Modeling and Optimization of Energy Hubs: A Comprehensive Review

Abstract

The concept of energy hubs has grown in prominence as a part of future energy systems, driven by the spread of Distributed Energy Resources (DERs) and the inception of the smart grid. This paper systematically reviews 200 articles about energy hubs, published from 2007 to 2017, and summarizes them based on their modeling approach, planning and operation, economic and environmental considerations, and energy hub applications. The common applications of energy hubs are considered, such as distributed energy resources, the consideration of Plug-in Hybrid Electric Vehicles (PHEVs), and the hydrogen economy. This paper examines modeling approaches towards energy hubs, including storage and its network models; it mentions some of the optimization strategies used to tackle the efficient operation and control of energy hubs. The novelty of this work lies in the classification of research papers related to energy hubs, the development of a generic framework for modeling these multiple energy flow carriers with storage and network considerations, and the provision of solution techniques in line with energy hub optimization.

1. Introduction

Historically, synergy in energy systems has been of interest for decades, and several studies have addressed problems in synergistic optimal energy carriers. The energy hub approach, also known as multi-energy systems, has played a vital role in addressing such problems, and many researchers have utilized this methodology and extended this concept in modeling, optimization, and application. This review paper aims to organize and classify literature regarding multi-energy systems or “energy hubs”, whilst identifying research gaps in this field of study. Moreover, this paper recommends new areas for further research as the subject matter will continue to develop significantly in the years to come.

In 2002, a research project entitled “Vision of Future Energy Networks (VoFEN)” was introduced, with the purpose of creating an optimal energy infrastructure for the target year of 2050 [1]. The project focused on developing a generic model and an analysis framework. In 2005, the same team introduced the concepts of energy hubs (EH) and energy interconnectors (EI) [2,3]. The latter, though not within the scope of this study, were proposed as an application in multiple energy carrier transmission [4]. The research was carried out envisioning the difficulty of making traditional systems economically and environmentally sustainable [2,5]. By considering these bridging elements (i.e., energy hubs and interconnectors), Geidl et al. [4] believed that current sub-optimal energy systems can be transitioned to optimal systems.

1.1. What is An “Energy Hub”?

Literature has referred to energy hubs as multi-energy systems, multiple energy carrier systems, multi-source multi-product systems, combined/hybrid energy systems, hybrid poly-generation energy systems, and distributed multi-generation systems. These hybrid energy systems can be described as integrated energy systems that consist of energy generation, conversion, and storage systems [6]. They are also defined as an interface between energy producers and consumers that are used to couple multiple energy carriers to meet different types of demands [1]. An energy hub receives inputs from various energy vectors. It is defined as a method to move and store energy, and includes, but is not limited to, electricity, natural gas (NG), heat, hydrogen, biogas, and liquid petroleum and alcohol fuels. Within such a hub, energy may be generated or transformed with technologies, such as wind turbines, solar photovoltaics, solar thermal technology, combined heat and power plants (CHP), heat exchangers, furnaces and boilers, and electrochemical devices, such as fuel cells. Energy can be stored in technologies, such as batteries, flywheels, and compressed air energy storage (CAES) systems in the form of hydrogen, or in thermal devices and arrays [7]. Energy hubs have been a topic of growing interest since their introduction by Geidl et al. in 2005 [6].

1.2. Significance

Current energy systems lack the following abilities: to accommodate increased future energy demand and to allow the integration of a large fleet of distributed energy resources (DERs) whilst meeting increasingly stringent environmental regulations [1]. They fail to manage the distribution of power based on user consumption at a regional scale, as well as the scale of small communities [8]. Additionally, concerns about energy efficiency are growing, as poly generation energy systems and decentralized generation technologies attract attention; thus, more flexible energy infrastructure is needed in terms of operation and distribution [8,9,10].

The Greenfield approach, used in other fields of study, advocates a strategy for designing future energy systems that eliminates constraints set by previous energy systems. Different forms of energy may be bridged together to establish synergism, as a fundamental step towards an optimum state. The linking of multiple energy carriers in centralized units was proposed in the early literature [1,4], i.e., energy hubs, where different forms of energy vectors may undergo transformation, conversion, and storage for later use. Devising and utilizing such bridging systems may lead to an optimal level of operation for energy systems. Figure 1 presents a schematic view for the transition to future energy systems.

This paper aims to organize and classify the literature regarding multi-energy systems or “energy hubs”, whilst identifying research gaps in this field. Although some studies discuss the concept of energy hubs, a clear knowledge gap exists when reviewing modeling and optimization approaches. Moreover, these papers often fail to build upon the work carried out on the common theme of applications of smart energy systems. Therefore, this review paper is written to provide readers with comprehensive and clear insight into energy hubs and to uncover future research concepts.

2. Literature Classification of Energy Hubs

This section aims to organize and classify literature regarding multi-energy systems or “energy hubs”, whilst identifying research gaps in this field of study. Figure 2 shows a concept map that outlines the areas highlighted in this paper.

This review is comprised of three main parts: (i) introduction, (ii) modeling, and (iii) optimization. Along with the definition of an energy hub and an overview of its research initiation, the article classifies the literature to date. As evident from Figure 2, the research focuses on (a) planning and operation, (b) economic and environmental impacts, and (c) multiple applications of energy hubs. Each area is explored in detail.

Since the introduction of optimal multiple energy carrier systems, numerous studies have explored modifying and further developing them to enhance their reliability and control [11,12,13,14]. The concept of the energy hub has been applied across different regions and fields of study [15,16,17]. Planning of energy hub networks and their operation has been the focus of several research projects [18,19,20,21], especially for aspects pertaining to economics and the environment [22,23,24]. In addition, recent studies have looked at the concepts of an energy internet, smart energy hubs, virtual power plants, and smart grids based on the energy hub approach [25,26,27,28,29,30,31].

Table 1. List of studies that review the energy hub concept.

Paper	Area of Focus	Reference
Geidl et al. (2007)	Energy hubs	[1]
Geidl et al. (2006)		[2]
Favre-Perrod (2005)		[3]
Geidl et al. (2007)		[4]
Krause et al. (2011)		[32]
Mohammadi et al. (2017)		[33]
Phdungsilp and Martinac (2016)	DER/DES	[34]
Mancarella (2014)		[35]
Chicco and Mancarella (2009)		[36]
Howell et al. (2017)		[37]
Houwing et al. (2006)		[38]
Alizadeh et al. (2016)	Renewable energy integration	[39]
Favre-Perrod et al. (2009)		[40]
Liserre et al. (2010)		[41]
Liu et al. (2014)	CCHP/CHP Integrated gas and electricity	[42]
Rubio et al. (2008)		[43]
Rubio-Barros et al. (2010)		[44]
Lund et al. (2016)		[45]
Mancarella et al. (2016)	Modeling/simulation	[46]
Allegrini et al. (2015)		[47]
Chiang and Zavala (2016)	Control	[48]
Rong and Su (2017)	Planning and optimization	[49]
Rubio-Barros et al. (2012)		[18]
van Beuzekom et al. (2015)		[50]
Klöckl et al. (2005)	Need and impact of energy hubs	[51]
Shabanpour-Haghighi and Seifi (2016)		[52]

lists review publications that discuss the concept of energy hubs within their study. However, when reviewing modeling and optimization approaches, a knowledge gap is evident.

In the following sections, relevant studies discussing the concept of energy hubs are chronologically listed in tables. These tables show the type of technologies and the energy vectors considered in the authors’ literature survey and indicate whether storage technologies and energy hub networks were considered. Some studies may cover more than one area; however, they are listed only once in the area they are most closely associated with.

Table 2. Table of abbreviations/acronyms used within classification tables.

Transormation and Generation Technologies
CHP	Combined heat and power systems
Micro	Microgrid
Solar	Solar energy
Wind	Wind energy
Hydro	Hydropower
Energy Vectors
Elec	Electricity
NG	Natural Gas
Heat	(District) Heat
Bio	Biomass/biofuel
H2	Hydrogen
Network	A network of energy hubs considered
Storage	Storage technologies such as hydrogen batteries

lists the acronyms and abbreviations used in this paper.

2.1. Planning and Operation

According to the classification, more than 150 studies are relevant to this aspect. When examining the issue of the planning and operation of multiple energy systems, there are several factors that must be considered:

• The size or/and capacity of each convertor and/or storage technology within energy hubs;
• The type of conversion and storage technologies to be implemented within hubs;
• The control methodology of power flow within energy hubs.

These characteristics not only govern the overall operational efficiency of the energy system in general, but they also specifically determine the reliability of the system when subjected to an increasing load.

