# Aggregation of Households in Community Energy Systems: An Analysis from Actors’ and Market Perspectives

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## Abstract

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## 1. Introduction

- ▪
- Neglecting the plurality of actors in the community, i.e., considering a single household type, for example, prosumers.
- ▪
- Simplified modeling of electricity market prices or energy demand. For example, [25] assumes that the unit electricity price of the grid has a variable component, which is proportional to the total grid load.
- ▪
- Considering the electricity production costs as the only component of the electricity tariff and modeling the electricity tariffs modeled without considering the influence of the regulatory frameworks.

- ▪
- We propose a bottom-up model to investigate the aggregation of households in a community energy system. To model the interactions between the actors of the community energy system, we employ a Stackelberg game approach. Stackelberg games are widely used to model hierarchical competitions in the energy system such as the one between a retailer and households [25,26,27,28]. By integrating a Stackelberg game structure in our model, we implement a real-time pricing tariff for the community. In contrast to the existing literature, we focus on the heterogeneity of actors in the community energy system and distinguish between households with an inflexible load and those with flexibility options, i.e., battery storage and heat pumps. Moreover, we avoid modeling of electricity market prices. Instead, we use real wholesale market prices and, by taking the regulatory influences into account, model the end-user prices endogenously.
- ▪
- We introduce an indicator to evaluate the market alignment of community energy systems. This indicator can assess the behavior of communities with decentralized generation potential with respect to the electricity wholesale market. We then use this indicator to evaluate the relative economic efficiency of an energy community compared to an idealized benchmark case that is completely aligned with wholesale market price signals.

## 2. Analysis Procedure

#### 2.1. Community Energy System Structure

#### 2.1.1. Actors and Physical System

- Inflexible households are households that do not operate any storage system and are, therefore unable to shift their electricity load or feed-in at any time of the day. In this category, we distinguish between the consumers and prosumers. Consumers are actors, who own neither a PV system nor a flexibility option. Similar to the consumers, prosumers do not have a flexibility option but they operate a PV system. Prosumers may generate electricity and cover part of their electricity demand themselves.
- Flexible households are actors with load and feed-in shifting potential. These actors are assumed to be equipped with smart meters, which enable them to receive price signals and manage their load and feed-in accordingly. We divide these actors into flexible consumers and prosumagers. Prosumagers are households, who are not only equipped with PV rooftop systems but also own battery storage systems. Prosumagers can use their battery capacity to shift both their grid electricity usage and grid feed-in. Flexible consumers are households that own heat pumps and thermal storage systems, which give them the potential to shift a part of their electricity load.

#### 2.1.2. External Environment: Market and Regulations

#### 2.2. Aggregation Scenarios

- (1)
- Electricity procurement charges, which denote the retailer’s average per unit cost of buying electricity on the market. These charges are part of the retailer’s business model.
- (2)
- Community grid charges (${p}_{CGC})$ as a fixed per-unit component of the electricity tariffs that cover the costs due to investment and maintenance of the community grid. We assume that these charges are also part of the business model (in the reality, the grid charges in Germany are a regulated part of the electricity tariff).
- (3)
- Value-added tax (${p}_{VAT}$) that is collected by the retailer and passed on to the policy agent (see also Figure 3). ${p}_{VAT}$ is a regulated component of the electricity tariff and, in contrast to the other building blocks, it is not part of the business model.

- ▪
- Static Pricing (SP): The SP tariff structure follows the status quo pricing logic in Germany. Charges regarding the procurement of the electricity are based on the mean cost of acquiring electricity from the market, which we assume to be the annual average value of the market prices (${p}_{M}^{ave}$). Therefore, this tariff contains no hourly varying component and the electricity prices for the customers are constant at any time of the day.
- ▪
- Market Real-Time Pricing (M-RTP): In this tariff, an hourly forecast of the market prices (${p}_{M}$) of the following day is used as a per-unit charge of acquiring electricity. The electricity prices in this tariff contain a real-time price component, which represents the market price signals.
- ▪
- Community Real-Time Pricing (C-RTP): This tariff consists of optimized real-time procurement charges (${p}_{proc,s}$), determined by the retailer. The values of these elements may be influenced not only by hourly market prices, but also by the level of local electricity generation and demand in each hour. These charges may fluctuate between ${p}_{proc}^{min}$ and ${p}_{proc}^{max}$ and adopt values higher or lower than market prices in each hour. The calculation of variable procurement elements in this tariff is discussed in Section 3.3.

