# Fair Virtual Energy Storage System Operation for Smart Energy Communities

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Prior Works

#### 1.3. Contributions

- Definition of the fairness index for a VESS operation: Fairness refers to the problem of dividing a set of resources among several units. No single principle is universally accepted; however, the fundamental theory suggests that resources should be allocated in proportion to some pre-existing claims [31]. In this study, the fairness of costs and resources was considered. Basically, fairness is defined according to the contribution of units. Cost fairness is defined as the reward of a unit given in proportion to the invested cost of the unit, and resource fairness is defined as the VESS usage of a unit in proportion to its allocated VESS capacity. Using these definitions, a fairness index that can be used for VESS operation is presented in Section 2.3.
- Fair VESS operation for the SEC: Two VESS operation problems for an SEC are formulated by considering fairness in Section 2.4. The first problem (P1) involves maximizing social welfare under VESS operation and resource fairness constraints. In P1, the resource fairness constraint prevents the VESS operation from being biased toward a specific unit; thus, welfare is softly distributed among the units. The second problem (P2) involves maximizing the minimum bound of the cost fairness index with the VESS operation constraints and resource and cost fairness constraints. In this case, welfare among units is distributed hardly, owing to the cost fairness constraint. Moreover, by maximizing the minimum bound, social welfare is increased while ensuring cost fairness among units. These two fair VESS operation problems satisfy convexity; thus, a solution can be obtained using the iterative method.
- Experimental results and discussions about a real data set: The performance of the proposed VESS operation is verified using a real data set measured in Korea. To confirm the impact in terms of SECs, the total benefit, cost, and resource fairness indices were measured by varying the VESS capacity; this is described in Section 3.2. In order to demonstrate the effect on the VESS and utility grid, the VESS operation cycle and the peak demand reduction were measured and are described in Section 3.3 and Section 3.4, respectively. The experimental results show that upon the application of the proposed VESS operation, units in the SEC can achieve fairly distributed benefits, and the benefit reduction is marginal at about 5% in relation to the VESS operation to maximize the benefit. Hence, the ways in which the proposed VESS operation achieves this benefit distribution upon varying the implemented VESS capacity and the effect of fairness constraints are investigated. Moreover, future research prospects of the VESS for SECs are discussed in Section 4, including ownership of VESS and its profit distribution, cost-effective VESS size and implementation, and energy transaction cost and large-scale expansion.

## 2. Methods

#### 2.1. SEC

#### 2.2. VESS

#### 2.3. Fairness

#### 2.4. Fair VESS Operation for SEC

## 3. Results

#### 3.1. Experimental Environment

#### 3.2. SEC

#### 3.3. VESS

#### 3.4. Utility Grid

## 4. Discussion

- The benefit or the net reward is directly proportional to the VESS capacity, and the cost using the VESS increases more rapidly, except for P0, as shown in Figure 3. The VESS is operated to achieve the maximum benefit using P0.
- The cost fairness index that represents the cost efficiency decreases with increasing VESS capacity, as shown in Table 3. This validates the previous point. The result indicates that the ESS cost is still high enough to act as a burden on ESS utilization.
- The comparison results of P1 and P2 as shown in Figure 4 and Table 3 indicate that the proposed fair VESS operation considering the cost and resource fairness can achieve approximately 95% of the total benefit performance of the VESS operation for the maximum benefit with the resource fairness constraint. It implies that the resource fairness limits the total benefit, and the cost fairness distributes the benefits to each unit. Figure 5 and Table 4 also show that the resource fairness distributes the welfare to units softly, but the cost fairness distributes the welfare hardly according to the cost contribution.
- As shown in Figure 6, the resource fairness constraint limits the VESS usage, which decides the VESS lifetime that is crucial for determining the ESS cost. The result states that the resource fairness constraint can be used as a management index for the VESS lifetime, which affects the VESS cost.
- Finally, using the VESS operation, the peak demand is effectively reduced, as shown in Figure 7. Peak-demand reduction can improve the system efficiency and defer the facility investment cost of the utility grid. It implies that the units in the SEC and the utility grid benefit enhancement can be used to measure the social welfare improvement.

- In this study, the SESP is considered to own and directly operate the VESS. It can be extended to the case of the third-party service provider owning the VESS, and the SESP rents the VESS capacity, where the benefit distribution between the third-party service provider and the units in the SEC can be researched as a new problem.
- This study defines cost fairness as the ratio of the reward to cost, and resource fairness as the ratio of the VESS usage to cost. In actuality, fairness is defined in various ways, and this study can be extended to various fairness formulations. For instance, proportional and balanced fairness can be studied [36].
- This study focuses on the VESS operation when the SEC and VESS are set up. Implementation issues such as cost-effective VESS sizing and selection of the appropriate size of community units can be studied further.
- This study did not include the energy transaction costs, such as distribution and transmission fees. This is because the SEC comprises units located in adjacent areas. It can be extended to large-scale grid connection systems considering the energy transaction costs.

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Constitution of a virtual energy storage system (VESS) for the smart energy community (SEC).

