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Article

Structural Vulnerability Analysis of Interdependent Electric Power and Natural Gas Systems

by
Olabode Amusan
1,
Shuomang Shi
1,
Di Wu
1,* and
Haitao Liao
2
1
Department of Electrical and Computer Engineering, North Dakota State University, Fargo, ND 58105, USA
2
Department of Industrial Engineering, University of Arkansas, Fayetteville, AR 72701, USA
*
Author to whom correspondence should be addressed.
Energies 2023, 16(19), 6918; https://doi.org/10.3390/en16196918
Submission received: 21 August 2023 / Revised: 24 September 2023 / Accepted: 29 September 2023 / Published: 1 October 2023
(This article belongs to the Section F: Electrical Engineering)
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Abstract

:
The growing use of gas-fired power generators and electricity-driven gas compressors and storage has increased the interdependence between electric power infrastructure and natural gas infrastructure. However, the increasing interdependence may spread the failures from one system to the other, causing subsequent failures in an integrated power and gas system (IPGS). This paper investigates the structural vulnerability of a realistic IPGS based on complex network theory. Different from the existing works with a focus on the static vulnerability analysis for an IPGS, this paper considers both static and dynamic vulnerability analysis. The former focuses on vulnerability analysis under random and selective failures without flow redistribution, while the latter concentrates on vulnerability analysis under cascading failures caused by flow redistribution. Also, different from the existing works with a focus on the IPGS as a whole, we not only analyze the vulnerability of the IPGS but also analyze the vulnerability of the power subsystem (PS) and gas subsystem (GS), in order to understand how the vulnerability of the IPGS is affected by its PS and GS. The analysis results show that (1) if the PS and GS are more susceptible to cascading failures than selective and random failures, the IPGS as a whole is also more vulnerable to cascading failures. (2) There are different dominant factors affecting the IPGS vulnerability under cascading failures and selective failures. Under cascading failures, the GS has a more significant impact on the IPGS vulnerability; under selective failures, the PS has a more important impact on the IPGS vulnerability. (3) The IPGS is more vulnerable to failures on the critical nodes, which are identified from the IPGS as a whole rather than from the individual PS or GS. The results provide insights into the design and planning of IPGSs to improve their overall reliability.

