Community Energy Markets with Battery Energy Storage Systems: A General Modeling with Applications

Abstract

Traditional models of power systems are undergoing a restructuring process, stimulated by the growing deployment of renewable energy sources, making them more decentralized and progressively increasing the focus on the consumer. New arrangements are being explored, allowing consumers to play a more active role in energy systems, highlighting the concept of consumer-centric markets. This work presents an optimization model that considers the insertion of the battery energy storage system (BESS) in the concept of community energy markets. This model aims to increase the community income and includes the degradation of BESS, also evaluating different arrangements of BESS in the community markets. In the investigated scenarios, discussions about the feasibility of inserting BESS through the analysis of social welfare (SW) and fairness indicators were carried out. With the results, it was possible to observe that there are structures that are more advantageous from the perspective of the communities and others from the perspective of the members of the communities, bringing some insights into the different impacts of a BESS in an energy community.

1. Introduction

1.1. Background and Motivation

The growing concern for sustainable development worldwide has led to the massive insertion of renewable energies in global electrical matrices [1]. Nonetheless, this process challenges the regular operation of power systems, not only regarding centralized generation (CG) but also distributed generation (DG). A convenient solution to mitigate these problems may be a battery energy storage system (BESS) [2,3]. Those BESSs may be used at utility scale, connected either in the transmission or distribution side. Another possibility is to allocate this on the consumer side through a small-scale BESS system [4]. It is expected that BESSs can benefit the electrical system by improving power quality, helping to reduce renewable energy curtailments [5,6]. In addition to providing several services, it offers various advantages in investments behind the meter, such as increasing the potential for using solar generation [4,7].

In the distribution sector, the increasing presence of so-called prosumers, i.e., consumers with the capacity to produce and eventually sell energy, draws attention [2]. As they are mainly characterized by solar photovoltaic (PV) systems on residential and commercial buildings, several issues arise due to their irregular consumption and uncoordinated injections of power into the grid [8,9]. Among the main ones are the overload of lines and transformers, reverse power flow, and protection systems issues [10]. In this way, BESSs also stand out because, when coupled to the internal electrical circuit of prosumers, they allow a portion of the produced energy to be stored instead of directly injected into the grid, thus avoiding its operating stress [2].

In this scenario, prosumers who own a BESS emerge, and those prosumers have been called prosumages in the recent literature [11]. When coupled directly to the grid, a BESS can provide or absorb energy amounts and perform other “grid services” to enable its proper operation [3]. Therefore, through price signals defined by regulation or local markets, BESS investors can actively manage their stored energy to maximize their revenues and make the grid operation more flexible [2,3,8,12]. It is worth noting that although BESS is still an incipient solution, its technological learning curve has been increasing due to the synergy with portable devices and electric mobility industries [2,8]. Therefore, its current high costs are expected to decline significantly in the coming years, and as a result, its penetration in the distribution sector will become more expressive [3].

In this expected scenario, where consumers are increasingly empowered and the grid operation becomes increasingly flexible, the structuring of a new energy market centered on the consumers seems attractive [13,14,15,16,17,18,19,20,21,22,23]. In general, this market view relies on peer-to-peer (P2P) and community-based structures [14]. The former is characterized by negotiations for the purchase and sale of energy that directly occur between peers without the need for third-party supervision [14]. In the latter, all peers, or community agents, communicate with a central node that supervises the negotiation process [14]. The presence of this supervisory node simplifies market regulation and its interface with the distribution system operator (DSO) [13]. For that reason, the community-based market has gained prominence in studies that expose the increase in flexibility, efficiency, and sustainability provided by consumer-centered markets to the power system [19,20,21,22,23,24,25].

From a practical point of view, the community-based market can be readily applied to groups of neighboring prosumers and prosumages, for example. Agents belonging to each group, say community, usually share common interests and play collaboratively to achieve a goal, such as maximizing community autonomy or peak-shaving services [13,15]. Since each agent has a particular energy requirement over a given period, the community’s internal and external transactions must be optimized to maximize SW in compliance with the community’s goal [13,14,15]. A general formulation for the community-based market optimization problem is presented in [13,15]. This formulation essentially consists of an objective function adaptable to different contingent situations and some linear constraints that hold the energy balance of the market. Additionally, it applies to different scales of the community-based market, regardless of the generation technology of their eventual prosumers and producers. Notwithstanding, this formulation was developed considering the community agent to be primarily a prosumer. Therefore, it does not address the technical requirements necessary for a prompt representation of an agent with a BESS, such as a prosumage or even a single BESS.

1.2. Literature Review

Recent studies point to the relevant role of the community market composed of agents with BESS will have in the future of energy systems and the need to design new business models that pave the way for its development [17,18]. Thus, it can be observed that the works published in recent years were developed based on different mathematical formulations of the community market with BESS, which are properly designed to meet certain market configurations and special operating rules.

Concerning shared storage, Ref. [22] models the problem of shared storage in smart grids through cooperative game theory but does not consider community markets. Two distinct configurations are analyzed: (i) a group of consumers having their own BESS cooperate and share their storage with each other and (ii) such consumers share a single BESS. They state that the sharing of stored energy in a cooperative manner is advantageous for both agents and society, yet their BESS technical modeling is oversimplified.

Similarly, Refs. [16,19,23,26,27] propose and analyze the community energy market in which agents can have BESS systems, but do not focus their analysis on the impact that BESS systems can have on that market. More precisely, Ref. [23] analyzes the impacts of a market structure, where the community is involved in P2P negotiations through a non-cooperative game, in a small community microgrid consisting of agents with photovoltaic and BESS systems. It concludes that P2P negotiations can bring financial and technical benefits to the community, yet the role of the BESS is minimal.

Focusing on reducing the operating costs of the community and its agents and with the battery in a secondary role in the analysis, Refs. [16,26] developed models to assess communities composed of agents with and without BESS. More specifically, the authors in [16] evaluate an operating model based on a double auction for a community energy market. The formulation developed in this work considered the basic technical constraints of BESS, and the resulting optimization problem was solved by an iterative algorithm. Through a two-stage mechanism, Ref. [26] investigates the sharing of energy in the energy community. In this work, agents trade in the day-ahead and real-time markets within the community and with the grid. The work in [19] analyzes the incorporation of the community market structure into existing local energy markets, in which some community members have BESS systems. It uses a decentralized method to solve the problem considering generation uncertainty, focusing its case on a current energy system of a city in the Netherlands. The authors of [27] developed a community energy model aimed at maximizing the social welfare (SW) of the community with and without BESSs.

