# Integrated Proactive Control Model for Energy Efficiency Processes in Facilities Management: Applying Dynamic Exponential Smoothing Optimization

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Optimization Approaches for System Efficiency in Sustainable Facilities Management

#### 2.2. Algorithms of Model Predictive Control

## 3. Methodology

#### 3.1. Predicting Temperature Changes: Forecasting Model Using Exponential Smoothing Method

#### 3.1.1. Single ESM Algorithm and Temperature Prediction

#### 3.1.2. Double ESM Algorithm and Temperature Prediction

#### 3.1.3. Triple ESM Algorithm and Temperature Prediction

#### 3.2. Dynamic Exponential Smoothing Optimization Algorithm

- For the values in the time series starting at a point of time $\mathrm{q}$, calculate the correlation coefficient of ${\mathsf{\rho}}_{\mathrm{q}+1},{\mathsf{\rho}}_{\mathrm{q}+2},\dots {\mathsf{\rho}}_{\mathrm{q}+\mathrm{M}}$, where $\mathrm{M}=\sqrt{\mathrm{n}}$, and $\mathrm{n}$ is the size of the series $\left\{{\mathrm{y}}_{1},{\mathrm{y}}_{2},\dots \dots {\mathrm{y}}_{\mathrm{n}}\right\}$. The constant parameter M is the modified length of the time series for correlation calculation. It is used to define the length of the time series. The calculation of M is based on empirical experiments or observations [49,52].
- Calculate the percentages of ${\mathsf{\rho}}_{\mathrm{k}}\le \frac{\mathrm{k}}{\sqrt{\mathrm{n}}}\sqrt{1+2{\displaystyle \sum}_{\mathrm{i}=1}^{\mathrm{t}}{{\mathsf{\rho}}_{\mathrm{i}}}^{2}}$, $\left(\mathrm{k}=1,2,\dots \right)$ in the number of M.
- Depending on whether the percentage of ${\mathsf{\rho}}_{\mathrm{k}}$ falls within the confidence interval and ${\mathsf{\rho}}_{\mathrm{k}}$ distribution in the region $\left[0,1\right]$, determine the stability of temperature time series.

- Traverse each smoothing coefficient ${\mathsf{\alpha}}_{\mathrm{i}}$ within a specific range $\left({\mathrm{such}\text{}\mathrm{as}\text{}\mathsf{\alpha}}_{\mathrm{i}}\in \left[0.1,\text{}0.4\right]\right)$, to calculate the $\mathrm{SSE}\left({\mathsf{\alpha}}_{\mathrm{i}}\right)$. When a value of ${\mathsf{\alpha}}_{\mathrm{i}}$ makes $\left|\mathrm{SSE}\left({\mathsf{\alpha}}_{\mathrm{i}}\right)\right|\le \mathsf{\epsilon}$, the value is selected and the iteration calculation stops.
- If $\left|\mathrm{SSE}\left({\mathsf{\alpha}}_{\mathrm{i}}\right)\right|>\mathsf{\epsilon}$ for all the ${\mathsf{\alpha}}_{\mathrm{i}}$ in the range, the algorithm finds a smoothing coefficient ${\mathsf{\alpha}}_{\mathrm{i}}$ which minimizes the $\left|\mathrm{SSE}\left({\mathsf{\alpha}}_{\mathrm{i}}\right)\right|$ in the range. The corresponding ${\mathsf{\alpha}}_{\mathrm{i}}$ is used as the target value.

#### 3.3. System Verification: Prediction Model Using Multi-Source Data

#### 3.4. Proactive Control Method

## 4. Experiment Design

- Use MATLAB 2014a simulation software (MathWorks, Natick, MA, USA) to analyze the effectiveness of temperature prediction algorithm.
- Analyze the effectiveness of the PCM-DTSP system for temperature simulation.
- Implement the controller program for air conditioners and use the optimized controller to test, analyze, and verify the results.

