Planning of Multi-Vector Energy Systems with High Penetration of Renewable Energy Source: A Comprehensive Review

Abstract

The increasing use of high shares of renewable energy sources (RESs) in the current electricity network introduces challenges to the design and management of the electricity network due to the variation and uncertainty nature of the RESs. Some existing energy infrastructures, such as heat, gas, and transport, all have some level of inbuilt storage capacity and demand response (DR) potentials that can be exploited in an energy system integration to give the electricity network some level of flexibility and promote an efficient transition to a low-carbon, resilient, and robust energy system. The process of integrating different energy infrastructure is known as multi-vector energy systems (MESs). This paper reviews different studies on the planning of MESs using the energy hubs (EHs) approach. The EHs model used in this paper links different energy vectors such as gas, electricity, and heat energy vectors in its planning model, as opposed to planning each energy vector independently, in order to provide more flexibility in the system, minimise total planning cost, and encourage high penetration of renewable energy source for future energy demands. In addition, different uncertainty modelling and optimization methods that have been used in past studies in planning of EH are classified and reviewed to ascertain the appropriate techniques for addressing RESs uncertainty when planning future EH. Numerical results show 12% reduction in the planning cost in the case of integrated planning with other energy vectors compared to independent planning.

1. Introduction

1.1. Background and Motivation

The global demand for energy is rising exceptionally due to the rise in population growth and increasing standard of living, and the energy demand is expected to rise further in the near future [1,2]. The conventional energy systems rely mainly on the supply of fossil fuel for their demand. These fossil fuels have limited supplies and they are geographically restricted, hence cannot continue with the growing demand for energy over a long period of time. Furthermore, the increase in the consumption of fossil fuel will lead to more air pollution, which contributes to global warming [2,3]. To reach both national and international climate targets and to curtail our reliance on fossil fuels, the share of electricity generation from RESs must be further increased in planning future energy systems. The high penetration of these RESs poses challenges to the current electricity network [4]. Power production through RESs such as wind and solar depend mainly on the condition of the weather; also, the irregularity of these RESs will make it even harder to maintain steady and reliable power services to the customers. Handling RESs at an extensive level requires well-organized techniques such as interconversion between individual energy carriers [5]. Presently, this is not the case, and it is affecting the existing electricity network, hence the need for modern technologies such as power-to-gas (P2G) technologies which convert large shares of renewable electricity generation into chemical fuels. These chemical fuels provide lifelong and extensive energy storage capacity and are usually converted into electricity through fuel cell technologies when there is high demand [6,7]. One advantage of the P2G technology is linking both the electricity and gas networks together by converting excess electrical energy into gas, through a two-stage technique: the use of water electrolysis to produce hydrogen, accompanied by converting hydrogen into methane (CH4) as synthetic gas (SNG) which can be supplied into the gas network [8,9]. On the other hand, some of the existing energy infrastructures, such as heat, gas, and transport networks, have some level of inbuilt storage capacity that can be exploited to give the electricity network some level of flexibility when required. When these energy infrastructures that have been traditionally operated independently are integrated, it will help minimize the issues of high penetration of RESs into the energy systems [4].

The approach for integrating the different energy infrastructures is known as multi-vector energy systems (MESs). MESs are the process of coupling multiple energy carriers to interact and complement each other for an efficient energy system. The EH approach, where multiple energy carriers are converted, conditioned, and stored to enrich the system’s energy efficiency and utilize energy resources, is one of the main recent approaches that have been used in modelling MESs and has undoubtedly enhanced the planning of MESs. However, studies on the EH model that compared the benefits of synergizing multiple energy carriers simultaneously versus traditional methods of planning individual energy carrier independently are limited. To the best of the authors’ knowledge, there are no studies that compare the benefits of integrated planning of MES using the EH approach, considering uncertainties related to RESs and demand response programs.

1.2. Related Reviews on Planning of Energy Hub

There are numerous papers which have reviewed the planning of EH in the literature. For instance, using the EH concept, the authors in Ref. [10] proposed an MES expansion method to plan CHP units, gas boiler, and a few other energy carriers, while the CHP units and natural gas distribution network were optimized in Ref. [11]. In Ref. [12], the planners of EH utilized mathematical models and considered operational constraints to guide energy planners and system operators towards the use of RESs in gas and electricity networks interconnection. A planning model for EHs interconnections with different energy infrastructures was proposed in Ref. [13], in order to increase the supply of heat and electricity to satisfy the end user’s demand by investigating gas and electricity network interactions. Ref. [14] presents an expansion planning formulation of interconnection of gas and electricity network integration. An MILP optimization problem was used to formulate the model in order to reduce both the cost of investment and operation when choosing the various technologies, location, and time of installation of modern gas and electricity network equipment. The co-planning of gas and electricity network was proposed in Ref. [15] to improve the gas turbine sizes and site and it led to a decrease in the cost of investment of the system. An expansion planning formulation was proposed in Ref. [16] under uncertainty for integrating electricity and gas system in order to improve social welfare. Ref. [17] considered an EH-based optimal planning framework to improve the boiler, combined cooling, heat and power, thermal storage, and electricity network sizes in a network of gas and electricity interconnection. Ref. [18] proposed a combined extension planning formulation for gas and electricity to increase efficiency in the gas and electricity extension planning. Ref. [19] proposed an MILP formulation that will optimally design a micro-sized CHP unit and the results showed that a high benefit of energy saving and a great reduction in carbon emission were achieved. In Ref. [10], an energy system integration planning configuration was proposed considering several levels using a decentralized approach, and results showed that the coordinated technique is cost-effective. The authors in [20] proposed an expansion formulation with long-term goals to choose the candidate generator, CHP, transmission lines, and gas pipelines for a multi-vector energy system, and the results showed that the proposed formulation was significantly good for maximizing expansion planning. Ref. [20] used the EH approach to enhance MES formulation as it relates to distributed RESs. Ref. [21] focused on planning the integration of PHEVs into EH networks, where the dynamic behaviour was simulated, and explored several constraints regarding the vehicle usage. In Ref. [14], the results demonstrated that there are greater benefits when gas and electricity networks are jointly planned in a multi-area expansion planning than in the traditional way of planning both networks separately. Ref. [15] examined a distribution expansion planning formulation to analyse both gas and electricity networks together using more distributed generation energy resources. The simulation results showed that there is a decrease in the cost of expansion planning of both networks compared with the cost when both were individually planned [17]. A bi-level formulation of an MES expansion planning integration was examined in Ref. [22], with the aim of considering the constraints related to the district carbon emission. The first formulation looked at the investigation of multi-regional area planning, and the second formulation analysed the lowest planning costs of integrating several energy infrastructures using EH concept at district level, considering carbon emission constraints. The benefits of the integration of gas and electricity systems planning were seen in the results of the simulation. An EH interconnection planning formulation with different energy infrastructure based on system reliability was examined in [23]. An optimal planning formulation for an EH with several energy carriers was considered in [24]. Ref. [25] proposed a methodology for the operation and planning of distributed multi-energy generation systems for the assessment of both investment and operation level within some level of uncertainty [26]. Refs. [27,28] proposed an expansion planning to formulate the optimization problem which examined the joint analysis of more than one type of generator. The target of the optimization problem was to minimize the gas pollution. A summary of some recent work carried out on optimal planning of EH is presented in