An energy community model considering different goals for the agents was proposed in [28] and solved through distributed optimization approaches based on artificial intelligence. Analyzing different configurations, this work provides several insights and concludes how the insertion of prosumages positively influences an increase in self-sufficiency in the community. However, the analyses explore the contribution of storage systems in a more individual way.

Not only analyzing the energy market with agents that have a BESS but also focusing on the benefits of the BESS, Ref. [29] analyzes transactions in a community market with P2P trading considering two distinct layouts of BESS participation. The first consists of a community of prosumers with individual BESSs, while the second layout considers a central BESS shared by the community. Promising results were found, especially referring to the integration of commerce of P2P and BESSs in the community market. Similarly, with a greater focus on the storage system, Ref. [30] proposes a two-stage stochastic linear program to deal with P2P sharing. In this study, P2P and BESS energy exchange interactions in residential communities are presented. The union of P2P trade with BESSs contributes to the reduction of agents’ electricity bills and to better integration of distributed energy resources. Although BESSs are essential for their analysis and conclusions, these works do not consider the inclusion of battery degradation in their models, which can impair the realism of the results.

A general comparison of the aforementioned works focusing on the energy community markets with BESSs is presented in

Table 1. Comparison of energy market studies with storage systems.

Reference	Year	Method	Energy Market	Market Structure				Battery Degradation	Battery Insertion Arrangement
				Hour-Ahead	Day-Ahead	Intra-Day	Real-Time		Prosumage	Intracommunity *	Intercommunity **
[23]	2018	Noncooperative game theory	Community-based P2P Market				X	No	X
[16]	2020	Noncooperative game/Bilateral Nash game	Community-based Market	X			X	No	X
[26]	2021	Two-stage mechanism	Community-based Market		X		X	Yes	X
[19]	2020	Stochastic programming/ADMM	Community-based Market		X		X	No	X
[27]	2019	Non-linear bilevel	Community-based Market		X			No	X
[28]	2021	Distributed artificial intelligence and optimization	Community-based Market		X			No	X
[29]	2018	Linear optimization	Community-based P2P Market		X			No	X	X
[30]	2019	Two-stage stochastic linear program	Community-based P2P Market		X	X		No	X
Proposed Model	2021	Linear optimization	Community-based Market		X			Yes	X	X	X

* Intracommunity: The BESS as an independent agent belonging to a community; ** Intercommunity: The BESS as an independent agent who does not belong to any community buttrades with all communities.

. One can observe that, although several analyses are carried out in the context of the community energy market considering prosumers with BESSs, these systems are not generally the main focus of the analysis. It is also possible to observe that some proposed models require a relatively high level of background theory that can make their application in real cases more difficult.

1.3. Main Contributions

Following the growing importance of inserting BESS systems in power systems combined with consumer-centric markets, this work proposes to fill one of the gaps identified through a general formulation of the community market to deal with the presence of BESSs considering different arrangements. This model, inspired by [13], is essential not only to facilitate the development of new studies but also to establish a common basis for the characterization of its agents with BESSs and comparison of the results obtained for the different operating rules. It is noteworthy that the resulting optimization model preserves the main characteristics verified in this general formulation, such as the adaptability of the objective function, the linearity of the constraints, and the scalability of the application. To illustrate its application and provide subsidies for relevant discussions, a comprehensive study is also developed to assess the energy, financial, and social impacts that the same storage capacity of a BESS can cause when inserted in different arrangements of a community-based market. In short, the main contributions of the proposed work are as follows:

• Development of an optimization model that includes a prompt and appropriate representation of BESSs in a community-based market;
• Analysis of the insertion of BESS at three different arrangements in the community market: (i) at the prosumer level (prosumage); (ii) as an individual agent in the community (intracommunity); (iii) as a separate community (intercommunity);
• Assessment of the impacts that BESS can cause on the SW of a community-based market, considering different market organizations;
• Analysis of the social effects that BESS can have on the community energy market, as well as on the satisfaction of its agents when inserted in different arrangements in the market.

1.4. Paper Structure

The rest of the paper is structured as follows. Section 2 briefly discusses the general energy dynamics of the community-based market and the effects caused by inserting the BESS in its context. In Section 3, the optimization model developed to represent the community market with a BESS is appropriately explained. In Section 4, the main information about the study carried out to illustrate the application of the developed model is presented. In Section 5, the results obtained in this study are presented and the impacts caused by the BESS in the different arrangements of the market are analyzed. Finally, Section 6 concludes this paper.

2. Overview of the Community-Based Market with Battery Energy Storage System

A community-based market can be formed considering a single or several communities. In turn, each of these communities can be composed of a different number of agents, which are not necessarily of the same type. For instance, they can be consumers, producers, prosumers, prosumages, or a single BESS. Additionally, this market can interface with other market structures, such as wholesale, balancing, and ancillary services [13], which are generically defined in this paper as external players.

The dynamics behind the energy transactions performed in the community-based market are described below. Then, the impacts brought by the admission of a BESS among its agents are discussed.

2.1. General Framework of the Community-Based Market

Following the formulation presented by [13], an agent can participate in the community-based market in two ways: as a consumer or as a producer. In the case of a prosumer, such a role is defined based on its net energy balance (p) in a given period. That is, for the sake of efficiency, the energy produced by its generation system tends to be primarily destined to meet the demand of its load [2]. Therefore, if this energy demand is greater than the energy produced ($p>0$), the prosumer will play in the market as a consumer, seeking to supply its remaining energy consumption [13]. In contrast, if this energy demand is lower than the energy produced ($p<0$), it will act as a producer, offering its excess energy in exchange for economic benefits [13].

In general, the energy needs of agents considered to be consumers and producers can be traded within a margin of tolerance ($\underline{p}<p<\overline{p}$) with any of the upper market levels [13]. Thus, an agent can meet its energy need in a given period by sharing energy (q) with other agents in its community, or import ($\alpha$) and export ($\beta$) exchanges with other communities or even an external player [13].

