time 5. Simulation Results and Discussion Figure 8. Resiliency curve of the SCN model for Case-IV. Based on the resiliency estimation framework discussed in the last section, we propose a simulation framework to estimate the resiliency of the SCN using ns-3. Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 14 of 21 5. Simulation Results and Discussion Based on the resiliency estimation framework discussed in the last section, we pro- Appl. Syst. Innov. 2023, 6, 7 13 of 20 pose a simulation framework to estimate the resiliency of the SCN using ns-3. 5.1. SCN Design and Implementation 5.1. SCN Design and Implementation We will consider the network topology shown in Figure 2. The parameters of the SCN are selected in conjunction with the synchrophasor application described in [30]. The We will consider the network topology shown in Figure 2. The parameters of the deployment of the network involves the configuration of five networks described as fol- SCN are selected in conjunction with the synchrophasor application described in [30]. The deployment lows. Netwo of rk theƝ1 network connectsinvolves the PMU the anconﬁguration d PDC througof h a ﬁve ded networks icated poi described nt-to-poias nt follows. channel with network address 191.168.1.0. The Internet is modelled using network Ɲ2, where Network N connects the PMU and PDC through a dedicated point-to-point channel with network nodes v2addr , v3, vess 4, an 191.168.1.0. d v5 are inter The med Internet iate routers is modelled that can using be con network figuredN to m , wher imic eth nodes e beha vv- , 2 2 v io,ur v o , f and the vInar ter enintermediate et, such as bar ckgro outers un that d tra can ffic, be rou conﬁgur ting daed ta, to etc mimic . To prthe ovide behaviour alternative of 3 4 5 the Internet, such as background trafﬁc, routing data, etc. To provide alternative routes to routes to the PMU and PDC, we consider two more networks, Ɲ3 and Ɲ4. Network Ɲ3 con- the PMU and PDC, we consider two more networks, N and N . Network N connects nects the PMU to the Internet using node v , whereas the PDC is connected to the Inter- 3 4 3 the PMU to the Internet using node v , whereas the PDC is connected to the Internet using net using network Ɲ4 with the help of node v . The network addresses of networks Ɲ3 network N with the help of node v . The network addresses of networks N and N 4 5 3 4 and Ɲ4 are 170.1.2.0 and 170.1.3.0, respectively. Furthermore, to model the background are 170.1.2.0 and 170.1.3.0, respectively. Furthermore, to model the background trafﬁc over traffic over the Internet, network Ɲ5 is constructed, which connects a node generating the Internet, network N is constructed, which connects a node generating background background traffic (corresponding to the PDR data flow) to the Internet Ɲ2. The network trafﬁc (corresponding to the PDR data ﬂow) to the Internet N . The network address for address for network Ɲ5 is 170.1.1.0. It should be noted that all networks are designed in network N is 170.1.1.0. It should be noted that all networks are designed in the class-B the class-B hierarchy. The design and implementation of the SCN in ns-3 are shown in hierarchy. The design and implementation of the SCN in ns-3 are shown in Figure 9. Figure 9. Figure 9. SCN design using ns-3. Figure 9. SCN design using ns-3. 5.2. Network Parameters and Conﬁgurations 5.2. Network Parameters and Configurations As discussed, the simulation scenario under consideration includes a total of ﬁve As discussed, the simulation scenario under consideration includes a total of five net- networks, N , N , N , N , and N . These networks are implemented in ns-3 and are 1 2 3 4 5 works, Ɲ1, Ɲ2, Ɲ3, Ɲ4, and Ɲ5. These networks are implemented in ns-3 and are shown in shown in Figure 9. Some of the key parameters used for the conﬁguration of these networks Figure 9. Some of the key parameters used for the configuration of these networks in ns-3 in ns-3 are comprehensively summarized in Table 1. are comprehensively summarized in Table 1. Table 1. Key ns-3 conﬁguration parameters for the SCN. Table 1. Key