One of the earliest studies on the operation planning of synergistic systems using energy hubs was conducted by Unsihuay et al. [53]. The work aimed to minimize the operation costs for an integrated hydrothermal and gas system. Another study, conducted by Robertson et al. [54], outlined energy infrastructure for the UK, as it progressed towards a lower-carbon economy. It employed the energy hub approach to determine the framework that would allow the most effective conversion and transfer of energy. Galus and Andersson [55] carried out research focusing on planning the integration of plug-in hybrid electric vehicles (PHEVs) into energy hub networks; driving behavior was simulated and different conditions pertaining to vehicle usage were explored.

2.1.1. Scheduling

The scheduling of energy hubs is important in integrating energy systems, tackling energy shortages, lessoning environmental impacts [56], and reducing operational costs [21,57]. As multiple energy carriers enter an energy hub, deciding what type of source of energy will meet the specific load can be challenging. If intermittent sources of energy are involved (commonly renewables), effective planning can reduce the operational costs and harmful greenhouse gas (GHG) emissions, while ensuring reliability of the energy systems.

Table 3. List of studies conducted on the scheduling of multi-energy carrier systems.

Reference	Paper	Technology			Energy Vectors				Network	Storage
		CHP	Solar	Wind	Elec	NG	Heat	Bio
[57]	Pazouki and Haghifam (2013)	✔		✔	✔	✔	✔			Y
[58]	Pazouki et al. (2013)	✔			✔	✔	✔	✔		Y
[59]	Haghifam et al. (2013)	✔		✔	✔	✔	✔			Y
[21]	Pazouki et al. (2013)	✔		✔	✔	✔	✔			Y
[60]	Rastegar and Fotuhi-Firuzabad (2014)	✔			✔	✔	✔			Y
[61]	Pazouki (2015)	✔	✔		✔	✔	✔			Y
[62]	Xu et al. (2015)	✔	✔		✔	✔	✔		✔	N
[63]	Ramírez-Elizondo and Paap (2015)	✔		✔	✔	✔	✔			Y
[64]	Vaccaro et al.(2015)	✔			✔	✔	✔			N
[65]	Moghaddam et al. (2016)	✔			✔	✔	✔			Y
[66]	Pazouki and Haghifam (2016)	✔		✔	✔	✔	✔			Y
[67]	Morvaj et al. (2016)	✔			✔	✔	✔		✔	Y
[68]	Zidan and Gabbar (2016)	✔	✔	✔	✔	✔	✔			N
[69]	Moghaddam et al. (2016)	✔			✔	✔	✔			Y
[70]	Pazouki (2016)	✔	✔		✔	✔	✔			Y
[71]	Moghaddam et al. (2016)	✔			✔	✔	✔			Y
[56]	Fan et al. (2016)	✔			✔	✔	✔			Y
[72]	Baghaee et al.(2016)		✔	✔	✔					Y
[73]	Zlotnik et al. (2017)	✔			✔	✔	✔		✔	N
[74]	El-Zonkoly (2017)	✔			✔	✔	✔			Y
[75]	Dolatabadi and Mohammadi-Ivatloo (2017)	✔		✔	✔	✔	✔			Y
[76]	Chen et al. (2017)	✔		✔	✔	✔	✔		✔	N

summarizes the publications on the scheduling of energy systems based on the concept of the energy hub.

Pazouki et al. conducted several studies on the scheduling of energy hubs, including a case study on an urban area in North-West Iran [21,57,58,61]. Economic scheduling resulted in the reduction of operational costs, an improvement in reliability, and a decrease in greenhouse gas emissions [21,57,58,61,68]. In another study, Moghaddaam et al. [65] presented a comprehensive profit-based model that allows the self-scheduling of energy hubs; the model was capable of adopting complex strategies, considering the cost of electricity and natural gas to maximize profit with a great accuracy and the potential of exchanging electricity with the grid. However, operation-scheduling always entails various sources of uncertainty. Vaccaro et al. [64] stated that these uncertainties mainly arise from the following: (i) unpredictable dynamics of energy prices, (ii) randomness of energy hub loads, and (iii) renewable energy converters. Nevertheless, the results obtained by Zidan et al. [68] showed significant enhancement in terms of emission reduction and reliability with the addition of renewable energy sources.

2.1.2. Control

Since hybrid energy systems are dynamic and susceptible to uncertainties, the need for communication and controller surfaces to ensure an effectively coordinated operation. These controllers are expected to adapt to changes in loads, based on the system dynamics and operational constraints [77]. Additionally, they keep these uncertainties within acceptable levels by using storage devices [78].

Intermittent renewable sources of energy are often termed energy vectors in the modeling of energy hubs [21,29]. However, as these sources of energy fail to provide a steady amount of energy throughout the year, the imbalance is either met by purchasing electricity off the grid or by backup generators [78]. Therefore, energy storage systems within hubs work as an asset that allows better control and, by extension, a more reliable, cost-effective energy system [77,78]. Approximately 50 of the publications reviewed modeled energy hubs with controllers and studied their effect on system performance. Several considered a model predictive control (MPC) approach, because MPCs allow flexible operations by self-adjusting their control definition based on controller objectives, operational constraints, and operating conditions.

Table 4. List of research studies with a focus on control technology in energy hubs.

Reference	Paper name	Technology				Energy Vectors					Network	Storage
		CHP	Micro	Solar	Wind	Elec	NG	Heat	Bio	H2
[79]	Arnold et al. (2008) – 1					✔	✔	✔			✔	N
[80]	Adamek (2008)	✔		✔	✔	✔	✔	✔	✔		✔	N
[81]	Arnold et al. (2008) – 2	✔		✔	✔	✔	✔	✔		✔	✔	N
[82]	Carradore and Turri (2009)	✔				✔		✔			✔	N
[83]	Ramirez-Elizondo and Paap (2009)	✔				✔	✔	✔				N
[77]	Arnold et al. (2009)	✔				✔	✔	✔			✔	Y
[84]	Barsali et al. (2009)	✔				✔	✔	✔				Y
[85]	Carradore and Turri (2009)	✔				✔	✔	✔			✔	Y
[86]	Negenborn et al. (2009)	✔				✔	✔	✔			✔	Y
[13]	Galus et al. (2010)	✔			✔	✔	✔	✔			✔	Y
[14]	Ulbig et al. (2010)					✔	✔			✔		Y
[87]	Arnold and Andersson (2010)	✔		✔		✔					✔	Y
[88]	Ramirez-Elizondo et al. (2010)	✔				✔	✔	✔				Y
[89]	Arnold et al (2010)					✔	✔	✔			✔	Y
[90]	Velez (2010)	✔			✔	✔	✔	✔				N
[91]	Almassalkhi and Hiskens (2011) – 1				✔	✔	✔	✔				Y
[92]	Almassalkhi and Hiskens (2011) – 2	✔			✔	✔	✔	✔			✔	Y
[93]	Parisio et al. (2011)	✔				✔	✔	✔		✔		Y
[78]	Arnold and Andersson (2011)	✔				✔	✔	✔			✔	Y
[94]	Sheikhi et al. (2011)	✔				✔	✔	✔				N
[95]	Arnold (2011)	✔				✔	✔	✔			✔	Y
[96]	Velez (2011)	✔			✔	✔	✔	✔				Y
[97]	Ulbig et al. (2011)	✔			✔	✔	✔	✔			✔	Y
[98]	Akgun and Cakmakci (2012)	✔				✔	✔	✔				Y
[19]	Galus et al. (2012)					✔	✔	✔			✔	Y
[99]	Pazouki et al. (2013)	✔		✔	✔	✔	✔	✔				Y
[59]	Haghifam et al. (2013)	✔			✔	✔	✔	✔				Y
[100]	Almassalkhi (2013)				✔	✔	✔	✔			✔	Y
[101]	Yu et al. (2014)	✔				✔	✔	✔				Y
[102]	Moeini-Aghtaie et al. (2014)	✔			✔	✔	✔	✔			✔	N
[103]	Soroudi et al. (2014)	✔			✔	✔	✔					Y
[104]	Kampouropoulos et al. (2014)	✔				✔	✔	✔				N
[105]	S. Moazeni et al. (2015)		✔		✔	✔						Y
[106]	Skarvelis-Kazakos et al. (2015)	✔				✔	✔	✔		✔	✔	Y
[107]	Moeini-Aghtaie et al. (2015)	✔			✔	✔	✔	✔				Y
[108]	Mitchell and Skarvelis-Kazakos (2015)	✔				✔		✔	✔			N
[109]	Rastegar et al. (2015)	✔				✔	✔	✔				Y
[110]	Salimi et al. (2015)	✔				✔	✔	✔			✔	Y
[62]	Xu et al. (2015)	✔	✔	✔		✔	✔	✔				Y
[20]	Pazouki et al. (2016)	✔			✔	✔	✔	✔				Y
[111]	Skarvelis-Kazakos et al. (2016)	✔		✔	✔	✔	✔	✔			✔	Y
[112]	Teng et al. (2016)	✔		✔	✔	✔	✔	✔				Y
[113]	Hashemi et al. (2016)	✔			✔	✔	✔	✔				Y
[114]	Hernández-Hernández et al. (2017)		✔	✔		✔						Y
[115]	Liu et al. (2017)	✔				✔	✔	✔				Y
[116]	Hernández-Hernández et al. (2017)		✔	✔		✔		✔				Y
[117,118]	Baghaee et al. (2017)		✔	✔	✔	✔				✔		Y

demonstrates the relevant studies that focused on control technology used in integrated energy systems.

