# Energy Saving with Zero Hot Spots: A Novel Power Control Approach for Sustainable and Stable Data Centers

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. System Model

#### 3.1. Computing Power Model

_{n,i}(t) = P

_{idel}+ (P

_{active}− P

_{idel}) × n

_{n,i}(t) is the power of the n-th server in the i-th rack at time t; P

_{idel}is the power when the server is idle; P

_{active}is the power when the server is working; and n is the number of the working servers.

#### 3.2. Thermal Model

_{p}fT(t)

_{p}is the specific heat capacity of the air; and f is the air flow rate. So, according to the change in air temperature, we obtain a simplified thermodynamic equation for frame $i$:

_{i}is the air mass in rack i; ${Q}_{in}^{i}\left(t\right)$ is the heat entering the rack; and ${Q}_{out}^{i}\left(t\right)$ is the heat output from the rack. If the cold air coming out of the CRAC can enter the rack without any influence at all, then the inlet air temperature of the rack would be directly equal to the output temperature of the CRAC. However, in reality, the air circulation within a data center is very complex, and the cold air output from the CRAC is influenced by the hot air generated by other racks. Therefore, the heat entering the rack can be expressed as:

_{sup}is the temperature supplied by CRAC; fi is the air flow rate in the rank i.

#### 3.3. Cooling Power Model

_{sup}(t) = ρc

_{p}f

_{sup}T

_{sup}(t). From this, the heat removed by CRAC is:

_{sup}(t)), to indicate the efficiency of the CRAC as a function of the target supply temperature. The power consumption of the CRAC units can then be provided by:

_{sup}(t)) = 0.0068T

^{2}

_{sup}(t) + 0.0008T

_{sup}(t) + 0.458

## 4. Problem Formulation

#### 4.1. Total Cost Model

_{computing}+ C

_{cooling}+ P

_{hs}+ P

_{e}

_{computing}is the energy consumption of computing; C

_{cooling}is the energy consumption of cooling; P

_{hn}is the number penalty for hot spot presence; P

_{ht}is the time penalty for hot spot presence; T

_{0}is the limit temperature in data centers; t

_{j}is the time when hot spots disappear; a is the penalty parameter for the number of hotspots appearance, which is related to total power; and b is the penalty parameter for the time of hotspots presence. These two parameters directly determine the performance of our approach, and their specific determination method is obtained by multiple experimental comparisons.

#### 4.2. Constraint

- Temperature constraint

^{3}and the specific heat capacity of air is 1 kj/kg·c, where the air flow rate when the fan is working is about 10 m/s. From Equation (2), it can be obtained that in the first case, the heat to be removed by dropping 5 °C is 65 W, and in the second case, the heat to be removed by dropping 15 °C is 195 W. From Equation (9), COP (20) = 3.19. We can assume that it takes 1 min to lower 1 °C. By Equation (12), the energy consumed by the CRAC to cool down the returned air to the required temperature is ${P}_{AC,1}=\frac{65}{3.19}\times 300=6114\mathrm{W}$, and ${P}_{AC,2}=\frac{195}{3.19}\times 450=\mathrm{55,008}\mathrm{W}$.

- 2.
- Power input constraint

- 3.
- The total power demand constraint

_{d}is the upper bound of total power demand.

## 5. Modified Self-Adaptive Differential Evolution Algorithm

#### 5.1. Individual Encoding Structure

#### 5.2. Population Initialization

_{0}denotes the value of decision variable j of i, j individual i (i∈{1, 2,..., χ}) in the first generation, and χ denotes the size of the population. The population is initialized as follows:

#### 5.3. Parametric Adaptive Design

_{l}= 0.1, F

_{u}= 0.9, the new F takes a value from (0.1, 1.0) in a random manner. The new CR takes a value from (0, 1). F

_{i,G+}

_{1}and CR

_{i,G}are obtained before the mutation is performed. So they influence the mutation, crossover, and selection operations of the new vector X

_{i,G+}

_{1}.

