1 Introduction

1.1 Research background

Energy, water, and the environment are necessary foundations for the sustainable development of human society. Figure 1 presents changes in population, total installed capacity, carbon emission, and human development index (HDI) over four decades in China. As the population grows, total installed capacity increases, contributing to China’s human development index and bringing massive carbon emissions. In particular, the total installed capacity has expanded 33 times, while per capita carbon emissions have increased 4.7 times. As the contradiction between energy demand and environmental crisis is further accentuated, the clean, low-carbon, safe, efficient, and sustainable energy system has become a national energy development strategy [1]. Therefore, some developing and developed countries have proposed net-zero carbon emissions targets [2].

Fig. 1
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Changes in China’s population, installed capacity, carbon emissions, and human development index over four decades

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Decarbonization, decentralization, and digitalization will be the leading energy systems driven by technology and the market [3]. Therefore, as an effective complement to centralized energy systems, distributed energy system has been proposed and has become a research topic as a kind of energy system [4,5,6]. However, there is no consistent, precise concept or definition of a distributed energy system. In 2006, Alanne and Saari [7] discussed the concept of distributed energy systems by analogy with information systems and summarized the pros and cons of a distributed energy system from flexibility, reliability, local and global well-being of humans, environment, and utilization of local resources and networks. In 2010, Yang [8] published a monograph “Distributed energy system” . Different designations of distributed energy systems are introduced in the monograph, such as distributed generation, decentralized generation, distributed power generation, and distributed energy sources [8]. The distributed energy system is relative to centralized energy supply methods such as large power grids and plants. It is an energy system arranged near the customer to meet its energy demand [8]. In 2018, Mehigan et al. [9] pointed out that there is no internationally accepted definition of distributed generation and considered that distributed generation is an electric power generation source connected to the distributed network. Based on the current development and applications, this review suggests the distributed energy system is a small-scale integrated energy supply system based on renewable energy or clean fossil fuels as energy source, isolated or connected only to the power distribution network, which is scalable as technology advances and evolves [8].

After nearly 20 years of development, distributed energy systems rely on clean fossil fuels or renewable energy sources, such as natural gas, hydrogen, solar energy, and wind energy, and are arranged near the users’ side, which can realize poly-generation of electricity, heating, and cooling [10]. Depending on users’ energy scale requirements, they can be divided into household-level, building-level, and community-level [5]. It mainly includes energy production unit, transport unit, and storage unit. Meanwhile, distributed energy systems-based users will transform from passive energy consumers to active, flexible prosumers. For example, Clarke and Searle [11] proposed the active building that integrates renewable energy technologies for electricity, heat, and transport and reduces operational energy consumption and carbon emissions by maximizing locally generated renewable energy utilization. Koirala et al. [12] have identified various approaches that can be used for energy system integration, such as Microgrids (MG), Integrated Energy Systems (IES), Virtual Power Plants (VPP), Energy hubs (EH), and Prosumer Community Groups (PCG). This research proposed the integrated community energy systems that can facilitate reliability and efficiency by integrating smart-grid technologies and demand-side management and achieving self-provision and system services. In all, distributed energy systems have become vital global energy systems. Figure 2 presents the policies related to energy system development in various countries worldwide.

Fig. 2
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Policies of different countries on energy systems

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1.2 Research status

Distributed energy systems are now becoming a research hotspot. This review searched “distributed energy system” by searching for “title, abstract, and keywords” in Scopus from 2010 to 2021 about 57,841 publications. Figure 3 presents these articles published annually, the percentage of different subjects, and the number of countries in the last decade of distributed energy systems. These publications on distributed energy systems have increased nearly 1.5 times from 2010 to 2021. Significantly, from 2018 to 2020, the number of articles published each year has exceeded 6500. These published articles are in Engineering, Computer science, Energy, Mathematics, Physics and astronomy, Environmental science, Materials science, Social sciences, Decision sciences, and others. Considering these publications by country, China and the United States have published the most articles, exceeding 10,000, followed by India, Italy, the United Kingdom, Germany, Iran, and Canada, with cumulative publications exceeding 2000 articles since 2010. It is clear that distributed energy systems have received great interest from researchers in various fields in many countries.

Fig. 3
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Research on distributed energy systems in the last decade: a articles published annually, b percentage of different subjects, c number of articles by country

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As early as 2010, Yang [8] published a monograph that systematically illustrated the advantages and disadvantages of distributed energy systems and analyzed the components, development status, problems, and future trends of distributed energy systems from technology, economic, and social aspects. In 2011, Manfren et al. [13] presented some available models for distributed generations planning and design of urban energy systems. In 2012, Basak et al. [14] reviewed the integration of distributed energy resources from microgrid’s control, protection, and stability. In 2013, Chen et al. [15] reviewed the gas-fired distributed energy system from political, technical, and economic perspectives in China. In 2017, Nosratabadi et al. [16] presented a comprehensive review of the distributed energy resources scheduling in power system by microgrid and virtual power plant perspectives. In 2018, Mavromatidis et al. [17] reviewed the uncertainty characterization approaches that will result in some suboptimal design decisions for the optimal design of distributed energy systems. In 2019, Fonseca et al. [18] provided a systematic literature review of distributed energy systems, including hydrogen as the energy vector from system design, plan, operation, and evaluation. Ahl et al. [19] holistically explored the potential challenges of blockchain-based P2P distributed energy. In 2020, Guerrero et al. [20] focused on transactive energy systems integrating with distributed energy sources, provided three general categories, and systematically analyzed different integration methods such as home energy management, optimal power flow, and P2P energy trading. In 2021, Khanna et al. [21] studied the household-level behavioral change for reducing energy consumption through interventions such as feedback, information, monetary incentives, motivation, social comparison. Moreover, Table 1 lists more review articles on distributed energy systems in the last decade. These review articles all focus on the planning, evaluation, modeling, optimization, control, and dispatch of distributed energy systems from different viewpoints, such as technical, economic, environmental, social, and political aspects [35], which are of significance for the integration and development of distributed energy systems.

Table 1 Some review publications about distributed energy systems in the last decade
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1.3 Research structure

Distributed energy systems have been proposed and developed for nearly two decades. With the introduction of carbon neutral and carbon peaking energy strategies by various countries, further promoting the development of distributed energy systems based on clean fossil fuels or renewable energy sources is imperative to improve energy efficiency and reduce carbon emissions [36]. As Berjawi et al. [3] said, a holistic view of the whole energy system considering the interactions of the components, is necessary for the planning, operation, and evaluation of future integrated energy systems [5, 37]. Based on the current research on distributed energy systems, this paper will systematically and holistically sort out the research contents, problems, and future development trends related to distributed energy systems. Figure 4 presents the review framework of distributed energy systems in this paper. Based on the current policy support, research status, and development of distributed energy systems, this review first introduces the generation unit, transport unit, and storage unit in distributed energy systems and then summarizes and discusses the essential characteristics of distributed energy systems. On this basis, this review provides a thorough overview of the current research on distributed energy systems from three aspects: system planning and evaluation, modeling and optimization, and operation and control, respectively.

Fig. 4
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Review framework of distributed energy systems

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The review focuses on the presentation and summary of the methods and ideas of the above three aspects. Sector 2 introduces distributed energy systems. Sectors 3 ~ 5 present system planning and evaluation, modeling and optimization, and operation and control methods. Finally, the research conclusions of this paper are presented in Sector 6.

2 Distributed energy systems

2.1 Energy generation unit

Clean and high-efficiency energy generation units can provide the primary energy for satisfying various user demands such as electricity, heating, and cooling. Energy generation technology mainly includes two types. One is based on clean fuel, such as natural gas, biomass, solar fuel, mainly internal combustion engine, micro gas turbine, fuel cell, Stirling engine, and other technologies. The other is based on renewable energy, such as wind energy and solar energy, mainly wind power, photovoltaic power, and photovoltaic solar thermal. These energy generation units are mainly characterized by multiple complementary sources, micro equipment, poly-generation of heat, cold and electricity, and low pollution.

2.1.1 Internal combustion and gas turbine engines

The internal combustion engine is the most familiar and widely used energy generation unit, with capacities ranging from kW to MW. They have the advantages of low-cost, high-power generation efficiency, flexible start-up, high reliability, excellent load following, and achieving waste heat recovery. Due to the fossil fuel-based operation of internal combustion engines, they produce about 10% of greenhouse gas emissions [38]. Therefore, the internal combustion engines transition from carbon-based to hydrogen-based fuels [39]. The efficiency improvement and reduced dependence on fossil fuels will become existing research directions for internal combustion engines [38]. Like the internal combustion engine, an alternative technology converting the internal energy of fuel combustion into electrical energy, gas turbines are also limited by the efficiency of the Carnot cycle. The combined cooling, heating, and power system composed of gas turbines can achieve an energy utilization efficiency of more than 80% and use clean fossil energy such as natural gas as fuel, which has better environmental performance.