#### 2.3. Evaluation Indicators

#### 2.3.1. Actor’s Perspective

#### 2.3.2. System Perspective

## 3. Community Energy System Model

#### 3.1. Data and Model Parameterization

#### 3.2. Actors’ Rationale

#### 3.2.1. Inflexible Households

#### 3.2.2. Flexible Households

#### 3.2.3. Retailer

#### 3.3. Endogenous Calculation of the Real-Time Pricing Components in the C-RTP Tariff

#### 3.3.1. Formulation of the Non-Cooperative Stackelberg Game

- $\left(H{\displaystyle \cup}R\right)$ is the set of actors, where the households in the set$H$ act as followers in response to the prices set by the retailer ($R)$ as the game leader.
- ${\left\{{E}^{h}\right\}}_{h\in H}$ is the set of strategies of households, at time$t$, from which they select their strategy. This strategy represents the grid interaction of households in each time step.
- $\mathcal{Q}$is the strategy set of the retailer at time$t$, which consists of electricity tariffs and purchase prices.
- ${\left\{{u}^{h}\left(t\right)\right\}}_{h\in H}$ is the set of households’ utilities at time $t$ as presented.
- $Z$ in the community competition scenario is the net income of the retailer for trading with users and the market at time $t$, ${u}_{Communitycompetition}^{ret}\left(t\right)$
**,**calculated from cost and revenue functions described in Equations (21) and (22). $Z$ in the self-sufficiency scenario represents the electricity exchange with the market at time $t$, $a\left(t\right)$, calculated from Equation (27).

**Definition**

**1.**

#### 3.3.2. Solving the Stackelberg Game

Algorithm 1 retailer’s side GA based real-time pricing algorithm |

1: Population initialization, i.e., generating a population of $L$ chromosomes randomly; each chromosome denotes an electricity acquiring price set for the optimization period. 2: for $l=1$ to $L$ do3: The retailer decodes the $l$ ^{th} chromosome (representing the ${p}_{proc,s}$ and ${p}_{proc,p}$) and by adding the other electricity tariff building blocks, i.e., ${p}_{CGC}$ and ${p}_{VAT}$, calculates its strategy $\mathcal{Q}$ (${p}_{s}^{ret}$and ${p}_{b}^{ret}$) for the${T}_{opt}$. The prices are then announced to the households.4: The retailer receives the optimal strategies of the households including the grid interaction forecasts for the optimization period: $\left\{{e}_{*}^{h}\left(t\right)\right\}$. 5: Considering the constraints in Equation (29), at this stage the retailer optimizes the CES using the dynamic programming model and then, depending on the aggregation goal, evaluates its net-income (${u}_{Communitycompetition}^{ret}$ ) or the amount of traded electricity($a$) for the optimization period (${T}_{opt})$ as the fitness value of its strategy based on the chromosome $l$.6: end for7: A new generation of chromosomes is created by using the crossover and mutation operations of the GA. 8: Steps 2–7 are repeated until the convergence condition is reached. 9: The retailer announces the finalized prices to the households at the beginning of the scheduling horizon. |

Algorithm 2 Households’ side grid interaction optimization |

1: Households receive electricity prices from the retailer. 2: Each household calculates its strategy, i.e., the grid interactions in response to prices, by solving the followers’ problem using the dynamic programming model. 3: Households send back the predicted grid interactions during the optimization period to the retailer. |