Arnold et al. [77] applied the MPC approach to a network of energy hubs and observed a decrease in the total operational costs, coupled with an increase in the computational efforts with longer prediction intervals. Almassalkhi [100] implemented a receding-model predictive controller (RHMPC) for the transmission of electricity involving renewables and storage systems. Del Real et al. [24] adopted a Lagrange-based distributed model predictive control (DMPC) framework that aids in the economic dispatch of smart grids based on the networks of energy hubs.

Existing literature on energy hub operation management often assumes a perfect forecast of prices and different types of demand [78,119]. Hence, uncertainty and stochastic conditions of these inputs over time are not usually accounted for when looking for optimal operation decisions. When all exogenous input variables such as demands and prices are assumed to be certain (which can be the case if the uncertainties are hedged by contracts such as forward contracts for prices), the optimal control of energy hubs can be computed by deterministic optimization, such as mixed integer linear/non-linear programming (MILP/MINLP) models. The authors of [120] considered an energy hub with a variety of electricity, heat and hydrogen generating plants, and energy storage devices to serve uncertain electricity and heat loads over a finite time horizon, in the presence of real-time uncertain prices. They modeled uncertainties in loads and prices by stochastic processes and developed a stochastic dynamic programming formulation for the energy hub operation management problem. This optimization model is aimed at obtaining a sequence of decision rules for the entire time horizon that adapts to the realized information at any time step. In this closed-loop optimization approach, decisions at any time step are readily derived by applying the decision rule for the system state, e.g., storage levels, and exogenous variables, such as demands and prices, at that time step. For systems involving multiple storage units and exposed to various sources of uncertainty, which is often the case for energy hubs, the dimension of the state variable is too high to solve the resulting dynamic programming optimization exactly. In this context, approximate dynamic programming (ADP) approaches seem appropriate. However, ADP approaches are not amenable to risk-averse considerations by the energy hub manager/controller. The importance of risk considerations when managing an energy system in the presence of uncertainty is discussed in [105]. Therefore, to compute a risk-averse dynamic energy hub operation management solution in [120], an ADP approach based on direct policy search and cost function approximations, proposed in [121,122], was adopted. This framework is capable of handling various operational and physical constraints, as well as a risk-averse objective function. The authors of [123] also proposed a new modeling approach for minimum uptime/downtime constraints of some assets within their proposed dynamic optimization framework, when the traditional methods for modeling these constraints fail.

2.1.3. Assessment

The assessment of flexible factors, such as hourly solar irradiation or wind speed within an energy hub, is crucial in the design and operation of processes [124]. Based on the outcome, scheduling may be carried out, and controllers may be added to a particular energy system. Upon implementation, the system can be further evaluated in terms of performance, economic, and environmental feasibility. Specifically, it may aid in examining the individual effects of each variation introduced into the system.

An assessment framework designed by Fabrizio et al. [124] utilized an hourly model to assess the performance of an entire system, and the integrated utilization of energy resources. Rather than modeling the dynamic nature of the system, they observed the differences between two successive states of operation under steady-state conditions [124]. With this data, they determined the layout and sizing of energy converters, as well as other components.

Table 5. Evaluation studies conducted on multi-energy carrier systems.

Reference	Paper	Technology					Energy Vectors					Network	Storage
		CHP	Micro	Solar	Wind	Hydro	Elec	NG	Heat	Bio	H2
[124]	Fabrizio et al. (2009)			✔			✔	✔	✔				Y
[125]	Martinez-Mares and Fuerte-Esquivel (2012)						✔	✔				✔	N
[126]	Anderson et al. (2013)	✔		✔	✔		✔	✔	✔			✔	N
[127]	Martinez-Mares and Fuerte-Esquivel (2013)				✔	✔	✔	✔	✔				N
[128]	Giaouris et al. (2013)		✔	✔	✔						✔	✔	Y
[129]	Orehounig et al. (2014)			✔		✔	✔		✔	✔			N
[130]	Xu et al. (2015)	✔	✔	✔	✔		✔	✔	✔	✔	✔	✔	N
[131]	Perera et al. (2015)			✔	✔		✔	✔	✔			✔	Y
[132]	Liu and Mancarella (2016)	✔					✔	✔	✔				N
[133]	Shabanpour-Haghighi and Seifi (2016)	✔					✔	✔	✔			✔	N
[134]	Pazouki and Haghifam (2016)	✔					✔	✔	✔				N
[135]	Shariatkhah et al. (2016)	✔					✔	✔	✔				N
[136]	Abeysekera (2016)	✔					✔	✔	✔				Y
[137]	Moeini-Aghtaie et al. (2017)	✔			✔		✔	✔	✔				Y
[138]	Ma et al. (2017)	✔	✔	✔	✔		✔	✔	✔				Y
[139]	Morvaj et al. (2017)	✔		✔			✔	✔	✔				Y

presents the literature in this field.

2.2. Economic and Environmental Considerations

Economic improvement and greenhouse gas mitigation are the significant intended outcomes of future energy systems. The focus of several studies in the literature surveyed was an evaluation of an energy hub system based on economic and environmental aspects. The energy systems were modeled using the energy hub approach and the results were then compared to previous case studies or present reality.

2.2.1. Economics and Financials

In the economic assessment of multiple energy carrier systems, the cost of available energy resources is one of the focal points of the study. Feasibility studies can be carried out to determine the viability of using a particular energy source, with or without an energy hub framework. On the other hand, the economic impact of a particular schedule, controller, or any other adjustment can be observed. In addition, models have been developed to devise energy systems economically whilst considering changes in energy prices and the future energy demand. Many of these studies have been listed in

Table 6. List of studies that include economic considerations.

Reference	Paper Name	Technology				Energy Vectors					Network	Storage
		CHP	Solar	Wind	Hydro	Elec	NG	Heat	Bio	H2
[140]	Egli (2007)					✔	✔	✔			✔	N
[81]	Arnold et al. (2008)	✔	✔	✔		✔	✔	✔		✔	✔	N
[141]	Iggland and Kienzle (2008)		✔	✔	✔	✔	✔	✔	✔		✔	N
[142]	Kienzle and Andersson (2014)	✔				✔	✔	✔	✔			N
[22]	Fabrizio et al. (2009)	✔	✔	✔	✔	✔	✔	✔	✔	✔	✔	N
[143]	Schulze and Del Granado (2009)	✔	✔	✔		✔	✔	✔	✔		✔	N
[144]	Kienzle (2010)	✔				✔	✔	✔	✔		✔	Y
[145]	Kienzle and Andersson (2010)	✔				✔	✔	✔			✔	Y
[146]	Shireen and Patel (2010)		✔			✔						Y
[147]	Favre-Perrod et al. (2010)					✔	✔				✔	N
[148]	Schulze et al. (2010)					✔		✔			✔	Y
[149]	Zafra-Cabeza et al. (2010)	✔		✔		✔		✔		✔		Y
[150]	Kienzle et al. (2011)	✔				✔	✔	✔	✔			Y
[151]	Ranjbar et al. (2011)	✔				✔	✔	✔				Y
[152]	Fabrizio (2011)	✔	✔			✔	✔	✔				N
[119]	Sheikhi et al. (2012)	✔				✔	✔	✔				Y
[153]	Bahrami and Safe (2013)	✔				✔	✔	✔				Y
[21]	Pazouki et al. (2013)	✔		✔		✔	✔	✔				Y
[154]	Adamek et al. (2014)	✔				✔	✔	✔			✔	Y
[102]	Moeini-Aghtaie et al. (2014)	✔		✔		✔	✔	✔			✔	N
[155]	Le Blond et al. (2014)		✔			✔	✔	✔				Y
[27]	Rayati et al. (2015)	✔				✔	✔	✔				Y
[156]	Maroufmashat et al. (2015)	✔				✔	✔	✔			✔	Y
[157]	Kamyab and Bahrami (2016)	✔	✔			✔	✔	✔			✔	Y
[158]	Moghaddam et al. (2016)	✔				✔	✔	✔			✔	N
[159]	Facchinetti and Sulzer (2016)											N
[160]	Sheikhi et al. (2016)	✔				✔	✔	✔				Y
[161]	Beigvand et al. (2017)	✔				✔	✔	✔			✔	N
[162]	Majidi et al. (2017)	✔		✔	✔	✔	✔	✔				Y
[163]	Li et al. (2017)	✔	✔			✔	✔	✔				Y
[164]	Rafea (2017)	✔		✔		✔	✔	✔		✔		Y
[165]	Sharif et al. (2014)	✔	✔	✔		✔	✔	✔	✔			Y

.

