
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12264-5
10.1016/j.heliyon.2024.e36233
e36233
Research Article
Enhancing energy hub efficiency through advanced modelling and optimization techniques: A case study on micro-refinery output products and parking lot integration
Jafari Saeed
Najafi Mojtaba mojtaba.najafi@iau.ac.ir
⁎
Pirkolachahi Naghi Moaddabi
Shirazi Najmeh Cheraghi
Department of Electrical Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran
⁎ Corresponding author. mojtaba.najafi@iau.ac.ir
29 8 2024
30 9 2024
29 8 2024
10 18 e362333 6 2024
30 7 2024
12 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
A new model of energy carriers (micro-refinery output products) in the concept of an energy hub is presented. In addition, in the presented model, the effect of different models of parking lot in an energy hub is analyzed. In this study, the uncertainty of the number of electric vehicles was modeled using the Monte Carlo method, and then considering the same conditions, the uncertainty of the number of electric vehicles was calculated using the Probability-Possibility hybrid method. In addition, the study uses a scenario-based approach to address uncertainties related to multi-carrier energy demand and multi-carrier energy prices. In the present paper, ensuring water demand is of great importance, which is why the proposed energy hub structure of a sea desalination unit and sour water treatment that is extracted from the micro refinery output was analyzed. The optimization model presented in this paper for the energy hub is a complex integer linear programming (MILP) that is solved using a CPLEX solver in the GAMS environment. The results show that the use of the Probability-Possibility method resulted in an 8 % reduction in the final energy supply cost in the energy hub compared to the Monte Carlo method.

Keywords

Energy hub
Micro refinery
Probability-possibility
Parking lot
Sour water
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pmc1 Introduction

1.1 Motivation and background

In recent years, energy supply has been one of the most pressing concerns for developing countries. These nations face the dual challenges of either supplying energy raw materials or using them efficiently through technology. Major issues include the depletion of fossil fuels, the alarming consequences of global warming and climate change, and the environmental effects of greenhouse gas emissions. Addressing these challenges requires the discovery of new sources of energy carriers and their transformation, rather than limiting efforts to specific energy sources. Energy hubs (EHs) have emerged as a viable strategy to simplify energy management by enabling the conversion of diverse energy sources [1]. This study models an energy hub designed to convert various energy sources, incorporating a micro-refinery aimed at converting petroleum products. Additionally, electric vehicles parks are increasingly being considered as distributed energy sources. When they inject the energy from electric vehicles into the power grid, they play a crucial role in energy carrier management within energy hubs [2]. However, since the energy supply behavior of these parking lots depends on the presence of electric vehicles (EVs), modeling the behavior of these vehicles on a large scale necessitates probabilistic modeling [3]. This study aims to present the effect of uncertainty modeling of parking lots using the probability-possibility method on energy carrier management within an energy hub, considering a micro-refinery and other common demands in the energy hub (see Table 1, Fig. 21).Table 1 The comparison Table of the literature review.

Table 1Ref	Multi-Energy Carriers	Water DR	Micro refinery	Parking lot Uncertainty	Optimization Type	Publication Year	
E	T	G	W	Nap	Di	Ker	Sour Water Treatment	
[4]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[5]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[6]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[7]	✓	✗	✗	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[8]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[9]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[10]	✓	✗	✗	✗	✗	✗	✗	✗	✗	✗	✓	Lp	2023	
[11]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2023	
[12]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2019	
[13]	✓	✓	✓	✗	✗	✗	✗	✗	✗	✗	✓	Milp	2021	
[Current study]	✓	✓	✓	✓	✓	✓	✓	✓	✓	✓	probability-possibility	Milp	–	
(E: Electrical energy, T: thermal energy, G: Gas energy, W: Drinking water, Nap: Naphtha, Di: Diesel, Ker: kerosene).

1.2 Literature review and challenges

The oil industry is a cornerstone of the global industrial sector, significantly impacted by instability, political unrest, and sudden price fluctuations in recent years [14]. Small refineries, which convert crude oil into various petroleum products, play a crucial role in this industry [15]. With global energy demand projected to increase by 48 % over the next two decades due to sharp population growth [16], researchers have proposed the concept of multi-carrier energy systems to address these challenges [17]. These systems enhance efficiency by coordinating the performance of different energy carriers [18]. Micro-refineries, as integral components of multi-carrier energy systems, contribute to the sustainable supply of energy carriers. They help reduce dependence on large oil resources and mitigate risks associated with price fluctuations by offering innovative solutions in refining and distribution. One of the key features of energy hubs is their ability to manage all energy carriers simultaneously, addressing uncertainties in demand and fluctuations in energy carrier prices [4].

Effective water management is a critical challenge recognized by researchers today. Water resources management is vital for human life, and addressing water scarcity is a significant issue. Including water as a crucial component among energy carriers in energy hubs presents a valuable and practical solution. For instance, micro-refineries consume substantial amounts of water in the conversion of petroleum products, posing a notable challenge [5]. Researchers have explored various solutions to manage water scarcity, including water demand management, optimal pricing, and the operation of desalination units within integrated energy hub systems [6]. This paper presents multiple strategies for managing water resources in energy hubs, aiming to optimize water resource management, tackle water management challenges, and ensure water availability in energy hubs (See Table 2).

Multi-carrier energy systems can effectively integrate electric vehicle charging stations (EVCs) and parking lots into energy infrastructures, promoting sustainable energy [7]. Recognizing the pivotal role of electric vehicles within energy hubs, recent studies have highlighted their importance and contributions. For example, one study analyzed urban transportation systems, including subways, electric vehicles, and parking lots, to optimize economic energy management within the energy hub. To tackle this challenge, an investigation was carried out in Ref. [8] utilizing actual EV usage patterns to examine this source of uncertainty. In Ref. [9], the role of electric vehicle driving behavior on the optimal setting of wireless charging stations is investigated [10]. proposes an integrated optimization platform for spatial-temporal modeling to model the behavior of electric vehicle charging infrastructure. Route mapping algorithms have been utilized to determine peak demand points in the power grid based on the electricity consumption of electric vehicles and their owners' behavioral patterns[11]. Researchers have investigated various methods to model the uncertainty associated with integrating electric vehicles into energy hubs. For instance, studies have utilized real-world usage patterns of electric vehicles to analyze uncertainty sources [12].

while others have employed stochastic models like Markov chains to describe behavioral uncertainties related to electric vehicles [13]. The Information-Guided Decision Theory (IGDT) has been used to optimize travel times and initial charge statuses of vehicles to maximize profit from battery discharges [19]. Deep learning methods have also been applied to predict electric vehicles charging levels upon entering parking, considering factors such as location and parking duration [20].

In [21], the uncertainty regarding the behavior of electric vehicles within a novel structure based on optimized two-stage scheduling in energy communities was introduced. The Monte Carlo simulation method has also been employed to model the uncertainties associated with electric vehicle patterns in the energy hub, particularly to illustrate the uncertainty of electric vehicle batteries within the energy hub, as discussed in Ref. [22]. In Ref. [23] carried out behavioral modeling to forecast the actions of electric vehicle owners by utilizing social and demographic inquiries.

In the literature review, researchers have explored a variety of techniques for modeling the uncertainty of electric vehicle (EV) owners' behavior in parking lots, categorizing them into two primary groups: methods that utilize real data and scenario-based approaches. The former depends on actual data to model uncertainty, while the latter encompasses techniques such as Markov chains, Info-Gap Decision Theory (IGDT), deep learning, Monte Carlo simulation, and social surveys. The Markov chain method, which involves sequential modeling of events with probabilities contingent on the state of the preceding event, can be impeded by a potentially large number of states and its reliance on historical data for transitions. This method may lose reliability when data is scarce. IGDT, which emphasizes decision-making under deep uncertainty by favoring the robustness of decisions, can sometimes yield suboptimal outcomes. Deep learning, despite its prowess in pattern recognition and handling complex problems with voluminous data, demands extensive datasets and computational resources, and there is a risk of it becoming a "black box" with limited interpretability. The Monte Carlo method, a statistical sampling technique for estimating solutions to intricate problems, may necessitate specific data and a considerable number of samples for precision. Poor sample selection can produce results that are detached from reality, and the method's parameter setting can be intricate. Social survey methods, which gather data on behaviors, opinions, or demographic information, can be susceptible to bias and may not always be indicative of larger populations. These methods frequently rely on raw data and can be impacted by data gaps or regional differences, leading to incomplete datasets. The method proposed in this study introduces a possibility-probability approach that synthesizes natural language methods, fuzzy logic, and probability theory to adeptly model complex uncertainties. This approach employs a blend of possibilities to denote the likelihood of events and probabilities to capture qualitative and ambiguous uncertainties. By merging these theories, the method aspires to offer a more holistic model of uncertainty, applicable across various fields and aiding in the enhancement of decision-making in uncertain contexts.

1.3 Contribution

This paper addresses critical research gaps by introducing a model to analyze the uncertainty of electric vehicles owners' presence behavior in parking lots within an energy hub system using the Probability-Possibility method. The proposed multi-carrier energy system integrates various energy types, including electrical, thermal, Gas, and water resources for commercial, domestic, and industrial centers. In addition to traditional energy carriers such as seawater desalination units, combined heating and power (CHP) units, boilers, and photovoltaic systems, this study uniquely incorporates diesel, kerosene, and naphtha supplied by a micro refinery. By optimizing the sour water purification process in the refinery, part of the energy hub's water consumption can be supplied, presenting a comprehensive approach to managing these energy carriers. This versatile approach is expected to enhance the system's potential for efficient energy management. Unlike previous studies that relied on past data or real-time online data to model the uncertainty of electric vehicles owners' behavior, this study assumes no extensive local data on electric vehicles owners' presence in parking lots. The proposed method's unique feature is its ability to model electric vehicles owners' behavior without relying on local information. Key Features of the Study:

1.3.1 Comprehensive framework

This paper presents a comprehensive framework for a multi-carrier energy system designed to integrate parking lots, aiding in the transition towards a greener and more sustainable energy system.

1.3.2 Focus on electric vehicles owners' behavior

The primary focus is on modeling the behavior of electric vehicle owners, a crucial component in complex energy systems.

1.3.3 Probability-possibility approach

The study employs a Probability-Possibility uncertainty approach to model electric vehicles owners' behavior, while the Monte Carlo method simulates changes in multi-carrier energy demand, energy prices, and photovoltaic (PV) systems.

