Multi-agent based coalition formation of prosumers in microgrids using the i * goal modelling

Abstract

In this paper, we discuss the role of microgrids as a “prosumer”. Microgrids are used to provide locally generated power (energy), and this concept is becoming increasingly prominent with time. Microgrids have added economic value when assuming the role of “prosumer” or “group of prosumers”. A new outlook in managing prosumers connected to the energy sharing network has led to the creation of prosumer coalition groups, which can subsequently manage numerous goals in microgrid energy systems. For achieving prosumer energy goals, Goal-Oriented Requirements Engineering (GORE) is deployed in this work. Hence, the purpose of this research is to develop prosumer coalition-GORE artefacts, strategising GORE players, modelling non-functional requirements and ensuring sustainable requirements engineering management in the microgrid energy system. In this research, an $i^{*}$ goal model has been used to design a payoff function based on the game theory concept. The key to the pricing function is its fair distribution of payoffs depending on their surplus energy generation, thus providing optimum satisfaction to the buyer. With the objective of maximising the profits earned by prosumers through intra-microgrid energy trading, this paper also designs multi-objective functions to provide optimal value by using the $i^{*}$ goal model. By integrating Java with the IBM CPLEX optimisation tool, a simulation model based on the proposed method was developed and analysed. The results show that the proposed approach yields better outcomes when meeting the requirements of fairness and efficiency, reducing the intermittency effect of generation through renewable resources.

Keywords

Requirements engineering goal models multi-objective optimisation decision-making non-functional requirements

1. Introduction

The power sector strives to provide a sustainable, manageable, and cost-effective power system arrangements to the consumers. Decades ago in developed countries, when electricity was distributed on a large scale, it was done only unidirectionally using transmission cables and transformers, which are not economically feasible in today’s times. The usage of such cables posed safety hazards and also incurred huge power loss during transmission. The socio-economic benefits such as the utilisation of local resources, security, shorter transportation, higher efficiency based on small community initiatives led the governments to review and revise policies related to the power companies. This led to the development of energy prosumption idea all over the world in urban and rural areas since the 1990s. A prosumer is a power user who uses power and at the same time also produces power and distributes the surplus power to other energy users [1].

The application of the prosumption idea and the modernisation of the electrical systems gave rise to the microgrid (MG) concept. A MG is an energy system which functions within a restricted area or a localised energy system. The MG generates, stores and consumes electric power within that area. The MG uses the locally distributed energy resources (DER) to generate power and independently satisfy demand within that local area. The MG does not depend on the main grid. The MG is connected to the nearby utility grid, which helps it to sell surplus energy, as well as to buy additional energy in the event of an energy deficit. This utility grid is made possible with the involvement of power companies and green sources, traditional power sources and loads, as well as new customer-owned devices such as storage units and electric vehicles [2]. Several years ago, power transactions had their own limitations, as they were hierarchical and the markets were centralised. In today’s times, smart grid deployment is derived after studying the requirements of a heterogeneous dynamic environment by modelling and analysing the requirements. The heterogeneous environment also requires an effective design and evaluation of power transaction methods among substations, the utility grid, renewable energy sources, electric cars and energy users.

Table 1
Different optimisation-based energy management system approaches in the literature

Refer- ences	Energy management system type	Approach	Advantages	Disadvantages
[26]	Centralised	Model predictive control method	Maximise the benefits at the network level	Failure in real-time communication, Dependence on central controller
[27]	Centralised	Centralised multi-objective optimisation algorithm	Improved the operation and performance resiliency of the entire system	Sensitive to single-point failure, weak plug and play functionality, lack of adaptability and flexibility
[28]	Decentralised	Constraint generation algorithm, second-order cone programming (SOCP)	Improve the economic efficiency of the whole distribution system	Difficult to establish a consensus for all MGs
[29]	Decentralised	Fuzzy cognitive map	Strong privacy protection, high computational efficiency	High operational cost, unawareness of system level resources
[30]	Decentralised	Alternating direction method of multipliers algorithm	High tolerance for communication error	Low resiliency in islanded mode
[31]	Decentralised	Column and constraint generation method	Information privacy, lower communication burden, quicker convergence speed	High energy trading between grids
[32]	Decentralised	Distributionally robust optimisation based algorithm	Low operational cost	Not over-conservative solution for the operation decisions
[33]	Decentralised	Decentralised partially observable Markov decision process	Improve the efficiency of the distributed storages and reduce the complexity of distribution network operation utilisation	Low resiliency
[34]	Hybrid	Multistep hierarchical optimisation algorithm	Easy to implement and computationally inexpensive	If central controller is compromised, all MGs will operate independently
[42]	Hybrid	Hierarchical power scheduling approach	Optimally manage power trading, storage, and distribution	Easy disclosing of partial customer privacy of MGs by central controller
[43]	Hybrid	Hierarchical decentralised SoS architecture	Addresses the problem of spatially unbalanced demand and generation	High dependence on communication networks
[44]	Hybrid	Multi-agent hierarchical energy management algorithm	Maximize the local consumption	High Dependence on communication networks
[45]	Decentralised	Agent-oriented trading algorithm trading algorithm	Dynamic energy trading, maximise profit maximise profit	Not scalable, does not handle security issues

1.1 Motivation

The power generated by the MG differs from time to time due to the irregular nature of DER, thus causing either a surplus or a shortage of power generation. Various energy management techniques have been suggested to curtail the ill effects of irregular power supply. These techniques include the use of storage devices such as batteries, flywheels, capacitors, etc., as well as of forecasting techniques, demand load management and backup generators. Another technique is to connect to nearby MGs that interchange power with each other. This technique can solve the issue of unsteady power supply caused by weather conditions. An agent-based architecture has been presented by Yasir et al. [3] for local energy distribution, where the group of MGs has a coordinator agent. This coordinator agent trades power with other interconnected groups to satisfy a group-wide power surplus or deficit.

MG created the concept of prosumer, namely consumers and energy producers. Prosumers sometimes generate excess renewable energy, which can be stored for future use or sold to buyers. Sometimes prosumers lack energy despite local production. Prosumers include DER, power loads, energy storage, electric vehicles, and smart meters. DER can be used in renewable energy sources such as rooftop solar systems and small-scale wind turbines, which produce green energy. Power loads operating under the regular and irregular energy requirements of different prosumer end users can be represented by heating and cooling devices, audio visual devices, lighting, etc. By accumulating unused energy in the battery, it can be used anytime in the future [4, 5]. Smart meters receive energy from the public grid and return it to the grid, making it two-way. Many consumers are becoming prosumers to reduce electricity bills and reduce negative impacts on the climate. The government has also tried to promote prosumer by introducing a generous feed-in tariff schemes [6]. With more and more prosumers on the market with complete freedom to share energy, it is important to focus on sustainable and reliable energy sharing models, so that prosumers can be managed in the most effective way. The motivational factor for single prosumers is that it allows the prosumer to make independent decisions, such as deciding how much energy to produce and how much energy to share with energy buyers. Prosumers have the option of signing a contract with a service provider of their choice. They also have the freedom to change suppliers depending on favorable electricity rates, contract terms and conditions of the mentioned public service provider company [6].

As opposed to traditional methods, the prosumer has tremendous control over renewable energy usage. This, together with the combination of green energy sources, rings about new opportunities for energy trading in the retail market. Therefore, prosumers have much more control in deciding where, when and in what amount to trade the energy produced. This association of the prosumers with the utility grid and energy management still has its limitations in energy production and distribution. Therefore, it is necessary to use analytical approaches to help understand the complicated association between independent and interdependent players.

A shortcoming of sharing energy directly from a single prosumer is that individual prosumers are not part of the wholesale energy market due to their perceived inefficiency and unreliability [7]. An individual prosumer does not have the larger energy-producing capacity, and therefore lacks real bargaining power. This can, in turn, force them to settle for a lower price per kilowatt. Another shortcoming is the uncertainty of the energy supply from individual distributed energy sources, due to their total dependence on unreliable climatic conditions [6]. There could be situations in which individual prosumers would be left out of the entire energy-sharing marketplace. Their inclusion depends on whether they will be able to satisfy the energy demands of the buyers. For example, solar systems and wind turbines are too small to compete with large scale power generators.

Individual prosumers generate electricity at a higher cost, but it is still cheaper than buying electricity from distribution companies. At the same time, prosumers hardly buy electricity during peak production, which increases demand for storage and finally storage costs of the system. The requirement is to build a grid using the latest technology that helps in optimising and at the same time distributing the energy. There is a need for a smart energy management system which consists of an active and improvised high technology power grid. This power grid caters to the gap caused by limited energy resources and the higher demand in the power supply.

To enable prosumers to generate higher volumes of energy, the concept of a coalition was created. A group of prosumers can come together to form a coalition with the aim of distributing electricity among themselves [3]. This is how coalitions can help generate more energy in the market. Individually, prosumers can produce green energy and, by forming coalitions, can sell larger amounts of energy. In this way, prosumers can get a higher price per kilowatt in the energy market. Compared to individual prosumers, coalitions of prosumers can produce larger amounts of energy, which can meet the needs of energy buyers in the most effective way. However, there is a downside to such coalitions, as they are not goal-oriented. This causes uncertainty among energy buyers regarding long-term energy supply.

There are some challenges in the prosumers’ coalition based energy sharing network, as it contains multiple opposing goals. During the development of complex systems in real-world scenarios, many of the stakeholders’ objectives are found to be conflicting in nature. For example, goals include the maximisation of external customer satisfaction, local energy demand satisfaction, quality of service, income, profit, etc. In order to manage and analyse goals in energy sharing network, it is necessary to model it using goal-oriented modelling. Also, it has been found that the presence of opposing goals was negatively impacting the decision-making process [8]. Given the challenges above, there is an urgent need for methods to improve coalition access to energy, resilience and reliability. Another major challenge that the energy coalition will need to reach an agreement that ensures a fair share of revenues and benefits [9].

This uncertainty led to our proposal, which includes the concept of goal-oriented prosumer coalitions provided in the given literature.

