Day Ahead Operation Cost Optimization for Energy Communities

Abstract

Energy communities constitute the main collective form for energy consumers to participate in the current energy transition. The purpose of this research paper is to present a tool that assists energy communities to achieve fair and sustainable daily operation. In this context, the proposed algorithm (i) assesses the day-ahead operation cost (or profit) of energy communities, taking into consideration photovoltaic (PV) production, battery energy storage system (BESS), and flexible loads, as well as the potential profit from selling energy to the power system, under the net billing scheme, and (ii) compares the derived cost for each member with the cost for non-cooperative operation, as single prosumers. Taking the aforementioned costs or profits into consideration, the developed algorithm then proposes three cost-sharing options for the members, peer-to-peer (P2P), so that their participation in the community is more beneficial than individual operation. The algorithm is tested on a hypothetical energy community in Greece, highlighting the importance of the cooperation amongst the members of the community for their mutual benefit; for the simulated case of different PV shares, the cooperation can result in a 24.5% cost decrease, while having a BESS can reduce the cost by 25.0%.

1. Introduction

Small-scale distribution systems, such as microgrids (MGs), energy communities, and smart buildings constitute a relatively new and promising concept for the decarbonization of the power sector [1,2]. In most cases, they are equipped with renewable energy sources (RESs), primarily photovoltaics (PVs), and in some cases with storage systems [3]. Furthermore, they utilize their flexible loads, e.g., electric vehicles (EVs) and heat pumps (HPs), the optimal scheduling of which can reduce the cost and emissions of the power system, significantly.

The backbone of the optimal scheduling of storage systems and flexible loads comprises smart meters, sensors, and IoT networks, monitoring the power system of the entire smart grid, which can be an MG, a building, an energy community, or even a smart city [4]. In this way, the decisions of the consumers as well as the decisions related to RES production and storage can be coordinated in order to achieve the desired objective, which is usually cost minimization.

While such solutions have proven to be effective in simulations or in a laboratory environment, their wider adoption is currently limited. The main identified obstacles that may hinder their market uptake are (i) the respective regulatory framework, which is either under development or different per country and (ii) consumer participation [5]. Therefore, policy makers have to consider various issues, such as metering and billing strategies and consumer incentivization, but also technical matters, including potential curtailments due to high RES penetration, power quality, and stability indicators, etc.

To this end, the main tool for scheduling the energy management of small power systems in a cost-efficient, environmentally sustainable, and technically secure manner is day-ahead optimization [6]. Day-ahead optimization is capable of taking into consideration the available distributed energy resource (DER) production, storage systems, flexible loads, and market prices, allowing the aggregator/operator to buy and sell energy to the main power grid, taking into account uncertainties.

In the literature, day-ahead optimization is mostly approached considering economic and technical aspects. For example, in [7], an energy community comprising several grid-connected prosumers on a daily time horizon is studied, aiming to minimize the total energy cost incurred by the community. The optimization methodology is based on fixed integer linear programming (MILP) and takes into consideration assets, such as PVs, battery energy storage systems (BESSs), EVs, and HPs. According to the results, the tariff structures which are based on dynamic pricing and reflect the day-ahead market best incentivize renewable energy community (REC) members to share energy between each other. In [8], the day-ahead scheduling of a local energy community (LEC) is presented using the alternating direction method of multipliers (ADMM). The objective is to minimize the total cost of power transactions with the utility grid during the upcoming day. The authors study two scenarios, where the prosumers are or are not equipped with batteries, respectively, taking into consideration the billing scheme of the LEC as well as the distribution losses. In [9], the role of energy communities in the power system balancing is assessed. The authors provide a tool for smart grid power system optimization focusing on energy-sharing strategies, such as peer-to-peer (P2P) and vehicle-to-cluster (V2C), which is similar to vehicle-to-grid (V2G). The use case entails buildings (as loads), PVs, EVs, and BESSs and presents the way that the aforementioned assets can contribute to power system stability and particularly to frequency regulation. In [10], the day-ahead optimization of isolated communities is studied, considering uncertainties. In this context, a novel stochastic and robust approach is developed, including P2P. The simulated community involves individual assets, such as controllable appliances and small rooftop PVs, and collective assets, comprising wind generators (WGs) and BESSs. The authors assess the impact of the number of prosumers as well as the value of the storage. In fact, according to the simulation results, BESSs can help towards the reduction of operating costs by 19% and enable a more efficient use of wind energy. In [11], a flexible load scheduling algorithm for RECs is presented. The approach is heuristic and follows an REC management program, in which consumers’ day-ahead flexible loads are shifted according to power availability, prices, and personal preferences, to balance the grid. The simulations are performed using the real consumption and flexibility data of an actual REC of fifty dwellings. The results show an average yearly cost reduction of 6.5%, with a peak reduction of 12.2% during the summer, as well as an average increase of individual self-consumption of 32.6%. Also, following the trend of sector coupling, in [12] a day-ahead scheduling tool for community energy management that aims to minimize the energy cost is developed, taking into consideration electricity and gas. The methodology is based on stochastic optimization, incorporating uncertain market prices and, in contrast to most community-related studies, in this case the system includes a combination of batteries, heaters, gas turbines, and thermal energy storage.

