# Machine Learning-Based Estimation of COP and Multi-Objective Optimization of Operation Strategy for Heat Source Considering Electricity Cost and On-Site Consumption of Renewable Energy

^{*}

## Abstract

**:**

_{2}emissions, alongside economic efficiency. This study proposes a mechanism to support stakeholders’ decision-making by calculating Pareto solutions based on the multi-objective optimization of economic and environmental characteristics for entities that own renewable energy generation facilities. Unlike many existing studies that assume a specific equation for COP (Coefficient of Performance) estimation, this study adopts a nonparametric COP estimation method using machine learning, resulting in a more realistic and flexible modeling of the system. The study also presents a model for selecting an operation strategy that balances environmental and economic goals, incorporating a thermal storage facility to improve the renewable energy rate. Specifically, we proposed and compared methods for calculating solutions using only the GA (Genetic Algorithm) and a two-step optimization method combining a GA and gradient-based optimization method, confirming the superiority of the two-step optimization method. The case study unveiled unique operational profiles corresponding to cost-saving, renewable-energy, and balanced orientation points, suggesting the existence of specific strategies tailored to each orientation. The findings of this study can help stakeholders make more informed decisions regarding energy management in air conditioning systems, with benefits for both the environment and the bottom line.

## 1. Introduction

#### 1.1. Background

_{2}emissions and achieving other environmental goals. In this study, we propose a multi-objective optimization approach to develop a strategy for the daily operation of existing HVAC (Heating, Ventilation, and Air Conditioning) equipment. The proposed method aims to minimize power costs while maximizing on-site consumption of renewable energy. It takes into account various variable factors such as equipment efficiency and solar power generation to reflect the reality of daily operations. To verify the effectiveness of our proposed approach, we conduct a case study using actual operating data of multiple heat source equipment and thermal storage units at an airport.

#### 1.2. Related Work

_{2}emissions and power usage costs. The object being optimized here is not the charging and discharging schedule, but rather the capacity and other parameters of the facility while the heat storage and heat dissipation and the charging and discharging are rule-based and fixed. Therefore, this is not a discussion of day-to-day operational strategies. Thus, in the multi-objective optimization of energy systems, including storage batteries, which are similar to the heat source and thermal storage equipment that are the subject of this study, the scale of the system installation that achieves both environmental and economic performance through multi-objective optimization has been calculated, but the effects were obtained through a multi-objective optimization of operational strategies at a certain installation scale. However, there is still room for research on the effects that can be obtained with a multi-objective optimization of operational strategies at a certain scale of installation.

_{2}emissions are also quantified, but they are not considered as objective functions of the multi-objective optimization. Lee et al. [15] performed an optimization of the installed equipment using the particle swarm algorithm to minimize the life cycle cost of air conditioning equipment, including ice thermal storage systems, and found the ice thermal storage air conditioning system. They studied and analyzed the increase in electricity consumption and CO

_{2}emissions due to the use of ice thermal storage air-conditioning systems. Here, the parameters related to the operational strategy and equipment installation were optimized simultaneously. However, CO

_{2}emissions were not the objective function of the optimization, and CO

_{2}emissions were only quantified for the optimization results in pursuit of economic efficiency. In addition, the efficiency COP of air conditioning equipment is fixed and does not consider changes in the COP due to the external environment; Zhou et al. [16] constructed a multi-objective optimization model based on the improved firefly algorithm (IFA) for the rational allocation of cooling load between chillers and ice thermal storage tanks. Energy consumption loss rate and operating cost are set as objective functions and minimized. The use of renewable energy within the energy system is not considered, and it is assumed that the consideration of the COP of the chiller depends only on the magnitude of the output and can be expressed as a quadratic function of the magnitude of the output.