1.2 Literature review

In general terms, Goal-Oriented Requirements Engineering (GORE) involves the design of a software system by using goals as the starting point. The goal model demonstrates how goals, actors, states, objects, tasks and domain characteristics are all interconnected in the specified system [10, 11, 8] with respect to software engineering. The Knowledge acquisition of Automated Space (KAOS) Model [12], $i^{*}$ goal model [13], Attributed Goal-oriented Requirements Analysis (AGORA) Model [14], Tropos Model [15] and Goal-oriented Requirements Language (GRL) [16] Model are some of the goal models which are widely used in the literature. The $i^{*}$ goal model is one of the most prominent and well-known goal models in the software engineering discipline. By using the $i^{*}$ model, goal-oriented modelling of technical socio-economic systems and organisations can be achieved. This model helps in the basic processes when modelling organisational context and in capturing the intentional structure of the actors and their dependencies. This work has used a widely accepted framework, namely, the $i^{*}$ framework, which is an example of an agent-based goal model framework. This $i^{*}$ framework was specially selected for designing early Requirements Engineering (RE) analysis, and the modelling framework is generally used as a syntactic superset for several related frameworks (for example, Non-Functional Requirements (NFR) [17], GRL and Tropos). At the initial stage of the software development life cycle, the $i^{*}$ model analysis not only considers the questions like “how” and “what”, but also includes the “why” questions. Thus, quality analysis is performed for software dependencies estimation and allows a constant treatment for the NFR and functional requirements.

From popular research studies, the $i^{*}$ framework was selected to be used as an illustration of the agent-goal model according to its ability and balance between expressiveness and flexibility for selecting specific components in the early RE phase [18]. The $i^{*}$ framework aims to define a flexible enough framework to facilitate modelling of early requirements and describes this framework to a certain degree of interpretation and adaptation. Also, it can model and analyse the relationship among the entities considered in a social network, where the entities involve different types of social structures and support organisational context [19]. During the development of complex systems in real-world scenarios, many of the stakeholders’ objectives are found to be conflicting in nature. Hence, during the requirements analysis process in a goal model, an analyst must analyse the most effective design option to accomplish all the goals of the actor.

The $i^{*}$ goal model within the GORE framework is a tool utilised for modeling and analysing the dependencies between all the elements in a socio-economic community environment [20, 21, 22, 23]. Hence, $i^{*}$ framework is the widely used for modelling social relationships in the transactive energy management system (TEM) system [24].

An important group of researchers applies the game theory to solve the energy management problem of prosumers [25]. Game theory is a set of mathematical techniques which can be used for logical and fair decision-making on energy trading and management among various players (substations, utility grid, renewable energy sources, electric cars and prosumers and energy users) in the smart grid. Game theory can be a beneficial tool in understanding independent and interdependent decision-making associated with various situations. There have been several research proposals in the past [26, 27, 28, 29], some using a single energy user (prosumer/consumer) for energy trading. Other research works involve grouping energy users [30, 31, 32] with no mention of prosumers. Few other types of researches involved grouping prosumers using agent-oriented methods. Another research approach is to group prosumers using a game-theoretical approach. Coalitions are formed to help in balancing supply and demand, backup storage and physical network limitations. Similarly, [31] proposed a cooperative game-theoretic approach where communities mutually decide to schedule the usage of appliances in a collaborative manner, thus reducing peak energy demand. Further research proposals [33] suggest an association between energy users and the grid, as opposed to prosumers and the grid. An effective proposition was made [34] to form a coalition between customers and MG to bring about efficient utilisation of energy. A comprehensive comparison of the different types of energy management systems is provided in Table 2.

Table 2
Impact values

Impacts	Fuzzy values	Defuzzified values
Break	(0.00, 0.00, 0.16)	0.00
Hurt	(0.00, 0.16, 0.32)	0.16
Some $-$	(0.16, 0.32, 0.48)	0.32
Some $+$	(0.32, 0.48, 0.64)	0.48
Help	(0.48, 0.64, 0.80)	0.64
Make	(0.64, 0.80, 1.00)	0.80

In the centralised type, all of the controllable generation and consumption devices are controlled by a central controller, failing to protect customer privacy. The central controller not only manages the power interaction among MGs and the generation scheduling, but also participates in market bidding, stability control, and switching of MG operation modes. In general, the centralised structure can maximise the overall benefits of all MGs. Nevertheless, the centralised structure requires a high computational capability as the penetration of renewable generation continues to grow. In the decentralised type, every MG is an autonomous entity and has a local controller to maximise its own profit. The local controller monitors the operation status of MG and then independently determines the operation condition and controllable loads. However, the decentralised type may bring in the competition between MGs, thus degrading the system wide performance. The global optimal control of MGs can be realised through the information exchange among MGs. The hybrid type, which contains a central controller at the system level and local controllers at the MG level, is developed to overcome the disadvantages of centralised and decentralised type. The local controller of each MG performs local energy management and optimisation, and only informs the central controller on the total amount of surplus/deficit energy. The central controller is used for negotiating the control inconsistencies and economic conflicts between MGs, ensuring that the system operates in a global optimal state. Besides, the hybrid structure has the advantages of flexibility and low operation cost, making it popular in the MG system. However, no mechanism was created for managing the prosumer coalition’s non-functional requirements in the given energy trade environment. In an environment which has dynamic energy requirements, all the earlier proposed techniques would not work, since the value of energy requirement is fixed after the load is created. After reviewing the techniques given above, it was found that these techniques focused on grouping prosumers and consumers in a static environment, and also did not address or satisfy the prosumers’ non-functional energy needs. The payoffs by the prosumers were also not properly distributed and were not based on their specific energy trade. None of the proposals and work done until now were able to develop a framework based on goal-oriented coalition formation in a dynamic and real-time environment. This would help in improving the technical and economical aspects, while also taking into account the non-functional requirements during the power trades. Another energy trading model was proposed based on the research done by Capodieci and Paganin [29]. According to this model, an energy trade was made possible between individual prosumers, the power companies and the energy users based on an agent-based technique, so that their independent and individual energy needs could be satisfactorily achieved. Lamparter et al. [35] also developed a proposal for energy trading, which was also an agent-based model. An agent can use the limitations or preferences which are based on the local policy-concerned bidding mechanism. Another model for energy trading proposed making energy trades in a localised distribution network. This proposal aimed to reduce energy consumption during peak hours, while strictly adhering to game theory. In spite of the numerous other research proposals for enabling active energy trades between consumers and power companies, it was observed that none of these proposals were based on energy trades between prosumer coalitions and energy buyers, nor were they based on game theory. Another major shortcoming in most of these proposals is that they are based on the traditional, non-cooperative and static environment, and only consider interactions of a single energy user with the power trading company. While some research proposals focused on assimilating the interdisciplinary characteristics of power systems, networking and communications for energy trades, all the other proposals focused on the energy demand aspect, along with the problem of optimisation for the grid. Hence it was concluded that all of the earlier research proposals were unable to develop a game goal-oriented model between prosumers and energy buyers, which could also take into account the strategic trading of the maximum amount of surplus energy. At the same time, these proposals did not take into account the non-functional requirements of the prosumers, the demand-side needs, and the problem of optimisation, which would be beneficial to the two parties participating in the energy trades.

Figure 1.

An example of a simple SD $i^{*}$ model.

In this proposed approach, the intentional strategic actor is modelled as the central unit. There are several characteristics that represents the intentional aspects of an actor such as goals, beliefs, ability and commitment [20]. An actor’s intention is to successfully and strategically attain the goal. The structural relationship of an actor in comparison to other actors in sharing resources or accomplishing goals by performing some tasks is also a significant aspect. Among functional goals, in other words, ‘hardgoals’, some preferred behaviours are captured by the non-functional goals also known as ‘softgoals’ [36]. The $i^{*}$ model aims at determining alternative choices through means-end (OR-decomposition) reasoning. This is possible with explicit clear representation of the goals in the $i^{*}$ model. The $i^{*}$ goal modeling comprises of two models representing the socio-economic systems: the Strategic Dependency (SD) model and the Strategic Rationale (SR) model [20, 21, 22, 23]. The SD model displays a high-level explanation of a process or a system in the form of a graph. In a graph representation, this model exhibits the actor’s dependency through behavioural goals or softgoals, tasks and resources. Figure 1 demonstrates an example of SD model where actors are depicted as circles, hardgoals as ovals, softgoals as cloud, resources as rectangles and tasks as hexagonal shapes. In the illustration SD model (Fig. 1), an actor $A$ depends upon actor $B$ for achieving softgoal $SD1$ . Actor $B$ has a task dependency on actor $D$ . Actor $D$ in turn depends on actor $C$ for a softgoal. Actor $A$ has a goal dependency on actor $D$ . Actor $C$ has a resource dependency with actor $A$ . Thus, the SD framework captures the dependency between various actors and hence captures the organisational context. The SR model plays the role of capturing and displaying the internal modelling and analysis of all actors in the framework. This is achieved based on the actors’ internal intentional inter-dependencies. Non-functional goals or softgoals form intended qualities of the system. The SR model like the SD model is also depicted in the form of a graph. Through the graph, nodes are represented as goals or tasks or resources or softgoals that are inter-connected by means-end links or task decomposition links or contribution links [23, 22]. The goals are connected to one or more tasks through AND (decomposition links) or OR (means-end links) relationships for accomplishing it. The contribution links can be Make, Break, Help, Hurt, Some $+$ , Some $-$ . These notions describe various types of contributions to various softgoals. This in turn leads to the satisfaction of softgoals [13, 23, 22]. Figure 2 demonstrates an example of an SR model. The $i^{*}$ model uses a top-down approach to identify the goals of each actors. This is achieved by breaking down the primary goals or hardgoals into a group of subgoals or tasks. Reasoning is performed by answering questions like, “How to achieve?” or “What to achieve?”. By answering, “How to achieve?”, the softgoal is decomposed further. This decomposition is repeated till each softgoal is atomic in nature represented as operationalisation of softgoals.

Figure 2.

An example of a simple SR $i^{*}$ model.

