**1. Introduction**

The portion of the world population inhabiting an urban environment has grown in the last decade from about 33% to 55% [1]. That growth has produced enormous demand and stress on the infrastructures and systems that deliver essential city services, resulting in significant interest in developing smart cities. The main purpose of smart city schemes is to create intelligent infrastructures for cities by harnessing innovations in cyber-physical systems, data science, and information and communication technology (ICT). Moreover, smart infrastructures are more dependent on both ICT and electrical power for proper operation. This increased dependence can introduce new vulnerabilities and lower infrastructure resilience [2]. In particular, severe weather (e.g., snow/ice storms, typhoons,

**Citation:** Almaleh, A.; Tipper, D.; Al-Gahtani, S.; El-Sehiemy, R. A Novel Model for Enhancing the Resilience of Smart MicroGrids' Critical Infrastructures with Multi-Criteria Decision Techniques. *Appl. Sci.* **2022**, *12*, 9756. https:// doi.org/10.3390/app12199756

Academic Editor: Luis Hernández-Callejo

Received: 21 August 2022 Accepted: 26 September 2022 Published: 28 September 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

tornadoes, drought-induced wildfires, etc.) is a growing vulnerability concern as the frequency, intensity, and geographic scope of severe weather events are predicted to increase with climate change [3]. Currently, severe weather events [4] are the number one reason for power outages in the United States, which are in turn, the top reason for outages in ICT services. For that, intelligent infrastructures provide more consistent and reliable system performance, new features/functions, and increased sustainability.

Industrial scale microgrids are basically self-supporting power systems typically in the 1.5–5 MW range. They have been advocated as a mechanism to improve the availability of power to significant societal and business facilities such as hospitals, military bases, and factories. Additionally, microgrids are promoted as an approach to incrementally incorporate shared renewable power production, such as wind and solar, into the bulk power grid in the case of disaster [5]. Mircrogrids are also proposed in the literature as a solution to achieve climate adaptation and mitigation goals [6].

Figure 1 gives a typical microgrid architecture. As shown in Figure 1, the building blocks of the microgrid are the controller, electrical power switches, local energy supplies (e.g., solar cells, wind turbines, and diesel generators), energy storage, and various loads. Microgrids are designed to operate in standalone mode and joined mode to the primary grid. In the joined mode scenario, the microgrid serves as additional energy back up to the bulk power system, decreasing peak loads, enhancing power stability, and reducing harmful emissions [7]. In island mode, the microgrid disconnects from the bulk grid and functions as a standalone power supply. The microgrid controller manages the transitions between modes seeking to maintain voltage and synchronization while minimizing load dropping and disruption.

**Figure 1.** Sample microgrid architecture.

Since the available power is limited in island mode, the power loads are grouped into their significance categories: mission critical, mission priority, and non-critical. Mission critical loads are given the highest priority and consists of the essential components of the critical infrastructures of interest (e.g., hospitals, water treatment plants, and cellular network base stations). Mission priority loads are given second priority and would include loads that are important to society but not essential to the functioning of smart critical infrastructures (e.g., drug store, gas station, etc.). Lastly, non-critical loads would include residential and non-essential businesses (e.g., movie theaters).

Generally, microgrids have fixed geographical limits and are planned in island mode to produce power sufficient to sustain mission-critical loads inside the geographic boundaries. Thus, based on the power accessible in island mode, the microgrid controller may implement load shedding, dropping non-critical loads and a portion of the mission priority loads [5]. Furthermore, microgrids are required to possess the capability to shift efficiently from island mode to grid-connected operation, providing re-synchronization with minimal consequence to significant loads through the transition phases.

Unlike the nanogrids used in residential settings, a significant obstacle to the implementation of industrial size microgrids is the high cost in constructing, operating, and maintaining a microgrid. Currently, industrial capacity microgrids are mostly owned by an individual private organization. Recognizing the non-linear economic costs of implementing microgrids [8], the authors in [9] advocated for shared mid-size microgrids, with the expense borne by both the vital infrastructure proprietors with critical loads (e.g., cellular network operators and hospitals) and the government organizations that will utilize the infrastructures during disaster recovery. This shared community use approach could be facilitated by government-sponsored financing and tax credits. Furthermore, it may justify either re-insurance or bonding mechanisms to help in reducing the cost. Here, the goal of this work is to design and place microgrids based on minimizing the overall expenses and to ensure power flow connected over the most vital critical infrastructure parts. Therefore, the proposed design is able to achieve significant techno-economical merits for microgrids.