2.1.2 Fuel cells

Fuel cells can directly convert the chemical energy of the fuel into electrical energy by some electrochemical reaction between natural gas, hydrogen, and oxygen [40]. This technology is a promising and attractive way to provide electricity and heat to rural areas and distributed homes, communities, etc., with a combined efficiency exceeding 80% [41]. Numerous fuel cells, such as Alkaline Fuel Cell (AFC), Phosphoric Acid Fuel Cell (PAFC), Solid Oxide Fuel Cell (SOFC), Molten Carbonate Fuel Cell (MCFC), Polymer Electrolyte Membrane Fuel Cell (PEMFC), and Direct Methanol Fuel Cell (DMFC) have been proposed and developed for applications in distributed generation, auxiliary power, transportation, and military space [42, 43].

2.1.3 Wind power

Wind energy is a clean and extremely abundant source of renewable energy. Wind power generation converts the wind’s kinetic energy into environmentally friendly electrical energy and is available in grid-connected and off-grid connections [44]. However, wind power generation is always characterized by randomness and uncertainty with variations in wind speed [17, 45]. These intermittent wind power will impact system reserves, reliability, expected carbon emissions, and costs [46]. Therefore, integrating wind power with other distributed generation technologies is necessary and feasible.

2.1.4 Solar energy

Solar energy generation is another clean and sustainable energy generation technology that is considered promising because of its inexhaustible supply, universality, high capacity, and environmental friendliness [47]. Lewis [48] pointed out that solar energy will be converted into electricity, heat, and fuel with much higher efficiencies, lower costs, and improved scalability. Recently, solar energy utilization contains solar electricity, thermal, and solar fuel technologies, such as photovoltaic, photovoltaic thermal, and solar hydrogen, that will be important for developing and applying a distributed energy system located at the user side [49].

2.1.5 Heat pump/air conditioner

To meet customers’ cooling and heating needs, heat pumps and air conditioners can efficiently convert electrical energy into thermal energy, thus realizing the integrated supply of cooling, heating, and electricity for distributed energy systems [50]. Air conditioners are driven by electrical energy to meet the cooling needs of users. Heat pumps can be classified as air-source, ground-source, or water-source heat pumps, driven by electrical energy, to meet users’ thermal energy needs [51,52,53]. Recently, heat pumps and air conditioners are essential high-efficiency and environmentally friendly heating/cooling technologies in distributed energy systems.

2.2 Energy transport unit

Distributed energy systems also comprise electrical energy transport, thermal energy transport, and working fluid transport, which deliver the generated energy from the generation units to the users. Since the physical properties of the transported quantities, such as electricity, heat, and fluids are different, their transmission devices, networks, and physical description processes are also different [54, 55].

2.2.1 Power distribution network

Different distributed generation units, such as wind power, solar power, fuel cell, gas turbine, and internal combustion engine, connect directly to power distribution networks by various power electronics devices [56] or directly provide the power for the consumers. The placement of distributed generation has a pivotal impact on the operation of the power distribution network. Appropriate distributed generation placement will reduce system loss, network capital, and operating cost and improve power quality, supply reliability, system stability, and loadability [57, 58]. Therefore, the power distribution network is the critical link between the distributed energy system and the electrical grid. On top of meeting the basic electricity demand of users, the power distribution network also undertakes the function of reverse power delivery to the grid [59]. Under this circumstance, the operation mode of the distributed energy system and power distribution network will be reconfigured due to the variations of the quantity and direction of active and reactive power and the distribution of voltage with the changes of users from traditional consumers to prosumers of electricity energy.

2.2.2 Heat network

Thermal energy is another primary energy demand of users, including hot water for bathing and heating in winter. For example, in the case of winter heating, it is usually satisfied by a centralized heat network at the district/community level or realized by an independent household heating network [60]. Such heating networks mainly include supply and return water networks and heat exchange equipment. Various heat networks consist of fluid flow, enthalpy flow, heat transfer rate, and other processes. The mass conservation, energy conservation, heat transfer equations and temperature, pressure, flow rate, and other parameters should be included in the network constraints with typical nonlinear features [61, 62].

2.2.3 Fluid network

In distributed energy systems, such as heating networks, natural gas networks, heat pump systems, and cooling systems, are composed of various fluid networks [63]. The fluid network mainly consists of components such as pipes, pumps, and valves. The usual fluids are natural gas, air, water, and refrigerants. Therefore, the flow characteristics of the fluid in the pipeline, the pump’s power characteristics, and the valve’s adjustment characteristics all need to be considered in the energy transport aspect of the distributed energy system [64, 65].

2.3 Energy storage unit

Due to the randomness and uncertainty of renewable energy sources such as wind and solar, energy storage units are essential for distributed energy systems to provide stable, reliable, economical electricity, heating, and cooling for users’ energy needs [66, 67]. Various energy storage technologies have been proposed and applied in distributed energy systems, such as electrochemical supercapacitors, flow batteries, lithium-ion batteries, superconducting magnetic energy storage, flywheel energy storage, compressed air storage, and thermal energy storage [68]. For the application scenarios of distributed energy systems, electrical energy storage and thermal energy storage are the more mature energy storage application technologies in distributed energy systems. For example, Sameti and Haghighat [69] considered electrical energy storage (battery bank) and thermal energy storage (hot water bank) in a district energy system which will bring significant economic and environmental benefits. Yuan et al. [70] integrated thermal energy storage into an internal combustion engine-based distributed energy system and presented that a thermal storage system can improve the primary energy efficiency. In different distributed energy storage application scenarios, the capacity, power, and response time of energy storage devices vary greatly.

2.4 System characteristic

Based on the development and application of distributed energy systems, this paper proposes and presents a sketch of a distributed energy system, as shown in Fig. 5. This distributed energy system contains electricity, heating, cooling, gas, and transportation. The energy generation unit includes photovoltaic (PV), wind power (WP), and fuel cell (FC) connected to the power distribution grid to satisfy the electric energy demand of customers and interact with the transmission grid through the distribution grid connection. Meanwhile, the fuel cell can convert clean fuels such as natural gas and hydrogen into electrical and thermal energy for cogeneration. A gas boiler (GB) is also introduced to generate heat to satisfy users’ thermal energy requirements. As an efficient energy conversion device, heat pumps (HP) and air conditioners (AC) can turn electricity into heating and cooling. This system introduces a heat storage (HS) device used to break the real-time balance constraint between heat supply and heat demand in the heating supply segment. The electricity supply segment introduces an electricity storage device (battery), which breaks the real-time power balance constraint between the electricity supply and demand. Besides, in the proposed distributed energy system, electrical energy can also be converted into hydrogen through some power to gas devices, which can be turned into fuel for storage by an electrochemical process. At the same time, fuel can be dispatched to meet part of users’ gas demand. In order to coordinate the production, transport, storage, and supply of different energies in the distributed energy system, it is also necessary and significant to develop a power conversion system (PCS) and energy management system (EMS) to regulate the distributed energy system for achieving efficient, clean, safe, and reliable operating of the distributed energy system [64, 71].

Fig. 5
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Sketch of a distributed energy system

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Based on the distributed energy system shown in Fig.5, this review concludes the characteristics of distributed energy systems: multi-energy interaction, multi-temporal scale, and multi-objective regulation (n-M characteristics). The multi-energy interaction includes multi-energy complementarity in the energy production sector, multi-energy flow synergy in the energy transport sector, and multi-mode coupling in the energy storage sector. Different application scenarios like household-level, building-level, community-level, and city-level are the characteristics of distributed energy systems with multiple spatial scales [64, 71]. As shown in Fig. 6, household-level distributed energy systems are kW-scale, while building-level and community-level distributed energy systems may be MW-scale, and various distributed energy systems at the city-level may form the GW-scale. Meanwhile, distributed energy systems contain multiple links of conversion, storage, and transmission between different forms of heat, electricity, and gas, covering a variety of physical processes such as heat transfer, mass transfer, fluid flow, and electrochemistry, involving different time scales from milliseconds, seconds, minutes to hours shown in Fig. 6, as well as multiple connection methods such as series, parallel and multi-loop layouts between components [54, 63, 64, 71]. In terms of users, different loads such as electricity, heat, and gas are also characterized by uncertainty and multiple time scales, such as second, minute, and hourly scales. In addition, due to the random and uncertain characteristics of wind power and photovoltaic power generation, sufficient system flexibility is necessary to ensure the complete and adequate accommodation of renewable energy. However, for energy conversion equipment such as fuel cells, heat pumps, and air conditioners, it is necessary to improve energy conversion efficiency and utilization as much as possible. Therefore, for different application scenarios and user needs, the system also has multi-objective regulation characteristics, including technical, economic, and social indicators, such as synergistic flexibility and efficiency indicators, synergistic technical and economic indicators, synergistic technical and social acceptability indicators.