## 5. Result Analysis

#### 5.1. Analysis of Temperature Prediction Algorithm

#### 5.2. Integration of Predicted and Sensed Temperatures

_{1}”, and the integrated temperature prediction results of “Group A

_{1}”. The prediction results of “Group A

_{1}” provide the foundation for the integration of multiple sensors. Figure 8 shows the integration results of temperature data from multiple sensors. According to the relationship between $\left|\left({\mathrm{T}}_{\mathrm{r}}-{\mathrm{T}}_{\mathrm{c}}\right)/{\mathrm{T}}_{\mathrm{r}}\right|$ and temperature difference rate $\Theta $ as shown in Figure 4, the PCM-DTSP model determines whether ${\mathrm{T}}_{\mathrm{c}}$ is involved in air conditioning coordination control. If ${\mathrm{T}}_{\mathrm{c}}$ participates in collaborative control of cooling systems, the temperature control of the air conditioner is $\mathrm{c}\left(\mathrm{t}\right)={\mathsf{\omega}\mathrm{T}}_{\mathrm{r}}+{\mathsf{\lambda}\mathrm{T}}_{\mathrm{c}}$; otherwise the system uses $\mathrm{c}\left(\mathrm{t}\right)$ to control the air conditioner. In Figure 8, the curve ${\mathrm{T}}_{\mathrm{c}}$ is an integrated result calculated based on the weight information of the Sensors ${\mathrm{S}}_{1},{\mathrm{S}}_{2},{\mathrm{S}}_{3}$, and the workflow in Figure 4.

#### 5.3. Statistical Analysis of Cooling Optimization Based on MPC

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Figure A1.**Forecasting results of static exponential smoothing method: (a) comparison of forecast temperatures and actual data when $\mathsf{\alpha}=0.1$; (

**b**) comparison of forecast temperatures and actual data when $\mathsf{\alpha}=0.2$; (

**c**) comparison of forecast temperatures and actual data when $\mathsf{\alpha}=0.3$; and (

**d**) comparison of forecast temperatures and actual data when $\mathsf{\alpha}=0.4$.

- When the smoothing coefficient $\mathsf{\alpha}=0.1$, as shown in Figure A1a, the static exponential smoothing method can only predict the overall trend of the temperature changes. However, it cannot accurately predict the occurrences of sudden changes in temperatures. The deviations between the predicted results and the actual values are significant. Using the predicted results of this parameter to control cooling systems would lead to serious shortage of refrigeration or excessive cooling supply at a local area in a certain time range.
- When the smoothing coefficient $\mathsf{\alpha}=0.2$, as shown in Figure A1b, relative to the situation when the smoothing coefficient $\mathsf{\alpha}=0.1$, the accuracy of the forecast has greatly improved. The predicted results can reflect local variations of the temperatures. However, it has obvious lags between the predicted results and the actual data. It lacks sensitivity to temperature changes. Using this result to control cooling systems would cause local temperatures to be overheated or undercooled.
- When the smoothing coefficient $\mathsf{\alpha}=0.3$, as shown in Figure A1c, the accuracy of the prediction is greatly improved. The prediction results can reflect local temperature variations. However, it has lags as well. If we use this result to control the cooling systems, it would create uneven cooling situations and waste energy consumption.
- When the smoothing coefficient $\mathsf{\alpha}=0.4$, as shown in Figure A1d, the prediction results have strong jitters, where the peak values of the predicted results exceed the actual detections. If we follow these prediction results, it would exacerbate the phenomenon that the temperature is locally overheated or undercooled. It has a negative impact on the temperature stability. However, the sensitivity of the prediction algorithm is improved compared to the previous parameters.

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**Figure 7.**Chart of dynamic smoothing coefficient changes (the smoothing coefficient is alpha or $\mathsf{\alpha}$).