Fabrizio et al. [22] carried out research to establish economic and environmental objectives and investigated their trade-offs. In another study by Fabrizio, the economic feasibility of applying the energy hub framework to health-care facilities was investigated in multiple scenarios. Schulze and Del Granado [143] concluded that feed-in tariffs to promote renewable energy were an effective methodology to increase overall benefits while satisfying the energy demand [140,141,142,143]. A study by Barsali et al. [84] investigated the viability of energy storage systems based on energy tariff changes across different hours of the day.

Kienzle [144] developed a model to optimize a portfolio of energy investments, applying the mean variance portfolio theory. He [142] also presented a method of evaluating energy hubs under uncertainty. Instead of utilizing historical price data as the basis for financial analysis, a Monte Carlo approach was used to account for policy and technology changes. Kienzle et al. [150] extended the Monte Carlo approach to incorporate demand-side management (DSM) of loads.

Maniyali et al. [166] formulated an energy hub model which incorporates nuclear energy and hydrogen storage, in addition to wind, solar, and biomass energy. Detailed analysis was conducted on the minimal cost scenario, minimal emissions scenario, and hydrogen economy scenario.

Sharif et al. [165] adapted the energy hub model to use natural gas as the main energy source to be supplemented by wind and solar energy as well as hydrogen energy storage. They developed a model in General Algebraic Modeling Software (GAMS) and considered three scenarios: a baseline single energy carrier scenario, a multi-energy carrier scenario, and a multi-energy carrier scenario with energy storage. The third scenario produced both the lowest cost and emissions.

2.2.2. Emissions

In recent years, aside from being more cost-competitive, renewable energy systems have also become technically feasible for small domestic applications, such as solar charging stations and thermal desalination processes [167,168]. Many research studies carried out the integration of renewable energy sources (RES) with the existing power grid and electricity markets [169]. Another major advantage of using renewables over non-renewables is the immense reduction of GHGs and water pollution [170]. Despite a study which argued that renewable energy sources, specifically hydropower, are not entirely "clean” and do have associated environmental impacts [171], the positive impact of renewables on the environment is a force to be reckoned with. Yet, according to statistics reported by the International Energy Agency (IEA) in 1998, fossil-based power generation systems emitted roughly 60–100 times more GHG emissions per kWh than those of renewables [172]. Several studies couple techno-economic feasibility research with the study of the environmental impacts of multiple energy systems. Some of them are given in

Table 7. List of research papers that include environmental considerations.

Reference	Paper name	Technology				Energy Vectors					Network	Storage
		CHP	Solar	Wind	Hydro	Elec	NG	Heat	Bio	H2
[173]	Chicco and Mancarella (2008)	✔										N
[22]	Fabrizio et al. (2009)	✔	✔	✔	✔	✔	✔	✔	✔	✔	✔	N
[174]	Galus et al. (2009)					✔	✔	✔			✔	N
[23]	Dai and Wang (2009)	✔				✔	✔	✔			✔	N
[155]	Le Blond et al. (2014)		✔			✔	✔	✔				Y
[175]	Orehounig et al. (2014)	✔	✔		✔	✔	✔	✔	✔		✔	Y
[156]	Maroufmashat et al. (2015)	✔				✔	✔	✔			✔	Y
[176]	LI et al. (2016)	✔	✔	✔		✔	✔	✔				Y
[177]	Fuentes-Cortés et al. (2016)	✔				✔	✔	✔	✔			Y
[34]	Phdungsilp and Martinac (2016)											-
[139]	Morvaj et al. (2017)	✔	✔			✔	✔	✔				Y
[162]	Majidi et al. (2017)	✔		✔	✔	✔	✔	✔				Y
[164]	Rafea (2017)	✔		✔		✔	✔	✔		✔		Y

.

Energy hubs can reduce emissions related to energy production and transmission since they can integrate multiple renewable energy carriers. Orehounig et al. [175] investigated the integration of renewable energies for a small village using the energy hub concept. They conducted further studies regarding the implementation of energy systems in the same village, including retrofitting buildings and neighboring. Similar to their previous study, they simulated a set of scenarios and found that the best performing scenario had an 86% reduction in carbon emissions [175].

Chicco and Mancarella focused on the energy and environmental evaluation of poly-generation systems, powered by natural gas [173]. An indicator was developed to assess the energy systems according to environmental factors. Moreover, it can aid policy makers to cultivate financially-motivated tactics to help mitigate CO₂ emissions [173]. Galus et al. [174] designed a framework for plug-in hybrid electric vehicles (PHEVs), using the energy hub approach to forecast a region-wide CO₂ emission decrease.

Del Real et al. [24] studied the power dispatch of energy hub networks by considering the cost of environmental impacts as part of an objective function. Morvaj et al. [127] investigated the impact on energy systems when mitigating carbon emissions from the electricity grid [136,137,138,139]. Several scenarios were simulated using the energy hub framework and a Pareto front was constructed for each. Increasing the share of renewables in the generation of power decreases carbon emissions, but at a financial cost [139].

2.3. Applications

The energy hub approach has opened up a wide spectrum of possibilities for the integration of various energy loads. Based on the literature reviewed, this approach has been perceived as one of the significant methods towards future energy systems. Moreover, the transition to future energy systems involves utilizing distributed energy resources (DERs), and green or zero-emission vehicles (ZEV), as well as building a hydrogen economy. A “hydrogen economy” is where hydrogen is generated via emission-free nuclear and renewable technologies and then used as an energy vector to store or distribute it to end-users, especially for power transportation applications. Many studies have established the application of energy hubs. During the inception of the energy hub approach, Geidl and Andersson carried out an example that included the proposed planning, scheduling, and security analysis for the application of energy hubs [178]. However, the distributed energy resources, electric vehicles, and hydrogen economy are the major research interests at present.

2.3.1. Distributed Energy Resources (DERs)

Distributed energy resources commonly referred to as decentralized power generation systems, as opposed to centralized power plants, are often located in remote or ”off grid” areas, providing energy to a specific region. These include, but are not limited to, microgrids, diesel generators, solar panels, wind turbines, combined heat and power (CHP), micro turbines, and energy storage systems [179]. With the methodology proposed by Geidl and Anderson, DER can be easily modeled using the energy hub approach [6]. It is reflected by the tables of research studies presented in this paper along with the renewable energy (RE) vectors.

In a study, Hemmes et al. [180] demonstrated five applications of energy hubs as distributed energy systems, including multiple energy carriers with CHP, the production of hydrogen, re-electrification by fuel cells with and without fluctuating renewable energy, and the integration of fuel cells into a natural gas network. Schulze et al. [181] applied the energy hub model with the aim of optimizing energy flow, using renewables. Franziska applied the energy hub approach to examine the optimal power supply for a larger region with an increasing renewable demand [80]. A multilevel model was introduced when determining the optimal power supply strategy for an area with varying power generation levels and various energy carriers. This study considered the impact of renewable energy power plants and storage systems of various sizes and costs, deciding which energy conversion and storage technologies to employ and where to place them, whilst minimizing the dependency on centralized power plants [80]. Maroufmashat et al. [182] developed an energy hub network, modeling a distributed energy system, considering combined heat and power (CHP) systems and solar energy. That study has shown that the proposed energy network has the ability to reduce the cost due to its potential to mitigate carbon emissions.

Del Real [183] performed an optimization study on a solar-hydrogen energy system, conceptualized through the energy hub approach and used for residential purposes. The model was able to determine the optimal power flow and hydrogen storage through the year, considering seasonal changes [183]. Anastasiadis et al. [184] examined the power losses in low-voltage micro-grids using energy hubs. The highest annual energy losses were observed in scenarios where no DER were considered. Moreover, independently operated DER, including wind turbines, solar photovoltaic (PV), and combined heat and power (CHP) technologies, showed about 59% less annual power loss than the former case (i.e., no DES) [183,184].

In a review study, Chicco and Mancarella described energy hubs as one of the emerging approaches towards decentralized and multi-generation systems, in addition to micro-grids and virtual power plants [36]. On the contrary, Buhler studied the integration of renewables into these energy systems and discussed how the energy hub approach should be used to enhance virtual power plants and micro-grids [29]. In a study conducted by Schule and Crespo Del Granado, three storage systems with intermittent renewable energy sources were optimized using the energy hub model. Moreover, an model-based optimization tool was developed to help reduce the computation time [185]. Robertson et al. developed a simulation tool called hybrid energy system analysis (HESA), based on the energy hub model, to investigate the impact of DER systems of various levels and sizes on the existing energy infrastructure [186].