Fig. 6
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Typical characteristics of the distributed energy system

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3 System planning and evaluation

3.1 System planning framework

3.1.1 Mixed-integer programming

The planning of distributed energy systems is sophisticated and multidimensional due to source-load uncertainties, coupling characteristics of devices, nonlinearity, and joint optimization objectives [72, 73]. In 2010, Ren and Gao [74] developed mixed-integer linear programming (MILP) model for the integrated plan and evaluation of distributed energy systems by minimizing overall energy costs under the given site energy loads, local climate data, utility tariff structure, and some technical and financial information of alternative equipment. Based on the MILP model, Mehleri et al. [75] developed the optimal planning and evaluation of distributed energy systems by integrating PV, CHP units, heating networks, thermal storage tanks, and electricity transmission lines and then determined the optimal combination, allocation, and operation strategies of distributed energy resources technologies. On this basis, Bracco et al. [76] presented a distributed energy system optimal design tool based on the MILP model to optimize a distributed energy system that provides heating, cooling, and electricity to an urban neighborhood. Huang et al. [77] presented a two-stage MILP approach that considers a district-level multi-energy system planning as a directed acyclic graph with multiple layers based on an energy hub model considering distributed renewable energy integration. This model can optimize the equipment option and multi-energy system configuration by sensitivity analysis of load profiles, energy prices, and equipment parameters. Similarly, Liu et al. [78] developed a distributed hydrogen-based multi-energy system and proposed an optimization planning model under the optimization objective of minimum annual capital and operation expenditure for ensuring the optimal component capacity and combination.

Besides, the MILP-based planning of distributed generation in the distributed energy system is also developed from the power system perspective. For example, Wouters et al. [79] proposed a MILP model to integrate microgrids and distributed energy systems in the current grid infrastructure that lacks locally appropriate economic and efficient energy design. The model integrated the operational characteristics and constraints of different distributed generation technologies to minimize the total annual cost of the residential energy system. Yang et al. [80] considered the annual cost of investing, maintaining, and operating of the distributed energy resource systems as the optimization objective and provided the optimal energy generation site, equipment type, capacity, and number based on the MILP model. Meanwhile, the energy storage system planning has caused more attention in recent distributed energy system planning. For example, Bai et al. [81] considered the new power electronic devices in the distributed energy storage planning by proposing an optimal planning model of distributed energy storage systems in active distribution networks based on the soft open points by the mixed-integer second-order-cone programming. Bozorgavari et al. [82] proposed a robust planning model for distributed battery energy storage systems from the perspective of distribution system operators based on an equivalent linear programming model. Mao et al. [83] proposed the mathematical formulation of the energy storage system into the generation expansion framework by integrating the dynamic charge/discharge efficiency, maximum cycle power, and cycle degradation of the lithium-ion battery system. Pirouzi et al. [84] proposed an effective hybrid planning of distributed generation and distribution automation in distribution networks for improving the reliability and operating indices under the minimum of the sum of the expected daily investment, operation, energy loss, and reliability costs by introducing a stochastic programming approach for the uncertainty parameters analysis.

Therefore, the mixed-integer linear programming method is an effective and feasible mathematical modeling approach for solving complex optimization tasks and identifying potential trade-offs between conflicting objectives. As a mathematical framework for distributed energy system planning optimization, it is particularly important for addressing the ability to discretize in time and space and for system planning the transition to a non-dispatchable energy-dominated system. Figure 7 presents the planning methodology flowchart as follows. 1) Collect problem-related input data and identify decision variables. 2) Model the system and determine the objective function of the system requirements. 3) Determine the constraints in the system such as equipment, economic, environmental, operational constraints, and other factors. 4) Simulate the model by substituting the input data under different conditions into the MILP model and solving it appropriately.5) Select the optimal solution and evaluate the planning results practically in various aspects to verify system feasibility.

Fig. 7
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The flowchart of the planning method

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3.1.2 Objective-oriented planning

Another part of planning studies on distributed energy systems focuses on different optimization, operation, and management levels considering different planning objectives such as technical, economic, environmental, social, and political. Therefore, this review article summarizes this type of research as objective-oriented planning based on planning optimization objectives. Falke et al. [85] provided an overview mode of the optimization problem of distributed energy system planning. This model includes input parameters, pre-processing, optimization model, and results. A multi-objective optimization model for the investment planning and operation management of distributed energy systems is proposed by considering energy efficiency and supply options. Meanwhile, Wu et al. [86] introduced the economic and environmental objectives for obtaining the optimal distributed energy generation components, the site and size of the solution technology, optimal operational schedule and layout of heating pipelines by combining the MILP model. The results show that user preference, load fluctuation, and fuel prices considerably impact the distributed energy network performance. On this basis, Wang et al. [87] proposed a multi-objective including technological, economic, environmental, and social criteria, such as the related primary energy saving ratio, payback period, carbon emission, and social acceptability, for the natural gas-based regional distributed energy system planning. Meanwhile, Jing et al. [88] explained the relationship between multi-objective optimization and multi-criteria evaluation and presented a novel two-stage framework for the optimal planning of distributed energy systems. The optimization stage considers the system design and dispatch by multiple-objectives ε-constraint method, and the evaluation stage consists of the analytic hierarchy process and gray relation analysis method for evaluating and ranking optimal solutions.

Meanwhile, the consideration of system operation performance and source-load uncertainties is also necessary and significant for the objective-oriented planning of distributed energy systems by the multi-layer planning method [89]. For example, Ahmadi et al. [90] proposed a multi-objective multiverse optimization method by introducing two basic objectives, voltage profile improvement and cost minimization of the planning for the optimal allocation and sizing of renewable distributed generation and operation of energy storage systems. Wang et al. [91] proposed a multi-objectives optimization method for the optimal design of distributed energy systems considering uncertainties combining Monte Carlo simulation and deterministic programming model. Fonseca et al. [92] also carried out the total annualized cost, CO2 emissions, and grid dependence as objection functions to present a multi-criteria optimization strategy for the optimal design and operation of the distributed energy system by considering the time-varying operation of energy conversion units and seasonal behavior of the storage system. Based on the dual-layer planning solution, Mu et al. [93] developed a dynamic energy hub model considering the time-varying-based efficiency correction model and built a double-layer planning model to determine the optimal planning and operation schemes for the integrated community energy system. Wang et al. [94] considered equipment exergy efficiency in the upper-level planning model and economy and exergy efficiency in the lower-level planning model for the regional integrated energy system planning. Therefore, multi-layer planning can introduce different optimization objectives and is an effective method for objective-oriented planning of distributed energy systems.

3.2 Objective and evaluation

Combined with the above planning summary of distributed energy systems, objective selection and system evaluation are extremely important for the planning and optimization of distributed energy systems. As early as the 1970s, Balderston [95] considered that the perspective placing environmental and social impacts on the heart of energy predicament would become essential to compare impacts generated by alternative energy options systematically, comprehensively, and objectively. Distributed energy systems are arranged directly on the customer side and contain different energy conversion, transport, and storage components, enabling direct interaction between energy generation and consumption. Therefore, when planning and evaluating the performance of distributed energy systems, it is necessary to consider the comprehensive performance and environmental impact of the system and the stability, safety, and reliability of the energy supply used by customers [96]. These optimization objectives and evaluation indicators include technical, economic, environmental, social, and political aspects. In addition, some scholars have also adopted a comprehensive evaluation that considers several aspects simultaneously to measure the performance of distributed energy systems [97].