## 4. Results

#### 4.1. Actor’s Perspective

- ▪
- The most prominent change in the retailer’s cost and revenue streams belongs to the imposed costs due to IPEG. These savings are proportional with reduced electricity imports to the community energy system (Table 7). The exemption from IPEG inside the community energy system gives the retailer an incentive to balance the electricity generation and consumption inside the community and reduce the exchange with the higher-level energy system.
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- The higher level of self-consumption inside the community lowers the retailer’s cost for electricity acquisition as well as the revenues from selling the electricity in the market. The lower accrued costs due to acquiring electricity from the market also results from the use of flexibility options for efficient market trading, i.e., purchasing electricity at lower prices. Besides CES, in the market signal and community competition scenarios, the flexibility of households is also used for more efficient electricity acquisition.
- ▪
- From the retailer’s perspective, the purchase prices offered to the prosumagers did not seem to have a significant effect on the performance of different scenarios. Similar results were observed when the range for ${p}_{proc,p}$ and ${p}_{proc,s}$ in the C-RTP tariff is expanded to [0, 10] cents/kWh. The reason for this observation is the high difference between the electricity tariff and purchase prices in this electricity tariff (due to community grid charges and value-added tax) that makes the self-consumption using the PV-storage system for the prosumagers more attractive than selling it to the retailer.
- ▪
- The retailer’s revenue from electricity sales to the households in all scenarios that involve real-time pricing is reduced. These losses can be traced back to the changes in the electricity consumption of flexible households in response to real-time pricing tariffs. The optimization of real-time prices by the profit-maximizing retailer in the community competition scenario reduces these revenue losses in comparison to the market signal scenario. The highest revenue losses appear in the self-sufficiency scenario, since the real-time prices in this scenario are optimized to minimize the interaction with the market and the prices are lower on average than in other scenarios (see Table 6).

#### 4.2. System Perspective

## 5. Discussion and Conclusions

#### 5.1. Policy Interpretation

#### 5.2. Limitations and Outlook

_{2}emissions of the electricity sector) can be examined. Another limitation of the MAI is that it does not consider the grid, especially the distribution grid [10]. For instance, the contribution of the community energy systems to alleviate stress on the distribution grid cannot be the current approach.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Table of Notation

Parameter | Meaning |
---|---|

$I$ | Set of actors: retailer ($ret)$, consumers ($cs)$, flexible consumers ($fcs)$, prosumers ($ps)$ and prosumagers ($psg)$ |

$H$ | Set of households: consumers, flexible consumers, prosumers and prosumagers |

$P$ | Set of households with generation potential: prosumers and prosumagers |

$R$ | Retailer |

${N}^{h}$ | Number of households in the category $h\in H$ |

${l}_{BD}^{h}\left(t\right)$ | Base electricity demand of the households $h\in H$ at time $t$ [kWh] |

${l}_{HD}^{fcs}\left(t\right)$ | Heat demand of the flexible consumers at time $t$ [kWh] |

${g}_{PV}^{p}\left(t\right)$ | Electricity generation of the households $p\in {\rm P}$ at time $t$ [kWh] |

${s}^{p}\left(t\right)$ | Residual load of the households $p\in {\rm P}$ at time $t$ [kWh] |

${e}_{G\to \partial}^{i}\left(t\right)$ | Electricity flow by actor $i\in {\rm I}$ at time t from grid to $\partial $ with $\partial $={Demand: D, Heat pump: HP, Battery: B, Electricity market: M} [kWh] |

${e}_{\partial \to G}^{i}\left(t\right)$ | Grid feed-in by actor $i\in {\rm I}$ from at time t from $\partial $ with $\partial $={Battery: B, PV systems: PV, Electricity market: M} [kWh] |

${e}_{HP\to TS}^{fcs}\left(t\right)$ | Energy inflow from heat pumps to thermal storage systems at time$t$ [kWh] |

${e}_{PV,B\to G}^{P}\left(t\right)$ | Total grid feed-in by all prosumers and prosumagers at time $t$ [kWh] |

${e}_{G\to D}^{H}\left(t\right)$ | Total grid usage by all households at time $t$ [kWh] |

${r}_{x}^{i}\left(t\right)$ | Revenue of actor $i\in {\rm I}$ in the scenario $x$ at time $t$ [cents] |

${c}_{x}^{i}\left(t\right)$ | Costs of actor $i\in {\rm I}$ in the scenario $x$ at time $t$ [cents] |

${u}_{x}^{i}\left(t\right)$ | Net income of actor $i\in {\rm I}$ in the scenario $x$ at time $t$ [cents] |

${U}_{x}^{i}$ | Net income of actor $i\in {\rm I}$ in the scenario $x$ for the simulation period [cents] |

