# Air Conditioning Load Forecasting and Optimal Operation of Water Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Description of Building and Air Conditioning

^{2}and a height of 99.8 m, with a total of 28 floors. The cold source adopted by the hotel is a magnetic suspension water chiller, and an energy management system was added. Data mining technology is used to analyze the monitoring data of the central air conditioning system so as to realize the monitoring and energy-saving diagnosis of the operating energy consumption of the system equipment and provide guidance for the daily operation and maintenance management of the hotel.

#### 2.2. Load-Forecasting Model

#### 2.2.1. Support Vector Regression Principle

_{1}, y

_{1}), (x

_{2}, y

_{2}), …, (x

_{n}, y

_{n})}, the linear regression function of SVR air conditioning load forecasting is given by Equation (1)

#### 2.2.2. Data Dimensionality Reduction Method

#### 2.2.3. Modeling Steps

#### 2.2.4. Model Evaluation Index

^{2}, and calculation time T are used as the evaluation indexes of the prediction performance of the model. In addition, the generalization performance of the model can be evaluated by comparing the RMSE and R

^{2}of the prediction results of the training set and the test set. The calculation formulas of root mean square error and goodness of fit are shown in Equations (4) and (5).

#### 2.3. Operation Optimization of Air Conditioning Water System

#### 2.3.1. Objective Function

#### 2.3.2. Optimizing Control Parameters

#### 2.3.3. Objective Function Constraints

- (1)
- Water chiller load rate is given by Equation (8).$$0.1\le PLR\le 0.9$$
- (2)
- Water chiller temperature is given by Equations (9)–(12).$$7\xb0\mathrm{C}\le {T}_{wo}\le 12\xb0\mathrm{C}$$$$15\xb0\mathrm{C}\le {T}_{ci}\le 35\xb0\mathrm{C}$$$${T}_{wo}\le {T}_{wi}$$$${T}_{ci}\le {T}_{co}$$
_{co}is the outlet temperature of cooling water, °C; and ${T}_{wi}$ is chilled water inlet temperature of water chiller, °C. - (3)
- Chilled and cooling water flow constraints are given by Equations (13) and (14).$$0.4{F}_{cp,0}\le {F}_{cp,all}\le 1.2{F}_{cp,0}$$$$0.4{F}_{wp,0}\le {F}_{wp,all}\le 1.2{F}_{wp,0}$$
^{3}/h, and ${F}_{wp,0}$ is the rated flow of chilled water system at 400 m^{3}/h. - (4)
- Heat-exchange constraints between equipment are given by Equations (15)–(18).$${Q}_{t}={Q}_{ch}+{P}_{ch}=c{m}_{{F}_{cp,all}}({T}_{ci}-{T}_{co})$$$${F}_{cp,all}=\frac{{Q}_{ch}+{P}_{ch}}{c\rho ({T}_{ci}-{T}_{co})}$$$${Q}_{ch}=c{m}_{{F}_{wp,all}}({T}_{wi}-{T}_{wo})$$$${F}_{wp,all}=\frac{{Q}_{ch}}{c\rho ({T}_{wi}-{T}_{wo})}$$
^{3}, ignoring the change of water density caused by the change of water temperature. - (5)
- Optimal cooling amplitude of cooling tower is given by Equation (19).$${t}_{co}-{t}_{wb}=3.5\xb0\mathrm{C}$$

#### 2.3.4. Objective Function Solution

## 3. Results

#### 3.1. Analysis of Load-Forecasting Results

^{2}= 0.9468 for the prediction result of the training set, and RMSE = 130.89, R

^{2}= 0.9289 for the prediction result of the test set. The prediction results of the test set and training set are similar, and the generalization performance of the model is good. The load-forecasting results of the training set and test set are shown in Figure 1.

^{2}= 0.8843 for the prediction results of the training set, RMSE = 180.33, R

^{2}= 0.8630 for the prediction results of the test set. The prediction results of the test set and the training set are similar, and the generalization performance of the model is good. The load-forecasting results of the training set and test set are shown in Figure 2.

^{2}is reduced by 6.6%, the RMSE of the test set is increased by 37.77%, and R

^{2}is reduced by 7.1%, but the modeling process time is reduced by 41.06%. In conclusion, using PCA to reduce the dimension of input parameters can avoid the increase in the model calculation cost caused by too many input parameters, but it will reduce the accuracy of load forecasting, which may be due to the loss of information when extracting principal components from high-dimensionality data.

