Bi-Level Resilience-Oriented Sitting and Sizing of Energy Hubs in Electrical, Thermal and Gas Networks Considering Energy Management System

Abstract

In this article, the planning and energy administration of energy hubs in electric, thermal and gas networks are presented, considering the resilience of the system against natural phenomena like floods and earthquakes. Each hub consists of bio-waste, wind and solar renewable units. These include non-renewable units such as boilers and combined heat and power (CHP) units. Compressed air and thermal energy storage are used in each hub. The design is formed as a bi-level optimization framework. In the upper level of the scheme, the energy management of networks bound to system resiliency is provided. This considers the minimization of annual operating and resilience costs based on optimal power flow equations in networks. In the lower-level model, the planning (placement and sizing) of hubs is considered. This minimizes the total building and operation costs of hubs based on the operation-planning equations for power supplies and storages. Scenario-based stochastic optimization models are used to determine the uncertainties of demand, the power of renewable systems, energy price and the accessibility of distribution networks’ elements against natural disasters. In this study, the Karush–Kuhn–Tucker technique is used to extract the single-level formulation. A numerical report for case studies verifies the potential of the plan to enhance the economic, operation and resilience status of networks with energy administration and the optimal planning of hubs in the mentioned networks. By determining the optimal capacity for resources and storage in the hubs located in the optimal places and the optimal energy administration of the hubs, the economic, exploitation and resilience situation of the networks are improved by about 27.1%, 97.7% and 23–50%, respectively, compared to load flow studies.

1. Introduction

To decrease environmental pollution and improve the technical and economic conditions of structured energy distribution networks, energy administration organizations suggest using a demand response program (DRP), energy storage (ES) and distributed generation (DG) in consumption areas [1]. DG systems include two types, non-renewable and renewable. Renewable energy sources (RESs) use natural phenomena to produce energy. For example, wind turbines (WTs) use wind speed to generate electrical energy. Photovoltaic (PV) systems use sunlight to produce electrical energy. Bio-waste units (BUs) use environmental waste to generate methane gas [2]. Non-renewable resources are based on the conversion of one energy into another, like a gas turbine that uses gas to produce electrical energy. Combined heat and power (CHP) units use gas to produce thermal and electrical energy to improve energy efficiency. Therefore, there is a dependency among structured energy distribution networks. For example, with CHP, the thermal (/active) power in the heat (/electrical) distribution network will depend on the gas network. Therefore, to increase energy efficiency, it is necessary to manage the energy of different networks at the same time [3]. To establish optimal energy administration in networks, it is first necessary to consider an integrated unit for sources, storage devices and DRPs. This topic relates to use of energy hubs (EHs) in energy networks [4]. EHs involve the aggregation and coordination of DG, ES and DRP units, which can play an effective role in the transmission and storage of various energies [4]. Of course, in order to be able to establish the optimal economic and technical conditions of energy hub administration in different networks, it is necessary to locate the hubs in optimal locations of the energy networks. Also, the optimal sizes for power supply and storage elements in the EH should be determined. In other words, it is predicted that optimal economic and technical conditions in energy networks can be achieved through optimal EH planning and implementing the optimal energy administration of hubs. Furthermore, energy distribution networks have a wide geographic range. Therefore, with the occurrence of an N-k event caused by natural disasters, it is expected that many consumers will lose power. But EHs are generally deployed in consumption areas [5]. Therefore, it is expected that they can compensate for part of the unavailable energy in such conditions. To put it simply, it is expected that hubs can improve the resilience of energy grids.

1.1. Literature Review

A multitude of studies and initiatives have been undertaken in the domains of energy management and EH design across diverse energy networks. A case-based stochastic methodology for synchronized hub energy management in a day-ahead market is delineated in Reference [6]. This technique integrates heat, gas and electric systems based on electricity and gas as inputs for the hub and heat and electricity as outputs. A smart city model incorporating several components, such as a microgrid, intelligent transit system and energy-harvesting technologies with energy transformation capabilities, is presented in [7]. The model considers off-grid smart city operation, transforming such systems into active off-grid networks that utilize gas, water, heat and electricity as energy transporters. An EH that combines several energy sources and energy storage techniques was created in Ref. [8]. For the EH, two methods were suggested—biomass-to-gas-to-power (B2X2P) and power-to-gas-to-power (P2X2P), which both utilize ammonia and hydrogen as energy carriers. Reinforcement learning and linear formulation techniques were used to control the EH’s scheduling in light of its adaptability and profitability. A multi-EH system driven by renewable energy is proposed in Ref. [9] and integrated with a power-to-ammonia facility based on the thermo-electrochemical effect. The proposed EH’s energy administration is thus reduced to a multi-agent coordinated model to reduce carbon dioxide production and operational costs while meeting restrictions. An artificial intelligence-based technique called reinforcement learning is suggested in [10] as a way to maximize an EH’s energy administration system (EMS). This EH has a gas furnace, CHP and RES. The available choices, including real-time and day-ahead purchases from the main grid, RES and natural gas usage, are properly incorporated to fulfill the demand for thermal and electrical energy. RESs are preferred since they lessen energy expenditures and pollutant emissions. Through the creation of a micro-EH, Ref. [11] presents an innovative method for a home EMS. The hub effectively combines adaptable resources from several residences, supported by the thorough modeling of appliance properties for improved energy administration precision.

The scheme in [12] considers the flexible EMS for EHs in the heat and electrical grids. In EHs, WT and PV generate active power, and a CHP-based BU is used to generate thermal and active power. Thermal storage (TS) and compressed air energy storage (CAES) manage the hubs’ flexibility. Ref. [13] presents a robust EMS to model EH operation. A max–min format of static robust formulation is used to model the uncertain parameters. DRP, CAES and electric vehicles are integrated to increase hub flexibility. Reference [14] presents a stochastic management that integrates risk formulation for an EH, addressing uncertain quantities associated with RES and consumption demands. The approach employs the Conditional Value at Risk (CVaR) technique for risk assessment and quantification. Reference [15] presents a bi-stage stochastic resource planning and operational strategy for several smart EHs. The initial phase optimizes the placement of each energy-harvester and the capacities of various assets. In second stage, it obtains the optimal condition for the discharging and charging rates of each asset and the power of parking lots. The study in [16] focused on reducing the costs associated with power generation over subsequent hours or days, while also addressing the dispersion of environmental pollution. This research study employs probabilistic modeling to address the microgrid’s operation, influenced by different resources of uncertainty, including load, the price of energy, the power of WTs, and solar cell output power, in the market. The bi-level scheme for optimal operation-planning of the hub, considering the uncertainty of demand and RESs, is provided in [17]. The optimal planning utilizing probability–stochastic methods is demonstrated at the initial level, while energy management based on these models is addressed at the secondary level.

Numerous studies exist in the domain of power network resilience. Reference [18] presents a resilience-oriented planning for microgrids, employing switchable transmission lines to improve the power grid resilience. The research examines a hydrogen-power-heat microgrid that derives gas from a gas grid, interacts with the primary power network, and integrates CHP, an electrolyzer, and thermal storage. Ref. [19] presents a quantitative assessment framework aimed at enhancing the power grid resilience in case of adverse phenomena. This framework encompasses the recognition of weak lines and the formulation of a developed resilience index. Initially, a vulnerability index is introduced, derived from a successive failure diagram that is established based on the failures of transmission lines under sustained disturbances. A resilience curve is employed to characterize system failure under varying event intensities. In [20], we present a novel simulation framework that incorporates the malware attack process and uncertainties associated with RES to quantitatively analyze the resilience of Cyber–Physical Power Systems. The summary of the background work conducted in the research is presented in

Table 1. Summary of the previous studies and papers.

Ref.	Model of EH Including			Resiliency Assessment in Network	EH Capable of Improving Resiliency	BU Model	CAES Model
	Operation	Sitting	Sizing
[6]	Yes	No	No	No	No	No	No
[7]
[8]						Yes
[9]						No
[10]
[11]
[12]						Yes	Yes
[13]						No
[14]							No
[15]		Yes
[16]			Yes
[17]
[18]		No	No	Electrical
[19]
[20]
Current study	Yes			Electrical, thermal and gas	Yes

.

1.2. Research Gaps

Relying on Table 1 and the research history presented in Section 1.2, some disadvantages and shortcomings of the literature in the field of EH operation and planning in the energy network are as follows:

-

In most studies, like [6,7,8,9,10,11,12,13,14], only the energy administration of EHs in various energy networks has been considered. But to create optimal economic and technical conditions in the energy network, it is necessary to check the planning and operation of the hubs [15,16,17]. Although energy administration can achieve an effective capability for the hub in energy networks, the non-optimal location and size of the hubs may reduce the positive effect of hub energy administration on the energy network. In planning, the optimal locations for the hubs are obtained and then the optimal size of their resources and storages are determined. In the following, hub energy administration is implemented in the energy network. This issue has been investigated in a few research studies such as [15,16,17], of which [15] considered only the placement and operation of hubs.