#### 1.3. Contribution of This Paper

#### 1.4. Structure of This Paper

## 2. Methodology

#### 2.1. Machine Learning Based COP Estimation

#### 2.2. Optimization of Operating Strategies for Economic Efficiency in the Case of Heat Source Equipment Only

**:**Heat demand to be supplied [GJ]

^{N}, which was O (2

^{N}). However, since the number of N refrigeration units in an individual air-conditioning system was assumed to be up to about 10 at most, the calculation was assumed to be realistic as far as the air-conditioning system was concerned. In the calculation of ${r}_{i,t}$, Sequential Least Squares Programming (SLSQP) was used. In general, $\frac{{P}_{i}{r}_{i,t}}{CO{P}_{i}\left({T}_{t},{r}_{i,t}\right)}$. in the objective function may have been a non-convex function because it depended on the COP function to be estimated, but if we assumed that increasing the output ${r}_{i,t}$ will increase the power consumption and $\frac{{P}_{i}{r}_{i,t}}{CO{P}_{i}\left({T}_{t},{r}_{i,t}\right)}$. was a monotonically increasing function with respect to ${r}_{i,t}$, it could be optimized with a gradient-based method.

#### 2.3. Multi-Objective Optimization Method Reflecting Economic and Environmental

## 3. Case Study

#### 3.1. Data Condition Setting

#### 3.2. Case Studies of Methods for Estimating COP Based on Actual Operational Data

#### 3.3. Case Study of a Heat Source Equipment Operation Planning Method Considering COP Variation

#### 3.4. Case Study of an Operational Planning Method Capable of Exploring Trade-Offs between Environmental and Economic Performance

## 4. Conclusions

## 5. Future Work

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 18.**Electricity consumption, heat supply, and heat storage through cost-saving oriented operation planning.

**Figure 20.**Electricity consumption, heat supply, and heat storage based on an RE oriented operating plan.

**Figure 22.**Electricity consumption, heat supply, and heat storage based on cost and RE balanced operation plan.

Data Period | 1 January 2021 to 31 December 2021 |

Number of chillers | 4 |

Number of thermal storage unit | 1 |

Chiller No. | Maximum Cooling Capacity [GJ/h] |
---|---|

Chiller 1 | 25.3 |

Chiller 2 | 25.3 |

Chiller 3 | 25.3 |

Chiller 4 | 15.2 |

Thermal storage unit | 12.7 |

Model | MAE | RMSE | MAPE |
---|---|---|---|

SVR(C = 1, kernel = ‘rbf’) | 0.189 | 0.246 | 0.030 |

K-Neighbors Regressor (n_neighbors = 20) | 0.191 | 0.249 | 0.030 |

Random Forest Regressor (max_depth = 10) | 0.201 | 0.259 | 0.032 |

SVR (C = 1, kernel = ‘poly’) | 0.201 | 0.258 | 0.032 |

MLP | 0.352 | 0.411 | 0.055 |

Model | MAE | RMSE | MAPE |
---|---|---|---|

SVR (C = 1, kernel = ‘poly’) | 0.201 | 0.255 | 0.030 |

K-Neighbors Regressor (n_neighbors = 20) | 0.209 | 0.264 | 0.031 |

SVR (C = 1, kernel = ‘rbf’) | 0.210 | 0.263 | 0.031 |

Random Forest Regressor (max_depth = 10) | 0.221 | 0.286 | 0.033 |

MLP | 0.340 | 0.407 | 0.050 |

Model | MAE | RMSE | MAPE |
---|---|---|---|

MLP | 0.615 | 0.757 | 0.065 |

SVR (C = 1, kernel = ‘rbf’) | 0.618 | 0.757 | 0.064 |

K-Neighbors Regressor (n_neighbors = 20) | 0.635 | 0.778 | 0.066 |

Random Forest Regressor (max_depth = 10) | 0.636 | 0.789 | 0.067 |

SVR (C = 1, kernel = ‘poly’) | 0.914 | 1.088 | 0.093 |

Model | MAE | RMSE | MAPE |
---|---|---|---|

SVR (C = 1, kernel = ‘rbf’) | 0.586 | 0.738 | 0.056 |

K-Neighbors Regressor (n_neighbors = 20) | 0.603 | 0.760 | 0.058 |

Random Forest Regressor (max_depth = 10) | 0.605 | 0.763 | 0.058 |

MLP | 0.622 | 0.783 | 0.059 |

SVR (C = 1, kernel = ‘poly’) | 1.016 | 1.244 | 0.112 |

**Table 7.**Comparison of proposed and actual electricity consumption and electricity prices (for COP model SVR).

Item | Actual | Actual after Adjustment for COP | Proposed Method |
---|---|---|---|