1. Introduction

There is an increasing use of gas-powered generation due to low carbon emission and high efficiency [1]. According to the U.S. Energy Information Administration and the U.S. Department of Energy, natural gas consumption for electricity generation has increased by 30.44% in 2018 compared to 2014 [2]. While the electrical power grid shows a significant share of the electricity generation from natural gas combined-cycle power generators, natural gas facilities also depend on a safe and reliable power supply for their operation. Due to the dependence between electric power and natural gas systems, local disturbances triggered on one subsystem may propagate to the other one and cause disruption. The interdependence of the power and gas systems may pose challenges to the reliable and secure operation of the integrated power and gas system (IPGS). For example, in February 2021, there was a blackout in Texas due to a sudden interruption of the gas supply [3]. This blackout caused about a 35.71% reduction in the power supply and affected more than 25 million customers. Thus, it is important to investigate the reliability of an IPGS operation.
In previous works, various approaches were proposed for the reliability analysis of IPGS. In [4], Monte Carlo simulation with power-to-gas devices and gas storage was used for IPGS reliability assessment. In [5], the integrated optimal energy flow techniques were proposed for IPGS reliability analysis. In [6], IPGS reliability was analyzed by a multi-state model. In [7], a new approach was proposed to assess IPGS reliability. In [8], Monte Carlo simulation was used for evaluating the IPGS reliability under extreme events. In [9], a approach was proposed based on a minimal cut–maximal flow algorithm to improve the IPGS reliability during the planning stage. Stochastic models were used for the joint planning of both power and gas systems [10,11] and for improving their operational security [12,13]. In [14,15], methods were proposed to improve the resilience to natural disasters and intentional attacks. In [16,17], two-stage optimization methods were applied to the electric power system and natural gas system. The interruptions of power generators and transmission lines were considered in [18]. In [13,19], an optimization model was proposed to assess the reliability of interdependent electricity and gas infrastructures. In [20], the dynamics of gas flow were taken into account in the scheduling model of the power and gas systems. In [21], the failures in a gas system that affect the IPGS operation were analyzed, and how to prevent the failures was studied. In [16], an integrated power and gas simulation model was proposed for failure analysis via interdependency simulation. In [22], a stochastic model was proposed to analyze the seismic impact on the security of integrated electricity and gas systems based on the Monte Carlo simulation. In [23], an integrated simulation approach was proposed to analyze the failure spreading over an integrated IPGS based on steady-state gas flow and power flow. However, these existing works have offered limited analyses of IPGS vulnerability.
The network-based approach has been widely used to analyze the vulnerability of critical infrastructures to improve their resilience through long-term planning [17,24,25,26,27,28]. The structural analysis of a complex system has been conducted traditionally from both static and dynamic views. In a static vulnerability analysis, a fraction of network components are removed without the need of redistributing any quantity transported by the network [29,30]. In a dynamic vulnerability analysis, when network components are deleted, the flow or load carried by them must be distributed over the remaining components in the network [30,31,32,33]. In [17], a graph theory was applied to analyze the vulnerability of IPGS.
In [24], the IPGS vulnerability was assessed by a geodesic-based metric. This metric was also employed for the vulnerability analysis of power systems [25,26]. In [27], the geodesic-based metric with node degree and average shortest-path length were used to analyze the topological vulnerability of an IPGS. In [34], the critical nodes of coupled natural gas and electricity infrastructures were identified based on complex network theory. In [35], the security of the interdependent electricity–gas network was assessed by identifying the critical nodes and links in the interdependent network. However, the existing studies focus on static vulnerability analysis rather than a dynamic counterpart. As a result, these studies cannot provide insights into the vulnerability of an IPGS subject to cascading failures and the relationship between the static and dynamic vulnerability of the IPGS. Also, the existing studies concentrate on the vulnerability analysis of an IPGS but ignore the vulnerability analysis of its PS and GS within the IPGS. Thus, these studies cannot provide insights into how the vulnerability of the IPGS is affected by its PS and GS.
To fill this gap, this paper investigates the inherent structural vulnerability of a realistic IPGS and its power subsystem (PS) and gas subsystem (GS). Both static and dynamic vulnerability analyses are carried out for the IPGS and its subsystems to understand the interaction between the PS and GS in the IPGS. The major contributions of this paper are summarized as follows:
(1)
Different from the existing works with a focus on the static vulnerability analysis of IPGSs, we consider both static and dynamic vulnerability analysis of a realistic IPGS to understand their relationship in this paper.
(2)
Different from the existing works with a focus on the IPGS, we not only analyze the vulnerability of the IPGS as a whole but also analyze the vulnerability of the PS and GS, in order to understand how the vulnerability of the IPGS is affected by its PS and GS via static and dynamic vulnerability analysis.
The rest of this paper is organized as follows. Section 2 presents a review of the topological method used for structural vulnerability analysis based on complex network theory. In Section 3, the realistic IPGS is first described, and then its structural vulnerability is analyzed. The conclusions are drawn in Section 4.