Table 1. A summary of recent works carried out on optimal planning of EH.

Refs.	Energy Vector	Conversion Technologies	Objective Function	HorizonTime	Problem	Solution Method	Mathematical Modelling Uncertainty	Emission	DR	Contribution	Energy Demand
[10] 2019	EN, NGN		Minimize net present value of total costs	6 years	MILP	GAMS Optimization Solver		Y	Y	A new planning framework is proposed that will allow for two-level integration with multiple subsystems, including the lower-level of several local communities and the upper-level of a combined gas and electricity distribution network.	E, H
[12] 2016	EN, WP, NGN, Water	T, CHP, GB, Wind Turbine	Minimize investment, operation. Reliability cost and emission	One year	MILP	GAMS Optimization Solver	Monte Carlo simulation (MCS)	Y	Y	Mathematical formulation was used for optimal planning of a developed EH considering operation constraints.	E, H, NG, Water
[13] 2017	EN, NGN	T, CHP, GB, AC	Minimize net present value, investment, operation,	Five years	MIQP	Fast iteration solver	Numerical method	Y		A new method is presented to model and formulate the optimal design of reconfiguration electricity and natural gas distribution systems.	E, C, H
[14] 2010	EN, NGN HYP LNG	T,	Minimize annual investment, operation costs	One year	MILP	GAMS Optimization Solver			Y	A new idea to analyse long-term multi-area expansion plan of gas systems was considered. It was seen that there is more benefit when electricity and gas are combined within the same system.	E, NG
[15] 2013	EN, NGN,	T,	Minimize energy and investment cost	One year	MINLP	GAMS Optimization Solver		Y	Y	A new direction of study towards the distribution expansion model that looks at the electricity distribution and natural gas networks as a system with a high penetration of DER.	E, NG
[17] 2015	EN, NGN, DHN	T, CHP, GB, AC, CC, HE	Minimize net present value	15 years	Nonlinear problem	MATLAB optimization toolbox	Monte Carlo scenario (MCS)	Y	Y	This study optimally designs and sizes interconnected energy hubs. The constraints on gas and electricity are analysed.	E, H, C
[18] 2016	EN, NGN	T	Minimize investment cost. Reliability		MILP	GAMS Optimization Solver			Y	The paper considered the designing of integrated gas and electricity network to solve the continuous demand.	E, H
[20] 2020	EN, NGN, DHN	CHP, GB	Minimize of MES total cost	10 years	MILP	Bender’s decomposition method		Y		A long-term coordinated planning model is proposed to determine the optimal expansion plans of generation units, GB, and CHP.	E, H
[22] 2018	EN, NGN	T, CHP, EB, GF	Minimize energy investment cost	One day	MILP	GAMS Optimization Solver		Y		This paper proposes a bi-level expansion planning model for MES to investigate the optimal planning scheme under the district emission constraints.	E, H
[24] 2015	EN, NGN	T, CHP, GF	Minimize energy costs, investment costs	Ten years	MILP	GAMS Optimization solvers		Y		The proposed planning model could be applied by system planners to evaluate and analyse efficiency of energy.	E, H
[26] 2019	EN, NGN, WP, DHN	CHP, GF,	Minimize net present value for planning cost	One year	MILP	GAMS Optimization Solver	Scenario Based Approached	Y		The optimal planning model of multi-type energy storage with wind power is established with the goal of minimum cost.	E, H
[27] 2018	EN, NGN, DHN	CHP, EB	Minimize energy cost, operation costs	One day	MILP	GAMS Optimization Solver		Y		An optimal expansion planning model was proposed to determine the candidate CHPs, EBs, and natural gas storages which satisfy the needs of various energy loads.	E, H
[29] 2020	EN, NGN, WC	CHP, EH, T, GF	Minimize overall power expenses	2 & 5 years	Limitation Optimization problem	Particle swarm optimization		Y	Y	An optimal expansion planning is proposed to mathematically model an optimization problem considering the optimal combination of services.	E, H
[30, 31] 2018	EN, NGN	GT, T	Minimize total energy cost		MILP	Particle swarm optimization (PSO) algorithm			Y	A collaborative planning model of the natural gas network and power system was built to configure the equipment capacity.	E, NG
[32, 33] 2019	EN, NGN, SP	CHP, HP, GB, PV	Minimize energy cost	One day	MILP	MATLAB Optimization toolbox	Scenario Based Approached	Y		This paper proposes a planning framework for integrating energy systems at different scales using a decentralized approach.	E, H

AC: absorption chiller, BS: battery storage, C: cooling, CA: compressed air, CC: compressor chiller, CHP: combined heat and power, DHN: district heat network, E: electricity, EB: electric boiler, EH: electric heater, EN: electricity network, GB: gas boiler, GF: gas furnace, GT: gas turbine, H: heating, HE: heat exchanger, HP: heat pump, H2: hydrogen, HYP: hydropower, LNG: liquefied natural gas, MIQP: mixed integer quadratic programming, NG: natural gas, NGN: natural gas network, NGS: natural gas storage, PV: photovoltaic, P2G: power-to-gas, SP: solar power, WP: wind power, T: transformer, TS: thermal storage, WC: wood chips, Y: yes, N: no.

