# Six-Segment Strategy for Prosumers’ Financial Benefit Maximization in Local Peer-to-Peer Energy Trading

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## Abstract

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## 1. Introduction

## 2. Related Work and Background

- A mathematical model of P2P energy trading in the local community is proposed to optimize the system cost and revenue of prosumers;
- Novel prosumer segmentation rules and reward limits were designed on the basis of peak and average power export, which resulted after the first phase of optimization;
- A second stage of optimization was implemented for prosumers’ reward maximization;
- The final results of six-segment strategies (SSSs) were compared with the three-segment results.

## 3. Proposed P2P Model

## 4. Mathematical Model

## 5. Case Study Details

## 6. Results and Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Indices | |

j | Households |

$\tau $ | Periods |

Parameters | |

${\mathrm{N}}_{j}$ | No. of households |

${\mathrm{N}}_{\tau}$ | No. of periods |

${\mathrm{\u01a4}}_{j,\tau}^{bmax}$ | Highest power buy |

${\mathrm{\u01a4}}_{j,\tau}^{smax}$ | Highest power sell |

${\mathrm{\u01a4}\mathrm{E}}_{peak}^{S1}$ | Highest power export in segment S1 |

${\mathrm{\u01a4}\mathrm{E}}_{peak}^{S2}$ | Highest power export in segment S2 |

${\mathrm{\u01a4}\mathrm{E}}_{peak}^{S3}$ | Highest power export in segment S3 |

${\mathrm{\u01a4}\mathrm{E}}_{peak}^{S4}$ | Highest power export in segment S4 |

${\mathrm{\u01a4}\mathrm{E}}_{peak}^{S5}$ | Highest power export in segment S5 |

${\mathrm{\u01a4}\mathrm{E}}_{peak}^{S6}$ | Highest power export in segment S6 |

${\mathrm{\u01a4}\mathrm{E}}_{avg}^{S1}$ | Average power export in segment S1 |

${\mathrm{\u01a4}\mathrm{E}}_{avg}^{S2}$ | Average power export in segment S2 |

${\mathrm{\u01a4}\mathrm{E}}_{avg}^{S3}$ | Average power export in segment S3 |

${\mathrm{\u01a4}\mathrm{E}}_{avg}^{S4}$ | Average power export in segment S4 |

${\mathrm{\u01a4}\mathrm{E}}_{avg}^{S5}$ | Average power export in segment S5 |

${\mathrm{\u01a4}\mathrm{E}}_{avg}^{S6}$ | Average power export in segment S6 |

${\mathrm{\u01a4}}_{j,ini}^{bat}$ | Initial battery power |

$d\tau $ | time period adjustment factor |

${\mathrm{Z}}_{\mathrm{j},\tau}$ | Fixed Cost |

${l}_{p2p}^{buy}$ | Power loss coefficient for power buy |

${l}_{p2p}^{sell}$ | Power loss coefficient for power sell |

${\mathrm{\u01a4}}_{j,\tau}^{l}$ | Power consumed by households |

${\mathrm{\u01a4}}_{j,\tau}^{gen}$ | Power generated by households |

${\mathsf{\eta}}_{j,ch}$ | Efficiency of battery while charging |

${\mathsf{\eta}}_{j,dch}$ | Efficiency of battery while dis-charging |

${\mathrm{\u01a4}}_{j,\tau}^{batmax}$ | Highest power in battery |

${\mathrm{\u01a4}}_{j,\tau}^{bcl}$ | Power limit for battery charging |

${\mathrm{\u01a4}}_{j,\tau}^{bdl}$ | Power limit for battery dis-charging |

${\mathrm{\u041b}}_{j,\tau}^{\mathrm{p}2\mathrm{p}}$ | P2P price |

${\mathrm{\u041b}}_{j,\tau}^{f}$ | Feed in rate |

${\mathrm{\u041b}}_{j,\tau}^{b}$ | Power purchase rate from grid |

${\mathrm{R}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ | Smallest incentive amount |

${\mathrm{R}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ | Highest incentive amount |

