# A Peer-to-Peer Energy Trading Model for Optimizing Both Efficiency and Fairness

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## Abstract

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## 1. Introduction

#### 1.1. Research Background

_{2}. To promote the widespread use of renewable energy among households, one of the measures implemented by governments globally is the established Feed-In Tariff (FIT) programs. Individuals who generate their own electricity are referred to as prosumers [3], since they both consume and produce electricity. Under FIT, public utilities are obligated to purchase surplus electricity from prosumers at a predetermined rate over a specified period. This mechanism enables prosumers to calculate the return on their investment in renewable energy systems. Moreover, in Japan, the Feed-In Premium (FIP) system was introduced in April 2022 [4]. Unlike the fixed-rate purchasing approach of FIT, the FIP system incentivizes the adoption of renewable energy by offering a premium or subsidy to prosumers when they sell their electricity on the wholesale market. Consequently, these programs have generated considerable interest among the general public. Governments in numerous countries have also implemented energy market frameworks to ensure efficient electricity utilization. As an example, Japan has introduced the concept of a virtual power plant (VPP), which aims to consolidate the capacities of various distributed energy resources into a unified system. Another illustration is the implementation of demand response (DR), which involves modifying consumers’ electricity consumption patterns to better match supply and demand conditions. In VPP and DR systems, third-party aggregators participate in local energy markets, acting as intermediaries for managing prosumers’ energy resources. However, these methods suffer from issues such as limited transparency and commissions incurred by aggregators for trading [5]. This study presents a novel energy trading model that aims to achieve two objectives: ensuring equitable distribution of benefits among prosumers and optimizing the efficient allocation of resources. The objective is to ensure fair benefits within the market, preventing monopolization by any particular prosumer and eliminating wasteful power trading to maximize overall market benefits. The evaluation metric for fairness, described in detail in Section 4.4 later, aims to minimize the standard deviation, to maximize the minimum benefit, and to suppress variability.

#### 1.2. Peer-to-Peer Energy Trading

#### 1.3. Related Work

#### 1.4. Contribution

- It envisions a decline in the economic strain exerted upon standard households that necessitate electricity. FIT and FIP, which are invariably shouldered by these households, are encompassed within the realm of renewable energy surcharges. The number of prosumers is undeniably escalating. Consequently, it is indisputable that the quantity of surplus electricity, which public utilities are obliged to procure, is consistently on the rise. However, if this surplus electricity is judiciously employed within a localized energy network, the need for public utilities to purchase it diminishes, thereby stimulating transactions amongst prosumers. As a result, this precipitates a decline in the renewable energy surcharges that typical households are burdened with.
- Secondly, the proposed method lends assistance to typical households in their pursuit of identifying suitable trading partners. Each prosumer is confronted with the decision to elect a supplier or purchaser during every transaction within the peer-to-peer energy trading domain. Given the overwhelming myriad of options, this process is often complex for individuals. However, the proposed method, when implemented in distributed power apparatuses such as smart meters, facilitates the automatic determination of trading partners.

#### 1.5. Paper Structure

## 2. Definitions

#### 2.1. Model Illustration

#### 2.2. Restrictions on the Volume of Trades

#### 2.3. Rate

#### 2.4. Reservation Price

#### 2.5. Prosumer’s Benefit

## 3. Problem Formulation

#### 3.1. Prosumer’s Benefit Maximization

#### 3.2. Minimum Prosumer’s Benefit Maximization

#### 3.3. Multi-Objective Optimization

## 4. Simulation Results

#### 4.1. Conditions

#### 4.2. Simulators

#### 4.2.1. For Single-Objective Optimization

#### 4.2.2. For Multi-Objective Optimization

- Non-dominated sorting genetic algorithms-II (NSGA-II)
- Generalized differential evolution-III (GDE3)
- Optimized multi-objective particle swarm optimization (OMOPSO)
- Speed-constrained multi-objective particle swarm optimization (SMPSO)
- Strength Pareto evolutionary algorithm-II (SPEA2)
- $\u03f5$-multi-objective evolutionary algorithm ($\u03f5$-MOEA)