There are some challenges in the prosumers’ coalition-based energy sharing network, as it contains multiple opposing goals. For example, goals include the maximisation of external customer satisfaction, local energy demand satisfaction, quality of service, income, profit, etc. In order to manage and analyse goals in energy sharing network, it is necessary to model it using the $i^{*}$ model. Hence we adopted $i^{*}$ based agent based architecture for modelling, managing and analysing goals in prosumer energy sharing network. In many cases, one goal is achieved at the cost of another goal. Hence, we identified a need to customise the goals for each prosumer individually. This would encourage not just the individual prosumer, but also the coalition, to achieve their goals. We also found that the presence of opposing goals was negatively impacting the decision-making process [8]. Hence, it was also important to consider the $i^{*}$ modelling of goals and interdependent actor relationships for managing goals. Goal management aims to analyse the overall goals of the coalition of prosumers based on multi-objective optimisation using decision-making techniques. The adoption of a realistic decision-making process in our approach allows us to go beyond analytical tools, like game-theoretic concepts.

1.3 Contributions

Motivated by the discussion presented, in this article we propose a game theory based prosumer coalition to sell the excess energy to customers. We also explain how coalition outcomes (payoffs) are shared equally among prosumers using the Shapley Value concept. Therefore, this paper proposes a new game theory based methodology to explore MG energy systems and implies an optimal evaluation of their NFR objective function. We have adopted an agent-based $i^{*}$ goal architecture for analysis, modelling and management purposes in a prosumer energy sharing network. In many cases, one goal is achieved at the expense of another. Therefore, we have identified the need to individually tailor objectives for each prosumer. This will encourage not only individual prosumers, but also coalitions, to achieve their goals. Therefore, it is also important to consider the $i^{*}$ goal model and the relationships between interdependent actors for goal management. Goal management aims to analyse the overall goals of the prosumer coalition on the basis of multi-objective optimisation with decision-making techniques. Adopting a realistic decision-making process in our approach allows us to go beyond analytical tools, such as game theory concepts. Game theory is a decision-making tool that offers a scientific mathematical explication. It has a significant part in competing situations for analysing issues and obtaining the payoff values based on the players’ results’. This paper proposes a novel methodology based on game theory for system exploration, which involves alternative design evaluation [37]. The reason for choosing the game theory idea is that it finds an ideal solution under conditions of conflict assuming that players are rational and act based on their interests [17] [38]., the benefits are divided among members in proportion to their value addition.

Following are the main contributions of the paper summarised as ready reference:

1.
We proposed a novel methodology based on game theory for exploring the MG energy system and implementing multi-agent based coalition formation of prosumers in MG to sell their surplus energy with customers.
2.
We proposed a fuzzy logic method to effectively interpret and evaluate the goals/requirements of the prosumer coalitions which are usually expressed in a more linguistic/subjective manner.
3.
We proposed an $i^{*}$ goal modelling concept to handle the ambiguity which usually arises due to the subjective preferences by the analyst/decision makers in the goal analysis stage.
4.
We implemented the game theory-based goal modelling approach using Shapely Value theory for optimally quantifying and evaluating payoffs from the coalition that are fairly shared among the prosumers in the presence of opposing NFRs.

2. Preliminaries

2.1 $i^{*}$ modelling

There are several characteristics that represents the intentional aspects of an actor such as goals, beliefs, ability and commitment [19]. An actor’s intention is to successfully and strategically attain the goal. The structural relationship of an actor in comparison to other actors in sharing resources or accomplishing goals by performing some tasks is also a significant aspect. Among functional goals, in other words, “hardgoals”, some preferred behaviours are captured by the non-functional goals also known as “softgoals” [23]. The $i^{*}$ model aims at determining alternative choices through means-end (OR-decomposition) reasoning. This is possible with explicit clear representation of the goals in the $i^{*}$ model.

The $i^{*}$ goal modeling comprises of two models representing the socio-economic systems: the Strategic Dependency (SD) model and the Strategic Rationale (SR) model [19, 20, 21, 22]. The SD model displays a high-level explanation of a process or a system in the form of a graph. In a graph representation, this model exhibits the actor’s dependency through behavioural goals or softgoals, tasks and resources. Figure 1 demonstrates an example of SD model where actors are depicted as circles, hardgoals as ovals, softgoals as cloud, resources as rectangles and tasks as hexagonal shapes. In the illustration SD model, an actor A depends upon actor B for achieving softgoal SD1. Actor B has a task dependency on actor D. Actor D in turn depends on actor C for a softgoal. Actor A has a goal dependency on actor D. Actor C has a resource dependency with actor A. Thus, the SD framework captures the dependency between various actors and hence captures the organisational context. The SR model plays the role of capturing and displaying the internal modelling and analysis of all actors in the framework. This is achieved based on the actors’ internal intentional inter-dependencies. Non-functional goals or softgoals form intended qualities of the system. The SR model like the SD model is also depicted in the form of a graph. Through the graph, nodes are represented as goals or tasks or resources or softgoals that are interconnected by means-end links or task decomposition links or contribution links [21, 22]. The goals are connected to one or more tasks through AND (decomposition links) or OR (means-end links) relationships for accomplishing it. The contribution links can be Make, Break, Help, Hurt, Some $+$ , Some $-$ . These notions describe various types of contributions to various softgoals. This in turn leads to the satisfaction of softgoals [12, 22].

Figure 2 demonstrates an example of an SR model. The $i^{*}$ model uses a top-down approach to identify the goals of each actors. This is achieved by breaking down the primary goals or hardgoals into a group of subgoals or tasks. Reasoning is performed by answering questions like, “How to achieve?” or “What to achieve?”. By answering, “How to achieve?”, the softgoal is decomposed further. This decomposition is repeated till each softgoal is atomic in nature represented as operationalisation of softgoals.

2.2 Game theory

Game theory uses scientific and mathematical explication in studying decision-making tools. Both conflict and cooperation among intelligent decision-makers are taken into account. It has a significant part in competing situations for analysing issues and obtaining the pay-off values based on the player’s results’. Game theory is a powerful interdisciplinary tool for the analysis of competitive situations (or situations of conflict) in multi-agent systems [17]. It was originally developed for the domains of mathematics and economics. It can effectively characterise the interaction between decision-makers. It is an appropriate tool to analyse challenges of requirements-based engineering design [39]. Also, game theory is applied to represent and help understand the complicated association between independent and interdependent players [28]. A game model can be organised either in a cooperative or a non-cooperative way to find the optimal values of the payoff. In a non-cooperative game model, the players have the option of making a decision themselves to optimise the payout values. However, in a cooperative game model, players are organised into multiple sets of coalitions and cooperate with each other to achieve the optimal payout value. The current research works prove that cooperative type of game models are more efficient and profitable than non-cooperative ones. A cooperative game theory method called Shapley Value is used in this approach to distribute the economic benefits of the cooperation between the prosumers. In a cooperative game model, multiple coalitions are possible if the number of players are more than two. It is a decision-making process that can resolve various types of conflicts between decision-makers and find maximum payoff. The game theory model is a combination of autonomous decision makers known as players, and they must play two or more in quantity. In addition, each player must have more than one choice to profit from the game, otherwise he/she cannot apply the strategy. This means that the game theory model is a combination of several players, strategies and payoff functions. Game theory is a great way to tackle various decision-making problems in MGs, where various renewable resources are used for generation purposes. In recent years, game theory techniques are used in various research fields to solve various technical problems, which confirms a solid basis for the contribution of the market to get their optimal profit. The main element of any game model is that the player and each player must have more than one option to implement their own strategy to find the maximum payoff. One of the main challenges facing community energy schemes using coalition game theory is the problem of scalability [40, 41]. In particular, when determining Shapley Value in a coalition, the calculations become very complex and time-consuming, as the number of players in the coalition increases. To overcome this computational challenge, we proposed a mechanism based on the marginal contribution of each players. The next section describes the prosumer coalition structure formation, its optimisation and the generation of optimal solutions.

Figure 3.

Layered structure of actors in prosumer coalition.

3. Coalition of prosumers

With the aim of saving costs in the power distribution sector, better coordination of activities between power generating companies and individuals (prosumers) with the other parties can be achieved by using a software controller, which would represent each coordination as shown in the Fig. 3. This led to the idea of forming coalitions using the three activities mentioned below:

(i)
Generating a coalition structure
(ii)
To solve the problem of optimising each coalition
(iii)
To divide the value of the generated optimal solution among prosumers

3.1 Generating a coalition structure

Prosumer coalitions are formed in such a way that prosumers within each coalition would coordinate their activities only within their own coalition. These coalitions do not interact or coordinate with any other coalitions. This created a need to make disjoint and exhaustive coalitions by partitioning them into what we call a Coalition Structure (CS).

3.2 To solve the problem of optimising each coalition

To optimally solve their coalition problems, the tasks and resources of the prosumers in the coalition are pooled together. The purpose of these coalitions is to maximise their total payoffs by further selling the surplus energy to the other energy buyers.

3.3 To divide the value of the generated optimal solution among prosumers

Prosumers can do an energy exchange with other prosumers within the same coalition or with other coalitions. The quantity of energy that is produced by each coalition group is denoted as the ’decision variables’ in this research proposal. In the absence of enough prosumers to form the coalitions, the coalition can consist of only one prosumer.

If $N$ denotes the set of prosumers, then in the given period, every $P_{i}$ ( $i$ is an element of $N$ ), produces power $G_{i}$ to satisfy $D_{i}$ , which is the demand for power. For $i^{\text{th}}$ prosumer, $P_{i}$ , we define surplus energy as:

$\displaystyle E_{i}=(G_{i}-D_{i})$ (1)

If $E_{i}<0$ , then it implies $P_{i}$ needs additional power to meet its demand. If $E_{i}>0$ , then it implies $P_{i}$ has surplus power which can be sold. If $E_{i}=0$ , then the demand is equal to the energy that was produced. We can divide $P_{i}$ into two sections, that is, “sellers” and “buyers” based on the factors mentioned above. “Sellers” have surplus power while “buyers” have a demand for this surplus power to fulfil their power needs. If $E_{i}=0$ , then $P_{i}$ can be considered interchangeably as either a “buyer” or a “seller” since the result will not change. The demand ( $D_{i}$ ) and the production ( $G_{i}$ ) are always assumed as random numbers. Moreover, we can further extend the concept of “buyers” and “sellers” to the groups or coalitions which are formed by a number of MGs. In addition to exchanging power with the Coalition Controller (CC) or the utility grid, the prosumers can also trade energy with others in the coalition. This happens because the power lost while transmitting power to the neighbouring prosumers is always lower than the power loss when transmitting between the utility grid and a prosumer. Hence, a need was created for prosumers to form cooperative groups, which we refer to as coalitions.