-

In most research studies in the field of hub planning and operation, it has been common to use batteries in EHs. Although the battery has a high power density and efficiency, its useful life is short, its construction cost is high, and it is more difficult to reach larger capacities. To address this shortcoming, some studies in the literature, including [8,15,16], have suggested the use of hydrogen storage. But this storage in the fuel cell sector has a low working efficiency of about 50% [21]. In other words, the energy loss of this storage device is high. Another suitable option is to use CAES in the hub. This storage has a significant efficiency of about 80%, its useful life is high, its construction cost is lower than the battery and hydrogen storage, and it is not difficult to reach the high capacity [22]. But the use of CAES has been considered in a few research studies such as [12,13]. In addition to this, the bio-waste unit (BU) is also an RES that is able to produce methane gas by consuming environmental waste. Also, if this unit uses a gas turbine or CHP in its output, it can play a role in generating electricity and heat power [12]. However, in most of the research in the field of hub energy administration, the use of wind and solar renewable sources has been common. But BU will certainly decrease environmental pollution by consuming environmental waste. Its use in EHs has been considered in a few research studies such as [8,12].

-

Natural phenomena like floods and earthquakes may damage various networks, including electrical, telecommunication, gas and thermal networks. However, in general studies such as [18,19,20], the resilience of the electrical network has been considered. But this network is dependent on the gas network, so if the gas network is damaged, the electric network will also suffer. In large industrial areas, if the heating network is damaged, there will be a very high cost per industrial unit. Therefore, in the event of natural disasters, it is necessary to check the resilience of different networks, because generally the networks are dependent on each other. In a few research studies, the resilience of different networks has been examined simultaneously.

-

EHs have various power source and storage elements that can play an effective role in the transfer and storage of various energies. In other words, if N-k events occur, EH is able to feed a certain percentage of consumers in different networks. Because EH is generally deployed at consumption points. Therefore, it is expected that EHs have a suitable capability of improving the resilience of energy networks. But this topic was addressed in fewer research studies.

1.3. Proposed Solution and Contributions

(A) Proposed solution: In this article, to address the shortcomings, the optimal allocation and rating of EHs considering the energy administration system in electric, thermal and gas networks bound to the resilience of the system against natural disasters such as floods and earthquakes is provided in Figure 1. Accordingly, EHs have wind, solar and bio-waste renewable resources. Wind turbines (WTs) and photovoltaics (PVs) are used to generate electrical energy in the hub, and BU is used to generate gas in EHs. There is a CHP in the hub that converts gas into electrical and thermal energy. The hub also includes a boiler that is used to generate heat. In addition, CAES and TS are used in the hub. CAES (TS) is used to store electrical (heat) energy. The plan is presented as a bi-level optimization method. In its upper level, the operation and resilience model of energy networks is expressed. Thus, at this level, the operator of the networks considers the minimization of the overall expected annual costs of resiliency and operation in the electric, thermal and gas networks. It is limited by the network’s optimal power flow model and resilience limitations in energy networks. At the lower-level formulation, the placement and sizing of EHs are included. The objective function of this level minimizes the total annual operation and construction costs for EHs. The construction cost includes the installation cost of renewable sources, CHP, boilers and energy storage devices. The EH purchasing energy cost received by energy networks is the EH operating cost. The total cost of building and operating a hub is known as the planning cost of EHs. The boundaries of the lower level include the operation-planning formulation of various power supplies and storage devices. This plan includes uncertain parameters such as the requested demand, energy prices, accessibility of energy network equipment against natural disasters, and renewable power. To accurately evaluate the resilience index, it is necessary to examine different scenarios of load, renewable power and availability of network equipment. In this article, expected energy not supplied (EENS) is adopted to check the resiliency of energy networks. Therefore, in this article, scenario-based stochastic optimization (SBSO) is utilized to provide a suitable model of the uncertain quantities. In addition, to obtain the optimal solution in the bi-level formulation based on conventional algorithms, it is necessary to achieve the single-level method for the proposed scheme. In this article, the Karush–Kuhn–Tucker (KKT) approach extracts the single-level formulation.

Note that in the proposed scheme, the energy network operator has different demands. The hub operator also has different demands. Therefore, one optimization model can be presented for the hub, and another optimization model can be used for the energy network. However, these models are dependent on each other. Therefore, in this paper, bi-level optimization was used, so the network and hub models are presented in separate problems. That is, the network model is expressed in the upper-level problem, and the hub model is presented in the lower-level problem. The goals of the network operator (hub) are also modeled in the objective function of the upper-level (lower-level) problem. In bi-level optimization, the dependence between the upper-level and lower-level problems is also considered. In addition, each of the upper-level and lower-level problems is based on single-objective optimization, so that each of them has an objective function and several constraints. The upper-level problem is based on nonlinear programming, but linear programming is used for the lower-level problem. In other words, the lower-level model is convex. Therefore, the KKT method can be used to convert the bi-level problem into a single-level one.

(B) Contributions: Finally, by comparing the solution and the research background, the following innovations are obtained for the proposed plan:

-

Optimal sitting and rating of EHs simultaneously in gas, thermal and electric networks, considering the energy administration system.

-

Using the compressed air energy storage elements in the EH to increase energy efficiency and reduce the planning cost of hubs.

-

Using the bio-waste unit in the hub to produce gas and reduce environmental pollution by consuming environmental waste.

-

Simultaneous analysis of the resilience of electric, thermal and gas networks against natural events such as floods and earthquakes.

-

Investigating the potential of EHs in boosting the resilience of energy networks in the condition of N-k contingency.

The bi-level operation-planning of EHs in energy networks, considering the model given for uncertain quantities, is provided in Section 2. Next, in Section 3, the single-level formulation of the suggested design is obtained. Numerical findings for various case studies are given in Section 4. Eventually, Section 5 provides the conclusions.

2. Bi-Level Planning of Networked EHs

In this section, the bi-level sizing and placement of hubs in gas, electrical and thermal systems are described. At the upper level of this issue, the optimal power flow of the networks is presented, taking into account the minimization of the operating and resilience costs of the networks. In the lower-level model, the optimal placement and sizing of EHs to minimize the planning cost is expressed. In the following, the model of the proposed scheme is presented.

(A) Operation of energy networks bound to resilience against natural disasters (upper-level model): Formulation (1) gives the energy administration model of the electric, thermal and gas networks considering the system resiliency in the condition of occurrence of N-k event. In relation (1a), the objective function of the network’s operator is expressed. The first row of this relationship considers the minimization of the annual network’s operation cost (the purchasing energy cost received by the upstream grid) [3]. The operation cost in each network can be found by multiplying the price of energy in this network and energy passing through the stations in this network [3]. The expression 365 is the total days for a year. The data of the scheme, such as the load profile and the production power of renewable resources, are different for various days. Therefore, the CF coefficient was used in relation (1a), which indicates the percentage of similarity of the data of the problem in all the days of a year with the data used in the plan [22]. In the second row of relation (1a), the resiliency cost minimization of the energy networks is presented. This function refers to the minimization of the blackout cost of consumers in the N-k event resulting from natural disasters such as floods and earthquakes. This function is equal to the product of the expected energy not supplied (EENS) and the value of lost load (VOLL) [23]. VOLL is a penalty price for the network operator, which is used to improve the network resiliency. In this regard, du represents the number of days that event N-k has occurred [23].

Constraints (1b)–(1u) represent the optimal power flow model bound to system resiliency in the electric, heat and gas networks. The expressed model for the electrical network is shown in relations (1b)–(1i) [3]. The power flow formulation in this grid corresponds to models (1b)–(1e), which, respectively, present the active/reactive power balance in the network buses. The reactive power of passive loads is based on the active power of loads and the power factor of the consumer. If a part of the load is turned off, its reactive power will decrease as in (1c). The limits of electric grid operation correspond to relations (1f)–(1h). In constraints (1f) and (1g), the apparent power limit of electrical lines and substations are stated, respectively. In relation (1h), the boundary of the magnitude of voltage in electric network buses has appeared [3]. Condition (1i) represents the network resilience limit, which represents the boundary of loads unfed in this network. The operation model of the thermal network considering the system resiliency is shown in relations (1j)–(1o) [4]. Constraints (1j) and (1k) represent the power flow formulation of the mentioned network, which refers to the balance of heat power in different nodes and the heat power in the pipelines, respectively. The boundary of thermal network operation includes the limitation of the heat power passing through pipelines and substations. The temperature limit in different nodes is presented in relations (1l)–(1n), respectively [4]. The resilience condition (limitation of unfed load) in the mentioned network corresponds to relation (1o). In relations (1p)–(1u), the resiliency-constrained operation model of the gas network is expressed. The balance of gas in different nodes of the network is proportional to relation (1p). In constraint (1q), the gas in the pipeline is computed [4]. The limitation of gas passing through pipelines and substations corresponds to equations (1s) and (1r), respectively. In Equation (1t), the gas pressure limitation in different nodes is stated [4]. The resilience condition or limitation of unfed load in the gas network is proportional to relation (1u). Parameters u, z and x refer to the accessibility of energy network elements during natural disasters such as floods and earthquakes. Thus, if these parameters have a value of 1 (0), the corresponding equipment is present (not present) in the network for N-k contingency.

