# A Time-Varying Incentive Optimization for Interactive Demand Response Based on Two-Step Clustering

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## Abstract

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## 1. Introduction

- In order to solve the problem of poor clustering under the complex electricity consumption situation of users in the existing research, we constructed a two-step clustering model based on the principle of reverse regulation. Our method can improve the poor clustering results of previous research that only adopted the first step of clustering based on a k-means clustering algorithm or the second step f clustering based on self-organizing competitive neural networks.
- In order to solve the problem that the single demand response strategy in the existing research is unable to effectively interact with the user side, we propose an interactive demand response optimization strategy based on two-step clustering. According to the clustering results of resident users, the peak and valley periods are determined by the primary class, and the peak–valley load time-sharing incentives are customized by the secondary subclass.
- The improved NSGA-II algorithm is used to solve the multi-objective peak–valley load time-sharing incentive model, which solves the problem that the existing research does not consider the difference of user power demand, and effectively improves the load characteristics of residential users through flexible incentive forms.

## 2. Related Work

## 3. A Two-Step Clustering Model Based on the Analysis of Consumer Behavior

#### 3.1. Analysis of Power Consumption Behavior of Users

#### 3.2. Two-Step Clustering Model

## 4. Interactive Response Strategy

#### 4.1. Residential Load Modeling

#### 4.2. Multi-Objective Peak–Valley Time-Varying Incentive Optimization Strategy Based on Two-Step Clustering

- The peak–trough load period is based on the user’s daily electricity consumption, which can reflect the load characteristics of the power user, and the user can participate in the peak–trough load time-varying incentive response by adjusting the usage of household appliances.
- The impact of peak–trough load incentives on the total daily electricity consumption of residents within a certain range is almost negligible, so the default total user load before the electricity price of peak–trough load period optimization is consistent with the total load after peak–trough load incentive optimization.

_{1}indicating stronger and k

_{2}weaker regulatory potential. From the primary k class, it can be determined that the peak and trough load periods of time-varying incentives for users’ classes are T

_{kf}and T

_{kg}, respectively. From the secondary subclasses, it can be determined that the peak and trough load time-varying incentives of subclass k

_{1}are ${p}_{{k}_{1}f}$ and ${p}_{{k}_{1}g}$, respectively, while the peak and trough load time-varying incentives of subclass k

_{2}are ${p}_{{k}_{2}f}$ and ${p}_{{k}_{2}g}$, respectively.

_{n}is the electricity consumption cost of the user n, while ${l}_{nf}(t)$ and ${l}_{ng}(t)$ are the responded loads to the peak and trough load periods, respectively, after the implementation of the incentive policy.

#### 4.3. Improved NSGA-II Multi-Objective Optimization Algorithm

_{i}is the number of successful offspring produced by i, while $\tau $ is a constant in order to avoid the loss of the genetic recombination operator in the iterative process. We set $\tau =1$.

## 5. Performance Validation

#### 5.1. Experimental Environment and Data Introduction

#### 5.2. Experimental Results

## 6. Conclusions

- A two-step clustering model based on the principle of reverse regulation was adopted to improve the poor clustering results of the first step clustering based on k-means clustering algorithm and the second clustering based on self-organizing competitive neural networks, as well as to improve the clustering quality and clustering accuracy.
- By customizing the peak–valley time-varying incentives for different types of residential users, and using the improved NSGA-II algorithm to solve the model, the goal of saving users’ electricity consumption costs and reducing the peak–trough differences in the grid’s power load was realized.

- This paper does not consider the differences in the electricity consumption behavior of users in different countries and regions. In the future, the demand response optimization strategy proposed in this paper should be applied to more measured datasets to analyze the applicability of this method.
- In the follow-up, the non-cooperative game problems formed by power suppliers formulating different sales strategies for different types of residential users will be further analyzed, and the game equilibrium of the power market will be further studied.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Interactive response strategy of time-varying excitation based on power consumption characteristics.

**Figure 7.**Results of two-step clustering based on the inverse correction principle. (

**a**) The first class. (

**b**) The second class. (

**c**) The third class. (

**d**) The fourth class.

User Category | Daily Average Load/kWh | Daily Mean Difference between Peak and Valley/kWh | Typical Load | |
---|---|---|---|---|

The second class | Subclass1 | 15.14 | 2.16 | Schedulable load |

Subclass2 | 15.28 | 2.25 | ||

The third class | Subclass1 | 21.54 | 2.87 | EV |

Subclass2 | 20.29 | 3.12 | ||

The fourth class | Subclass1 | 30.98 | 3.71 | Energy storage device |

Subclass2 | 33.21 | 4.19 |

**Table 2.**Comparison of electricity consumption costs to a customer under the two demand response cases.

Case | Average Cost before Optimization/CNY | Optimized Average Cost/CNY | Cost Saving/CNY |
---|---|---|---|

Case A | 14.13 | 12.34 | 1.79 |

Case B | 14.13 | 11.85 | 2.28 |

User Category | Peak-Hour Excitation/(CNY/kWh) | Valley-Hour Excitation/(CNY/kWh) | |
---|---|---|---|

The second class | Subclass1 | −0.231 | +0.128 |

Subclass2 | −0.252 | +0.136 | |

The third class | Subclass1 | −0.202 | +0.141 |

Subclass2 | −0.211 | +0.147 | |

The fourth class | Subclass1 | −0.133 | +0.064 |

Subclass2 | −0.168 | +0.088 |

**Table 4.**Average daily peak–valley difference and power costs before and after the implementation of the strategy.

User Category | Daily Mean Difference between Peak and Valley/kWh | Average Cost before Optimization/CNY | Optimized Average Cost/CNY | Cost Saving/CNY | |
---|---|---|---|---|---|

The second class | Subclass1 | 1.27 | 7.26 | 5.98 | 1.28 |

Subclass2 | 1.31 | 7.34 | 5.92 | 1.42 | |

The third class | Subclass1 | 1.33 | 10.34 | 8.43 | 1.91 |

Subclass2 | 1.39 | 9.74 | 7.95 | 1.79 | |

The fourth class | Subclass1 | 1.89 | 14.87 | 12.41 | 2.46 |

Rubclass2 | 1.72 | 15.94 | 13.05 | 2.89 |

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**MDPI and ACS Style**

Li, F.; Gao, B.; Shi, L.; Shen, H.; Tao, P.; Wang, H.; Mao, Y.; Zhao, Y.
A Time-Varying Incentive Optimization for Interactive Demand Response Based on Two-Step Clustering. *Information* **2022**, *13*, 421.
https://doi.org/10.3390/info13090421

**AMA Style**

Li F, Gao B, Shi L, Shen H, Tao P, Wang H, Mao Y, Zhao Y.
A Time-Varying Incentive Optimization for Interactive Demand Response Based on Two-Step Clustering. *Information*. 2022; 13(9):421.
https://doi.org/10.3390/info13090421

**Chicago/Turabian Style**

Li, Fei, Bo Gao, Lun Shi, Hongtao Shen, Peng Tao, Hongxi Wang, Yehua Mao, and Yiyi Zhao.
2022. "A Time-Varying Incentive Optimization for Interactive Demand Response Based on Two-Step Clustering" *Information* 13, no. 9: 421.
https://doi.org/10.3390/info13090421