D | Cost saving |

${\mathsf{\Phi}}_{j,\tau}^{S1}$ | Reward upper limit in segment S1 |

${\mathsf{\Phi}}_{j,\tau}^{S2}$ | Reward upper limit in segment S2 |

${\mathsf{\Phi}}_{j,\tau}^{S3}$ | Reward upper limit in segment S3 |

${\mathsf{\Phi}}_{j,\tau}^{S4}$ | Reward upper limit in segment S4 |

${\mathsf{\Phi}}_{j,\tau}^{S5}$ | Reward upper limit in segment S5 |

${\mathsf{\Phi}}_{j,\tau}^{S6}$ | Reward upper limit in segment S6 |

Variables | |

${\mathrm{Q}}_{j,\tau}^{g}$ | Cost of the power while buying from grid |

${\mathrm{Q}}_{j,\tau}^{p2p}$ | Cost of the power while buying from peer |

${\mathrm{R}}_{j,\tau}^{g}$ | Revenue while selling power to grid |

${\mathrm{R}}_{j,\tau}^{p2p}$ | Revenue while selling power to peer |

${\mathrm{\u01a4}}_{j,\tau}^{b}$ | Power buy from the utility grid |

${\mathsf{\beta}}_{j,\tau}^{\mathrm{\u01a4}\mathrm{b}}$ | Binary variable for power buy from the utility grid |

${\mathrm{\u01a4}}_{j,\tau}^{b\mathrm{p}2\mathrm{p}}$ | Power buy from peer |

${\mathsf{\beta}}_{j,\tau}^{\mathrm{\u01a4}\mathrm{b}\mathrm{p}2\mathrm{p}}$ | Binary variable for power buy from peer |

${\mathrm{\u01a4}}_{j,\tau}^{imp}$ | Power import |

${\mathrm{\u01a4}}_{j,\tau}^{exp}$ | Power export |

${\mathrm{\u01a4}}_{j,\tau}^{s}$ | Power sold to grid |

${\mathsf{\beta}}_{j,\tau}^{\mathrm{\u01a4}\mathrm{s}}$ | Binary variable for power sold to grid |

${\mathrm{\u01a4}}_{j,\tau}^{b\mathrm{p}2\mathrm{p}}$ | Power sell to peer |

${\mathsf{\beta}}_{j,\tau}^{\mathrm{\u01a4}\mathrm{b}\mathrm{p}2\mathrm{p}}$ | Binary variable for power sell to peer |

${\mathrm{R}}_{j,\tau}^{S1}$ | Financial incentive for S1 segment |

${\mathsf{\beta}}_{{\mathrm{R}}_{j,\tau}^{S1}}$ | Binary variable of financial incentive for S1 segment |

${\mathrm{R}}_{j,\tau}^{S2}$ | Financial incentive for S2 segment |

${\mathsf{\beta}}_{{\mathrm{R}}_{j,\tau}^{S2}}$ | Binary variable of financial incentive for S2 segment |

${\mathrm{R}}_{j,\tau}^{S3}$ | Financial incentive for S3 segment |

${\mathsf{\beta}}_{{\mathrm{R}}_{j,\tau}^{S3}}$ | Binary variable of financial incentive for S3 segment |

${\mathrm{R}}_{j,\tau}^{S4}$ | Financial incentive for S4 segment |

${\mathsf{\beta}}_{{\mathrm{R}}_{j,\tau}^{S4}}$ | Binary variable of financial incentive for S4 segment |

${\mathrm{R}}_{j,\tau}^{S5}$ | Financial incentive for S5 segment |

${\mathsf{\beta}}_{{\mathrm{R}}_{j,\tau}^{S5}}$ | Binary variable of financial incentive for S5 segment |

${\mathrm{R}}_{j,\tau}^{S6}$ | Financial incentive for S6 segment |

${\mathsf{\beta}}_{{\mathrm{R}}_{j,\tau}^{S6}}$ | Binary variable of financial incentive for S6 segment |

${\mathrm{\u01a4}}_{j,\tau}^{bat}$ | Power in the battery |

${\mathrm{\u01a4}}_{j,\tau}^{ch}$ | Charging power of the battery |

${{\mathsf{\beta}}_{\mathrm{\u01a4}}}_{j,\tau}^{ch}$ | Binary variable of charging power of the battery |

${\mathrm{\u01a4}}_{j,\tau}^{dch}$ | Discharging power of the battery |

${{\mathsf{\beta}}_{\mathrm{\u01a4}}}_{j,\tau}^{dch}$ | Binary variable of discharging power of the battery |

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Cases | Strategy | Financial Incentive | Incentive Function |
---|---|---|---|