ns-3 configuration parameters for the SCN. Parameters Network Parameters Network Remarks Network Data Rate Delay Address Network Data Rate Remarks (Kbps) (ms) Address Delay (ms) (Kbps) Dedicated network for PMU and N 191.168.1.0 2000 2 1 Dedicated network for PMU PDC Ɲ1 191.168.1.0 2000 2 and PDC N 191.88.1.0 2000 2 Mimics the Internet N 170.1.2.0 2000 2 Backup path Ɲ 3 2 191.88.1.0 2000 2 Mimics the Internet N 170.1.3.0 Variable 2 Backup path N 170.1.1.0 2000 2 Background trafﬁc Each node in the network is configured with the dynamic global routing protocol to populate the routing data for routing. The OSPF protocol is used as a dynamic global routing Appl. Syst. Innov. 2023, 6, 7 14 of 20 protocol that works on link-state algorithms to discover networks, find optimum paths, and maintain the routing information. In ns-3, the dynamic global routing protocol in a node is configured using the following command: Ipv4GlobalRoutingHelper::PopulateRoutingTables(), which enables routing capability in all nodes during simulation. This function calls other ns-3 functions, BuildGlobalRoutingDatabase () and InitializeRoutes (), to build a routing database and initialize routing tables, respectively. Nodes v and v are used as the source and 1 6 destination, respectively. The PMU is configured with the CBR applications supported by the UDP transport protocol to generate the application at a data rate of 300 Kbps. In particular, an on–off application helper is used to create an application in ns-3. The desired data rate in ns-3 can be set using Equation (21). To achieve a PMU data rate equal to 300 Kbps, the 25 packets/s that result in a packet transmission time of 1/25 s are considered, with each packet being equal to 1.5 KB. In ns-3, such applications with the desired data rate are configured using OnOffHelper. Packet size Data rate = (21) Packet transmission time 5.3. Simulation Results The key simulation parameters for the SCN in ns-3 are summarized in Table 2. Table 2. Some of the key simulation parameters for the SCN. Simulation Parameters Value Application UDP (Packet Size = 50 KB, Data rate = 10 Kbps) Simulation start at (s) 0.001 Simulation stop at (s) 300 Application start at (s) 1 Application stop at (s) 299 Point-to-point link fails at (s) 50 Point-to-point link restores at (s) 110 Point-to-point link fails at (s) 140 Point-to-point link restores at (s) 210 Point-to-point link fails at (s) 240 Point-to-point link restores at (s) 280 The network is designed and configured, and events are scheduled per the require- ments referring to Tables 1 and 2. The network is simulated under three cases for effectively analysing the resiliency of the synchrophasor communication network, which will be dis- cussed subsequently. Nevertheless, the network animation remains the same for all cases. 5.3.1. Case I: Complete Link Failure with No Backup Path In this case, we conﬁgure the SCN N in such a way that there is no backup path. This can be conﬁgured by disabling network N . Furthermore, network N is disabled for 50 s 4 1 to 110 s. The SCN is simulated for 110 s. 5.3.2. Case II: Complete Link Failure with a Partially Failed Backup Path In this case, we conﬁgure the SCN N in such a way that a backup path exists. The backup path is considered through the Internet, which is modelled using network N . Node v is connected to the Internet through network N . Node v is connected to the 1 3 6 Internet through network N . Thus, the backup path comprises networks N , N , and 4 2 3 N . To conﬁgure the backup path in the partially failed state, we conﬁgure the Internet with 75% background trafﬁc. Furthermore, network N is disabled for 150 s to 210 s. The SCN is simulated from 110 s to 210 s. 5.3.3. Case III: Link Failure with a High-Capacity Backup Path Here, we conﬁgure the SCN N in such a way that there exists a backup path that has sufﬁcient capacity to support the data rate generated at source node v . Like the last 1 Appl. Syst. Innov. 