# A Network Flow Model for Price-Responsive Control of Deferrable Load Profiles

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## Abstract

**:**

## 1. Introduction

#### Paper Organization

## 2. Proposed Framework

#### 2.1. Assumed Market Design

#### 2.2. Conditions on Imbalance Settlement

#### 2.3. Deferrable Load Profile Representation

#### 2.4. Initial Setup of Deferrable Load Profiles

#### 2.5. Flow-Based Formulation for the Flexibility

#### 2.6. Network Flow Properties

## 3. Example of the Application of the Proposed Framework

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Input Data | Description |
---|---|

${\lambda}_{t}$ | Price information $t\in \left[0,\Delta t+\Delta p-1\right)$ |

${\tilde{f}}_{t}$ | Number of loads expected to join $u\in \left[0,\Delta t\right)$ |

${\tilde{b}}_{s}$ | Number of loads in buffer slot $s\in \left[0,\Delta s\right)$ |

Input Data | Description |
---|---|

$\tilde{{N}_{t}}$ | Total nomination with $t\in \left[0,\Delta t+\Delta p-1\right)$ |

$\tilde{{Q}_{t}}$ | Controllable nomination $t\in \left[0,\Delta t+\Delta p-1\right)$ |

Variables | Description |
---|---|

${b}_{st}$ | Number of loads in the buffer slot s scheduled to be activated in time slot t, $s\in \left[0,\Delta s\right)$, $t\in \left[0,s\right]$ |

${f}_{ut}$ | Number of loads expected in time slot u rescheduled to a time slot t, with $u\in \left[0,\Delta t\right)$, $t\in \left[u,max(\Delta t-1,u+\Delta s)\right]$ |

${f}_{ub}$ | Number of loads expected in the time slot u that will be used to replenish the buffer, with $u\in \left[\Delta t-\Delta s,\Delta t\right)$ |

Auxiliaries | Description |
---|---|

${b}_{s}$ | Number of loads assigned to final buffer slot s with $s\in \left[0,\Delta s\right)$ |

${f}_{t}$ | Auxiliary variable containing the number of loads activated in slot t of the rolling window, with $t\in \left[0,\Delta t\right)$ |

${E}_{t}$ | Energy consumption flexibility at each time slot t, with $t\in \left[0,\Delta t+\Delta p-1\right)$ |

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## Share and Cite

**MDPI and ACS Style**

Camargo, J.; Spiessens, F.; Hermans, C. A Network Flow Model for Price-Responsive Control of Deferrable Load Profiles. *Energies* **2018**, *11*, 613.
https://doi.org/10.3390/en11030613

**AMA Style**

Camargo J, Spiessens F, Hermans C. A Network Flow Model for Price-Responsive Control of Deferrable Load Profiles. *Energies*. 2018; 11(3):613.
https://doi.org/10.3390/en11030613

**Chicago/Turabian Style**

Camargo, Juliano, Fred Spiessens, and Chris Hermans. 2018. "A Network Flow Model for Price-Responsive Control of Deferrable Load Profiles" *Energies* 11, no. 3: 613.
https://doi.org/10.3390/en11030613