For achieving equilibrium in energy distribution from prosumers to the other energy buyers (customers), a small communication overhead between one another is required in order to make strategic choices for forming a coalition among prosumers. If any excess energy remains after a coalition payoff function has taken place, the CC promptly informs the customers after assigning values to the excess energy, $E$ , and the cost per unit, $p$ . Upon receiving these values, the customer arrives at a decision based on their individual payoff function and any additional energy requirements they have. If, however, the customer does not agree to the coalition based on the values received, then the CC modifies the values it assigned earlier to the cost per unit, $p$ . The process of reassigning values to the cost per unit, $p$ , is repeated by the CC, until both parties are satisfied to enter into a coalition. The CC works with the sole aim of maximising revenue by selling any surplus energy to customers who are in need of this surplus energy. Here we notice that we can dynamically reassign new values to $p$ , to modify the coalition payoff function. An explanation is given in the next sections about the effect of the different payoff functions.

Figure 4.

Block diagram of prosumer coalition-based goal management.

4. Definition of a coalition-based goal management framework for a microgrid

A detailed explanation is presented in this Section, providing a framework for prosumers’ goal-based environment as shown in Fig. 4.

4.1 Theoretical explanation of the goal-based framework

This subsection explains a brief synopsis of the goal-based framework for the prosumers in the coalition. The following Fig. 4 illustrates the framework. A key requirement for making the prosumers goal-oriented is ensuring that their goals are managed after a clear understanding of the overall aims and objectives for this model, which depends on prosumers’ coalition-based energy sharing. We also need to take into account the effective tools that are used to tackle the numerous conflicting goals. At the same time, there was a need to optimise these functions so as to achieve multiple goals (objectives). There are several challenges that we encountered while sharing energy in this coalition-based environment. As an example, limitations due to income and costs, profit maximisation, etc. are some goals that created many oppositions and conflicts. On the other hand, there are some goals that can be achieved only by sacrificing some other goals. For example, the numbers of prosumers in each coalition need to be kept as low as possible, so that the overhead cost of managing these prosumers can also be kept low in order to achieve the goal of maximum profit from these coalitions. However, the drawback here is that the total energy produced and shared will be reduced, further affecting the payoffs (or total tariff income) received from the energy buyers due to the lower number of prosumers. Hence there is a pressing need to work with these limitations by ensuring that multiple conflicting goals are handled most effectively, while also keeping in check all the alterations and changes made in the required parameters for achieving all the goals satisfactorily. Moreover, all the goals determined for the prosumers need to be further categorised into customised goals for the different prosumers which have entered into a coalition. This would ensure that these prosumers stay motivated and inspired to achieve their respective goals. After further studying the above-mentioned factors, it seemed necessary to develop an effective methodology in this framework for managing the prosumers and their goals. We also had to define and present alternative design options so that the prosumers’ goals could be achieved to their maximum satisfaction. This paper presents the development of an effective goal-oriented framework to obtain an optimised set of overall goals within the prosumers’ coalition-based energy sharing model.

Our sole focus is to achieve the strategic goals while also keeping all the limitations in mind, which would help in optimising the overall strategy by using proper logic and reasoning methods. We present below a detailed explanation of the steps that must be taken in this framework, which are completely based on the prosumers’ goals.

4.1.1 An analysis of the stakeholders

In order to analyse the stakeholders, we first need to clearly identify the actors (stakeholders) that should be considered, clearly identify their goals and objectives, and also ascertain the impact of using the different alternatives. These different alternatives are again based on the subjective understanding of the stakeholders’ preference for solving their problems. A bottom-up approach is used to understand the stakeholders’ perspective on the methods used to attain their objectives. This approach helps in identifying all the non-functional energy requirements, while also noting the implications of using various alternatives. The very first step in this framework is the identification of the two actors for the proposed coalition-based energy sharing model: i.e. the Prosumer and CC.

In order to achieve the goal of effective energy management, the five non-functional requirements for the prosumer were identified. The identification of these non-functional requirements was based on the various factors related to the prosumers’ energy management profiles in the existing literature. The five non-functional requirements identified are:

(i)
To maximise revenue by maximising the

a)
surplus energy sold to the energy buyers with more demand,
b)
satisfaction of the external customer, and;
c)
quality of service provided.

(ii)
To minimise costs by minimising overheads of

a)
managing prosumer coalition,
b)
storing information about the energy needs of each member,
c)
total money invested, and;
d)
operation and maintenance of the coalition.

(iii)
To maximise the profit by

a)
minimising the overall costs, and;
b)
maximising the revenue generated.

In the proposed coalition-based energy sharing framework, solar panels and windmills were also considered as options or design alternatives for sourcing energy. Three non-functional needs for the CC are mentioned below, so that the energy is managed effectively and the payoff to each prosumer within the coalition is distributed as fairly as possible. These non- functional needs are:

(iii) (i)
each prosumer should get maximum payoffs;
(ii)
the price function needs to be optimised, and;
(iii)
the total surplus energy in each coalition needs to be maximised.

4.1.2 Multi-objective functions need to be formalised

Figure 5.

An Example $i^{*}$ Goal model of an actor with two alternatives.

In this Section so far, we have provided a completely generalised framework of the $i^{*}$ goal model. To further enable this framework to work successfully, it was concluded that the multi-objective functions, with respect to the softgoals, tasks and resources involved, all need to be strictly formalised [8, 46]. The techniques provided in this framework formalise the multi-objective functions of correlated actor dependencies, which, in turn, are based on the technique of generating the scores (values) of leaf softgoals.

For better understanding and clarity, a brief description of the methods used to derive the scores of softgoals is presented in this Section. To formalise the suggested framework and techniques provided, an example is shown in Fig. 5 for a clear understanding of the SR $i^{*}$ goal model. Figure 5 represents a single stakeholder (actor) with various elements mentioned below:

$G=$ goal of stakeholder (actor), Task1 and Task2 $=$ the two alternatives (tasks), IL11k means impact on leaf softgoal $L_{1}$ of Task1 alternative under actor $k$ and IL21k means impact on leaf softgoal $L_{2}$ of Task1 alternative under actor $k$ , $L_{1}$ and $L_{2}=$ two leaf softgoals, $SG_{1}$ and $SG_{2}=$ two intermediate softgoals, and; $TS_{1}$ and $TS_{2}=$ two top softgoals.

Here, it is assumed that the goal ( $G$ ) can be achieved by both $A_{1}$ or $A_{2}$ , which are the two alternative design options. Based on their percentages of relative significance, weighted values are allocated to the softgoals which are lower in the hierarchy, i.e. the leaf softgoals. Let the weights of the leaf softgoals $L_{1}$ and $L_{2}$ be $\omega_{L_{1}}$ and $\omega_{L_{2}}$ , respectively. The contributions of alternatives to each softgoal are illustrated by impacts such as Make, Help, Hurt, Break, Some $-$ , Some $+$ . For further details on how to generate scores, readers are directed to [8, 39]. The impacts are represented as fuzzy numbers [47] to show the extent to which an alternative option fulfils a leaf softgoal.

The decision makers would find it very difficult to express their requirements and preferences in exact numbers, due to the ambiguous data and complex problems which arise during the desision-making process. The respective defuzzified values for the softgoal contributions are shown in Table 2. In order to find the scores of top softgoals to achieve maximum satisfaction levels, the impacts that softgoal preferences would have on the top softgoals are generated. The generation of leaf softgoal scores is done in a backward direction so that the scores of top softgoals can be ascertained as accurately as possible. Many contribution links are received by the softgoals.

Let us consider that there are $t$ hierarchy levels in the given graph. At level zero of the given graph, the leaf softgoals are defined. Here we assume that,

$\omega_{L_{i}}=$ weight of the $i^{\text{th}}$ leaf softgoal, $\textit{Impact}_{L_{ijk}}=$ impact on the $i^{\text{th}}$ leaf softgoal of the $j^{\text{th}}$ alternative of the $k^{\text{th}}$ actor, $m=$ number of softgoals, $n_{c}=$ children and; $n_{d}=$ dependencies for the $i^{\text{th}}$ softgoals at level one.

If any softgoal has $t>1$ , then its score is calculated by multiplying its impact by each of its child scores. The score of the $t^{\text{th}}$ level softgoal is generalised in this section. We start this process by generalising the score of the $i^{\text{th}}$ leaf softgoal for the $j^{\text{th}}$ alternative for the $k^{\text{th}}$ actor, as shown by the equation given below:

$\displaystyle\textit{Score}_{L_{ijk}}=\textit{Impact}_{L_{ijk}}t\times\omega_{% L_{ijk}}+\sum_{d_{L_{i}}=1}^{n_{d_{i}}}(\textit{Score}_{d_{L_{i}}}\times% \textit{Impact}_{d_{L_{i}}})$ (2)

where, $\textit{Score}_{d_{L_{i}}}=$ score of the $d_{L}^{\text{th}}$ dependent of the $i^{\text{th}}$ leaft softgoal; $\textit{Impact}_{d_{L_{i}}}=d_{L}^{\text{th}}$ dependent impact of the $i^{\text{th}}$ leaf softgoal, and; $n_{d_{i}}=$ number of dependencies for the $i^{\text{th}}$ leaf softgoal at level zero.

If $t$ represents levels in the directed graph hierarchy, then at $t=1$ , the score of the $i^{\text{th}}$ softgoal ( $S G$ ) for the $j^{\text{th}}$ alternative for actor $k$ is generalised as per the equation given below:

$\displaystyle\textit{Score}_{SG_{i_{1}jk}}=\sum_{x=1}^{n_{c}}\left(\textit{% Impact}_{x}\times\textit{Score}_{L_{xjk}}\right)+\sum_{{d_{i}}_{1}=1}^{n_{i}}% \left(\textit{Score}_{{d_{i}}_{1}}\times\textit{Impact}_{{d_{i}}_{1}}\right)$ (3)

In the above equation, $n_{c}=$ number of children for each $i^{\text{th}}$ softgoal at $t=1$ , and; $n_{i}=$ number of dependencies at level $t=1$ for the $i^{\text{th}}$ softgoal.