2023, 6, 7 15 of 20 case study, the backup path is considered to be through the Internet, which is modelled using network N . Node v is connected to the Internet through network N . Node 2 1 3 v is connected to the Internet through network N . Thus, the backup path comprises 6 4 networks N , N , and N . To conﬁgure a high-capacity backup path, networks N , 2 3 4 2 N , and N are conﬁgured with data rates R , R , and R , respectively, such that 3 4 N N N 2 3 4 min R , R , R 2R , where R is the data rate at v . In particular, the bandwidth N N N v v 1 1 1 2 3 4 of the channel belonging to networks N , N , N , and N is considered to be 2 Mbps. 1 2 3 5 The bandwidth of network N is also considered to be 2 Mbps. However, its effective available bandwidth is variable, subject to the applied background trafﬁc. To elaborate, the effective available bandwidth for the PMU data rate becomes only 1Mbps when network N is subjected to 50% background trafﬁc. In a nutshell, PointToPointHelper and Csma- Helper syntax in ns-3 are used to conﬁgure different attributes related to the dedicated and shared CSMA channels, respectively. After conﬁguring all network parameters, network N is disabled for 240 s to 280 s. Moreover, the SCN is simulated for 300 s. 5.4. Discussion of ns-3 Simulation Results The simulation results are summarized in Table 3. Table 3. NS-3 simulation results for the SCN based on the graph-theoretic approach. Number of Number of Packets Total Total Observation Packets Sent Received at 170.1.3.2 Number Number of of Stop PDR From Source Interface From Source Interface Start Time (s) Packets Packets Time (s) Sent Received 191.168.1.1 170.1.2.1 191.168.1.1 170.1.2.1 0 10 224 0 224 0 224 224 1 10 20 250 0 250 0 250 250 1 20 30 250 0 250 0 250 250 1 30 40 250 0 250 0 250 250 1 40 50 250 0 250 0 250 250 1 50 60 0 250 0 0 250 0 0 60 70 0 250 0 0 250 0 0 70 80 0 250 0 0 250 0 0 80 90 0 250 0 0 250 0 0 90 100 0 250 0 0 250 0 0 100 110 0 250 0 0 250 0 0 110 120 249 0 249 0 249 249 1 120 130 251 0 251 0 251 251 1 130 140 250 0 250 0 250 250 1 140 150 250 0 250 0 250 250 1 150 160 0 250 0 190 250 190 0.76 160 170 0 250 0 156 250 156 0.624 170 180 0 250 0 156 250 156 0.624 180 190 0 250 0 157 250 157 0.628 190 200 0 250 0 156 250 156 0.624 200 210 0 250 0 156 250 156 0.624 Case study II Case study I Appl. Syst. Innov. 2023, 6, 7 16 of 20 Table 3. Cont. Number of Number of Packets Total Total Observation Packets Sent Received at 170.1.3.2 Number Number Stop of of From Source Interface From Source Interface PDR Start Time (s) Packets Packets Time (s) Sent Received 191.168.1.1 170.1.2.1 191.168.1.1 170.1.2.1 210 220 250 0 250 0 250 250 1 220 230 250 0 250 0 250 250 1 230 240 250 0 250 0 250 250 1 240 250 0 250 0 250 250 250 1 250 260 0 250 0 250 250 250 1 260 270 0 250 0 250 250 250 1 270 280 0 250 0 250 250 250 1 280 290 250 0 250 0 250 250 1 290 300 225 0 225 0 225 225 1 When the network is simulated for 50 s, since network N is operational, data are communicated over this network from the PMU with an IP address of 191.168.1.1 to the PDC with an IP address of 170.1.3.2. The PMU communicates 1224 packets to the PDC with a packet loss ratio of 0%. Thus, all packets are received at the PDC, which results in a PDR value equal to 1. This can also be validated using Table 3. When the network is simulated for 110 sec, since network N is operational only up to 50 s, data are communicated over this network from the PMU at interface 191.168.1.1 to the PDC at interface 170.1.3.2 up to 50 s only. Further, the PDC receives all 1224 packets sent from the PMU through interface 191.168.1.1, as the packet loss ratio is 0% at the 170.1.3.2 interface of the PDC corresponding to this ﬂow. For the simulation beyond 50 s and up to 110 s, as network N fails, no data can be communicated using this network. In response to the failure of network N , the PMU reroutes data through the alternative route at interface 170.1.2.1, which is through network N over the Internet N . Nevertheless, network N is disabled to ensure the 3 2 4 absence of a backup path between the PMU and PDC. Therefore, PDC does not receive data corresponding to this ﬂow as the packet loss ratio is 100% at the 170.1.3.2 interface of the