This section presents the findings from the thorough analysis of 25 studies based on model purposes and outputs, agents, their decision-making frameworks and interactions, technologies and policies covered, spatial and temporal aspects, and empirical grounding.
4.1. Model Purposes and Outputs
The review by [
17] highlights that ABM is well-suited to answer two kinds of energy-demand questions: those related to policy design and evaluation and those related to system design and infrastructure planning. The review process reflects the existence of these two motivations for modelling, of which we only focus on those that are relevant for policy design. These studies evaluate the agents’ behavioural response to external stimuli in the form of a policy, regulation, observation or feedback, and peer influence. Rai & Robinson [
51] present a well-validated example of an ABM used to test the influence of the regulatory framework on adopting renewable technology. They examine how additional rebates (i.e., partial refund of an item’s cost) for low-income households and changes in the amount of rebate, affect the adoption of rooftop PV in Austin, Texas.
A model’s purpose or objective must be “clear, concise and specific” [
52], which is essential for others to understand why some aspects of reality are included in a model while others are omitted. It is because each a model should be a “purposeful” abstraction of reality [
55]. The purposes of the 25 selected models are diverse. However, we identified two main thematic clusters: diffusion and exploratory ABMs (see
Figure 3).
One large thematic cluster is the exploration of technology adoption that has its foundations in innovation diffusion theories [
56]. This type of ABM is often named “agent-based diffusion model” [
22,
36,
56,
57]. They aim to analyse adoptions of energy-efficient or renewable energy technology by households, firms and other entities, often due to certain policy interventions [
3,
51,
58,
59,
60,
61,
62,
63,
64]. Usually, such models’ outputs are the number of adopters or adopted units, energy or emissions saved over time (see
Table 1). This approach allows us to observe what factors affect the adoptions of technologies in which ways. The term “diffusion” encompasses concepts like social learning and dissemination [
65]. Thus, this approach is also well-suited to represent the dissemination of energy-related practices and behaviours, such as energy-saving [
47,
49], energy-efficient ventilation behaviour [
66,
67], user learning (i.e., energy saving) after authoritative smart meter adoption [
68], building renovation behaviour [
69], weatherisation (i.e., making apartments weather-proof) [
70], buying energy-efficient appliances and switching an energy provider [
71]. Similar to technology adoption, these studies investigate how energy-related behaviours are adopted and how much energy can be saved. Three models [
66,
67,
68] focus on both technology adoption and the resulting behaviour dissemination.
The remaining works have more exploratory purposes and are less established than diffusion ABMs. Fouladvand et al. [
72] investigate how Thermal Energy Communities (TEC) can be formed and sustained, where agents can either join a new or existing community or decide to drop-out based on financial, technological and energy plan (e.g., self-consumption) evaluations. Busch et al.’s [
73] model is distinguished from other models by representing the continuous process of engagement and district-heating development instead of instantaneous decisions (e.g., to adopt, to invest). In these studies, the output metrics are very specific to the purpose and subject studies (see
Table 2).
4.2. Agents
Agent is a key element in this modelling approach. Many previous studies highlight that there is no common definition of an agent [
44,
78], as its properties depend on the model’s purpose and application area. Nevertheless, many authors refer to the following basic definition presented by [
79]: “Agent is an encapsulated computer system that is situated in some environment, and that is capable of flexible, autonomous action in that environment in order to meet its design objectives”. In the ODD protocol, agents are one of the model’s “entities”, along with spatial units and the overall environment [
54]. It is due to the parallels between the agent-based modelling approach and Object-Oriented Programming (OOP) (i.e., the ‘classes’ or its instances in OOP could be equivalent to ‘entities’ in ABM). It might lead to confusion among readers who are new to Agent-based modelling or use different implementation tools. In the current article, we differentiate between agents and other entities, where we refer to “agents” as autonomous entities that can make decisions (i.e., implement certain algorithms) and interact (i.e., obtain information from its environment or other agents) in order to reach its objectives.