${U}_{x}^{i,rel}$ | Net income of actor $i\in {\rm I}$ in the scenario $x$ relative to BAU scenario for the simulation period [-] |

$a\left(t\right)$ | Amount of traded electricity in the market by the retailer at time $t$ [kWh] |

${S}_{PV}^{max}$ | Peak power of PV system [kW] |

$P{R}_{PV}$ | Performance ratio of PV system [-] |

${K}_{B}^{psg}$ | Battery storage capacity in PV storage systems [kWh] |

${S}_{HP}^{max}$ | Peak power of heat pump [kW] |

$co{p}_{HP}$ | Heat pump COP [-] |

${K}_{TS}^{fcs}$ | Thermal storage capacity in the heat pump systems [kWh] |

${K}_{CES}^{ret}$ | CES capacity [kWh] |

${\eta}_{d}$ | Battery discharge efficiency in CES and PV storage systems [-] |

${\eta}_{c}$ | Battery charge efficiency in CES and PV storage systems [-] |

$E2P$ | Battery energy to power ratio in CES and PV storage systems [-] |

${C}_{CES}^{O\&M}$ | CES operation and maintenance costs expressed as a ratio of initial investment costs [%] |

${I}_{CES}^{0}$ | CES-specific investment cost [€/kWh] |

${r}_{dis}$ | Discount rate [%] |

${L}_{CES}$ | Battery lifetime [years] |

$FiT$ | Feed-in tariff [cents/kWh] |

${p}_{levies}$ | EEG and other support levies [cents/kWh] |

${p}_{GC}$ | Public grid charges [cents/kWh] |

${p}_{CGC}$ | Community grid charges [cents/kWh] |

${p}_{taxes}$ | Electricity tax [cents/kWh] |

${p}_{VAT}$ | Value added tax [cents/kWh] |

VAT | Value added tax [%] |

${p}_{m}^{ave}$ | Annual mean value of market prices [cents/kWh] |

${p}_{m}\left(t\right)$ | Market price in time $t$ [cents/kWh] |

${p}_{MP}\left(m\right)$ | Market premium in the month $m$ [cents/kWh] |

$m{v}_{PV}\left(m\right)$ | Market value of PV electricity in the month $m$ [cents/kWh] |

${p}_{s}^{ret}\left(t\right)$ | Retailer’s electricity tariff in time $t$ [cents/kWh] |

${p}_{p}^{ret}\left(t\right)$ | Retailer’s electricity purchase price in time $t$ [cents/kWh] |

${p}_{proc,s}\left(t\right)$ | Electricity procurement price component in ${p}_{s}^{ret}\left(t\right)$ [cents/kWh] |

${p}_{proc,p}\left(t\right)$ | Electricity procurement price component in ${p}_{p}^{ret}\left(t\right)$ [cents/kWh] |

${W}_{x}^{ret}$ | Welfare of retailer in the scenario $x$ for the simulation period [cents] |

${W}_{x}^{com}$ | Welfare of community in the scenario$x$ for the simulation period [cents] |

${W}_{x}^{com,rel}$ | Welfare of community in the scenario $x$ for the simulation period relative to BAU scenario [cents] |

$MA{I}_{x}^{rel}$ | Market alignment indicator for scenario $x$ relative to BAU scenario [-] |

$MA{I}_{x}$ | Market alignment indicator for scenario $x$ [-] |

${T}_{opt}$ | Optimization period [Hours] |

${T}_{sim}$ | Simulation period [Hours] |

${E}^{h}$ | Strategy set of households $h\in H$ in time $t$ |

$\mathcal{Q}$ | Strategy set of the retailer in time $t$ |

## Appendix B. Dispatch Optimization

#### Appendix B.1. Constraints for Flexible Consumers’ Optimization Model

#### Appendix B.2. Constraints for Prosumagers Optimization Model

#### Appendix B.3. Constraints for Community Energy Storage Optimization Model

## Appendix C. Dynamic Programming Model

**Figure A1.**Schematic sketch of the dynamic programming model and an exemplary calculation of the cost of the optimal sub-strategy ($cos{t}_{{T}^{opt}-2}^{SO{C}_{Max}}$) for the state $SO{C}_{Max}$ in the time step ${T}^{opt}-2$.