PDC. Consequently, the PDR drops to 0 for the simulation from 50 s up to 110 s. This can also be corroborated by Table 3. When the network is simulated for 210 s, then network N fails again (ﬁrst failure in case study-I) at 150 s and remains in the failed state up to 210 s. Therefore, no data can be communicated by the PMU over this network from the PMU at interface 191.168.1.1 to the PDC at interface 170.1.3.2 from 150 s to 210 s. This can be veriﬁed, as the last packet transmitted corresponding to this ﬂow is at 149.96 s. Moreover, network N is operational for up to 150 s. Thus, the PDC receives all 2224 packets transmitted by the PMU. Thus, all packets are received at the PDC, which results in a PDR value equal to 1 for this ﬂow. For simulation beyond 150 s and up to 210 s, as network N remains failed, no further data can be communicated using this network. In response to the failure of network N , PMU reroutes data through an alternative route at interface 170.1.2.1, which is the through network N over the Internet N . Nevertheless, network N is now available, 3 2 4 but conﬁgured with 75% background trafﬁc (with a data rate of 10 Kbps). This ensures the existence of a backup path between the PMU and PDC. Therefore, the PDC receives 1995 packets out of 3000 transmitted packets by the PMU at interface 170.1.2.1, resulting in a packet loss ratio of 30.7051%. Consequently, the performance of the network in terms of the PDR is better as compared with case study-I. Speciﬁcally, the average PDR corresponding to both ﬂows is equal, corroborated by Table 3. Case study III Appl. Syst. Innov. 2023, 5, x FOR PEER REVIEW 18 of 21 Appl. Syst. Innov. 2023, 6, 7 17 of 20 When the network is simulated for 280 s, network Ɲ1 is configured to fail again (first When the network is simulated for 280 s, network N is conﬁgured to fail again (ﬁrst failure in case study-I and second failure in case study-II) at 240 s and remains failed up failure in case study-I and second failure in case study-II) at 240 s and remains failed up to to 280 s. Therefore, no data can be communicated by the PMU over this network from the 280 s. Therefore, no data can be communicated by the PMU over this network from the PMU at interface 191.168.1.1 to the PDC at interface 170.1.3.2 from 240 s to 280 s. This can PMU at interface 191.168.1.1 to the PDC at interface 170.1.3.2 from 240 s to 280 s. This can be verified as the last packet transmitted at 239.96 s corresponds to this flow. be veriﬁed as the last packet transmitted at 239.96 s corresponds to this ﬂow. For this simulation period, in response to the failure of network Ɲ1, the PMU reroutes For this simulation period, in response to the failure of network N , PMU reroutes 1 the data through an alternative route at interface 170.1.2.1, which is through network Ɲ3 over data through an alternative route at interface 170.1.2.1, which is through network N over the the Internet Internet NƝ2. Ne . Nevertheless, vertheless, netw network ork Ɲ4 N is no is w now avail available able and and config conﬁgur ured wi ed thwith only only 25% 2 4 25% backgro backgr und ound traffic traf (wi ﬁc th (with a data a data rate o rate f 30of Kbps) 30 Kbps). . This ens This ure ensur s a ba esckup a backup path w path ith suff with i- sufﬁciently high bandwidth between the PMU and PDC. Therefore, the PDC receives all ciently high bandwidth between the PMU and PDC. Therefore, the PDC receives all 4000 4000 packets transmitted by the PMU at interface 170.1.2.1, resulting in a packet loss ratio packets transmitted by the PMU at interface 170.1.2.1, resulting in a packet loss ratio of of 0%. Consequently, the performance of the network in terms of PDR is superior to that 0%. Consequently, the performance of the network in terms of PDR is superior to that in in earlier case studies. Speciﬁcally, the average PDR corresponding to both ﬂows is equal, earlier case studies. Specifically, the average PDR corresponding to both flows is equal, which can be corroborated by Table 3. which can be corroborated by Table 3. A graph of PDR as a function of the simulation time