2.3.2. Plug-in Hybrid Electric Vehicles and Battery Electric Vehicles

Several studies have been conducted that have demonstrated the modeling and optimization research performed on plug-in hybrid electric vehicles (PHEVs) and battery electric vehicles (BEVs), charging infrastructure, and integration into the current system, using energy hubs. Note that since BEVs and PHEVs draw electrical power from the grid or energy hub and store it on-board, the vehicle can be used in a grid-to-vehicle (G2V) or vehicle-to-grid (V2G) model.

Table 8. List of research studies conducted on electric vehicles and infrastructure sorted chronologically.

Reference	Paper Name	Technology				Energy Vectors				Network	Storage
		CHP	Micro	Solar	Wind	Elec	NG	Heat	H2
[188]	Galus and Andersson (2008)	✔				✔	✔	✔		✔	N
[189]	Galus and Andersson (2009) – 1					✔	✔		✔		Y
[55]	Galus and Andersson (2009) – 2	✔				✔	✔	✔		✔	Y
[174]	Galus et al. (2009)					✔	✔	✔		✔	N
[190]	Acha et al. (2009)	✔				✔	✔			✔	N
[191]	Syed et al. (2010)					✔			✔		Y
[13]	Galus et al. (2010)	✔			✔	✔	✔	✔		✔	Y
[14]	Ulbig et al. (2010)					✔	✔		✔		Y
[146]	Shireen and Patel (2010)			✔		✔					Y
[192]	Schulze and Riveros (2010)					✔				✔	N
[193]	Syed (2011)				✔	✔		✔	✔		Y
[194]	Whitefoot (2012)		✔	✔		✔					Y
[19]	Galus et al. (2012)					✔	✔	✔		✔	Y
[59]	Haghifam et al. (2013)	✔			✔	✔	✔	✔			Y
[195]	Waraich et al. (2013)	✔				✔	✔			✔	Y
[60]	Rastegar and Fotuhi-Firuzabad (2014)	✔				✔	✔	✔			Y
[196]	Damavandi et al. (2014)	✔				✔	✔	✔			Y
[107]	Moeini-Aghtaie et al. (2015)	✔			✔	✔	✔	✔			Y
[197]	Rastegar and Fotuhi-Firuzabad (2015)	✔		✔	✔	✔	✔	✔			Y
[67]	Morvaj et al. (2016)	✔				✔	✔	✔		✔	Y
[198]	Yazdani-Damavandi et al. (2016)	✔			✔	✔	✔	✔	✔		Y
[199]	Neyestani (2016)	✔			✔	✔	✔	✔			Y

shows many of these studies, along with the technology and energy vectors considered within them [187].

Galus and Andersson applied the methodology to demonstrate the potential of the energy hub approach for the implementation of PHEVs in different applications [55,189]. Different operating states, such as driving, charging, refueling, and regulation services of the electricity network, can be easily modeled using the proposed framework [189]. In addition to easily extending the model with various other architectures, the energy hub model allows extensive space for optimization.

Prior to implementing PHEVs on a large scale, a reliable infrastructure needs to be provided. Andrade et al. modeled a parking lot that served as a charging station for electric vehicles [200]. Three different scenarios (i.e. early morning, morning, and afternoon) were examined to analyze power flow in the electric parking lot, using MATLAB Simulink. It was observed that the electricity consumption by the electric vehicles was much higher than the daily peak demand. Therefore, a bigger transformer and an effective energy management system were required [200]. Another study, by Damavandi et al., considered the parking lot as a storage system [196]. The results indicated that the operation of energy hubs was very flexible and allowed changes to meet the energy demand [196]. In addition to parking lots, Rastegar and Fotuhi-Firuzabad were able to determine optimal charge scheduling for PHEVs at home, using the energy hub model, based on time-differentiated electricity pricing [60].

The integration of PHEVs with a smart grid, modeled by four energy hubs, was studied by Waraich et al. [200]. The energy demand of PHEVs was simulated using an agent-based traffic demand model, and various charging policies were tested. The proposed approach was successful in determining whether a particular energy infrastructure was capable of handling a certain penetration of PHEVs [200]. Using the energy hub approach, Morvaj et al. [67] were able to successfully develop a framework that minimized carbon emissions while meeting the energy demand for electric vehicles and buildings in a residential area. Haghifam et al. [59] integrated PHEVs and renewable energy sources with the gas and electricity infrastructure, using the energy hub approach. Operational costs decreased since less electricity was purchased from the grid.

2.3.3. Hydrogen Economy

With the aim of reducing greenhouse gas emissions, and utilizing distributed energy generation technologies, including hydrogen storage and fuel cell vehicles (FCVs), significant research has been carried out for developing a hydrogen economy for urban settlements [201,202,203,204,205]. Some notable studies, based on the energy hub concept, are shown below in

Table 9. List of some research studies with hydrogen economy considerations within the energy hubs.

Reference	Paper	Technology			Energy Vectors					Storage
		CHP	Solar	Wind	Elec	NG	Heat	Bio	H2
[16]	Hajimiragha et al. (2007)	✔			✔	✔	✔		✔	Y
[207]	Hajimiragha et al. (2008)	✔			✔	✔	✔		✔	Y
[183]	Del Real et al. (2010)		✔		✔				✔	Y
[166]	Maniyali et al. (2013)		✔		✔			✔	✔	Y
[208]	Proietto et al. (2014)		✔	✔	✔				✔	Y
[202]	Maroufmashat et al. – 1 (2015)	✔	✔		✔	✔	✔		✔	Y
[204]	Maroufmashat et al. – 2 (2015)	✔	✔		✔	✔	✔		✔	Y
[209]	Bucher et al. (2015)				✔	CO2, H2O, H2, O2			✔	Y
[210]	Mukherjee et al. (2015)				✔	✔			✔	Y
[211]	Maroufmashat et al. (2016)	✔	✔	✔	✔				✔	Y
[212]	Ban et al. (2017)	✔		✔	✔	✔	✔		✔	Y
[213]	Mukherjee et al. – 1 (2017)				✔	✔			✔	Y
[214]	Mukherjee et al. – 2 (2017)				✔	✔			✔	Y
[215]	Mukherjee et al. – 3 (2017)		✔	✔	✔				✔	Y
[216]	Baghaee et al.( 2017)		✔	✔	✔				✔	Y

. These studies consider hydrogen as an energy vector, which is an integral part of society. Therefore, they align with the goal of promoting a hydrogen economy [206].

Hydrogen has the potential to link multiple renewable and non-renewable energy resources in various applications. It can be easily generated through “clean” techniques, and vehicles can be promptly refueled with hydrogen [205]. With the rapid development of hydrogen vehicles, the development of a hydrogen economy has resulted in much research interest [203]. During the inception of the energy hub concept, Geidl and Andersson [6] discussed the possibility of including hydrogen within the hybrid system view. It had been perceived as a promising area of research that could facilitate other energy generation technologies, such as fuel cells and micro-turbines. Hajimiragha et al. [16] considered a comprehensive energy hub approach, within their research, focusing on the production, distribution, and utilization of hydrogen along with storage technologies. The study showed that greater flexibility was attained within the energy hub due to the inclusion of hydrogen; the latter allowed ease in the planning and operation of energy systems. This literature [207] applied the general optimal energy flow model of integrated energy systems to a three energy hub system comprised of electricity and natural gas networks, with electricity, heat, and hydrogen demands. The impact of the external hydrogen cost, as well as the size and efficiency of three major plants, i.e., electrolyzers, fuel cells, and CHP, on the optimal operation of the aforementioned integrated energy system was studied. For example, it explores the efficiency targets for electrolyzers and fuel cells for a given price of external hydrogen (produced by other processes) so that electrolysis-based hydrogen production and fuel cell-based power generation can be justified. Maroufmashat et al. [204] developed a generic mathematical model for the optimal energy management of a future hydrogen economy. In another study, Maroufmashat et al. [202] developed an MILP model of a network of smart energy systems to demonstrate the benefits of distributed hydrogen production within an urban dwelling. Based on an environmental and economic assessment, the study found that the distributed generation of hydrogen is beneficial over centralized hydrogen delivery. Moreover, it discussed how a network of energy hubs is economically and environmentally better than an independent hydrogen refueling station.

Maniyali et al. [166] developed an energy hub model to replace a coal-based power plant using nuclear power and hydrogen storage, illustrating the economic benefits of converting surplus off-peak power to hydrogen via electroyzers, in industrial and transport sectors. As discussed earlier, Del Real et al. [183] designed a residential solar power plant that comprised hydrogen and battery storage, considering seasonal variations of solar irradiation and temperature. The simulations indicated that hydrogen was excessively stored during the middle months of the year while being consumed in the earlier and later parts of the year.