These energy exchanges in the community-based market are coordinated by a non-profit virtual node called the community manager (CM). In addition to ensuring that the energy needs of all agents are met, the CM is also responsible for filling the community’s goal. Therefore, its decision-making process is guided by the technical constraints and energy prices practiced by prosumers, the charges incurred on internal ($c_{com}$) and external ($c_{imp}$, $c_{exp}$) energy transactions for the community, and the strategic behavior defined by the community agents [13].

It is important to highlight that in this paper, market levels or market arrangements will be considered as battery insertion configurations in the community market. That is, three different levels will be considered: (i) prosumage; (ii) intracommunity battery; (iii) intercommunity battery.

2.2. BESS Operational Complexity

Similar to the lack or excess of energy of a prosumer, the capacity to acquire or supply energy from a BESS is also an energy asset that can be traded in the community-based market. Nonetheless, quantifying this energy asset is not an easy task.

When the state of charge, or simply SoC, ($\varphi$) of the battery that makes up BESS is at an intermediate level to its minimum and maximum limits ($\underline{\varphi }<\varphi <\overline{\varphi }$), BESS has enough acquisition capacity and stored energy to assume both the role of consumer or producer in the market. Given this flexibility, the BESS role in a given period is not directly defined by the agent (or its owner) but by the CM. During this process, the CM must consider the dynamics verified in the rest of the market, as well as the technical constraints of the BESS.

Regarding the technical constraints of BESS, it is worth highlighting that they have two origins: technological and contextual. The technological constraints are related to the performance of specific parameters of the BESS components. From an energy perspective, such parameters can be summarized to the main characteristics of its battery, such as SoC limits; charge (${\eta }_{ch}$) and discharge (${\eta }_{dh}$) efficiencies; and charge (${\lambda }_{ch}$), discharge (${\lambda }_{dh}$), and self-discharge (${\lambda }_{sd}$) rates [16,31,32,33,34]. It is important to note that these parameters determine the limits of the amount of energy (s) that the BESS can trade on the market in a given period. Additionally, when the battery SoC is at its minimum limit ($\varphi \to \underline{\varphi }$), they force the BESS to play as a consumer in the market; otherwise, its self-discharge rate will cause the violation of such minimum limit—see (1f).

In turn, the contextual constraints are related to the BESS positioning in the market and agreements signed for its operation. To make this clearer, Figure 1 illustrates the possible positions occupied by BESS in a community-based market. Accordingly, these positions can be summarized as (a) a part of a prosumage; (b) an independent agent belonging to a community, i.e., an intracommunity agent; or (c) an independent agent who does not belong to any community but trades with all communities, i.e., an intercommunity agent.

Regarding prosumage, it is interesting to note that it constitutes one of the most intricate types of agents on the market. This is because it does not have only one, but two energy assets to be traded: (i) the net balance of its consumption and production; and (ii) the capacity to acquire or supply energy from BESS. Then, depending on its interests and the agreements made with its community, different constraints may be imposed on trading these assets. In a free scenario, both can be traded independently in the different market levels. However, the BESS would have its operation restricted to the agent’s needs in a conservative scenario, establishing only one asset to be traded on the market. In this case, such assets would be defined by the net balance between the load demand, the energy produced by the generation system, and the energy stored or supplied by the BESS.

For the intracommunity agent, only one asset is considered, which is the BESS’s capacity to acquire or supply energy. In this case, different conditions may arise related to the operating constraints. To better exemplify, suppose the community’s agents have invested in the BESS. In this case, its operation in the market may be understandably restricted to meeting the community’s energy needs. In addition, service preference can be given to those agents who have contributed most expressively to such investment. In contrast, if a third party has made this investment, the BESS would be more likely to operate freely in the different market levels.

It is worth mentioning that these considerations made for the intracommunity agent extend to the case of the intercommunity agent. If the BESS is a property of two or more communities, different constraints and preferences can be noticed.

This brief discussion shows that contextual constraints define the degree of freedom that the BESS has in the market and, eventually, define its operating preferences.

3. Modeling of the Community-Based Market with Battery Energy Storage System

As discussed above, the insertion of a BESS in the context of a community-based market considerably increases the complexity of its energy dynamics. To obtain a model that allows to appropriately represent the new issues brought by the BESS, the general formulation presented in [13] for a community-based market composed of prosumers was expanded to accommodate the presence of BESS in different arrangements of the market and its technical constraints [33,34]. An overview of the proposed analysis methodology is presented in Figure 2, while the respective optimization model is described in the next subsections.

3.1. Proposed Model

Aiming to allow for correct and flexible inclusion of a BESS in the general formulation of the community-based market, the following assumptions were made:

• The community agent can be primarily modeled as a prosumage (Figure 1a), as it is the type of agent that has the greatest variety of energy assets to be traded;
• The community agent can assume only one role (consumer/producer) within its community, but this is not necessarily the same assumed in the scope of the external market. For example, a prosumage can play in a given period as a consumer at the community level and as a producer for the external player;
• In the case of agents without a BESS, such as consumers, producers, and prosumers, their respective roles are predefined by themselves. In contrast, the role of agents with BESS, such as the prosumages and the intra and intercommunity BESS agents, are respectively defined by the CM, as discussed in the previous section.

The complete formulation of the community-based market model including BESS is presented in (1), considering n the number of agents that make up the community $\Theta$ (indexed as $j=1,\dots ,n$) and $\Gamma =(p_j,s_j,q_j,{\alpha }_j,{\beta }_j)$ the set of decision variables.