$$\begin{array}{c}\min \hspace{1em}ANC=365\times CF\times \left({\displaystyle \sum _{b,t,s}{\rho }_s{\gamma }_{E t,s}{P}_{S b,t,s}}+{\displaystyle \sum _{n,t,s}{\rho }_s{\gamma }_{H t,s}{H}_{S n,t,s}}+{\displaystyle \sum _{g,t,s}{\rho }_s{\gamma }_{G t,s}{G}_{S g,t,s}}\right)\\ \hspace{1em}+VOLL\times \stackrel{EENS}{\overbrace{du\times CF\times \left({\displaystyle \sum _{b,t,s}{\rho }_s{P}_{N b,t,s}}+{\displaystyle \sum _{n,t,s}{\rho }_s{H}_{N b,t,s}}+{\displaystyle \sum _{g,t,s}{\rho }_s{G}_{N b,t,s}}\right)}}\end{array}$$

(1a)

Subject to:

$$P_{S b,t,s}+{\displaystyle \sum _i{I}_{E b,i}{P}_{H i,t,s}}+{\displaystyle \sum _k{J}_{E b,k}{P}_{L b,k,t,s}=P_{D b,t,s}}-P_{N b,t,s}\hspace{1em}\hspace{1em}\forall b,t,s$$

(1b)

$$Q_{S b,t,s}+{\displaystyle \sum _k{J}_{E b,k}{Q}_{L b,k,t,s}=Q_{D b,t,s}}\hspace{1em}\hspace{1em}\forall b,t,s,Q_{D b,t,s}=\left(P_{D b,t,s}-P_{N b,t,s}\right)\times \tan \left({\cos }^{-1}\left(P{F}_D\right)\right)$$

(1c)

$$P_{L b,k,t,s}=\left(g_{L b,k}{\left(V_{b,t,s}\right)}^2-V_{b,t,s}{V}_{k,t,s}\left\{g_{L b,k}\cos \left({\alpha }_{b,t,s}-{\alpha }_{k,t,s}\right)+b_{L b,k}\sin \left({\alpha }_{b,t,s}-{\alpha }_{k,t,s}\right)\right\}\right)u_{L b,k,s}\hspace{1em}\forall b,k,t,s$$

(1d)

$$Q_{L b,k,t,s}=\left(-b_{L b,k}{\left(V_{b,t,s}\right)}^2+V_{b,t,s}{V}_{k,t,s}\left\{b_{L b,k}\cos \left({\alpha }_{b,t,s}-{\alpha }_{k,t,s}\right)-g_{L b,k}\sin \left({\alpha }_{b,t,s}-{\alpha }_{k,t,s}\right)\right\}\right)u_{L b,k,s}\hspace{1em}\forall b,k,t,s$$

(1e)

$$\sqrt{{\left(P_{L b,k,t,s}\right)}^2+{\left(Q_{L b,k,t,s}\right)}^2}\le {\overline{S}}_{L b,k}\hspace{1em}\forall b,k,t,s$$

(1f)

$$\sqrt{{\left(P_{S b,t,s}\right)}^2+{\left(Q_{S b,t,s}\right)}^2}\le {\overline{S}}_{S b}{u}_{S b,s}\hspace{1em}\forall b,t,s$$

(1g)

$$\underset{\_}{V}\le V_{b,t,s}\le \overline{V}\hspace{1em}\forall b,t,s$$

(1h)

$$0\le P_{N b,t,s}\le P_{D b,t,s}\hspace{1em}\hspace{1em}\forall b,t,s$$

(1i)

$$H_{S n,t,s}+{\displaystyle \sum _i{I}_{H n,i}{H}_{H i,t,s}}+{\displaystyle \sum _k{J}_{H n,k}{H}_{L n,k,t,s}=H_{D n,t,s}}-H_{N n,t,s}\hspace{1em}\hspace{1em}\forall n,t,s$$

(1j)

$$H_{L n,k,t,s}=C_{L n,k}\left(T_{n,t,s}-T_{k,t,s}\right)z_{L n,k,s}\hspace{1em}\forall n,k,t,s$$

(1k)

$$\left|H_{L n,k,t,s}\right|={\overline{H}}_{L n,k}\hspace{1em}\forall n,k,t,s$$

(1l)

$$\left|H_{S n,t,s}\right|={\overline{H}}_{S n}{z}_{S n,s}\hspace{1em}\forall n,t,s$$

(1m)

$$\underset{\_}{T}\le T_{n,t,s}\le \overline{T}\hspace{1em}\forall n,t,s$$

(1n)

$$0\le H_{N n,t,s}\le H_{D n,t,s}\hspace{1em}\hspace{1em}\forall n,t,s$$

(1o)

$$G_{S g,t,s}+{\displaystyle \sum _i{I}_{G g,i}{G}_{H i,t,s}}+{\displaystyle \sum _k{J}_{G g,k}{G}_{L g,k,t,s}=G_{D g,t,s}}-G_{N g,t,s}\hspace{1em}\hspace{1em}\forall g,t,s$$

(1p)

$$G_{L g,k,t,s}=x_{L g,k,s}{K}_{L g,k}\sqrt{\left|{\left(p_{g,t,s}\right)}^2-{\left(p_{k,t,s}\right)}^2\right|}\hspace{1em}\hspace{1em}\forall g,k,t,s$$

(1q)

$$\left|G_{L g,k,t,s}\right|={\overline{G}}_{L g,k}\hspace{1em}\forall g,k,t,s$$

(1r)

$$\left|G_{S g,t,s}\right|={\overline{G}}_{S g}{x}_{S g,s}\hspace{1em}\forall g,t,s$$

(1s)

$$\underset{\_}{p}\le p_{g,t,s}\le \overline{p}\hspace{1em}\forall g,t,s$$

(1t)

$$0\le G_{N g,t,s}\le G_{D g,t,s}\hspace{1em}\hspace{1em}\forall g,t,s$$

(1u)

(B) Planning and operation of EHs (lower-level model): In problem (2), the placement and sizing of EHs are presented. The objective function is mentioned in relation (2a). The first line of this relationship shows the minimization of the annual construction cost of hub elements such as the CHP, boiler, WT, PV, BU, CAES and TS [22]. The annual construction cost of each mentioned element is equal to the product of the optimal size of the element and the unit price of the construction of this element [22]. In the second line of relation (2a), the minimization of the annual operation cost of EHs is given, which refers to minimizing the purchasing energy cost of EHs from the electric, thermal and gas networks [3]. The energy cost of the hub in each network can be found by multiplying the energy received by the hub from this network and the price of energy in the grid. In constraints (2b)–(2x), the operation and sizing model of resources and storage in the EH format is presented. The active, thermal and gas output power of the hub (from the view point of the energy network) is obtained from relations (2b)–(2d), respectively. The hub active power is the total active power produced by CHP, WT, PV, CAES in the discharge operation minus the total active power received by the passive load and CAES in the charge mode. The EH thermal power is equal to the sum of heat power generated by the CHP, boiler and TS in discharge mode minus the thermal power received by load and TS in charging operation. The gas of the hub is the production gas power of BU minus the gas power demand of the passive load, boiler and CHP. The CHP formulation appears in constraints (2e) and (2f) [4]. In expression (2e), the CHP production active power constraint is given, and the optimal size limit of CHP is expressed in Equation (2f). CHP receives gas for its input and produces electricity and heat at its output. The amount of heat output of this source is calculated by ${\displaystyle \frac{\left(1-{\eta }^T\right){\eta }^H}{{\eta }^T}}{P}_C$.

Based on Equation (2c), which is a coefficient of the CHP active power. CHP input gas is also calculated by ${\displaystyle \frac{1}{{\eta }^T}}{P}_C$ based on Equation (2d) [4]. In Constraints (2g) and (2h), the boiler model is stated, and these relationships, respectively, express the limit of the production thermal power of the boiler and the boundary of the optimal size of this resource in EHs [3]. The input gas of boiler can be calculated by ${\displaystyle \frac{1}{{\eta }^B}}{H}_B$ based on Equation (2d). The formulation of renewable resources such as wind system, photovoltaic and bio-waste unit is presented in relations (2i)–(2n) [22]. Thus, the active power produced by WT and PV, and the gas produced by BU are calculated from the relations (2i), (2k) and (2m), respectively. Based on these relationships, the power of individual RES can be obtained by multiplying the source’s rating and the production power rate of said source. The optimal capacity limit of the WT, PV and BU in EHs is based on constraints (2j), (2l) and (2n), respectively. The CAES operation-planning model is expressed in formulations (2o)–(2s) [22]. The CAES consists of a compressed-air tank (CAT), generator and motor. In the CAES charging model, the motor is activated and stores electrical energy in the form of compressed air in the CAT. In the CAES discharge operation, the generator is activated, which receives compressed air from the CAT, and it generates electrical energy in its output. Therefore, relations (2o) and (2p), respectively, express the limitation of motor and generator capacity in the CAES [22]. The maximum capacity of these elements is a coefficient of the optimal capacity of the CAES. In these relationships, τ_ch represents the charging duration of the CAES. In other words, τ_ch refers to the time that the motor can fill the CAT with compressed air. τ_dch represents the discharge duration of the CAES, which is equal to the time that the generator can discharge the CAT’s compressed air. In addition, the CAES cannot be placed in two charging and discharging modes simultaneously. Therefore, the motor and generator are not active at the same time. This issue is stated in Equation (2q). In constraint (2r), the boundary of stored energy in the CAT is also provided [22]. Based on this relationship, the stored energy in the CAT for hour t is equal to the sum of the CAT primary energy and the received energy for the CAES in charging operation mode until hour t minus the discharged energy in the CAES for discharging mode until hour t. The minimum stored energy in the CAT ($\delta \times C_{CAES}$) and the initial energy of the CAT ($\chi \times C_{CAES}$) are coefficients of the optimal size of the CAES. The optimal capacity limit of the CAES in EHs is proportional to constraint (2s). The TS formulation is based on constraints (2t)–(2x) [3]. The boundary of the TS’s power in charging and discharging operation modes are expressed in terms (2t) and (2u), respectively. The maximum charge and discharge rate in the TS is a multiple of the optimal size of the TS in EHs. Equation (2v) prevents the simultaneous utilization of discharging and charging in the TS. The limit of stored energy in the TS is the same as (2w) [3], which at hour t is the sum of the primary energy and the received energy in charging mode up to hour t and the reduced energy in discharging operation mode up to hour t. The optimal size limit of the TS in EHs follows condition (2x). Finally, the terms λ and μ represent the dual variables for the lower-level model constraints.

