# Model Predictive Control Home Energy Management and Optimization Strategy with Demand Response

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## Abstract

**:**

## 1. Introduction

## 2. Model Predictive Control

^{2}throughout the horizon of prediction N, from the dynamic information available up to that moment (measurements of the process variables and inputs passed up to the current time t) and a postulated or future control law [u(t|t), ..., u(t + N|t)], along the prediction horizon, as shown in Figure 3 [48].

_{i}are the sampled values obtained by subjecting the process to an impulse unit of amplitude equal to the sampling period. This sum is truncated and only N values are considered (therefore, it only allows representing stable processes and without integrators), having:

_{i}are the sampled values before the step input y:

_{0}can be taken as 0 without loss of generality, with which the predictor will be:

## 3. The Model of the Room

_{ac}embodies the cooling power input to the room, T

_{out}is the variable that represents the ambient temperature, the temperature of the room is given by T

_{in}, T

_{wl}symbolizes the wall temperature and C

_{wl}symbolizes the thermal capacitance of the wall. The thermal resistance of the wall is given by R

_{wl}, the thermal resistance of the windows is characterized by R

_{wd}, C

_{in}represents the thermal capacitance of the interior air and Q

_{s}gives the heat flow into an exterior surface of the room exposed to the solar radiation. In this model, h

_{o}represents the combined radiation and convection heat transfer coefficient, and A

_{w}symbolizes the area of the wall while the temperature of the surface of the wall is given by T

_{s}. Lastly, the binary variable that can simulate the turn-on and turn-off of the ON/OFF is represented by S(t). In this model, the running of the AC unit is characterized by a power switch block in which is assumed that no internal losses occur. All the variables and constants that were not recorded from this study were extracted from [63].

#### Time-of-Use (ToU) Electricity Rates

## 4. Result Analysis

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 10.**The temperature of the room by using PID (proportional-integral-derivative) control option.

**Figure 12.**The consumed energy cost in cents by the ON/OFF of the controlled AC unit by employing the 6 options of ToU rates.

**Figure 13.**The consumed energy cost in cents by the PID of the controlled AC unit by employing the 6 options of ToU rates.

**Figure 14.**The consumed energy cost in cents by the MPC of the controlled AC unit by employing the 6 options of ToU rates.

Type of Tariff | Without VAT (in €) | With VAT (in €) |
---|---|---|

Flat Tariff | 0.1634 | 0.2010 |

Two tier ToU rate Valley | 0.1002 | 0.1232 |

Two tier ToU rate Non-Valley | 0.1909 | 0.2348 |

Three tier ToU rate Valley | 0.1002 | 0.1232 |

Three tier ToU rate Peak | 0.1716 | 0.2111 |

Three tier ToU rate Critical Peak | 0.2169 | 0.2668 |

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**MDPI and ACS Style**

Godina, R.; Rodrigues, E.M.G.; Pouresmaeil, E.; Matias, J.C.O.; Catalão, J.P.S.
Model Predictive Control Home Energy Management and Optimization Strategy with Demand Response. *Appl. Sci.* **2018**, *8*, 408.
https://doi.org/10.3390/app8030408

**AMA Style**

Godina R, Rodrigues EMG, Pouresmaeil E, Matias JCO, Catalão JPS.
Model Predictive Control Home Energy Management and Optimization Strategy with Demand Response. *Applied Sciences*. 2018; 8(3):408.
https://doi.org/10.3390/app8030408

**Chicago/Turabian Style**

Godina, Radu, Eduardo M. G. Rodrigues, Edris Pouresmaeil, João C. O. Matias, and João P. S. Catalão.
2018. "Model Predictive Control Home Energy Management and Optimization Strategy with Demand Response" *Applied Sciences* 8, no. 3: 408.
https://doi.org/10.3390/app8030408