On a lower level, in [13], a residential energy management system is presented. The proposed system is stochastic and minimizes the cost and inconvenience of the residents. For this purpose, the authors include a thermal model of the building in the methodology and study the resulting thermal comfort. Furthermore, the battery degradation is incorporated in the cost minimization as well. The residents are considered to have PVs, EVs, BESSs, and HPs and, according to the case study, the proposed method can provide up to 51% and 22% cost savings compared to inflexible non-optimal scheduling strategies and deterministic optimization-based methods, respectively. In a similar manner, in [14], a day-ahead energy market participation strategy for smart home aggregators is proposed. Robust optimization is used to include uncertainties in PV production, price, and demand and the non-linear cycling aging of the BESS is included in the optimization model too. The objective is to minimize the cost of energy and the cost of battery cycling. According to the results, robust optimization may lead to cost reduction up to 5.7% and standard deviation reduction up to 36.4%. In [15], the authors develop an energy management system for large-scale building prosumers with low computational requirements. The authors consider RESs, EVs, and thermal and electric loads, and examine the operation both islanded and connected to the main power grid, reaching a cost reduction of 27%.

Also, in [16], a bidding strategy for MGs participating in day-ahead markets is proposed. The strategy is based on stochastic and robust optimization, and involves formulating an MILP solution, the objective of which is to maximize the MGs’ expected benefit, or to equivalently minimize its expected net cost. The authors test the proposed methodology on a simulated MG comprising a WG, PVs, a BESS, a fuel cell, a micro-turbine, a diesel generator and a responsive load. In [17], a robust optimization framework for MG day-ahead optimization is proposed, including WGs, PVs, natural gas micro-turbines, and BESSs. The uncertainties, namely the wind and solar generation, demand, and prices, are modeled using bounded intervals within the adaptive robust optimization method. The purpose is the cost minimization for the MG operator, taking into account worst case scenarios, and is tested on a simulated 69-node distribution system. In [18], a day-ahead optimization of urban energy systems is presented, focusing on the interactions between urban electrical and gas systems. The authors aim to minimize the day-ahead dispatch cost, which, in this case, consists of day-ahead energy cost, reserve capacity cost, and balancing cost. The methodology is tested on a coupled 13-node urban electricity network and 9-node urban gas network, as well as on a coupled 26-node urban electricity network and 18-node urban gas network, including PVs, WGs, generators, combined heat and power (CHP) systems and gas furnaces. Focusing on the development of the solver, in [19], a day-ahead optimization method for gas–electric integrated systems is presented, based on second-order cone programming. More specifically, the goal is to minimize the day-ahead operation cost, and a second-order cone programming method is utilized to solve the optimization problem, which is a mixed integer non-convex and nonlinear programming problem. The authors study the relaxation gaps of the power and gas systems. According to the results, the day-ahead operation cost of the integrated energy system is lower than it would be if the power and gas systems operated independently.

The purpose of this paper is to propose a day-ahead optimization algorithm for the cost minimization of future energy communities, where all the members will have smart meters and participate in the market under the net billing scheme, supported by aggregators, cooperating with each other in order to maximize their profit. Therefore, this research expands the purpose of [7,8,9,10,11,12,13,14,15,16,17,18,19]. The proposed algorithm is applicable on communities with PV systems and BESS, as well as flexible loads, as in Figure 1, and aims to share the benefit from exploiting the PV production and the BESS in a fair manner for all members, proposing different sharing mechanisms. To showcase its effectiveness, the algorithm is applied on a hypothetical energy community in Greece, investigating a variety of scenarios.

2. Methodology

The proposed algorithm comprises three main stages, as shown in the flow chart in Figure 2. The first stage is profit maximization on community level, sharing the PV production and BESS. This provides the proposed dispatch, including BESS scheduling, energy bought from and sold to the distribution system operator (DSO), and each member’s flexible load scheduling. The second stage is the hypothetical individual profit maximization, where each member can only utilize its own share of PV and BESS, without cooperating with the other members of the community. This stage is critical in order to assess the community’s benefit from the cooperative operation proposed in the first stage. The third stage is the profit/cost-sharing between the members in order to ensure that the coordinated dispatch (proposed in the first stage, and overall more beneficial than the one proposed in the second stage, due to the members’ cooperation) is fair for all members.

In all formulas, the energy-related variables are in kWh, the power is in kW, and the economic values are in Euros (€). The methodology is developed in Pyomo (https://www.pyomo.org/, accessed on 22 October 2024), which is Python’s environment for optimization.