Most of the agents in the selected studies are “households” (15 out of 25) and three studies also denote them as “energy consumers” [
3,
68,
71] (see
Table 2). Since most of these studies model the adoption of PV or other technologies, “households” are most common decision-makers in this regard. Majority of these models limit their agent population to the households that live in a single-family building, because installation of renewable energy in other types of housing (rented apartments, multi-family housing) is subject to additional legal or physical constraints. However, few models are exceptions: [
3,
61] differentiate agents into tenants and house owners, where only house owners can buy and install PV and tenants can choose from green electricity or community solar program; Nava Guerrero et al. [
76] attempts to represent group decision-making regarding heating system, insulation or RE system installation in multi-family houses. In other models, building (or building block) owner [
60,
69] and building agents [
59] can make building-level decisions, i.e., adopting PV or renovation. The rationale of these models is that there is only one building owner that can make such a decision.
While the above-mentioned studies focus predominantly on one type of stakeholder, there are few models that involve different types of stakeholders as agents [
73]. For example, in [
73], instigator agents (i.e., local authorities, commercial, and community-based developers) are driving the development of projects, whereas “projects” are management agents responsible for carrying out actions on behalf of their parent instigators [
73]. In models with multiple types of stakeholders, it is becoming more challenging to draw a line between agents and other entities, e.g., as in [
47], as all of them are essentially realised as classes. However, one can observe the tendency to call human-like entities “agents”, e.g., instigator agents, and passive entities like grid cells and projects [
73] as just “entities”.
Figure 4 summarises the types of agents we identified in the reviewed models.
The essential part of ABMs is decision rules that govern the actions of agents. Decision rules are realised with the help of attributes that describe agents [
43]. Moreover, interaction and social influence play a significant role in agent’s decision making. Hence, the following subsections give an overview of the decision-making rules and agent interaction strategies implemented in the reviewed models.
4.3. Agent Decision Rules
Decision-making rules (also called behavioural rules, decision rules or models, or just “rules”) are methods by which agents’ dynamic states can change their value and translate into agent action [
43]. Behaviour is the overall sum of agent actions and state changes [
43]. However, authors often use the terms “actions”, “behaviours” and “decisions” interchangeably [
80]. The ODD protocol suggests to include a detailed description of individual decision-making [
81]. The information such as identifying subjects and objects, the method, the uncertainty, and other aspects must be part of this documentation [
81]. However, in practice, such protocols are rarely adhered to by the authors.
The articles describing the diffusion ABMs are more explicit about the decision-making algorithms. In such models, agents decide to adopt or not adopt (i.e., to invest or not invest in a certain technology or to perform a certain energy-related action) based on specific rules or algorithms. Decision rules range from simple ad-hoc rules to most elaborate models, such as psychosocial or cognitive models [
43]. The classification of existing decision models has been previously done by [
80] for human agents in ecological ABMs, by [
56,
57] for agents in ABMs innovation diffusion and by [
43] for ABMs of socio-technical systems. The ODD+D by [
81] clusters agent decision algorithms based on the nature of the underlying assumptions:
theory-based (e.g., microeconomic and psychosocial models)
empirical-based (e.g., statistical regression models, heuristic rules),
ad-hoc rules (i.e., dummy rules and pure assumptions that are not based on theories or observations),
combinations of the above methods (see
Figure 5).
Most of the diffusion ABMs cited in this article apply theory-based decision models, namely, psychosocial (also called “socio-psychological” or “cognitive”) and microeconomic models. Psychosocial models are based on social psychology theories that assume that human decisions are based on psychological rules, rather than on rational economic rules. The most frequently used psychosocial theory in the selected models is the Theory of Planned Behaviour (TPB) by [
82]. It states that human behaviour results from the intention to perform the behaviour; individual attitudes, subjective norms, and perceived expectations can influence the agent to perform such behaviour [
83]. Usually, the more favourable these three aspects of human psychology are, the stronger is the person’s intention to perform a certain behaviour [
83]. The standard form of TPB is static, i.e., it describes how these three components are translated into intention and action at a given time. The models by [
51,
66,
67] are examples of implementing this theoretical model. Other psychosocial models including “consumat” model by [
84] in [
68], Norm Activation theory by [
85] in [
71], the goal-framing theory by [
86] in [
74], and Influence, Susceptibility, and Conformity Model by [
87] in [
49], are also used. Several models rely on models from microeconomic or network theories, namely on innovation diffusion models. Azar & Al Ansari [
47] draw on the opinion dynamics models by [
88,
89,
90] to represent the effect of energy feedback interventions among building residents.