1.3.4 Micro refinery integration

The proposed energy hub model includes a micro refinery to meet the demand for diesel, kerosene, and naphtha.

1.3.5 Water optimization

The model analyzes the water used in the refinery, including the sour water purification process, for optimization.

This study offers a novel approach to modeling the uncertainty of electric vehicles owners' behavior in parking lots and provides a detailed framework for integrating various energy carriers into an energy hub system.

1.4 Paper organization

The primary content of this paper is structured as follows: Section 1 provides a detailed figure of parking lot modeling in the context of energy hubs and micro refineries. In section 2, it presents the formula of the problem. Part 3, uncertainty modeling of energy hub parameters including, Probability-Possibility modeling of parking lot, uncertainty modeling of parking lot performance using Monte Carlo method, uncertainty modeling of demand and prices of energy carriers using the method Monte Carlo has taken place. Section 4 presents the results and findings of our numerical studies. Finally, section 5 Real-world applications of the proposed framework.

2 Structure description

The proposed energy hub model is shown in Fig. 1. In this model, the parking lot is considered as one of the sources of electrical energy supply (when discharging an electric vehicle) in the energy hub. In order to model the uncertainty of the behavior of electric vehicles owners in the parking lot (the presence of electric vehicles owners delivering energy to the energy hub), the Probability-Possibility method has been analyzed. The proposed method features modeling uncertainties without the availability of local data. In addition, in the proposed energy hub model, various other resources are considered to supply energy carriers. Sources of input to the energy hub include the upstream electrical grid, upstream thermal network, upstream drinking water network, upstream gas network, seawater, solar energy, and crude oil. In addition, in this study, the use of energy carriers converting units was investigated, except for the input sources of energy carriers introduced to supply energy carriers. In this study, CHP power plants receive gas energy to supply part of thermal and electrical energy. Another unit that receives gas energy is a boiler, the intended boilers receive the gas energy and convert it into thermal energy. In the intended model, using seawater tap water purification action provides part of the drinking water required by the proposed model. In the energy hub model, a micro refinery and the task of supplying the demand for three oil products including diesel, kerosene, and naphtha.Fig. 1 Proposed energy hub model.

Fig. 1

In the proposed micro refinery model, a series of physical and chemical processes are carried out in order to achieve the petroleum products. The most important operation is in micro crude oil (distillation). The purpose of distillation operations is to separate crude oil into oil cuts. The distillation process is the separation and separation of crude oil into a series of oil cuts based on the difference between the weld distance of the products. Crude oil entering the micro refinery is first introduced into the salt refinery equipment to completely remove the salts from it. Following, crude oil passes through the heat source for preheating. This heat source actually transfers heat from the distillation tower products to the incoming crude oil. During this heat transfer, the temperature of crude oil reaches about 280 °C. At this stage, crude oil must be heated in the furnace for full heating. The temperature of crude oil after exiting the furnace reaches about 350 °C. At this stage, crude oil is practically two-phase and is a mixture of liquid and vapor phases. After reaching the two-phase temperature, crude oil enters the distillation tower and oil-cutting operations are carried out according to the intended oil products. The output flows from the distillation tower are vaporized and liquid after passing through the condensers. Usually, with each oil cut, some lighter materials are removed from the distillation tower. This can cause the flash point to go down. To remedy this, the outgoing slices from the distillation tower are sent to a small striping tower. The oil cuts in the striping tower come in contact with steam and lighter materials are separated from them. Fig. 2 shows the operation of converting crude oil into petroleum products in a refinery. In micro refinery, it is one of the most energy efficient water carriers. Water is used for cooling, steam production, process steam washing, desalination and other applications.Fig. 2 Crude oil refining process in refiner.

Fig. 2

In this paper, in order to optimize water consumption in a micro refinery, a sour water treatment plant has been used. The steps of purifying sour water are as follows:1 Increasing the temperature of sour water until it reaches boiling point

2 Occurrence of chemical reactions reciprocating

3 Reducing the partial pressure of gases released by steam flow and their exit from the water phase

4 Complete water purification

In order to better perform the purification of sour water from the micro-refinery to useable water, Figure(3) shows this process.Fig. 3 Sour water treatment process discharged from micro refinery.

Fig. 3

After the sour water exits the micro-refinery, the process of separating ammonia, hydrogen sulfide, and other toxic substances from the sour water stream is carried out. Various methods can be used for this, and in this article, the use of a heat exchanger is suggested. Following this stage, the output passes through filters that separate ammonia, hydrogen sulfide, and other chemical contaminants, resulting in the extraction of stripped water. The obtained stripped water enters the second stage of purification. The stored water in this stage undergoes the coagulation process, where suspended particles in the water are removed. At this stage, alum and other chemicals are added to the water to form small sticky particles called "floc" that attract dirt particles. The combined weight of the dirt and alum (floc) becomes heavy enough to settle at the bottom during sedimentation. After that, the resulting water enters another tank called Flocculation & Clarification, where the heavy particles (floc) settle at the bottom, and the clear water moves towards filtration. In the next stage, the purified water passes through filters, some of which are made of sand or charcoal, to help remove smaller particles. Following this stage, a small amount of chlorine is added to the purified water in another tank, or other disinfection methods are used to eliminate bacteria and microorganisms present in the water. In the final stage, the water is stored in a closed tank for final disinfection and then flows through pipes to homes and businesses in the community.

2.1 Objective function (OF)

The formulation of the energy hub problem is presented by considering the flexibility of storage resources of energy carriers and the demand response in Equation (1). The objective function (OF) of this study is EQ (1) study with respect to the different uncertainty(s) scenarios for minimizing the cost of energy carrier operations in the proposed energy hub model:(1) OF=Min∑s=1Nsρs.Costs=∑s=1Nsρs{CostsE+CostsW+CostsT+CostsG+CostsPL+CostsDiesel+CostsNa+CostsKe+CostsEES+CostsTES+CostsDWS+CostsNaS+CostsKeS+CostsDiS+CostSFlexibilityDR,E+CostSFlexibilityDR,T+CostSFlexibilityDR,DW+CostSFlexibilityDR,Diesel+CostSFlexibilityDR,Na+CostSFlexibilityDR,Ke}

The final cost of supplying energy carriers in each scenario s (Costs) is calculated by equation (1). In this equation CostsE, the cost of receiving electrical energy from the upstream network in each scenario s, CostsW the cost of receiving water from the upstream network in each scenario s, CostsT the cost of receiving thermal energy from the upstream network hub of the energy in each scenario s, CostsG the cost of receiving gas energy from the upstream network of the energy hub in each scenario s, CostsPL the cost of receiving electrical energy from the parking lot in each scenario s, CostsDiesel the cost of converting petroleum products (Diesel) by the micro refinery in each scenario s, CostsNa the cost of converting petroleum products (Naphtha) by the micro-refinery in each scenario s, CostsKe the cost of conversion of petroleum products (kerosene) by the micro refinery in each scenario s is considered, CostsEES the cost of operating the electrical storage resource in each scenario s, CostsTES the cost of operating the thermal storage resource the cost of operating the electrical storage resource in each scenario s, CostsDWS the cost of operating the water storage resource the cost of operating the electrical storage resource in each scenario s, CostsNaS the cost of operating the Naphtha storage resource, CostsKeS the cost of operating the kerosene storage resource, and in the final section the cost of operating the electrical storage resource in each scenario s, CostsDiS the cost of operating the storage source diesel the cost of operating the electrical storage resource in each scenario s.(2) CoctSE=∑t=1Nt[πt,sE,netPt,sE,net]

(3) CoctSG=∑t=1Nt[πt,sG,netPt,sG,net]

(4) CoctST=∑t=1Nt[πt,sT,netPt,sT,net]

(5) CoctSW=∑t=1Nt[πt,sW,netPt,sW,net]

(6) CostsPL=∑t=1Nt[πt,sEVPt,sEV]

(7) CoctSDiesel=∑t=1Nt[(πt,soil,net*ϑocc−oil−Diesel)Pt,sDiesel]

(8) CoctSNa=∑t=1Nt[(πt,soil,net*ϑocc−oil−Na)Pt,sNa]

(9) CoctSKe=∑t=1Nt[(πt,soil,net*ϑocc−oil−Ke)Pt,sKe]

In equations (10), (11), (12), (13), (14), (15) the method of calculating the costs of storage resources in each scenario(s) is presented. Eq (10) for electrical energy storage, Eq (11) for thermal energy storage, Eq (12) for drinking water storage, Eq (13) for diesel storage, Eq (14) for naphtha storage and Eq (15) kerosene storage are provided. In this paper, to more accurately model the behavior of energy carrier storage systems and thus achieve more precise results, the efficiency coefficient of these resources during charging and discharging has been multiplied by the performance efficiency of the charge (ηEESCh , ηTESCh, ηDWSCh, ηDieselCh, ηNaCh, ηKeCh) and discharge (ηEESDis, ηTESDis, ηDWSDis , ηDieselDis, ηNaDis , ηKeDis) levels in all equations modeling energy carrier storage systems.(10) CostSEES=∑t=1Nt[(πOPEES(1ηEESChPt,sEES,Ch+ηEESDisPt,sEES,Dis)+πt,sE,net(1ηEESChPt,sEES,Ch−ηEESDisPt,sEES,Dis))]

(11) CostSTES=∑t=1Nt[(πOPTES(1ηTESChPt,sTES,Ch+ηTESDisPt,sTES,Dis)+πt,sT,Net(1ηTESChPt,sTES,Ch−ηTESDisPt,sTES,Dis))]

(12) CostSDWS=∑t=1Nt[(πOPDWS(1ηDWSChPt,sDWS,Ch+ηDWSDisPt,sDWS,Dis)+πt,sW,Net(1ηDWSChPt,sDWS,Ch−ηDWSDisPt,sDWS,Dis))]

(13) CostsDiS=∑t=1Nt[((πOPDiesel(1ηDieselChPt,sDiesel,Ch+ηDieselDisPt,sDiesel,Dis))+((πt,soil,net*ηdieselE*ηdieselT*ηdieselW)(1ηDieselChPt,sDiesel,Ch−ηDieselDisPt,sDiesel,Dis))]

(14) CostSNaS=∑t=1Nt[((πOPNa(1ηNaChPt,sNa,Ch+ηNaDisPt,sNa,Dis))+(πt,soil,net*ηNaE*ηNaT*ηNaW)(1ηNaChPt,sNa,Ch−ηNaDisPt,sNa,Dis))]