2.1. Profit Maximization on Community Level

In the first step, to perform the day-ahead optimization for the entire community, it is assumed that the members cooperate with each other, sharing the PV system and the community’s BESS. Regarding the demand side, each member has their own regular load curve and flexible load, the total demand of which needs to be served within the day. The decision variables are the power charged to or discharged from the BESS at each time step, i.e., $C_t$ and $D_t$, respectively, as well as each member’s flexible load served per time step, $L_{m,t}^{flex}$. The community can either buy or sell energy to the power system, and the purpose of the day-ahead optimization is to maximize the collective profit, as presented in the objective function (1), according to the net billing scheme. The first term of (1) is the energy sold to the power system operator at time-step t, where $P_t^{sell}$ is the average power sold, ${\Delta }_t$ is the duration of the time-step, $u_t^{sell}$ is the binary variable which indicates that the community sells energy to the power system operator at time-step t, and $p_t$ is the price at which the energy is sold. According to the net billing policies, this price is defined by the electricity market. On the other hand, the second term of (1) refers to the energy bought from the power system at time-step t, where $P_t^{buy}$ is the average power bought, ${\Delta }_t$ is the duration of the time-step, $u_t^{buy}$ is the binary variable which indicates that the community buys energy from the power system at time-step t, and $c_t$ is the respective cost. According to the net billing policies, this cost is not fixed and shall be related to the electricity market prices. However, at this point it has not been defined in most countries (including Greece) and will, most likely, become apparent over the course of 2025.

$$maxF=\sum _{t=1}^{24}(p_t·P_t^{sell}·{\Delta }_t·u_t^{sell}-c_t·P_t^{buy}·{\Delta }_t·u_t^{buy})$$

(1)

The objective function is subjected to constraints (2)–(11). Specifically, constraints (2)–(4) refer to the members’ loads. According to (2), each member’s total load per time-step, $L_{m,t}$, comprises the regular, $L_{m,t}^{reg}$, and flexible load served, $L_{m,t}^{flex}$. Moreover, according to (3), the entire demand for each member’s flexible load, $E_m^{flex}$, needs to be served within the day, and (4) ensures that each member’s total load per time-step is limited by its maximum $L_m^{max}$.

$$L_{m,t}=L_{m,t}^{reg}+L_{m,t}^{flex} \forall m,t$$

(2)

$$\sum _{t=1}^{24}{L}_{m,t}^{flex}·{\Delta }_t=E_m^{flex} \forall m$$

(3)

$$L_{m,t}\le L_m^{max} \forall m,t$$

(4)

Constraint (5) is the community’s power balance, where $P_t^{PV}$ is the PV production, and $u_t^{ch}$ and $u_t^{dis}$ are the binary variables indicating if the BESS is being charged or discharged, respectively. Constraints (6)–(10) denote the BESS’s operation, where $E_t$ is the stored energy, ${\eta }_{ch}$ is the efficiency for charging and ${\eta }_{dis}$ is the efficiency for discharging. The BESS’s energy balance is presented in (6); the stored energy is limited by its maximum and minimum values, $E^{max}$ and $E^{min}$, respectively, according to (7), and the power charged to or discharged from the BESS, is limited by $C^{max}$, $C^{min}$, $D^{max}$, and $D^{min}$ according to (8) and (9), respectively. Also (10), ensures that the BESS is not charged and discharged at the same time. Finally, (11) ensures that energy cannot be sold and bought during the same time-step. Regarding constraint (10), if, for some reason, there is a time-step where the BESS should be neither charged or discharged, one of two binary variables will be set equal to one, and the respective value of power with which it is multiplied will be set equal to zero. The same applies for the binary variables of constraint (11).

$$\sum _m{L}_{m,t}+C_t·u_t^{ch}+P_t^{sell}·u_t^{sell}=P_t^{PV}+D_t·u_t^{dis}+P_t^{buy}·u_t^{buy} \forall t$$

(5)

$$E_t=E_{t-1}+C_t·{\Delta }_t·u_t^{ch}·{\eta }_{ch}-{\displaystyle \frac{D_t·{\Delta }_t·u_t^{dis}}{{\eta }_{dis}}} \forall t$$

(6)

$$E^{min}\le E_t\le E^{max} \forall t$$

(7)

$$C^{min}\le C_t\le C^{max} \forall t$$

(8)

$$D^{min}\le D_t\le D^{max} \forall t$$

(9)

$$u_t^{ch}+u_t^{dis}=1 \forall t$$

(10)

$$u_t^{sell}+u_t^{buy}=1 \forall t$$

(11)

2.2. Profit Maximization per Member

Having assessed the community’s maximum profit, assuming cooperative behavior, the next step is the day-ahead optimization assuming non-cooperative behavior amongst the members. This means that each member, $m$, wants to maximize their own profit, utilizing their own share of PV production, $P_{m,t}^{PV}$, and their own share of BESS, defined by $E_m^{max}$. In this case, the objective function of each member is (12), where $P_{m,t}^{sell}$ is the power sold by the $m$-th member, $P_{m,t}^{buy}$ is the power bought by the $m$-th member, and $u_{m,t}^{sell}$ and $u_{m,t}^{buy}$ are the respective binary variables.

$$max{G}_m=\sum _{t=1}^{24}(p_t·P_{m,t}^{sell}·{\Delta }_t·u_{m,t}^{sell}-c_t·P_{m,t}^{buy}·{\Delta }_t·u_{m,t}^{buy}) \forall m$$

(12)

