# Proactive Energy Optimization in Residential Buildings with Weather and Market Forecasts

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## Abstract

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## 1. Introduction

## 2. Previous Work

#### 2.1. Grid Stabilization

#### 2.2. Demand Side Management

#### 2.3. Forecasting Methodology

#### 2.4. Model Predictive Control in Building Energy Management

#### 2.5. Accounting for Forecast Uncertainty and System Disturbances

#### 2.6. Use of MHE in MPC

## 3. Contributions

- A home energy management system (HEMS) that uses a combined MHE and MPC approach that estimates residential home building parameters and optimizes home energy in real time. Mathematical building models are often very complicated and computationally expensive. This work overcomes this obstacle by using a lumped parameter model that is adapted to fit a high-fidelity model.
- A hybrid approach manages the on/off behavior of air conditioners as a continuous function using a mathematical program with complementarity constraints (MPCC). Discrete variables increase the number of potential solutions which require more computation resources and time. By using MPCC’s, the discrete behaviors are converted into a continuous function that is solved with continuous optimization.
- A combined renewable energy, energy storage, forecasts, cooling system, variable rate electricity plan, and multi-objective function residential house model is presented and tested on a simulated home in Phoenix, Arizona. This combination includes all major energy flows within a home as well as important outside disturbances. Accounting for these factors allows for a complete home energy optimization assessment with controlled conditions to assess the potential benefit from the HEMS approach.

## 4. Theory and Methods Used in Developing Energy Management Software

#### 4.1. Methods

#### 4.2. Theory/Overview

#### 4.3. Simulation

#### 4.4. Building House Model

#### 4.4.1. Initial Model

#### 4.4.2. Improved Model

#### 4.5. Air Conditioner Load Model

#### 4.6. Battery Model

#### 4.7. Ambient Temperature Prediction Model

#### 4.8. Miscellaneous Building Power Prediction Model

#### 4.9. Solar Power Production Prediction Model

#### 4.10. Moving Horizon Estimation and Model Predictive Control Theory

#### 4.11. Moving Horizon Estimation with Lumped Parameters

#### 4.12. Model Predictive Controller with Forecasts

## 5. Case Study Results

#### 5.1. Base Case

#### 5.2. Optimized Case

#### 5.3. Comparison to Base Case

#### 5.4. MPC Only HEMS Case Study

#### 5.5. Comparison to Full HEMS Application

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Property | Value |
---|---|

Battery Voltage | 50 V |

Battery Usable Capacity | 13.5 kWh |

Round Trip Efficiency | 90% |

Maximum charge/discharge Power | 5 kW |

Lithium-ion Cell Capacity | 1 Ah |

Lithium-ion Cell Voltage | 3.6 V |

Symbol | Description |
---|---|

${I}_{battery}$ | Current In/Out of Battery |

${I}_{cell}$ | Current In/Out of Cell |

$N\_Cell{s}_{parallel}$ | Number of Cells in parallel |

$N\_Cell{s}_{series}$ | Number of Cells in Series |

${P}_{inv}$ | DC Power |

$in{v}_{eff}$ | Efficiency of the Inverter |

${P}_{in/out}$ | AC Power |

${V}_{battery}$ | Battery Voltage |

${V}_{cell}$ | Cell Voltage |

${Q}_{discharged}$ | Cell capacity discharged |

${Q}_{battery}$ | Battery capacity |

${Q}_{cell}$ | Cell capacity |

$SO{C}_{battery}$ | State of Charge of the Battery |

**Table 3.**Objective Function Terms from [33] for MHE and MPC.

Symbol | Description |
---|---|

$\mathsf{\Phi}$ | objective function |

${y}_{x}$ | measurements ${({y}_{x,0},...,{y}_{z,n})}^{T}$ |

y | model values ${({y}_{0},...,{y}_{n})}^{T}$ |

${w}_{m},{W}_{m}$ | measurement deviation penalty |

${w}_{p},{W}_{p}$ | penalty from the prior solution |

${c}_{\mathsf{\Delta}p}$ | penalty from the prior parameter values |

$db$ | dead band for noise rejection |

$x,u,p,d$ | states $(x)$, inputs $(u)$, parameters $(p)$, or disturbances $(d)$ |

$\mathsf{\Delta}p$ | change in parameters |

$f,g,h$ | equation residuals, output fraction, and inequality constraints |

${e}_{U},{e}_{L}$ | slack variable above and below dead-band measurement |

${c}_{U},{c}_{L}$ | slack variable above and below a previous model value |

${y}_{t},{y}_{t,hi},{y}_{t,lo}$ | desired trajectory target or dead band |

${W}_{hi},{W}_{lo}$ | penalty outside trajectory dead band |

${c}_{y},{c}_{u},{c}_{\mathsf{\Delta},u}$ | cost of y, u and $\mathsf{\Delta}u$, respectively |

${\tau}_{c}$ | time constant of desired controlled variable response |

${e}_{lo},{e}_{hi}$ | slack variable below or above the trajectory dead band |

$sp,s{p}_{lo},s{p}_{hi}$ | target, lower, and upper bounds to final set-point dead band |

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**MDPI and ACS Style**

Simmons, C.R.; Arment, J.R.; Powell, K.M.; Hedengren, J.D. Proactive Energy Optimization in Residential Buildings with Weather and Market Forecasts. *Processes* **2019**, *7*, 929.
https://doi.org/10.3390/pr7120929

**AMA Style**

Simmons CR, Arment JR, Powell KM, Hedengren JD. Proactive Energy Optimization in Residential Buildings with Weather and Market Forecasts. *Processes*. 2019; 7(12):929.
https://doi.org/10.3390/pr7120929

**Chicago/Turabian Style**

Simmons, Cody R., Joshua R. Arment, Kody M. Powell, and John D. Hedengren. 2019. "Proactive Energy Optimization in Residential Buildings with Weather and Market Forecasts" *Processes* 7, no. 12: 929.
https://doi.org/10.3390/pr7120929