#### 5.4. Mutation-DE/Current-to-gr-Best/1

#### 5.5. Crossover and Selection

Algorithm 1 HE: Hot spot elimination and Energy saving. |

Input:Task load to be computed in the observed time. - 1.
**Begin**- 2.
- Parameter settings
- 3.
- $a,b,c,e,n,i,{\gamma}_{ji},m,{c}_{p},\rho ,{P}_{active},{P}_{idle},{P}_{max},{P}_{d},\overline{P}\leftarrow $BasicParameterSet()
- 4.
- $J,{T}_{0,sup},\leftarrow $ InterParameterSet()
- 5.
- Perform the Initialization with (19)
- 6.
- Parametric adaptive design with (20) and (21)
- 7.
- $g\leftarrow $1
- 8.
**While**g$\le $G do- 9.
**For i**$\leftarrow $ 1 to I do- 10.
- Perform the mutation with(22)
- 11.
- Perform the crossover with (23)
- 12.
- Perform the selection with (24)
- 13.
**End for**- 14.
- g $\leftarrow $ g + 1
- 15.
**End while**
Output:Solution S contains supply temperature ${T}_{sup}$, computing power ${P}_{computing}$ and minimized total cost ${C}_{min}$. |

## 6. Performance Evaluation

#### 6.1. Parameters Setting

#### 6.2. Experimental Results

#### 6.3. Comparison Results

- (1)
- Our approach can achieve an average temperature below 25 degrees, ensuring that there is no possibility of hot spots throughout the operation of the data center;
- (2)
- Our approach allows for more uniform heat distribution in data centers than others;
- (3)
- Our approach has the smallest difference between the maximum and minimum temperature of the data center racks, contributing to energy savings.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Symbol | Definition | unit |

P_{n},_{i} | The power of the n-th server in the i-th rack at time t | W |

P_{idel} | The power when the server is idle | W |

P_{active} | The power when the server is working | W |

P_{hs} | The total penalty for hot spot presence | ¥ |

P_{e} | The penalty for energy overload | ¥ |

${P}_{AC}$ | The power of cooling | W |

${P}_{hn}$ | The number penalty for hot spot presence | ¥ |

${P}_{ht}$ | The time penalty for hot spot presence | ¥ |

$\overline{P}$ | The nominal parameter for average of power | W |

${P}_{max}$ | The maximum power that can be provided by the data center power supply | W |

${P}_{total}$ | The total energy consumption of all running servers | W |

${P}_{d}$ | The upper bound of total power demand | W |

${Q}_{in}^{i}$ | The heat entering the rack | kJ |

${Q}_{out}^{i}$ | The heat output from the rack | kJ |

${Q}_{rem}$ | The heat that the CRAC has to remove from the air | kJ |

${Q}_{ret}$ | The heat returned from all the racks to the CRAC | kJ |

${Q}_{sup}^{i}$ | The heat supplied to rack i by CRAC | kJ |

${T}_{sup}$ | The temperature supplied by CRAC | °C |

T_{0} | The limit temperature in data centers | °C |

C | The total cost of a data center | ¥ |

C_{computing} | The energy consumption of computing | ¥ |

C_{cooling} | The energy consumption of cooling | ¥ |

a | The penalty parameter for the number of hotspots appearance | ¥/time |

b | The penalty parameter for the time of hotspots presence | ¥/s |

e | The penalty parameter for energy overload | ¥/W |

n | The number of the working servers | unit |

${t}_{i}$ | The time when hot spots appear | s |

${t}_{j}$ | The time when hot spots disappear | s |

c_{p} | The specific heat capacity of the air | J/kg·°C |

${\gamma}_{ji}$ | The percentage of flow from rack j to rack i | % |

${f}_{i}$ | The air flow rate in the rank i | m/s |

F | Zoom factor | |

CR | Crossover probability |

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**Figure 7.**Comparison of the number of hotspots and hotspot elimination time results: (

**a**) case 1, (

**b**) case 2, (

**c**) case 3, (

**d**) case 4.

**Figure 8.**Comparison with the total cost of the four cases: (

**a**) case 1, (

**b**) case 2, (

**c**) case 3, (

**d**) case 4.

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**MDPI and ACS Style**

Li, D.; Zhang, Y.; Song, J.; Liu, H.; Jiang, J.
Energy Saving with Zero Hot Spots: A Novel Power Control Approach for Sustainable and Stable Data Centers. *Sustainability* **2022**, *14*, 9005.
https://doi.org/10.3390/su14159005

**AMA Style**

Li D, Zhang Y, Song J, Liu H, Jiang J.
Energy Saving with Zero Hot Spots: A Novel Power Control Approach for Sustainable and Stable Data Centers. *Sustainability*. 2022; 14(15):9005.
https://doi.org/10.3390/su14159005

**Chicago/Turabian Style**

Li, Danyang, Yuqi Zhang, Jie Song, Hui Liu, and Jingqing Jiang.
2022. "Energy Saving with Zero Hot Spots: A Novel Power Control Approach for Sustainable and Stable Data Centers" *Sustainability* 14, no. 15: 9005.
https://doi.org/10.3390/su14159005