Constraints (2)–(4) apply in this sub-problem for the $m$-th member as well. On the other hand, (5)–(11) need to be modified by adding the index referring to the $m$-th member, according to (13)–(19). This means that this sub-problem (i) focuses on the power balance of the $m$-th member only, instead of the community, according to (13), (ii) the $m$-th member can use only its own share of storage, limited by $E_m^{max}$, and (iii) makes its own decisions about charging, discharging, buying, and selling energy, according to (18) and (19).

$$L_{m,t}+C_{m,t}·u_{m,t}^{ch}+P_{m,t}^{sell}·u_{m,t}^{sell}=P_{m,t}^{PV}+D_{m,t}·u_{m,t}^{dis}+P_{m,t}^{buy}·u_{m,t}^{buy} \forall t$$

(13)

$$E_{m,t}=E_{m,t-1}+C_{m,t}·{\Delta }_t·u_{m,t}^{ch}·{\eta }_{ch}-{\displaystyle \frac{D_{m,t}·{\Delta }_t·u_{m,t}^{dis}}{{\eta }_{dis}}} \forall t$$

(14)

$$E_m^{min}\le E_{m,t}\le E_m^{max} \forall t$$

(15)

$$C_m^{min}\le C_{m,t}\le C_m^{max} \forall t$$

(16)

$$D_m^{min}\le D_{m,t}\le D_m^{max} \forall t$$

(17)

$$u_{m,t}^{ch}+u_{m,t}^{dis}=1 \forall t$$

(18)

$$u_{m,t}^{sell}+u_{m,t}^{buy}=1 \forall t$$

(19)

2.3. P2P Trading

Since energy communities are focused on self-consumption rather than selling energy, it is most likely that the value of the objective function (1), $F$, will be negative, therefore defining the optimal cost, $Y$, as in (20). This cost is expected to be lower (more beneficial) than $Z$, which is the sum of costs, $Z_m$, derived from (12), defined in (21), (22):

$$Y=-F$$

(20)

$$Z_m=-G_m \forall m$$

(21)

$$Z=-\sum _m{Z}_m$$

(22)

However, if the aforementioned cost, $Y$, is shared according to each member’s consumption, as in (23), some members will have a higher cost compared to their non-cooperative operation, $Z_m$ while others will have a lower cost. This happens because in the cooperative model the members are allowed to use the PV and BESS regardless of their share.

$$Y_m=Y·{\displaystyle \frac{\sum _t{L}_{m,t}}{\sum _m\sum _t{L}_{m,t}}} \forall m$$

(23)

To address this issue, the community needs to make an arrangement between the members, also known as peer-to-peer (P2P) trading. First, it is important to define the amount to be shared. The members that got a bill increase, $I_{m^{\prime }}$, according to (24), due to the cooperation, would ideally like to share amongst themselves the total cost reduction achieved by the rest of the members (for which $Z_m$ is higher than $Y_m$), and are indexed with $m^{\prime }$. On the other hand, the members that managed to reduce their cost (where $R_{m^{″}}$ is the reduction, according to (25)) due to the cooperative operation would, ideally, like to compensate the rest of the members only with their total bill increase, and are indexed with $m^{″}$. Since there is no fixed way to share the community’s benefit due to the cooperative operation mode, $S$, defined in (26), this paper proposes three options.

$$I_{m^{\prime }}=Y_{m^{\prime }}-Z_{m^{\prime }} if Y_m>Z_m$$

(24)

$$R_{m^{″}}=Z_{m^{″}}-Y_{m^{″}} if Y_m<Z_m$$

(25)

$$S=\sum _m{Z}_m-\sum _m{Y}_m=\sum _{m^{″}}{R}_{m^{″}}-\sum _{m^{\prime }}{I}_{m^{\prime }}$$

(26)

The first option, which is the simplest one, but not necessarily the fairest, is to divide the benefit, $S$, by the number of the members, $M$, and subtract it from the individual-operation cost, $Z_m$, resulting in the final cost, $Y_m^{\prime }$, according to (27). The advantage of this option is its simplicity, meaning it can be easily understood and agreed upon by community members.

$$Y_m^{\prime }=Z_m-{\displaystyle \frac{S}{M}} \forall m$$

(27)

Another option, defined in (28), would be to share the benefit, $S$, amongst the members, according to the participation in the community’s internal market, i.e., according to the sum of $I_{m^{\prime }}$ and $R_{m^{″}}$. In this case, only the members that participate in the transactions get a discounted cost, $Y_m^{″}$. The rest of the members pay the initial, individual-operation cost, $Z_m$. The advantage of this option is that it encourages participation in P2P, without affecting the members that choose to not participate.

$$Y_m^{″}=\left\{\begin{array}{c}{Z}_m-I_m·{\displaystyle \frac{S}{\sum _m|{{\rm Z}}_m-Y_m|}} , if Y_m\ge Z_m \\ Z_m-R_m·{\displaystyle \frac{S}{\sum _m|{{\rm Z}}_m-Y_m|}} , if Y_m<Z_m\end{array}\right.$$

(28)