2. Topological Approach for Structural Vulnerability Analysis

In complex network theory, the robustness (or, on the contrary, vulnerability) of a network is referred to as the ability of this network to keep functioning when a fraction of its constitutive components are damaged. For critical infrastructures, such as electric power systems and natural gas systems, vulnerability analysis is important since it may provide insights into the resilience of the infrastructures. In this paper, we will investigate both static and dynamic vulnerability in the IPGS and its PS and GS.
The IPGS, PS, or GS can be represented as an undirected graph Y = {V, E}, where V (dim{V} = NV) is the set of nodes; each node can be identified by index i; E (dim{E} = NE) is the set of links; an edge denoted by lij represents a connection between nodes i and j. Particularly, in IPGS, PS, or GS, nodes have different functions and can generally be classified as generation, transmission, and demand, respectively. Thus, V = G ⋃ T ⋃ D, where G is a set of generation nodes (dim{G} = NG), T is a set of transmission nodes (dim{G} = NG), and D is the set of demand nodes (dim{D} = ND). To evaluate the structural vulnerability of graph Y, we will use various network metrics, including degree, betweenness, and network efficiency, in this paper.
Degree is an index to measure the importance of node i. When a node has a higher degree than others, this node is more important than others. In an unweighted network, the degree of node i is the number of links that are connected to this node [36]:
k i = ∑ j = 1 N V l i j
Also, a network can be classified into a homogeneous or heterogeneous network by its degree cumulative distribution P(ki ≥ K). The cumulative distribution is the probability that the degree of a node randomly chosen in the network is larger or equal to a given number K. The degree cumulative distribution of a homogeneous network tends to be a Poisson distribution since the degree of each node is similar in the network. The degree cumulative distribution of a heterogeneous network tends to be an exponential distribution or a power law distribution since the degrees of many nodes are small but degrees of a few nodes are large. Thus, a heterogeneous network is more vulnerable to intentional removal of those nodes with large degrees but robust to random removal of those nodes with small degrees.
Betweenness is also an index to measure the importance of a node in a network. This index measures the importance of a node by the number of all the shortest paths that connect each pair of nodes passing through a given node in a network [37,38]. When a node has a higher betweenness, this node has a greater number of the shortest paths passing through it. Therefore, a higher betweenness implies a more important role of a node in a network. The important nodes can be identified by the betweenness index. In [39], the betweenness is viewed as a proxy for how much physical quantity is transmitted through a node, and thus it is an alternatively termed load. When betweenness is evaluated for a given node, it is considered that a unit of physical quantity flows along the shortest path between a pair of nodes. When considering the classification of nodes in the IPGS, PS, or GS, a unit of a physical quantity flows from a generation node g to a demand node d. Thus, in this paper, the betweenness is defined in terms of the shortest paths between whichever pair of generation and demand nodes in a network. To be precise, suppose that pgd(i) is the number of the shortest paths between generation node g to demand node d that passes through node i, and suppose that ngd is the number of shortest paths between all pairs of nodes g to d. Thus, the betweenness of node i is:
b ( i ) = 1 N G N D ∑ g ∈ G ∑ d ∈ D p g d ( i ) / n g d
The network efficiency quantifies the efficiency of the physical quantity flowing between each pair of nodes in a network. To analyze the performance of a network, the concept of network efficiency is introduced into complex network theory [40]. A low value of network efficiency indicates that the physical quantity travels between many nodes. The definition of network efficiency assumes that a unit of physical quantity flows between a pair of nodes through distance Dij [41], which is the number of links in the shortest path between nodes i and j [42]. However, when considering the classification of nodes in the IPGS, PS, or GS, a unit of a physical quantity is transmitted from a generation node g to a demand node d. Here, the network efficiency is defined based on the shortest paths between each pair of generation and demand nodes in graph Y as:
E ( Y ) = 1 N G N D ∑ g ∈ G ∑ d ∈ D 1 D g d
Based on (3), the efficiency-based vulnerability V(Y) is defined as an index to measure the network performance against failures in terms of network efficiency E(Y):
V ( Y ) = E ( Y − 1 ) E ( Y )
where E(Y − 1) represents the network efficiency after removing a node in each iteration from graph Y. This index V(Y) ranges between zero and one.

3. Structural Vulnerability Analysis of the IPGS

3.1. Description of the Investigated IPGS

We will analyze the structural vulnerability of a realistic IPGS, as shown in Figure 1. Table 1 presents the topological information of this IPGS and its PS and GS. Table 2 presents the coupling between the PS and GS in the IPGS, including gas-fired electric generators, electricity-driven gas compressors, and gas storage.

3.2. Structural Vulnerability Analysis of the IPGS

The structural vulnerability of the IPGS is analyzed based on the aforementioned network metrics, including the degree in Equation (1), betweenness in Equation (2), and efficiency-based vulnerability in Equation (4). First, we analyze the static vulnerability of this IPGS and its PS and GS without considering the flow redistribution under failures. Then, we investigate the dynamic vulnerability of the IPGS and its PS and GS by considering the flow redistribution under failures. We compare the results of the static vulnerability analysis with those of the dynamic vulnerability analysis to understand the impact of the coupling between the PS and GS on the IPGS performance from the perspective of structural vulnerability.