Bucher et al. modeled the power-to-gas technology, through the energy hub approach, and conducted an evaluation study [209]. Power-to-gas includes the integration of the generation of hydrogen and biogas, and their distribution and storage through existing natural gas systems. It was found that the implementation of this technology was not currently viable (i.e., 2015). However, with further improvement in the efficiency of energy conversion systems and in the sale of hydrogen, the power-to-gas plants can become economically feasible. On the other hand, Mukherjee et al. [210] proposed an energy hub that considered natural gas when modeling power-to-gas technology. The model, which included hydrogen storage, proposed injecting hydrogen into the natural gas network. This action could potentially generate revenue from carbon credits brought about by reducing emissions. Therefore, in agreement with Bucher et al. [209], economic viability can increase with the sale of hydrogen. Another study, conducted by Mukherjee et al. [213], outlined the pricing mechanisms that can be optimized in order to achieve economic gains in the coming years. In a later study, Mukherjee et al. [214] modeled power-to-gas technology using a two-stage stochastic programming approach, that considered the uncertainty in hourly electricity price, the number of fuel cell vehicles serviced, and the amount of hydrogen refueled.

Ban et al. conducted a study regarding the integration of wind generation along with energy hubs consisting of electrolyzers and gas-to-power units [212]. The study illustrated the ability of the energy hubs to effectively manage a variable power profile using hydrogen storage technologies. Mukherjee et al. [215] designed a renewable, hydrogen-powered microgrid and studied its technical and economic viability using a case study in Canada. This microgrid was to serve as a backup power system to meet the energy demand for two days only using renewables and hydrogen. A comprehensive feasibility study showed that a higher pricing mechanism and government subsidies would be required to overcome the higher system cost [217].

3. Modeling

Energy hubs, in addition to optimal multi-energy carrier systems, are identified as interfaces between different energy generations and loads, as depicted in Figure 4 [1,178]. The unit is commonly comprised of three elements: direct connections, converters, and storage. The connections include the different energy carriers, i.e., electricity grid and natural gas that enter the system, as well as the outputs to the consumers. Energy hubs are composed of a set of conversion technologies and energy storage systems for the scheduled dispatch of various forms of energy.

The more notable advantages of this methodology are added reliability, load flexibility, and enhanced performance of the system [6]. Using the energy hub approach, a wide spectrum of energy-related problems can be addressed throughout the residential, commercial, and industrial areas [156].

Geidl et al. developed a model for multiple energy carrier systems and expressed the energy hub model in terms of energy conversion technologies; then, they incorporated energy storage systems [6]. They emphasized that their formulation of the energy hub leaves significant room for optimization since the efficiency of the technologies is nonlinear.

As illustrated in Figure 3, the energy from carrier 1 is split between energy conversion technologies A and B. In contrast, energy from carrier 2 is split into two further energy vectors after passing through the conversion technology C. D and E are other components for further conversions. For example, in the case where C may be a co-generation system, E may represent a chiller cascaded with C to meet the demand of Load 2, which is the cooling load.

3.1. Generic Framework

One of the main objectives of future energy system projects [4] is to develop a generic modeling and analysis framework, in which the economical, ecological and technical effects related to systems can be studied. This generic structure would allow high flexibility in modeling without posing any constraint on the size of the system. Hence, to model an energy conversion technology, as described in the previous section, Geidl et al. [218] proposed using a coupling matrix C that would transform the input energy to the required energy vectors. Maroufmashat et al. [144] modified this formulation, as shown in the following equation. Equation (1) shows a mathematical expression used to define the overall energy mapping process.

$$\left[\begin{array}{c}{L}_1\\ L_2\\ .\\ L_i\\ .\\ L_I\end{array}\right]={\left[\begin{array}{c}{C}_{11}{C}_{12}..C_{1j}\\ C_{21}{C}_{22}..C_{2j}\\ ....\\ ..C_{ij}..\\ ....\\ C_{I1}...C_{IJ}\end{array}\right]}_{I\times J}·I_{J\times J}·b·{\left[\begin{array}{c}{P}_1\\ P_2\\ .\\ P_j\\ .\\ P_J\end{array}\right]}_{J\times 1}$$

(1)

L and P, in the above equation, denote the load demand and the input energy carrier I, j, respectively. b is a vector that converts the units of energy from the input to power, consistent with that of the load. $I_{J\times J}$ is added to the equation to allow uniformity for matrix multiplication. The entities of the coupling matrix C represent the efficiency with which energy is converted. If a particular entity within the coupling matrix is zero, it indicates that no conversion of energy is taking place. If a single conversion technology is utilized, the efficiency of that conversion process is considered the coupling factor. Additionally, if the load demand is the result of one or more energy conversion technologies, the product of the efficiencies is considered the coupling factor. On the other hand, the input energy carriers may possess certain operational limits, based on their capacities. Therefore, their power needs to be constrained by lower and upper boundaries (i.e., min/max), as expressed by Equation (2).

$$P^{min}\le P\left(t\right)\le P^{max}\forall t$$

(2)

Many authors [2,15,219] have introduced the “dispatching Factor” as a new variable to specify how much energy flows to Converter A and how much flows to Converter B. This was redundant as it could complicate the problem by introducing the further dimension of non-linearity.

Overall, this simple model can either be utilized under steady-state conditions or further developed to tackle dynamic systems with control strategies, while including energy storage and losses. Moreover, the unidirectional and bidirectional flow of power can be considered based on energy hub configuration [181]. For example, an electrical transformer would be able to realize reverse power flow whilst a turbine may not [6]. Based on this generic structure, the model opens a wide range of possibilities for optimization [80,180,181]. Stochastic models can be collated alongside the structure for the planning and operation of energy sources [36,183,184]. In addition, interactions between the energy carriers can be studied to assess the reliability and performance [185,186].

3.2. Energy Storage Modeling

Energy storage is one of the key elements of the energy hub considered by Geidl et al [1,4,6]. More than half of the publications adhering to multi-energy systems have incorporated energy storage within their models, as evident from the classification. It is essential to account for time dependency when energy storage is considered, as energy accumulates over a certain period. Hence, the conversion technologies are perceived as discrete temporal systems [156].

$${\dot{M}}_q={\alpha }_q^{ch}{Q}_q^{ch}-\frac{1}{{\alpha }_q^{dis}}{Q}_q^{dis}$$

(3)

Equation (3) shows an energy balance of the storage technology, accounting for energy entering the storage system (i.e., charging) and leaving it (i.e., discharging). $Q_q^{ch}$ represents the power in-flow through the storage technology q at an efficiency ${\alpha }_q^{ch}$, while $Q_q^{dis}$ represents the power flowing out of it at an efficiency of ${\alpha }_q^{dis}.$

As mentioned earlier, dynamic modeling is required when considering storage systems. Therefore, the storage function needs to be discretized into separate time periods, as has been done using the forward difference formula in Equation (4).

$${\dot{M}}_q=M_q\left(t\right)-M_q\left(t-1\right)+M_q^{stdby}$$

(4)

$M_q\left(t\right)$ and $M_q\left(t-1\right)$ represent the energy stored in time periods (t) and (t − 1), respectively. In order to account for losses, the $M_q^{stdby}$ term is added to the expression to express energy loss when the storage system is in its standby state. By compiling Equations (3) and (4), the overall equation for the q^th storage device at time period (t) can be written as expressed in Equation (5).

$$M_q\left(t\right)=M_q\left(t-1\right)+{\alpha }_q^{ch}{Q}_q^{ch}\left(t\right)-\frac{1}{{\alpha }_q^{dis}}{Q}_q^{dis}\left(t\right)-M_q^{stdby}\forall \mathrm{q},\forall \mathrm{t}$$

(5)

In matrix representation, Equation (5) may be expressed as Equation (6).

$$M\left(\mathrm{t}\right)=M\left(t-1\right)+A^{ch}{Q}^{ch}\left(t\right)-A^{dis}{Q}^{dis}\left(t\right)-M^{stdby}\forall \mathrm{t}$$

(6)

As written, $A^{ch}$ and $A^{dis}$, in Equation (6), are diagonal matrices representing charging and discharging efficiencies, respectively, to allow matrix multiplication. In addition to the above model equations, technical constraints need to be structured to define the inability of the storage technology. For instance, simultaneous charging and discharging of a storage system is not possible. Hence, Equation (7) is comprised of two binary variables, ${\delta }_q^{dis}\left(t\right)$ and ${\delta }_q^{ch}\left(t\right)$, which are introduced for each storage technology at each time period t to define the situation.

$${\delta }_q^{dis}\left(t\right)+{\delta }_q^{ch}\left(t\right)\le 1\forall q.\forall t$$

(7)

Equation (8) shows the additional limitations on the capacity and exchange energy of each storage system.

$$\begin{gathered} M_q^{min}\le M_q\left(t\right)\le M_q^{max}\forall q.\forall t \\ {\delta }_q^{ch}\left(t\right)·Q_q^{ch,min}\le Q_q^{ch}\left(t\right)\le {\delta }_q^{ch}\left(t\right)·Q_q^{ch.max} \\ {\delta }_q^{dis}\left(t\right)·Q_q^{dis,min}\le Q_q^{dis}\left(t\right)\le {\delta }_q^{dis}\left(t\right)·Q_q^{dis.max} \end{gathered}$$

(8)

$M_q^{min}$ and $M_q^{max}$ represent the minimum and the maximum level of energy stored in the q^th storage system. Moreover,$Q_q^{ch.min},Q_q^{dis.min},Q_q^{ch.max}$ and $Q_q^{dis.max}$ represent the minimum and maximum energy that can flow through the q^th storage technology during the energy charging and discharging process.