A third option, inspired by [20], would be to share part, $\pi$, (usually set equal to 50%) of the community’s benefit due to the cooperative operation mode, $S$, and also compensate the members that got an increase, according to (29), leading to the corrected cost, $Y_m^{‴}$. On the other hand, according to (29), the members that got a reduction will have to pay the respective amount. The formulas of (29) are proven in (30a) and (30b). It should be noted that in the rare case that no member’s cost is increased, then (29) does not apply. Furthermore, it would not apply for any member that has neither cost increase or decrease.

$$Y_m^{‴}=\left\{\begin{array}{c}{Y}_m-I_m-\pi ·S·{\displaystyle \frac{I_m}{\sum _{m^{\prime }}{I}_{m^{\prime }}}} , if Y_m>Z_m\\ Y_m+(\pi ·S+{\displaystyle \sum _{m^{\prime }}}{I}_{m^{\prime }})·{\displaystyle \frac{R_m}{\sum _{m^{″}}{R}_{m^{″}}}} if Y_m<Z_m\end{array}\right.$$

(29)

$${{\rm Z}}_m-\pi ·S·{\displaystyle \frac{I_m}{\sum _{m^{\prime }}{I}_{m^{\prime }}}}{=Y}_m-I_m-\pi ·S·{\displaystyle \frac{I_m}{\sum _{m^{\prime }}{I}_{m^{\prime }}}} , if Y_m>Z_m$$

(30a)

$$\begin{gathered} {{\rm Z}}_m-\left(1-\pi \right)·S·{\displaystyle \frac{R_m}{\sum _{m^{″}}{R}_{m^{″}}}}=Y_m+R_m-\left(1-\pi \right)·S·{\displaystyle \frac{R_m}{\sum _{m^{″}}{R}_{m^{″}}}} \\ =Y_m+R_m·{\displaystyle \frac{\sum _{m^{″}}{R}_{m^{″}}}{\sum _{m^{″}}{R}_{m^{″}}}}-\left(1-\pi \right)·S·{\displaystyle \frac{R_m}{\sum _{m^{″}}{R}_{m^{″}}}} \\ =Y_m+{\displaystyle \frac{R_m}{\sum _{m^{″}}{R}_{m^{″}}}}·\left(\sum _{m^{″}}{R}_{m^{″}}-S+\pi ·S\right) \\ =Y_m+(\pi ·S+\sum _{m^{\prime }}{I}_{m^{\prime }})·{\displaystyle \frac{R_m}{\sum _{m^{″}}{R}_{m^{″}}}}, if Y_m<Z_m \end{gathered}$$

(30b)

A limitation of the aforementioned options is that they do not take into consideration the cost of the battery usage as a function of the depth of discharge. Also, to be applicable, smart meters and an open-access (open to the community members) cost calculation system relying on the aforementioned methodology should be implemented, in order to ensure the transparency and fairness of the transactions.

3. Test Case

The proposed methodology is tested on a hypothetical energy community. To compose this community, data from various actual Greek energy communities, supported by Electra [21], are taken into account, as presented in Table 1. These energy communities only have PV systems and operate on net metering scheme. However, most of them are in the process of installing smart meters and are considering future PV and BESS installations following the net billing scheme.

Calculating the medians and the average values of Table 1, a reasonable assumption would be that a representative community comprises 60 members and has a PV system of 250 kW, the estimated production of which is derived from [22]. To match the size of this PV, according to the local storage systems manufacturers, [23], a BESS of 100 kW/200 kWh could be installed, with stored energy ranging from 20% up to 95%. However, this is only an estimation based on the market and, ideally, an optimal sizing algorithm should be implemented, which is out of scope for this paper and will be part of future work. The parameters are summarized in

Table 2. Test community.

Parameter	Nominal Value
PV	250 kW
Members	60
BESS	100 kW/200 kWh, 20–95%

, and for the purpose of this study it is assumed that the BESS’s state of charge (SOC) starts and ends at 50%.

Table 1. Energy communities.

Community	PV (kW)	Members	Ratio (kW/Member)	Reference
HYPERION	493.5	113	4.37	[24]
COMMONEN	200	53	3.77	[25]
WEnCoop	1000	73	13.70	[26]
Iliotropio	100	30	3.33	[27]
Solarity	400	90	4.44	[28]
Collective Energy	100	47	2.13	[29]

Table 1. Energy communities.

Community	PV (kW)	Members	Ratio (kW/Member)	Reference
HYPERION	493.5	113	4.37	[24]
COMMONEN	200	53	3.77	[25]
WEnCoop	1000	73	13.70	[26]
Iliotropio	100	30	3.33	[27]
Solarity	400	90	4.44	[28]
Collective Energy	100	47	2.13	[29]

For the simulated day, it is assumed that the cost of energy for the members follows the curve presented in Figure 3 [30], where the price for selling energy is depicted as well, according to [31]. The secondary axis of the figure presents the typical PV production according to [22], and is influenced by external conditions, such as solar radiation, temperature, and panel positioning.