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1.3. Literature Search Strategy

Figure 1 depicts the methodology used to locate suitable literature for review. Google Scholar and Scopus are the primary tools for locating suitable studies [34]. These search engines contain the most comprehensive abstract and citation database of peer-reviewed literature [35]. The queries used in the search engine were as follows:

• “Multi-vector energy systems planning” AND “Renewable energy source”.
• “Energy hub planning” AND “Renewable energy source”.
• “Integrated Energy systems planning” AND “Renewable energy source”.

All of the results from Google Scholar and Scopus searches were thoroughly reviewed and filtered. The papers included in this review are those in which MES planning using EH approaches was explicitly used in the studies.

1.4. Structure of the Review

This paper reviews past studies carried out between the years 2010 to 2022 on the planning of MES using EH approach, considering uncertainties related to RESs and demand response program. The reminder of this paper is structured as follows. Firstly, Section 2 provides the fundamental background for this review, by giving the full meaning of MES explicitly, the various categories of energy vectors integration, benefits, and challenges of MESs. Section 3 provides MES network models using the electricity, gas, and heat network models connected to the EH, an overview of EH, EH model, and its concept. Section 4 reviews the design and planning of MESs via the EH approach by analysing the deterministic and probabilistic methods, EH planning objective functions, and constraints. Furthermore, analysis of the simulation results is given, where the main findings in the comparison of the cost of planning integrated energy carriers such as gas, heat, and electricity versus the traditional independent planning are discussed, while the different uncertainty modelling and optimization methods that have been used in past studies in planning the energy hub are classified and reviewed to ascertain the appropriate techniques for addressing RES uncertainty when planning future energy hubs. Section 5 reviews the demand response strategies in planning MES. Finally, conclusions and recommendations for future work are given in Section 6.

2. Multi-Vector Energy System

2.1. Definition of Multi-Vector Energy Systems

There are different definitions of MESs in existing literatures. Ref. [37] defines an MES as an innovative integration used to describe the way in which energy sectors (e.g., gas, water, electricity, cooling, heat, transport, etc.) will increasingly interact among each other at different stages in order to allow more services and profitable streams that produce a more advanced and resilient energy system with less carbon emission. Ref. [38] defines an MES as a system where heat, gas, cooling, electricity, transport, etc., optimally interact with each other at different stages to constitute a good chance for technical, economic, and environmental performance that is much more different to the traditional energy systems where each of the sectors are managed separately. Ref. [39] defined their own MES as the process of linking and integrating of extended energy services and systems for the purpose of reducing waste and carbon dioxide in a profitable way to decarbonize different aspects of energy system while using different resources in a feasible way to provide a more flexible system by including resilient and more diverse energy sources. In general, an MES harmonizes the operation, planning, and scheduling of integrated energy systems, covering different channels and topographical areas to provide a more stable and rewarding energy service with little or negligible effect on the environment [40,41]. Figure 2 gives a detailed illustration of a possible future MES.

2.1.1. Various Categories of Energy Vectors Interactions and Interdependencies

The MES approach in energy system management has broadened the scale of opportunities when integrating different energy infrastructures. Various studies carried out recently show that the MES approach is recognized as the solution for future energy systems. Transition to future energy systems that place more emphasis on the move to zero-carbon emission can only be realized through this approach by integrating more RESs to move away from overdependence on fossil fuel in the power sector, using P2G technologies to decarbonize the gas and transport sectors and combined heat and power (CHP) to link the gas heating and electricity networks. The various categories of energy vectors interactions undertaken in an MES can be categorised as follows:

• Natural gas and electricity networks.
• District heat and electricity networks.
• Natural gas, district heat, and electricity networks.

2.1.2. Natural Gas and Electricity Networks Interdependencies

Currently, natural gas and electricity networks interactions are possible through the increasing use of modern devices such as gas-fired generators and CHP. These devices enable the coupling of both networks. Natural gas serves as a backup for the intermittent characteristics of renewable energy power generation in the electricity network. Ref. [42] studied how coupling of natural gas and electricity networks with high penetration of renewable energy sources can provide more flexibility to the whole system. It was observed that the conversion of renewable energy sources power production into hydrogen and other types of energy vectors using modern technologies provides significant flexibility to the electricity network. Ref. [43] proposed a unique method of integration of natural gas and electricity networks to solve the problems of wind power generation forecast uncertainty.

2.1.3. District Heat and Electricity Networks Interdependencies

The district heat and electricity interactions take place at either the community stage or at the district stage. This interaction occurs through the use of cogeneration technologies such as CHP for the production of heat and electricity simultaneously [44]. In addition, as the world look towards net zero, the electrification of the heating system is a good option to cut off carbon emission through the use of electric heating technologies such as heat pump versus the current use of gas boilers for heating which produces carbon emission. Ref. [45] investigated the planning and operation of cogeneration with references to the coupling of the district heat and electricity networks. The study showed a high reduction in carbon emission when CHP was used to produce both heat and electricity simultaneously, and a total cost reduction. Ref. [46] studied the possible linkage between district heating and electricity networks using demand response by considering to what extent domestic energy costs could be reduced with intelligent and price-based control concepts. The simulation results showed an added value of the proposed intelligent control approach over the standard approach in terms of reduced variable energy costs.

2.1.4. Natural Gas, District Heat, and Electricity Networks Interdependencies

The cogeneration technologies such as CHP serve as a link of interaction between the natural gas, district heating, and electricity networks. The natural gas serves as an input to CHP units, which in turn simultaneously produce heat and electricity to supply heating to the heating network and electricity to the electricity network or end users. Ref. [47] used a Sankey diagram to explain how the energy flows take place in integrated natural gas, heating, and electricity networks using different penetration of technologies such as CHP and electric heat pumps. It further analysed the effect of different technologies on the steady-state operational parameters of each network. Ref. [48] examined the effect of gas and heating networks when considering decarbonisation in the electricity network, and the results showed that gas and heating storage systems provided some level of flexibility to the electricity network.

2.2. Benefits

Multi-vector energy systems have several benefits compared to traditional independent energy systems. These are classified based on their technical, economic, and environmental benefits, as described in

Table 2. Benefits of multi-vector energy systems [49].

