# Microgrids Real-Time Pricing Based on Clustering Techniques

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background, Motivations and Aims

#### 1.2. Literature Review and Contributions

- This paper proposes a clustering-based pricing scheme for microgrids through which a microgrid operator can assign proper price tariffs on its consumers based on the load curves clustered in distinctive classes.
- As for clustering techniques, this paper applies an improved weighted fuzzy average k-means to overcome the drawbacks of the traditional k-means techniques.

## 2. Methodology Framework

#### 2.1. Clustering Process

^{(1)},…, l

^{(p)}} as a set of p numbers. The algorithm initially considers the sample mean µ(0) and variance σ

^{2}to start the process, to determine the weighted fuzzy average. Considering a vector of L with H components, the cluster center is calculated as follows:

^{2}on several iterations and then uses it as a fixed number. This could lead to a sufficiently close WFA.

- The distance between two load curves (e.g., between two hours l
^{(i)}and l^{(j)}, of the set L^{(k)}) is defined as:$$d({l}^{(i)},{l}^{(j)})=\sqrt{\frac{1}{H}{\displaystyle \sum}_{h=1}^{H}{({l}_{h}^{(i)}-{l}_{h}^{(j)})}^{2}}$$ - The distance between a cluster center r
^{(k)}and the subset L^{(k)}is:$$d({r}^{(k)},{L}^{(k)})=\sqrt{\frac{1}{{n}^{(k)}}{\displaystyle \sum}_{m=1}^{{n}^{(k)}}{d}^{2}({r}^{(k)},{l}^{(m)})}$$^{(k)}is the number of load curves in k-th cluster.

#### 2.2. Microgrid Pricing Scheme

## 3. Numerical Results

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclatures

${\mu}_{(h)}^{(r)}$ | The hth component of weighted fuzzy average in the rth iteration |

${\sigma}^{2}$ | Variance of WFA k-means |

${\sigma}_{h}^{2}$ | Variance of the hth component of load profiles |

${\overline{\sigma}}^{2}$ | Average variance |

$a$ | Adjusting parameter |

$b$ | Adjusting parameter |

${l}^{(p)}$ | The pth input curve |

${l}_{h}^{(p)}$ | The hth component of pth input curve |

${r}^{(k)}$ | Centeriod of the kth cluster |

${r}_{h}^{(k)}$ | The hth component of centeriod of the kth cluster |

${r}_{kh}^{(0)}$ | The hth component of initial centeriod of the kth cluster |

${w}_{(p,n)}^{(r)}$ | The hth component of computed weight of the pth curve in the rth iteration |

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**MDPI and ACS Style**

Liu, H.; Mahmoudi, N.; Chen, K.
Microgrids Real-Time Pricing Based on Clustering Techniques. *Energies* **2018**, *11*, 1388.
https://doi.org/10.3390/en11061388

**AMA Style**

Liu H, Mahmoudi N, Chen K.
Microgrids Real-Time Pricing Based on Clustering Techniques. *Energies*. 2018; 11(6):1388.
https://doi.org/10.3390/en11061388

**Chicago/Turabian Style**

Liu, Hao, Nadali Mahmoudi, and Kui Chen.
2018. "Microgrids Real-Time Pricing Based on Clustering Techniques" *Energies* 11, no. 6: 1388.
https://doi.org/10.3390/en11061388