3.2.1. Static Vulnerability Analysis

To understand the static vulnerability of the IPGS and its PS and GS, we first investigate their degree distributions to identify if these systems have a homogeneous or heterogeneous network structure. A heterogeneous network is more vulnerable than a homogeneous network since a heterogeneous network has hubs, which are a small fraction of nodes with higher degrees than others in the network, and intentional attacks on hubs cause a significant decrease in network performance. Then, we analyze the static vulnerability of the IPGS and its PS and GS by comparing their network vulnerability under random failures and selective failures. Here, the network vulnerability is quantified by the metric given in Equation (4); random failures are modeled by randomly removing nodes from a network; and selective failures are modeled by removing critical nodes from a network according to their evaluation results in terms of the degree metric given in Equation (1).
By using the degree metric, we evaluate the degree of each node in the IPGS and its PG and GS and then obtain the complementary degree distributions in these systems, as shown in Figure 2. It can be observed from Figure 2 that these degree distributions follow exponential distribution models. This indicates that both the PG and GS appear to be heterogeneous networks. Thus, the entire IPGS is also a heterogeneous network. That is, there exist some critical nodes with high degrees in each of the three systems.
Furthermore, we investigate the static vulnerability of the IPGS and its PS and GS under random and selective node failures using the V(Y) metric in Equation (4). The results are presented in Figure 3 and Figure 4. Figure 3 shows the vulnerability of the PS, GS, and IPGS under random and selective failures, while Figure 4 compares the vulnerability of the PS, GS, and IPGS under selective failures. For random failures, 20% of nodes are randomly chosen and then removed from each system in one simulation while the V(Y) change is assessed. Figure 3 and Figure 4 show the average of the V(Y) changes by averaging 100 simulations of random failures in each system. For selective failures, the first 20% of the most critical nodes ranked by the degree metric in (1) are successively removed from a system while the V(Y) change is evaluated. Since the IPGS system is composed of the PS and the GS, when a node has a link coupling another node either in the PS or in the GS, its removal also deletes its coupling node in the IPGS.
It can be observed from Figure 3 that both the PS and GS are vulnerable to selective failures but relatively robust to random failures since each of these two systems is a heterogeneous network, where hub failures lead to a significant drop in network performance. As a result, the IPGS consisting of the PS and the GS is also vulnerable to selective failures but relatively robust to random failures. For example, the IPGS has about 20% of the original network efficiency after randomly removing 20% of nodes; on the other hand, when removing 20% of critical nodes ranked by degree metric, the IPGS has less than 10% of the original network efficiency. Similar observations can be obtained for the PS and the GS.
It can be observed from Figure 4 that the vulnerability of the IPGS under selective failures is mainly affected by the PS since the PS is more vulnerable than the GS under selective failures. When 20% of critical nodes are removed from the GS, it retains about 15% of the original network performance. However, when 20% of critical nodes are removed from the PS, PS only has about 5% of the original network performance. Similarly, when 20% of critical nodes are removed from IPGS, IPGS has about 5% of the original network performance.
Figure 5 further compares the vulnerability of the IPGS under three scenarios of selective failures. In scenario 1, selective failures are composed of 10% of the first top critical nodes in the GS and another 10% of the first top critical nodes in the PS. In scenario 2, selective failures consist of 10% of the first top critical nodes in the PS and another 10% of the first top critical nodes in the GS. In scenario 3, selective failures are made up of 20% of the first top critical nodes in the entire IPGS. It can be seen from Figure 5 that the IPGS is more vulnerable under scenario 3 of selective failures than the other two scenarios of selective failures. That is, the IPGS is more vulnerable to the selective failures on the critical nodes which are identified from the IPGS as a whole rather than from the individual PS or GS. Under scenario 1, after 20% of nodes are removed from the IPGS, the network efficiency of the IPGS is decreased to about 60% of the original network efficiency. Under scenario 2, removing 20% of nodes from the IPGS reduces the network efficiency to more than 20% of the original network efficiency. Under scenario 3, removing 20% of nodes from the IPGS leads to a decrease in the network efficiency to about 10% of the original network efficiency.