(15) CostSKeS=∑t=1Nt[((πOPKe(1ηKeChPt,sKe,Ch+ηKeDisPt,sKe,Dis))+((πt,soil,net*ηKeE*ηKeT*ηKeW)(1ηKeChPt,sKe,Ch−ηKeDisPt,sKe,Dis))]

In equations (16), (17), (18), (19), (20), (21), the method of calculating the costs of responsive loads of energy carriers in each scenario(s) is presented. Eq (17) the performance of thermal responsive loads, Eq (18) the performance of drinking water-responsive loads, Eq (19) the performance of the diesel responsive loads, Eq (20) the performance of the naphtha responsive loads and Eq (21) the performance of kerosene responsive loads.(16) CostSFlexibilityDR,E=∑t=1Nt[πt,sE,net((It,sE,HighPt,sE,DR)−(It,sE,DownPt,sE,DR))]

(17) CostSFlexibilityDR,T=∑t=1Nt[πt,sT,net((It,sT,HighPt,sT,DR)−(It,sT,DownPt,sT,DR))]

(18) CostSFlexibilityDR,DW=∑t=1Nt[πt,sW,net((It,sDW,HighPt,sDW,DR)−(It,sDW,DownPt,sDW,DR))]

(19) CostSFlexibilityDR,Diesel=∑t=1Nt[πt,soil,net*ηdieselE*ηdieselT*ηdieselW((It,sDiesel,HighPt,sDiesel,DR)−(It,sDiesel,DownPt,sDiesel,DR))]

(20) CostSFlexibilityDR,Na=∑t=1Nt[πt,soil,net*ηNaE*ηNaT*ηNaW((It,sNa,HighPt,sNa,DR)−(It,sNa,DownPt,sNa,DR))]

(21) CostSFlexibilityDR,Ke=∑t=1Nt[πt,soil,net*ηKeE*ηKeT*ηKeW((It,sKe,HighPt,sKe,DR)−(It,sKe,DownPt,sKe,DR))]

2.2 Constraints

Hub energy technical constraints are a set of technical restrictions and requirements that are considered for the optimization and efficient operation of multi-carrier energy systems (equations 22–105). These restrictions are compiled in order to ensure the correct and optimal performance of the energy hub and also to ensure the stability and reliability of the system. In equations (22), (23), (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37), (38), (39), (40), (41), (42), (43), (44), (45), the constraints of energy carriers entering the energy hub include the input of electrical energy, the entry of gas, the entry of thermal energy, the entry of crude oil, and the entry of water into the energy hub.

In the optimization problem of energy hub operations, energy balance constraints should be considered for all energy carriers. Eq (22) shows the demand for crude oil. This demand must be equal to the aggregate demand for petroleum products in the micro refinery (diesel production (Pt,sDiesel), naphtha production (Pt,sKe) and kerosene production (Pt,sNa)).(22) Pt,sOil,net=[Pt,sOil,diesel+Pt,sOil,Ke+Pt,sOil,Na]

In equations (23), (24), (25), the demand for crude oil of each petroleum product is shown based on the efficiency of converting crude oil into each of the petroleum products (η) in the micro-refinery.(23) Pt,sDiesel=[ηDieselOilPt,sOil,Diesel]

(24) Pt,sKe=[ηKeOilPt,sOil,Ke]

(25) Pt,sNa=[ηNaOilPt,sOil,Na]

Eq (26) shows that the demand for electrical energy should be equal to the total electrical energy input from the grid (Pt,sE,net), the energy injected from PV (Pt,sE,solar), the energy supplied from the electrical storage (Pt,sEES,Ch−Pt,sEES,Dis), the electrical component of CHP output, the electrical charge reduced or increased by the electrically responsive charges, and the electrical energy injected by the lot parking lot.(26) PsE,De=[ηTransEPt,sE,net+ηdc−acE_solarPt,sE,solar+ηCHPEPt,sG,CHP+(Pt,sEES,Ch−Pt,sEES,Dis)−ηsea−drikEPt,sW,sea+(Pt,sE,Down−Pt,sE,High)+ηdc−acE_Parking_lotPt,sE,Parking_lot−ηNaEPt,sNa−ηkeEPt,ske−ηdieselEPt,sdiesel−ηSourwatertreatmentplantEPt,sW,Sourwatertreatmentplant]

Where ηTransE represents the efficiency of the electrical transformer, ηdc−acE_solar represents the efficiency of the PV intermediate converter, ηCHPE is the efficiency of gas to electricity efficiency in CHP, ηdc−acE_Parking_lot is the efficiency of the intermediate converter of the parking lot, ηsea−drikE Shows the efficiency of the sea water to water converter, ηSourwatertreatmentplantE Shows the efficiency of the sour water Sour water treatment plant. Eq (27) indicates that the water demand should equal the sum of the total water input from the network, water received from the seawater desalination unit, water supplied from storage, the load reduced by water, and the water demand by the micro-refinery.(27) Pt,sW,De=[Pt,sW,net+Pt,sW,swa+(Pt,sDWS,Ch−Pt,sDWS,Dis)+(Pt,sW,Down−Pt,sW,High)−ηNaWPt,sNa−ηkeWPt,ske−ηDieselWPt,sDiesel]

In Eq (27), Pt,sW,net water received from the upstream network, Pt,sW,swa is sea water desalination output. Also, Eq (28) shows that gas energy demand (boiler, CHP) should be equal to the total energy input from the network.(28) Pt,sG,net=[Pt,sG,CHP+Pt,sG,B]

Eq (29) shows that the thermal energy demand should be equal to the total input energy from the grid (Pt,sT,net), energy injected from the boiler (Pt,sT,Boil), energy supplied from thermal storage (Pt,sTES,Ch−Pt,sTES,Dis), thermal component of CHP output (ηCHPTPt,sG,CHP), and load reduced by thermal DRP (Pt,sT,Down−Pt,sT,High), And the amount of energy required to convert crude oil into petroleum products includes (ηNaTPt,sNa, ηKeTPt,sKe, ηdieselTPt,sdiesel).(29) PsT,De=[Pt,sT,net+ηBoilTPt,sT,Boil+ηCHPTPt,sG,CHP+(Pt,sTES,Ch−Pt,sTES,Dis)+(Pt,sT,Down−Pt,sT,High)−ηNaTPt,sNa−ηKeTPt,sKe−ηdieselTPt,sdiesel]

Where ηBoilT represents the efficiency of the boiler, ηCHPT represents the efficiency of the gas to heat converter of the CHP power plant.

Eq (30) shows that the diesel (PsDiesel,De) demand should be equal to the total input diesel, diesel injected (Pt,sDiesel) from the micro refinery, supplied from micro refinery storage (Pt,sDiesel,Ch−Pt,sDiesel,Dis), load reduced demand diesel (Pt,sDiesel,Down−Pt,sDiesel,High).(30) PsDiesel,De=[Pt,sDiesel+(Pt,sDiesel,Ch−Pt,sDiesel,Dis)+(Pt,sDiesel,Down−Pt,sDiesel,High)]

Eq (31) shows that the naphtha (PsNa,De) demand should be equal to the total input naphtha, naphtha injected (Pt,sNa) from the micro refinery, supplied from micro refinery storage (Pt,sNa,Ch−Pt,sNa,Dis), load reduced demand naphtha (Pt,sNa,Down−Pt,sNa,High).(31) PsNa,De=[Pt,sNa+(Pt,sNa,Ch−Pt,sNa,Dis)+(Pt,sNa,Down−Pt,sNa,High)]

Eq (32) shows that the kerosene (PsKe,De) demand should be equal to the total input kerosene, kerosene injected from the micro refinery (Pt,sKe), supplied from micro refinery storage (Pt,sKe,Ch−Pt,sKe,Dis), load reduced demand kerosene (Pt,sKe,Down−Pt,sKe,High).(32) PsKe,De=[Pt,sKe+(Pt,sKe,Ch−Pt,sKe,Dis)+(Pt,sKe,Down−Pt,sKe,High)]

It is important to consider the technical constraints of the energy hub. These constraints determine the maximum amount of energy that can be produced by each source. In Eq (33), PtE,net represents the maximum capacity of imported energy from the electricity network. In Eq (34), PtG,net represents the maximum capacity of imported gas energy. In Eq (35), PtW,net represents the maximum capacity of water imported from the water network. Finally, in Eq (36), PtT,net denotes the maximum capacity of imported energy from the thermal network. In Eq (37), Ptoil,net denotes the maximum capacity oil of imported from the oil network.

These energy transfer constraints are determined based on the transmission infrastructure, while considering factors such as the capacity of transmission lines.(33) 0≤PtE,net≤PnetmaxE

(34) 0≤PtG,net≤PnetmaxG

(35) 0≤PtW,net≤PnetmaxW

(36) 0≤Ptoil,net≤Pnetmaxoil

(37) 0≤PtT,net≤PnetmaxT

Constraints (38-45) determine the availability of the energy level of each energy carrier and the energy hub manager determines the optimal value of each energy carrier based on the available capacity per hour. The parameters PTransinput, PCHP_maxinput, PBoil_maxinput, Psea_maxW, Psour−water_maxW, PmaxDiesel, PmaxNa, PmaxKe are respectively the maximum capacity of electrical transformer, CHP, boiler, Sour water treatment plant, diesel, naphtha, kerosene and desalinated seawater. Eqs (38), (39), (40), (41), (42), (43), (44), (45) constraints determine the performance of these parameters within their permissible constraints.(38) 0≤PtE,net≤PTransinput

(39) 0≤PtG,CHP≤PCHP_maxinput

(40) 0≤PtG,Boil≤PBoil_maxinput

(41) 0≤PtW,sour−water≤Psour−water_maxW

(42) 0≤PtDiesel≤PmaxDiesel

(43) 0≤PtNa≤PmaxNa

(44) 0≤PtKe≤PmaxKe

(45) 0≤PtW,sea≤Psea_maxW

2.3 Energy carriers’ storage constraint

The purpose of determining the technical constraints of energy carriers' storage resources in an energy hub is a set of technical constraints and requirements that are determined to ensure the optimal and efficient operation of energy storage systems in an energy hub. These restrictions are imposed in order to ensure the stability, efficiency, and security of the energy storage system and to optimize energy storage and discharge processes. These technical constraints are designed to improve the performance and efficiency of energy storage systems in energy hubs and play an important role in ensuring the sustainability and security of multi-carrier energy systems. To model storage systems in energy hub operation, system-specific constraints are added to the formulation. Eqs (46), (47), (48), (49), (50), (51) shows these constraints [24]. The energy balance of the electrical storage system, thermal storage system, water storage system, diesel storage system, naphtha storage system and kerosene storage system are depicted in Eqs (46), (47), (48), (49), (50), (51). In this context, positive values are assigned to the charge and capacity variables, while a negative sign is used to model the discharge and losses of the storage system. In equations (46), (47), (48), (49), (50), (51), it determines the available capacity of energy storage resources per hour. According to the output of equations (46), (47), (48), (49), (50), (51), it is determined that the final functional state of the storage resources carrying energy is in the state of energy injection or energy reception.(46) Pt,sEES,S=Pt−1,sEES,S+Pt,sEES,Ch−Pt,sEES,Dis−Pt,sEES,loss