Technical	Economic	Environmental
Enhancement and increased reliability, flexibility, and security of electrical power systems. Use of energy storage to balance demand and supply.	Reduction in capital and operational costs of energy networks through exploitation of greater flexibility provided by an integrated system. Reduction in fuel costs due to increased overall efficiency. Makes customers active elements of the system.	Reduction of total carbon emission. Better management of variable renewable generation.

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2.3. Challenges

There are a few challenges that are required to be addressed for an effective implementation of MESs [37]. These challenges are grouped into technical, economic, social challenges, and regulatory policies, as shown in Figure 3 and

Table 3. Description of multi-vector energy system challenges [37].

Challenges	Description
Technical	The complexity of highly integrated energy systems. Necessity of a multidisciplinary effort in research and development that will be required to bring about a fully integrated, low-carbon energy system. Variability of load due to intermittent nature of RESs.
Economic	Traditional market for energy sector is fragmented and requires careful redesign to ensure that the overall system’s needs are met.
Social	The awareness of the end users is inadequate. It will require a long time and much handiwork to become familiar with it.
Regulatory	There is no familiar scheme and established signal for innovators. Energy trading scheme needs to be developed. There is no clear understanding about the benefits of flexibility in the energy system’s low policy stability.

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3. Multi-Vector Energy Systems Models

Planning of MESs requires advanced modelling techniques and tools for a proper coupling of different energy carriers, such as electricity, heat, and gas networks [38]. The network model should be chosen based on the precise application being examined. This is because there are numerous options available, varying from basic linear network models to comprehensive mathematical formulations of network steady-state or dynamic conditions. The EH approach is used in most studies for planning an MES model [50,51]. The EH concept was designed to illustrate how power flows in interconnected MESs [52]. Ref. [53] highlighted the economic importance of the EH concept, stating the importance of moving beyond the old way of developing big and extensive power plants with a controlled rate of return and moving towards a more decentralised energy system where the consumers will also participate actively. The EH concept, as a driver in implementing MESs, offers perfect ideas with regards to the efficiency of energy with the ability to convert complex energy infrastructures in a peculiar system interconnection [54]. Another benefit of the EH approach is its ability to synergise different energy carriers, thus expanding the system boundary beyond only one energy sector [47].

An electricity, gas, and heat network model will include each network’s model along with coupling components in the EH (e.g., heat pumps, cogeneration, etc.) that are linked to various networks. This is noticeable when analysing network models, such as Newton’s approach, because no coupling components appear in the Jacobian matrix [55]. Each network can be analysed separately in such situations, eliminating the need for larger MES network models. In this study, the EH model is used to link electricity, gas, and heating networks individually and compared to the case when all networks are linked.

Starting with the electricity network, Equations (1)–(4) are used to depict the electricity network model. Equation (1) is used to model the link from network buses and an EH model. Equations (2)–(4) represent the traditional electricity flow formulas, along with heat and voltage limits [56].

$$P_{en,t}^{Elec}+j{Q}_{en,t}^{Elec}={\displaystyle \sum }_{b\in en}{c}_{en,b}^{Elec}\left(E{i}_{b,t}^{EH}-E{o}_{b,t}^{EH}\right)$$

(1)

$$P_{en,t}^{Elec}+j{Q}_{en,t}^{Elec}={\displaystyle \sum }_i\left(Y_{en,em}^{Elec}\right)\ast V_{en,t}^{Elec}{\left(V_{em,t}^{Elec}\right)}^{\ast }$$

(2)

$$\lceil Y_{en,em}^{Elec}{V}_{en,t}^{Elec}\rceil \le I{x}^{Elec}$$

(3)

$$V{n}^{Elec}\le \left|V_{en,t}^{Elec}\right|\le V{x}^{Elec}$$

(4)

where P and Q represent the net active (kW) and reactive (kVAr) powers, respectively, $c_{en,b}^{Elec}$ is an EH efficiency matrix linking the buses in the electricity network to the EH, subscript Y represents admittance matrix of the electricity network, subscripts V and I represent voltages (V) and currents (A), respectively, and $en$ and $em$ represent the buses in the electricity network, while the line linking two electricity buses $\left(en \mathrm{and} em\right)$ is denoted by $l$. The input and output electricity (kW) are denoted by $Ei$ and $Eo$, respectively, while $t$ denotes time periods, and, finally, $Elec$ and $EH$ are used to represent electricity network and energy hub model, respectively.

A steady state model is used for natural gas to modelling in Ref [57]. Using a similar approach to the electricity network, Equation (5) represents the connection of the EH model to the natural gas network. Equations (6) and (7) represent the precise hydraulic equations used in these studies [47]. Natural gas introduced into or derived from a node as a nonlinear steady-state function of pressure is denoted in Equation (6); furthermore, the maximum and minimum pressure of the network model is denoted in Equation (7).

$$q_{gn,t}^{Gs}=\nabla t{\displaystyle \sum }_{b\in gn}{c}_{gn,b}^{Gs} G{i}_{b,t}^{EH}$$

(5)

$$q_{gn,t}^{Gs}={\displaystyle \sum }_{gm}\left\{K_{gn,gm}^{Gs}sing\left(p_{gn,t}^{Gs},p_{gm,t}^{Gs}\right)\times \sqrt[2]{sign\left(p_{gn,t}^{Gs},p_{gm,t}^{Gs}\right)\left[{\left(p_{gn,t}^{Gs}\right)}^2-{\left(p_{gm,t}^{Gs}\right)}^2\right]}\right\}$$

(6)

$${\left(p{n}^{Gs}\right)}^2\le \left|{\left(p_{gn,t}^{Gs}\right)}^2\right|\le {\left(p{x}^{Gs}\right)}^2$$

(7)

where $q$ represents the amount of gas injected into a node $\left({\mathrm{m}}^3/\mathrm{h}\right)$, $Gi$ stands for natural gas consumption, the pipeline constant is represented by the letter $K,$ the nodal pressures are denoted by $p$, the maximum and minimum pressure limits are represented by $px$ and $pn$, respectively, $c$ is an EH efficiency matrix linking the natural gas import from the EH and nodal flows [58], the gas nodes are represented by $gm$ and $gn$, and, finally, $Gs$ and $EH$ are used to represent natural gas network and energy hub model, respectively. It is important to note that in Equation (6), the sign function is +1 when $p_{gn,s}^{Gs}>p_{gm,s}^{Gs} \mathrm{and} -1$ otherwise.