This process of calculating the score for each softgoal is generated upwards, as explained above. That is, the scores of a level $t$ softgoal [i.e. the top softgoals $\textit{TS}_{1},\textit{TS}_{2},\ldots,\textit{TS}_{n}$ ] for an actor with a relation of dependence can be denoted and formalised using the equation given below:

$\displaystyle\textit{Score}_{SG_{i_{t}{jk}}}=\prod_{l=1}^{t}\textit{Impact}_{% ijl}\sum_{i=1}^{m}\left[\sum_{d=1}^{n_{c}}\left[\left(\textit{Impact}_{d_{ij}}% \times\textit{Impact}_{d_{L_{ijk}}}\times\omega_{d_{L_{ijk}}}\right)\right]% \right.+\sum_{y=1}^{n_{c}}\left(\sum_{b=1}^{n_{d}}\left({\textit{Score}_{i}}_{% d_{by}}\times{\textit{Impact}_{i}}_{d_{by}}\right)\right)+\left.\sum_{b=1}^{n_% {d}}\left({\textit{Score}_{i}}_{d_{b}}\times{\textit{Impact}_{i}}_{d_{b}}% \right)\right]$ (4)

Thus, we see that the objective function of the top softgoals with regards to each actor is generated based on the score calculation in Eq. (4). This is explained further in the following Section.

4.1.3 Develop objective functions

Consideration has to be given to both strategic dependencies and rationale diagrams of the $i^{*}$ goal model in case there is an inter-actor dependent relationship. Here, an assumption is made that this approach takes into consideration only the softgoal interdependence relationships. If an actor has n alternatives, there will be $n$ objectives available for each top softgoal. To achieve a maximum score for each top softgoal under each alternative, the $n$ objective functions need to be maximised using the equation given below:

$\displaystyle f_{i}(\omega_{1})=\textit{Score}_{T_{i_{1_{k}}}}=\max\left[\prod% _{l=1}^{t}\textit{Impact}_{i1l}\right.\sum_{i=1}^{m}\left[\sum_{d=1}^{n_{c}}% \left(\textit{Impact}_{d_{i1}}\times\textit{Impact}_{d_{L_{i1k}}}\times\omega_% {d_{L_{i1k}}}\right)\right]+\sum_{y=1}^{n_{c}}\left(\sum_{b=1}^{n_{d}}\left({% \textit{Score}_{i}}_{d_{by}}\times{\textit{Impact}_{i}}_{d_{by}}\right)\right)% +\left.\sum_{b=1}^{n_{d}}\left({\textit{Score}_{i}}_{d_{b}}\times{\textit{% Impact}_{i}}_{d_{b}}\right)\right]$ (5) $\displaystyle f_{i}(\omega_{2})=\textit{Score}_{T_{i_{2_{k}}}}=\max\left[\prod% _{l=1}^{t}\textit{Impact}_{i2l}\right.\sum_{i=1}^{m}\left[\sum_{d=1}^{n_{c}}% \left(\textit{Impact}_{d_{i2}}\times\textit{Impact}_{d_{L_{i2k}}}\times\omega_% {d_{L_{i2k}}}\right)\right]+\sum_{y=1}^{n_{c}}\left(\sum_{b=1}^{n_{d}}\left({% \textit{Score}_{i}}_{d_{by}}\times{\textit{Impact}_{i}}_{d_{by}}\right)\right)% +\left.\sum_{b=1}^{n_{d}}\left({\textit{Score}_{i}}_{d_{b}}\times{\textit{% Impact}_{i}}_{d_{b}}\right)\right]\ldots\ldots\ldots\ldots\ldots\ldots$ (6) $\displaystyle f_{i}(\omega_{n})=\textit{Score}_{T_{i_{n_{k}}}}=\max\left[\prod% _{l=1}^{t}\textit{Impact}_{inl}\right.\sum_{i=1}^{m}\left[\sum_{d=1}^{n_{c}}% \left(\textit{Impact}_{d_{in}}\times\textit{Impact}_{d_{L_{ink}}}\times\omega_% {d_{L_{ink}}}\right)\right.\left.+\sum_{y=1}^{n_{c}}\left(\sum_{b=1}^{n_{d}}% \left({\textit{Score}_{i}}_{d_{by}}\times{\textit{Impact}_{i}}_{d_{by}}\right)% \right)\right]+\left.\sum_{b=1}^{n_{d}}\left({\textit{Score}_{i}}_{d_{b}}% \times{\textit{Impact}_{i}}_{d_{b}}\right)\right]$ (7)

Such that

$\displaystyle 0\leqslant\omega_{d_{L_{jk}}}\leqslant 100\text{ for∼{} }d=1% \text{ to∼{} }n_{c}$

To enable all the actors in the goal model to reach optimal solution values, these multi-objective functions are also optimised. In the next Section, we elaborate on how conflicting goals, which can be maximum or minimum in nature, can be optimised for the multi-objective functions.

4.1.4 Obtain an optimised set of goals using the optimisation technique

An optimised set of overall goals for energy sharing in this coalition-based model decides the output in the goal-oriented energy management phase. In this proposal, we assume that each actor has two conflicting top softgoals ( $\textit{TS}_{1}$ and $\textit{TS}_{2}$ ) as well as two alternate design options, i.e. $A_{1}$ and $A_{2}$ . We can generate two optimal solutions separately by optimising the objective function for the top softgoals ( $\textit{TS}_{1}$ and $\textit{TS}_{2}$ ). This optimisation process is evaluated by using the IBM ILOG CPLEX optimisation tool [48]. In order to figure out the most accurate and logical choices, the IBM ILOG CPLEX optimiser is used in such business mathematical models. A modelling feature called ‘Concert’ that is present in IBM ILOG CPLEX enables programming languages like Java to be integrated with CPLEX. All simulations and computations were performed on a computer with Intel i7-8565U CPU of 1.80 GHz and with 16.00 GB RAM. The ideal solutions for the objective functions of top softgoals i.e. $\textit{TS}_{1}$ and $\textit{TS}_{2}$ in the given actor, are expressed by the two alternative design options, $A_{1}$ and $A_{2}$ .

The following equation defines the optimal solutions, as shown below:

$\displaystyle(x_{TS_{1}A_{1}},x_{TS_{1}A_{2}},x_{TS_{1}A_{3}},\ldots,x_{TS_{1}% A_{n}},$ $\displaystyle x_{TS_{2}A_{1}},x_{TS_{2}A_{2}},x_{TS_{2}A_{3}},\ldots,x_{TS_{2}% A_{n}})$ (8)

Moreover, multi-objective function values are generated for all the actors present in the goal model. These optimal values denote the potential of each alternative in order to attain the objectives of the actor (stakeholder). In these muliti-objective problems, a set of optimal solutions is referred to as the Pareto optimal set. In this environment, which contains objective functions in multi-objective optimisation problems, the Pareto optimal set helps in evaluating a collection of solutions which are not mutually controlling, but are instead superior to the rest of the search area. In this goal-based model, we pay special attention to the design of agents and the derivation of organisations from the goal-oriented needs. At this stage, we find that there is a need to manage multiple conflicting goals in a coalition-based energy sharing matrix so that an optimal set of goals can be achieved.

A linear goal programming technique is used here so that a formula can be derived to reach an optimal solution, which in turn contains the problem of conflicting goals. Now, the objectives are allocated for the optimal achievement, also keeping in mind their relative priority at each level. These objectives are considered to be the softgoals which need to be achieved, and hence efforts are made to find an optimal solution which is “as accurate as possible” to the optimal satisfaction. Goal programming models have earlier been used successfully in numerous application areas, such as environmental, health and academic planning [49]. These goal programming models have a good track record as a means for handling multiple conflicting goals in a feasible and efficient manner. However, this model has been rarely used in such energy sharing networks. In this model, we use and further develop Multi-Choice Goal Programming (MCGP) methodology for our solution framework as presented in Fig. 6.

Figure 6.

Proposed goal-oriented framework for prosumer coalitions using $i^{*}$ model.

5. Goal-oriented

i^{*}

framework for prosumer coalition

In a socio-economic community environment [20, 21, 22, 23], the GORE network specifically $i^{*}$ , has been a very efficient and effective tool used for modelling and analysing dependencies. Therefore, in this proposal, we preferred using the $i^{*}$ framework to model the reasoning for conflicting goals. The core entity to be modelled in this view is the intentional strategic actor. We can characterise the intentional aspects of an actor using goals, values, capability and commitments [20]. A real world example of smart grid modelling with goals, softgoals, leaf softgoals, dependencies and tasks was explained in detail in [24]. A strategic actor is defined as an actor who intends to achieve the goals effectively. The actors involved in this model are also concerned about their structural relationships with other actors while sharing resources and performing many other activities to achieve their goals. In order to find alternative choices, means-end (OR-decomposition) reasoning and specifically clear representation of goals in the $i^{*}$ model are used. Mostly, a softgoal (or non-functional goal) captures certain behavioural preferences among those captured by the functional goals (hardgoals). Different phases in the $i^{*}$ goal modelling of socio-economic organisations are shown in Fig. 7.

Figure 7.

Proposed phases in the $i^{*}$ goal modelling of socio-economic organisations.

The goal modelling of the $i^{*}$ framework uses two models to represent socio-economic systems: the model of SD and the model of SR [20, 21, 22, 23]. These two models are the most important components of the $i^{*}$ model. Each of these components contains many elements. The SD model is depicted by a graph which is a high-level description of a process or a softgoal. It also depicts the dependencies of the actors by their behavioural goals or softgoals, tasks and available resources.

The proposed phases in the $i^{*}$ goal modelling of socio-economic organisations, as shown in Fig. 7, are:

(i)

Analysing Requirements:

–

The SD and the SR models are used to define and specify requirements.