Note that the energy hub is connected to a bus, a thermal node and a gas node in the electrical, thermal and gas networks, respectively. Renewable and non-renewable resources, thermal and compressed-air storages are connected to these nodes and buses. These sources and storages are in two-way coordination. Each of them has a local controller. The integrated unit of these resources and storages in the form of an energy hub also has a central controller. The local controllers send their data to the central controller. Then, the central controller is responsible for managing the energy of the various resources and storage devices based on the demands of the hub and the energy networks.

$$P_{H i,t,s},H_{H i,t,s},G_{H i,t,s}\in \arg \left\{\begin{array}{r}\min \hspace{1em}AHC={\displaystyle \sum _i\left(\begin{array}{l}A{C}_{C i}{C}_{C i}+A{C}_{B i}{C}_{B i}+A{C}_{WT i}{C}_{WT i}+A{C}_{PV i}{C}_{PV i}\\ +A{C}_{BU i}{C}_{BU i}+A{C}_{CAES i}{C}_{CAES i}+A{C}_{TS i}{C}_{TS i}\end{array}\right)}\\ +365\times CF\times {\displaystyle \sum _{i,t,s}\left({\gamma }_{E t,s}{P}_{H i,t,s}+{\gamma }_{H t,s}{H}_{H i,t,s}+{\gamma }_{G t,s}{G}_{H i,t,s}\right)}\end{array}\right.$$

(2a)

Subject to

$$P_{H i,t,s}=P_{C i,t,s}+P_{WT i,t,s}+P_{PV i,t,s}+\left(P_{G i,t,s}-P_{M i,t,s}\right)-P_{D i,t,s}:{\lambda }_{P i,t,s}\hspace{1em}\forall i,t,s$$

(2b)

$$H_{H i,t,s}={\displaystyle \frac{\left(1-{\eta }^T\right){\eta }^H}{{\eta }^T}}{P}_{C i,t,s}+H_{B i,t,s}+\left(H_{DIS i,t,s}-H_{CH i,t,s}\right)-H_{D i,t,s}:{\lambda }_{H i,t,s}\hspace{1em}\forall i,t,s$$

(2c)

$$G_{H i,t,s}=G_{BU i,t,s}-{\displaystyle \frac{1}{{\eta }^T}}{P}_{C i,t,s}-{\displaystyle \frac{1}{{\eta }^B}}{H}_{B i,t,s}-G_{D i,t,s}:{\lambda }_{G i,t,s}\hspace{1em}\forall i,t,s$$

(2d)

$$0\le P_{C i,t,s}\le C_{C i}:{\underset{\_}{\mu }}_{PC i,t,s},{\overline{\mu }}_{PC i,t,s}\hspace{1em}\forall i,t,s$$

(2e)

$$0\le C_{C i}\le {\overline{C}}_{C i}:{\underset{\_}{\mu }}_{C i},{\overline{\mu }}_{C i}\hspace{1em}\forall i$$

(2f)

$$0\le H_{B i,t,s}\le C_{B i}:{\underset{\_}{\mu }}_{HB i,t,s},{\overline{\mu }}_{HB i,t,s}\hspace{1em}\forall i,t,s$$

(2g)

$$0\le C_{B i}\le {\overline{C}}_{B i}:{\underset{\_}{\mu }}_{B i},{\overline{\mu }}_{B i}\hspace{1em}\forall i$$

(2h)

$$P_{WT i,t,s}=C_{WT i}{\phi }_{WT i,t,s}:{\lambda }_{WT i,t,s}\hspace{1em}\forall i,t,s$$

(2i)

$$0\le C_{WT i}\le {\overline{C}}_{WT i} :{\underset{\_}{\mu }}_{WT i},{\overline{\mu }}_{WT i}\hspace{1em}\forall i$$

(2j)

$$P_{PV i,t,s}=C_{PV i}{\phi }_{PV i,t,s}:{\lambda }_{PV i,t,s}\hspace{1em}\forall i,t,s$$

(2k)

$$0\le C_{PV i}\le {\overline{C}}_{PV i}:{\underset{\_}{\mu }}_{PV i},{\overline{\mu }}_{PV i}\hspace{1em}\forall i$$

(2l)

$$G_{BU i,t,s}=C_{BU i}{\phi }_{BU i,t,s}:{\lambda }_{BU i,t,s}\hspace{1em}\forall i,t,s$$

(2m)

$$0\le C_{BU i}\le {\overline{C}}_{BU i}:{\underset{\_}{\mu }}_{BU i},{\overline{\mu }}_{BU i}\hspace{1em}\forall i$$

(2n)

$$0\le P_{M i,t,s}\le {\displaystyle \frac{C_{CAES i}}{{\tau }_{ch}}} :{\underset{\_}{\mu }}_{PM i,t,s},{\overline{\mu }}_{PM i,t,s}\hspace{1em}\forall i,t,s$$

(2o)

$$0\le P_{G i,t,s}\le {\displaystyle \frac{C_{CAES i}}{{\tau }_{dch}}}:{\underset{\_}{\mu }}_{PG i,t,s},{\overline{\mu }}_{PG i,t,s}\hspace{1em}\forall i,t,s$$

(2p)

$$P_{M i,t,s}{P}_{G i,t,s}=0:{\lambda }_{CAES i,t,s}\hspace{1em}\forall i,t,s$$

(2q)

$${\delta }_i{C}_{CAES i}\le {\chi }_i{C}_{CAES i}+{\displaystyle \sum _{h=1}^t\left({\eta }^M{P}_{M i,h,s}-\frac{1}{{\eta }^G}{P}_{G i,h,s}\right)}\le C_{CAES i}:{\underset{\_}{\mu }}_{EC i,t,s},{\overline{\mu }}_{EC i,t,s}\hspace{1em}\forall i,t,s$$

(2r)

$$0\le C_{CAES i}\le {\overline{C}}_{CAES i}:{\underset{\_}{\mu }}_{CAES i},{\overline{\mu }}_{CAES i}\hspace{1em}\forall i$$

(2s)

$$0\le H_{CH i,t,s}\le {\displaystyle \frac{C_{TS i}}{{\tau }_{ch}}}:{\underset{\_}{\mu }}_{HC i,t,s},{\overline{\mu }}_{HC i,t,s}\hspace{1em}\forall i,t,s$$

(2t)

$$0\le H_{DIS i,t,s}\le {\displaystyle \frac{C_{TS i}}{{\tau }_{dch}}} :{\underset{\_}{\mu }}_{HD i,t,s},{\overline{\mu }}_{HD i,t,s}\hspace{1em}\forall i,t,s$$

(2u)

$$H_{CH i,t,s}{H}_{DIS i,t,s}=0 :{\lambda }_{TS i,t,s}\hspace{1em}\forall i,t,s$$

(2v)

$${\delta }_i{C}_{TS i}\le {\chi }_i{C}_{TS i}+{\displaystyle \sum _{h=1}^t\left({\eta }^{CH}{H}_{CH i,h,s}-\frac{1}{{\eta }^{DIS}}{H}_{DIS i,h,s}\right)}\le C_{TS i}:{\underset{\_}{\mu }}_{ET i,t,s},{\overline{\mu }}_{ET i,t,s}\hspace{1em}\forall i,t,s$$

(2w)

$$0\le C_{TS i}\le {\overline{C}}_{TS i}:{\underset{\_}{\mu }}_{TS i},{\overline{\mu }}_{TS i}\hspace{1em}\forall i$$

(2x)

The decision variables in the upper-level problem include the active, thermal and gas power of the energy hubs. These variables are calculated based on the lower-level model. In the lower-level problem, the aforementioned variables depend on the size of the various resources and storage devices and their power. Therefore, to optimize the operating and resilience costs in the upper-level problem, an optimal value for the power variables and the size of the resources and storage devices is calculated first. Then, the optimal amount for the active, thermal and gas power of the hubs is obtained, such that the operating and resilience costs of the network are minimized. For example, to minimize these functions, it is necessary to obtain a high size for renewable resources. In this situation, the injected power of the hubs to the network increases, and consequently the aforementioned costs decrease. Of course, for the objective function of the lower-level problem (minimization of planning cost) to also be satisfied, renewable resources with a lower planning cost are selected. This issue is discussed in Section 4.2(A).