Regarding the load curves (for the regular, non-flexible load), due to lack of actual data, six profiles are composed according to the benchmark load curves of [32], presented in Figure 4, and it is assumed that the members are classified in groups of ten, where each group member follows the respective load curve. In real life conditions, the smart meters of each member are expected to provide less smooth load curves; however, these data are not currently available due to technical (limited smart meter installations) but also regulatory (sensitive data) issues. The flexible loads of each group are assumed to have the daily energy demand presented in

Table 3. Daily demand of each group member.

Member	Regular Load (kWh)	Flexible Load (kWh)	Total Load (kWh)
Group #1	18.05	1.00	19.05
Group #2	27.99	1.50	29.49
Group #3	25.16	2.00	27.16
Group #4	26.57	2.50	29.07
Group #5	23.02	3.00	26.02
Group #6	21.61	3.50	25.11

, considered to be representative according to [33,34].

4. Results

4.1. Results with BESS

This section presents the results of the algorithm for the selected test case. The resulting schedule for the community’s BESS is presented in Figure 5. It is noted that the SOC ranges between 20% and 95%, according to the respective constraints. Also, the BESS is charged during noon, at 12:00–13:00 and at 14:00–15:00, when the PV production is high, and discharges mostly during the first hours of the day and during the evening, when the PV production has stopped. Furthermore, the excess PV production is sold, according to Figure 6, mostly during noon but not at 13:00–14:00 and 14:00–15:00, because during these hours, the price for selling electricity is low. Therefore, during these hours the community charges its BESS and serves the flexible loads. More specifically, the load profiles are presented in Figure 7, showcasing the self-consumption in the time interval 12:00–14:00, and particularly at 13:00. Finally, the BESS covers the load without any contribution from the main power system during the first two hours of the day and then again at 19:00, in combination with the PV production.

For the cost sharing, to begin with, due to lack of data, it is assumed that all members have purchased equal shares of the PV and BESS system, i.e., 4.167 kW of PV and 3.333 kWh of BESS, each. The cost is presented in

Table 4. Energy community cost, with equal PV and BESS shares.

Member	$\mathbf{Cost} {\mathit{Z}}_{\mathit{m}}$ (€)	$\mathbf{Cost} {\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Difference} {\mathit{Z}}_{\mathit{m}}-{\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{\prime }}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{″}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{‴}}$ (€)
Group #1	0.104	1.007	−0.903	0.103	0.101	0.101
Group #2	2.516	1.559	0.957	2.514	2.512	2.513
Group #3	1.360	1.435	−0.076	1.358	1.359	1.359
Group #4	1.986	1.537	0.450	1.985	1.985	1.985
Group #5	1.421	1.375	0.045	1.419	1.420	1.420
Group #6	0.863	1.327	−0.464	0.861	0.861	0.861
Total	82.496	82.395	0.101	82.395	82.395	82.395

, equal to 82.395 €. If the members operated independently and could only use their own share of PV and BESS, then the cost would be 82.496 €. Therefore, the coordinated operation is indeed more beneficial. Although the benefit for one day is small, i.e., 0.101 €, when the entire year is taken into consideration, the annual amount is substantial and, therefore, the application of the proposed algorithm is deemed important. It is noted that when having equal shares of PV and BESS, the final costs for all three sharing mechanisms of Section 2.3 are almost equal to $Z_m$. The effect of the cooperation is mostly reflected in the cost reduction of the members of the first and sixth group. This happens because these members operate during the daytime and their demand is low; therefore, they do not need their PV or their storage as much as the rest, and the community pays them to use their shares as well. The positive impact of this cooperation is also reflected in the cost reduction for the members of the second group, because they not only have a high daily energy consumption but their demand is mostly observed in the late afternoon, around 20:00, meaning that they require energy from the community’s BESS.

The importance of having a cost-sharing mechanism is highlighted when the PV and BESS shares differ amongst the members. To present the algorithm’s effectiveness in such cases, it is assumed that the members following the profile of the first group have no BESS share and the members following the profile of the sixth group have a double BESS share compared to the rest. Of course, the solution in terms of day-ahead dispatch (including BESS scheduling and flexible load management) would be the same as presented in Figure 5, Figure 6 and Figure 7. Nevertheless, the comparison with the standalone schedule (Section 2.2) would be different and, therefore, the trading amongst the members would be different as well. More specifically, according to

Table 5. Energy community cost, different BESS shares (member of the 1st group: 0 kWh, 2nd group: 3.333 kWh, 3rd group: 3.333 kWh, 4th group: 3.333 kWh, 5th group: 3.333 kWh, and 6th group: 6.667 kWh).

Member	$\mathbf{Cost} {\mathit{Z}}_{\mathit{m}}$ (€)	$\mathbf{Cost} {\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Difference} {\mathit{Z}}_{\mathit{m}}-{\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{\prime }}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{″}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{‴}}$ (€)
Group #1	0.571	1.007	−0.436	0.563	0.564	0.564
Group #2	2.516	1.559	0.957	2.508	2.500	2.500
Group #3	1.360	1.435	−0.076	1.352	1.358	1.358
Group #4	1.986	1.537	0.450	1.979	1.979	1.979
Group #5	1.421	1.375	0.045	1.413	1.420	1.420
Group #6	0.433	1.327	−0.894	0.425	0.418	0.418
Total	82.863	82.395	0.468	82.395	82.395	82.395

, the community’s cost would be better than the individual/independent operation by 0.468 €, which is mostly beneficial for the members of the sixth group, who reduce their cost 1.8–3.4%, depending on the cost-sharing mechanism. The members of the first group also have a lower cost than if operating independently, because they cooperate with the rest of the members (and utilize their assets), rather than only interacting with the main power system. Of course, their daily cost is higher than in Table 4, i.e., 0.563–0.564 € instead of 0.101–0.103 €, reflecting the importance of storage systems.