Figure 8 concluded the main optimization objectives and evaluation indicators of distributed energy systems from technical, economic, environmental, social, and political aspects [3, 12, 30, 64, 71, 98,99,100]. In the technical aspect, energy efficiency [101], primary energy saving ratio [102], and exergy efficiency [102] have been proposed and applied in the optimization and planning evaluation for the distributed energy systems. Energy efficiency is defined as the ratio of the total energy output of a system to its energy input. The primary energy saving ratio is defined as the ratio of primary energy reduction of the proposed system compared to the separated production system to the primary energy consumption of the separated production system. Similar indicators include primary energy savings [103] and primary energy saving [104]. Besides, exergy analysis is also a reasonable and efficient method to identify the types, magnitudes, and locations of irreversibility in a thermodynamic system [105]. In terms of environmental, emissions such as carbon dioxide are generally calculated using multiplying the emission equipment output with the intensity factor of the relevant emissions. The common environmental evaluation indicators according to this calculation method are CO2 emission reduction ratio [106], the PM2.5 emission reduction ratio [107], and greenhouse gasses reduction [103]. Besides, the planning and optimization of distributed energy systems also focus on the economy, such as the annual total cost saving ratio [106], operating cost savings [108], net present value [109], and payback period [110]. The operating consumption can be calculated by multiplying the power output of different energy sources by the corresponding energy consumption coefficients. The net present value relates all incomes and outcomes existing through the lifespan of the plant to the initial investment. The ratio of the additional capital cost to the saving of the distributed energy system’s operating cost compared with the centralized energy system.

Fig. 8
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Optimization objectives and evaluation indicators of distributed energy systems

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However, a single evaluation method often yields results that are not comprehensive enough, so in the study of actual objects, researchers often use multiple evaluation methods to achieve the advantages and overcome the flaws of the evaluation methods. After determining the common evaluation indicators of distributed energy systems and the analysis of individual indicators, the comprehensive performance of the research object can be evaluated by considering all types of indicators together. Hou et al. [111] introduced the annual costs, main energy rates, and annual carbon emissions to comprehensively evaluate distributed energy systems. Berjawi et al. [3] provided a whole energy system approach for system evaluation from multidimensional, multivectoral, systemic, futuristic, and applicability characteristics. Table 2 also presents some literatures on comprehensive evaluation methods for distributed energy systems. These evaluation methods are mainly subjective, objective, and other methods. Subjective methods include the Delphi method, Analytic Hierarchy Process (AHP), and fuzzy assignment. Objective methods include the Entropy Information method and Grey Relation Analysis (GRA). However, Fattahi et al. [120] considered that the traditional consumer would become the prosumer that plays an essential and active role in the distributed energy system. Therefore, the modeling of the distributed energy system should also consider technological and social factors. Although quantifying the social parameters is usually difficult, the behavior of the prosumer should be considered in the distributed energy system planning and modeling. Koirala et al. [12] also showed the assessment criteria from locality, modularity, flexibility, intelligence, synergy, customer engagement, and efficiency, which will become more critical for designing and analyzing distributed energy systems. Therefore, For the planning of distributed energy systems, comprehensive, quantitative, and operational optimization objectives and evaluation indicators should be further established, taking into full consideration different aspects such as technical, economic, environmental, social, and political aspects.

Table 2 Literatures on comprehensive evaluation methods for distributed energy systems
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In summary, with the development and application of energy storage and renewable energy technologies and the active participation of end-users, the future planning of distributed energy systems will be directly oriented to users. The planning should clarify different users and revenue generators, determine acceptable planning targets for multiple parties, and fully consider the complementarity and uncertainty of multi-energy production and multiple types of user loads, including geographical differences, climate, user behavior forecasts, and market price fluctuations. The planning should also consider the multi-scenario operation characteristics of the system and realize the optimal dynamic planning of the distributed energy system by synergizing the system flexibility and the efficiency of each device under different time scales. Meanwhile, in the face of future distributed energy systems clustered on the power distribution network side, there is necessary to develop artificial intelligence computing techniques that combine efficiency and accuracy to accommodate more complex optimal planning and evaluation of distributed energy systems.

4 Modeling and optimization method

Distributed energy systems are typical heterogeneous energy flow systems. The simple coupling of different forms of energy flow makes the mathematical models describing the physical processes highly heterogeneous, resulting in system equations with strong nonlinearities and low computational efficiency [5, 64, 71]. Koirala et al. [12] reviewed the primary problems and trends of the integrated community energy system. Some technologies, actors, institutions, and market mechanisms complicate the implementation of local energy systems that need a more bottom-up solution for capturing all the benefits of distributed energy sources and increasing the global welfare. Fattahi et al. [120] reviewed 19 integrated energy system models and provided seven current and future low-carbon energy system modeling challenges that are increasing flexibility need, further electrification, the emergence of new technologies, technological learning and efficiency improvements, decentralization, macroeconomic interactions, and social behavior role. For example, social behavior is usually difficult to quantify and neglected in the quantitative energy models. However, this is important in decentralized energy systems such as distributed energy systems [121]. In fact, various integration and modeling options such as Microgrid, Virtual power plant, Energy hub, and Prosumer community groups have been proposed for the planning, modeling, optimization, and operation [5, 122]. In these modeling methods, microgrid modeling focuses on electricity generation and demand optimization, including power reliability, security, and sustainability [123]. In addition, the virtual power plants can aggregate various distributed energy generation and consumption to form flexibility capacity equivalent to a power plant [12, 122]. The energy hub favors the multi-carrier optimization of electricity, gas, heating, and cooling within a district by optimal dispatch [12]. Prosumer community group is defined as “a network of prosumers having relatively similar energy sharing behavior and interests, which purser a mutual goal and jointly compete in the energy market [124]”, and puts more effort into energy exchange among prosumers having similar goals [12].

The integration and coupling of various energy carriers increase the complexity and interconnectedness of components in distributed energy systems [3, 37, 125]. According to the essential characteristics of distributed energy systems, a unified modeling perspective covering the conversion, transmission, and storage processes of different forms of energy, such as electricity, heat, and mass, is significant and essential [64, 71, 126]. Different modeling methods have their own characteristics and are suitable for different application scenarios. From the perspective of the power system, distributed energy system makes the source-load interaction on the user side. It focuses more on system characteristics such as power balance, stability, flexibility, and controllability. From the perspective of the thermal system, distributed energy system has electrical energy, chemical energy, and thermal energy conversion between each other, more focused on the concern of energy conversion efficiency, irreversible losses, and the exergy efficiency of the system. Meanwhile, various devices are often connected through transmission processes such as electrical energy, thermal energy, and kinetic energy transmission in distributed energy systems. The modeling of distributed energy systems should also be analyzed from the perspective of energy transmission. Therefore, in the modeling and optimization method sector, based on these perspectives of electrical energy transmission, energy conversion, thermal energy transmission, etc., this review will provide some current critical research perspectives such as the energy hub method, thermodynamic analysis method, heat current method, and data-driven method, respectively.

4.1 Energy hub method

Energy hub was proposed by Prof. G. Anderson in 2006 [127, 128], i.e., “transformation, conversion, and storage of various forms of energy in centralized units,” which is a powerful approach for next-generation energy systems and is feasible for the distributed energy system modeling and optimization. Figure 9 presents an energy hub example sketch that contains a transformer, natural gas-based microturbine, heat exchanger, furnace, absorption chiller, battery storage, and hot water storage. This model can be considered a black-box component with multiple energy flow inputs and outputs [129]. Recently, Mohammadi et al. [130, 131] have developed a review of the Energy hub, provided the utilization of the dominant structure for energy hub models, identified and discussed weaknesses, strengths, and challenges.

Fig. 9
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Energy hub example sketch [128]

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The energy hub model has been used for the planning, modeling and optimization of distributed energy systems [132]. Mohammadi et al. [131] present some important research in the field of the energy hub, such as planning, optimal operation, demand response, and energy management at various levels. For example, Ma et al. [133] introduced a micro-energy grid integrating the power, heating, and cooling sector based on the energy hub and developed a genetic modeling method for the energy flow of the micro energy grid. Finally, a day-ahead dynamic optimal operation model combined with demand response is formulated to minimize the daily operation cost. Mostafavi et al. [134] stated that numerous publications had discussed energy hub elements optimization in a single-objective state by assuming some constant coupling matrix parameters. Therefore, a new energy management strategy for a sustainable coastal urban energy supply system was obtained by modeling and optimizing the energy hub network under a comprehensive thermodynamic analysis. Li et al. [135] proposed an optimal user-level integrated energy system planning framework based on the extended energy hub by considering synergistic effects under multiple uncertainties. Qi et al. [136] established a smart energy hub model consisting of combined heat and power, an HVAC system, heat storage, and electricity storage units. This model proposed an energy cost minimization strategy by dynamic control of the heat-power ratio of combined heat and power, flexible load management, and energy storage system control.