3.2.2. Dynamic Vulnerability Analysis

We further analyze the dynamic vulnerability of the IPGS and its PS and GS. In the dynamic vulnerability analysis, network nodes are deleted, and the flow or load carried by them is redistributed over the remaining network [31,32,33,34]. Then, the nodes with the heavy flow or loads will be deleted in the remaining network [31,32,33,34], and the flow or load carried by them is redistributed again. The process will continue until the network completely loses its network efficiency. The dynamic vulnerability analysis mimics the cascading failure process in a network. The load carried by each node is modeled by the betweenness. The most critical node with the largest load will be identified by the betweenness metric and then deleted from a network in the dynamic vulnerability analysis. Every time the most critical node is deleted, the network vulnerability will be evaluated using the V(Y) metric in Equation (4). It should be noted that when a node has links coupling another node either in the PS or in the GS of the IPGS system, its removal also deletes its coupling node from the IPGS. The results of the dynamic vulnerability analysis are presented in Figure 6 and Figure 7.
Figure 6 shows the vulnerability of the PS, GS, and IPGS under random, selective, and cascading failures. It can be seen from this figure that both the PS and GS are more vulnerable to cascading failures than random failures and selective failures. Thus, the IPGS composed of the PS and GS is also more vulnerable to cascading failures than random failures and selective failures. When the IPGS has 12% of nodes under cascading failures, it completely loses its network performance. However, when the IPGS has 20% of nodes under selective failures (or random failures), it retains 10% (or 20%) of the original network performance.
Figure 7 compares the vulnerability of the PS, GS, and IPGS under cascading failures. It can be observed from Figure 7 that the vulnerability of the IPGS under cascading failures is mainly affected by the GS since the GS is more vulnerable than the PS under cascading failures. When the PG has 12% of nodes under cascading failures, it still retains 10% of the original network performance. When the GS has 12% of nodes under cascading failures, it loses its network performance completely. Similarly, when the IPGS has 12% of nodes under cascading failures, it also loses its network performance completely.
Figure 8 further compares the vulnerability of the IPGS under three scenarios of selective failures. In scenario 1, cascading failures are composed of 10% of the first top critical nodes in the GS and another 10% of the first top critical nodes in the PS. In scenario 2, cascading failures consist of 10% of the first top critical nodes in the PS and another 10% of the first top critical nodes in the GS. In scenario 3, cascading failures are made up of 20% of the first top critical nodes in the entire IPGS. It can be seen from Figure 8 that the IPGS is the most vulnerable under scenario 3. That is, the IPGS is more vulnerable to the cascading failures on the critical nodes which are identified from the IPGS as a whole rather than from the individual PS or GS. Under scenario 1, after 20% of nodes are removed from the IPGS, the network efficiency of the IPGS is decreased to about 60% of the original network efficiency. Under scenario 2, removing 20% of nodes from the IPGS reduces the network efficiency to 30% of the original network efficiency. Under scenario 3, removing 20% of nodes from the IPGS leads to the complete malfunction of the IPGS.

4. Conclusions

In this paper, we analyzed the static and dynamic vulnerability of a realistic IPGS from the topologic perspective using complex network theory. We have found the following results, which may be helpful in guiding the design and planning of the IPGS to improve its resiliency and reliability.
(1)
If the PS and GS are more susceptible to cascading failures than selective and random failures, the IPGS as a whole is also more vulnerable to cascading failures. When the IPGS has 12% of nodes under cascading failures, it completely loses its network performance. However, when the IPGS has 20% of nodes under selective failures (or random failures), it retains 10% (or 20%) of the original network performance.
(2)
There are different dominant factors affecting the IPGS vulnerability under cascading failures and selective failures. The static vulnerability analysis shows the vulnerability of the IPGS under selective failures is mainly affected by the PS since the PS is more vulnerable than the GS under selective failures. When 20% of critical nodes are removed from the GS, it retains about 15% of the original network performance. However, when 20% of critical nodes are removed from the PS, the PS only has about 5% of the original network performance. Similarly, when 20% of critical nodes are re-moved from the IPGS, IPGS has about 5% of the original network performance. The dynamic vulnerability shows the vulnerability of the IPGS under cascading failures is mainly affected by the GS since the GS is more vulnerable than the PS under cascading failures. When the PG has 12% of nodes under cascading failures, it still retains 10% of the original network performance. When the GS has 12% of nodes under cascading failures, it loses its network performance completely. Similarly, when the IPGS has 12% of nodes under cascading failures, it also loses its network performance completely.
(3)
The IPGS is more vulnerable to the failures on the critical nodes which are identified from the IPGS as a whole rather than from the individual PS or GS. If the cascading failures occur on the 20% of critical nodes identified from the IPGS as a whole, the IPGS loses its network performance completely; however, if the cascading failures occur on the 20% of critical nodes identified from the individual PS or GS, the IPGS still retains more than 30% of the original network performance. Similarly, if the selective failures occur on the 20% of critical nodes identified from the IPGS as a whole, the IPGS retains 10% of its original network performance completely; however, if the selective failures occur on the 20% of critical nodes identified from the PS or GS, the IPGS still retains more than 20% of the original network performance.