(C) Uncertainty modeling: the proposed plan with formulations (1) and (2) has uncertainties in load, P_D, Q_D, G_D and H_D, the price of energy, γ_G, γ_E and γ_H, the accessibility of the electric line and substation, u_L and u_S, the accessibility of the thermal pipeline and substation, z_L and z_S, the accessibility of the gas pipeline and substation, x_L and x_S, against natural disasters such as floods and earthquakes, and the generation power rate in the WT, PV and BU, φ_WT, φ_PV and φ_BU. In this section, for the accurate modeling of the resilience index, scenario-based stochastic optimization (SBSO) is used [24]. For accurate calculation of the resilience index, different scenarios of load, accessibility of the network elements needing to be examined in N-k event, and renewable power must be considered. Next, the SBSO method relies on the mix of the roulette wheel mechanism (RWM) and the simultaneous backward method (SBM) [24]. RWM is a scenario-generation technique; thus, it produces a high number of scenarios. The value of the load, energy price and production power rate of renewable resources in each scenario are found using their standard deviation and average values. The availability of network equipment is also determined by the forced outage rate (FOR) of the equipment [25]. Then, the normal probability model helps to find the probability of different uncertainties in each scenario. The probability of scenarios will be obtained by multiplying the uncertainties’ probability in this scenario. SBM is a scenario-reduction approach. It uses a certain number of newly-produced scenarios that have the smallest distance from each other. The selected scenarios are used in problems (1) and (2). The formulation of this technique is presented in [24]. Finally, the probability of each new scenario is the probability of that scenario in the RWM divided by the total probability of the selected scenarios in the RWM.

3. Single-Level Optimization for Networked EH Planning

The formulation of the proposed plan in models (1) and (2) is a bi-level formulation. To solve it with traditional techniques, it is necessary to obtain a single-level model for the scheme [25]. Mathematical techniques for converting the bi-level model to a single-level formulation are based on the duality approach and the KKT method [25]. The condition of using these methods is the convexity of the lower-level model (2). Formulation (2) generally has linear relations: only two relations (2q) and (2v) are in a non-linear form of the second degree. These equations are convex, so model (2) is convex. In the duality method, only the dual variables of constraint (2) are calculated. In the KKT technique, dual and primary variables are calculated simultaneously. Based on Equation (2a), it is necessary to calculate the EH power variables, and they are the primary variables of the lower-level formulation. Therefore, KKT technique converts the bi-level problem to a single-level structure. In this method, the single-level model of the scheme consists of the formulation of the upper level, (1), and the KKT model of the lower-level equations, (2), based on formulations (3) and (4) [25].

Upper-level model, (1)

(3)

KKT model of lower-level formulation of (2)

(4)

In the KKT model of a problem, first the Lagrange function (L) is obtained for the model [25]. It is the sum of the constraints’ penalty function and the objective function. The penalty function for a ≤ b and a = b is equal to μ.max(0, a–b) and λ.(a–b), respectively [22]. λ and μ are the dual variables of equal and unequal equation, respectively. The KKT model for a problem is obtained by equalizing the derivative of L to the primary and dual variables with zero. ∂L/∂λ = 0 is the equality constraint of the problem. For the proposed plan, it is in the form of Equation (5). ∂L/∂μ = 0 has two models. In model 1, the inequality constraint of the problem is obtained, which for the proposed design is proportional to constraint (6). In model 2, μ.(a–b) = 0 is obtained. This issue for the proposed scheme for the dual variables of different inequality constraints is presented in (7). In (8), the equations obtained by equating the derivative of L to the primary variables of problem (2) with zero are presented. Finally, the limitation of the dual variables of problem (2) is stated in constraint (9) [25].

Constraints (2b)–(2d), (2i), (2k), (2m), (2q) and (2v): ∂L/∂λ = 0

(5)

Constraints (2e)–(2h), (2j), (2l), (2n)–(2p), (2r)–(2u), (2w) and (2x): First condition of ∂L/∂μ = 0

(6)

$$P_{C i,t,s}{\underset{\_}{\mu }}_{PC i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{PC i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7a)

$$\left(P_{C i,t,s}-C_{C i}\right){\overline{\mu }}_{PC i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{PC i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7b)

$$C_{C i}{\underset{\_}{\mu }}_{C i}=0 :{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{C i}}}=0\hspace{1em}\forall i$$

(7c)

$$\left(C_{C i}-{\overline{C}}_{C i}\right){\overline{\mu }}_{C i}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{C i}}}=0\hspace{1em}\forall i$$

(7d)

$$H_{B i,t,s}{\underset{\_}{\mu }}_{HB i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{HB i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7e)

$$\left(H_{B i,t,s}-C_{B i}\right){\overline{\mu }}_{HB i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{HB i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7f)

$$C_{B i}{\underset{\_}{\mu }}_{B i}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{B i}}}=0\hspace{1em}\forall i$$

(7g)

$$\left(C_{B i}-{\overline{C}}_{B i}\right){\overline{\mu }}_{B i}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{B i}}}=0\hspace{1em}\forall i$$

(7h)

$$C_{WT i}{\underset{\_}{\mu }}_{WT i}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{WT i}}}=0\hspace{1em}\forall i$$

(7i)

$$\left(C_{WT i}-{\overline{C}}_{WT i}\right) {\overline{\mu }}_{WT i}=0 :{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{WT i}}}=0\hspace{1em}\forall i$$

(7j)

$$C_{PV i}{\underset{\_}{\mu }}_{PV i}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{PV i}}}=0\hspace{1em}\forall i$$

(7k)

$$\left(C_{PV i}-{\overline{C}}_{PV i}\right){\overline{\mu }}_{PV i}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{PV i}}}=0\hspace{1em}\forall i$$

(7l)

$$C_{BU i}{\underset{\_}{\mu }}_{BU i}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{BU i}}}=0\hspace{1em}\forall i$$

(7m)

$$\left(C_{BU i}-{\overline{C}}_{BU i}\right){\overline{\mu }}_{BU i}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{BU i}}}=0\hspace{1em}\forall i$$

(7n)

$$P_{M i,t,s}{\underset{\_}{\mu }}_{PM i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{PM i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7o)

$$\left(P_{M i,t,s}-{\displaystyle \frac{C_{CAES i}}{{\tau }_{ch}}}\right) {\overline{\mu }}_{PM i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{PM i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7p)

$$P_{G i,t,s}{\underset{\_}{\mu }}_{PG i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{PG i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7q)

$$\left(P_{G i,t,s}-{\displaystyle \frac{C_{CAES i}}{{\tau }_{dch}}}\right){\overline{\mu }}_{PG i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{PG i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7r)

$$\left({\delta }_i{C}_{CAES i}-\left({\chi }_i{C}_{CAES i}+{\displaystyle \sum _{h=1}^t\left({\eta }^M{P}_{M i,h,s}-\frac{1}{{\eta }^G}{P}_{G i,h,s}\right)}\right)\right){\underset{\_}{\mu }}_{EC i,t,s}=0 :{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{EC i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7s)

$$\left({\chi }_i{C}_{CAES i}+{\displaystyle \sum _{h=1}^t\left({\eta }^M{P}_{M i,h,s}-\frac{1}{{\eta }^G}{P}_{G i,h,s}\right)}-C_{CAES i}\right){\overline{\mu }}_{EC i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{EC i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7t)

$$C_{CAES i}{\underset{\_}{\mu }}_{CAES i}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{CAES i}}}=0\hspace{1em}\forall i$$

(7u)

$$\left(C_{CAES i}-{\overline{C}}_{CAES i}\right){\overline{\mu }}_{CAES i}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{CAES i}}}=0\hspace{1em}\forall i$$

(7v)

$$H_{CH i,t,s}{\underset{\_}{\mu }}_{HC i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{HC i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7w)

$$\left(H_{CH i,t,s}-{\displaystyle \frac{C_{TS i}}{{\tau }_{ch}}}\right){\overline{\mu }}_{HC i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{HC i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7x)

$$H_{DIS i,t,s}{\underset{\_}{\mu }}_{HD i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{HD i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7y)

$$\left(H_{DIS i,t,s}-{\displaystyle \frac{C_{TS i}}{{\tau }_{dch}}}\right) {\overline{\mu }}_{HD i,t,s}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{HD i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7z)

$$\left({\delta }_i{C}_{TS i}-\left({\chi }_i{C}_{TS i}+{\displaystyle \sum _{h=1}^t\left({\eta }^{CH}{H}_{CH i,h,s}-\frac{1}{{\eta }^{DIS}}{H}_{DIS i,h,s}\right)}\right)\right){\underset{\_}{\mu }}_{ET i,t,s}=0 :{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{ET i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7α)

$$\left({\chi }_i{C}_{TS i}+{\displaystyle \sum _{h=1}^t\left({\eta }^{CH}{H}_{CH i,h,s}-\frac{1}{{\eta }^{DIS}}{H}_{DIS i,h,s}\right)}-C_{TS i}\right){\overline{\mu }}_{ET i,t,s}=0 :{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{ET i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(7β)

$$C_{TS i}{\underset{\_}{\mu }}_{TS i}=0 :{\displaystyle \frac{\partial L}{\partial {\underset{\_}{\mu }}_{TS i}}}=0\hspace{1em}\forall i$$