$$\begin{array}{}\mathrm{(1a)}& \underset{\Gamma }{\max }& \sum _{j=1}^n{f}_j(p_j,s_j,q_j,{\alpha }_j,{\beta }_j)+g(q_{imp},q_{exp})\mathrm{(1b)}& \mathrm{s}.\mathrm{t}.& p_j+s_j+q_j-{\alpha }_j+{\beta }_j=0,& \forall j\in \Theta \mathrm{(1c)}& & \sum _{j=1}^n{q}_j=0\mathrm{(1d)}& & \sum _{j=1}^n{\alpha }_j=q_{imp}\mathrm{(1e)}& & \sum _{j=1}^n{\beta }_j=q_{exp}\mathrm{(1f)}& & {\varphi }_j={\varphi }_{t-\tau ,j}·\left(1-{\lambda }_{sd,j}\right)+\frac{s_j}{b_j},& \forall j\in {\rm Y}\mathrm{(1g)}& & s_j·{\eta }_{ch,j}\le \left(\overline{{\varphi }_j}-{\varphi }_j\right)·b_j,& \forall j\in {\rm Y}\mathrm{(1h)}& & -s_j·{\eta }_{dh,j}\le \left({\varphi }_j-\underline{{\varphi }_j}\right)·b_j,& \forall j\in {\rm Y}\mathrm{(1i)}& & s_j\le {\lambda }_{ch,j}·b_j·\tau ,& \forall j\in {\rm Y}\mathrm{(1j)}& & -s_j\le {\lambda }_{dh,j}·b_j·\tau ,& \forall j\in {\rm Y}\mathrm{(1k)}& & \underline{p_j}\le p_j\le \overline{p_j},& \forall j\in \Psi \mathrm{(1l)}& & {\alpha }_j,{\beta }_j\ge 0,& \forall j\in \Theta \mathrm{(1m)}& & p_j,s_j,q_{j}free& \forall j\in \Theta \end{array}$$

The objective function represented by (1a) has two components. The former is given by a function f and aggregates all costs related to the energy transactions of each community agent. Therefore, it includes SW, as well as the costs due to sharing energy within the community and the import and export exchanges. The latter is given by a function g, representing the community’s goals and its interaction with the exterior market. This function is commonly defined by the global variables $q_{imp}$ and $q_{exp}$. As given by the constraints (1d) and (1e), the variables $q_{imp}$ and $q_{exp}$ represent the energy import and export exchanges between the community and the exterior market, respectively.

Regarding other constraints, (1b) shapes the particular energy balance of each agent in the community, and (1c) shapes the energy balance of the community. As (1b) fundamentally describes a prosumage, this one differs from the respective equation initially presented in [13] by including the free variable $s_j$, which represents BESS energy transaction. Moreover, it is pertinent to note that representing the agent’s energy transaction with the community in (1b) by the free variable $q_j$ guarantees that it will assume only a single role in the community.

Note that the free variable $s_j$ follows the same representation logic exposed in the previous section for the free variable $p_j$. That is, $s_j>0$ means that the BESS is acquiring energy (charging the battery), and $s_j<0$ means that the BESS is supplying energy (discharging the battery). In contrast, to satisfy the energy balance, the free variable $q_j$ follows the inverse representation logic; therefore,$q_j>0$ means that the agent is providing energy for sharing with other agents in the community and $q_j<0$ that the agent is consuming the energy shared by other agents of its community.

In turn, constraints (1f)–(1j) ensure that the technical constraints of each BESS present in the community (${\rm Y}\subset \Theta$) are respected. In this way, constraint (1f) defines the SoC of the battery that makes up the BESS in a given period, considering its previous level (${\varphi }_{t-\tau ,j}$), the self-discharge rate, and the ratio between its energy transaction and nominal capacity ($b_j$). Inequalities (1g) and (1h) represent the limits imposed by the charge and discharge efficiencies of the battery to the BESS energy transaction. In this same line, (1i) and (1j) represent the limits imposed by the charge and discharge rates of the battery within a time interval ($\tau$). It is important to note that the signs in (1g) and (1i) have been adjusted to make them active only when the BESS charges. Similarly, the signs (1h) and (1j) have been adjusted to make them active only when the BESS supplies energy.

Finally, constraint (1k) defines the margin of tolerance for the trade of the energy asset, referring to the net balance between the energy consumption and production of each agent who owns such an asset ($\Psi \subset \Theta$). As this balance is previously known, an agent has $\overline{p_j}$ > $\underline{p_j}$ > 0, if it plays as a consumer, and $\underline{p_j}$ < $\overline{p_j}$ < 0, if it plays as a producer.

Despite assuming that prosumages fundamentally characterize community agents, it is essential to emphasize that the model presented in (1) can be easily adapted to represent any other type of agent, regardless of whether it has a BESS or not. Some of these adaptations are pertinently discussed below.

3.2. Adjustments for the Intra/Intercommunity BESS

The adjustment required to represent an intracommunity BESS (Figure 1b) as a community agent in the context of the proposed model is set $\overline{p_j}=\underline{p_j}=0$ since there is no energy consumption or production in addition to its battery.

Nonetheless, some additional adjustments may be necessary for specific studies. For instance, assuming that the intracommunity BESS must play in the market exclusively oriented to its battery, (1a) must be rewritten as in (2a). In the latter, import and export exchanges are especially represented by the free variable ${\delta }_j$ and no longer by two non-negative variables, ${\alpha }_j$ and ${\beta }_j$. The use of this variable, together with the additional constraints (2b)–(2d), ensures that the intracommunity BESS will not consume or supply energy beyond the amount limited by its battery and, therefore, will not arbitrarily play in the market. It is important to note that (2b) defines ${\delta }_j<0$ as an import exchange and ${\delta }_j>0$ as an export exchange.

$$\begin{array}{}\mathrm{(2a)}& & s_j+q_j+{\delta }_j=0\mathrm{(2b)}& & {\delta }_j=-{\alpha }_j+{\beta }_j\mathrm{(2c)}& & 0\le {\alpha }_j\le \left|{\delta }_j\right|\mathrm{(2d)}& & 0\le {\beta }_j\le \left|{\delta }_j\right|\mathrm{(2e)}& & {\delta }_{j}free\end{array}$$

These adjustments discussed for the intracommunity BESS can be straightly extended to represent the intercommunity BESS (Figure 1c) in the context of the proposed model. In this case, however, such an agent must be stated as a single member of a separate community.

3.3. Adjustments for Agents without BESS

The adjustments required to represent consumers, producers, and prosumers in the context of the proposed model are set to $s_j=0$ and, consequently, inhibit the application of the restrictions related to the BESS, (1f)–(1j), on this agent. It is crucial to note that the model originally presented by [13] is fully recovered when making these adjustments.

Furthermore, with just a few additional adjustments, it is also possible to represent an external player in the context of the proposed model. An external player capable of meeting any remaining energy needs of a community market, for example, can be understood as an additional community of this same market. This community comprises two agents that cannot share energy, i.e., $q_j=0$. One of these agents is modeled as a great consumer, with $\underline{p_j}=0$ and $\overline{p_j}\to \infty$, and is prohibited from trading export exchanges, i.e., ${\beta }_j=0$. The other agent is modeled as a great producer, with $\overline{p_j}=0$ and $\underline{p_j}\to -\infty$, and is prohibited from trading import exchanges, i.e., ${\alpha }_j=0$. Thus, with their attention entirely focused on the other communities, these two agents can meet any energy needs of the market.