Another class of frequently used agent decision-making model is the empirical-based heuristic models. They are described as models “not built on any grounded theories” and “having the impression of being ad-hoc” [
57]. Agents are often assigned rules derived from empirical data, and also model parameters are selected such that results match simulated output against a real-life observation [
57,
80]. They might not represent the process of agent decision-making very accurately or realistically, but have the advantage of being easy to implement and to interpret [
57]. Heuristic decision rules can be implemented in various ways. Several modellers favour data-driven approaches, thus, implementing machine learning algorithms, such as logistic regression models [
59] and artificial neural networks [
77]. In this approach, several sets of factors that can affect the adoption of PV or energy-saving behaviour, given that data about those factors are available, are tested. The more qualitative approach is followed by [
72,
73], who created the decision rules relying on the stakeholder’s expertise.
Some models rely on ad-hoc rules without any validated theory or empirical grounding. Huang et al. [
70] derives the agents’ decision logic from relevant secondary literature and assumes that social influence plays a great role in deciding to adopt weatherisation of a dwelling. In this model, agents decide between adopting weatherisation with the Weatherization Assistance Program or without and it depends on several attributes, memory length about the energy costs, current satisfaction level and information level about the assistance program. Mittal et al. [
3] developed a decision model similar to [
51], but do not apply the TPB. The agents assess the affordability of PV options (i.e., buy, loan, community PV) and the attitudinal factors in the corresponding submodels and make the adoption decision based on certain if-else type rules. The remaining studies are summarised in
Table 3.
4.4. Agent Interaction
Emergent phenomena to be observed via ABM is the result of not only individual decision-making but also agent interactions [
21,
78]. The behaviour of agents is often influenced by the information fed from its environment, including other agents. In the ODD the authors differentiate conceptually between ’sensing’ and ’interaction’: the first concept defines what state variables of which other individuals and entities can an agent perceive; the latter is the direct (via communication) or indirect (e.g., via a common resource) interaction between agents or between agents and other entities. However, in practice it is challenging to differentiate between those. For example, human agents’ social influence (also known as ‘peer effect’ or ‘neighbourhood effect’) can be represented using either (or even both) of those concepts, as it seen from the pool of the reviewed papers. Hence, in this work, we consider ‘sensing’ as one of the ways of representing interaction (as depicted in
Figure 6).
In the selected studies, one must, first of all, differentiate between studies where agents can interact and influence each other and those where agents do not interact. Only two studies have not considered agent interactions in any way [
62,
69]. In [
73,
77], interactions are considered as important, however, treated in an abstract and implicit way.
Table 3 shows how interactions are represented in each reviewed study.
The majority of studies which include agent interaction agents are often placed in a network structure, often called “social network”, that imitates the relationship between agents, through which they can exert an influence upon each other based on certain rules (i.e., “peer influence” or “social influence”). The resulting structure allows modelling the social interactions of agents, resulting in the spread of desirable, or non-desirable, ideas, products, or behaviours [
91,
92] (also called “opinion dynamics”). One common way of doing so is through making an agent’s decision dependent on other agents’ (either selected group of agents or all agents) choice or decisions.
A social network typically consists of two components: individuals or agents (represented by nodes) and social connections (represented by edges or links). It can also have various topologies, e.g., small-world network, and created by various algorithms, e.g., Watts-Strogatz algorithm. Some modellers test the effect of varying the topology and other characteristics (e.g., number of links per node) of social networks [
47,
48,
49]. A modeller should also specify between which agents interaction (or ‘sensing’) occurs, between all agents or certain group of agents or between agents and other entities (e.g., grid cells). In a social network, usually, agents that have a link can interact or the influence of connected agents is more significant compared to those with whom the agent doesn’t have one. This assumption is based on the empirical findings: friends and family have a larger impact on each other’s behaviour than strangers [
66,
67]. In some cases, agents interact based on similarity (also called ‘homophily’) [
3] or geographical proximity [
51] (‘neighbour effect’).
Another choice that a modeller should take is regarding the frequency of interactions. Huang et al. [
70], for example, let agents that are linked with each other interact every time step, whereas “strangers” (without direct links) interact with a probability of 0.10. The “strength” of the influence can also be characterised in various ways. The most used is the opinion dynamics model by relative agreement algorithm, where agents with similar opinions have a stronger influence on each other than those whose opinions are more polarised [
93]. To sum up, there are usually four key things a modeller should consider when characterising an interaction of agents, as we summarise in
Figure 6.