(7γ)

$$\left(C_{TS i}-{\overline{C}}_{TS i}\right){\overline{\mu }}_{TS i}=0:{\displaystyle \frac{\partial L}{\partial {\overline{\mu }}_{TS i}}}=0\hspace{1em}\forall i$$

(7δ)

$$-{\underset{\_}{\mu }}_{C i}+{\overline{\mu }}_{C i}-{\displaystyle \sum _{t,s}{\overline{\mu }}_{PC i,t,s}}=A{C}_{C i}:{\displaystyle \frac{\partial L}{\partial C_{C i}}}=0\hspace{1em}\forall i$$

(8a)

$$-{\underset{\_}{\mu }}_{B i}+{\overline{\mu }}_{B i}-{\displaystyle \sum _{t,s}{\overline{\mu }}_{HB i,t,s}}=A{C}_{B i}:{\displaystyle \frac{\partial L}{\partial C_{B i}}}=0\hspace{1em}\forall i$$

(8b)

$$-{\underset{\_}{\mu }}_{WT i}+{\overline{\mu }}_{WT i}-{\displaystyle \sum _{t,s}{\lambda }_{WT i,t,s}{\phi }_{WT i,t,s}}=A{C}_{WT i}:{\displaystyle \frac{\partial L}{\partial C_{WT i}}}=0\hspace{1em}\forall i$$

(8c)

$$-{\underset{\_}{\mu }}_{PV i}+{\overline{\mu }}_{PV i}-{\displaystyle \sum _{t,s}{\lambda }_{PV i,t,s}{\phi }_{PV i,t,s}}=A{C}_{PV i}:{\displaystyle \frac{\partial L}{\partial C_{PV i}}}=0\hspace{1em}\forall i$$

(8d)

$$-{\underset{\_}{\mu }}_{BU i}+{\overline{\mu }}_{BU i}-{\displaystyle \sum _{t,s}{\lambda }_{BU i,t,s}{\phi }_{BU i,t,s}}=A{C}_{BU i}:{\displaystyle \frac{\partial L}{\partial C_{BU i}}}=0\hspace{1em}\forall i$$

(8e)

$$\begin{array}{r}-{\underset{\_}{\mu }}_{CAES i}+{\overline{\mu }}_{CAES i}+{\displaystyle \sum _{t,s}\left(\frac{1}{{\tau }_{ch}} \left({\overline{\mu }}_{PM i,t,s}-{\underset{\_}{\mu }}_{PM i,t,s}\right)+\frac{1}{{\tau }_{dch}} \left({\overline{\mu }}_{PG i,t,s}-{\underset{\_}{\mu }}_{PG i,t,s}\right)+\left({\delta }_i-{\chi }_i\right){\underset{\_}{\mu }}_{EC i,t,s}+\left({\chi }_i-1\right){\overline{\mu }}_{EC i,t,s}\right)}\\ =A{C}_{CAES i}:{\displaystyle \frac{\partial L}{\partial C_{CAES i}}}=0\hspace{1em}\forall i\end{array}$$

(8f)

$$\begin{array}{r}-{\underset{\_}{\mu }}_{TS i}+{\overline{\mu }}_{TS i}+{\displaystyle \sum _{t,s}\left(\frac{1}{{\tau }_{ch}} \left({\overline{\mu }}_{HC i,t,s}-{\underset{\_}{\mu }}_{HC i,t,s}\right)+\frac{1}{{\tau }_{dch}} \left({\overline{\mu }}_{HD i,t,s}-{\underset{\_}{\mu }}_{HD i,t,s}\right)+\left({\delta }_i-{\chi }_i\right){\underset{\_}{\mu }}_{ET i,t,s}+\left({\chi }_i-1\right){\overline{\mu }}_{ET i,t,s}\right)}\\ =A{C}_{TS i}:{\displaystyle \frac{\partial L}{\partial C_{TS i}}}=0\hspace{1em}\forall i\end{array}$$

(8g)

$${\lambda }_{P i,t,s}=365\times CF\times {\gamma }_{E t,s}:{\displaystyle \frac{\partial L}{\partial P_{H i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8h)

$${\lambda }_{H i,t,s}=365\times CF\times {\gamma }_{H t,s}:{\displaystyle \frac{\partial L}{\partial H_{H i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8i)

$${\lambda }_{G i,t,s}=365\times CF\times {\gamma }_{G t,s}:{\displaystyle \frac{\partial L}{\partial G_{H i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8j)

$$-{\lambda }_{P i,t,s}-{\displaystyle \frac{\left(1-{\eta }^T\right){\eta }^H}{{\eta }^T}}{\lambda }_{H i,t,s}+{\displaystyle \frac{1}{{\eta }^T}}{\lambda }_{G i,t,s}-{\underset{\_}{\mu }}_{PC i,t,s}+{\overline{\mu }}_{PC i,t,s}=0:{\displaystyle \frac{\partial L}{\partial P_{C i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8k)

$${\lambda }_{WT i,t,s}-{\lambda }_{P i,t,s}=0:{\displaystyle \frac{\partial L}{\partial P_{WT i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8l)

$${\lambda }_{PV i,t,s}-{\lambda }_{P i,t,s}=0:{\displaystyle \frac{\partial L}{\partial P_{PV i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8m)

$${\lambda }_{P i,t,s}-{\underset{\_}{\mu }}_{PM i,t,s}+{\overline{\mu }}_{PM i,t,s}+{\lambda }_{CAES i,t,s}{P}_{G i,t,s}+{\displaystyle \sum _{h=t}^{24}{\eta }^M\left({\overline{\mu }}_{EC i,h,s}-{\underset{\_}{\mu }}_{EC i,h,s}\right)}=0:{\displaystyle \frac{\partial L}{\partial P_{M i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8n)

$$-{\lambda }_{P i,t,s}-{\underset{\_}{\mu }}_{PG i,t,s}+{\overline{\mu }}_{PG i,t,s}+{\lambda }_{CAES i,t,s}{P}_{M i,t,s}-{\displaystyle \sum _{h=t}^{24}\frac{1}{{\eta }^G}\left({\overline{\mu }}_{EC i,h,s}-{\underset{\_}{\mu }}_{EC i,h,s}\right)}=0:{\displaystyle \frac{\partial L}{\partial P_{G i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8o)

$$-{\lambda }_{H i,t,s}+{\displaystyle \frac{1}{{\eta }^B}}{\lambda }_{G i,t,s}-{\underset{\_}{\mu }}_{HB i,t,s}+{\overline{\mu }}_{HB i,t,s}=0:{\displaystyle \frac{\partial L}{\partial H_{B i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8p)

$${\lambda }_{H i,t,s}-{\underset{\_}{\mu }}_{HC i,t,s}+{\overline{\mu }}_{HC i,t,s}+{\lambda }_{TS i,t,s}{H}_{DIS i,t,s}+{\displaystyle \sum _{h=t}^{24}{\eta }^{CH}\left({\overline{\mu }}_{ET i,h,s}-{\underset{\_}{\mu }}_{ET i,h,s}\right)}=0:{\displaystyle \frac{\partial L}{\partial H_{CH i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8q)

$$-{\lambda }_{H i,t,s}-{\underset{\_}{\mu }}_{HD i,t,s}+{\overline{\mu }}_{HD i,t,s}+{\lambda }_{TS i,t,s}{H}_{CH i,t,s}-{\displaystyle \sum _{h=t}^{24}\frac{1}{{\eta }^{DIS}}\left({\overline{\mu }}_{ET i,h,s}-{\underset{\_}{\mu }}_{ET i,h,s}\right)}=0:{\displaystyle \frac{\partial L}{\partial H_{DIS i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8r)

$${\lambda }_{BU i,t,s}-{\lambda }_{G i,t,s}=0:{\displaystyle \frac{\partial L}{\partial G_{BU i,t,s}}}=0\hspace{1em}\forall i,t,s$$

(8s)

$$\lambda \in \left(-\infty ,+\infty \right), \mu \ge 0$$

(9)