3.4. Battery Degradation

To present results closer to reality, battery degradation was included in the optimization model. The BESS’s storage capacity decreases due to factors such as aging and the number of charging and discharging cycles. Degradation can be included in the model by adjusting the nominal capacity of the BESS. Therefore, the restrictions (1f)–(1j) are updated daily.

To perform the degradation calculation and update its nominal capacity [35], as presented in (7), some processes are executed.

BESS degradation occurs as a result of calendar and cyclic aging (${\xi }_{cal}$, ${\xi }_{cyc}$). These losses need to be accounted for within a chosen period; in this way, the present work considers a daily horizon to be in accordance with the day-ahead market dynamics.

According to (3), ${\xi }_{cal}$ can be estimated [35], where $T_{shelf}$ represents the BESS life reported by the manufacturer in its datasheet and the BESS’s end-of-life (EOL) is commonly defined when its capacity reaches 80% of its original capacity [8,36,37].

$${\xi }_{cal}=1-0.8^{\frac{1}{T_{shelf}}}$$

(3)

Through (4), ${\xi }_{cyc}$ can be estimated [35], where $L(DoD=100\%)$ represents the total number of charge/discharge cycles that BESS can perform when considering a DoD of 100%. It is important to note that this information can commonly be found in the datasheet provided by the manufacturer.

$${\xi }_{cyc}=1-0.8^{\frac{1}{L(DoD=100\%)}}$$

(4)

The Rainflow algorithm was used to identify the various charge/discharge cycles with different levels of DoD performed by BESS throughout the day, as better detailed by [2,38]. As the cycles correspond to different levels of DoD, it is necessary to obtain an equivalence, that is, to place them all in the same base. Thus, considering that the loss of the life cycle is a constant [39,40], through (5), the calculation of the number of equivalent cycles is performed. This equation represents the equivalence between the results obtained through the Rainflow algorithm and the number of cycles that would be achieved if considering a DoD of 100%.

$$n{c}_{eq}=L(DoD=100\%)·\frac{n{c}_{DoD}}{L\left(DoD\right)}$$

(5)

where $L\left(DoD\right)$ is a non-linear function that relates the total number of cycles and DoD, its coefficients can normally be obtained from the BESS datasheet [2,39]. As shown by [39], one can address the $L\left(DoD\right)$ as shown by (6).

$$L\left(DoD\right)=a_1+a_2·e^{a_3·DoD}+a_4·e^{a_5·DoD}$$

(6)

It is important to note that sometimes only a few points on the curve are presented. In these cases, where there are few reported points, without major impacts, the coefficients $a_4$ and $a_5$ can be considered null [2].

Thus, through these procedures, it was possible to estimate the battery degradation, as presented in (7) in a very convenient and practical way for the performed analyses.

$$b_{j,d}=b_{j,d-1}·\left[1-\left({\xi }_{cal}+n{c}_{eq}·{\xi }_{cyc}\right)\right]$$

(7)

where $b_{j,d-1}$ is the nominal capacity of the battery the day before.

4. Study Description

To illustrate a potential application of the proposed model, a comprehensive study was pertinently designed to assess the impacts that the same storage capacity resource in the BESS can cause when inserted into different arrangements in a community-based market. The details of this study are presented below.

4.1. Base Case—A Community Market without BESS

As a basis for the study, a community market composed of nine prosumers equipped with different sizes of PV systems was considered. The prosumers’ energy consumption and production data were originally collected from households in Australia between July 2012 and June 2013 [41]. To make up a more diversified market, these nine prosumers were distributed in three communities according to their generation capacity. As shown in

Table 2. Nominal generation capacity of the prosumers.

Agent	Community 1	Community 2	Community 3
Prosumer 1	2 kWp	2 kWp	6.2 kWp
Prosumer 2	2.7 kWp	4.2 kWp	8 kWp
Prosumer 3	3 kWp	8 kWp	9.9 kWp

, three prosumers with lower generation capacity were gathered in Community 1, and the other three with greater capacity were gathered in Community 3. The three remaining prosumers, who have a more dispersed generation capacity, were gathered in Community 2.

To model the cost function of the energy assets of these prosumers ($c_j^{Net}$), the quadratic cost formulation proposed by [13] was initially considered. In general terms, the coefficients of this formulation are determined based on the prices practiced by a reference market and on the defined margin of tolerance for trading the energy asset of the prosumer in a given period [13]. By using this information, this quadratic function can produce tangible prices for the market reality and simulation of scale gains. That is, the cost of an energy unit produced by a prosumer with greater generation capacity is cheaper than the cost of an energy unit produced by one with less capacity.

Therefore, assuming that the community market is cleared over 24 h (as in [13]), the quadratic cost functions of the energy assets of prosumers were obtained based on the day-ahead market prices available on the Australian Energy Market Operator (AEMO) website for the same period in which the prosumers’ data were collected. Additionally, a margin of tolerance equal to $\pm 20$% of the respective $p_j$ value obtained from the prosumers’ data was adopted to provide further malleability to the problem. Notwithstanding, it was observed that the cost curves generated by this formulation for the prosumers had slight curvatures. Reinforcing this statement, a comparison between the quadratic and linear curves is shown in Figure 3. Therefore, these curves were conveniently linearized. Due to this consideration, the proposed model for representing the community market in question assumed a completely linear nature without causing losses to the analysis. A more detailed discussion on the topic is presented in [42].

Thus, the cost function of each prosumer was defined as (8). For the context of the present study, a cost of $c_{com}=1$ m.u./MWh was defined.

$$f_j=c_j^{Net}·p_j+c_{com}·\left|q_j\right|$$

(8)

For the sake of convenience, the costs incurred on import and export exchanges of prosumers were globally considered in the model adopted for the community’s goals. Therefore, assuming that all communities have the common objective of prioritizing their autonomy, this model is given by (9), where $c_{spr}=10$ m.u./MWh represents a spread between the import ($c_{imp}$) and export ($c_{exp}$) costs penalties for energy import.

$$g=c_{exp}·q_{exp}-\left(c_{imp}+c_{spr}\right)·q_{imp}$$

(9)

In addition to these three communities, the existence of an external player capable of absorbing any production surplus or supplying any lack of energy in this community market was considered. Given the small size of the community market in question, it was assumed that communities trade energy as a price-taker with the external player. In this way, the prices practiced by this external player were assumed to be equivalent to the prices recorded by AEMO.