3.3. Network Modeling

In many cases, a single energy hub model suffices for representing the entire energy system. Yet, for large-scale planning and operational problems, a network of energy hubs is considered [156,178,189,200]. These energy hubs are interconnected, facilitating energy transfer among them.

Figure 4 shows a network of energy hubs with a focus on energy hub s. Each energy hub within the network either receives energy from outside the network (i.e. grid, renewable energy sources, etc.) or from other energy hubs in the network. Likewise, each energy hub produces energy to meet the demand within the hub or to supply other interconnected energy hubs. As is evident in Figure 4, three energy carriers have a flow of power into energy hub s. The total energy from hub s supplied to other connected energy hubs is represented by T_s. This total is the summation of the individual energy output, Tr_sk, to each connected energy hub, k, from energy hub s. This relationship can be expressed mathematically in the following way:

$$T_s={\displaystyle \sum }_{k\in S-\left\{s\right\}}T{r}_{sk}$$

(9)

Similar to the coupling factors in the coupling matrix, as well as energy storage efficiencies, a coefficient may be multiplied by $T{r}_{sk}$ to account for the losses due to the transmission of energy from energy hub s to k. All the energy vectors that exist between the interconnected energy hubs can be written in matrix form, as shown below.

$${\left[\begin{array}{c}{T}_1\\ T_2\\ ·\\ ·\\ ·\\ T_s\\ ·\\ ·\\ Ts\end{array}\right]}_{S\times 1}={\left[\begin{array}{ccccc}0& T{r}_{12}& T{r}_{13}& \cdots & T{r}_{1k}\\ T{r}_{21}& 0& T{r}_{23}& \cdots & T{r}_{2k}\\ ·& ·& \cdots & & \\ ·& ·& \cdots & & \\ ·& ·& \cdots & & \\ T{r}_{s1}& T{r}_{s2}& \cdots & & T{r}_{sk}\\ ·& & & & \\ ·& & & & \\ Tr& & \cdots & & 0\end{array}\right]}_{S\times S}·{\left[\begin{array}{c}1\\ 1\\ ·\\ ·\\ ·\\ 1\\ ·\\ ·\\ 1\end{array}\right]}_{S\times 1}$$

(10)

The first column vector contains the sum of all energy vectors leaving a particular energy hub (i.e., T_s). The Tr matrix contains each vector that leaves a particular energy hub s and enters energy hub k. The column vector on the right-hand side of the expression is a vector with each element equal to 1 to allow matrix multiplication.

4. Optimization Problem for the Energy Hub Concept

Mathematical programming, better known as optimization, is the scientific method used to analyse complex models. The purpose of optimization is to help alleviate the toll of decision-making with respect to quantifiable systems with a large number of possible solutions. Cost reduction is a major concern for energy hub installations. Depending on the energy hub application, a wide variety of converters, e.g., energy generation and/or storage devices, may exist with different start-up/shut-down costs, as well as fuel consumption rates or efficiencies. Moreover, there are plenty of operational constraints/limitations specific to each asset. In view of all these considerations, making decisions about controlling the energy hub, e.g., dispatching different converters to achieve minimum operational and environmental costs, is a challenging task that cannot usually be done through a simple rule-based approach. Instead, this challenge should be resolved through an optimization process, commonly referred to as energy hub optimal dispatch or the generation scheduling problem, which is basically a multi-interval optimization problem since the decisions are made for the present and future time, i.e., the prediction horizon. This optimization problem should include a variety of operational considerations, such as the lower and upper bounds of powers/charge states and the number of start-ups/shut-downs, ramp rates, loading factors, and minimum up-time/down-time [123]. To model these operational considerations, discrete (integer/binary) variables and complex constraints need to be defined; these definitions result in mixed integer linear/non-linear programming (MILP/MINLP) formulations. Since the status of assets in the hub, e.g., availability or offline/online states, may change over time, and loads, renewable power sources, and energy prices have a time-varying nature, decisions must be updated by rerunning the optimization calculations every few minutes/hours, i.e., the dispatch time. This method is commonly referred to as rolling time horizon (RTH) or model predictive control (MPC) [220,221,222].

In general, in the context of energy hub cost minimization or the optimal dispatch problem, two approaches are distinguished, namely, open-loop and closed-loop optimization. In open-loop optimization [223], decision variables $X_0,X_1,X_2,\dots ,X_k$ are made at once at time 0, without waiting to see the subsequent demand, renewable power, and energy price levels. This solution can be obtained by the previously-mentioned MILP/MINLP formulations. In closed-loop optimization [224], the decision variable $X_k$ is postponed until the last possible moment (time k), when the current system state, e.g., demands, renewable powers, energy prices, and storage charge levels, will be known. In fact, the information that becomes available between time 0 and k is used to enhance the quality of the decisions. In this type of optimization approach, finding the optimal numerical values of the decisions is not the matter of concern; instead, the objective is to find an optimal rule or function for selecting a decision $X_k$ at each period of k for each possible value of the system state that can occur. MPC/RTH is an approximate solution for closed-loop optimization; however, it is computationally expensive for real-world applications as the whole optimization problem is resolved at every single time step after updating the expectations. For a limited dispatch time, e.g., few minutes and typical energy hub configurations with limited numbers of generation and storage assets, one needs to deal with an extremely large problem with complex constraints. It is difficult to implement and be solved by an embedded energy management or supervisory control system with a limited memory and processing capability. Most of the existing contributions within the area of energy hub optimal dispatch fall into the category of open-loop and MPC approaches [115,225,226,227]. To illustrate, reference [120] is a new attempt to introduce a closed-loop optimization approach to the field of energy hubs.

Terms of nonlinearity in the energy hub modeling depend on the objective function and the coupling matrix variables. One can use the energy hub model for the optimal design and operation of complex integrated energy systems. In this part, some techniques are presented to linearize energy hub modeling for the optimal design and operation of a hybrid energy system.

The variable and linearity classification is further broken-down into three sub-classifications based on whether non-linear and linear terms exist in the constraints and objective function, namely, linear programming (LP), non-linear programming (NLP), and mixed integer linear programming (MILP).

LP provides a solution that must satisfy all linear constraints and determines the minimum or maximum value of the defined linear objective function. LP methods are the fastest of the three types of programs. They are useful for the operational optimization of an energy hub when there is no energy storage in the system [11,204].

Nonlinear programming (NLP) consists of linear and nonlinear objective functions and constraints; either the constraints or the objective function must incorporate one nonlinear term. In problem solving, both the theoretical and practical features of NLP problems are considered, rendering them more difficult to solve than LPs. Mathematical formulation, algorithm development, and the analysis of a specific problem are all practical issues. One method of solving an NLP problem is by removing the variable with the nonlinear term from the formula and solving the given problem explicitly. NLP is the slowest of the three mathematical methods. Here, we present some methods to convert nonlinearity in the objective function or in the coupling matrix of an energy hub in linear programming to make it easier to solve and find the global optimized solution [228].

Models that consist of both continuous and integer variables are known as mixed-integer programming (MIP). Generally, MIPs are expressed as follows:

$$\begin{array}{c}minf\left(x.y\right)\\ subjecttog\left(x.y\right)\le b\\ x_{min}\le x\le x_{max}\\ y\in {\left\{0.1\right\}}^q\end{array}.$$

(11)

The model uses finite variables with integer values, such as the existence or nonexistence of power plant units as a binary variable termed one or zero, respectively. Another example is a tray of distillation columns, with terms one, two, three, etc. If only the integer variables are used, the problem is classified as an integer programming (IP) model. Finally, if only variables with the values of 1−0 are used, the problem is considered a binary integer programming (BIM) model. Moreover, the MILP model only consists of linear equalities and inequalities, while the MINLP model includes linear and nonlinear ones. The most advantageous attribute of MILP is its ability to formulate logical constraints. The MILP’s integer variable property allows for the modeling of non-convexities. On the other hand, the MILP’s greatest disadvantage is its lack of a standard formulation or analytical solution [229,230]. In addition, MILP problems are much more difficult to solve than LP problems.

4.1. Formulation of Strategies for MILP

The main objective of using mixed-integer linear programming (MILP) according to [231] is to provide a statement of the actions performed, allowing the system to move from a primary status toward the defined objective.