^{2}= 0.9468, RMSE = 130.89, and R

^{2}= 0.9289; after data dimensionality reduction with PCA, T = 256.74 s, RMSE = 169.72, and R

^{2}= 0.8843 for the prediction results of training set, and RMSE = 180.33 and R

^{2}= 0.8630 for the prediction results of the test set. Therefore, whether PCA is used for dimensionality reduction or not, the prediction results of the test set and training set are similar, which shows that the model has good generalization performance; that is, the operation-load-forecasting method of an air conditioning system based on data mining proposed in this paper is feasible.

#### 3.2. Analysis of Water System Operation Optimization Results

- (1)
- Optimal operation control strategy of a groundwater system with different load rates

- (2)
- Energy consumption analysis of the water system

## 4. Conclusions

- (1)
- The air conditioning load-forecasting model based on the SVR principle has similar prediction results in the test set and the training set, indicating that the model generalization performance is good. Moreover, whether PCA is used for dimensionality reduction or not, the load-forecasting model has good generalization performance. The advantage of PCA is that it can significantly reduce the calculation cost of the SVR model, but it reduces the accuracy of load forecasting. The reason for this may be the information loss caused by extracting principal components from high-dimensionality data.
- (2)
- Based on each equipment model of the water system, the objective function of energy consumption optimization of the water system is established. The operating conditions of each piece of equipment and the energy conservation of the heat-exchange process are taken as the constraint conditions, and the predicted air conditioning load is taken as the disturbance variable. SQP is used to solve the energy consumption optimization problem of the hotel air conditioning water system with controllable variables and disturbance variables and realize the optimization of operating parameters of sewage system at different load rates. After optimization, the average energy-saving rate of the water system with different load rates is 12.40%, which shows that the water system optimization based on load forecasting proposed in this paper has a good energy-saving effect.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Huang, Z.; Gan, L.; Jiang, L.; Shen, Z. Study on the current situation of energy consumption and energy quota of public buildings in Maanshan. Build. Energy Effic.
**2020**, 48, 125–127, 138. [Google Scholar] - Zhang, T.; Lu, Y.; Huang, Z.; Hiroshi, Y. Analysis of the composition of CO
_{2}emissions in residential buildings during the use phase. HVAC**2012**, 42, 106–109. [Google Scholar] - Zhang, Z.; Li, Y.; Zhang, Y.; Wu, X.; Di, H.; Zhang, X. Research and analysis on energy consumption of existing public buildings in hot summer and warm winter areas. Build. Energy Effic.
**2020**, 48, 11–15. [Google Scholar] - Ding, X.; Hu, C.; Liu, X.; Sun, L. Research on energy consumption of typical high star hotel buildings in southern Jiangsu and analysis of energy saving potential. Jiangsu Archit.
**2020**, S1, 90–93. [Google Scholar] - Li, Y.; O’Neill, Z.; Zhang, L.; Chen, Z.; Im, P.; Degraw, J. Grey-box modeling and application for building energy simulations—A critical review. Renew. Sustain. Energy Rev.
**2021**, 146, 111174. [Google Scholar] [CrossRef] - Deb, C.; Schlueter, A. Review of data-driven energy modelling techniques for building retrofit. Renew. Sustain. Energy Rev.
**2021**, 144, 110990. [Google Scholar] [CrossRef] - Cui, Z.; Cao, Y.; Wei, J.; Mao, X.; Li, R.; Tang, Y. Progress of research application of data mining technology in the field of building HVAC. Build. Sci.
**2018**, 34, 85–97. [Google Scholar] - Yan, C.C.; Wang, S.W.; Xiao, F.; Gao, D. A multi-level energy performance diagnosis method for energy information poor buildings. Energy
**2015**, 83, 189–203. [Google Scholar] [CrossRef] - Liang, Z.; Wu, J.; Xie, Z. Identification of actual operation patterns of variable frequency air conditioners and data mining. J. Mech. Eng.
**2019**, 55, 194–202. [Google Scholar] - Zheng, Z.X.; Li, J.Q.; Duan, P.Y. Optimal chiller loading by improved artificial fish swarm algorithm for energy saving. Math. Comput. Simul.
**2018**, 155, 227–243. [Google Scholar] [CrossRef] - Wang, T. Study on Optimization of Chiller Plant and Chilled Water Pump Operation Based on Real Measurement. Master’s Thesis, Dalian University of Technology, Dalian, China, 2017. [Google Scholar]
- Cheng, R.; Yu, J.; Zhang, M.; Feng, C.; Zhang, W. Short-term hybrid forecasting model of ice storage air-conditioning based on improved SVR. J. Build. Eng.
**2022**, 50, 104194. [Google Scholar] [CrossRef] - Feng, C.; Li, Q.; Wang, G.; Li, H. Hourly load forecasting of nZEB in severe cold area based on dest simulation and gs-svr algorithm. J. Shenyang Archit. Univ. (Nat. Sci. Ed.)
**2022**, 38, 149–155. [Google Scholar] - Zhou, X.; Zi, X.; Liang, L.; Fan, Z.; Yan, J.; Pan, D. Forecasting performance comparison of two hybrid machine learning models for cooling load of a large-scale commercial building. J. Build. Eng.
**2019**, 21, 64–73. [Google Scholar] - Wei, D.; Jiao, H.; Feng, H. Nonlinear Predictive Control of Freezing Station System Based on Load Prediction. Control. Theory Appl.
**2021**, 1–12. Available online: http://kns.cnki.net/kcms/detail/44.1240.TP.20210311.1555.032.html (accessed on 12 August 2021). - Li, Z.; Li, C.; Zhu, H. Parameter optimization research based on SVR air conditioning load prediction model. Build. Energy Conserv.
**2021**, 49, 43–48. (In English) [Google Scholar] - Luo, X.; Chen, H.; Lu, X.; Xiong, Y. SVM mill load prediction based on grid search and cross-validation. China Test.
**2017**, 43, 132–135, 144. [Google Scholar] - Liu, G.; Liu, Z.; Yan, J.; Zhou, X. Research on operational characteristics analysis and energy-saving optimized operation method of centralized air-conditioning chilled water system. Build. Sci.
**2018**, 34, 127–140. [Google Scholar]