4.6. Spatial and Temporal Aspects
Identifying the spatial and temporal scale of the models is important in order to understand the system modelled. Moreover, certain patterns and processes can be dependent on the scale [
94] and, thus, they need to be clearly stated. By spatial scale, we mean “geographic scale”, defined as a research area’s spatial extent in a study [
94]. The geographic scale of the models considered range from “group of buildings” [
47] to an entire city, such as Hamburg [
69]. 16 studies describe community, or district, or neighbourhood-scale models, while nine studies are in city-scale [
51,
67,
68,
69,
73,
77]. Although these articles present the models as having been applied to specific geographic scales (i.e., via case studies), it is difficult to say if they can be scaled up or down, as it might depend on many factors.
The chosen scale in ABM usually determines the number of entities (i.e., agents) covered [
33]. This can be limited by computers’ processing capacity, especially if decision algorithms are sophisticated, much data is used, or a considered city is very large, e.g., like in [
59]. Therefore, the majority of selected models opt for district or neighbourhood scale. Those whose models are in city-scale focus on smaller cities of about 100–150,000 [
62,
66,
67]. Only one model has modelled a city of approx. 174,000 households and the simulation had to be carried out on a supercomputer [
51]. There are also such models whose scale depend on the topic of research. For example, DH network development is usually city-scale phenomena [
73], the development or properties of energy communities are explored on a neighbourhood or district level [
3,
72].
Although traditionally ABMs have not focused on the geographic environment and spatial representation, more and more models are striving to represent space explicitly and realistically (e.g., using GIS techniques) [
95]. According to [
95], models can have three levels of spatial explicitness: (1) implicit and non-geographic representation of space (e.g., social networks that are only partially tied to space); (2) explicitly represented but abstract in how it maps onto reality (e.g., Schelling’s segregation model); (3) explicit and realistic spatial representation. Among the reviewed models, only a few are spatially explicit and realistic. For instance, [
51,
58,
59,
64] join building information with actual geographical locations of those buildings and have a clearly defined boundaries of the study area. The rest of the models integrate spatial properties in different, semi-abstract ways. For example, in [
3,
61] agents in the same community, i.e., neighbours, are defined by a community ID, and each agent in a community becomes aware when somebody in that community installs a PV.
The temporal scale is a duration of a process observed, i.e., time horizon between the start and end of a single simulation run. Temporal resolution represents the unit of a time step in a considered model. According to temporal scale and resolution, the reviewed studies have time horizons of several years and resolutions of 1 month or three month-periods. These models have large simulation horizons and resolutions because the behavioural dynamics captured in those models occur in lower temporal resolutions. For example, in real life, people’s attitudes do not change in a matter of hours. Such time horizons and resolutions are characteristic of policy-guiding models, aiming to observe the effect of a policy intervention over the years. In their models, the authors [
51,
59] choose the years when adoption data are available, which makes it possible to improve their empirical model in such a way that the simulated outputs fit the real adoption data.
4.7. Empirical Grounding
Empirical grounding of ABMs is becoming more important, especially for models that aim to reflect a specific real-world situation and provide decision support for policymakers and stakeholders [
57,
96]. As opposed to hypothetical or theoretical (or highly abstract) ABMs, empirical ABMs use real-life data to parameterise models, initialise simulations, and evaluate model validity [
57]. Modellers try to improve the realism of agent decision-making algorithms by consulting with system-relevant actors [
72,
73] or relying on empirical data [
59,
64,
66], e.g., geospatial information on buildings. It is becoming more feasible due to the contemporary trends we observe the availability of high-resolution data sets, the spread of open data culture in science, advances in data analytics, machine learning, and computational power. Therefore, we aim to assess for what purpose, what kind of, and how empirical data is used in the selected ABMs of district energy systems. By empirical data, we mean both qualitative and quantitative data based on observation or experiment.