–

Both SD and SR models are used to analyse and describe the dependency between actors, organisations and also the rationale of the actors.

(ii)

Designing Agents:

–

To design the agents in detail, SD and SR models are used.

–

A classification of the elements is finalised into actor, goals, resources, alternative design options, actions, impacts, dependencies, decompositions and context models.

–

A series of actions are specified in this design to find a way for the actors to achieve their goals.

(iii)

Designing Organisations:

–

Even though organisations are designed in detail just like the agents, there are differences with respect to the actions and roles of the organisation versus those of agents.

–

In an organisation, roles are also played by other agents and/or organisations at run time. The organisations do not perform all the actions on their own.

–

A role is explained in detail with a set of goals, a context model and two conditions.

–

For an organisation to achieve its goal, plans of the goal are pursued by a goal of roles instead of actions by an agent.

In the following Section, an explanation of the proposed fair distribution between prosumers based on the Shapley Value method is presented.

5.1 Proposed method for energy management in a microgrid with a coalition of prosumers

Using the tools and techniques given in this proposal, the objectives of prosumers are formulated in such a manner that the total revenue is maximised by minimising the overhead costs and expenditures. The total costs involve the cost of producing energy, such as fuel cost, and overheads such as operation and maintenance costs. Each prosumer’s objective functions are derived individually. These objective functions are dependent on decision variables, such as the quantity of local energy production, the amount of surplus energy available for sale with the prosumer, the expenditure of initial investment, operation and maintenance costs, quality of services provided, etc. The latter conducted the authors of this paper to formulate in this section an optimum payoff characteristic function in this Section such that the profits gained by prosumers in the coalition are maximised. This, in turn, is achieved by trading energy locally and by using a fair calculation technique based on the Shapley Value method [38]. The numerical reproduction of the results is presented towards the end of this Section, which shows that the proposed technique can maximise the payoff of the prosumers when they are in a coalition. However, in the absence of these coalitions, the payoffs are not as optimal. The concept of the cooperative game-theory solution presented in the Shapley Value method helps in fairly compensating the energy exchange between the prosumer and the utility grids. The Shapley Value criteria can be applied in many scenarios in this coalition-based energy sharing environment. For example, this method can be used in order to fairly allocate emission [50] or transmission expansion [51] costs.

The numerous applications and favourable properties of this method ensure that the payoffs are distributed fairly and that the $i^{*}$ model can be set up. The use of the $i^{*}$ model enables maximising profits for each prosumer by forming a coalition among the prosumers. The $i^{*}$ model also recommends a price calculation function, which fairly compensates for the energy transferred through power transactions within a coalition. There are a number of ways which can be used for achieving the “best” distribution of the value of the game with respect to the total payoff value. One beneficial way is fairness, which is ensured by analysing the player’s contribution to the value of the coalition.

The Shapley Value is defined as the distribution of payoff value that is canonically held to fairly divide the value of a coalition. This method is used to allocate the income of a coalition to each individual prosumer in that coalition. This method is arguably the most significant payoff plan and is used in coalition games for regulating the payoffs. Within game theory, special attention has been placed on the Shapley Value method due to its well-defined approach to solving the problems of complex strategic interplay [52]. To enhance the cooperation within associations, numerous authors have developed and used methods based on the Shapley Value. The average payoff contribution of all the viable orders of the prosumers is considered as the Shapley Value of a prosumer. This Shapley Value supports a mutual understanding of how the payoffs will be divided as fairly as possible, among the prosumers.

The Shapley Value $\psi_{i}(f)$ of the prosumer, $i$ , can be mathematically conveyed as:

$\displaystyle\psi_{i}(f)=\frac{1}{N!}\sum_{S\in N}|S|!(N-|S|-1)!-(f(S\cup\{i\}% -f(S)))$ (9)

where $S=$ number of players in the coalition; $N=$ total number of players in the game; $f=$ characteristic function, which represents the earned payoffs or benefits of a coalition $S$ ; $i=$ any prosumer in the game; $(f(S\cup\{i\}-f(S)))=$ the marginal contribution of the ith prosumer in $S$ ; $\psi_{i}(f)=$ the Shapley Value of the $i^{\text{th}}$ prosumer; $|S|!(N-|S|-1)!=$ various viable combinations, in which marginal contributions can be made.

As a consequence, the Shapley Value $\psi_{i}(f)$ is allocated to player $i$ , as per the given function $f$ , which evaluates the gain $f(S)$ for a coalition game $(N,f)$ with the transferable payoff for player set $N$ , which is measured by a function for any non-empty subset $S\in N$ . We found this method to be advantageous, since it takes into account budget-balancing and also guarantees the existence of equilibrium in any game without any dependence on its parameters. At the same time, we noticed some valuable properties present in this method, such as:

Pareto-efficiency: It distributes the total values of a coalition among all its players.

Symmetry: Notwithstanding the number of players, the value can be ascertained by using this method.

Additivity: This property requires any of the two games:

$\displaystyle\psi_{\{i\}}(N,f),\psi_{\{i\}}(N,f\star)$

that is:

$\displaystyle\psi_{\{i\}}(N,f)+\psi_{\{i\}}(N,f\star)=\psi_{\{i\}}(N,f+f\star)% ∼{}∼{}\forall i\in N.$ (10)

Zero player: A player would gain a value of zero,

$\displaystyle f(S\cup\{i\})=f(S)∼{}∼{}\forall S\in\psi_{\{i\}}(f)=0$ (11)

in case the marginal value of the player in any possible coalition is zero.

In order to fairly distribute the payoffs using the Shapley Value method, we need to ask some questions to apply this coalitional game theory. The questions to be asked are:

(2) (1)

Will a coalition be formed?

(2)

How will the players in the coalition divide their payoffs?

The answer to the first question is usually the ‘grand coalition’, which is the name assigned to the coalition of all the prosumers in $N$ . However, this might again depend on making the right choices while answering the second question.

The cooperative game is still described in terms of a characteristic function, which specifies (for every group of players (for example prosumer coalitions)) the total payoff that the members of $S$ can obtain by reaching a consensus among themselves. To reach a consensus, they can sign an agreement between themselves so that this payoff can be fairly distributed among all the players in the group. The Shapley Value method supports providing a fair and distinctive solution to the problem of fair distribution of payoffs among all the players (prosumers), while also taking into account the worth of each coalition (group). Hence we see that the Shapley Value method ensures that each player gets rewarded as per their marginal contribution to each coalition. To find this average, all orders of players are considered as equally likely to be receiving benefits.

Figure 8.

An $i^{*}$ goal modelling structure for the MG energy management using prosumer coalitions.

6. Example

i^{*}

model for prosumer coalition

Figure 8 shows an example $i^{*}$ model diagram for analysing the non-functional requirements of each prosumer forming a coalition using multi-objective optimisation. This example shows that intentional elements can be decomposed, and that many alternatives may have various impacts on different concerns of the prosumers involved, with no obvious global solution that would satisfy everyone. In an attempt to illustrate our proposal most effectively, we considered a case study $i^{*}$ model involving four prosumers (or players) denoted as $P_{1}$ , $P_{2}$ , $P_{3}$ and $P_{4}$ . These four players agree to enter into a coalition. We also assume that each of these players has a surplus amount of energy, as shown in Table 3.

Based on the given scenario, total no. of coalitions among four prosumers $=2^{4}=16$ , and; number of ways to build the grand coalition $=4!=24$ .

Table 3
Surplus Energy in kWh

Prosumers	Amount of surplus energy in kWh (Es)
$P_{1}$	90
$P_{2}$	80
$P_{3}$	60
$P_{4}$	70

Table 4

Characteristic function values based on each coalition set (S)

Coalitions	Value of the characteristic function
$S=\{\emptyset\}$	$f(s)=0$
$S=\{P_{1}\}$	$f(s)=810$
$S=\{P_{2}\}$	$f(s)=640$
$S=\{P_{3}\}$	$f(s)=360$
$S=\{P_{4}\}$	$f(s)=490$
$S=\{P_{1},P_{2}\}$	$f(s)=2890$
$S=\{P_{1},P_{3}\}$	$f(s)=2250$
$S=\{P_{1},P_{4}\}$	$f(s)=2560$
$S=\{P_{2},P_{3}\}$	$f(s)=1960$
$S=\{P_{2},P_{4}\}$	$f(s)=2250$
$S=\{P_{3},P_{4}\}$	$f(s)=1690$
$S=\{P_{1},P_{2},P_{3}\}$	$f(s)=5290$
$S=\{P_{1},P_{2},P_{4}\}$	$f(s)=5760$
$S=\{P_{1},P_{3},P_{4}\}$	$f(s)=4840$
$S=\{P_{2},P_{3},P_{4}\}$	$f(s)=4410$
$S=\{P_{1},P_{2},P_{3},P_{4}\}$	$f(s)=9000$

We further initiate

$\displaystyle f(E_{s})=0.1*(E_{s})^{2},$

which is the convex characteristic function based on the amount of surplus energy. This formula for $f(E_{s})$ is used to quantify the benefit derived from a different coalition of prosumers.