(47) Pt,sTES,S=Pt−1,sTES,S+Pt,sTES,Ch−Pt,sTES,Dis−Pt,sTES,loss

(48) Pt,sWDS,S=Pt−1,sWDS,S+Pt,sWDS,Ch−Pt,sWDS,Dis

(49) Pt,sDiesel,S=Pt−1,sDiesel,S+Pt,sDiesel,Ch−Pt,sDiesel,Dis−Pt,sDiesel,loss

(50) Pt,sNa,S=Pt−1,sNa,S+Pt,sNa,Ch−Pt,sNa,Dis−Pt,sNa,loss

(51) Pt,sKe,S=Pt−1,sKe,S+Pt,sKe,Ch−Pt,sKe,Dis−Pt,sKe,loss

Where Eqs (52), (53), (54), (55), (56), (57) model the losses of electrical, thermal, diesel, naphtha, kerosene and water storage systems, which presents a realistic aspect of storage systems.(52) Pt,sEES,loss=αlossEESPt,sEES,S

(53) Pt,sTES,loss=αlossTESPt,sTES,S

(54) Pt,sWDS,loss=αlossWDSPt,sWDS,S

(55) Pt,sKe,loss=αlossKePt,sKe,S

(56) Pt,sNa,loss=αlossNaPt,sNa,S

(57) Pt,sDiesel,loss=αlossDieselPt,sDiesel,S

Eqs (58), (59), (60), (61), (62), (63) ensure that the energy levels of electrical, thermal, diesel, naphtha, kerosene and water storage are maintained within the acceptable range. In other words, technical constraints restrict the storage from operating in any desired ranges. The variables αMin and αMax represent the minimum and maximum power level ratios of the storage, respectively. Pcapa denotes the capacity of the storage.(58) αMinEESPcapaEES≤Pt,sEES,S≤αMaxEESPcapaEES

(59) αMinTESPcapaTES≤Pt,sTES,S≤αMaxTESPcapaTES

(60) αMinWDSPcapaWDS≤Pt,sWDS,S≤αMaxWDSPcapaWDS

(61) αMinKePcapaKeS≤Pt,sKeS≤αMaxKePcapaKeS

(62) αMinNaPcapaNaS≤Pt,sNaS≤αMaxNaPcapaNaS

(63) αMinDieselPcapaDieselS≤Pt,sDieselS≤αMaxDieselPcapaDieselS

Constraints (64-75) specify the technical constraints of the amount of power to charge or discharge the storage resources of energy carriers to what capacity per hour should be in each scenario. Where βMin and βMax represent the minimum and maximum allowable charging rates for electrical, thermal, diesel, naphtha, kerosene and water storage devices, respectively. The charging and discharging efficiency of the storage devices are denoted by ηCh and ηDis. The constraints for charging and discharging of electrical storage are indicated in Eqs (64), (65), also those for thermal storage are outlined in Eqs (66), (67), also those for diesel storage are outlined in Eqs (68), (69), The constraints for charging and discharging of naphtha storage are indicated in Eqs (70), (71), while those for kerosene storage are outlined in Eqs (72), (73) for water storage in Eqs (74), (75).(64) βMinEESPcapaEES(1ηEESCh)It,sEES,Ch≤Pt,sEES,Ch≤βMaxEESPcapaEES(1ηEESCh)It,sEES,Ch

(65) βMinEESPcapaEESηEESDisIt,sEES,Dis≤Pt,sEES,Dis≤βMaxEESPcapaEESηEESDisIt,sEES,Dis

(66) βMinTESPcapaTES(1ηTESCh)It,sTES,Ch≤Pt,sTES,Ch≤βMaxTESPcapaTES(1ηTESCh)It,sTES,Ch

(67) βMinTESPcapaTESηTESDisIt,sTES,Dis≤Pt,sTES,Dis≤βMaxTESPcapaTESηTESDisIt,sTES,Dis

(68) βMinWDSPcapaWDS(1ηWDSCh)It,sWDS,Ch≤Pt,sWDS,Ch≤βMaxWDSPcapaWDS(1ηWDSCh)It,sWDS,Ch

(69) βMinWDSPcapaWDSηWDSDisIt,sWDS,Dis≤Pt,sWDS,Dis≤βMaxWDSPcapaWDSηWDSDisIt,sWDS,Dis

(70) βMinKePcapaKeS(1ηKeSCh)It,sKeS,Ch≤Pt,sKeS,Ch≤βMaxKePcapaKeS(1ηKeSCh)It,sKeS,Ch

(71) βMinKePcapaKeSηKeSDisIt,sKeS,Dis≤Pt,sKeS,Dis≤βMaxKePcapaKeSηKeSDisIt,sKeS,Dis

(72) βMinNaPcapaNaS(1ηNaSCh)It,sNaS,Ch≤Pt,sNaS,Ch≤βMaxNaPcapaNaS(1ηNaSCh)It,sNaS,Ch

(73) βMinNaPcapaNaSηNaSDisIt,sNaS,Dis≤Pt,sNaS,Dis≤βMaxNaPcapaNaSηNaSDisIt,sNaS,Dis

(74) βMinDieselPcapaDieselS(1ηDieselSCh)It,sDieselS,Ch≤Pt,sDieselS,Ch≤βMaxDieselPcapaDieselS(1ηDieselSCh)It,sDieselS,Ch

(75) βMinDieselPcapaDieselSηDieselSDisIt,sDieselS,Dis≤Pt,sDieselS,Dis≤βMaxDieselPcapaDieselSηDieselSDisIt,sDieselS,Dis

Eqs (76), (77), (78), (79), (80), (81) prevent the simultaneous operation of charging and discharging within the storage system in either mode.(76) 0≤It,sEES,Dis+It,sEES,Ch≤1

(77) 0≤It,sTES,Dis+It,sTES,Ch≤1

(78) 0≤It,sWDS,Dis+It,sWDS,Ch≤1

(79) 0≤It,sKeS,Dis+It,sKeS,Ch≤1

(80) 0≤It,sNaS,Dis+It,sNaS,Ch≤1

(81) 0≤It,sDieselS,Dis+It,sDieselS,Ch≤1

2.4 Responsive load carrier constraints

equations 87–82 indicate that in the planned time interval of energy carriers, the amount of energy decreased and increased energy of the responsive loads should be equal in the total planned times. The present paper proposes 6 response programs aimed at reducing the cost of system operation. In order to implement these programs in the problem, Eqs (82), (83), (84), (85), (86), (87) have been considered in accordance with the electrical, thermal, water, diesel, naphtha and kerosene demand response programs:(82) ∑t=1NtPt,sE,Down=∑t=1NtPt,sE,High

(83) ∑t=1NtPt,sT,Down=∑t=1NtPt,sT,High

(84) ∑t=1NtPt,sW,Down=∑t=1NtPt,sW,High

(85) ∑t=1NtPt,sKe,Down=∑t=1NtPt,sKe,High

(86) ∑t=1NtPt,sNa,Down=∑t=1NtPt,sNa,High

(87) ∑t=1NtPt,sDiesel,Down=∑t=1NtPt,sDiesel,High

Eqs (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98), (99) represent the equilibrium between top and bottom displaced loads. Based on this model, the total load reduction by the customer must be equal to the increase in load displacement over a 24-h period.(88) 0≤Pt,sE,High≤LPFHighEPt,sE,DeIt,sE,HighV

(89) 0≤Pt,sE,Down≤LPFDownEPt,sE,DeIt,sE,Down

(90) 0≤Pt,sT,High≤LPFHighTPt,sT,DeIt,sT,High

(91) 0≤Pt,sT,Down≤LPFDownTPt,sT,DeIt,sT,Down

(92) 0≤Pt,sW,High≤LPFHighWPt,sW,DeIt,sW,High

(93) 0≤Pt,sW,Down≤LPFDownWPt,sW,DeIt,sW,Down

(94) 0≤Pt,sKe,High≤LPFHighKePt,sKe,DeIt,sKe,High

(95) 0≤Pt,sKe,Down≤LPFDownKePt,sKe,DeIt,sKe,Down

(96) 0≤Pt,sNa,High≤LPFHighNaPt,sNa,DeIt,sNa,High

(97) 0≤Pt,sNa,Down≤LPFDownNaPt,sNa,DeIt,sNa,Down

(98) 0≤Pt,sDiesel,High≤LPFHighDieselPt,sDiesel,DeIt,sDiesel,High

(99) 0≤Pt,sDiesel,Down≤LPFDownDieselPt,sDiesel,DeIt,sDiesel,Down

where LPFHigh and LPFDown are maximum ratios of shifted up and shifted down demand. Eqs. (88), (89), (90), (91), (92), (93), (94), (95), (96), (97), (98), (99) present upper limit of shifted up and shifted down load electrical, thermal, water, diesel, naphtha, kerosene respectively.(100) 0≤It,sE,Down+It,sE,High≤1

(101) 0≤It,sT,Down+It,sT,High≤1

(102) 0≤It,sW,Down+It,sW,High≤1

(103) 0≤It,sKe,Down+It,sKe,High≤1

(104) 0≤It,sNa,Down+It,sNa,High≤1

(105) 0≤It,sDiesel,Down+It,sDiesel,High≤1

Eqs. (100)–(105) prohibits the unit to shift up and shift down the load at the same time.

