# Analysis of Cooling Load Characteristics in Chinese Residential Districts for HVAC System Design

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## Abstract

**:**

## 1. Introduction

^{2}among households in the same building. An et al. [5] studied the household cooling usage distribution in a community of approximately 400 households and found that the house with the highest energy consumption consumed 8000 kWh of cooling energy in two months, which was equal to three times the average cooling energy use. Brounen et al. [6] investigated 305,001 Dutch homes and found a wide variation in household consumption. Parker et al. [7] verified a home energy-saving suite for an online simulation by conducting a detailed year-long study. The homes studied exhibited a three-fold variation in the measured energy use, with variations at the end-use level being even larger. Gouveia and Seixas [8] revealed the differences in the daily electricity consumption of different households and obtained ten typical residential electricity consumption patterns using clustering to represent the significant differences in daily and total electricity consumption.

## 2. Literature Review and Research Gaps

#### 2.1. Literature Review

**Metrics for individual buildings**.

**Table 1.**Metrics used in analyzing load characteristics of individual buildings in previous studies.

Parameter | Metric | Reference | |
---|---|---|---|

Peak load | Maximum value of hourly loads | [13,14] | |

Total consumption level | Daily average load and seasonal power consumption intensity | [13,14,15] | |

Load volatility | Daily | Hourly load profile | [18] |

$\overline{CV}=\frac{1}{365}{\displaystyle \sum _{j=1}^{365}}\frac{\sqrt{\left({{\displaystyle \sum}}_{i=1}^{24}{\left({P}_{h,ij}-{P}_{d,j}\right)}^{2}/24\right)}}{{P}_{d,j}}$ where P _{h} is the hourly load and P_{d} is the daily average load
| [15] | ||

${\overline{LF}}_{daily}=\frac{1}{365}{\displaystyle \sum _{j=1}^{365}}\frac{{P}_{d,j}}{\underset{1\le i\le 24}{\mathrm{max}}\left\{{P}_{h,ij}\right\}}$ where P _{h} is the hourly load and P_{d} is the daily average load
| [15] | ||

$LR=\frac{averageload}{peakload}$ | [10,13] | ||

$DailyPeak-valleydifferenceratio=\frac{peakload-valleyload}{peakload}$ | [10,13] | ||

Annual relative daily variation, ${G}_{a}=\frac{\frac{1}{2}{{\displaystyle \sum}}_{i=1,j=1}^{8760,365}\left|{P}_{h,i}-{P}_{d,j}\right|}{{P}_{a}\xb78760}\xb7100\%$ where P _{h} is the hourly average load, P_{d} is the daily average load and P_{a} is the annual average load. | [17] | ||

Weekly | $Weeklyimbalancerate=\frac{dailymaximumhourlyload}{maximumhourlyloadintypicalweek}$ | [13] | |

Seasonal/ annual | Load duration curve | [18] | |

$SD=\sqrt{\left({\displaystyle \sum _{i=1}^{n}}{\left({P}_{h,ij}-{P}_{d,j}\right)}^{2}/n\right)}$ where n is the total hours of load, P _{h} is the hourly load and P_{d} is the daily average load
| [10] | ||

$\mathrm{Seasonal}\mathrm{load}\mathrm{rate}=\frac{dailymaximumhourlyload}{maximumhourlyloadinheating/coolingseasons}$ | [13] | ||

$L{F}_{annual}=\frac{{P}_{a}}{\underset{1\le i\le 24,1\le j\le 365}{\mathrm{max}}\left\{{P}_{h,ij}\right\}}$ where P _{h} is the hourly load, P_{d} is the daily average load and P_{a} is the annual average load
| [15] | ||

Annual relative seasonal variation, $W=\frac{24\xb7\frac{1}{2}{{\displaystyle \sum}}_{j=1}^{365}\left|{P}_{d,j}-{P}_{a}\right|}{{P}_{a}\xb78760}\xb7100\%$ where P _{d} is the daily average load and P_{a} is the annual average load. | [17] |