#### 4.3. Evolutionary Algorithms

#### 4.3.1. NSGA-II

#### 4.3.2. GDE3

#### 4.3.3. OMOPSO

#### 4.3.4. SMPSO

#### 4.3.5. SPEA2

#### 4.3.6. $\u03f5$-MOEA

#### 4.4. Evaluation Metrics

#### 4.5. Results and Discussion

#### 4.5.1. Prosumer’s Benefit Maximization Results

#### 4.5.2. Minimum Prosumer’s Benefit Maximization Results

#### 4.5.3. Multi-Objective Optimization Results

#### 4.5.4. Discussions

#### 4.5.5. Computational Time

## 5. Conclusions and Future Works

#### 5.1. Conclusions

#### 5.2. Future Work

- Considering the environmental impact of prosumersRenewable energy generation is inherently variable due to factors such as seasonal changes and weather conditions. Moreover, prosumers’ consumption patterns fluctuate based on their individual lifestyles. However, this paper does not consider the specific dynamics of prosumer’s production and consumption. We believe that one approach to consider to take lifestyle into account is using a weighted multi-objective method [25]. This approach allows for considering multiple factors and assigning different weights based on their importance. Furthermore, forecasting the real-time production and consumption of prosumers based on predefined measured values can be a direction to consider.
- Considering the introduction of fluctuating electricity pricesThe electricity rate is fixed in this paper; however, prices fluctuate in a realistic trading system due to different demand levels during peak and off-peak periods. Therefore, by setting electricity rates that fluctuate based on demand, we can make the trading system more realistic.
- Considering other factors of prosumer’s benefit in addition to priceThe EAs are used as meta-heuristics methods in this paper. Since our definitions of prosumer’s benefit considered only monetary gain, other factors of prosumer’s benefit should be considered to explain more real behavior of prosumers.
- Considering the security aspectAlthough we have not considered security aspects at this stage, we believe it would be appropriate to incorporate the STRIDE methodology, a vulnerability assessment method, into the process for conducting a comparison between the conventional transaction model and the new approach [26].
- Considering the pursuit of speed for optimizationThis paper can be led to an optimized solution; however, it is taking too long to reach a solution. We need to revise these codes and, at this stage, should consider implementing machine learning.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

EA | Evolutionary Algorithm |

TEPCO | Tokyo Electric Power Company |

PBMP | Prosumer’s Benefit Maximization Problem |

MPMP | Minimum Prosumer’s Benefit Maximization Problem |

MOP | Multi-objective Optimization Problem |

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

# of prosumers | 10 |

${p}_{i}$ [Wh] | Randomly decided between 349 Wh and 749 Wh |

${c}_{i}$ [Wh] | Randomly decided between 302 Wh and 702 Wh |

${r}_{s}$ [yen/kWh] | 29.05 |

${r}_{b}$ [yen/kWh] | 8.05 |

${r}_{i}$ [yen/kWh] | 18.55 |

$\mathcal{T}$ | 1000 |

p1 | p2 | p3 | p4 | p5 | p6 | p7 | p8 | p9 | p10 | |
---|---|---|---|---|---|---|---|---|---|---|

PBMP | 0.0021 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

MPMP | $7.35\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | $9.45\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | $7.35\times {10}^{-4}$ | 0.001155 |

EPsMOEA | $3.76\times {10}^{-17}$ | $5.53\times {10}^{-17}$ | $2.06\times {10}^{-15}$ | $8.41\times {10}^{-15}$ | $3.11\times {10}^{-15}$ | $2.87\times {10}^{-16}$ | $2.01\times {10}^{194}$ | $7.98\times {10}^{-17}$ | $3.98\times {10}^{-17}$ | $1.3\times {10}^{-17}$ |

GDE3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

NSGAII | $3.72\times {10}^{-12}$ | $2.63\times {10}^{-16}$ | $1.29\times {10}^{-11}$ | $2.21\times {10}^{-16}$ | $6.46\times {10}^{-12}$ | $1.45\times {10}^{-13}$ | $1.25\times {10}^{-14}$ | $2.0\times {10}^{-16}$ | $2.44\times {10}^{-12}$ | $1.72\times {10}^{-14}$ |