**Figure 1.**Load-forecasting results without PCA dimensionality reduction. (

**a**) Training set prediction results; (

**b**) test set prediction results.

**Figure 2.**Load-forecasting results after dimension reduction by PCA. (

**a**) Training set prediction results; (

**b**) test set prediction results.

No. | Name | Rated Parameters | Number |
---|---|---|---|

1 | Magnetic suspension water chiller | Cooling capacity 800RT, power 432 kW, rated COP 6.51 | 1 |

2 | Chilled water pump (inverter) | Flow rate 200 m^{3}/h, power 30 kW, lift 33 m | 3 |

3 | Cooling water pump (inverter) | Flow rate 300 m^{3}/h, power 18.5 kW, lift 16 m | 3 |

4 | Cooling tower (fixed frequency) | Air volume 250,000 m^{3}/h, water volume 300 m^{3}/h, fan power 7.5 kW | 2 |

Influence Factor | Main Component 1 | Main Component 2 | Main Component 3 | Main Component 4 | Main Component 5 | Main Component 6 |
---|---|---|---|---|---|---|

N1 | −0.02 | −0.01 | −0.02 | 0.00 | 0.05 | 0.96 |

N2 | 0.02 | 0.10 | 0.08 | 0.26 | 0.02 | 0.00 |

N3 | 0.07 | 0.07 | −0.01 | −0.63 | −0.03 | −0.02 |

N4 | −0.01 | 0.18 | 0.11 | 0.18 | 0.02 | −0.09 |

N5 | 0.33 | −0.15 | −0.02 | −0.10 | −0.05 | 0.00 |

N6 | 0.01 | 0.10 | 0.06 | 0.13 | 0.06 | 0.04 |

N7 | 0.03 | 0.16 | −0.07 | −0.05 | −0.06 | 0.08 |

N8 | −0.01 | 0.20 | −0.05 | −0.07 | 0.01 | 0.07 |

N9 | 0.03 | −0.28 | −0.21 | 0.27 | −0.08 | 0.07 |

N10 | 0.03 | −0.19 | −0.10 | −0.21 | 0.08 | 0.18 |

N11 | −0.25 | 0.45 | 0.00 | −0.13 | −0.13 | 0.06 |

N12 | −0.07 | −0.12 | −0.03 | 0.02 | 0.99 | 0.06 |

N13 | 0.03 | 0.17 | 0.58 | 0.03 | −0.17 | 0.01 |

N14 | −0.05 | 0.06 | 0.48 | 0.02 | 0.17 | −0.04 |

N15 | 0.33 | −0.15 | −0.02 | −0.10 | −0.05 | 0.00 |

N16 | 0.37 | −0.22 | −0.02 | −0.05 | −0.02 | 0.01 |

Work Conditions | Load Rate (%) | Actual Load (kW) | Load Forecasting (kW) | Relative Error (%) | Wet Bulb Temperature (°C) | Cooling Water Discharge Temperature (°C) | Chilled Water Discharge Temperature (°C) | Cooling Water Flow (m ^{3}/h) | Chilled Water Flow (m ^{3}/h) | Energy Consumption of the Water System before Optimization (kw·h) | Optimized Water System Energy Consumption (kw·h) |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 25.4 | 715.9 | 715.9 | 0.00 | 22.79 | 29.13 | 12.00 | 240.0 | 205.2 | 177.0 | 124.9 |