The program’s developer is responsible for meeting the stated objective, as well as incorporating detailed components of the system. The modeler’s most important function is to ensure that there is a compromise between tractable formulations and representational fidelity. Introducing additional binary variables to an MILP problem, unlike LP, is advantageous as it reduces the number of branches that must be searched. Contrary to LP-based problems, the addition of constraints in MILP is used to reformulate so that the convex hull of feasible continuous variables approaches the convex hull of feasible integer variables.

4.2. Solution Strategies

MILP-based problems are generally difficult to solve through the simplex algorithm [231]. In fact, there is no defined systematic method to solve such problems; rather, the existing solution algorithms may take an exponential amount of time or, even worse, only provide an approximation. Regarding reference [232], the following is a list of the methods developed to solve integer programming problems. The first group includes exact algorithms (rounding method, cutting-plane method, dynamic programming), which guarantee an optimal solution, but require an exponential number of iterations. The second group includes approximate algorithms, which provide less accurate solutions by bounding the sub-optimal solution using a heuristic algorithm. Lastly, the most reliable branch-and-bound method considers each problem as a binary tree whose efficiency is dependent on the quality of the bounds at each node of the solution tree.

4.3. Strategies to Linearize the Energy Hub Model

Adopting different objectives in the process of optimization leads to a nonlinear model for the energy hub. Some useful steps can convert the nonlinear term to a mixed integer programming model. To illustrate this, when dealing with nonlinearity in the design and planning of energy systems based on energy hubs, determining the number of fixed-size technologies can be a challenging problem. In order to change the integer variables to binary ones, the following equation can be implemented:

$$N=y_0·2^0+y_1·2^1+y_2·2^2+y_3·2^3+\cdots +y_n·2^n{N}_{min}\le N\le N_{max}$$

(12)

where N is an integer variable and $y_i$ represents binary ones.

By this conversion, it is easier to convert nonlinear terms to mixed-integer ones; specifically, when the multiplication of integer and continuous variables is involved. This paper will explain later how the multiplication of binary and continuous variables can be linearized.

The efficiencies of energy conversion technologies vary as the load changes. The relation between the output (L(t)) and input power (p(t)) of energy conversion technologies depends on the efficiency, which is a function of several variables, such as the operational condition or even output power. The efficiency of an energy conversion technology can be presented as a function of other variables, resulting in nonlinearity in the modeling of energy hubs. Therefore, the optimization of such a system creates more difficulties.

Piecewise linear formulation is employed for a variety of applications to estimate nonlinear functions, either in objective functions or problem constraints, through the addition of more continuous and discrete variables. This kind of formulation can be applied in different domains, such as transportation and production planning. The application of this technique in engineering design, as well as process systems, is also presented in [233,234,235]. In addition, it can be used for the planning of natural gas networks [236]. Different approaches have been implemented for the piece-wise linearization of nonlinear functions [237,238,239,240]. The incremental cost and convex combination are two types of mixed integer formulation [241].

Nonlinear functions, along with various integer variables, can be incorporated into an MINLP-based model, which is one of the hardest types of optimization problems to solve. It is possible to perform a piecewise linearization of the nonlinear functions and convert them to an MILP. The solution procedure for integer programming is fully developed; however, the number of integer variables is noticeably increased by employing an MILP-based model, leading to a lower accuracy of the optimization solution. The prior literature suggests that the advantages of an MIP-based model far outweigh the objections [242]. The stepwise formulation is typically employed to model the efficiency of resources over time. It is a special case of the piecewise linear function where all the slopes are equal to zero.

Through energy hub modeling, as can be seen in Equation (1), there is a nonlinearity due to the multiplication of two continuous variables, including the coupling matrix (C(t)) and input power flow (P(t)). The coupling matrix can become a step-wise linearization, as shown in Equation (13). Therefore, the nonlinear product becomes the product of one binary variable and one continuous variable, which can be transformed to the MIP-based problem:

$$L_i\left(t\right)={\displaystyle \sum }_j{C}_{i,j}\left(t\right)·P_j\left(t\right)·b_j={\displaystyle \sum }_j({\displaystyle \sum }_k{n}_{i,j,k}\left(t\right)·y_{i,j,k}\left(t\right))·P_j\left(t\right)·b_j.$$

(13)

where, $n_{i,j,k}$ is the step-wise efficiency and $y_{i,j,k}$. is the binary variable regarding the selection of the step-wise efficiency and k represents the number of steps.

To implement this method, the curve of part load efficiency is estimated as a piecewise constant function, the step length is not fixed, and the optimum step length of each piece can be determined by minimizing its error. Different methods were applied to this problem in the literature, including analytical methods and dynamic programming [243,244].

To select only one piece in each step, Equation (14) is introduced. The upper and lower bound of each step is constrained by the following equation:

$${\displaystyle \sum }_k{y}_{i,j,k}=1.$$

(14)

By piecewise constant linearization of efficiency, nonlinearity remains in the equations due to the product of step-wise binary variables (y) and the input energy flow to each energy hub ((p(t)). This nonlinearity can be converted into bilinear products by employing the procedure stated in [245], [246]. In order to solve this issue, a new variable ($\acute{P}$), which is the multiplication of the binary variable (y) and continuous variable (P), is added to the model along with the following constraints (Equation (15) and Equation (16)):

$$n_{i,j,k}·y_{i,j,k}·P_{j,k}=\acute{P_{i,j,k}}0\le \acute{P_{i,j,k}}\le n_{i,j,k}·P_j.$$

(15)

$$n_{i,j,k}·P_j-n_{i,j,k}^{max}·P_j^{max}\left(1-y_{i,j,k}\right)\le \acute{P_{i,j,k}}\le n_{i,j,k}^{max}·P_j^{max}·y_{i,j,k}$$

(16)

where, ${\eta }^{max},P^{max}$ are the upper limit of efficiency and input power, respectively.

5. Summary and Concluding Points

Several studies have been carried out in the area of synergistic optimal energy transformation, storage, and carrier problems. The energy hub approach has played a vital role in addressing such problems. Many researchers have utilized this methodology and extended this concept in modeling, optimization, and application. This paper has mainly presented a comprehensive review of energy hub modeling and optimization. It constitutes an introduction to this novel concept with various definitions of this proposed idea. Furthermore, it outlines the importance of smart energy systems and demonstrates the advancement of the energy hub approach since its inception. In addition, the use of different energy generation, conversion, and storage technologies in each study is outlined. This paper considers previous review studies that have focused on energy hubs or multi energy systems or other aspects pertaining to them. These review studies have focused on effectively defining the energy hub concept, but gaps remain in the areas of modeling, optimization, and energy hub application.

Among the various themes identified within this paper, planning and operation is a major one in which significant research work has been carried out regarding the scheduling and control methodologies for energy hubs. Due to the intermittent nature of renewables, controllers are needed to ensure that an optimal and reliable power flow will be satisfied in the energy hub. In addition, assessment studies regarding the scheduling scheme of energy hubs and control technologies were discussed. In addition to reliability studies, various research has focused on the economic and environmental considerations of energy hubs; this research includes studies with single objective functions to optimize the cost or greenhouse gas emissions and multi-objective functions to incorporate both. A number of studies that have presented case studies to illustrate the economic and environmental gain due to the energy hub approach have been mentioned. In terms of application, the studies in which energy hubs are commonly considered have been outlined. It is noteworthy that we have categorized the application of this approach based on the design and management of distributed energy resources and plug-in hybrid vehicles (PHEV), as well as on the development of a hydrogen economy. In each of these areas, the contributions made by researchers have been listed, and the important findings have been emphasized. For distributed energy systems, the results demonstrate that the energy hub-modeling tool is capable of simulating systems at various levels and sizes. Studies on battery electric vehicles (BEV) and PHEVs state that this approach opens a wide space for optimization. In the development of a hydrogen economy, the ability of smart energy systems to consider the hydrogen vector results in a significant decrease in costs and carbon emissions. Since hydrogen is one of the promising energy vectors of future energy systems, the energy hub approach can help integrate the whole system while considering the hydrogen economy.

In the modeling section, a generic framework for smart energy system modeling has been presented. Provisions for modeling storage technologies and modeling a network of energy hubs have also been illustrated in a step-by-step manner. The optimization strategies for facing energy hub modeling issues have been described. Different strategies to linearize the energy hub model and convert it to the MILP-based model have been introduced.

Future work regarding energy hubs will be at the cutting edge of the use of artificial intelligence for the modeling and optimization of energy hubs; smart energy systems including smart homes and smart cities; and the hydrogen economy for sustainable transportation systems, as well as for industrial facilities. The direction of future work regarding energy hubs lies at the intersection of artificial intelligence and the hydrogen economy. Artificial intelligence can be used to model and optimize energy hubs or smart energy systems (e.g., smart homes and smart cities), whereas the hydrogen economy targets sustainable transportation systems and industrial facilities.