Meanwhile, the energy hub concept can also be used to model and optimize the integration of multiple distributed energy systems. For example, Moghaddam et al. [137] provided an innovative energy flow-based method for energy hub modeling containing electricity, heating, and cooling loads. This energy hub modeling incorporates the potential technical interconnections between different distributed energy system components: CHP generation system, electric heat pump, absorption chiller, electrical energy storage, and thermal energy storage. Sobhani et al. [138] stated that an individual energy hub’s optimal operation and schedule could affect other energy hubs in a large network. Therefore, a congestion game is used in this research to model the interaction between energy hubs and propose a distributed algorithm that can achieve Nash equilibrium. In the game process, each energy hub player participating in the dynamic energy price market can maximize the related payoff under the constraints of energy demand. Rastegar et al. [139] designed a renewable energy-based energy hub framework on the residential level to present the interaction of energy carriers, including combined heat and power plug-in hybrid electric vehicles, solar panels, and electrical storage systems. On this basis, an optimization program was proposed to obtain the energy hub’s optimal operational modes under minimizing customer payment costs. Meanwhile, Yang et al. [140] proposed a distributed planning framework that is different from centralized planning, based on the alternating direction method of multipliers. Each energy hub is considered the decoupling node of the electricity and gas networks in this framework. Wang et al. [141] proposed a standardized matrix modeling method for building the multiple energy coupling matrix based on the energy hub concept and reduced the nonlinearity of the energy hub-based optimization model.

Besides, in considering system uncertainty and microgrid, Nikmehr [142] introduced the energy hub concept into the networked microgrids structure to reveal the potential capabilities of microgrids in satisfying various energy demands. Chen et al. [143] proposed a two-stage robust planning-operation co-optimization method for the energy hub that considers uncertainties of renewable energy and multi-load demands, the selection problem, and the exact economic model of the energy storage system. Meanwhile, Shams et al. [144] proposed an energy hub-based microgrid model for the optimal scheduling of electrical and thermal resources, which considers such stochastic variables as renewable generations, electricity, and thermal loads by probability distribution functions. Lu et al. [145] established an energy hub-based environmentally-aware load dispatch model that considers the electrical and thermal demand response programs and analyzed the proposed robust optimization approach to analyze the uncertainty of electricity prices. Hu et al. [146] introduced scenario-based stochastic programming into the energy hub models presenting the intrinsic coupling relationship among different energy carriers for considering the uncertainty of renewable energy sources.

In conclusion, the energy hub method provides a practical and alternative solution that identifies four main functionalities: input, conversion, storage, and output [131]. This approach is a holistic view that establishes the relationship between different energy storage, conversion, and transfer by describing the external properties of the components such as the allocation matrix and the coefficient matrix. However, for the source-load uncertainty and the deep involvement of users in distributed energy systems, accurate analysis of the dynamic characteristics of different components and construction of their operation models are the basis for improving the efficiency and flexibility of distributed energy systems. Therefore, Future research should focus on accurately characterizing the complex properties of conversion, transport, and storage among multiple energies, the multi-time scale dynamics, and nonlinear interactions in modeling distributed energy systems.

4.2 Thermodynamic analysis method

The direct conversion process of electrical, thermal, and chemical energy is an elementary part of the distributed energy system. Renewable energy-based devices such as wind power and photovoltaic are characterized by randomness and uncertainty, focusing on considering the system’s flexible regulation capability. In contrast, clean fossil fuel-based fuel cells, micro gas turbines, and electro-thermal conversion devices such as heat pumps focus more on energy conversion efficiency. Therefore, coordinating system flexibility and efficiency at the level of distributed energy systems are extremely critical for efficient and reliable system operation. Exergy is derived from the second law of thermodynamics and measures energy quality such as heat, electricity, and fossil fuels. Since different energy demands are characterized by different energy quality levels, such as building heating or cooling, hot water, electric appliances, and lighting, the exergy analysis can be used to promote the matching of energy quality levels between energy supply and demand [147, 148]. Distributed energy systems can match the quality levels of energy supply and demand and have a unique opportunity to obtain the exergy analysis benefits [147]. Therefore, exergy analysis-based thermodynamic modeling and analysis of distributed energy systems have been developed and focused on in many literatures by energy conversion, exergy, and exergy-economic concepts [149,150,151,152]. Park et al. [153] reviewed both energy and exergy analyses of typical energy systems based on solar energy utilization.

On the one hand, for the energy cascade utilization in distributed energy systems, in 2015, Di et al. [147] considered that the application of exergy principles in building energy supply energy systems could achieve rational energy resource utilization by introducing the different quality levels of energy resources and demands. That is, the energy cascade utilization based on different energy quality levels can effectively improve the overall exergy efficiency of distributed energy systems. For example, low-temperature energy sources should be used to meet the low-quality thermal energy demands. Meanwhile, the multi-objective considering the economic and exergetic objectives is formulated to choose an optimal operation strategy. Yan et al. [154] applied the exergy principles in the operational optimization of distributed energy systems by considering the whole energy supply chain from energy resources to energy demands. The energy networks with the exergy loss model are established at the energy conversion step and capture complicated interactions. The minimization of total energy cost and exergy loss results demonstrated that reducing high-quality energy resource utilization could reduce the exergy loss and lead to sustainability of energy supply systems. Wang et al. [155] pointed out that matching waste heat recovery technologies and various heat sources at different temperatures based on the energy quality is essential and can improve the whole distributed energy system efficiency.

On the other hand, renewable energy-based fuels are becoming significant for distributed energy systems. For example, Liu et al. [49] proposed a solar-hybrid fuel-fired distributed energy system. The overall efficiency, exergy efficiency, and net solar-energy-to-electricity efficiency are used to analyze the system performance and state the efficient utilization solution of solar and clean fuel in distributed energy systems. Moreover, Zhang et al. [156] proposed a solar-assisted combined cooling, heating, and power system for improving the energy conversion and utilization efficiency of renewable energy in the distributed energy systems and analyzed the system performance by introducing the solar-to-electricity efficiency and exergy efficiency concepts. Zheng et al. [157] proposed a new distributed energy system that considers solar thermochemical hydrogen production by upgrading the energy level from thermal to chemical energy. On this basis, the solar-based produced hydrogen is converted into power by cascaded utilization of solid oxide fuel cells and micro gas turbines. The proposed system combining power, cooling, and heating is analyzed from thermodynamic, energy, and exergy perspectives. Yuan et al. [158] proposed two combined cooling and power systems for satisfying the diversified power and cooling demands of distributed energy systems. Based on the established mathematical models, detailed exergy and thermoeconomic analysis were performed for the optimal system performance. Wang et al. [159] proposed a solar-assisted gas turbine-based combined cooling, heating, and power distributed energy system. It analyzed the system performance by combining energy, exergy, exergoeconomic, and environmental. Yang and Zhao [160] put forward the solid oxide fuel cell-steam-injected gas turbine-based distributed energy system fueled by liquefied natural gas with CO2 recovery. They calculated the system’s exergy, thermal, and power efficiencies and then analyzed the influences of some critical parameters on the system thermodynamic performance. Guo et al. [161] considered that the thermodynamic performance and optimization design of novel distributed energy systems combining with solar utilization and hybrid energy storage are still insufficient. On this basis, this research proposed a distributed energy system with hybrid energy storage, analyzed system thermodynamic performance by parameter analysis method considering exergy efficiency and primary energy ratio, and optimized the configuration by a cooperative optimization method considering system configuration and operation.

Table 3 lists more literature about distributed energy systems by energy and exergy analysis methods. Di et al. [173] concluded that the economic assessments-based design and optimization of distributed energy systems for short-run benefits is insufficient. Applying exergy principles can improve energy utilization efficiency for the long-run sustainability of the energy supply. Moreover, Li et al. [174] stated that the energy storage operation status has a significant influence on the hourly energy generation in the distributed energy system, energy-saving and energy efficiency performance are not enough for the hourly optimization of energy cascade utilization. On this basis, this research proposed the exergy loss rate as the hourly operation optimization objection of the distributed energy system for obtaining the hourly off-design output of various components.

Table 3 Literatures on thermodynamic analysis method for distributed energy systems
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Consequently, distributed energy systems contain thermodynamic systems based on clean fossil fuels and non-thermal systems based on renewable energy sources. The complementarity of multiple energy sources in terms of quantity and quality is the key to the distributed energy system to achieving energy cascading. The comprehensive analysis of different energy conversion, storage, and transmission processes and the dynamic characteristics of distributed energy systems from a thermodynamic perspective is a crucial foundation for the future application of thermodynamic methods for modeling, analysis, and evaluation. On the one hand, the high efficiency of distributed energy systems should be pursued. The energy conversion process of non-fossil fuels should also be analyzed and evaluated from the thermodynamics perspective to promote the efficient utilization of multiple forms of energy such as electricity, heat, and gas. In addition to the pursuit of efficiency, distributed energy systems should also consider the flexible regulation capability of the system under different time scales. Considering the dynamic operating characteristics of distributed energy systems from the thermodynamics perspective is significant in achieving efficient and rapid regulation of distributed energy systems.