Finally, the heat network is also interconnected to the other networks via energy conversion links, and it consists of a thermal module and a hydraulic module. The hydraulic module, similar to the natural gas network, is based on conventional steady-state equations [59]. As a result, the connections that link the EH model and the heat network are defined by Equation (8), which employs an efficiency matrix approach. Equation (9) represents the water nodal balance, and Equation (10) is used to calculate each pipeline water flow. Lastly, Equation (11) is used for pressure limits imposition [60].

$$q_{hn,t}^H=∆\mathrm{t}{\displaystyle \sum }_{b\in hn}{c}_{hn,b}^H\left(H{i}_{b,t}^{EH}-H{o}_{b,t}^{EH}\right)/∆T_{hn,t}^H$$

(8)

$$q_{hn,t}^H={\displaystyle \sum }_{l\in hm}q{l}_{l,t}^H$$

(9)

$$q{l}_{l,t}^H=K_{hn,hm}^{H}sing\left(p_{hn,t}^H,p_{hm,t}^H\right)\times \sqrt[2]{sign\left(p_{hn,t}^H,p_{hm,t}^H\right)\left[{\left(p_{hn,t}^H\right)}^2-{\left(p_{hm,t}^H\right)}^2\right]}$$

(10)

$$p{n}^H\le p_{hn,t}^H$$

(11)

In the above correlations, $q$ and $ql$ represent flows, i.e., if there is water, injected into a node and flowing through pipe $\left({\mathrm{m}}^3/\mathrm{h}\right)$, respectively. $c_{hn,b}^H$ are energy hub efficiency matrix elements that link heat import from the energy hub to nodal flows [61], the temperature drop (°C) is denoted by $∆T$, K stands for pipe constant, minimum pressure limits are denoted by $pn$, while pressure is denoted by $p$, the gas network nodes are presented by $hm$ and $hn$, and the heat network and energy hub models are represented by H and EH, respectively.

3.1. What Is an Energy Hub (EH)?

The EH approach has been a subject of growing interest by researchers in the implementation of MESs since when Geidl et al. introduced it for the first time in 2005 [62]. Ref. [63] defined an EH, relating it to a form of virtual box where energy carriers are converted into load energy demand. There are different technologies within the virtual box that convert and store energy, as shown in Figure 4.

Most studies refer to EHs as multi-energy, multiple energy carriers, multi-source, and multi-product systems [65]. Ref. [66] classified the EH in terms of size, stating that EHs could either be micro or macro EHs. They divided the micro EHs into residential, commercial, industrial, and agricultural micro EHs while stating that the EHs could serve as either of them. When micro EHs are integrated within an upper stage, they become inter-networks of connections of EHs which are referred to as macro EHs. The macro EH is defined as a collection of a network of more than one EHs that are organized and regulated in a coordinated way [67]. Therefore, an enlarged energy system such as a whole city or a region can be modelled with the concept of macro EH [66].

3.1.1. Energy Hub Model

A coupling matrix C is used to form a common EH model. Figure 5 represents an EH model with several input and output coupling factors [68].

The illustration of the coupling matrix is shown below:

$$\left[\begin{array}{c}{I}_1\\ I_2\\ ⋮\\ I_m\end{array}\right]\left[\begin{array}{cccc}{C}_{11}& C_{12}& \cdots & C_{1n}\\ C_{21}& C_{22}& \cdots & C_{2n}\\ ⋮& ⋮& \ddots & ⋮\\ C_{m1}& C_{m2}& \dots & C_{mn}\end{array}\right]=\left[\begin{array}{c}{L}_1\\ L_2\\ ⋮\\ L_m\end{array}\right]$$

The coupling coefficients across the input–output carrier, subscripts I and L, respectively, are denoted with $C_{mn},$ while the numbers of input–output carriers are represented with m and n, respectively [69].

3.1.2. The Energy Hub Basic Concept

The EH consists of the input and output units, conversion units, and the energy storage units.

Hence, it could be described as the generalization or extension of power system network nodes [70,71]. Figure 6 presents a sketch illustration of EH structure with numerous energy carriers. The structure contains inputs including natural gas, electricity, and district heat networks, and energy conversion elements such as natural gas boiler (NGB), CHP, transformer (TR), heat exchanger (HE), electric heat pump (EHP) and absorption chiller, as well as storage devices such as battery storage (BS) and thermal storage (TS), and finally the outputs demand such as heat, cool and electricity [54,72].

The EH consumes various energy carriers at the input, which are converted into other energy vectors to provide certain energy services at the output [54]. Furthermore, coal and petroleum products can also be used as inputs. Additionally, hydrogen, biomass, and municipal waste are other input energy carrier options that could be also examined. Besides the energy carriers mentioned earlier, chemical reactants, waste, water, and air could be used as energy if properly examined [50,73]. The approach of the EH in developing the system modelled is not restricted to a particular size. It allows the integration of any random number choice of energy carriers and products, with enough resilience in modelling of the system [74]. Technically, EH can be considered within the following four basic areas:

• Inputs: Energy vectors at the input (fossil fuels, solar and wind energy, electricity, hydrogen, water, gas).
• Converters: Used in the conversion of different energy resources (boilers, chillers, CHP unit, heat pump, fuel cell, electrolyser (P2G)).
• Energy storage systems (ESSs): Used to store or preserve surplus energy (heat storage, hot water tank, hydrogen tank, battery, ice storage, and flywheel).
• Output: The hub energy demands for end users (electricity, heat, cooling, gas, water, hydrogen) [75].

4. Planning and Management

The difficulties in MES planning and management are to determine the best mixtures of energy supply, storage, and conversion technologies, along with the network infrastructure, to meet the exact energy needs [44]. According to recent studies, integrated planning and management of MESs is preferable to the independent expansion implemented today [15]. In this study, we use deterministic or probabilistic methods to analyse the planning of MESs using the EH approach.