The review by [
36] highlights that empirical data in ABMs are used for two general purposes: (1) to form the agent decision-making algorithm; (2) to determine the specific properties of technologies, policies, etc. that an agent can access to use in their decision rules. In the first case, empirical data from surveys, statistical data (i.e., census), interviews, and other sources are used to determine the attributes (both which attributes and their values) of the agents that are further incorporated in a decision-making framework (as described in
Section 4.3). Jensen et al. [
66] describe how they utilised empirical data for creating household agents and their social network in the appendix of their article. Building data (i.e., floor area, spatial information, etc.) are connected to agents, and the commercial geo-marketing data defines the “lifestyle” of agents, which further define their affinity for technology and behaviour adoption. Social influence is modelled by introducing a social network based on interviews with households. The second purpose of integrating empirical data involves using statistical data and secondary literature to define other, for example, scenario-relevant information or model parameters (i.e., global parameters). For example, Azar et al. [
47] use building energy consumption survey data to initialise the model-level parameter “building energy intensity” and the number of agents in each building. However, it is not easy to determine for all models for what the specific data is used, as authors do not sufficiently describe it. Sometimes the authors refer to another article for detailed information about surveys or stakeholder interviews [
73,
74].
In general, there are three processes in model building where the use of empirical data make models more reliable and realistic: parametrisation, calibration and validation [
37]. The parameterisation is the process of connecting model and target system (i.e., the real system being modelled) via assigning the set of parameters and their values to enable simulation [
96]. In line with observations of [
37], only a few modellers explicitly differentiate their modelling process into these three phases. Moreover, if calibration and validation are somewhat known to data-driven modellers, the process of parameterisation is not recognised as much. Among the selected models, only [
66,
67] describe parameterisation in more detail: they select the parameter values to reflect the empirical patterns of ventilation behaviour adoption derived from survey data.
Calibration is the adjustment of parameters to ensure that model output matches the relevant empirical data, e.g., in a specific location and application [
37]. The difference to validation is that the parameters are tuned to match a specific context (i.e., location, time), which does not necessarily mean that the model will exhibit accurate results and be predictive upon application in another context. To achieve that it has to be first validated on a separate set of data independent of data used for calibration [
57]. The following models describe how they calibrated their models: [
62] calibrates the parameters of the logistic function governing the adoption of PV based on the secondary literature and publicly available data; Ramshani et al. [
63] performs the partial calibration (i.e., only of the financial submodel) based on the values reported in the literature, experts’ opinions and publicly available datasets; Jensen et al. [
66] provides an indirect calibration with three empirical patterns, the same used for parameterisation in [
67]. As for the remaining models, some do not differentiate between validation and calibration [
60], some call calibration “model fitting” [
51], but the majority do not mention calibration at all. Often authors mention the lack of data for calibration as their limitations [
63,
73].
Validation aims to achieve the matching between the observations of the models and reality. It should not be confused with “verification”, which is the process of making sure the model implementation is carried out correctly with respect to the conceptual model [
97]. As ABM is a highly multi-disciplinary and flexible framework, its validation is a highly debated topic. For more detail, we suggest referring to the works of [
57,
98] that explore this topic in more detail. Our observations are mostly limited to the validation processes provided in the selected works, the majority of which either do not mention validation, state it as a limitation and future task, or have insufficient information on the validation.
Among the models which consider validation, there are two following generic approaches. The first approach is an aggregate behaviour validation, mainly based on statistical data fitting. Rai & Robinson [
51] and Lee & Hong [
59] applied this way of validation, because they had empirical data on the number of adopters in a given location, over a certain period. Lee & Hong [
59] use the Wald test (i.e., Wald Chi-squared test) which tests the significance of a set of independent variables in a statistical model. Rai & Robinson [
51] first calibrate the six model parameters by an iterative fitting via historical adoption data and then validate the model in terms of predictive accuracy, i.e., comparing predicted adoption with empirical adoption level for the period starting after the last date in the calibration dataset. Also, they carry out temporal, spatial, and demographic validation [
51]. Another group of modellers [
47,
49,
73] pay more attention to the validation of social processes and, by drawing on the work of [
99], offer conceptual, operational or structural, and technical validation (by this, [
47] refer to verification). Conceptual validation is the process of determining that the theories and assumptions underlying the conceptual model are correct [
99] and usually achieved by basing the model on validated concepts [
47,
49] or the insights from stakeholder workshops [
73].