OMOPSO | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

SMPSO | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

SPEA2 | $2.39\times {10}^{-8}$ | $1.70\times {10}^{-6}$ | $1.63\times {10}^{-6}$ | $9.70\times {10}^{-8}$ | $1.33\times {10}^{-7}$ | $1.13\times {10}^{-7}$ | $2.44\times {10}^{-7}$ | $3.04\times {10}^{-7}$ | $2.28\times {10}^{-7}$ | $8.26\times {10}^{-7}$ |

p1 | p2 | p3 | p4 | p5 | p6 | p7 | p8 | p9 | p10 | |
---|---|---|---|---|---|---|---|---|---|---|

capacity | 804.8463 | 792.5969 | 527.1893 | 739.5148 | 506.7915 | 694.2612 | 653.2675 | 749.6945 | 635.1398 | 690.4667 |

demand | 562.647 | 607.578 | 696.4479 | 753.1572 | 844.3062 | 665.5017 | 886.1528 | 704.568 | 676.5624 | 785.0377 |

PBMP | 2.5431 | 1.94271 | 1.77723 | 0.143325 | 3.340995 | 0.30198 | 0 | 0.47376 | 0 | 0 |

MPMP | 2.5431 | 1.94271 | 0.143325 | 0.143325 | 1.101765 | 0.30198 | 2.44524 | 0.47376 | 0.43491 | 0.992985 |

EPsMOEA | 0.445365 | 0.390073 | 0.066981 | 0.011476 | 0.094538 | 0.115392 | 0.080478 | 0.154343 | 0.022629 | 0.042448 |

GDE3 | 1.71181 | 1.154414 | 0.003779 | 0 | 0.579017 | 0.114801 | 0.275869 | 0.155032 | 0 | 0.005253 |

NSGAII | 0.456026 | 0.509109 | 0.068836 | 0.016035 | 0.108889 | 0.081164 | 0.055153 | 0.17269 | 0.029628 | 0.053791 |

OMOPSO | 0.008554 | 0.024892 | $2.18\times {10}^{-4}$ | $2.27\times {10}^{-5}$ | $9.16\times {10}^{-5}$ | 0.003203 | $5.46\times {10}^{-4}$ | 0.007332 | $1.99\phantom{\rule{-0.166667em}{0ex}}\times \phantom{\rule{-0.166667em}{0ex}}{10}^{-5}$ | 4.67 × 10${}^{-4}$ |

SMPSO | $3.03\times {10}^{-7}$ | 0 | 0 | 0 | 0 | 0 | 0 | $1.39\times {10}^{-6}$ | $6.88\times {10}^{-6}$ | 0 |

SPEA2 | 0.599343 | 0.895141 | 0.137731 | 0.015724 | 0.242896 | 0.107725 | 0.127837 | 0.189232 | 0.053723 | 0.117297 |

Problem (Algorithm) | Time [s] |
---|---|

PBMP | 5.401 |

MPMP | 4.956 |

Weighted (average) | 4.263 |

MOP(NSGA-II) | 3519 |

MOP(GDE3) | 2972 |

MOP(OMOPSO) | 3036 |

MOP(SMPSO) | 2883 |

MOP(SPEA2) | 4065 |

MOP($\u03f5$-MOEA) | 3508 |

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**MDPI and ACS Style**

Kusatake, E.; Imahori, M.; Shinomiya, N.
A Peer-to-Peer Energy Trading Model for Optimizing Both Efficiency and Fairness. *Energies* **2023**, *16*, 5501.
https://doi.org/10.3390/en16145501

**AMA Style**

Kusatake E, Imahori M, Shinomiya N.
A Peer-to-Peer Energy Trading Model for Optimizing Both Efficiency and Fairness. *Energies*. 2023; 16(14):5501.
https://doi.org/10.3390/en16145501

**Chicago/Turabian Style**

Kusatake, Eiichi, Mitsue Imahori, and Norihiko Shinomiya.
2023. "A Peer-to-Peer Energy Trading Model for Optimizing Both Efficiency and Fairness" *Energies* 16, no. 14: 5501.
https://doi.org/10.3390/en16145501