4. Discussion on Simulation Results

4.1. Test System

The suggested design is used for the studied system in Figure 2. The system under study includes an IEEE 69-bus electrical system [26], a 14-node heating grid [27] and a 4-node gas grid [4]. The electrical system has a base power of 1 MVA, and its base voltage is 12.66 kV. Bus 1 is known as the slack bus, the magnitude and angle of voltage of which in this bus are, respectively, equal to 1 p.u. and 0 radians. The specifications of distribution lines and station along with the date of peak load and the power factor of consumers for this network are presented in [26]. In the thermal system, the base power is 1 MW, and the base temperature is 100 °C. The slack node is equal to node 1. In this node, the temperature is 1 p.u. The specifications of pipes, substation and peak load are stated in [27]. The gas system includes a base power of 1 MW, and the base pressure is equal to 10 bar. Node 1 is the slack node, and the pressure in this node is 1 p.u. The specifications of substations and pipelines in this network are stated in [4]. There is no passive load in this network and the only consumers are the hubs. Therefore, G_D in this network is equal to zero. The permissible range [0.95–1.05] per-unit is considered for the voltage magnitude [28,29,30,31,32], temperature and pressure. The amount of load per hour is equal to the product of the load factor and peak load [33,34,35,36,37]. The expected daily load factor curve in heat and electrical networks is drawn in Figure 3 [22]. The price of energy for different networks is stated in [3]. According to [3], the energy price for the electrical grid in the hours of 1:00–7:00 (17:00–22:00) is equal to 17.6 (33) USD/MWh, and in the remaining periods, it is 26.4 USD/MWh. The price of energy in the heat (gas) network for the hours 5:00–15:00 (5:00–22:00) is equal to 30 (18) USD/MWh, and it is equal to 22 (12) USD/MWh in the other hours. According to [25], the coincidence factor (CF) is considered equal to 0.7. In Figure 2, feeders with red color indicate flood-prone areas, and other feeders are located in earthquake-prone areas. It is assumed that if a flood or an earthquake occurs, the damage to the network will be resolved after 14 days. In other words, du is equal to 14. FOR is considered equal to 10% for all equipment. The standard deviation for uncertainties of demand, rate of renewable power, and price of energy is considered to be 10%. To have high resilience in the studied system, VOLL is equal to 150 USD/MWh. It is considered that 44 EHs can be connected in the mentioned grids, and their suggested locations are presented in

Table 2. The proposed locations for installing EHs.

EH	Location (b, n, g)	EH	Location (b, n, g)	EH	Location (b, n, g)	EH	Location (b, n, g)
1	3, -, -	12	37, -, -	23	-, 7, 3	34	29, 2, 3
2	4, -, -	13	40, -, -	24	-, 12, 2	35	32, 6, 4
3	10, -, -	14	45, -, -	25	-, 13, 4	36	35, 12, 4
4	11, -, -	15	48, -, -	26	3, 2, 3	37	37, 3, 3
5	18, -, -	16	54, -, -	27	4, 3, 3	38	40, 7, 2
6	19, -, -	17	58, -, -	28	10, 6, 3	39	45, 13, 2
7	26, -, -	18	64, -, -	29	11, 7, 3	40	48, 6, 3
8	27, -, -	19	65, -, -	30	18, 12, 2	41	54, 2, 3
9	29, -, -	20	-, 2, 2	31	19, 13, 2	42	58, 3, 4
10	32, -, -	21	-, 3, 4	32	26, 12, 4	43	64, 7, 3
11	35, -, -	22	-, 6, 3	33	27, 13, 4	44	65, 13, 2

. In this table, the suggested location of the hubs is included at the beginning, middle and end of the feeder. The beginning and middle of the feeder were suggested because they have a high line capacity. Feeder ends were proposed to improve voltage, temperature and pressure profiles. The cost of building for the WT, PVs, BU, CHP and boiler in each hub is 0.16, 0.24, 0.32, 0.11 and 0.08 MUSD/year.MW, respectively [22,38]. The construction cost of the CAES and TS is equal to 0.3 and 0.25 MUSD/year. MWh, respectively. The maximum installable capacity for sources is 2 MW, and it is 4 MWh for storage. The boiler efficiency is 80%, and η_T and η_H in the CHP are 37% and 39%, respectively. The motor and generator efficiency in the CAES is 79% and 78%, respectively [22]. The efficiency of the TS in charge and discharge mode is 80% and 79%, respectively. In storage devices, charging and discharging time is assumed to be 3 h [39,40,41,42,43]. Initial and minimum energy are equal to 10% of storage capacity. The expected daily generated power rate curve for the WT, PV and BU is presented in Figure 3 [2,22]. The load of each hub is equal to 50% of the load at the EH location.

Note that the formulation presented in Section 2 is not limited to being implemented on different data sets of energy networks, resources, and storage devices in different geographical regions. In each geographical region, the values of the problem parameters (such as the distribution line data, load data, renewable power generation rate and other parameters) must also be determined and applied to the problem. Then, the formulation of Section 2 obtains numerical results appropriate to the specific geographical region.

4.2. Results and Discussion

The design was coded in the GAMS software environment according to the data in Section 4.1. The mentioned problem has a non-linear model, so the IPOPT algorithm was used to solve the mentioned problem. This solver has a toolbox in the mentioned software. In uncertainty modeling, RWM generates 2000 scenarios, and then SBM selects 80 scenarios and incorporates them into the problem.

(A) Optimal planning of hubs in energy grids:

Table 3. Optimal placement of EHs, optimal size of storage and sources in EHs and EH planning cost.

EH	Size (MW) of					Size (MWh) of		Annual Cost (MUSD/year) of
	CHP	Boiler	WT	PVs	BU	CAES	TS	Investment	Operation	Planning
7	0	0	0.4	0.2	0	2	0	0.712	−0.12	0.592
11	0	0	0.6	0.2	0	2	0	0.744	−0.14	0.604
14	0	0	0.6	0.2	0	2	0	0.744	−0.14	0.604
19	0	0	0.4	0.2	0	2	0	0.712	−0.12	0.592
25	0	0.5	0	0	0.5	0	2	0.7	−0.08	0.62
27	0.8	0.8	0.6	0.3	1.5	4	3	2.75	−0.68	2.07
30	0.4	0.5	0.4	0	1	3	2	1.868	−0.49	1.378
35	0.4	0.5	0.4	0	1	3	2	1.868	−0.49	1.378
41	0.6	0.6	0.4	0.2	1.5	4	3	2.656	−0.66	1.996
43	0.4	0.5	0.4	0	1	3	2	1.868	−0.49	1.378

shows the results of hub planning in electric, thermal and gas systems. According to this table, 10 hubs are installed in the mentioned networks. The selected hubs are equal to EHs 7, 11, 14, 19, 25, 27, 30, 35, 41 and 43, whose locations are specified in Table 2. According to Table 2, hubs 7, 11, 14 and 19 are only installed in the electrical network, which are generally at the end of the feeder. Therefore, it is expected that the aforementioned hubs have a significant ability to improve the voltage profile until the status of the electric network’s operation indicators is improved. Based on Table 3, these hubs have a WT, PV and CAES. The capacity of the PVs and CAES in these hubs are the same, but the capacities of the WTs are different. This issue is due to the different capacity of the electric lines connected to the EH location. Also, according to Section 4.1, the installing cost of a WT is lower than a PV, so the planner is more inclined to build the WT. Hub 25 is connected to the heat and gas network, which has a boiler, BU and TS. According to Table 2, this hub is located at the end of the heat network feeder, which is used to improve the temperature profile. In this hub, the boiler can supply its input gas from the BU. But it is possible that in some hours the boiler gas is less or more than the BU gas. Therefore, Hub 25 is connected to the gas network until this network is a backup for Hub 25. That is, when the BU gas was less (more) than the boiler gas, the gas network provided (received) the shortage (surplus) of gas. Hubs 27, 30, 35, 41 and 43 are connected to all three electrical, gas and thermal networks. They are generally attached to the beginning and middle of the feeders. They have a higher capacity for their resources and storage than other hubs because the lines connected to the EH location in these buses or nodes have a high capacity. The high capacity of hubs can be useful in reducing the operating cost and increasing the resilience of energy networks. In these hubs, if the total capacity of the boiler, CHP, WT and PVs is high, then the capacity of the BU and storage is also high. In other words, the capacity of the BU and storage systems are determined according to the size of the boiler, CHP, WT and PVs. In Table 3, the annual construction, operation and planning costs of hubs are also reported. The planning cost can be found by summing the operating and construction costs. The operating cost in these hubs has a negative value. This means that the hubs have injected energy into the energy networks in most hours. Therefore, they do not have operating costs, but they obtain revenue from energy injection. According to Table 3, hubs that have a high capacity of resources and storage have a higher construction cost, revenue and planning cost.

In Figure 4, the annual cost of construction, operation and planning of all hubs is shown for different values of VOLL. Based on this figure, with the increase in VOLL, the cost of building and planning hubs increases and their income decreases. However, with the increase in VOLL, it is expected that hubs will be able to reduce a high percentage of the energy not supplied during an N-k event. Therefore, it is necessary to install a high capacity for hubs, i.e., high-capacity use of sources and storage. This issue has the result of increasing the cost of EH planning.