4.3 Heat current method

Distributed energy systems also contain conversion, storage, and transmission of thermal energy, such as various heat exchangers, heat exchanger networks, pumps, heat pumps, air conditioners, radiators, etc. The unit models of these devices are a vital part of the system analysis and overall modeling. For example, in a typical heat exchanger, the heat transfer process is a multi-stream coupling process containing fluid flow, enthalpy flow, and power flow. Many parameters such as temperature, pressure, mass flow rate, and heat transfer rate are coupled with strong nonlinear characteristics [175]. Meanwhile, fluid flow, heat conversion, heat storage, and transfer processes have different characteristic time scales in dynamic analysis, which further increases the difficulties of dynamic modeling and analysis of distributed energy systems. Therefore, the modeling and optimization of distributed energy systems from the perspective of heat transfer is also a very worthwhile research effort.

An accurate and complete description of the performance of heat exchange equipment in distributed energy systems is necessary for system modeling and scheduling optimization. Recently, based on the entransy dissipation theory [176, 177], Chen et al. [178] have proposed the heat current/power flow method for describing and analyzing heat exchangers [179, 180], heat transfer systems [181], thermal systems [182, 183], and distributed energy systems by combining with thermoelectrical analogy method. The heat current method was firstly proposed and also termed as power flow method in Ref. [178], which is based on the power flow perspective rather than the work mass flow perspective and takes into account the dual characteristics of heat energy conservation and irreversibility in the heat transfer process of the heat exchanger. In the heat current model, the general thermal resistance is redefined as the ratio of linear temperature difference, such as inlet temperature, to the heat transfer rate [175, 184]. The general thermal resistance provides a linear form between the temperature difference and heat transfer rate, convenient for system modeling. Considering the basic structure of thermal subsystem in distributed energy system, Chen et al. [178] proposed three kinds of basic heat transfer networks, i.e., series layout, parallel-layout, and multi-loop layout and building the related heat current models, respectively. On this basis, Chen et al. [185] established the heat current model of a heat recovery-based power generation system and derived the heat transfer and conversion constraints combining with circuit principle. Moreover, Chen et al. [186] developed a real-time optimization platform for thermal system and applied the heat current method to model the cogeneration system, meanwhile proposed a high-efficiency simulation procedure by the hierarchical and categorized algorithm.

Besides, Hao et al. [187, 188] introduced an electric-heat conversion and heat transfer/heat storage units into the power system. They considered that the transmission natures of heat and electricity result in a complex and challenging power system analysis. The heat current method and Kirchhoff’s law have been used to deduce the heat transport matrix and construct a uniform power flow model of the power system with the electric-heat conversion and heat transfer/storage units. The wind power accommodation case analysis concluded that considering the heat transfer constraints in the entire system will improve the system’s scheduling accuracy. On this basis, Chen and Zhao [189] introduced a heat recovery and thermal energy storage subsystem into the battery system to achieve the combined heat and power generation and utilization. The system modeling used the new power flow method (heat current method) by combining with the traditional power system power analysis method to establish the overall power flow model of the integrated electric and thermal energy system. Inspired by the common nature of irreversibility of electric transmission and heat transfer phenomena, He et al. [190] applied a redefined thermal resistance of heat exchange facilities used in the distributed energy system and proposed a heat current model of thermal system, which was consistent with the power flow model of power systems in physics and provided an accurate and holistic modeling method for the distributed energy system. Meanwhile, the proposed multi-energy flow model of the integrated power and thermal systems can be solved by some existing power system simulators based on a multi-time scale hybrid simulation algorithm proposed in Ref. [190]. Zhao et al. [191] considered efficient modeling and simulation impressive for thermal system analysis, optimization, and integration into the distributed energy system. Figure 10 presented a standardized heat current modeling strategy that consists of three steps, 1) construct a preliminary system hear current model based on the traditional mass flow topologies of components; 2) construct a final system heat current model based on the preliminary model; (3) obtain global system constraints by applying Kirchhoff’s laws [191].

Fig. 10
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Heat current modeling procedure [191]

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Table 4 shows more applications of the heat current method in various types of thermal systems and distributed energy systems. These studies focused more on the steady-state modeling and variable operating conditions optimization of the system. Based on the research status, the heat current method realizes cross-level modeling from heat transfer components, heat transfer systems, and thermal systems to distributed energy systems from the heat transfer perspective, which is a kind of electrification, standardization, and systematic modeling idea. The heat current method can electrify the thermal system model in the distributed energy system, reduce the repetition of component operating parameters in the system modeling, and greatly simplify the complex and nonlinear model of the thermal system by separating linear and nonlinear equations. The “physical analogy and mathematical consistency” solution can realize the electric and thermal system homogenization analysis and modeling. However, in the face of distributed energy systems with complex application scenarios, more research in the future should focus on integrating the heat flow method with modeling methods of power networks and fluid networks. Combining with big data technology, we study the dynamic modeling methods driven by physics and data under different time scales, separate the coupling relationship between nonlinearity and linearity, and propose the solution method with high accuracy and fast solution speed. Based on the quantification of user behavior, the overall coordination strategy of multi-user, multi-network, and multi-energy flow should be studied from the perspective of power flow.

Table 4 Research and applications of heat current method
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4.4 Data-driven method

Energy-hub, thermodynamic analysis, and heat current methods are three different approaches focusing on different research perspectives and have provided feasible and efficient applications for various distributed energy systems. However, Capturing some epistemic and aleatory uncertainties of intermittent renewable resources, consumer behavior variability-related energy demand, and market costs of generation construction and storage infrastructure is also necessary and significant for analyzing socio-technical complexities but limited by deterministic modeling methods [201, 202]. Zhang et al. [203] also proposed that accurate and effective modeling of distributed energy resource uncertainties must be holistically improved. Aliramezani et al. [204] considered that modeling and subsequent control of internal combustion engines are critical and significant for improving performance efficiency and reducing harmful emissions. However, the high nonlinearity and the complex phenomena impose considerable obstacles to performance prediction, optimization, and control. For example, Mirnaghi et al. [205] considered that knowledge-based and model-based systems are for the fault detection and diagnosis of building energy supply system.

Data-driven design, modeling, and optimization method have been proposed and used in various distributed energy systems [203, 206]. Li and Wen [207] considered that agent-based modeling is a new modeling strategy that has made “remarkable progress” in controlling and optimizing distributed energy systems. Alvarado et al. [208] proposed a technology selection and operation model that is a data-driven framework for the optimal selection and operation of distributed energy systems by utilizing the holistic energy demands, prices, and the portfolio of available technologies. Chen et al. [209] reviewed the data-driven methods for operational optimization of integrated energy systems and provided that these component/equipment-level modeling and network/system-level modeling have been developed by artificial neural network model [210], genetic algorithms [211], and particle swarm [212]. Meanwhile, deep neural networks [213] and deep reinforcement learning [214] have also been proposed to model and optimize distributed energy systems. Besides, Wang et al. [215] considered that the contradiction between accuracy and efficiency limits the model-driven method application and could be integrated with the data-driven method in the complex power system, and proposed serial, parallel, and embedded integration approaches between model-driven and data-driven.

Compared with the physics-driven modeling approach, the data-driven approach does not have sufficient physical laws of the system and lacks interpretability. Meanwhile, these methods require a large amount of training data for modeling and are limited to high data quality. Besides, due to the increased complexity and uncertainty of distributed energy systems with various power electronics and flexible loads, more online continuous learning or meta-learning is essential to deal with continuously generated unmolded dynamics [214]. Therefore, studying online measurement and data collection techniques for distributed energy systems is the basis for data-driven modeling, such as measuring and collecting the operating parameters of individual devices in different subsystems such as power distribution networks, thermal systems, and natural gas systems. In addition, the physics-driven and data-driven modeling and optimization methods are more meaningful for distributed energy systems. The data-driven modeling of distributed energy systems should be investigated with stacked data processing methods such as data cleaning, feature parameter screening, and overall modeling. Further study of the data and physical dual-driven modeling approach should be developed to increase the interpretability of the data model based on the complete analysis of the uncertainty of system output and load.