## Appendix D. Preparation of the Model’s Input Data

**Figure A2.**Share of total PV electricity generation to installed PV capacity in Germany in the year 2018 (own presentation based on the data from [35]).

## Appendix E. Electricity Prices in Different Tariffs

Scenario | Jan–Mar | Apr–Jun | Jul–Sep | Oct-Dec |
---|---|---|---|---|

Market signal | 25.85 | 25.77 | 27.80 | 27.66 |

Community competition | 26.86 | 26.84 | 26.82 | 26.83 |

Self-sufficiency | 26.60 | 26.58 | 26.61 | 26.59 |

Scenario | Jan–Mar | Apr–Jun | Jul–Sep | Oct–Dec |
---|---|---|---|---|

Market signal | 1.98 | 1.81 | 1.48 | 2.19 |

Community competition | 0.92 | 0.95 | 1.04 | 0.90 |

Self-sufficiency | 0.98 | 1.00 | 1.03 | 1.01 |

## Appendix F. Exemplary Dispatch Optimization Results

#### Appendix F.1. 48 h Flexible Consumers’ Schedule in Response to M-RTP Tariff

**Figure A5.**Flexible consumers’ response to the M-RTP tariff for the first 48 h in January. (

**A**) Flexible consumers’ heat demand and electricity load; (

**B**) state of charge of the thermal storage and electricity tariffs.

#### Appendix F.2. 48 h Prosumagers’ Schedule in Response to M-RTP Tariff

**Figure A6.**Prosumagers’ reaction to M-RTP tariff: (

**A**) 48h electricity tariffs and purchase prices (

**B**) schedule details of battery systems (

**C**) 48h usage of PV generated electricity.

## Appendix G. NPV Calculations

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**Figure 1.**Community Energy Storage (CES) business models as a complex socio-technical system (own presentation based on [12]).

**Figure 3.**Overview of the regulatory induced financial flows in the model. Arrows with similar patterns or color show related financial flows.

**Figure 8.**Actor’s utilities relative to BAU scenario. A positive value indicates an increase in the net income, negative values represent a decrease in net income.

**Figure 9.**Retailer’s cost and revenue streams relative to the BAU scenario; negative values show the reduction of each stream relative to the corresponding stream in the BAU scenario.

**Figure 11.**Relative market alignment indicator and reduced exchange with market compared to the BAU scenario.

Tariff | ${\mathit{p}}_{\mathit{s}}^{\mathit{r}\mathit{e}\mathit{t}}\left(\mathit{t}\right)$ | Real-Time Component |
---|---|---|

SP | ${p}_{CGC}+{p}_{VAT}+{p}_{M}^{ave}$ | None |

M-RTP | ${p}_{CGC}+{p}_{VAT}+{p}_{M}\left(t\right)$ | ${p}_{m}\left(t\right)$, exogenous model input |

C-RTP | ${p}_{CGC}+{p}_{VAT}+{p}_{proc,s}\left(t\right)$ | ${p}_{proc,s}\left(t\right)$, derived endogenously (See Section 3.3) |

Scenario | Tariff | Aggregation Goal |
---|---|---|

Business As Usual (BAU)—no storage | SP | None |

Static tariff | SP | Maximum profit |

Market signal | M-RTP | Maximum profit |

Community competition | C-RTP | Maximum profit |

Self-sufficiency | C-RTP | Maximum self-sufficiency |

Input Parameter | Unit | Resolution | Mean | Min | Max | Total |
---|---|---|---|---|---|---|

