# An Integrated Approach to Adaptive Control and Supervisory Optimisation of HVAC Control Systems for Demand Response Applications

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## Abstract

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## 1. Introduction

#### 1.1. Motivation

#### 1.2. Previous Work

_{th})—a piece of information specified by the consumer to adjust or maintain a setpoint was presented in [16]. If the retail price of electricity was higher than the P

_{th}, a 1 °C step increase in setpoint temperature was applied to the thermostat at each control interval. On the other hand, when the retail price was lower than the P

_{th}, the nominal setpoint temperature was maintained. Other HVAC applications of RBC can be found in [17,18].

#### 1.3. Current Contributions

#### 1.4. Structure

## 2. System Description

#### 2.1. HVAC Process Models

_{hcll}= 0 in (1), and measured temperature, T, is the output of the closed loop system, then the HVAC process can be described around a local operating point by the simple first-order transfer function below [6,9]:

#### 2.2. Digital Adaptive Controller

_{s}[23]. The digital adaptive controller was previously proposed in [24] based upon earlier work in [18]. It enables the direct propagation of a predictive controller D(z) using the preferred closed-loop pole specification, which is encoded in the polynomial P(z), if the open-loop numerator of the process (i.e., B(z) including zeros and time delay) is scaled and embedded in the closed-loop transfer function. The below controller design accomplishes the specification [23]:

_{p}made in a manner that ensures the closed-loop transfer function has unit gain and the controller contains an integrator (see [18]). Implanting the open-loop zeros of the process in the closed-loop response as presented here has many advantages, including the ability to flexibly track changes in the time delay without having to implement an elaborate delay-estimation to the polynomial B(z) and robustness against inverse response (unstable zeros) in the HVAC process [23].

#### 2.3. MPC Objective Function

_{c}to be as low as possible. If the local controller is configured for other HVAC variable control, such as humidity, then a suitable deviation from setpoint criteria for such a variable may be used instead.

#### 2.4. Simplified Case

## 3. Implementation

#### Simulation Cases

_{th})—this was approximately £0.035. If the P

_{th}was higher than the current price of electricity (E

_{TOU}), the setpoint value of the thermostat was set to 22 °C. Conversely, if E

_{TOU}was greater than P

_{th}, the setpoint was adjusted to 0 °C—meaning the thermostat was turned off. This is to reduce HVAC consumption during peak times.

## 4. Results and Analysis

#### 4.1. Maximum Economic Cost Saving (λ = 0)

#### 4.2. Higher Preference for Economic Cost Saving (λ = 0.25)

#### 4.3. Equal Preference for Thermal Comfort and Energy Cost (λ = 0.50)

#### 4.4. Higher Preference for Thermal Comfort (λ = 0.75)

#### 4.5. Maximum Thermal Deviation Saving (λ = 1)

## 5. Discussions and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Supervisory model predictive control (MPC) plan showing a detailed breakdown of the inner loop adaptive controller. The MPC optimiser continued iterating until a setpoint trajectory that produced the least cost was found. These generated setpoints were then sent to the localised adaptive controller, which in turn sent control signals to the heating, ventilating, and air-conditioning (HVAC) model.

**Figure 2.**Basic closed loop representation of Figure 1, showing the inner loop digital adaptive controller D(z) and the controlled process G(z), where U(z) is the controller output.

**Figure 4.**Room temperature and MPC-generated setpoints over 24 h when λ is set to 0—indicating maximum preference for energy saving.

**Figure 5.**Room temperature and MPC-generated setpoints over 24 h when λ is set to 0.25—indicating higher preference for energy saving with some consideration for thermal comfort.

**Figure 6.**Room temperature and MPC-generated setpoints over 24 h when λ is set to 0.5—indicating balanced preference for energy saving and thermal comfort.

**Figure 7.**Room temperature and MPC-generated setpoints over 24 h when λ is set to 0.75—indicating a higher preference for thermal comfort with some consideration for energy cost.

**Figure 8.**Room temperature and MPC-generated setpoints over 24 h when λ is set to 1—indicating maximum preference for thermal comfort.

**Figure 9.**Room temperature and MPC-generated setpoints over 24 h using sample spring season price data.

**Figure 10.**Room temperature and MPC-generated setpoints over 24 h using sample summer season price data.

**Figure 11.**Room temperature and MPC-generated setpoints over 24 h using sample autumn season price data.

Simulation Case Type | Description | Setpoint |
---|---|---|

Base | Fixed setpoint control | 22 °C |

Case 1 | Rule-based thermostatic control | 22 °C or 0 °C, depending on E_{TOU} |

Case 2 | Supervisory MPC (at λ = 0, 0.25, 0.5, 0.75 and 1) | Varied, depending on λ |

Case 3 | Supervisory MPC (at λ = 0.25) for different seasons | Varied, depending on λ |

Thermal Deviation Range | Thermal Comfort |
---|---|

0–1000 | Very comfortable |

1000–1999 | Comfortable |

2000–2499 | Slightly comfortable |

2500–2999 | Uncomfortable |

3000+ | Very uncomfortable |

Simulation Case Type | Energy Consumption (KWh) | Economic Cost (£) | Thermal Deviation | Average Room Temp. (°C) | Comfortability |
---|---|---|---|---|---|

Base(Fixed setpoint control) | 533 | 21.87 | 75 | 21.90 | Very comfortable |

Case 1(RBC strategy) | 326 | 13.40 | 12,467 | 13.50 | Very uncomfortable |

Case 2(MPC strategy) | |||||

λ = 0.00 | 473 | 19.43 | 4123 | 19.50 | Very uncomfortable |

λ = 0.25 | 490 | 20.13 | 2565 | 20.20 | Uncomfortable |

λ = 0.50 | 516 | 21.20 | 1237 | 21.30 | Comfortable |

λ = 0.75 | 527 | 21.62 | 527 | 21.70 | Very comfortable |

λ = 1.00 | 533 | 21.87 | 75 | 21.90 | Very comfortable |

Season | Energy Consumption (KWh) | Economic Cost (£) | Thermal Deviation | Average Room Temp. (°C) | Comfortability |
---|---|---|---|---|---|

Winter | 490 | 20.13 | 2565 | 20.20 | Uncomfortable |

Spring | 492 | 18.30 | 2494 | 20.24 | Slightly comfortable |

Summer | 492 | 20.86 | 2458 | 20.86 | Slightly comfortable |

Autumn | 497 | 16.90 | 2172 | 20.48 | Slightly comfortable |

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**MDPI and ACS Style**

Adegbenro, A.; Short, M.; Angione, C.
An Integrated Approach to Adaptive Control and Supervisory Optimisation of HVAC Control Systems for Demand Response Applications. *Energies* **2021**, *14*, 2078.
https://doi.org/10.3390/en14082078

**AMA Style**

Adegbenro A, Short M, Angione C.
An Integrated Approach to Adaptive Control and Supervisory Optimisation of HVAC Control Systems for Demand Response Applications. *Energies*. 2021; 14(8):2078.
https://doi.org/10.3390/en14082078

**Chicago/Turabian Style**

Adegbenro, Akinkunmi, Michael Short, and Claudio Angione.
2021. "An Integrated Approach to Adaptive Control and Supervisory Optimisation of HVAC Control Systems for Demand Response Applications" *Energies* 14, no. 8: 2078.
https://doi.org/10.3390/en14082078