Related work on microgrids includes using microgrids to improve radial distribution power grid restoration after a natural disaster [5,10] and dynamically forming local microgrids around distributed generation sources after a disaster [11]. Kelly-Pitou [6] introduced the notion of employing a microgrid for the purpose of enhancing both power resilience and for alleviating climate change impacts. Nevertheless, this early work did not propose a method for determining the location of microgrids to improve the resilience of different critical infrastructures viewed as a group. In [12], the authors suggested using an algorithm to achieve multi-agent resource allocation in distributed scenarios through a shared microgrid, including residential and commercial buildings, with the least amount of information exchange between the users. However, their study lacks the commercial and residential segments by not assigning the priorities to critical nodes in the network.

The bulk of the research literature on critical infrastructures within smart-city schemes has focused on optimizing performance and providing new functionalities. Previous work covering smart-city resilience has focused specifically on developing frameworks [13] or "solidifying" critical infrastructures. Traditionally, policy-makers mandated or supported hardening techniques such as constructing flood barriers and rebuilding levees according to the probability of 1 in 100-year situations. However, when considering smart critical infrastructures and the increasing weather variability, planners need to move beyond physical hardening techniques, adopting new preparedness methods and policies that acknowledge the dependence on both power and ICT.

In [9], a structure for providing power and ICT is developed to enhance smart city critical infrastructure services in post-disaster conditions. The proposed method in this work employs multi-user microgrids to generate electricity concurrently with cellularbased communications, which are dynamically re-adjusted into a mesh network along with local edge computing to control/operate smart critical infrastructures. The main aim of the framework is to construct districts within a mid size zone that act as secure area, including essential critical infrastructure functions operating at limited but acceptable levels. Guaranteeing that the combination of microgrids, cellular-based catastrophe recovery mesh network, and edge computing are geographically located in this "socially planned" fashion will assist in reducing at-risk districts and bolster the economic argument for microgrids.

Related work on enhancing critical infrastructure resilience has focused on hardening [14,15] the essential elements in every infrastructure. Various techniques have been

introduced in the literature for discovering the most vital components in a critical infrastructure, such as graph theoretic analysis, simulation-based analysis, stochastic modeling, and expert judgment [14]. Graph centrality measures have been utilized in developing critical infrastructure protection strategies, including vulnerability studies of power systems. A heuristic approach introduced in [16] uses five graph centrality measures, namely degree centrality, between centrality, centered centrality, eccentricity centrality, and radially. The authors evaluated the nodes with each of the five centrality measures. If a node is highly ranked by at least two measures, it is considered a critical node. The model was applied to assess the impact of potential attacks on the Swiss power network. However, the author utilized the proposed model considering the impact on the power network's infrastructure, neglecting the dependency on other infrastructures that could potentially have a higher effect. In [17], the authors introduced a scheme to determine the critical nodes of a smart power network according to the highest power flow in the system. However, their investigation concentrated on the betweenness centrality as the primary graph measure, which could lead to a bias in the outcome by neglecting other essential centrality measures in networks, such as node degrees and closeness. The authors of [18] considered the centrality metrics of a dependency risk graph, exploring the connection between dependency risk paths and graph centrality. They mapped different critical infrastructures into one graph and applied the centrality metrics on each node, assuming that the links are represented by the escalating failure values between nodes from different infrastructures. The primary motivation for that was to identify the critical infrastructure nodes between interdependent critical infrastructures that noticeably impact the essential routes of risk in the network and then to analyze cascading failures to different nodes or links in the network.

In [19], the authors proposed a model to identify the most critical nodes in interdependent critical infrastructures. They developed an integer linear programming optimization formulation that models the approach of an attacker who targets a collection of nodes with the intention of compromising or damaging them. They assumed that the attacker is motivated by three objectives: (i) minimizing the size of the largest connected component, (ii) maximizing the number of disconnected components, and (iii) minimizing the cost of an attack. All three objectives are based on graph theory metrics and can be used to determine where to hardened the infrastructure. Here, the problem of where to harden multiple infrastructures as a group using a microgrid is considered.