4.1. Deterministic Models

When the variables affecting the investment are assumed to be known with a high degree of certainty, deterministic methods are used. To assess the profitability of an investment, the discounted cash flow method with NPV (net present value), IRR (internal rate of return), and payback time indicators has traditionally been used. Ref. [76] investigated the economic assessment of CHP coupled district heating systems using the NPV and IRR indicators. Ref. [48] investigated a method for distribution-level expansion planning of an integrated electricity, heat, and gas system with a high penetration of gas-fired power generators. The study claims lower investment costs than methods that consider the expansion of each energy system separately. Ref. [49] investigated a method for planning the expansion of combined gas and electricity networks at the transmission level. The model was used to examine the expansion of the UK gas and electricity systems under various low-carbon scenarios. Ref. [50] investigated the design of multi-energy supply infrastructure for new build schemes with carbon emissions constraints. The study’s goal was to find the best combination of onsite and building-level energy supply technologies to meet energy service demand while also meeting greenhouse gas emission targets at the lowest possible cost to the developer. Ref. [42] investigated a method for determining the optimal coupling between networks in an integrated energy system that includes electricity, natural gas, and district heating infrastructure.

4.2. Probabilistic Models

Because of the uncertainties in the energy sector introduced by energy markets (e.g., natural gas price) and large volumes of intermittent generation, stochastic (or probabilistic) models are being used in design studies. Ref. [51] investigated a method for computing probabilistic NPV and IRR indicators for cogeneration planning under uncertainty using Monte Carlo simulations. Ref. [52] investigated a method for valuing investments in multi-energy conversion, storage, and demand side management under uncertainty. The ability to provide demand side management in the face of uncertain and volatile market prices was valued alongside the efficiency gains from integrating energy systems. In Ref. [42], the study was expanded to include location-dependent valuation of energy hubs with storage. Ref. [53] investigated a method for determining the optimal design of integrated energy systems based on their ability to respond to forecasted marker prices. Ref. [54] proposed a method for infrastructure expansion planning under uncertainty based on real options theory.

4.3. Planning Objective Functions (OFs) of Energy Hubs

The planning objective functions (OFs) could be described as the objective of making decisions when planning EHs. The planning objective could be grouped into technical, economic, and the environment. Figure 7 shows an example of an EH planning model flowchart. The OFs that are mainly used in planning EH models are minimization of investment cost, operational cost, and greenhouse gas emissions (e.g., investment cost of energy converters, storage devices) [64,77]. However, most of the papers reviewed on planning MESs focus on the economic and technical objectives, while only a few consider the environmental objectives. Furthermore, there is limited research on comparing the benefits of planning an EH synergizing multiple energy carriers with independent energy carrier planning considering the following objective functions mentioned below.

• Minimization of investment and operating cost.
• Minimization of lifecycle cost (LCC).
• Maximization of the share of RESs penetration.
• Minimization of energy cost and emissions.
• Minimization of primary energy consumption.
• Maximization of system reliability and profits.
• Maximization of social welfare.

4.3.1. Energy Hubs Planning Constraints

Constraints are the restrictions or limitations on decision variables. Constraints could either be equality or inequality constraints. The abovementioned OFs are subject to either operational or structural constraints. These comprise EH operating constraints along with the ESS and converters constraints. Power system constraints, the operational constraints of the power system, including the power balance equation, ramping rate limits, wind power availability constraint, and transmission flow limits. Gas system constraints, the operational constraints for a gas system, including nodal balance equations, well-flow capacity limits, nodal pressure limits, compressor constraints, and pipeline limits.

4.3.2. Decision Variables

These are the variables which will decide the output demand of the EH. In planning the EH to achieve the desired output, it is essential to first identify the decision variables that will help solve operational challenges. The EH planning model simultaneously picks appropriate energy converters and storage devices, selects their connection interrelation, and gives operating strategies for divergent cases. Therefore, decision variables include:

• Binary variable: e.g., identifying if the energy converter or storage device is chosen.
• Continuous variable: e.g., the energy flow of scenario at time [64].

4.3.3. Basic Framework for EH Optimization

Optimization models linked to EH can be classified into two basic optimization modes, namely:

• Structural optimization (i.e., finding the optimal topology and structure of an EH based on a specific demand and corresponding OFs).
• Operational optimization (optimal power dispatch in an EH or optimal power flow in the network of interconnected EHs for a given structure of the system).

4.3.4. Simulation Results

This section shows the results of two case studies that compares the benefits of planning an EH model that synergises multiple energy carriers, such as natural gas, electricity, and heat, simultaneously compared to that each energy carrier is planned independently under four schemes. Numerical results in Figure 8 show the comparison of the total planning costs of both case studies, while Figure 9 shows percentage of total costs reduction in the four different schemes used when the EH is planned synergising multiple energy carriers simultaneously compared to independent energy carriers planning.

Therefore, we can conclude that we will have an average of 12% reduction in the total planning costs.

4.4. Uncertainty Modelling Methods

With the high penetration of RES generation and the interconnection of the gas and electricity networks, there are uncertainties in the operation and investment decision-making process [78]. Many variables used in modelling are not constant and have random behaviour in nature, which can cause uncertainty if not properly checked. Hence, the consequences of this uncertainty should be considered in the optimization [78]. Uncertain parameters in energy systems are usually available in two groups, namely, uncertainty in a mathematical sense (i.e., measurements differences, estimated value and true values including errors in observation or calculation, etc.) and sources of uncertainty (i.e., weather forecast which affects RESs such as wind and solar, fuel price, energy price, market rules, unplanned outages, demand, etc.). Hence, to have a realistic result in the modelling and optimization process of the EH, it is essential to understand the effect of uncertainty on the system modelling and performance in order to select an appropriate technique to analyse their behaviour. A categorisation of uncertainty modelling techniques is provided in Figure 10 [78,79,80]. These techniques are robust optimization, interval-based analysis, probabilistic approaches, information gap decision theory, and hybrid probabilistic techniques. The goal of these techniques is to check uncertain input parameters’ effects on the output parameters of the system modelling and performance; however, each technique has different approaches in implementing various uncertainty of the input parameters [81].