corresponding to all case studies A graph of PDR as a function of the simulation time corresponding to all case studies is plotted in Figure 10. From the ﬁgure, it can be seen that the ﬁrst failure event of network is plotted in Figure 10. From the figure, it can be seen that the first failure event of network N occurs at 50 s. Before the failure of the network, the PDR remains equal to 1. As there Ɲ1 occurs at 50 s. Before the failure of the network, the PDR remains equal to 1. As there is no backup path under this case study, PDR drops to 0 in response to the failure event. is no backup path under this case study, PDR drops to 0 in response to the failure event. Moreover, during the 50 s to 110 s simulation time, PDR remains at 0. Thus, the SCN loses Moreover, during the 50 s to 110 s simulation time, PDR remains at 0. Thus, the SCN loses its functionality. its functionality. Figure 10. Resiliency curve using the simulation framework of the SCN. Figure 10. Resiliency curve using the simulation framework of the SCN. F Fu urther rtherm m oo rre e, ,t htehd e eg dregr ada atd io a n tio ran te ra uste ingusi Eqn ug a tiE on qua (3)tio can n b(e 3) e st ca im na tbe ed testim o be xated= to 0.1 be. deg From=− Fi 0g .1 u.r e Fro 10m , t Fi= gure 50 s ,1t 0, = t 60 = 50 s, P s, DR t = 60 = 1s ,, and PDR ,= an 0d . The perform . The ancepe grrf ap oh r- t PDR = t1 PDR = 0 1 2 deg 1 2 1 t 2 t 1 2 for case study-II shows the period of 110 s to 210 s. Network N restores at 110 s, which mance graph for case study-II shows the period of 110 s to 210 s. Network Ɲ1 restores at improves the PDR to 1 compared with the failure event of case study-I, where the PDR is 0. PDR 110 s, which improves the to 1 compared with the failure event of case study-I, Furthermore, the recovery rate using the equation can be estimated to be x = +0.1. From rec where the PDR is 0. Furthermore, the recovery rate using the equation can be estimated Figure 10, t = 110, t = 120, PDR = 0, and PDR = 1. Here, network N fails again at t t 4 5 1 4 5 to be  =+0.1 . From Figure 10, t = 110 , t = 120 , , and . Here, PDR = 0 PDR = 1 rec 4 5 t t 4 5 150 s; thus, the PDR degrades. However, the PDR does not become 0, i.e., 0 < PDR < 1. network Ɲ1 fails again at 150 s; thus, the PDR degrades. However, the PDR does not be- Moreover, the degradation rate using Equation (3) can be estimated to be x = 0.0188. deg 01  PDR come 0, i.e., . Moreover, the degradation rate using Equation (3) can be esti- From Figure 10, t = 150, t = 170, PDR = 1, and PDR = 0.624. Further, the recovery 2 t t 1 2 r m ata eted us in to g Ebe qu ation=− (4) 0.c 0a 1n 88be . eF srom tima te Fi dgure to b e1x0, = t =+ 150 0.0376 , .t F= ro 170 m F, igure 10, t = , 210 and , PDR = 1 rec 1 2 4 deg t t = 220, PDR = 0.624, and PDR = 1. t t 4 5 . Further, the recovery rate using Equation (4) can be estimated to be PDR = 0.624 Hence, the performance of the SCN is better in the event of a failure than in the earlier . From Figure 10, , , , and .  =+0.0376 t = 210 t = 220 PDR = 0.624 PDR = 1 rec 4 5 t t case study, where there is no alternative route. Moreover 4, the recovery rate is 5better when Appl. Syst. Innov. 2023, 6, 7 18 of 20 network N restores at 110 s as compared with that at 210 s. The performance graph for case study-III shows the period from 210 s to 300 s. Network N restores at 210 s, which improves the PDR to 1 compared with the failure events of case study-II and, of course, case study-I. Here, network N fails again at 240 s. However, the PDR remains at 1, as a backup path with sufﬁciently large bandwidth exists. Hence, it is conclusive that the performance of the SCN is superior to that in the earlier case studies in the event of failure. 