Case 01 Without P2P | - | × | - |

Case 02 With P2P | 01 | ✓ | Identical to all |

02 | ✓ | 40% of revenue | |

03 | ✓ | Peak power export | |

04 | ✓ | Avg power export |

Segment | Strategy 3 | Strategy 4 | ||
---|---|---|---|---|

Peak Power Export (kW) | Incentive Limit (% of Max Reward) | Average Power Export (kW) | Incentive Limit (% of Max Reward) | |

S1 | 0–1 | 50% | 0–0.1 | 25% |

S2 | 1–2 | 60% | 0.1–0.15 | 50% |

S3 | 2–3 | 75% | 0.15–0.2 | 70% |

S4 | 3–4 | 100% | 0.2–0.25 | 90% |

S5 | 4–5 | 130% | 0.25–0.3 | 120% |

S6 | >5 | 160% | >0.3 | 150% |

Parameter | Value/Range | Unit |
---|---|---|

${\mathrm{N}}_{j}$ | 33 | - |

${\mathrm{\u01a4}}_{j,\tau}^{bmax}$ | 4.6 to 10.35 | kW |

${\mathrm{\u01a4}}_{j,\tau}^{\mathrm{s}\mathrm{m}\mathrm{a}\mathrm{x}}$ | 2.3 to 5.175 | kW |

${\mathrm{Z}}_{j,\tau}$ | 0.32 to 0.62 | EUR/day |

${\mathrm{\u041b}}_{j,\tau}^{b}$ | 0.06 to 0.18 | EUR/kWh |

${\mathrm{\u041b}}_{j,\tau}^{f}$ | 0.045 | EUR/kWh |

${\mathrm{\u041b}}_{j,\tau}^{\mathrm{p}2\mathrm{p}}$ | 0.068 to 0.093 | EUR/kWh |

${\mathrm{\u01a4}}_{j,\tau}^{l}$ | 0 to 6.47 | kW |

${\mathrm{\u01a4}}_{j,\tau}^{gen}$ | 0 to 7.75 | kW |

${\mathrm{\u01a4}}_{j,\tau}^{batmax}$ | 13.5 to 15 | kWh |

${\mathrm{\u01a4}}_{j,\tau}^{bcl}$ | 2.86 to 5.0 | kW |

${\mathrm{\u01a4}}_{j,\tau}^{bdl}$ | 2.86 to 5.0 | kW |

${l}_{p2p}^{buy}$ | 1.023 | - |

${l}_{p2p}^{sell}$ | 0.975 | - |

${\mathsf{\eta}}_{j,ch}$ | 90% | - |

${\mathsf{\eta}}_{j,dch}$ | 90% | - |

System Cost (EUR) | |
---|---|

Without P2P | 103.42 |

With P2P | 90.10 |

Cost Saving (D) = 13.32 |

Strategy | Min Reward (EUR) | Max Reward (EUR) | Average Reward (EUR) | Overall Incentive (EUR) |
---|---|---|---|---|

Strategy 1 | 0.444 (Identical to all) | 13.32 | ||

Strategy 2 | 0.003 | 0.784 | 0.241 | 7.24 |

Strategy 3 | 0.222 | 0.710 | 0.408 | 12.25 |

Strategy 4 | 0.110 | 0.667 | 0.444 | 13.32 |

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## Share and Cite

**MDPI and ACS Style**

Mochi, P.; Pandya, K.; Faia, R.; Soares, J.
Six-Segment Strategy for Prosumers’ Financial Benefit Maximization in Local Peer-to-Peer Energy Trading. *Mathematics* **2023**, *11*, 3933.
https://doi.org/10.3390/math11183933

**AMA Style**

Mochi P, Pandya K, Faia R, Soares J.
Six-Segment Strategy for Prosumers’ Financial Benefit Maximization in Local Peer-to-Peer Energy Trading. *Mathematics*. 2023; 11(18):3933.
https://doi.org/10.3390/math11183933

**Chicago/Turabian Style**

Mochi, Pratik, Kartik Pandya, Ricardo Faia, and Joao Soares.
2023. "Six-Segment Strategy for Prosumers’ Financial Benefit Maximization in Local Peer-to-Peer Energy Trading" *Mathematics* 11, no. 18: 3933.
https://doi.org/10.3390/math11183933