The probabilistic methods use probability density function (PDF) to express uncertainty and are used when sufficient data are available, and the PDF of uncertain parameters is known. They are grouped into two main categories, namely, analytical and numerical methods. Analytical methods generally are based on approximation and the use of mathematical expressions to display the system input and output. One part of the analytical method is based on linearization and its main aim is to make output PDF from input PDF [74]. Mathematical operations such as calculating the coefficients of expansions, convolution, etc., are used to obtain output parameters in this method. However, due to the complexity and errors associated with the linearization method, the PDF approximation method was developed. The PDF approximation method is based on creating a good approximation of the input parameter’s PDF using the proper sample. The point estimation method uses sample data to calculate the best estimate and forecasts of a parameter’s value [76].

The unscented transformation method is the proper method used to examine the correlation between random variables and a very good method to calculate the output of random variables under a set of nonlinear transformations. This method is extremely effective; increasing the number of random variables does not reduce its accuracy but, rather, its run time relies on a few numbers of random variables and the PDF of the input parameters. Generally, uncertain parameters have several realizations that are sometimes not possible to examine completely. Nevertheless, they can be converted into a few limited and countable scenarios. Hence, this necessitated the bedrock for the development of a scenario method [76]. The scenario method converts continuous space to the limited numbers of discrete scenarios with the related probabilities, thereby increasing computational effectiveness. The scenario method, similar to every other approximation method, needs the statistical information of the input parameters. Furthermore, size of the model increases if the dimensions of the system are large, or the number of components is too high. Compared to the other methods under the approximation method, the scenario method is the most widely used and has many applications in the modelling of uncertainties and in relation to multiple uncertainties [78]. According to Ref. [82], the scenario method was used to examine energy price, demand, and wind power generation uncertainties in the optimal management of EHs. The study developed a multi-objective decision model for the examination of energy cost and the associated risks which provided the ability to make decisions under uncertainty by creating a trade-off between cost and reliability of the system. Pazouki et al., in [12], examined the consequences of distributed energy resource, DR, and the ESSs on the operation of a commercial EH to handle the uncertainties created by wind power, energy prices, and demand. They used MCS to produce an uncertainties scenario tree, while a sizeable number of generated scenarios was reduced with the help of the GAMS scenario reduction tool [83]. The numerical method is usually based on random sampling. Research from past studies on planning uncertainty in EHs shows that the MCS method is widely used due to its accuracy in handling complex uncertain variables. Furthermore, the MCS is very flexible, simple to run, functional in both convex and non-convex matters, and supports all kinds of PDFs. However, apart from being too expensive when computational aspect is considered, the number of desired simulations increases by increasing the solution space’s degree of freedom. Hence, there is need for a lot of simulations in order to obtain the desired result that is needed, thereby increasing the computational load. From another perspective, analytical methods such as probabilistic methods and point estimation methods can overpower this disadvantage of MCS, but some mathematical suppositions are needed in order to assist in simplifying the problem. The scenario method that is based on approximation has been proposed to overcome the shortages of MCS and some of the analytical methods. At times when the uncertainty parameters formulation is complex and when a lot of scenarios are used, the computational burden will increase. Therefore, this problem can be solved if the numbers are brought down to fewer useful scenarios [84]. Zarif et al., in [85], used MCS and created five different scenarios for different levels of uncertainty to analyse the influence of energy hub on reducing cost of energy and increasing profits in the presence of uncertainty of electricity prices. Kienzle et al., in [86], examined the optimal management of an EH in a model under uncertainty and changes in electricity prices. They considered the prices of all input and output energy carriers as random variables and MCS looked at several possibilities in prices of these energy carriers. Ref. [17] examined the optimal EHs interconnection sizing considering gas and electricity system physical constraints and environmental issues. MCS was used to study the impact of uncertainty in electrical and thermal loads. To enhance the system operation economic efficiency, a formulation for the capacity allocation of hybrid ESSs was proposed in Ref. [87] and the capacity allocation of hybrid ESS was obtained by MCS. The fuzzy method is a coherent method of solving uncertainty-related issues and modelling the actual behaviour. One of the main applications is the modelling and expression of the uncertainties and ambiguities of energy systems. The use of fuzzy logic to deal with uncertainties leads to model realization and obtaining more accurate results which facilitate optimization and decision-making processes. The fuzzy logic is used to accomplish realistic models and obtain desired results due to its ability to quantify the qualitative and linguistic terms, and it has a wide application in modelling and scheduling of energy systems. The fuzzy sets use the idea of fuzzy membership functions for uncertainty modelling. The fuzzy models are generally applied to realize system conditions and the characterization linguistic terms. There are several applications that are associated with the hybrid models in energy systems, ranging from the design of control systems to locate and determine RES optimal combinations, while there are mostly many computational loads in multi-criteria models with different applications such as the system control, emissions, financial risks reduction, and performance optimization [78,88]. Ref. [89] examined a method for levelling the RESs output changes with the help of fuzzy control. It controls the power output of PV according to system conditions and considering the solar radiation to make maximum use of sunlight. The results show that the fuzzy control makes a trade-off between reducing fluctuations and increases the use of radiation. The robust optimization (RO) approach is applied when the input parameters’ statistical information is not enough and it might result in additional PDF parameter uncertainties [90]. The RO method is very conservative; this is because instead of PDF, the interval values are used for displaying uncertainty and the problems are solved even for the worst case at the interval. RO assures the decision-maker that even if there are errors in the prediction of uncertainty parameters, the OFs value will remain optimized when a parameter is characterized by uncertainty [78].