It is important to highlight that the pricing adopted for internal exchanges ($c_{com}$) and the penalties for importing and exporting energy can influence agents as if the costs of internal exchanges are advantageous, agents will have more incentives to prioritize negotiations within the community. The same happens with external exchanges, if agents were heavily penalized they will prioritize their autonomy. Thus, it is possible to observe the dependence of the results on the adopted pricing schemes. However, an analysis of energy exchanges in the system is also important to verify the coherence of pricing.

4.2. Study Cases—Insertion of BESS in Different Arrangements of the Market

To analyze the impacts that a specific storage capacity can have on the community market described above, the three positioning possibilities of the BESS presented in Figure 1 are considered. To establish the same basis of comparison, the data presented in

Table 3. Main technical parameters of the BESS.

Parameter	Value	Reference
$\underline{\varphi }$/$\overline{\varphi }$	0.2/0.8	[33]
${\lambda }_c$/${\lambda }_d$	0.5/0.9375	[43]
${\lambda }_{sd}$	8.6086 × ${10}^{-6}$	[43]
${\eta }_c$/${\eta }_d$	0.96/0.96	[43]
$a_2$/$a_3$	38,200/−0.02686	[39,43] *

* Calculated based on [39] with data from [43].

were considered as parameters for the characterization of the BESS in all cases.

Therefore, in Case 1, it was considered that all nine prosumers acquired a particular BESS, thus becoming prosumages (Figure 1a). The storage capacity of each BESS was determined according to the average consumption of the agent. Thus, the results presented in

Table 4. Nominal storage capacity adopted for agents.

Case	Agent	Community
		1	2	3	Extra
1	Prosumage 1	1.65 kWh	1.65 kWh	3.3 kWh	-
1	Prosumage 2	1.65 kWh	1.65 kWh	3.3 kWh	-
1	Prosumage 3	3.3 kWh	3.3 kWh	3.3 kWh	-
2	Intracommunity	6.6 kWh	6.6 kWh	9.9 kWh	-
3	Intercommunity	-	-	-	23.1 kWh

were obtained. Concerning the operation of these BESSs, no contextual constraints (see Section 2) have been established. So, each prosumage was considered free to share or trade its BESS energy asset in the market, in addition to the energy asset resulting from the net balance between its consumption and production.

In Case 2, it was considered that all communities agents own the battery that belongs to that community, i.e., each community would acquire an intracommunity BESS (Figure 1b) instead of each prosumer acquiring a particular BESS. As seen in Table 4, the storage capacity of each intracommunity BESS was defined by the sum of the capacities determined in Case 1 for each of the agents of their respective communities. Regarding their operation, it was defined that each intracommunity BESS would equally meet all the respective agents of its community, and the cost incurred on their energy sharing would be the same applied to any other community agent. Furthermore, it was established that each intracommunity BESS could interact with the external market, similar to any other agent. Nonetheless, it was defined that they could not consume or supply energy beyond the amount limited by their respective batteries, i.e., they could not arbitrarily play in the market.

In Case 3, it can be considered that the three communities that make up the market jointly acquired an intercommunity BESS or that the battery belongs to an external aggregator (Figure 1c). As shown in Table 4, the intercommunity BESS storage capacity was defined by the sum of the storage capacities determined in Case 1 for all agents. Regarding its operation, it was established that the cost incurred on its energy transactions with the other communities would be the same as that applied to import and export exchanges between the other communities.

In these three cases, the cost of BESS energy transactions ($c_j^{Battery}$) in each study case was obtained following the same procedures used to determine the cost function of the prosumer energy asset in the Base Case. That is, a quadratic cost function was initially obtained based on the prices recorded by the AEMO and on its respective storage capacity; then, this quadratic cost function was linearized. In that way, the cost function of each prosumage in Case 1 was defined as given in (10). In Case 2, the product referring to the energy asset $p_j$ in (10) was disregarded in the cost function of each intracommunity BESS. Finally, in Case 3, both the products referring to energy assets $p_j$ and shared energy $q_j$ were disregarded in the cost function of the intercommunity BESS.

$$f_j=c_j^{Net}·p_j+c_j^{Battery}·s_j+c_{com}·\left|q_j\right|$$

(10)

4.3. Simulation Details

As mentioned above, a day-ahead market framework was considered for applying the proposed model (Section 3) to represent the community markets designed in each aforementioned case. In this way, the simulations were solved for a total period of 365 days, with each interval of 24 h (full day) approached as a single linear optimization problem.

Nonetheless, some additional considerations were made to make the results more reliable. The first one was to consider that at the end of a simulated day, the sum of energy transactions referring to $p_j$ of a prosumer or prosumage would be equal to the daily net balance between consumption and production collected of this agent. Therefore, there is no loss of validity.

The other was to define the initial and final values of SoC of the respective batteries that make up the BESS present on the market as obligatorily equal to 50%. Thus, battery depletion over a simulated day was avoided.

4.4. Key Performance Indicators—Fairness and Economic Approaches

To carry out an adequate assessment of the results obtained in the performed simulations, some figures of merit commonly employed in energy market studies were rated. From an economic perspective, one of the main parameters used to compare the performance of different community-based markets is the SW [13,14]. The maximization of the SW of the market is aimed at being beneficial to the participating agents. Therefore, the SW of each designed case study was calculated as presented by (11), where $\Delta =1,\dots ,8760$ represents all simulated periods.

$$\mathrm{SW}=\sum _{t\in \Delta }\left(\sum _{j\in \Psi }{c}_{j,t}^{Net}·p_{j,t}+\sum _{j\in {\rm Y}}{c}_{j,t}^{Battery}·s_{j,t}\right)$$

(11)

From a social perspective, two complementary fairness indicators were used: quality of service (QoS) and quality of experience (QoE) [13,15]. As given by (12), QoS is directly influenced by the volumes of energy shared within the community [13,15,44]. Thus, low levels of QoS indicate that the community agents produce different impacts on their strategic behavior, which is not interesting from the point of view of the collective.