5 Operation and control method

Distributed energy system includes diverse types of energy conversion, storage, and transmission devices such as fuel cells, micro gas turbines, wind power, photovoltaic, electric heat pumps, and energy storage, which will supply power and heat directly to users through power electronics connected to the electrical network and heat exchangers connected to the thermal network, respectively [81]. The directly customer-facing system realizes the interactivity of supply and demand of different forms of energy such as electricity, heat, and gas in a limited region, thus forming an efficient energy supply system with multi-energy integration and complementary utilization. Different types of distributed power sources such as wind power, photovoltaic, and fuel cell can operate by connecting with the grid, forming a local interaction of source-grid-load coexistence. The coupling linkage at the consumer side is different from the source-grid-load spatial scale in traditional energy power production and consumption. Different types of distributed generation and load demand on the user side have different degrees of volatility and uncertainty, and their corresponding dynamic response characteristics vary greatly. This dual stochastic of multiple types of distributed generations and loads will break through the dynamic response boundary conditions for optimal integration and operation control of distributed energy systems, reshape the dynamic response characteristics and stability of distributed energy systems, and bring new challenges for the coordinated control, safe and stable operation of distributed energy systems [216]. Therefore, the operation and control of distributed energy systems are becoming more important. Based on the above planning, modeling, and optimization, this research will review the operation and control for distributed energy systems from the optimal operation and scheduling strategy, the disturbance analysis and the control method.

5.1 Optimal operation and scheduling strategy

According to different application scenarios of distributed energy systems, researchers have proposed appropriate and effective control strategies to ensure a highly efficient distributed energy system [70, 217, 218]. The operation and control types of distributed energy systems include island control and interactive control with the power system. Interactive control can be divided into centralized, decentralized, and distributed control types [219]. Rahman et al. [220] introduced and reviewed the operation and control strategies of distributed energy sources from the micro-grid perspective and concluded the main features of some typical control strategies including the grid-connected mode or stand-alone mode. And then, they considered that different distributed energy systems with energy storage units will produce some challenges due to their operation and control methods. Moreover, Zhang et al. [55] provided a comprehensive review of the modeling and solutions for the optimal operation of integrated electricity and heat systems. The review presented that the operational characteristics and dispatch mechanism depend on system modeling and are greatly influenced by dynamic characteristics, various flexible devices, and uncertainty of supply and demands.

In the conventional power system, day-ahead schedule and short-term/real-time dispatchers based on the different time scales have been differentiated in the economic dispatch and unit commitment [219]. Tian et al. [221] proposed a static model of the multi-energy microgrid coupling system based on unified energy flow and an analog energy storage model representing dynamic energy transfer and established a MILP-based optimal scheduling model using segmented linear approximation and convex relaxation methods. The feasibility of the system model and the optimal scheduling method are verified practically in a multi-energy microgrid. Liu et al. [222] proposed the two-level interactive mechanism for the day-ahead scheduling optimization of distributed networks with multi-microgrids. The lower-level economic dispatch of each microgrid considered the renewable energy generation and load uncertainties. The upper-level interactive model ensures the operational quality by the distribution network operator.

From the multi-generation perspective, Ma et al. [26, 27] integrated the cogeneration, photovoltaic, and ground source heat pump to propose a new distributed energy system and introduced a multi-objective optimization consisting of annual energy-saving, cost-saving, and emission reduction ratios for developing the seasonal operation strategy by combining differential evolution and particle swarm optimization hybrid algorithm. Li et al. [223] focused on a distributed renewable energy system with heterogeneous residential, commercial, and industrial end-users. They proposed a hierarchical framework for the energy demand-side management by integrating smart contracts and blockchain technologies. Wen et al. [107] applied the genetic algorithm to design optimization and performance analysis under seven operation strategies. Liu et al. [78, 132, 224] proposed a two-phase collaborative optimization method for optimal operation strategy by prioritizing renewable energy utilization in the distributed energy system with a multi-energy storage system including cold, heat, and electricity during a typical day. Meanwhile, Liu et al. [225] proposed a day-ahead optimal operation strategy by an interconnected multi-energy system framework considering the renewable energy generation fluctuations and demand variations by a reformulated chance-constrained programming technique. Hao et al. [187] also proposed a day-ahead scheduling strategy for the integrated electrical and thermal energy systems to obtain optimal wind power accommodation. Besides, Zhu et al. [226] proposed an optimal design solution and presented an hourly operation strategy for the renewable energy-combined cooling, heating, and power coupled system by considering the comprehensive economic and environmental evaluation. Chen et al. [227] proposed a hierarchical control framework combining the model-based method for upper-level scheduler that solving the optimal power flow problem and the model-free method for lower-level distributed energy resources controllers that absorb real-time disturbances and uncertainties.

In conclusion, a distributed energy system connects directly with users and the grid, which should respond to the regulation and control commands of the grid and have the ability of self-coordination and control. The optimal control and scheduling strategy of distributed energy system should prioritize meeting the needs of users, maximizing the operational efficiency of the system, and meeting the flexibility needs of the grid based on giving full play to the demand response of users and energy stepping utilization. It is also necessary to further integrate users, distributed energy systems, and distribution grids, break through their respective dynamic response boundaries, and develop optimal operation strategies for systems with different time-scale dynamic responses. In the future, the cluster of distributed energy systems will become an effective supplement to centralized energy production, which requires the development of intelligent, autonomous, coordinated and reliable distributed regulation and control technologies to achieve global stability and optimal regional operation of the cluster of distributed energy systems.

5.2 Disturbance analysis and control methods

The distributed energy system’s safe and stable operation is the foundation of optimal control [64, 71]. Recently, more literature has developed disturbance analysis and stability control methods from the power system perspective. For example, Hasan et al. [228] used the sensitivity analysis method to assess the influence of parameters on the stability of the power system under small perturbations. Based on the calculation results, it was possible to derive several parameters that had the greatest degree of influence on the system after a disturbance, thus focusing on adjusting and optimizing parameters in this category. Wang et al. [229] used the energy hub concept to model the energy coupling component divided into three sub-modules according to the supply, conversion, and demand of energy and performed multi-energy flow calculations for three representative disturbances in the energy hub, such as emergency gas supply stoppage on the supply side, boiler failure and sudden increase in demand, and derived the corresponding changes of each energy flow of the system under three disturbance cases. Wang et al. [230] proposed an individual-based model (IBM) capable of disassembling large-scale heterogeneous complex systems and applied it to the multi-time scale dynamic analysis of integrated energy systems. Using the IBM model, the literature presented a phased dynamic analysis of the propagation mechanism of four typical disturbances: stable operation phase, disturbance generation phase, power side response phase, pipe network response phase, and multi-energy flow balance and the next stable operation phase. This modeling method reduced the computation time and improved the efficiency of interaction analysis compared with the traditional step-by-step analysis method. Wang et al. [231] proposed a system-level stability assessment model based on critical energy functions to explore the small disturbance stability region in order to maintain a stable and healthy energy network. The small disturbance stability region was estimated based on the energy function theory, and the modeling process was optimized with a big data approximation analysis algorithm, which reduced the computational complexity with higher accuracy.

Meanwhile, from the thermal disturbance perspective in a thermal system, Yao et al. [232] introduced a potential circuit analysis technique that is an analysis tool to improve the safety and reliability of circuit control systems and analyzed the prospect and implementation of the potential analysis method applied to thermal systems. After improving the traditional potential analysis method applied to mass flow, Yao et al. [233] proposed a network tree topology model based on power flow to describe the heat transfer process in thermal systems by introducing the concept of power flow/heat current. According to the design function of the thermal system, all possible heat transfer paths of the thermal system were obtained by defining the heat source and cold source of the system as the starting point and the ending point of the path search, respectively. The application of this method could target the possible perturbations and other situations that make the system unstable in the multi-energy flow system. O’Dwyer et al. [234] proposed an identification method incorporating artificial intelligence for unmeasured perturbations in building-level distributed energy systems. The quantized particle swarm optimization algorithm was first used for finding and identifying the disturbances. Finally, the identification results of the particle swarm algorithm were refined by using principal component analysis to derive the main disturbances. Sun et al. [235] proposed a robust coordinated optimization method for distributed energy systems by considering thermal inertia uncertainty, which provided a feasible method for coordinated multi-energy regulation of distributed energy systems containing perturbations. Moon [236] investigated the adaptability of a residential-based distributed system to changes in environmental parameters through a thermal control logic based on artificial neural networks (ANN). The adaptability and stability of the approach was demonstrated by incorporating the predictive function of the neural network into the conventional control logic and testing the system for disturbances in relevant parameters, such as changes in internal loads and changes in climatic conditions. The proposed ANN-based predictive and adaptive thermal control method had shown its potential to be used for the regulation of small distributed multi-energy systems.