3 Energy hub uncertainty

3.1 Uncertainty modeling of the parking lot

In the strategic plans of the European Union and the International Energy Agency (IEA), several initiatives have been developed for the use of electric vehicles. For example, the Green Deal program aims to reduce environmental pollutants using renewable and clean energy, with electric vehicles playing a key role in this strategy. Another program, part of the Green Deal, is the Fit for 55 initiative, which aims to reduce carbon emissions in Europe by 55 % by 2030. A key strategy of this program is to increase the use of electric vehicles and develop their charging infrastructure. Various other programs have also been introduced with the goal of using clean energy to reduce environmental pollutants. The injection of electric energy by electric vehicles into the power grid, known as Vehicle-to-Grid (V2G) technology, is an innovative approach to improving the stability and efficiency of the power grid. This technology allows electric vehicles to act as energy storage sources and return the energy stored in their batteries to the grid when needed. This can help moderate fluctuations in electrical demand and enhance grid stability. Today, among researchers, the uncertainty of the presence of electric vehicles in charging stations and parking lots is considered a significant challenge. These uncertainties arise from various factors, such as the unpredictable behavior of electric vehicle owners, irregular charging and discharging patterns at different times, sudden decisions by electric vehicle owners to inject or receive electrical energy from the charging station, inadequate forecasting by system administrators, and climatic and environmental impacts during charging and discharging times. These factors lead to insufficient data and make it difficult for researchers to accurately predict the behavior of electric vehicle owners at charging stations or parking lots. One of the effective methods for predicting complex uncertainties dependent on human behavior is the probabilistic-fuzzy method. This approach combines fuzzy logic with probabilistic techniques to address intricate human uncertainties. In the first part, a fuzzy range (number and probability of occurrence) is determined using the knowledge of experts and specialists, considering the behavior of electric vehicle owners in parking lots (based on the number of vehicles present). For the second part (probability), it is necessary to collect data on the behavior of electric vehicle owners in parking lots from another similar area. Finally, this uncertainty is calculated by integrating the second factor (probability) with the first factor (possibility). The process of solving this problem is discussed below, First Stage:

Experts' Opinions on Defining Intervals for the Number of Electric Vehicles Entering the Parking Lot (Fig. 4):Fig. 4 Numerical range obtained from the consensus of experts.

Fig. 4

Second Stage:

Experts' Opinions on Defining Probability Zones for the Entry of Electric Vehicles into the Parking Lot (Fig. 5). Probabilistic sets can be classified as uncertain, near-certain, certain, and completely certain.(106) Q={€A=(€1,€3)Uncertain=(low<€1<€3)€B=(€2,€4)Almostsure=(€2<€4)€C=(€3,€5)Safe=(€3<€5)€D=(€4,€6)Absolutelysure=(€4<€6<Max)

(107) R={лA=(л1,л3)Uncertain=(low<л1<л3)лB=(л2,л4)Almostsure=(л2<л4)лC=(л3,л5)Safe=(л3<л5)лD=(л4,л6)Absolutelysure=(л4<л6<Max)

Fig. 5 Numerical range obtained from the consensus of experts.

Fig. 5

After defining the level of participation of electric vehicles in the parking lot and possible scenarios, the probabilistic-fuzzy complexes are calculated according to Table 3:Q	R	Considered Totals of the Level of Participation of Electric Vehicles by Experts	
Uncertain	Uncertain	F1=(Uncertain, Uncertain)=(€A, лA)	
Almostsure	F2=(Uncertain, Almostsure)=(€A, лB)	
Safe	F3=(Uncertain, Safe)=(€A, лC)	
Absolutelysure	F4=(Uncertain, Almostsure)=(€A, лD)	
Almostsure	Uncertain	F5=(Almostsure, Uncertain)=(€B, лA)	
Almostsure	F6=(Almostsure, Almostsure)=(€B, лB)	
Safe	F7=(Almostsure, Safe)=(€B, лC)	
Absolutelysure	F8=(Almostsure, Absolutelysure)=(€B, лD)	
Safe	Uncertain	F9=(Safe, Uncertain)=(€C, лA)	
Almostsure	F10=(Safe, Almostsure)=(€C, лB)	
Safe	F11=(Safe, Safe)=(€C, лC)	
Absolutelysure	F12=(Safe, Almostsure)=(€C, лD)	
Absolutelysure	Uncertain	F13=(Absolutelysure, Uncertain)=(€D, лA)	
Almostsure	F14=(Absolutelysure, Almostsure)=(€D, лB)	
Safe	F15=(Absolutelysure, Safe)=(€D, лC)	
Absolutelysure	F16=(Absolutelysure, Absolutelysure)=(€D, лD)	

Table 2 Summary of different techiques in solving modeling the presence behavior of electric vehicles owners at parking lot.

Table 2		
Techniques	Ref. No.	
Modeling by considering real data	[[7], [8], [9], [10]], [11], [12]	
Scenario-based method	[[13], [19], [20], [21], [22], [23]]	
Incomplete uncertainly data modeling approach	Proposed Model	

Table 3 Comparison between Monte Carlo and Pr-Po methods of electric energy consumption.

Table 3	Mc	Pr-Po	
Performance of electrical storage source	528 kw	587 kw	
Performance of electrical responsive loads	1829 kw	1765 kw	
Used electrical energy of sea water desalination	17914 kw	17926 kw	
The electrical energy consumed by the micro refinery's sour water desalination plant	3240 kw	3245 kw	
Electric energy input to the energy hub	101944 kw	101264 kw	
total	125455 kw	124787 kw	

Third Stage:

After calculating the sets of Table 3, the output power of the parking lot is obtained according to equation (108):(108) P˜(Parkinglot)=P˜.ηdc−acParkinglot=(F1˜+F2˜+F3˜+F4˜+F5˜+F6˜+F7˜+F8˜+F9+˜F10˜+F11˜+F12˜+F13˜+F14˜+F15˜+F16˜−(∩(€2,€3),∩(л2,л3))−(∩(€3,€4),∩(л3,л4)−(∩(€4,€5),∩(л4,л5)).ηdc−acE

Considering that problem solving (Eq (108)) is of the probabilistic-fuzzy type, it is necessary to convert the probabilistic part of the problem to classical fuzzy sets for simpler calculations. For this purpose, the intervals obtained from the probabilistic set are converted to classical fuzzy sets using the alpha-cut method. The general process of solving the alpha-cut problem is explained in Ref. [25].(109) лiα=∪α=0α=1qα,α={0,Δα,2Δα,...,1}

After incorporating the results obtained from the alpha-cut method into Table 3, it is necessary to de fuzzy all the states (F1, …, F16) to solve all the scenarios in Table 3, given that the results are fuzzy [26].(110) η=∫−∞+∞(R˜Prob,μR˜t(R˜Prob))dR˜Prob∫−∞+∞(μR˜t(R˜Prob))dR˜Prob

In the final stage of the proposed method, to calculate the final power injected from the parking lot to the energy hub and to increase the accuracy of the calculations, the obtained results should be multiplied by the probability of their occurrence, which is derived from the probability function of the same area. The authors of this article have used historical data and experiences [27] to form this function Eq (111).(111) EnergyParkinglot=(∫0x12πexp(−(X−μ)22σ2,dx)P˜(Parkinglot)

The aim of this study is to examine the uncertainty modeling of parking lot during the process of injecting energy into the energy hub. In order to effectively model this uncertainty, Probability-Possibility has been used, as they possess the capability to represent uncertainties without relying on local information. Fig. 6 shows the flowchart of the solution steps of the Probability-Possibility method in order to calculate the electrical output power of the parking lot.Fig. 6 Probability-Possibility modeling flowchart of electric vehicle parking lot.

Fig. 6

3.2 Modeling the uncertainties of energy carriers and prices

In the practical realm, energy hub operators encounter a multitude of uncertainties. This study examines several parameters of uncertainty, including electrical price, water price, thermal energy price, electrical demand, water demand, thermal energy demand, and solar energy production. To effectively model these uncertainties, the MC method is utilized [28].

3.3 The sequence of model development

In this section, Fig. 7 is presented to illustrate the relationship between input data, methods, tools, and proposed solutions. The Monte Carlo method is employed to model the uncertainty of solar radiation and the loads of flexible energy carriers and storage of flexible energy carriers utilizing the prices of energy carriers. Additionally, the Probability-Possibility method is utilized in another part of this structure to model the uncertainty of electric vehicles owners' behavior at the Parking lot. Finally, the results obtained from the uncertainty modeling of the Monte Carlo method and the behavior of electric vehicles owners are incorporated into the objective function of energy hub using the Probability-Possibility method. The obtained results are then analyzed using the CPLX solver in the Gams software.Fig. 7 The structural relationship between input data, methods, tools, and solutions of the studied energy hub.

Fig. 7

4 Numerical studies

4.1 Numerical results

The proposed structure is modeled as a mixed-integer linear program (MILP) problem. In addition, the solver of CPLEX has been in GAMS 24.1.2. The proposed structure in accordance with Fig. 1 applies to the energy hub system taking into account a micro-refinery and lot parking. The proposed structure has 7 blocks. Incoming blocks receive energy carriers and convert energy output blocks. Responding to the demand of energy carriers is intended as a flexible energy resource to increase the efficiency of the energy hub system's operations. In addition, in this paper, the charging and discharging performance of storage resources increases the flexibility of operation in the energy hub system.

Fig. 8 illustrates the demands for electrical, thermal energy, drinking water, and petroleum products, calculated randomly using the Monte Carlo method. Fig. 9 displays the prices of the energy carriers entering the energy hub, also calculated using the Monte Carlo method and shown for each hour. In Fig. 10, the demand for electrical energy required to convert crude oil into various petroleum products in the micro-refinery is depicted, based on the efficiency coefficient of electrical energy relative to the demand for petroleum products.Fig. 8 Electrical, thermal and water micro refinery.

Fig. 8

Fig. 9 The price of energy carriers.

Fig. 9

Fig. 10 Calculated electrical demand of the micro refinery.

Fig. 10

In Fig. 11, the performance situation of the parking lot in terms of the number of electric vehicles and the injection of electrical energy into the energy hub in two modes Monte Carlo and Probability-Possibility. These results show that in the feasibility and probability, more electric vehicles have entered the parking lot and have supplied their excess electrical energy to the electrical grid. Also, in this figure the performance of the CHP power plant in two modes of Monte Carlo and Probability-Possibility modes considering the electrical energy injected by the parking lot. The results show that the performance of parking lot has no effect on the performance of the CHP power plant, due to the lower price of electrical energy than the price of gas and thermal energy of the upstream network.Fig. 11 Electrical energy injected by combined heat and power & Parking lot (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo).