Electricity demand (${l}_{BD}^{h}$) | kWh | Hour | 0.53 | 0.19 | 1.33 | 4685 |

Heat demand (${l}_{HD}^{h})$ | kWh | Hour | 2.28 | 0.12 | 7.17 | 19,996 |

Parameter | Unit | Value | Source |
---|---|---|---|

$FiT$ | cent/kWh | 12.3 | German Solar Association [37] |

${p}_{levies}$ | cent/kWh | 7.68 | BDEW [29] |

${p}_{GC}$ | cent/kWh | 7.3 | BDEW [29] |

${p}_{taxes}$ | cent/kWh | 3.71 | BDEW [29] |

${p}_{CGC}$ | cent/kWh | 18 | Model assumption |

VAT | % | 19 | Förster et al. [43] |

${S}_{PV}^{max}$ | kW | 6 | Model assumption |

$P{R}_{PV}$ | % | 84 | Khalid et al. [44] |

${K}_{B}^{psg}$ | kWh | 6 | Model assumption |

${S}_{HP}^{max}$ | kW | 8 | Model assumption |

$co{p}_{HP}$ | - | 3 | Forsén et al. [45] |

${K}_{TS}^{fcs}$ | kWh | 14 | Model assumption |

${K}_{CES}^{ret}$ | kWh | 100 | Thorman et al. [46] |

${\eta}_{d}$ | % | 95 | Klein et al. [10] |

${\eta}_{c}$ | % | 95 | Klein et al. [10] |

$E2P$ | - | 1 | Thorman et al. [46] |

${C}_{CES}^{O\&M}$ | % | 1 | Klein et al. [10] |

${r}_{dis}$ | % | 4 | Model assumption |

${L}_{CES}$ | years | 20 | Model assumption |

${I}_{CES}^{0}$ | €/kWh | 510 and 250 | Schick et al. [47] |

${T}_{opt}$ | hours | 24 | Model assumption |

${T}_{sim}$ | hours | 8760 | Model assumption |

**Table 5.**GA parameters; the detailed description of the parameters can be found in [50].

Parameter | Value |
---|---|

Population size | 60 |

Offspring fraction | 0.2 |

Mutation | 0.6 |

Single point crossover | 1 |

Population convergence threshold | 0.01% |

Scenario | Tariff | Mean Value [cents] | Standard Deviation [-] | Price Range ^{1} [cents] |
---|---|---|---|---|

BAU/Static tariff | SP | 26.76 | 0 | [26.76, 26.76] |

Market signal | M-RTP | 26.76 | 2.09 | [14.40, 36.68] |

Community competition | C-RTP | 26.83 | 0.96 | [24.99, 28.56] |

Self-sufficiency | C-RTP | 26.58 | 1.01 | [24.99, 28.56] |

^{1}The price range shows the minimum and maximum values of the electricity tariffs during the simulation time.

Scenario | Relative Import (%) | Relative Export (%) |
---|---|---|

Static tariff | −9.6 | −45.0 |

Market signal | −9.9 | −46.3 |

Community competition | −12.4 | −53.1 |

Self-sufficiency | −13.0 | −59.5 |

^{1}Relative electricity import and export refers to the purchased and sold electricity in the market by the retailer relative to the corresponding values in the BAU scenario.

Scenario | Unit | NPV_510 | NPV_250 |
---|---|---|---|

Static tariff | € | −17,280.1 | 16,512.9 |

Market signal | € | −13,795.8 | 19,997.2 |

Community competition | € | −11,671.7 | 22,121.4 |

Self-sufficiency | € | −27,043.5 | 6749.5 |

^{1}NPV_510 and NPV_250 refer to the NPVs for battery prices of 510 and 250 (€/kWh) respectively.

Scenario | Grid Charges (€) | EEG Levy (€) |
---|---|---|

Static tariff | −1202.51 | −1120.15 |

Market signal | −1242.57 | −1157.46 |

Community competition | −1551.29 | −1445.03 |

Self-sufficiency | −1628.25 | −1516.72 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sarfarazi, S.; Deissenroth-Uhrig, M.; Bertsch, V.
Aggregation of Households in Community Energy Systems: An Analysis from Actors’ and Market Perspectives. *Energies* **2020**, *13*, 5154.
https://doi.org/10.3390/en13195154

**AMA Style**

Sarfarazi S, Deissenroth-Uhrig M, Bertsch V.
Aggregation of Households in Community Energy Systems: An Analysis from Actors’ and Market Perspectives. *Energies*. 2020; 13(19):5154.
https://doi.org/10.3390/en13195154

**Chicago/Turabian Style**

Sarfarazi, Seyedfarzad, Marc Deissenroth-Uhrig, and Valentin Bertsch.
2020. "Aggregation of Households in Community Energy Systems: An Analysis from Actors’ and Market Perspectives" *Energies* 13, no. 19: 5154.
https://doi.org/10.3390/en13195154