**Metrics for building aggregations**.

**Peak load**

**Load volatility**

**Table 2.**Metrics used in analyzing load characteristics of building aggregations in previous studies.

Parameter | Metric | Analysis Method | Reference | |
---|---|---|---|---|

Peak load | $ADMD=max\left({\displaystyle \sum _{i=1}^{n}}{Q}_{i.t}\right)$ $\mathrm{where}{Q}_{i,t}$ is the hourly load of building i at time t. | Deterministic | [22] | |

Stochastic | [21,23] | |||

$DF=\frac{{{\displaystyle \sum}}_{i=1}^{n}max\left({Q}_{i.t}\right)}{max\left({{\displaystyle \sum}}_{i=1}^{n}{Q}_{i.t}\right)}$ $\mathrm{where}{Q}_{i,t}$ is the hourly load of building i at time t. | Deterministic | [12,21,22] | ||

Stochastic | [24] | |||

$CF=\frac{max\left({{\displaystyle \sum}}_{i=1}^{n}{Q}_{i.t}\right)}{{{\displaystyle \sum}}_{i=1}^{n}max\left({Q}_{i.t}\right)}=\frac{1}{DF}$ $\mathrm{where}{Q}_{i,t}$ is the hourly load of building i at time t. | Deterministic | [15] | ||

$PLR=\frac{{Q}_{AISpeakload}-{Q}_{CSpeakload}}{{Q}_{AISpeakload}}$ ${Q}_{AISpeakload}={\displaystyle \sum}_{i=1}^{n}\mathrm{max}\left({Q}_{i.t}\right)$, ${Q}_{CSpeakload}=\mathrm{max}\left({{\displaystyle \sum}}_{i=1}^{n}{Q}_{i,t}\right)$ $\mathrm{where}{Q}_{i,t}$ is the hourly load of building i at time t. | Deterministic | [9] | ||

Load volatility | Hourly load profile and load duration curve | Deterministic | [18] | |

Daily | $\overline{CV}$$,{\overline{LF}}_{daily}$ (mentioned in Table 1.) | Stochastic | [15] | |

Annual | $L{F}_{annual}$ (mentioned in Table 1.) | Stochastic | [15] | |

$Gini=1-\frac{1}{{n}^{2}\overline{\lambda}}{\displaystyle \sum _{i=1}^{n}}\left(2n-2i+1\right){\lambda}_{i}$ where n. is the total hours of loads, ${\lambda}_{i}$ is the normalized load and $\overline{\lambda}$ is the average value of the weighted normalized load. | Stochastic | [25] |

#### 2.2. Summary and Research Gap

## 3. Data and Method

#### 3.1. Data Collection

#### 3.2. Parameters for Load Characteristics

_{i}represents the instantaneous load at moment i, $\overline{x}$ is the mean value of the hourly load data and n is the amount of hourly load data.

#### 3.3. Analysis Process

## 4. Analysis of Load Characteristics in a Residential District

#### 4.1. Load Diversity among Different Households

^{2}, for which most cases were concentrated in the range 40–90 W/m

^{2}. The peak load distribution was approximately normal. The total load consumption was 0.2–122.4 kWh/m

^{2}/a, and most cases had less than 40 kWh/m

^{2}/a.

#### 4.2. Smoothing Effect of the Cooling Loads

^{2}. Because of the load diversity among different households, the peak loads of different households had different values and occurred at different times; therefore, the peak load of a large system should be much smaller and more stable than an individual peak load.

## 5. Discussion

#### 5.1. Suggestions for HVAC System Design

^{2}, which was close to the average household peak cooling load (i.e., 64.8 W/m

^{2}) but significantly larger than the average value of the peak cooling loads of systems serving 150 households (i.e., 20.4 W/m

^{2}), which was partly because HVAC engineers use the same value to determine the capacity for spilt air conditioners and the chillers of central air conditioning systems. If we use the average value for the individual peak loads of every household to select the chiller, the chiller will most likely be significantly oversized; for example, approximately 3.25 times the actual peak load of the district in the case study, resulting in a waste of investment and the low-efficiency operation of chillers.