Fig. 11

Fig. 12 shows the performance of receiving electrical energy from the upstream grid in two different performance modes of parking lot. The results show that due to the more electrical energy injected in the Probability-Possibility mode, less electrical energy is received from the upstream network than the Monte Carlo state, which is an economic advantage.Fig. 12 Electrical energy received from the upstream network and Solar (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo).

Fig. 12

In Fig. 13, the performance of electrical responsive loads and electrical storage sources upstream in two different modes of parking lot is analyzed. The results show that at 15 o'clock due to the higher price of the electrical energy supplied from the parking lot compared to the price of electric energy from the upstream network, in this hour, the electrical responsive loads have more performance. Regarding the performance of storage resources, the results show that in the feasibility and probability mode, it has better performance than Monte Carlo (see Fig. 16).Fig. 13 Performance of storage resources and electrical demand response (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo, shift UP: Increased load in load response mode, shift Down: Reduced load in load response mode, Charge: The amount of energy received in order to store in the storage source, Discharge: The amount of energy discharged from the storage source).

Fig. 13

Fig. 14, Fig. 17 show that due to the supply of more electrical energy from the parking lot in the Probability-Possibility state than Monte Carlo and the more favorable price of this energy than the electrical energy of the upstream network, the desalination in the Probability-Possibility state injected 35880 cubic meters of drink water to the energy hub in 24 h, while in Monte Carlo 35835 cubic meters of water to the hub energy is injected In Fig. 12 thermal storage resources and thermal responsive loads in two different modes of parking lot are analyzed, the results show that different performance of parking lot has no effective effect on the performance of storage resources and thermal responsive loads (see Fig. 18).Fig. 14 Electrical energy required for sea water desalination and sour water treatment (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo).

Fig. 14

Fig. 15 Performance of storage resources and thermal demand response (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo, shift UP: Increased load in load response mode, shift Down: Reduced load in load response mode, Charge: The amount of energy received in order to store in the storage source, Discharge: The amount of energy discharged from the storage source).

Fig. 15

Fig. 16 The performance of the thermal part of the combined heating and power plant, boiler and receiving thermal energy from the upstream network (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo).

Fig. 16

Fig. 17 Getting drinking water from sea water and purifying sour water from the micro-refinery (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo).

Fig. 17

Fig. 18 Performance of storage resources and drink water demand response (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo, shift UP: Increased load in load response mode, shift Down: Reduced load in load response mode, Charge: The amount of energy received in order to store in the storage source, Discharge: The amount of energy discharged from the storage source).

Fig. 18

In Fig. 15, the performance of receiving thermal energy from the upstream network, receiving thermal energy from the CHP plant, and also the performance of the boiler has been examined. The results show that the performance of none of the thermal energy sources has been affected by the different performance of electric vehicles, which is one of the reasons why thermal energy and gas prices are more favorable than the price of electrical energy received from the upstream network.

Fig. 17 shows the functions of storage resources and the responsive loads of drinking water in the energy hub in two different modes of parking lot. At 9 o'clock, it is observed that the performance of increasing and decreasing responsive loads as well as drinking water storage resources in Probability-Possibility mode are different from the Monte Carlo parking lot. The reason for this is a variety of reasons, including the difference between the injection of electrical energy by the parking lot, the higher electrical price of the upstream network than the upstream network drinking water, and the price of electrical energy to get the parking lot and also the suitability of the parking lot than the drinking water price of the upstream network.

At 9 o'clock, the number of electric vehicles entering the parking lot in Monte Carlo mode is lower than in the Probability-Possibility mode, which results in less electrical energy than the Probability-Possibility mode injected into the energy hub from the parking lot. Therefore, factors such as the prices of energy carriers and the amount of energy injected from the parking lot have caused the performance of the increased responsive loads and the charging performance of drinking water storage resources in Monte Carlo state is somewhat higher than the Probability-Possibility, and also at the same hour in the responsive loads mode decreased, and the amount of discharged drinking water storage sources of drinking water storage sources has a Probability-Possibility performance relative to Monte Carlo has more of a plan.

As you can see, at 15 o'clock different performance than 9 o'clock, this is due to the higher energy price of the parking lot than other energy carriers. It is also observed that at 23 and 24 h, the performance of responsive electrical loads and drinking water storage sources are different from each other, at 23 h the price of receiving electrical energy from the upstream network compared to receiving electrical energy from the parking lot of the has a little more, which causes more water to be received from tap water and this is a reason for the increase in the level of water stored in the resources The storage is drinking water, but at 24 o'clock this function has occurred differently due to the increase in the electrical price of the parking lot compared to the upstream electrical grid.

In Fig. 19 output of micro-refinery oil products. The results show that in the hours where the price of electrical energy of the upstream network is higher than the price of the electrical supplied from the parking lot (e.g., 4–13 h), the oil products in Monte Carlo state are higher than the Probability-Possibility method and in the hours when the price of electrical energy is lower than the parking lot, the oil products in Monte Carlo state are lower than the Probability-Possibility method (see Fig. 20).Fig. 19 Petroleum products received from the micro-refinery (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo).

Fig. 19

Fig. 20 Performance of storage resources and kerosene demand response (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo, shift UP: Increased load in load response mode, shift Down: Reduced load in load response mode, Charge: The amount of energy received in order to store in the storage source, Discharge: The amount of energy discharged from the storage source).

Fig. 20

Fig. 21 Performance of storage resources and nefta demand response (PR-PO: Probability-Possibility, Mc: Monte-Carlo, shift UP: Increased load in load response mode, shift Down: Reduced load in load response mode, Charge: The amount of energy received in order to store in the storage source, Discharge: The amount of energy discharged from the storage source).

Fig. 21

Illustrations 20, 21, and 22 of the performance of responsive loads and storage resources of petroleum products are displayed. Due to the limitation of the oil input power to the micro refinery, the values should be calculated in such a way that all constraints are observed according to the prices of energy carriers. For example, at 1 a.m., as it can be seen, in kerosene and naphtha, responsive loads are in decreasing mode, while diesel responsive loads are in an increasing state. But at 11 o'clock the response times of kerosene and naphtha are in incremental mode, while diesel responsive loads are in a decreasing state.

Also, the results show that in the hours when the price of electrical energy supplied by the parking lot is lower than the upstream electrical grid, the increased responsive loads of oil products have been more efficient in the Probability-Possibility state, for example, at 8–12 h the price of electrical energy supplied by the parking lot is higher than the upstream grid. Therefore, less electrical energy than the parking lot in the Probability-Possibility mode is received and oil prices are lower than electrical energy at this hour, so increasing responsive charges are in active operation.

At 15–18 h the response loads are in decline, mainly due to the price of oil being more than electrical energy, during this period the state of electrical performance is higher in the Probability-Possibility than Monte Carlo (see Fig. 22).

Fig. 23 illustrates the energy hub's final cost performance in both Monte Carlo and possibility-probability scenarios. The graph displays the results over a 24-h period, demonstrating an 8 % cost reduction achieved by the proposed method compared to the Monte Carlo approach. This reduction is attributed to higher energy injection into the energy hub from electric vehicles at the parking lot, which optimizes all energy carriers and lowers the final cost. These findings underscore that the proposed method achieves better economic outcomes than the Monte Carlo method due to its more accurate calculation of uncertainties associated with the behavior of electric vehicle owners. In the proposed approach, experts' opinions regarding the possibility and probability of electric vehicle presence behaviors are initially gathered. Subsequently, real data on electric vehicle owner presence in the same area are collected and integrated, multiplying the results derived from expert opinions by the probability obtained from the probability distribution function of the real data. This method yields superior results compared to the Monte Carlo method.Fig. 22 Performance of storage resources and diesel demand response (PR-PO: Study in mode probability-possibility, Mc: Study in mode Monte Carlo, shift UP: Increased load in load response mode, shift Down: Reduced load in load response mode, Charge: The amount of energy received in order to store in the storage source, Discharge: The amount of energy discharged from the storage source).

Fig. 22

Fig. 23 The comparison of the final cost of energy carriers using the fuzzy method with the Z-number method.

Fig. 23

To demonstrate the effectiveness of the proposed method and the impact of the energy injected from the parking lot, the outcomes of this method have been compared with those obtained from modeling the uncertainty of EV owners' behavior using the Monte Carlo method. This comparison is examined below:

The results presented in Table 3 reveal that when modeling the uncertainty of EV owners' presence in the parking lot at the Energy Hub, there is a reduction of 668 kW in electric energy consumption. Furthermore, Table 3 indicates that since the electric energy injected by the parking lot is priced lower than other sources of electric energy supply, the energy stored in the electric storage source using the proposed method exceeds that of the Monte Carlo method. Additionally, in the case of electric responsive loads, the proposed method has resulted in fewer electric loads being placed compared to the Monte Carlo method, which could lead to increased satisfaction among electric energy consumers. The performance of the Purification water sources within the proposed hub model is noteworthy; due to the availability of cheaper energy, these two drinking water supply sources have outperformed the Monte Carlo method, leading to a reduction in the costs of drinking water supply. In the final section of Table 3, the results demonstrate that under the conditions of modeling the uncertainty of the parking lot using the proposed method, 680 kW less of electrical energy have been drawn from the upstream network compared to the Monte Carlo method. This reduction also lowers the final cost for ISO in providing energy carriers.

Table 4 illustrates the performance of drinking water storage sources and the output of drinking water supply sources, including the sea water treatment plant and the sour water treatment plant of the micro refinery. The results indicate that due to the more favorable pricing of electricity obtained from the parking lot in the modeling of the proposed method compared to the Monte Carlo method, the efficiency of both the sea water desalination plant and the sour water treatment plant of the micro refinery is higher in the proposed method than in the Monte Carlo method. This contributes to a reduction in the final cost. Additionally, the level of water stored in the drinking water storage source is higher in the proposed method due to the lower cost of drinking water compared to the Monte Carlo method. This factor not only reduces costs but also results in a decrease in the demand on drinking water responsive loads in the proposed method, which is less than in the Monte Carlo method, thereby enhancing customer satisfaction. However, the receipt of drinking water from the upstream network remains consistent in each district. To evaluate the performance of the proposed method in the output products of the micro refinery, Table 5 is presented for analysis.Table 4 The performance of the proposed method for drinking water storage sources and the output of drinking water supply sources compared with Monte Carlo method.