2 | 30.3 | 853.4 | 791.6 | −7.24 | 22.77 | 29.64 | 12.00 | 240.0 | 244.6 | 182.8 | 141.7 |

3 | 35.1 | 988.1 | 983.4 | −0.47 | 24.79 | 32.24 | 11.95 | 240.0 | 276.8 | 210.4 | 183.7 |

4 | 40.6 | 1142.2 | 1192.6 | 4.41 | 23.60 | 31.90 | 11.68 | 240.0 | 308.8 | 244.0 | 211.3 |

5 | 45.7 | 1286.6 | 1268.6 | −1.40 | 25.04 | 33.70 | 11.47 | 240.0 | 309.0 | 264.8 | 235.0 |

6 | 50.1 | 1408.4 | 1387.8 | −1.46 | 24.73 | 32.86 | 11.38 | 240.0 | 329.6 | 284.5 | 250.9 |

7 | 55.2 | 1553.5 | 1507.4 | −2.97 | 24.77 | 34.45 | 11.13 | 240.0 | 334.9 | 329.4 | 283.9 |

8 | 60.3 | 1695.9 | 1676.9 | −1.12 | 24.20 | 34.62 | 10.93 | 240.0 | 354.5 | 418.6 | 321.5 |

9 | 65.3 | 1837.4 | 1911.0 | 4.01 | 26.27 | 37.79 | 10.41 | 240.0 | 357.8 | 432.7 | 405.2 |

10 | 70.9 | 1994.9 | 1994.9 | 0.00 | 28.06 | 38.00 | 10.09 | 314.9 | 349.3 | 513.2 | 442.0 |

11 | 76.0 | 2137.6 | 2220.3 | 3.87 | 27.45 | 38.00 | 9.82 | 323.3 | 368.9 | 525.4 | 510.4 |

12 | 80.4 | 2261.2 | 2268.2 | 0.31 | 28.40 | 38.00 | 9.62 | 383.4 | 362.3 | 535.6 | 533.3 |

13 | 84.8 | 2386.9 | 2400.4 | 0.56 | 28.49 | 38.00 | 9.40 | 414.6 | 368.2 | 617.9 | 580.9 |

14 | 89.0 | 2504.7 | 2594.2 | 3.58 | 27.20 | 38.00 | 9.30 | 371.8 | 391.5 | 687.7 | 645.9 |

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**MDPI and ACS Style**

Huang, Z.; Chen, X.; Wang, K.; Zhou, B.
Air Conditioning Load Forecasting and Optimal Operation of Water Systems. *Sustainability* **2022**, *14*, 4867.
https://doi.org/10.3390/su14094867

**AMA Style**

Huang Z, Chen X, Wang K, Zhou B.
Air Conditioning Load Forecasting and Optimal Operation of Water Systems. *Sustainability*. 2022; 14(9):4867.
https://doi.org/10.3390/su14094867

**Chicago/Turabian Style**

Huang, Zhijia, Xiaofeng Chen, Kaiwen Wang, and Binbin Zhou.
2022. "Air Conditioning Load Forecasting and Optimal Operation of Water Systems" *Sustainability* 14, no. 9: 4867.
https://doi.org/10.3390/su14094867