$$\mathrm{QoS}=\frac{{\sum }_{j=1}^n{\left|q_j\right|}^2}{n\times {\sum }_{j=1}^n{q}_j^2}$$

(12)

In turn, QoE was calculated as presented by (13), where $\sigma \left({\zeta }_j\right)$ is the standard deviation of the auxiliary variable ${\zeta }_j$ [13,15,45]. As given by (14), the latter is determined by dividing the sum of costs or revenues obtained through trades carried out both with the community and the exterior market by the net energy consumed or produced by an agent [13,15]. Therefore, the closer QoE is to 1 (maximum value), the smaller the community agents’ price variation, and the greater the agents’ satisfaction in being part of a community.

$$\mathrm{QoE}=1-\frac{\sigma \left({\zeta }_j\right)}{c_{spr}}$$

(13)

$${\zeta }_j=\frac{c_{exp}·{\beta }_j-\left(c_{imp}+c_{spr}\right)·{\alpha }_j-c_{com}·q_j}{p_j}$$

(14)

5. Simulations

Note that the input data for this study are available in Mendeley Data. Input data on the generation and consumption of various prosumers for a period of 24 h and 365 days are included. As well as the specific data used in this study, we used data referring to battery storage systems (https://data.mendeley.com/datasets/7jhvbsxfdc/1, accessed on 1 September 2022).

5.1. Computational Performance

The simulations were performed in MATLAB [46] software on an Intel(R) Core(TM) i5-4210U @ 1.70 GHz CPU with 8 GB of RAM. To solve the optimization problem, a MATLAB’s mixed-integer linear programming solver, INTLINPROG [47], was used.

The use of this solver was necessary because MATLAB’s continuous linear solver [48] does not deal with absolute numbers. The methodology presented in [49] aligned with INTLINPROG is then used to carry out the optimizations. It is worth mentioning again that the formulated optimization model is continuous linear and the use of binary variables was necessary due to a limitation of the available solvers to carry out the optimizations.

We emphasize that the computational time was approximately 5 min in the annual simulation for all cases, with the exception of Case 2, which took approximately 10 min.

5.2. Results

The main results found in the simulations performed for each case study described in the previous section are reported in

Table 5. Main results found in the performed simulations.

Case Analyzed	SW	Shared Energy Inside the Communities (${\mathit{q}}_{\mathit{j}}$)		Energy Exchanges in the Market (${\mathit{q}}_{\mathbf{imp}}$, ${\mathit{q}}_{\mathbf{exp}}$)		QoS		QoE
		Provided	Consumed	Imported	Exported	Mean	St. Dev.	Mean	St. Dev.
Base Case	2649.60 m.u.	1456.10 kWh	−1456.10 kWh	43,754 kWh	43,754 kWh	0.7344	0.0850	0.7529	0.4014
Case 1	2359.10 m.u.	2096.20 kWh	−2096.20 kWh	37,809 kWh	37,809 kWh	0.7361	0.0952	0.3955	0.3656
Case 2	2885 m.u.	44,459 kWh	−44,459 kWh	45284 kWh	45,284 kWh	0.6875	0.0695	0.8955	0.1978
Case 3	2976.30 m.u.	1451.70 kWh	−1451.70 kWh	57,506 kWh	57,506 kWh	0.7392	0.0858	0.7526	0.4006

. Regarding the results presented for the fairness indicators, it is pertinent to clarify that their mean values were calculated considering just the three communities that effectively exist in each case study. Furthermore, to provide greater sensitivity to the discrepancy between these values and those calculated for each community, the respective standard deviations are also presented.

Analyzing the results reported for Case 1, it is noted that the total amount of energy shared within the communities increased by approximately 44% in relation to the respective amount verified in the Base Case. Nevertheless, the fact that the mean QoS calculated in Case 1 is close to the mean QoS calculated for the Base Case reveals that the increase in this energy sharing occurred in a balanced way, without changing the impact of each agent on the strategic behavior of their respective community. However, it is observed that the total amounts referring to the communities’ import and export exchanges were reduced by approximately 14% in relation to the amounts verified in the Base Case. Through this result, it is possible to infer that the prices experienced in this market configuration led agents characterized by prosumages to self-liquidate their two energy assets and, therefore, to become less dependent on the community. This finding is corroborated by the mean QoE, which is almost half the value calculated for the Base Case. Furthermore, this greater autonomy of the agents is reflected in the SW, which suffered a small but significant reduction in relation to the SW verified in the Base Case.

In turn, the results reported in Table 5 for Case 2 demonstrate that the total amount of energy shared within the communities has increased approximately 30 times compared to the respective amount verified in the Base Case. On the other hand, it is observed that the total amounts referring to the communities’ import and export trade increased in a much less expressive way in relation to the amounts verified in the Base Case. It is pertinent to note that as the intracommunity BESS does not consume or produce any energy, this agent works only as an internal energy node. Therefore, this situation reveals that the prices experienced in this market configuration led agents characterized as intracommunity BESS to concentrate largely on the energy negotiations in internal communities. As the communities now have an additional and very active agent, the balancing of communities suffers a small negative impact, which translates into a reduction of approximately 6% of the mean QoS in relation to the value calculated for the Base Case. However, it appears that the presence of an intracommunity BESS makes other community agents less subject to external market price variations, which increases their satisfaction in participating in this market structure. This statement is confirmed by the increase of almost 19% in the mean QoE in relation to the value calculated in the Base Case. Additionally, it is essential to note that the standard deviation verified for the QoE reduces to approximately half the value verified in the Base Case. This situation suggests that the intracommunity BESS acts as a homogenizing agent of the community. This favorable situation is reflected in the increase of almost 10% of the SW in relation to the value verified in the Base Case.

Finally, the results reported in Table 5 for Case 3 demonstrate that the intercommunity BESS presence does not significantly affect the total amount of shared energy within the communities and their respective balances. For this reason, the results calculated for the QoS are close to those verified in the Base Case. Nonetheless, it is observed that the total amounts referring to the communities’ import and export exchanges are approximately 32% higher than the amounts verified in the Base Case, while the results calculated for the QoE are very similar. This situation confirms that the intercommunity BESS does not impact the energy dynamics of the communities, which see it only as a “second external player”. Moreover, as the intercommunity BESS does not produce or consume any energy by itself, this situation reveals that the prices experienced in this market configuration led it to play as a midpoint between the communities and the external player. This interesting situation is reflected in the 12.33% increase in SW in relation to the value verified in the Base Case.