Noting that microgrids are the most costly element in our framework, our focus is on where to place a microgrid in order to promote smart critical infrastructure operations postdisaster. An holistic approach is adopted for the microgrid location problem, considering multiple critical infrastructures at once, and focuses on factors such as component importance within a critical infrastructure, the geospatial placement of infrastructures, power requirements, and microgrid cost. Optimization problems are formulated to determine the location of a microgrid in a geographic space that optimizes a weighted combination of the relative importance of nodes across all critical infrastructures and the cost. Furthermore, a simple heuristic method for positioning microgrids is presented and demonstrated. This method is compared with the optimization problem. Numerical results using Pittsburgh as a case study are given to illustrate the effectiveness of the methodology and its trade-offs.

This paper is structured as follows. Section 2 presents the proposed methodology, which determines the placement of microgrids. In Section 3, the numerical results and a discussion of implementing the proposed method are presented. Section 4 provides the findings of the study and future work.

### **2. Materials and Methods**

### *2.1. Microgrid Location Methodology*

Consider a neighborhood or section of a city where multiple infrastructures geographically overlaid co-exist, as illustrated in Figure 2. For instance, the three infrastructures shown could include an intelligent water network, a natural gas pipeline system, and a

healthcare system consisting of a hospital and community health clinics. The proposed approach to determining the location of a microgrid essentially has four steps as follows:


**Figure 2.** Geographic overlaid infrastructures connected to a microgrid.

### *2.2. Critical Infrastructure Analysis*

Critical infrastructures are grouped into two classes according to the applicability of modeling the infrastructure with a network graph: (1) interconnected infrastructures and (2) standalone infrastructures.

### 2.2.1. Interconnected Infrastructure

Network science methods based on graph theory have been applied to analyze critical infrastructures that include the interconnected elements or operations, such as power grids [20], transportation networks [21], water systems [22], and optical backbone communication networks [23]. Interconnected infrastructures are modeled with a graph *G* = (*V*, *E*), where *V* is the set of vertices or network nodes (e.g., power plants and substations, pumps and pipe junctions, and optical switches), and *E* is the set of edges or links or connections (e.g., power lines, water pipes, and optical fibers) joining the nodes. Given a graph model of an interconnected infrastructure, one can use network science methods in part to determine the relative importance of nodes in the infrastructure based on graph metrics. This paper adopted centrality metrics similar to [16], as explained in the following.

### Degree Centrality

Node degree denotes the total number of neighbor nodes to which a node is immediately attached. The degree of centrality is a primary graph analysis measure that can be calculated as the total of edges connected to node *v*, which is called degree *deg*(*v*), and identified as centrality degree *Cd*(*v*), which is provided as follows:

$$\mathbb{C}\_d(v) = \deg(v) \tag{1}$$

Betweenness Centrality

Betweenness centrality is a benchmark of centrality measure used in graph networks that reflects the shortest paths within couples of vertices *s* and *t*. It can be calculated as the percentage of shortest paths that cross through a vertex *v* ∈ *V*(*G*). Hence, *Cb*(*v*) can be written as follows:

$$\mathcal{C}\_b(\upsilon) = \sum\_{s \neq \upsilon \neq t} \frac{\sigma\_{st(\upsilon)}}{\sigma\_{st}} \, , \tag{2}$$

where *σst* signifies the number of shortest routes from node *s* to node *t*, and *σst*(*v*) equals the total number of these routes that cross within *v*.

### Closeness Centrality

In any connected graph, the normalized closeness centrality *Cc*(*v*) of a particular node *v* ∈ *V*(*G*) equals the average distance of the shortest routes connecting node *v* to all additional nodes in the graph. The closeness can be defined as follows:

$$\mathcal{C}\_{\mathfrak{c}}(v) = \frac{1}{\sum\_{s} dist(s, v)}\,, \tag{3}$$

In the above equation *dist*(*s*, *v*) denotes the length connecting vertices *s* and *v*.

### Power Requirements

The power *Cp*(*v*) required for vertex *v* ∈ *V*(*G*) is one of the factors considered and is assumed to be given.