(B) Investigating the operation of resources and storage systems in EHs: In Figure 5, Figure 6 and Figure 7, the expected daily active, heat and gas power curve of hubs and their sources and storage are drawn. According to Figure 5, the active power for PVs and WTs is proportional to their production power rate in Figure 3. The CHP active power is equal to their maximum capacity in EHs at all operation hours. This is because, according to Section 4.1, the price of electricity and heat exceeds that of gas. The CAES was put in charging mode in cases where the price of electricity was cheap, and it acted in discharging mode during other hours. In other words, during the hours of 17:00–22:00, when the price of electric energy is at its highest, the CAES injects electric energy to the hub. But in other hours, it saves electrical energy. As shown in Figure 6, the heat produced by the CHPs is constant in all hours, because the active power was constant in all hours. Boilers also inject heat power equal to their maximum size to the hubs because the price of gas energy is lower than the price of thermal energy at all times based on Section 4.1. The TSs are in discharge mode in hours 5:00–15:00 and they inject thermal energy to the hub because the price of heat is the maximum at these hours. In the remaining periods, it consumes thermal energy, because the price of heat is the lowest in these hours. The gas of boilers, CHPs and BUs is shown in Figure 7. The gas of BU is proportional to its production power rate in Figure 3. The gas of the boilers and CHPs is also fixed because the active power of the CHPs and heat power of boilers were constant in all hours. According to Figure 5 and Figure 6, the hubs are in the role of producing electricity and heat in most hours, but according to Figure 7, the hubs are gas consumers in most hours because the CHP and boilers consume high gas power in hubs. BUs were also not able to provide gas for the CHPs and boilers. Therefore, hubs are gas consumers in the gas network.

(C) Investigating the state of resilience, operation and economy of energy grids: In Figure 8, the EENS curve of all energy networks is drawn per VOLL. As is observed, with increasing VOLL, EENS is decreased until for VOLL > 160 USD/MWh when EENS reaches its saturation value and has a constant value. In Figure 9, the curve of the annual resilience cost of energy grids is drawn in terms of VOLL. The resilience cost according to Equation (1) is equal to the product of VOLL and EENS. With the increase in VOLL up to 40 USD/MWh, the cost of resilience increases. But for VOLL > 40 USD/MWh to VOLL = 140 USD/MWh, the increase in VOLL decreases the resilience cost. At VOLL > 140 USD/MWh, the amount of EENS is constant; therefore, increasing VOLL will increase the cost of resilience. Finally, the annual operating cost curve of energy grids based on VOLL is shown in Figure 10. As the figure illustrates, with increasing VOLL, the operating cost increases, until it reaches its saturation state and has a constant value for VOLL > 160 USD/MWh. As VOLL increases, it is expected that more EHs will be connected to the network, or their capacity will increase. Therefore, they inject more active and heat power into the electrical and thermal systems. Hence, a high percentage of consumer outages are compensated for by hubs. Therefore, the EENS and the resilience cost are reduced. But injecting high power of hubs into the network increases energy losses. For example, in this situation, it is possible to increase the amount of current in the direction of the hub to the slack bus. This issue increases energy losses. Therefore, the operation cost of networks increases with the increase in VOLL.

In

Table 4. Value of network operation and resilience indices in the different studies for VOLL = 160 USD/MWh.

Index	Case I	Case II	Case III	Case IV	Case V
Annual operation cost (MUSD/year)	29.2	21.3	20.9	21.8	23.2
EENS (GWh)	859.1	19.6	19.3	20.2	20.6
Annual energy loss (GWh)	2.37	1.82	1.78	1.89	1.98
MVD (p.u.)	0.092	0.046	0.045	0.047	0.046
MOV (p.u.)	0	0.012	0.0118	0.013	0.012
MTD (p.u.)	0.073	0.041	0.041	0.041	0.041
MOT (p.u.)	0	0.008	0.0089	0.008	0.008
MPD (p.u.)	0	0.035	0.035	0.035	0.042
MOP (p.u.)	0	0	0	0	0

, the amount of operation indicators including maximum pressure drop (MPD), temperature (MTD) and voltage (MVD), annual energy loss, and maximum over-temperature (MOT), voltage (MOV) and pressure (MOP); the economic index such as the annual energy cost of grids; and the resilience index such as EENS are reported for the following case studies:

-

Case I: Load flow study of energy grids.

-

Case II/III/IV: Proposed scheme considering CAES/battery/hydrogen storage as electrical storage.

-

Case V: Case II without BU.

In Case III, a battery is used for electrical storage. Its charging and discharging efficiency is around 92%. Its useful life is around 5 years, and its construction cost according to [38] is around 0.6 MUSD/year.MWh. Its other specifications are considered the same as the CAES. Hydrogen storage is used in Case IV. Its charging efficiency is equal to 75%, but its discharge efficiency is around 51%. Its construction cost is 0.4 MUSD/year.MWh [21]. According to Table 4, the highest amount of energy loss, operating cost, EENS, temperature and voltage drop is seen in Case I. But the proposed plan considering CAES can reduce the operating cost by about 27.1% ((29.2 − 21.3)/29.2) compared to Case I. The EENS, energy loss, MVD and MTD in the proposed design have been reduced by about 97.7%, 23.2%, 50% and 43.8%, respectively, compared to the load flow studies. These results have been obtained for increases in MOV, MOT, and MPD of about 0.012, 0.008, and 0.035 per-unit, respectively. But these values are less than the allowed value, i.e., 0.05 = 1 − 1.05 = 1 − 0.95. The presence of batteries instead of CAES in the proposed design (Case III) has produced a better situation for various indicators compared to Case II. But this improvement is insignificant: the status of all the mentioned indicators in Case III have been improved by about 1.5% to 2.2% compared to Case II. But the cost of building batteries is much higher than that of a CAES, which will lead to a significant increase in the cost of hub planning. The presence of hydrogen storage in the proposed plan (Case IV) does not have more favorable results based on Table 4 than the presence of the CAES in the proposed plan (Case II), because the energy loss in the hydrogen storage is more than the CAES. Finally, in Case V, the presence of BUs has been removed from the proposed plan. By comparing Cases II and V, the presence of BUs in the proposed plan improves the operation cost of the network, EENS, energy losses, and MPD by around 8.2%, 2.9%, 8.1%, and 16.7%, respectively. The situation of the other indicators is not changed.

5. Conclusions

In this article, sitting and sizing along with the energy administration of EHs in electric, thermal and gas networks considering the resilience of these networks against natural disasters such as floods and earthquakes are described. The proposed design was based on bi-level optimization. At its upper level, the optimal operation of energy networks bound to resilience was presented. The objective function in this problem was to minimize the total expected annual cost of resilience and operation of the mentioned grids. This problem is constrained to the model of optimal power flow and resilience limitation in the energy networks. In the lower-level model, the planning of hubs was presented with the aim of determining the optimal location for hubs in energy networks, and determining the optimal size for storage and resources in hubs. It was responsible for minimizing the total cost of building and operating the hubs. The limitations of the problem included the operation and planning model of different resources and storage devices. Next, the KKT approach was used to extract the single-level model. Also, scenario-based stochastic optimization was used to model uncertainties of load, renewable power, energy price and network equipment availability. Based on the simulation results, it was observed that EHs are installed at the beginning, middle and end of the feeder. The capacity of the hubs installed at the end of the feeder is low, and they are used to improve the voltage and temperature profile. Hubs with a high capacity can be installed in the first and middle nodes of the feeder. These hubs have a significant ability to reduce the operation cost of the network and increase the resilience of the networks. Finally, by determining the optimal location and size for the hubs and then managing the energy of resources and storage in the hubs, it was observed that the proposed plan is able to improve the economic, operation and resilience status of the energy networks about 27.1%, 97.7% and 23–50%, respectively, compared to load flow studies. In other words, the practical implications of these results are as follows: (1) As economic conditions improve, the cost of purchasing energy from the upstream network decreases. In other words, consumers receive energy at a lower cost. (2) As operating conditions improve, the network has a smoother voltage, temperature and pressure profile, and energy losses are low. (3) Improving resilience refers to reducing consumer outages in the event of natural disasters. In addition, compressed air storage in hubs instead of hydrogen storage creates a more favorable situation for energy network indicators, and their planning cost is lower. But the batteries improve the technical and economic status of the network by 1.5% to 2.2% compared to compressed air storage, but they greatly increase the cost of hub planning.

In this paper, the demand-side management capabilities in energy networks are not examined. However, it should be noted that demand response is one of the energy management solutions for consumers, which can be useful in improving the technical and economic conditions of the network. In addition, it is able to manage the energy consumed by loads in critical situations such as a fault event. Therefore, it can play a significant role in improving the network’s resilience. This will be added to the proposed design in future work. In addition, to implement the proposed design in energy networks, it is necessary that the smart platform is placed in the networks and hubs. Therefore, it is possible that cyber-attacks will be directed at the smart platform, disrupting the performance of the hubs and energy networks. Improving network resilience in the proposed design with respect to cyber-attacks will be considered in future work. As another point, electric vehicles are new electric consumers that receive their required energy from the electric network. Therefore, their presence in the electric network is inevitable. Therefore, the proposed design in the presence of electric vehicles will be considered as a future work. The presented bi-level problem has a large number of variables and constraints. Solving this problem for large-scale data may be complex and difficult, requiring extensive calculations, in which case the cost of solving the problem will be high. One way to compensate for this is to use decomposition algorithms such as Benders decomposition algorithm. This algorithm accelerates the solution of the problem. Therefore, a proposed scheme based on the aforementioned algorithm will be considered in future work. There are the different challenges in real-world deployment, such as real-time data acquisition, communication delays and policy support. However, this paper only examined the planning capabilities of energy hubs. A proposed scheme based on the mentioned challenges will be considered in future work.