5.3. Energy Balance

To analyze in a more concrete way the changes that took place in the studied energy market and to validate the proposed model, the energy balance for day 6, hour 14 is presented in

Table 6. Energy balance—Case 1.

Market Agents	p	q	$\mathit{\alpha }$	$\mathit{\beta }$	s
Community 1
Prosumage 1	−0.4872	0.8491	0	0	−0.3619
Prosumage 2	1.9780	−0.8491	0.6534	0	−0.4755
Prosumage 3	1.6740	0	0.7298	0	−0.9442
Community 2
Prosumage 1	−0.4872	0.4045	0	0.4872	−0.4045
Prosumage 2	0.6852	−0.7902	0	0	0.1050
Prosumage 3	−1.9350	0.3857	0	1.9350	−0.3857
Community 3
Prosumage 1	−0.0296	0	0	0.0444	−0.0148
Prosumage 2	−1.9350	0	0	1.9350	0
Prosumage 3	−1.4388	0	0	1.4388	0
External Player	4.4572	0	4.4572	0	0

. It is noteworthy that the results presented in this subsection refer to Case 1, as it is the scenario with the greatest insertion of BESSs. Through Figure 4 it is possible to observe the SoC of the BESSs throughout the same day.

The results presented from the energy balance can be interpreted as follows:

• Community 1: (i) Prosumage 1 exports 0.4872 kWh of its solar generation and 0.3619 kWh from its BESS to its community; (ii) Prosumage 2 imports the amount from Prosumage 1 and 0.4755 kWh from its own BESS, in addition to 0.6534 kWh from other communities; (iii) Prosumage 3 imports 0.9442 kWh from its BESS and 0.7298 kWh from other communities;
• Community 2: (i) Prosumage 1 exports 0.4872 kWh of its solar generation to other communities/external players and 0.4045 kWh from its BESS to Prosumage 2; (ii) Prosumage 2 imports 0.7902 kWh from its own community to supply the domestic load and charge its BESS; (iii) Prosumage 3 exports 1.9350 kWh from its solar generation to other communities/external player and 0.3857 kWh from its BESS to Prosumage 2;
• Community 3: (i) Prosumage 1 exports 0.0296 kWh of its solar generation and 0.0148 kWh of its BESS to other communities/external players; (ii) Prosumage 2 exports 1.9350 kWh of its solar generation to other communities/external player; (iii) Prosumage 3 exports 1.4388 kWh of its solar generation to other communities/external player;
• External player imports 4.4572 kWh from Communities 2 and 3.

From the presented results, it is possible to observe that Community 2 is able to supply its own needs in the considered time, and export the remainder of the energy, where the BESS plays a fundamental role in the community’s self-sufficiency. Community 3, which is made up of the largest prosumages, exports all of its production surplus, without the need for internal sharing. On the other hand, Community 1, formed by smaller prosumages, in addition to internal exchanges, needs to import energy to meet the needs of all its agents. In this context, it is possible to verify that an optimized alignment of the configurations and objectives of the communities’ members can positively assist the market and the system.

5.4. Discussions

Actions taken to modernize energy systems have increasingly moved towards consumer empowerment and flexibility in grid operation. In this context, community-based markets composed of agents with BESSs are increasingly emerging as a palpable and relevant energy market configuration to consolidate the future of the electricity sector. Aware of this, this work presented a broad discussion on the possibilities of insertion and operational issues brought by the BESS to the energy dynamics of a community market. Based on this discussion, a general formulation was developed to represent this market.

Considering the different parts that make up the energy market and the goal of seeking the best balance between them, this study was able to present a broader panorama of the insertion of BESS in the structure of the community market. As the objective is to maximize the social welfare of communities, it is possible to analyze that, despite the increase in market costs, there is also an increase in end-user satisfaction. It is possible to conclude that some of the benefits that BESS brings to communities outweigh the increase in market costs, as they lead to greater overall satisfaction.

Finally, given the growing notoriety that BESSs have been gaining in the energy system and their various benefits, it is interesting to discuss the need for an increasingly stronger inclusion of this technology in system planning analyses. Regulations around the world should consider issues such as those discussed in the article to reorganize guidelines and encourage a guided use of storage systems in local energy markets.

6. Conclusions

A linear optimization model was developed aiming at maximizing the revenues from transactions carried out in a community-based energy market, considering different provisions for the insertion of BESS. The model stands out for its adaptability to different contingency situations, the linearity of its constraints, and the scalability of its application. Furthermore, to the best of our knowledge, this is the first general formulation proposed in the literature for community-based markets with BESS.

To illustrate the application of this general formulation and provide subsidies for relevant discussions, a comprehensive study was performed to assess the impacts that the specific storage capacity resource in BESS can cause when inserted in different arrangements in a community-based market. The results obtained showed that the BESS, when inserted as part of a prosumage, allows this agent to become more autonomous, reducing its dependence and satisfaction in participating in a community and causing a reduction in the SW of the market. On the other hand, when the BESS is inserted as an independent agent belonging to a community, it attenuates the price variation perceived by other agents, improving their satisfaction with the community and increasing the SW of the market. In turn, the BESS, when inserted as an independent agent who does not belong to any community but trades with all communities, plays as a midpoint of the system, not influencing agents’ experience concerning the market, but promoting a significant increase in the SW of the market.

Given the technological incipience and the great need for studies related to community-based energy markets with BESSs, the contributions brought by this paper can serve as a basis for the development of several new works. Business models that mitigate the negative impacts or economically exploit the improvements pointed out here by inserting BESS in different arrangements of the market can be assessed based on the proposed general formulation. In addition, the problems related to battery degradation that make up BESS can be addressed in other ways, for example, by incorporating them into the BESS usage pricing model; thus evaluating the impact of a more detailed model on the solution and the increase of computational time.

Other possibilities for future research can be found in the insertion of siting and sizing models of batteries for communities. Additionally, in the insertion of asset management issues, the objective is to analyze a faihrer battery insertion for all the agents involved. In addition, another important point is to investigate ways to implement the proposed optimization model in energy management systems.