4.5. Mathematical Techniques and Solution Algorithm for Planning Energy Hubs

The mathematic programming used in the planning of EHs is also referred to as optimization techniques. It is a scientific method used in analysing complex models. In addition, the optimization techniques could be described as the process of finding an optimal solution among a set of possible answers (an optimization problem includes a set of OFs, constraints of both equality and inequality, and, finally, decision variables) [78]. The aim of optimization is to solve the difficulty involved in making decisions with regards to significant systems with high percentage of possible solutions. One main issue with regards to EH installation is the reduction of cost. Due to a lot of operational constraints in the system, making decisions about controlling the EH needs a systematic approach which could not be solved using a simple rule-based approach. Rather, the challenges could be solved by the optimization process [65]. Discrete variable and complex constraints must be clarified in order to model the operational factors, and the clarification will lead to the formulation of either the mixed integer linear programming or the mixed integer nonlinear programming (MINLP). This is because the estimation of assets in the EH may change over time, and loads, RESs, and energy prices have a time-varying nature. Hence, decisions must be updated by re-running the optimization calculations after some interval known as the dispatch time, and the method is referred to as a model-predictive control (MPC) or rolling time horizon (RTH) [65]. The methods used for solving optimization problems are the mathematical (non-heuristic) and heuristic (intelligent search-based) methods. However, in this paper we focus mainly on the mathematical methods. The optimization methods related to EHs can be categorized as linear programming (LP), nonlinear programming (NLP), MILP, MINLP, etc. LP refers to the mathematical technique employed for the optimization of linear OFs and linear constraints [91]. The quickest method is the LP when compared to NLP and MILP. LP is beneficial for the operational optimization of an EH when ESSs are not available in the system [92,93]. LP is a method for finding the minimum or maximum of a linear function on a convex polygon. In a situation where the OFs and constraints are linear and decision variables are continuous, the optimization problem will be a linear problem. Hence, when the OFs is convex, the optimization problem will have a special solution. LP can be considered as the easiest and fastest optimization method, and even when there are many variables and constraints, the optimization problem can still be solved easily [94], while the NLP refers to the fact that the computation in this method is based on the derivatives [79]. NLP consists of both linear and nonlinear OFs and constraints; either the OFs or the constraints must incorporate one nonlinear term. Furthermore, if the OFs and constraints over a set of unknown real variables are nonlinear, the optimization problem becomes a nonlinear problem [78]. Refs [62,95] formulated a nonlinear structure for structural optimization, optimal dispatch, and optimal power flow of EHs accordingly. Both the practical and theoretical characteristics of NLP problems are considered when solving a problem, thus making it more difficult to solve when compared to LPs. The NLP problem could also be solved once the variable has been removed by a nonlinear term NLP is the slowest mathematical method when compared to both LP and MILP [65]. Ref. [96] used some methods to convert nonlinearity in the coupling matrix. For integer programming (IP), most or all variables are integers. MILP is the most widely used form of IP. MILP is similar to LP, with their difference being that in addition to continuous variables, the problem has integer and binary variables. In addition, similar to LP, the main objective of MILP is to find the minimum and maximum of a linear function over a space with linear constraints. However, the existence of discrete variables leads to discrete and non-convex solution space. Hence, solving this kind of optimization problem will require special methods such as branch and bound, unlike the LP-based problems (MILP problems are much more complex to solve than LP problems) [64,78]. In EHs, binary control variables, caused by ESSs, or describing the state of equipment using discrete steps, such as on/off and standby, the LP or NLP problems turn into MILP or MINLP. Studies have shown that most of the optimization problems related to EHs are either NLP or MINLP. Now, two groups of method are used in solving optimization problems in EHs. The linear equivalents method, which converts NLP problems to LP problems, and the linear relaxation method, which converts MINLP problems to MILP problems [78]. In the context of the EH, Refs. [94,97] used the linear relaxation method to convert MINLP problem into MILP [78].

5. Demand Response (DR)

DR program is an essential strategy for stabilizing the supply and demand of electrical power systems using the electricity market platform with smart technologies. DR can be used to balance electricity supply by providing various DR incentives to consumers in order to shift their consumption from peak demand period to off-peak period. It is important to state that in DR programs, participation of consumers is clearly based on volunteering acceptance of consumers [98]. Hence, it is the incentive payments and market-driven prices that are the main factors that attract consumers to participate in DR programs. DR programs are classified into two important groups: the incentive-based and time-based programs, shown in Figure 11.

Time-based DR, such as critical peak pricing (CPP), real-time pricing (RTP), and time of use (TOU), are tariffs that facilitate consumers’ time-varying rates that reflect the value and cost of electricity in different time periods. It is worthy to note the time-based DR program incentives or penalties are not applied to the consumers. RTP tariffs vary continuously during the day, reflecting the wholesale price of electricity. The TOU tariff establishes two or more daily periods. The CPP applies real-time prices in periods of extreme system peak. Incentive-based DR, such as emergency DR (EDRP), capacity market program (CAP), direct load control (DLC), interruptible/curtailable (I/C), ancillary service (A/S), and demand bidding (DB) programs, can assist participating consumers to reduce their loads at times requested by the program sponsor, issued either by a grid reliability problem or by high electricity prices [84,99]. While the CAP and I/C are mandatory programs and the participating consumers must pay some penalties if they do not curtail when directed, the EDRP and DLC programs are voluntary options and if consumers do not interrupt their consumption, they are not penalized. DB programs persuade consumers to provide load reductions at a price at which they are willing to be curtailed at posted prices [84]. Ref [100] Examined the issue of getting more response from DR. He recognized some technology that employed quick, reliable, automated communication that is essential for the effective implementation of DR program. Ref [101] Formulated a price-based gas-electricity DR via price-sensitive DB curves while also considering DR participation levels.

6. Conclusions and Future Work

Multi-vector energy system (MES) is the future of global energy systems, with its ability to synergise different energy sectors, such as the coupling of electricity and the natural gas network, that were traditionally operated independently to now operate under a single unit, paving the way for new opportunities which, if properly utilized, will create wealth for the energy sector. This paper will help academia and new researchers to better understand the concept of planning of MES using the EH approach.

This paper reviewed several studies in planning EHs which have been carried out to develop an effective model in the planning of MESs and also studies the energy hub planning model that compared the benefits of synergizing multiple energy carriers simultaneously compared to the traditional planning of individual energy carriers. Numerical results show 12% reduction in the planning cost in the case of simultaneous planning compared to independent planning. The sequence of this study considered detailed insight into MES explanations, definitions, and various categories of energy vectors integration. Benefits and challenges of MESs were thoroughly reviewed, to effectively understand the concept of MES. Furthermore, a comprehensive review of MES network models was undertaken, using the electricity, gas, and heat network models of each connected to the EH, while the deterministic and probabilistic models, uncertainty modelling methods, and optimization techniques in power system and the application of this methods in EH planning problems were reviewed systematically. Moreover, the DR strategies of MES in a liberalized electricity market were also highlighted.