#### 5.2. Impact of Sampling Methods on the Load Characteristics

#### 5.3. Limitations

## 6. Conclusions

**Significant load diversity among different households.**In a cooling season, the peak cooling loads of different households was 3.7–123.7 W/m

^{2}, the total load consumption varied from 0.2 to 122.4 kWh/m

^{2}/a and the load distributions and hourly load profiles in one day differ significantly among households. In addition, in most households, cooling is distributed unevenly and the hourly cooling load in one day fluctuates significantly.

**Decreased peak values and fluctuations owing to building aggregation.**Owing to the load diversity among different households, when a system supplies cooling to multiple households, the load volatilities of the different households cancel each other out, further affecting the load characteristics of the system. Therefore, the variation range of the peak load, total load consumption, temporal load distribution, hourly load profile, mean value of peak load, Gini index for temporal load distribution and CV index for hourly load profile decreases rapidly with an increase in system scale until the system serves approximately 50 households, after which the variation range and mean value change less as the system scale increased further. However, the mean value of the total load consumption remains almost constant as the system scale increases.

**Specialized considerations in system design for different building scales.**The different characteristics of the cooling load between large and small systems significantly influence the design of HVAC equipment, such as chillers and energy storage devices. Taking the residential district investigated in this study as an example, an oversized chiller would be selected without considering the smoothing effect of cooling loads in hundreds of households, leading to a waste of investment and low-efficiency chiller operation. In addition, the load distribution of a large system differs from that of a split air conditioner, which can affect the matching of multiple chillers. Therefore, the cooling load characteristics of HVAC systems for different scales should be considered in future designs.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 8.**Cooling load distribution in the cooling season for 177 households: (

**a**) Cumulative distribution of cooling loads; (

**b**) Distribution of Gini index.

**Figure 9.**Hourly cooling load on a typical day for 177 households. (

**a**) Daily cooling load profiles; (

**b**) Distribution of CV index.

**Figure 12.**Variation in total cooling consumption for combinations with different numbers of households.

**Figure 14.**Cumulative distribution of cooling load in a cooling season for combinations of different numbers of households.

**Figure 19.**Comparison of cooling load distribution in a cooling season for combinations with 1 and 150 households.

**Figure 20.**Comparison of Gini index for combinations with 1 and 150 households. (

**a**) 1 household; (

**b**) 150 households.

**Figure 21.**Comparisons of key metrics under five repetitions. (

**a**) Peak load; (

**b**) Total consumption; (

**c**) Gini index; (

**d**) CV index.

**Figure 22.**Comparisons of key metrics with different sampling frequencies. (

**a**) Peak load; (

**b**) Total consumption; (

**c**) Gini index; (

**d**) CV index.

Number | Parameters | Metrics | Applications |
---|---|---|---|

1 | Peak cooling load | Maximum value of hourly cooling load during the cooling season | Total capacity selection of cooling devices |

2 | Total cooling consumption | Sum of hourly cooling load during the cooling season | Evaluation of total cooling consumption |

3 | Temporal load distribution | Gini index to evaluate the distributed load feature in a quantitative way | Selecting different combinations of cooling devices |

4 | Hourly load profile | Coefficient of variation to evaluate the load volatility in one day | Evaluation of control strategy of cooling devices |

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**MDPI and ACS Style**

An, J.; Zhou, X.; Yan, D.
Analysis of Cooling Load Characteristics in Chinese Residential Districts for HVAC System Design. *Buildings* **2023**, *13*, 2450.
https://doi.org/10.3390/buildings13102450

**AMA Style**

An J, Zhou X, Yan D.
Analysis of Cooling Load Characteristics in Chinese Residential Districts for HVAC System Design. *Buildings*. 2023; 13(10):2450.
https://doi.org/10.3390/buildings13102450

**Chicago/Turabian Style**

An, Jingjing, Xin Zhou, and Da Yan.
2023. "Analysis of Cooling Load Characteristics in Chinese Residential Districts for HVAC System Design" *Buildings* 13, no. 10: 2450.
https://doi.org/10.3390/buildings13102450