# Electricity Customer Clustering Following Experts’ Principle for Demand Response Applications

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## Abstract

**:**

## 1. Introduction

**Figure 1.**Hierarchical clustering result with the single linkage method (number of clusters, k = 3). Hierarchical clustering provides a dominant cluster and other small clusters. (

**a**)–(

**c**) Clusters 1–3.

## 2. k-Sliding Distance

**Figure 2.**Representative samples for calculation of similarity. Two customers in (

**a**–

**c**) are considered as they are similar. Customers in (

**d**) are not similar. (

**a**)–(

**d**) Load patterns 1–4.

## 3. Verification of k-Sliding Distance

#### 3.1. Experimental Setup

**Figure 3.**Clustering result by an expert with the data from southern part of Gyeonggi Province. (

**a**)–(

**j**) Clusters 1–10.

**Figure 4.**Daily profiles of 10 randomly selected customers. Each line is considered to be a virtual customer. There are a total of 180 virtual customers. (

**a**)–(

**j**) Customers 1–10.

_{i}is the i

_{th}resulting cluster, N is the number of total nodes, L

_{j}is the load profile of expected cluster j, and |X| is the size of set X.

#### 3.2. Experimental Result

## 4. Finding Clustering Principle Using Genetic Programming

**Figure 14.**Example tree of genetic programming. The presented distance measure is the sum of the k-sliding distance in the frequency domain with a weight of 0.3 and the Euclidean distance in the time domain with a weight of 0.8.

Node Type | Parameters | |
---|---|---|

Leaf (Distance between two customers) | Distance Option | Distance between statistical values, (average, standard deviation), Euclidean distance, DTW distance, Pearson correlation coefficient distance, k-sliding distance |

Input Domain | Time domain, Frequency domain, Slope domain | |

Weight | 0~1 | |

Additional Factors | Unity operator: sin, cos, square, 1/x, square root, Peak parameter: peak-weight, peak-penalty | |

Non-Leaf | Summation, Subtraction, Maximum, Minimum, Average, Multiplication |

## 5. Assessment of Distance According to Genetic Programming

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Kang, J.; Lee, J.-H. Electricity Customer Clustering Following Experts’ Principle for Demand Response Applications. *Energies* **2015**, *8*, 12242-12265.
https://doi.org/10.3390/en81012242

**AMA Style**

Kang J, Lee J-H. Electricity Customer Clustering Following Experts’ Principle for Demand Response Applications. *Energies*. 2015; 8(10):12242-12265.
https://doi.org/10.3390/en81012242

**Chicago/Turabian Style**

Kang, Jimyung, and Jee-Hyong Lee. 2015. "Electricity Customer Clustering Following Experts’ Principle for Demand Response Applications" *Energies* 8, no. 10: 12242-12265.
https://doi.org/10.3390/en81012242