Type | Example | Feature | Limitations |
---|---|---|---|

Optimize airflow organization of cooling systems | Ham et al. [18] | Modular building; closed cold/hot channels to arrange airflow. | Low efficiency. |

Ogawa et al. [22] | Natural-air cooling systems to reduce energy consumption | Easily affected by exterior temperatures. | |

Hiroshi et al. [19] | Cooling control method based on the predictions of the thermal management requirements at a modular building. | Depended excessively on the air temperature of external environment; Low efficiency. | |

Reduction on redundant cooling supply | Oxley et al. [23] | Improvement of computer room air conditioners (CRAC) for heterogeneous high-performance systems under thermal and energy constraints | Static method, especially when using templates generated offline to assist the online resource manager to make thermal-aware decisions based on the incoming workload and state of the HPC facility. Not been tested by real-world data. |

Ogawa et al. [22] and Durand-Estebe et al. [17] | Optimize the controls of fan speeds. | Only gives the optimized approximating linear manifold in the configuration space represented by the data. | |

Thota et al. [25] | Forecast cooling loads for temperature control; Similar day selection, wavelet decomposition, and neural networks; Different sub-bands (frequency components) and training a separate neural network for each component; | Neural networks cannot be retrained. If users add data later, it is almost impossible to add to an existing network. | |

Huang et al. [20] | Determine the set points of CRAC based on the utilization level of the building. Applied a feedback-control approach on fans to achieve a trade-off between leakage power in circuit and fan power. | Failed to minimize the overall energy consumption of the systems and fans. | |

Zhou et al. [26] | Localized and optimized cooling resources. Adaptive vent tiles mounted on floor and control cooling provisions to reduce costs. | Did not consider the power consumption of fans. | |

Yin and Sinopoli [45] | Coordinated service provision with thermal-load awareness in job scheduling. | Very limited consideration on the dynamic features of cooling systems. |

Cooling Equipment | Group ${A}_{1}$ | Group ${A}_{2}$ |
---|---|---|

Associated Sensor | $\langle {\mathrm{A}}_{1}{|\mathrm{S}}_{1},{\mathrm{S}}_{2},{\mathrm{S}}_{3}\rangle $ | $\langle {\mathrm{A}}_{2}{|\mathrm{S}}_{2},{\mathrm{S}}_{4},{\mathrm{S}}_{5},{\mathrm{S}}_{6}\rangle $ |

Sensor Weights | $\left(\begin{array}{c}{\mathrm{S}}_{1}\left|0.28;{\text{}\mathrm{S}}_{2}\right|0.41;\\ {\text{}\mathrm{S}}_{3}|0.31\end{array}\right)$ | $\left(\begin{array}{c}{\mathrm{S}}_{2}\left|0.23;{\text{}\mathrm{S}}_{4}\right|0.18;\\ {\text{}\mathrm{S}}_{5}\left|0.31;{\text{}\mathrm{S}}_{6}\right|0.28\end{array}\right)$ |

Associated Server | $\langle {\mathrm{A}}_{1}|\begin{array}{c}{\mathrm{SP}}_{1},{\mathrm{SP}}_{2},{\mathrm{SP}}_{3}\\ {\mathrm{SP}}_{4},{\mathrm{SP}}_{6},{\mathrm{SP}}_{7}\end{array}\rangle $ | $\langle {\mathrm{A}}_{2}|\begin{array}{c}{\mathrm{SP}}_{5},{\mathrm{SP}}_{6},{\mathrm{SP}}_{7}\\ {\mathrm{SP}}_{8},{\mathrm{SP}}_{9},{\mathrm{SP}}_{10}\end{array}\rangle $ |

Collection Time | Sensor | The Predicted Value at Different Cycles | Sensor Prediction (from Equation (14)) | Group ${A}_{1}$ Prediction (from Equation (15)) | |||
---|---|---|---|---|---|---|---|