On the other hand, if it is assumed that the PV shares differ amongst the members, with the first group having none while the sixth has twice as much as the rest (and they all have equal BESS shares), the results of the algorithm are modified, as presented in

Table 6. Energy community cost, with different PV shares (member of the 1st group: 0 kW, 2nd group: 4.167 kW, 3rd group: 4.167 kW, 4th group: 4.167 kW, 5th group: 4.167 kW, and 6th group: 8.333 kW).

Member	$\mathbf{Cost} {\mathit{Z}}_{\mathit{m}}$ (€)	$\mathbf{Cost} {\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Difference} {\mathit{Z}}_{\mathit{m}}-{\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{\prime }}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{″}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{‴}}$ (€)
Group #1	4.881	1.007	3.874	4.436	3.586	3.910
Group #2	2.516	1.559	0.957	2.071	2.196	2.276
Group #3	1.360	1.435	−0.076	0.915	1.334	1.322
Group #4	1.986	1.537	0.450	1.542	1.836	1.874
Group #5	1.421	1.375	0.045	0.976	1.405	1.409
Group #6	−1.256	1.327	−2.583	−1.700	−2.119	−2.552
Total	109.073	82.395	26.678	82.395	82.395	82.395

. In this case, the difference between non-cooperative and cooperative operation is equal to 26.678 €, i.e., 24.5% reduction. The members of the first group have a cost of 3.586–4.436 € (depending on the cost-sharing mechanism) instead of 4.881 €, because they utilize the community’s PV, instead of purchasing energy from the main grid. Most importantly, the members of the sixth group have surplus PV production, resulting in a profit of 1.700–2.552 € (depending on the cost-sharing mechanism) instead of 1.256 €, which would have been the profit for non-coordinated operation, resulting in a profit increase of up to 103.2%. This outcome highlights the importance of cooperation between the members of energy communities.

4.2. Results Without BESS

The importance of having a BESS in energy communities operating under the net billing scheme is quantified in Figure 8 and Figure 9. The results assuming (i) equal PV shares and (ii) different PV shares, as in Section 4.1, i.e., the first group has no PV share while the sixth has double PV share, are presented in

Table 7. Energy community cost, equal PV shares, without BESS.

Member	$\mathbf{Cost} {\mathit{Z}}_{\mathit{m}}$ (€)	$\mathbf{Cost} {\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Difference} {\mathit{Z}}_{\mathit{m}}-{\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{\prime }}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{″}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{‴}}$ (€)
Group #1	0.571	1.343	−0.772	0.571	0.570	0.570
Group #2	2.980	2.079	0.900	2.979	2.979	2.979
Group #3	1.817	1.915	−0.098	1.816	1.817	1.817
Group #4	2.442	2.050	0.392	2.442	2.442	2.442
Group #5	1.876	1.835	0.042	1.876	1.876	1.876
Group #6	1.309	1.770	−0.461	1.309	1.309	1.309
Total	109.958	109.930	0.029	109.930	109.930	109.930

and

Table 8. Energy community cost, with different PV shares, without BESS (member of the 1st group: 0 kW, 2nd group: 4.167 kW, 3rd group: 4.167 kW, 4th group: 4.167 kW, 5th group: 4.167 kW, and 6th group: 8.333 kW).

Member	$\mathbf{Cost} {\mathit{Z}}_{\mathit{m}}$ (€)	$\mathbf{Cost} {\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Difference} {\mathit{Z}}_{\mathit{m}}-{\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{\prime }}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{″}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{‴}}$ (€)
Group #1	4.881	1.343	3.537	4.512	3.840	4.077
Group #2	2.980	2.079	0.900	2.611	2.715	2.775
Group #3	1.817	1.915	−0.098	1.448	1.788	1.776
Group #4	2.442	2.050	0.392	2.073	2.327	2.353
Group #5	1.876	1.835	0.042	1.507	1.864	1.867
Group #6	−0.789	1.770	−2.559	−1.158	−1.542	−1.855
Total	132.068	109.930	22.139	109.930	109.930	109.930

, respectively. More specifically, the flexible loads are still served during noon, and the excess PV production is sold, but since there is no storage, more energy is bought from the main power system, especially during early morning and late evening hours, resulting in an optimal cost of 109.930 €, instead of 82.395 €, meaning that a storage system would decrease the cost by 25.0%. With equal PV shares the benefit of the cooperation is relatively low, i.e., 0.029 € (instead of 0.101 €) for the entire community. However, in the second scenario, presented in Table 8, it is equal to 22.139 € (instead of 26.678 €) and the sharing mechanism allows the member of the sixth group to have a profit ranging from 1.158 € up to 1.855 €, instead of 0.789, which would have been the profit of non-coordinated operation.