**Figure 5.**Probability distribution of the welfare change in each unit. (

**a**) Welfare changes between the P0 and P1 cases with γ = 2. (

**b**) Welfare changes between the P0 and P2 cases with γ = 2.

Ref. | Year | Methodology | Objective | Contribution | Limitation |
---|---|---|---|---|---|

[16] | 2019 | Linear programming | Total operation cost minimization | Proposed a joint VESS scheduling method including electrical and thermal energy storage | No consideration for fairness |

[17] | 2020 | Multi-optima problem | Profit maximization of aggregator and units | Formulated and solved a two-stage problem for determining the VESS investment and pricing, and operating the VESS | No consideration for fairness |

[18] | 2020 | Linear programming | Total operation cost minimization | Proposed a VESS operation for a building-integrated photovoltaic microgrid | No consideration for fairness |

[19] | 2022 | Multi-stage distribution optimization | Total operation cost minimization | Proposed a VESS operation to address temporal uncertainties in the day-ahead dispatch | No consideration for fairness |

[20] | 2022 | Linear programming | Total benefit maximization | Proposed a VESS operation considering the usage-limited constraint. | No consideration for fairness |

[21] | 2016 | Modified auction | Total cost saving maximization | Determined the auction price by a non-cooperative Stackelberg game | No consideration for fairness |

[22] | 2018 | Combinatorial auction | Total benefit maximization | Proposed and solved a combinatorial auction by the genetic algorithm with particle swarm optimization | No consideration for fairness |

[23] | 2019 | Coalitional game | Total energy cost minimization | Solved a cost allocation problem in individual and shared ESS investment cases | No consideration for fairness |

[24] | 2020 | Non-cooperative game | Total operation cost minimization | Formulated an energy capacity trading and operation game and determined the Nash equilibrium | No consideration for fairness |

[25] | 2022 | Non-cooperative game | Electricity cost minimization | Determined a generalized Nash equilibrium for a VESS operation using the alternating direction multiplier and heavy ball method | No consideration for fairness |

[26] | 2020 | SARSA-based reinforcement learning | Renewable uncertainty minimization | Proposed a VESS operation based on an expected state-action-reward-state-action approach for wind farm | No consideration for fairness |

[27] | 2021 | Q-learning | Social cost minimization | Proposed a VESS operation combined with peer-to-peer energy transactions | No consideration for fairness |

Demand Price (USD/kW) | Energy Price (USD/kWh) | ||
---|---|---|---|

Off-Peak | Mid-Peak | On-Peak | |

18.45 | 0.22 | 0.25 | 0.25 |

VESS Capacity | P0 | P1 with $\mathit{\gamma}=2$ | P1 with $\mathit{\gamma}=1$ | P2 with $\mathit{\gamma}=2$ | P2 with $\mathit{\gamma}=1$ |
---|---|---|---|---|---|

Mean | |||||

116 kWh | 88.64 | 6.54 | 4.64 | 5.44 | 4.02 |

174 kWh | 59.75 | 5.67 | 4.00 | 4.36 | 3.35 |

232 kWh | 45.73 | 5.36 | 3.48 | 3.72 | 2.90 |

290 kWh | 34.51 | 4.71 | 3.23 | 3.29 | 2.59 |

348 kWh | 27.92 | 3.48 | 3.04 | 2.97 | 2.35 |

Standard deviation | |||||

116 kWh | 239.97 | 3.66 | 2.26 | 0 | 0 |

174 kWh | 161.72 | 3.74 | 1.98 | 0 | 0 |

232 kWh | 123.76 | 3.72 | 1.83 | 0 | 0 |

290 kWh | 91.94 | 3.44 | 1.87 | 0 | 0 |

348 kWh | 73.65 | 2.73 | 1.84 | 0 | 0 |

VESS Capacity | P0 | P1 with $\mathit{\gamma}=2$ | P1 with $\mathit{\gamma}=1$ | P2 with $\mathit{\gamma}=2$ | P2 with $\mathit{\gamma}=1$ |
---|---|---|---|---|---|

Mean | |||||

116 kWh | 282.89 | 2.00 | 1.00 | 2.00 | 1.00 |

174 kWh | 185.94 | 2.00 | 1.00 | 1.99 | 1.00 |

232 kWh | 140.36 | 2.00 | 1.00 | 1.99 | 1.00 |

290 kWh | 109.47 | 1.99 | 1.00 | 1.98 | 1.00 |

348 kWh | 87.94 | 1.91 | 1.00 | 1.97 | 1.00 |

Standard deviation | |||||

116 kWh | 789.47 | 0 | 0 | 0.01 | 0 |

174 kWh | 517.70 | 0 | 0 | 0.09 | 0 |

232 kWh | 390.13 | 0.04 | 0 | 0.13 | 0.01 |

290 kWh | 303.13 | 0.08 | 0 | 0.15 | 0.04 |

348 kWh | 242.81 | 0.18 | 0.01 | 0.18 | 0.05 |

VESS Capacity | Peak Demand | Mean Demand | Original $\mathbf{Bill}\left({\mathit{B}}_{\mathit{u}}(\cdot )\right)$ | Allocated $\mathbf{Capacity}\left({\mathit{e}}_{\mathit{u}}\right)$ |
---|---|---|---|---|

Welfare changes between the case of P0 and P1 | ||||

116 kWh | 0.45 | 0.14 | 0.20 | 0.65 |

232 kWh | 0.45 | 0.20 | 0.25 | 0.30 |

348 kWh | 0.40 | 0.21 | 0.25 | 0.32 |

Welfare changes between the case of P0 and P2 | ||||

116 kWh | 0.52 | 0.20 | 0.27 | 0.99 |

232 kWh | 0.57 | 0.25 | 0.31 | 0.99 |

348 kWh | 0.53 | 0.21 | 0.27 | 0.99 |

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**MDPI and ACS Style**

Oh, E.
Fair Virtual Energy Storage System Operation for Smart Energy Communities. *Sustainability* **2022**, *14*, 9413.
https://doi.org/10.3390/su14159413

**AMA Style**

Oh E.
Fair Virtual Energy Storage System Operation for Smart Energy Communities. *Sustainability*. 2022; 14(15):9413.
https://doi.org/10.3390/su14159413

**Chicago/Turabian Style**

Oh, Eunsung.
2022. "Fair Virtual Energy Storage System Operation for Smart Energy Communities" *Sustainability* 14, no. 15: 9413.
https://doi.org/10.3390/su14159413