${T}_{i1}\left({A}_{1}\right);{\mathsf{\phi}}_{1}$ | ${T}_{i2}\left({A}_{1}\right);{\mathsf{\phi}}_{2}$ | ${T}_{i3}\left({A}_{1}\right);{\mathsf{\phi}}_{3}$ | ${T}_{i4}\left({A}_{1}\right);{\mathsf{\phi}}_{4}$ | ||||

12 March 2017 08:12:10 | ${\mathrm{S}}_{1}$ | 23.5; 0.4 | 23.7; 0.3 | 23.8; 0.2 | 23.8; 0.1 | 23.65 | 23.58 |

${\mathrm{S}}_{2}$ | 24.1; 0.4 | 24.0; 0.3 | 23.9; 0.2 | 23.8; 0.1 | 24.0 | ||

${\mathrm{S}}_{3}$ | 22.9; 0.4 | 23.0; 0.3 | 23.0; 0.2 | 23.1; 0.1 | 22.97 | ||

12 March 2017 08:17:21 | ${\mathrm{S}}_{1}$ | 23.8; 0.4 | 23.8; 0.3 | 23.9; 0.2 | 24.0; 0.1 | 23.84 | 23.71 |

${\mathrm{S}}_{2}$ | 24.1; 0.4 | 24.0; 0.3 | 23.8; 0.2 | 23.8; 0.1 | 23.98 | ||

${\mathrm{S}}_{3}$ | 23.2; 0.4 | 23.2; 0.3 | 23.3; 0.2 | 23.4; 0.1 | 23.24 | ||

12 March 2017 08:22:05 | ${\mathrm{S}}_{1}$ | 23.8; 0.4 | 23.9; 0.3 | 23.9; 0.2 | 24.0; 0.1 | 23.87 | 23.70 |

${\mathrm{S}}_{2}$ | 23.9; 0.4 | 23.8; 0.3 | 23.8; 0.2 | 23.7; 0.1 | 23.83 | ||

${\mathrm{S}}_{3}$ | 23.3; 0.4 | 23.4; 0.3 | 23.5; 0.2 | 23.6; 0.1 | 23.4 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Temperature setting | 25 °C | Scale coefficient | 0.2 |

Integral coefficient | 0.15 | Differential coefficient | 0.2 |

Integral upper offset | 5 | Integral lower offset | −5 |

Integral separation | 20 | Sampling period | 1000 ms |

Optimization | Avg. Temp. (°C) | Max. Temp. (°C) | Min. Temp. (°C) |
---|---|---|---|

Before | 28.6 | 30.6 | 21.5 |

After | 26.3 | 26.7 | 23.3 |

Optimization | Rated Power (kw) | Avg. Power(kw) | Max. Power (kw) | Min. Power (kw) |
---|---|---|---|---|

Before | 3.56 | 3.43 | 3.48 | 3.39 |

After | 3.56 | 3.26 | 3.31 | 2.85 |

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## Share and Cite

**MDPI and ACS Style**

Ruan, S.; Xie, H.; Jiang, S.
Integrated Proactive Control Model for Energy Efficiency Processes in Facilities Management: Applying Dynamic Exponential Smoothing Optimization. *Sustainability* **2017**, *9*, 1597.
https://doi.org/10.3390/su9091597

**AMA Style**

Ruan S, Xie H, Jiang S.
Integrated Proactive Control Model for Energy Efficiency Processes in Facilities Management: Applying Dynamic Exponential Smoothing Optimization. *Sustainability*. 2017; 9(9):1597.
https://doi.org/10.3390/su9091597

**Chicago/Turabian Style**

Ruan, Shunling, Haiyan Xie, and Song Jiang.
2017. "Integrated Proactive Control Model for Energy Efficiency Processes in Facilities Management: Applying Dynamic Exponential Smoothing Optimization" *Sustainability* 9, no. 9: 1597.
https://doi.org/10.3390/su9091597