5.5. Some Future Research Directions SCNs are vital to the success of SGs as they provide real-time monitoring capabilities to the marvellous power system. In this paper, an approach was presented in the resiliency evaluation paradigm. Some of the future research directions to further augment the resiliency paradigm are enumerated below: The dynamic characteristics of all the nodes in terms of failure, repair, etc. can be studied for resiliency analysis of the SCN; The effect of variable bandwidth on all channels can be studied to observe the perfor- mance of the SCN in terms of resiliency parameters; A more complex SCN can be modelled and the presented work can be extended on such a complex SCN for resiliency analysis; A more peculiar SCN model can be developed with the objective of designing a testbed for SG design, implementation, and performance evaluation; Last, but not least, more comprehensive deﬁnitions and resiliency metrics can be proposed in future work. 6. Conclusions and Future Work The synchrophasor communication network of a smart grid caters to the basic needs to meet the goals of the smart grid. The SCN is subjected to several challenges leading to operational hindrances. To overcome such issues, resiliency estimation of an SCN of an SG was considered in this paper. To evaluate the resiliency estimation, a simpliﬁed graph-theoretic approach was presented to model the SCN analytically. An SCN was designed, implemented, and simulated using a discrete event-based network simulator, ns-3. The resiliency estimation was conducted with the packet delivery ratio as a ﬁgure of merit. Nevertheless, the proposed graph-theoretic-based resiliency framework can be regarded as the ﬁrst such attempt that can be extended to generic communication networks. The inclusion of a case study is considered future work. With respect to case study-I, the SCN was observed to lose its functionality, such that x = 0.1 and x = +0.1. Contrary rec deg to case study-I, the SCN remained in a functional state in case study-II, with x = 0.0188 deg and x = +0.0376. If the bandwidth available is sufﬁciently large compared with the rec background trafﬁc and synchrophasor data rate, then an SCN with at least one backup path remains fully functional (normal state), as observed in case study-III. Author Contributions: Conceptualization, A.V.J.; methodology, A.V.J.; software, A.V.J.; validation, B.A.; formal analysis, A.V.J. and B.A.; investigation, N.B. and P.T.; resources, B.A. and N.B.; data curation, A.V.J.; writing—original draft preparation, A.V.J.; supervision, N.B. and B.A.; project administration, N.B. and P.T.; funding acquisition, P.T.; writing—review and editing: A.V.J., B.A., P.T. and N.B. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the Framework Agreement between the University of Pitesti (Romania) and King Mongkut’s University of Technology North Bangkok (Thailand), in part by an International Research Partnership “Electrical Engineering—Thai French Research Center (EE-TFRC)” under the project framework of the Lorraine Université d’Excellence (LUE) in cooperation between Université de Lorraine and King Mongkut’s University of Technology North Bangkok, and in part by the National Research Council of Thailand (NRCT) under Senior Research Scholar Program under Grant No. N42A640328. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Appl. Syst. Innov. 2023, 6, 7 19 of 20 Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Fotis, G.; Dikeakos, C.; Zafeiropoulos, E.; Pappas, S.; Vita, V. 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A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks

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ISSN: 2571-5577
DOI: 10.3390/asi6010007
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Abstract

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Applied System Innovation – Multidisciplinary Digital Publishing Institute

Published: Jan 5, 2023

Keywords: smart grid; synchrophasor communication system; resiliency; network simulator

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A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks

A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks

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A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks

A Graph-Theoretic Approach for Modelling and Resiliency Analysis of Synchrophasor Communication Networks

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