Table 5

Marginal contribution of each prosumer within the coalition of four prosumers

Different possibilities of a grand coalition	Marginal contribution of Prosumer1	Marginal contribution of Prosumer2	Marginal contribution of Prosumer3	Marginal contribution of Prosumer4
$P_{1},P_{2},P_{3},P_{4}$	$f(P_{1})-f(\varnothing)=810$	$f(P_{1}P2)-f(P_{1})=2080$	$f(P_{1}P2P3)-f(P_{1}P2)=2400$	$f(P_{1}P2P3P4)-f(P_{1}P2P3)=3710$
$P_{1},P_{2},P_{4},P_{3}$	$f(P1)-f(\varnothing)=810$	$f(P_{1}P2)-f(P_{1})=2080$	$f(P_{1}P2P4P3)-f(P_{1}P2P4)=3240$	$f(P_{1}P2P4)-f(P_{1}P2)=2870$
$P_{1},P_{3},P_{2},P_{4}$	$f(P_{1})-f(\varnothing)=810$	$f(P_{1}P_{3}P_{2})-f(P_{1}P_{3})=3040$	$f(P1P3)-f(P1)=1440$	$f(P1P3P2P4)-f(P1P3P2)=3710$
$P_{1},P_{3},P_{4},P_{2}$	$f(P_{1})-f(\varnothing)=810$	$f(P1P3P4P2)-f(P1P3P4)=4160$	$f(P1P3)-f(P1)=1440$	$f(P1P3P4)-f(P1P3)=2590$
$P_{1},P_{4},P_{2},P_{3}$	$f(P_{1})-f(\varnothing)=810$	$f(P1P4P2)-f(P1P4)=3200$	$f(P1P4P2P3)-f(P1P4P2)=3240$	$f(P1P4)-f(P1)=1750$
$P_{2},P_{1},P_{3},P_{4}$	$f(P2P1)-f(P2)=2250$	$f(P2)-f(\varnothing)=640$	$f(P2P1P3)-f(P2P1)=2400$	$f(P2P1P3P4)-f(P2P1P3)=3710$
$P_{2},P_{1},P_{4},P_{3}$	$f(P2P1)-f(P2)=2250$	$f(P2)-f(\varnothing)=640$	$f(P2P1P4P3)-f(P2P1P4)=3240$	$f(P2P1P4)-f(P2P1)=2870$
$P_{2},P_{3},P_{1},P_{4}$	$f(P2P3P1)-f(P2P3)=3330$	$f(P2)-f(\varnothing)=640$	$f(P2P3)-f(P2)=1320$	$f(P2P3P1P4)-f(P2P3P1)=3710$
$P_{2},P_{3},P_{4},P_{1}$	$f(P2P3P4P1)-f(P2P3P4)=4590$	$f(P2)-f(\varnothing)=640$	$f(P2P3)-f(P2)=1320$	$f(P2P3P4)-f(P2P3)=2450$
$P_{2},P_{4},P_{1},P_{3}$	$f(P2P4P1)-f(P2P4)=3510$	$f(P2)-f(\varnothing)=640$	$f(P2P4P1P3)-f(P2P4P1)=3240$	$f(P2P4)-f(P2)=1610$
$P_{2},P_{4},P_{3},P_{1}$	$f(P2P4P3P1)-f(P2P4P3)=4590$	$f(P2)-f(\varnothing)=640$	$f(P2P4P3)-f(P2P4)=2160$	$f(P2P4)-f(P2)=1610$
$P_{3},P_{1},P_{2},P_{4}$	$f(P3P1)-f(P3)=1890$	$f(P3P1P2)-f(P3P1)=3040$	$f(P3)-f(\varnothing)=360$	$f(P3P1P2P4)-f(P3P1P2)=3710$
$P_{3},P_{1},P_{4},P_{2}$	$f(P3P1)-f(P3)=1890$	$f(P3P1P4P2)-f(P3P1P4)=4160$	$f(P3)-f(\varnothing)=360$	$f(P3P1P4)-f(P3P1)=2590$
$P_{3},P_{2},P_{1},P_{4}$	$f(P3P2P1)-f(P3P2)=3330$	$f(P3P2)-f(P3)=1600$	$f(P3)-f(\varnothing)=360$	$f(P3P2P1P4)-f(P3P2P1)=3710$
$P_{3},P_{2},P_{4},P_{1}$	$f(P3P2P4P1)-f(P3P2P4)=4590$	$f(P3P2)-f(P3)=1600$	$f(P3)-f(\varnothing)=360$	$f(P3P2P4)-f(P3P2)=2450$
$P_{3},P_{4},P_{1},P_{2}$	$f(P3P4P1)-f(P3P4)=3150$	$f(P3P4P1P2)-f(P3P4P1)=4160$	$f(P3)-f(\varnothing)=360$	$f(P3P4)-f(P3)=1330$
$P_{3},P_{4},P_{2},P_{1}$	$f(P3P4P2P1)-f(P3P4P2)=4590$	$f(P3P4P2)-f(P3P4)=2720$	$f(P3)-f(\varnothing)=360$	$f(P3P4)-f(P3)=1330$
$P_{4},P_{1},P_{2},P_{3}$	$f(P4P1)-f(P4)=2070$	$f(P4P1P2)-f(P4P1)=3200$	$f(P4P1P2P3)-f(P4P1P2)=3240$	$f(P4)-f(\varnothing)=490$
$P_{4},P_{1},P_{3},P_{2}$	$f(P4P1)-f(P4)=2070$	$f(P4P1P3P2)-f(P4P1P3)=4160$	$f(P4P1P3)-f(P4P1)=2280$	$f(P4)-f(\varnothing)=490$
$P_{4},P_{2},P_{1},P_{3}$	$f(P4P2P1)-f(P4P2)=3510$	$f(P4P2)-f(P4)=1760$	$f(P4P2P1P3)-f(P4P2P1)=3240$	$f(P4)-f(\varnothing)=490$
$P_{4},P_{2},P_{3},P_{1}$	$f(P4P2P3P1)-f(P4P2P3)=4590$	$f(P4P2)-f(P4)=1760$	$f(P4P2P3)-f(P4P2)=2160$	$f(P4)-f(\varnothing)=490$
$P_{4},P_{3},P_{1},P_{2}$	$f(P4P3P1)-f(P4P3)=3150$	$f(P4P3P1P2)-f(P4P3P1)=4160$	$f(P4P3)-f(P4)=1200$	$f(P4)-f(\varnothing)=490$
$P_{4},P_{3},P_{2},P_{1}$	$f(P4P3P2P1)-f(P4P3P2)=4590$	$f(P4P3P2)-f(P4P3)=2720$	$f(P4P3)-f(P4)=1200$	$f(P4)-f(\varnothing)=490$

We have provided Table 4 to show different sets of coalitions $(S)$ , as well as the corresponding values of the characteristic function $(f(s))$ . The benefits from each coalition are divided among prosumers based on their marginal and individual contributions. This implies that the payoff each prosumer gains is equal to the value that they bring to the coalition. The marginal contributions are calculated for the four prosumers, as shown in Table 5. After calculating the marginal contribution of prosumers for each case in which the grand coalition can be formed, we can calculate their Shapley Value, as shown below:

$\displaystyle\psi_{1}(f)=\frac{1}{4!}(6\times 810+2\times 2250+2\times 3330+6% \times 4590+2\times 3510+2\times 1890+2\times 3150+2\times 2070)=\$2700$ $\displaystyle\psi_{2}(f)=\frac{1}{4!}(6\times 640+2\times 2080+2\times 3040+6% \times 41600+2\times 1600+2\times 2720+2\times 3200+2\times 1760)=\$2400$ $\displaystyle\psi_{3}(f)=\frac{1}{4!}(6\times 360+2\times 2400+2\times 1440+6% \times 3240+2\times 2280+2\times 1200+2\times 1320+2\times 2160)=\$1800$ $\displaystyle\psi_{4}(f)=\frac{1}{4!}(6\times 490+2\times 2870+2\times 2590+6% \times 3710+2\times 1750+2\times 2450+2\times 1610+2\times 1330)=\$2100$

Table 6 shows the Shapley Values of each prosumer with and without a coalition.

6.1 Calculation of shapley value with and without a coalition for various characteristic functions

So that the best pricing characteristic function can be chosen, we consider the various pricing characteristic functions – Linear, convex and concave functions. The characteristic functions $f(E_{s})$ given below are defined for each of the individual cases as:

Table 6
Shapley values of each prosumer with and without coalition

Prosumer	With coalition (Fair distribution)	Without coalition
$P_{1}$	2700	810
$P_{2}$	2400	640
$P_{3}$	1800	360
$P_{4}$	2100	490

Linear:

$\displaystyle f(E_{s})=0.1\times E_{s}$ (12)

Convex:

$\displaystyle f(E_{s})=0.1\times(E_{s})^{2}$ (13)

Concave:

$\displaystyle f(E_{s})=0.1\times\sqrt{E_{s}}$ (14)

where the value 0.1 is considered as the ‘cost per unit’. We consider coalitions of various numbers of prosumers, so as to choose the most suitable pricing characteristic function.

Table 7

Marginal contribution of each prosumer for different characteristic functions

Coalitions	Amount of surplus energy in kWh (Es) of each prosumer in different coalitions	Convex with coalition	Convex without coalition	Linear with coalition	Linear without coalition	Concave with coalition	Concave without coalition
Coalitions of 3 prosumers
(P1, P2, P3)	(90, 80, 60)	(2070, 1840, 1380)	(810, 640, 360)	(9, 8, 6)	(9, 8, 6)	(0.67, 0.67, 0.67)	(0.95, 0.89, 0.77)
Coalitions of 4 prosumers
(P1, P2, P3, P4)	(90, 80, 60, 70)	(2700, 2400, 1840, 2100)	(810, 640, 360, 490)	(9, 8, 6, 7)	(9, 8, 6, 7)	(0.75, 0.42, 0.42, 0.42)	(0.95, 0.89, 0.77, 0.84)
Coalitions of 5 prosumers
(P1, P2, P3, P4, P5)	(90, 80, 60, 70, 100)	(3600, 3200, 2400, 2800, 4000)	(810, 640, 360, 490, 1000)	(9, 8, 6, 7, 10)	(9, 8, 6, 7, 10)	(0.45, 0.367, 0.367, 0.367, 0.45)	(0.95, 0.89, 0.77, 0.84, 1.0)

We observe from Table 7 and Fig. 9 that the linear and concave pricing functions do not show a considerable gain when coalitions containing different numbers of prosumers are formed. Hence, it was found that the individual prosumers gained better benefits when the characteristic function used was a convex function, i.e. Convex $f(E_{s})=0.1\times(E_{s})^{2}$ .

6.2 Use of goal-based optimisation tool to maximise profits of prosumers in coalition

Figure 9.

Marginal contribution using shapley value method of each prosumer for different characteristic functions.