Table 4	Mc	Pr-Po	
The performance of drinking water storage source	861 m3	998 m3	
Performance of drinking water responsive loads	1616 m3	1546 m3	
Drinking water received from desalinated sea water	35831 m3	35870 m3	
Drinking water received from micro-refinery desalination plant	6459 m3	6463 m3	

Table 5 The performance of the proposed method for the output products of the micro refinery compared with Monte Carlo method.

Table 5	Mc	Pr-Po	
Responsive diesel load performance	1234 m3	1370 m3	
Diesel storage resource performance	217 m3	217 m3	
Nefta responsive load performance	1215 m3	1418 m3	
Responsive storage resource performance Nefta	353 m3	353 m3	
Responsive load performance of kerosene	915 m3	1050 m3	
Performance of kerosene storage	214 m3	214 m3	

The results of Table 5 show that the response load performance of micro-refinery output products in the condition of parking lot modeling by the proposed method is higher than the Monte Carlo method, this factor can be factors such as crude oil price, thermal input energy to energy hub and price Energy carriers are petroleum products. The set of factors presented in Table 3, Table 4, Table 5 has made the set of costs of supplying energy carriers in the conditions of modeling the uncertainty of the behavior of EV owners by the proposed method to $31670 and the set of costs obtained in the conditions of modeling the uncertainty of the presence of EV owners by the Monte Carlo method to $34,440, which results show that modeling with the proposed method leads to an 8 % reduction in the final cost of providing energy carriers by ISO.

4.2 Real world applications of the proposed framework

In recent years, the global energy crisis has prompted increased attention towards energy hub systems as a viable solution for energy management and environmental preservation. Today, parking lots are recognized as a significant source of electrical energy supply. Therefore, it is crucial to consider parking lots as an effective source for optimal energy management of energy carriers. Each electric vehicles can be viewed as a small electrical energy source, making it essential to examine the role of parking lots in energy carrier management within energy hubs. This article proposed a new method for predicting the number of electric vehicles owners present at a parking lot energy. Accurately predicting the number of electric vehicles owners at a parking lot is a critical factor in calculating the injected electrical energy by the parking lot, especially when local information for modeling is unavailable. The proposed solution in this article demonstrates that calculating the number of electric vehicles yields higher accuracy compared to methods that rely on aggregate data, such as the Monte Carlo method used for comparison in this study. The results indicate that this method not only provides accurate calculations but also reduces the overall cost of energy carriers in an energy hub system. Additionally, this modeling approach is applicable to any type of electrical network or commonly used energy carriers in real-world applications, regardless of the network type. Ultimately, the proposed approach leads to reduced utilization of upstream network energy in practical scenarios, thereby freeing up capacity within the network.

5 Conclusion

In this article, a possibility-probability model is introduced to model the uncertainty of EV owners' behavior in parking lots. The challenge faced by the researchers in this study is the absence of travel information for these EVs, which is crucial for modeling such uncertainty. To address this, a probabilistic method using incomplete data is proposed for modeling this type of uncertainty within energy hubs. In this context, the parking lot is regarded as a source of distributed electric energy generation, leveraging the capacity to inject electric energy into the hub. The energy hub model discussed in this paper consists of a micro-refinery (with consideration of three oil products, diesel, kerosene and naphtha), thermal loads, electrical and drinking loads within the city, sea freshwater basin, micro refinery sour water treatment plant, and finally parking lot. In the energy hub model considered for all the loads considered, the model of responsive loads is considered. In addition, in this study, various components such as CHP, boiler, and solar power plant are included. To ensure accurate documentation of uncertainties related to electrical demand, thermal demand, solar power plant output, drinking water demand, petroleum products demand, electrical energy price, thermal energy price and drinking water prices, oil prices, and gas prices is recommended using the Monte Carlo method. The results indicate that the electric energy injected from the parking lot into the energy hub via the Monte Carlo method amounts to 2342 kW, whereas the electric energy injected using the method proposed in this article is 3043 kW and a reduction of 668 kW in electric energy consumption. The set of factors presented in results has made the set of costs of supplying energy carriers in the conditions of modeling the uncertainty of the behavior of EV owners by the proposed method to $31670 and the set of costs obtained in the conditions of modeling the uncertainty of the presence of EV owners by the Monte Carlo method to $34,440, which results show that modeling with the proposed method leads to an 8 % reduction in the final cost of providing energy carriers by ISO.

This significant reduction underscores the potential for cost savings when employing a probabilistic approach to model the uncertainty of the number of electric vehicles in the parking lot within the energy hub. Overall, this research has offered valuable insights into the effective management and optimization of various energy sources, loads, and demands in the context of an energy hub. By accurately modeling the number of EVs, better decision-making can be facilitated, leading to enhanced resource allocation and cost efficiency. It is worth noting that there may be instances where the number of electric vehicles obtained using an alternative random method exceeds that of the method presented in this paper. This is to be expected, but the primary objective of this paper is to model the uncertainty of EV owners' behavior with greater accuracy.

Data availability

Data will be made available on request.The amount of proposed energy hub parameters [28].

Parameter	Amount	Parameter	Amount	
ηTransE	0.9	ηWDSCh	0.9	
ηEESDis	0.92	ηdc−acE	0.92	
ηEESCh	0.92	ρs	0.2	
ηCHPE	0.4	LPFUpE	0.2	
ηsea−drikE	0.92	LPFDownE	0.2	
ηCHPT	0.35	LPFUpT	0.2	
ηBoilT	0.85	LPFDownT	0.2	
ηTESDis	0.92	LPFUpW	0.2	
ηswaW	0.9	LPFDownW	0.2	
ηTESCh	0.92	πOPEES	0	
πOPDWS	0	πOPTES	0	
ηWDSDis	0.9	PCHP_maxinput	950	
PcapaTES	700	βMinEES	0.05	
PcapaWDS	900	βMaxTES	0.95	
PBoil_maxinput	900	βMinWDS	0.05	
PcapaEES	700	βMinTES	0.05	
βMaxEES	0.95	αlossEES	0.02	
σ_demands	98.2	σ_price	0.9	
βMaxWDS	0.95	αlossTES	0.02	

General indices

T	time (hour) index	S	scenario index	

Acronyms

CHP	Combined heat and power	PDF	Probability distribution function	
MILP	Mixed-integer linear program	DRP	Demand Response Programs	
EVCSs	Electric Vehicles Charging Stations	EVs	Electric Vehicles	
SDU	Seawater Desalination Units	PV	Photo Voltaic	
FDEs	Fuzzy Differential Equations	DR	Demand Response	
DRR	Demand Response Resource	MCDM	Multi-Criteria Decision Making	
overall cost of energy carriers	Final Cost Calculated by the Objective Function			

Parameters

Parameters	
ηsea−drikE	Efficiency coefficient of electric energy consumption of sea water desalination	ηCHPE	Gas to electrical energy conversion efficiency CHP	
ηCHPT	Gas to thermal energy conversion efficiency CHP	ηBoilT	Gas to thermal energy conversion efficiency Boiler	
ηTESDis	Thermal storage discharge efficiency coefficient	ηTESCh	Thermal storage charge efficiency coefficient	
ηEESDis	Electrical storage discharge efficiency	ηEESCh	Electric storage charge efficiency	
ηWDSDis	Drink water storage discharge efficiency	ηWDSCh	Drink water storage charge efficiency	
ηDieselDis	Diesel storage discharge efficiency	ηDieselCh	Diesel storage charge efficiency	
ηNaDis	Naphtha storage discharge efficiency	ηNaCh	Naphtha storage charge efficiency	
ηKeDis	Kerosene storage discharge efficiency	ηKeCh	Kerosene storage charge efficiency	
ηDieselE	Electrical efficiency of microrefinery during conversion of crude oil to diesel	ηNaE	Electrical efficiency of microrefinery during conversion of crude oil to naphtha	
ηKeE	Electrical efficiency of microrefinery during conversion of crude oil to kerosene	ηDieselT	Thermal efficiency of microrefinery during conversion of crude oil to diesel	
ηNaT	Thermal efficiency of microrefinery during conversion of crude oil to naphtha	ηKeT	Thermal efficiency of microrefinery during conversion of crude oil to kerosene	
ηDieselW	Water efficiency of microrefinery during conversion of crude oil to diesel	ηKeW	Water efficiency of microrefinery during conversion of crude oil to kerosene	
ηNaW	Water efficiency of microrefinery during conversion of crude oil to naphtha	ηDieselOil	Efficiency microrefinery during conversion of crude oil to diesel	
ηNaOil	Efficiency microrefinery during conversion of crude oil to naphtha	ηKeOil	Efficiency microrefinery during conversion of crude oil to kerosene	
ηdc−acE,Parkig_lot	DC to AC electrical energy converter efficiency parking lot	ηSourwatertreatmentplantE	Electrical efficiency of micro-refinery sour water treatment	
ηTransE	Transformer electrical efficiency	LPFHighE	the Maximum amount of electrical demand response shifted up	
ηdc−acE_solar	DC to AC electrical energy converter efficiency pv	LPFDownT	the Maximum amount of thermal demand response shifted down	
LPFDownE	the Maximum amount of electrical demand response shifted down	LPFHighT	the Maximum amount of thermal demand response shifted up	
LPFDownW	The maximum amount of drinking water demand response shifted down	αlossTES	thermal storage coefficient losses	
LPFDownKe	The maximum amount of kerosene demand response shifted down	LPFHighKe	The maximum amount of kerosene demand response shifted up	
LPFDownNa	The maximum amount of naphtha demand response shifted down	LPFHighNa	The maximum amount of naphtha demand response shifted up	
LPFDownDiesel	The maximum amount of diesel demand response shifted down	LPFHighDiesel	The maximum amount of diesel demand response shifted up	
LPFHighW	the Maximum amount of drinking water demand response shifted up	αlossEES	Electrical storage loss coefficient	
αlossWDS	Drink water storage loss coefficient	αlossKe	Kerosene storage loss coefficient	
αlossNa	Naphtha storage loss coefficient	αlossDiesel	Diesel storage loss coefficient	
αMaxKe	The kerosene storage maximum ratio	αMaxNa	The naphtha storage maximum ratio	
αMaxDiesel	The diesel storage maximum ratio	αMinKe	The kerosene storage minimum ratio	
αMinNa	The naphtha storage minimum ratio	αMinDiesel	The diesel storage minimum ratio	
αMaxTES	The thermal storage maximum ratio	αMaxEES	The decisive factor is the highest level of electric storage charge	
αMinEES	The electrical storage minimum ratio	αMinTES	The thermal storage minimum ratio	
αMinWDS	The Drink water storage minimum ratio	αMaxWDS	The Drink water storage maximum ratio	
βMinEES	The electrical storage minimum charge ratio	βMaxEES	The Electric storage maximum charge ratio	
βMinKe	The kerosene storage minimum charge ratio	βMaxKe	The kerosene storage maximum charge ratio	
βMinNa	The naphtha storage minimum charge ratio	βMaxNa	The naphtha storage maximum charge ratio	
βMinDiesel	The diesel storage minimum charge ratio	βMaxDiesel	The diesel storage maximum charge ratio	
βMinTES	The thermal storage minimum charge ratio	βMaxTES	The thermal storage maximum charge ratio	
βMaxWDS	The Drink water storage maximum charge ratio	βMinWDS	The Drink water storage minimum charge ratio	
ρs	Scenario participation coefficient S			