Electricity consumption [MWh] | 7326 | 7320 | 7030 |

Electricity cost [thousand yen] | 102,600 | 102,500 | 98,400 |

Reduction rate [%] (vs. actual) | - | - | 4.04 |

Reduction rate [%] (vs. actual after COP adjustment) | - | - | 3.96 |

**Table 8.**Comparison of proposed and actual electricity consumption and electricity prices (for COP model K-nearest neighbor).

Item | Actual | Actual after Adjustment for COP | Proposed Method |
---|---|---|---|

Electricity consumption [MWh] | 7326 | 7302 | 7092 |

Electricity cost [thousand yen] | 102,600 | 102,200 | 99,300 |

Reduction rate [%] (vs. actual) | - | - | 3.20 |

Reduction rate [%] (vs. actual after COP adjustment) | - | - | 2.88 |

COP Estimation Model | Computing Time [s] |
---|---|

SVR: RBF | 445 |

KNN(k = 20) | 1154 |

$CO{P}_{freeze}$: COP (constant) for heat storage (Calculated from actual operation data) | 4.48 |

$CO{P}_{melt}$: COP at heat dissipation (Calculated from actual operation data) | 23.8 |

${I}_{upper}$: Capacity of heat storage [GJ]. | 200 |

${I}_{t}$: Heat storage capacity at the start of time t [GJ]. | 0 |

${p}_{t}^{retail}$: Unit price of electricity purchased from retailers [yen/kWh] | 14 |

${p}_{t}^{pv\_sell}$: Unit price for selling PV power surplus [yen/kWh]. | 12 |

${p}_{t}^{pv\_cost}$: Cost of PV power generation [yen/kWh]. | 8 |

${P}_{freeze}$: Upper limit output for heat storage [GJ]. | 38.0 |

${P}_{melt}$: Upper output limit for heat dissipation [GJ]. | 38.0 |

Number of Search [Times]. | Execution Time [s] | |
---|---|---|

Only GA | 2 Step Method | |

1000 | 470 | 1239 |

2000 | 960 | 2493 |

3000 | 1473 | 3761 |

4000 | 2013 | 4964 |

5000 | 2582 | 6156 |

6000 | 3178 | 7320 |

7000 | 3795 | 8502 |

8000 | 4424 | 9702 |

9000 | 5079 | 10,950 |

10,000 | 5766 | 12,293 |

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## Share and Cite

**MDPI and ACS Style**

Sagawa, D.; Tanaka, K.
Machine Learning-Based Estimation of COP and Multi-Objective Optimization of Operation Strategy for Heat Source Considering Electricity Cost and On-Site Consumption of Renewable Energy. *Energies* **2023**, *16*, 4893.
https://doi.org/10.3390/en16134893

**AMA Style**

Sagawa D, Tanaka K.
Machine Learning-Based Estimation of COP and Multi-Objective Optimization of Operation Strategy for Heat Source Considering Electricity Cost and On-Site Consumption of Renewable Energy. *Energies*. 2023; 16(13):4893.
https://doi.org/10.3390/en16134893

**Chicago/Turabian Style**

Sagawa, Daishi, and Kenji Tanaka.
2023. "Machine Learning-Based Estimation of COP and Multi-Objective Optimization of Operation Strategy for Heat Source Considering Electricity Cost and On-Site Consumption of Renewable Energy" *Energies* 16, no. 13: 4893.
https://doi.org/10.3390/en16134893