Besides, The coupling between different energy sources in a distributed energy system will lead to the propagation of disturbances or faults from the non-power subsystem to the power system through the multi-energy coupling devices [64, 71]. Therefore, from the coupling perspective of electricity and heat, Jiang et al. [237] proposed the concept, method, and implementation of an integrated energy network security region to assess the reliability and security of the system by considering the multi-energy flow coupling effects. The method considered the operational constraints of multi-energy networks, including heat, voltage, pressure, temperature, and transmission capacity limitations in distributed energy. A hyperplane-based segmental approximation method was proposed to approximate the safety region boundary, and a general energy flow optimization model was developed. The proposed general optimization method based on the track solution and the hyperplane-based segmental approximation method could construct heterogeneous types of multidimensional safe regions in distributed energy with high computational accuracy and efficiency. Thilker et al. [238] developed a perturbed short-term prediction model based on advanced physical description and statistical methods to predict changes in cloud cover, solar radiation, net radiation, and ambient air temperature, respectively. The stochastic differential equations and short-term perturbation prediction methods were also integrated into the model predictive control (MPC) scheme, which enabled MPC to optimize better the control of distributed energy systems incorporating renewable energy sources. Jin et al. [239] established a distributed energy system model containing a micro-combustion engine, photovoltaic, lithium battery, and ground source heat pump. Then this paper analyzed the dynamic characteristics of electric and thermal energy flow in it. After that, the traditional MPC control strategy was improved, and a centralized MPC control strategy with a dual-input and dual-output control system is proposed, which could cope with the electric and thermal load fluctuations and renewable energy side disturbances and regulate the electric and thermal energy flows separately, and then became a system-level disturbance coping control scheme. Based on the operation mechanism and scheduling mode of distributed energy system, Huang et al. [240] developed a discrete system model for optimal control of the system under the disturbance input. According to this model, an accurate and fast optimal control algorithm was designed to plan and allocate the optimal operating power of distributed energy devices. Different disturbance inputs were used and compared with the classical optimization algorithm Adaptive Particle Swarm Optimization in an example analysis. The results showed that the optimal control model could effectively suppress the disturbance effects and obtain fast and satisfactory control results.

In conclusion, the proposed stability analysis methods and control strategies rely on a single energy flow perspective for the stability analysis and overall control of distributed energy systems under multiple scenarios and variable operating conditions. The distributed energy system is a complex dynamical system with high dimensionality, multi-scale, strong stochasticity, and strong nonlinearity. The disturbance concept, occurrence, and propagation forms in electric, thermal, and gas subsystems are also different in each subsystem. For example, disturbances in the power distribution network refer to power fluctuations, voltage variations, and impulse disturbances. Disturbances in the thermal network refer to hydraulic and thermal conditions, such as fluctuations in the work mass flow and temperature. Disturbances are affected by the propagation medium in each energy system, and the propagation speed varies. Such as, the disturbance time scale in power systems is usually in the millisecond, microsecond level. In thermal systems, the disturbance occurs with the work mass propagation, and the speed is slow. The time scale is usually in the minutes, hourly, or daily. Moreover, the causes of perturbations are diverse, such as input perturbations, external change perturbations, internal system change perturbations, modeling inaccuracies, and small perturbations, which make the mechanism of system perturbation propagation evolution more complex. In addition, the electric and thermal networks do not operate separately in distributed energy systems. They can be coupled by electric and thermal conversion devices, resulting in the cross-system propagation of perturbations in the thermal and electric distribution networks that can follow the transformation of energy forms. Therefore, future research should fully consider the dynamic characteristics of multi-energy conversion and transmission of electricity, heat, and gas based on a unified physical model, study the cross-propagation mechanism of disturbances in different energy conversion and transmission components in the system, propose stability analysis methods and coordinated control strategies for distributed energy systems, and guarantee the safe, reliable and efficient operation of the system under multiple operating conditions.

6 Conclusions

The vigorous development of distributed energy systems based on renewable energy and clean fossil fuels is one of the significant ways to achieve the goal of carbon peaking and carbon neutrality [241]. This review first introduces the essential components and characteristics of distributed energy systems. According to different definitions, distributed energy systems are generally arranged on the consumer side and mainly consist of units for energy generation, energy transfer, and energy storage, which are capable of off-grid or grid-connected operation through energy management systems. The composition and application of distributed energy systems are characterized by multi-energy complementarity, multi-energy flow synergy, multi-component coupling, multi-scenario coexistence, and multiple time scales (n-M characteristics). The review provides a systematic and macroscopic understanding of current research on distributed energy systems from three levels: system planning and evaluation, modeling and optimization, and operation and control. Figure 11 presents the research focus on different approaches in distributed energy systems. Among them, the planning of distributed energy systems requires integrated technical, economic, environmental, and social factors for comprehensive and optimal planning under regional environmental, resource, and policy constraints, considering the system’s equipment performance, process architecture, capacity configuration, and source-load uncertainty. In terms of modeling and optimization, energy hub, thermodynamics analysis, heat current, and data-driven methods are introduced to model distributed energy systems. Finally, regarding system operation and control, the optimal system operation and scheduling strategies, disturbance analysis, and related control methods are discussed from the perspective of power and thermal systems.

Fig. 11
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Research focus on different approaches in distributed energy systems

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In view of the aforementioned research and needs at different levels, distributed energy systems have become the frontier of interdisciplinary research in engineering thermophysics, electrical engineering, control science and engineering, economic and social sciences [126]. Improvement of comprehensive utilization efficiency is always charming and desirable for the development and applications of distributed energy systems. From the view of system composition, clarifying the dynamic characteristics and common laws of different energy conversion, storage, and transmission components from the physical level depends on a homogeneous modeling method for reconstructing the mathematical models of each component in different time scales and proposing efficient solution strategies. Meanwhile, in terms of the application level, the dynamic interaction characteristics of source-network-load are significant for proposing stability analysis methods and coordinated control strategies for distributed energy systems to ensure safe, stable, efficient, and flexible operation.

Energy conversion is imperative for utilizing renewable energy sources and clean fossil fuels in distributed energy systems. The integration of thermal and non-thermal systems can realize the multi-energy complementary utilization of the system. Further consideration of the dynamic process of thermal system energy conversion from a thermodynamic perspective at multiple time scales and the energy conversion characteristics and flexible requirements of non-thermal systems are necessary. Entropy and exergy can be used to analyze some advanced thermal cycles in future distributed energy systems, but with some challenges due to the integration of renewable energy. Besides, electricity, heating, cooling, and gas are the main energy demands for consumers. The integration and interaction of power distribution, heat, and fluid networks increase the difficulties of capturing complex system operations and network constraints due to the multi-parameters, strong coupling, multiscale, and non-linear characteristics. Therefore, unifying mass transport with the transport processes of different energy grades (electricity, heating with different temperatures) and constructing unified intrinsic equations are the basis for the synergy of multiple energy flows in distributed energy systems. Besides, quantifying user behavior is another important research direction for system modeling due to the impact of user behavior, participation, and acceptability on system modeling and operation. Incorporating user behavior into the system model provides an alternative energy-balanced relationship different from the real-time rigid energy demand balance characteristics. Meanwhile, considering the intrinsic characteristics and differences of different forms of energy transmission and storage ways is necessary for deeply exploiting the regulating ability of the system to realize efficient conversion and energy accommodation utilization from the interaction perspective of efficiency and flexibility. For the multi-scenario applications of distributed energy systems, their related and appropriate resolution is also necessary to meet the modeling and computational demands, such as technical detail, temporal and spatial resolutions, and stakeholder’s behavior presence [120]. The decentralized control architecture is also significant for the coordination control and flexile operation of distributed energy systems by developing and using the new blockchain technology [19, 63, 64, 71]. Meanwhile, With the increase in system complexity, model granularity, and data resolution, state estimation and online processing and analysis of operational data of distributed energy systems need to be further developed and studied for optimal energy management and scheduling.

Consequently, distributed energy systems are complex in composition and involve many physical processes, and it is difficult for a single theory and method to fully realize the comprehensive analysis of the system. More research is still needed to propose new research paradigms for planning, modeling, optimization and control from a multidisciplinary, multi-perspective and multi-disciplinary deep intersection perspective, which is crucial and significant for the development and application of distributed energy systems.