Author Contributions

Conceptualization, O.A. and D.W.; methodology, O.A. and D.W.; software, O.A., S.S. and D.W.; validation, O.A., S.S. and D.W.; formal analysis, O.A. and D.W.; investigation, O.A.; resources, D.W.; data curation, O.A., S.S. and D.W.; writing—original draft preparation, D.W.; writing—review and editing, O.A., S.S., H.L. and D.W.; visualization, O.A.; supervision, D.W.; project administration, D.W.; funding acquisition, D.W. All authors have read and agreed to the published version of the manuscript.

Funding

The authors express their gratitude for the funding provided to support this study from the National Science Foundation (NSF) EPSCoR RII Track-2 Program under grant number OIA-2119691. The findings and opinions expressed in this article are those of the authors only and do not necessarily reflect the views of the sponsors.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

We greatly acknowledge the support from Encoord, the company that developed the Scenario Analysis Interface for Energy Systems (SAInt) software version 3.3.1.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. The IPGS topology. Red links represent the transmission lines in the PS; blue links represent the lines in the GS; and green links represent the lines coupling the PS with GS.
Figure 1. The IPGS topology. Red links represent the transmission lines in the PS; blue links represent the lines in the GS; and green links represent the lines coupling the PS with GS.
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Figure 2. The complementary degree distributions of the IPGS and its PG and GS.
Figure 2. The complementary degree distributions of the IPGS and its PG and GS.
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Figure 3. Comparison of V(Y) change under random failures and selective failures: (a) V(Y) change in PS; (b) V(Y) change in GS; (c) V(Y) change in IPGS.
Figure 3. Comparison of V(Y) change under random failures and selective failures: (a) V(Y) change in PS; (b) V(Y) change in GS; (c) V(Y) change in IPGS.
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Figure 4. Comparison of V(Y) change in the PS, GS, and IPGS under selective failures.
Figure 4. Comparison of V(Y) change in the PS, GS, and IPGS under selective failures.
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Figure 5. Comparison of V(Y) change in the IPGS under three scenarios of selective failures.
Figure 5. Comparison of V(Y) change in the IPGS under three scenarios of selective failures.
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Figure 6. Comparison of V(Y) change under random failures, selective failures, and cascading failures; (a) V(Y) change in the PS; (b) V(Y) change in the GS; (c) V(Y) change in the IPGS.
Figure 6. Comparison of V(Y) change under random failures, selective failures, and cascading failures; (a) V(Y) change in the PS; (b) V(Y) change in the GS; (c) V(Y) change in the IPGS.
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Figure 7. Comparison of V(Y) change in the IPGS, PS, and GS under cascading failures.
Figure 7. Comparison of V(Y) change in the IPGS, PS, and GS under cascading failures.
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Figure 8. Comparison of V(Y) change in the IPGS under three different types of cascading failures.
Figure 8. Comparison of V(Y) change in the IPGS under three different types of cascading failures.
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Table 1. Number of components in the IPGS and its PG and GS.
Table 1. Number of components in the IPGS and its PG and GS.
PSGSIPGS
Nodes75147222
Links89178277
Table 2. Coupling links between the PG and GS in the IPGS.
Table 2. Coupling links between the PG and GS in the IPGS.
No. of Coupling Links Nodes in PSNodes in GSFunction
170192Gas-fired power generator
221162Electricity-driven gas compressor
31198Electricity-driven gas compressor
414216Gas-fired generator
534159Electricity-driven gas compressor
670174Electricity-driven gas compressor
770176Electricity-driven gas storage
858175Electricity-driven gas storage
945150Electricity-driven gas storage
102150Electricity-driven gas storage
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Amusan, O.; Shi, S.; Wu, D.; Liao, H. Structural Vulnerability Analysis of Interdependent Electric Power and Natural Gas Systems. Energies 2023, 16, 6918. https://doi.org/10.3390/en16196918

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Amusan O, Shi S, Wu D, Liao H. Structural Vulnerability Analysis of Interdependent Electric Power and Natural Gas Systems. Energies. 2023; 16(19):6918. https://doi.org/10.3390/en16196918

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Amusan, Olabode, Shuomang Shi, Di Wu, and Haitao Liao. 2023. "Structural Vulnerability Analysis of Interdependent Electric Power and Natural Gas Systems" Energies 16, no. 19: 6918. https://doi.org/10.3390/en16196918

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