In this Section, we formulate the objective problem and constraint functions of the optimisation framework. These functions enable energy management for prosumers in the coalition. A detailed $i^{*}$ goal-oriented framework for analysing the requirements of each prosumer forming a coalition is presented in Fig. 8. This framework is based on game theory and develops an optimised $i^{*}$ goal model, which represents the non-functional requirements of the prosumer. We formalise and optimise the profit calculation function for different numbers of prosumers within a coalition. This profit calculation function is described as a function which includes the total cost involved and the income generated from the energy sold during the various energy tradings. We transform this framework into a mixed-integer linear program by using a mathematical program. Hence, we are able to formulate a linear optimisation problem so that the profit for the prosumers can be maximised.

To illustrate the goal-based optimisation framework, we consider the same case study which we used and discussed in the earlier Section, where we took the example of forming coalitions with four prosumers. We have chosen this case study since it is simple and has been interpreted in easy terms. The two main actors presented in the figure have been simplified significantly as Prosumer and Coalition Controller. The mandatory non-functional requirements or top softgoals of the actors (i.e. Prosumer and Coalition Controller) have been identified as Profit and Payoff, respectively. We can achieve both Profit and Payoff by using Solar Panel and Windmill as alternatives for generating energy, so as to bring down this overhead cost. The actor Prosumer, benefits by achieving the topmost softgoal of maximising Profit through maximising Income and by minimising Total cost incurred. The impacts (Make; Help; Hurt; Break; Some $-$ ; Some $+$ ) show the extent to which the respective softgoals are realised by an event. These impacts lead us to the top softgoal, while also taking into account the softgoal preferences, which express the level of satisfaction indicated by the scores of the top softgoals. The values of defuzzified impacts are listed in Table 2. These values are used to determine the objective functions of the top softgoal.

6.2.1 Multi-objective function definition for the actor prosumer

In order to obtain a maximum score for each top softgoal as defined in the $i^{*}$ goal model, we formalise and use the objective functions, which are defined in Section 4.1.2. The payoffs are calculated using the Shapley Value method, based on the formal techniques provided in the above Section. Then we calculate the maximum objective functions for the Prosumer’s top softgoal (Profit), which are dependent on the alternative design options, Solar Panel and Windmill.

The value of the top softgoal Profit can be obtained from the softgoals Total Cost and Income, as shown in Fig. 8. The objective function for the softgoal Income is given below:

$\displaystyle F_{\textit{Income}}{(\omega)_{\textit{Prosumer}}}=\max(\textit{% Score}_{\textit{Income}})=\max(\textit{Help}\times(\textit{Help}\times(\textit% {Help}\times\textit{Help}\times(\textit{Make}\times\omega_{3}+\textit{Help}% \times\omega_{3})+\textit{Help}\times\textit{Help}\times\omega_{4})+\textit{% Help}\times\textit{Make}\times\omega_{5})+\textit{Make}\times\textit{score}(% \textit{Payoff})_{\textit{Coalition Controller}})$ (15)

where $\textit{score}(\textit{Payoff})_{\textit{Coalition Controller}}$ is the maximum payoff value received by the prosumer through the coalition. The fair payoff function of each prosumer is calculated by using the convex function defined above. The objective function for the softgoal Total Cost is given below:

$\displaystyle F_{\textit{Total Cost}}{(\omega)_{\textit{Prosumer}}}=\min(% \textit{Total Cost})=\min(\textit{Help}\times(\textit{Some}^{-}\times(\textit{% Help}\times\omega_{1}+\textit{Help}\times\omega_{1}))+\textit{Help}\times% \textit{Help}\times(\textit{Some}^{+}\times\omega_{2}+\textit{Some}^{-}\times% \omega_{2}))$ (16)

The objective function for the top softgoal Profit can be found from the softgoals Total Cost and Income, as shown below:

$\displaystyle F_{\textit{Profit}}{(\omega)_{\textit{Prosumer}}}=\textit{Help}% \times F_{\textit{Income}}{(\omega)_{\textit{Prosumer}}}-\textit{Help}\times F% _{\textit{Total Cost}}{(\omega)_{\textit{Prosumer}}}=\textit{Help}\times(\max(% \textit{Help}\times(\textit{Help}\times(\textit{Help}\times\textit{Help}\times% (\textit{Make}\times\omega_{3}+\textit{Help}\times\omega_{3})+\textit{Help}% \times\textit{Help}\times\omega_{4})+\textit{Help}\times\textit{Make}\times% \omega_{5})+\textit{Make}\times\textit{score}(\textit{Payoff})_{\textit{% Coalition Controller}}))-(\textit{Help}\times(\min(\textit{Help}\times(\textit% {Some}^{-}\times(\textit{Help}\times\omega_{1}+\textit{Help}\times\omega_{1}))% +\textit{Help}\times\textit{Help}\times(\textit{Some}^{+}\times\omega_{2}+% \textit{Some}^{-}\times\omega_{2}))))$ (17)

As an example, we considered the profit calculation from each prosumer in the case study (Table 6). The above equation can be further simplified as shown below:

$\displaystyle\max(\textit{Income})=\max(0.64\times(0.64\times 0.64\times 0.64% \times 0.8\times\omega_{3}+0.64\times 0.64\times 0.64\times 0.64\times\omega_{% 3}+0.64\times 0.64\times 0.64\times\omega_{4}+0.64\times 0.8\times\omega_{5}+0% .8\times 2700))=0.2416\times\omega_{3}+0.1678\times\omega_{4}+0.3277\times% \omega_{5}+1382.4$ (18) $\displaystyle\min(\textit{Total Cost})=\min(0.64\times 0.32\times 0.64\times% \omega_{1}+0.64\times 0.32\times 0.64\times\omega_{1}+0.64\times 0.64\times 0.% 48\times\omega_{2}+0.64\times 0.64\times 0.32\times\omega_{2})=0.2621\times% \omega_{1}+0.3277\times\omega_{2}$ (19)

6.2.2 Solutions of multi-objective functions

The IBM ILOG CPLEX tool is used to interpret the multi-objective function defined in the above sub-section.

Figure 10.

Optimal values of each prosumer with and without coalition formation.

In order to test the effect of coalition, we first considered three different characteristic functions (concave, linear and convex), and studied the Shapley Value with and without coalitions. In the investigation of the three different characteristic functions, we have found that for the linear function, no payoff was achieved by forming a coalition. In the case of concave functions, the overall payoffs are reduced by making coalitions. Higher payoffs are attained by forming a coalition only when we have a convex function. In the proposed work, a greater number of prosumers can be considered and investigated by using the Shapley Value. We also optimise the formation of a coalition and define the members that can be part of the coalition. All the multi-objective functions obtained are in linear form, so we use linear programming to find an optimal solution for the game. Hence, by solving the multi-objective formulations using the IBM ILOG CPLEX tool, the optimal and proportional values of the strategies are ascertained. Tables 8 and 9 and Fig. 10 are provided for ready reference with regard to the optimised values of the Pareto optimal multi-objective function, both with and without the coalition of prosumers. The results of simulation show that the proposed approach of coalition formation based on goal modelling of prosumers using the $i^{*}$ model yields improved results. Hence we can safely conclude that the prosumers that are in coalition yield more profit than those which are not in coalition.

Table 8

Pareto optimal values of each softgoals of each prosumers in coalition

Prosumers	Income	Total cost	Profit
Prosumer1	1414.9	26.28	1388.62
Prosumer 2	1261.3	26.28	1235.62
Prosumer 3	954.097	26.28	927.817
Prosumer 4	1107.7	26.28	1081.42

Table 9

Pareto optimal values of each softgoals of each prosumers without coalition

Prosumers	Income	Total cost	Profit
Prosumer1	414.72	26.28	388.44
Prosumer 2	327.68	26.28	301.4
Prosumer 3	184.32	26.28	158.04
Prosumer 4	250.88	26.28	224.6

7. Conclusion

This study examines the coalition of prosumers and suggests a method to fairly compensate for surplus energy exchange through power transactions based on the individual contributions. Thus, we proposed the $i^{*}$ goal model to optimally maximise the profits of each prosumer involved in the coalition. This method also helps in optimally minimising the total costs involved. The multi-objective optimisation $i^{*}$ goal model presented here was implemented and solved using CPLEX as a linear programming software. ILOG’s CPLEX helped to effectively solve the problems instead of using standard algorithms. By integrating Java with the IBM CPLEX optimisation tool, a simulation model based on the proposed method was developed. The results of simulation show that the proposed approach for forming the coalition based on $i^{*}$ goal modelling of prosumers yields better results by meeting the requirements of fairness and efficiency, and thus reduces the intermittency effect of generation through renewable resources. We shall experimentally validate this proposal with an industry partner in the near future, amid real-time and real-world settings. Some of the limitations of this work is that this paper does not talk about the ICT communication backbone, control parameters or protocols for MG coalition advancement for sustainable development, and its objectives such as deciding the monetary motivations, helping the prosumers’ positive practices, making awareness among the prosumers around the related benefits, etc. In the future, during the analysis of real-time systems, indicative learning algorithms can be used to ascertain how incomplete or inaccurate are the given set of requirements. Rough set-based techniques can also be used in the future to be able to deal with ambiguity in data. To improve the comprehension and application of goal model analysis by applying visualization methods, future work should continue to devise new techniques.

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Multi-agent based coalition formation of prosumers in microgrids using the i * goal modelling

Abstract

Keywords

1. Introduction

Table 1 Different optimisation-based energy management system approaches in the literature

1.2 Literature review

Table 2 Impact values

2.1 i * modelling

2.2 Game theory

(i) Generating a coalition structure (ii) To solve the problem of optimising each coalition (iii) To divide the value of the generated optimal solution among prosumers 3.1 Generating a coalition structure

3.2 To solve the problem of optimising each coalition

3.3 To divide the value of the generated optimal solution among prosumers

4.1 Theoretical explanation of the goal-based framework

4.1.1 An analysis of the stakeholders

Table 3 Surplus Energy in kWh

Table 6 Shapley values of each prosumer with and without coalition

References

Table 1
Different optimisation-based energy management system approaches in the literature

Table 2
Impact values

2.1 $i^{*}$ modelling

(i)
Generating a coalition structure
(ii)
To solve the problem of optimising each coalition
(iii)
To divide the value of the generated optimal solution among prosumers

3.1 Generating a coalition structure

Table 3
Surplus Energy in kWh

Table 6
Shapley values of each prosumer with and without coalition