Binary Variables

	
It,sEES,Dis	The binary variable of energy electricity storages discharge	It,sEES,Ch	The binary variable of energy electricity storages charge	
It,sTES,Dis	The binary variable of energy thermal storages discharge	It,sTES,Ch	The binary variable of energy thermal storages charge	
It,sWDS,Dis	The binary variable of energy Drink water storages discharge	It,sWDS,Ch	The binary variable of energy Drink water storages charge	
It,sKeS,Dis	The binary variable of energy kerosene storages discharge	It,sKeS,Ch	The binary variable of energy kerosene storages charge	
It,sNaS,Dis	The binary variable of energy naphtha storages discharge	It,sNaS,Ch	The binary variable of energy naphtha storages charge	
It,sDieselS,Dis	The binary variable of energy diesel storages discharge	It,sDieselS,Ch	The binary variable of energy diesel storages charge	
It,sE,Down	The binary variable of electrical demand responses shifted down	It,sE,High	The binary variable of electrical demand responses shifted up	
It,sT,Down	The binary variable of thermal demand responses shifted down	It,sT,High	The binary variable of thermal demand responses shifted down	
It,sDW,Down	The binary variable of Drink water demand responses shifted down	It,sDW,High	The binary variable of Drink water demand responses shifted down	
It,sDiesel,Down	The binary variable of diesel demand responses shifted down	It,sDiesel,High	The binary variable of diesel demand responses shifted down	
It,sNa,Down	The binary variable of naphtha demand responses shifted down	It,sNa,High	The binary variable of naphtha demand responses shifted down	
It,sKe,Down	The binary variable of kerosene demand responses shifted down	It,sKe,High	The binary variable of kerosene demand responses shifted down	

Variables

	
Costs	Cost of energy carriers in each scenario	CostsG	Cost of receiving thermal energy from the network upstream of the energy hub	
CostsE	Cost of receiving electrical energy from the network upstream of the energy hub	CostsT	Cost of thermal energy	
CostsW	Cost of drink water energy	CostsPL	Cost of purchasing electricity from an parking lot	
CostsDiesel	The final cost of converting oil to diesel petroleum products	CostsKe	The final cost of converting oil to kerosene petroleum products	
CostsNa	The final cost of converting oil to naphtha petroleum products	CostsNaS	Cost of naphtha energy storages	
CostsEES	Cost of electrical energy storages	CostsDWS	Cost of drink water storages	
CostsDieselS	Cost of diesel energy storages	CostsTES	Cost of thermal energy storages	
CostsKeS	Cost of kerosene energy storages	CostSFlexibilityDR,Ke	Cost of kerosene flexibility responsive loads	
CostSFlexibilityDR,Diesel	Cost of diesel flexibility responsive loads	CostSFlexibilityDR,Na	Cost of naphtha flexibility responsive loads	
CostSFlexibilityDR,E	Cost of electrical flexibility responsive loads	CostSFlexibilityDR,T	Cost of thermal flexibility responsive loads	
CostSFlexibilityDR,DW	Cost of drink water flexibility responsive loads	Pt,sE,net	The share of electrical energy input to the energy hub from the upstream grid	
PsE,De	The electrical demand of energy hub at time t and scenario s			
Pt,sE,DR	Electrically Responsive Load	Pt,sKe,DR	kerosene Responsive Load	
Pt,sT,DR	Thermal Responsive Load	Pt,sDW,DR	Drink water Responsive Load	
Pt,sDiesel,DR	Diesel Responsive Load	Pt,sNa,DR	naphtha Responsive Load	
Pt,sT,Boil	Thermal output power by the boiler	Pt,sW,net	The amount of drink water energy input to the energy hub	
Pt,sE,EV	The output power of the Parking lot	Pt,sT,net	The amount of thermal energy input to the energy hub	
Pt,sEES,Dis	The amount of discharge level in the electrical storage	Pt,sEES,Ch	The amount of charge level in the electrical storage	
Pt,sTES,Dis	The amount of discharge level in the thermal storage	Pt,sTES,Ch	The amount of charge level in the thermal storage	
Pt,sDWS,Dis	The amount of discharge level in the drink water storage	Pt,sDWS,Ch	The amount of charge level in the drink water storage	
Pt,sDiesel,Dis	The amount of discharge level in the diesel storage	Pt,sDiesel,Ch	The amount of charge level in the diesel storage	
Pt,sNa,Dis	The amount of discharge level in the naphtha storage	Pt,sNa,Ch	The amount of charge level in the naphtha storage	
Pt,sKe,Dis	The amount of discharge level in the kerosene storage	Pt,sKe,Ch	The amount of charge level in the kerosene storage	
PsDiesel,De	The diesel demand of energy hub at time t and scenario s	PsKe,De	The kerosene demand of energy hub at time t and scenario s	
Pt,sE,Down	Reduced electrical responsive loads	PsNa,De	The naphtha demand of energy hub at time t and scenario s	
Pt,sOil,net	Crude oil imported into the microrefinery	Pt,sOil,Diesel	Crude oil converted to diesel in a microrefinery	
Pt,sOil,Ke	Crude oil converted to kerosene in a microrefinery	Pt,sOil,Na	Crude oil converted to naphtha in a microrefinery	
Pt,sDiesel	Diesel received from micro refinery	Pt,sNa	Naphtha received from micro refinery	
Pt,sKe	Kerosene received from micro refinery	Pt,sW,Sourwatertreatmentplant	Refined sour water from the micro-refinery	
Pt,sE,High	Incremental electrical responsive load	Pt,sE,solar	Electric power received from a solar power plant at time t and scenario s	
PnetmaxG	The maximum input power of gas energy to the energy hub	Pt,sG,CHP	The amount of gas required CHP	
Pt,sW,De	The drink water demand of energy hub	Pt,sW,sea	Receiving seawater (sweetener water input to energy hub)	
Pt,sW,Down	Decreasing drink water responsive load	Pt,sW,High	Incremental drink water responsive load	
Pt,sDiesel,Down	Reduced diesel responsive loads	Pt,sDiesel,High	Increased diesel responsive loads	
Pt,sKe,Down	Reduced kerosene responsive loads	Pt,sKe,High	Increased kerosene responsive loads	
Pt,sNa,Down	Reduced naphtha responsive loads	Pt,sNa,High	Increased naphtha responsive loads	
Pt,sG,net	The amount of gas entering the energy hub	Pt,sG,B	The amount of gas required boiler	
PsT,De	The thermal demand of energy hub	Pt,sT,Down	Decreasing thermal responsive load	
Pt,sT,High	Incremental thermal responsive load	Pt,sEES,S	electrical Energy Storages	
Pt,sEES,loss	Level of electrical storage losses	Pt,sTES,S	Thermal Energy Storages	
Pt,sTES,loss	Level of thermal storage losses	Pt,sWDS,S	Drink water Energy Storages	
Pt,sDiesel,loss	Level of diesel storage losses	Pt,sKe,loss	Level of kerosene storage losses	
Pt,sNa,loss	Level of naphtha storage losses	PcapaEES	The amount of drink electrical energy stored level	
Pt,sDiesel,S	Diesel Energy Storages	Pt,sNa,S	Naphtha Energy Storages	
Pt,sKe,S	kerosene Energy Storages	PcapaNaS	The amount of naphtha stored level	
PcapaTES	The amount of thermal energy stored level	PcapaWDS	The amount of drink water energy stored level	
PcapaKeS	The amount of kerosene stored level	PcapaDieselS	The amount of diesel stored level	
πt,sE,net	Purchased electrical energy Price	πt,sG,net	Purchased gas energy Price	
πt,sT,net	Purchased thermal energy Price	πt,sW,net	Purchased drink water energy Price	
πt,soil,net	Purchased crude oil energy Price	ϑocc−oil−Diesel	Operator cost of converting crude oil to diesel	
ϑocc−oil−Na	Operator cost of converting crude oil to naphtha	ϑocc−oil−Ke	Operator cost of converting crude oil to kerosene	
πOPEES	Electrical storage operation price	πOPTES	Thermal storage operation price	
πOPDiesel	Diesel storage operation price	πOPNa	Naphtha storage operation price	
πOPKe	Kerosene storage operation price	Psour_water_maxW	The maximum amount of treated sour water, output of the micro-refinery	
PnetmaxOil	Maximum amount of crude oil input to the hub	PmaxDiesel	The maximum amount of diesel output of the micro refinery	
πOPDWS	Drink water storage operation price	πtEV	Purchased electric vehicles energy Price	
PmaxNa	The maximum amount of naphtha output of the micro refinery	PmaxKe	The maximum amount of kerosene output of the micro refinery	
PnetmaxE	Maximum amount of electrical energy input to the hub	PTransinput	Maximum amount of electrical input energy of the transformer	
PnetmaxT	Maximum amount of thermal energy input to the hub	PBoil_maxinput	Maximum boiler power	
PCHP_maxinput	Maximum CHP power	PnetmaxW	Maximum amount of drink water input to the hub	
Psea_maxW	Max Receiving seawater (sweetener water input to energy hub)			

Table Software performance at the time of optimization

Computational parameter	Detail	
Optimization	GAMS	
Solver	Cplex	
Relative gap	0.00	
Absolute gap	0.00	
Computational time	19.2s	
MILP status	Optimal	

CRediT authorship contribution statement

Saeed Jafari: Writing – original draft, Supervision, Software, Resources, Project administration, Methodology, Formal analysis, Data curation, Conceptualization. Mojtaba Najafi: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Naghi Moaddabi Pirkolachahi: Writing – review & editing, Visualization, Validation. Najmeh Cheraghi Shirazi: Writing – review & editing, Visualization, Validation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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