4.3. Sensitivity Analysis

To showcase the impact of PV and BESS size on the community’s cost, a sensitivity analysis is carried out. In Figure 10, the community’s cost for various PV and BESS combinations is presented, from 0 up to 1.4 times the PV nominal value, i.e., 250 kW, and from 0 up to 1.4 times the BESS nominal value, i.e., 200 kWh, where both BESS energy and power nominal values are adjusted accordingly. As expected, the higher the PV and BESS size, the lower the cost. Without their participation in the energy community, i.e., without PV and BESS system, the total cost would be equal to 399.021 €, split into 4.880 €, 7.560 €, 6.955 €, 7.443 €, 6.652 €, and 6.411 € for each group member, respectively.

Furthermore, it is worth investigating the benefit of the cooperation for various PV and BESS combinations. Assuming equal PV and BESS shares, the sensitivity analysis of the benefit is presented in Figure 11 and Figure 12, focused in an area of installed PVs from 0.5 up to 0.8 of the reference value (250 kW). Figure 11 reveals that there is an area, around the straight section starting from 0.575 (of the reference value, 250 kW) PV and no BESS (which is also the point of maximum benefit, equal to 6.526 €) where the benefit is maximized, showcasing the importance of cooperation amongst the members. For all other combinations (outside this straight section), the benefit is low for two main reasons: (i) either the system’s capability for self-consumption is too low, therefore, the transactions between the community are few, or (ii) the system’s capability for self-consumption is high enough to allow each member to cover their own needs without relying on cooperation. Therefore, the straight section of high benefit, presented in Figure 11 and Figure 12, is the breaking point between the aforementioned states, which are presented in both sides of the surface.

The analysis of the point of maximum benefit is presented in Figure 13 and Figure 14 and the costs are presented in

Table 9. Energy community cost, point of maximum benefit.

Member	$\mathbf{Cost} {\mathit{Z}}_{\mathit{m}}$ (€)	$\mathbf{Cost} {\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Difference} {\mathit{Z}}_{\mathit{m}}-{\mathit{Y}}_{\mathit{m}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{\prime }}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{″}}$ (€)	$\mathbf{Final} \mathbf{Cost} {\mathit{Y}}_{\mathit{m}}^{\mathit{‴}}$ (€)
Group #1	1.529	2.095	−0.566	1.420	1.351	1.269
Group #2	3.984	3.242	0.742	3.876	3.751	3.807
Group #3	3.146	2.986	0.159	3.037	3.096	3.108
Group #4	3.645	3.197	0.448	3.537	3.504	3.538
Group #5	2.876	2.861	0.015	2.767	2.871	2.873
Group #6	2.614	2.760	−0.146	2.505	2.568	2.547
Total	177.942	171.415	6.526	171.415	171.415	171.415

. In this case, the community does not sell PV production to the main grid, because it is low and, therefore, self-consumed. According to Table 9, the total cost, considering cooperation between the members, is equal to 171.415 €, whereas non-cooperative operation would have a total cost of 177.942 €. The benefit of the cooperation, i.e., 6.526 €, is shared amongst the members, giving each member of the first group a cost reduction from 0.109 € up to 0.259 €, depending on the sharing mechanism, for sharing their excess PV production with the rest of the community, instead of selling it to the main grid. Moreover, if the presented day is considered to be a representative day of the year, the yearly cost would be equal to 62,566.475 € for cooperative and 64,948.830 € for non-cooperative operation, resulting in 2382.355 € savings per year without additional installations. Also, compared to the cost without participation in the energy community, which is 399.021 € per day, translating into 145,642.665 € per year, these results indicate that with a 143.75 kW PV plant, the consumers save 83,076.190 € in a year.

5. Conclusions

This paper proposes an optimal day-ahead schedule for energy communities with PV, BESS, and flexible loads, aiming at the cost minimization (or profit maximization) of the community. To reach the optimal outcome, the members have to cooperate with each other, sharing their respective production and storage and, in the end, three cost-sharing mechanisms for the fair sharing of the resulting benefit are proposed. Scenarios with and without storage, considering equal but also different PV and BESS shares, are studied, and it is found that a BESS can reduce the cost of the community from 109.930 € to 82.395 € per day, in the basic scenario, meaning 25.0% reduction. Moreover, it is proven, according to the sensitivity analysis, that there are combinations of PV and BESS installations, forming a straight line, for which the benefit of the cooperation is particularly high, as presented in Figure 12. In more detail, there is a PV and BESS combination, potentially resulting in 83,076.190 € savings (2,382.355 € of which are attributed to their cooperation, without requiring equipment installations) compared to non-participation in energy communities, in a year, for a 143.75 kW PV plant without BESS, which is the point of maximum benefit. In future work, a similar sensitivity analysis will be conducted (for various PV and BESS combinations) for a representative year, aiming to identify the optimal investment considering net present values, investment payback periods, and environmental indicators, at the planning level, for a typical energy community operating under the net billing scheme.