Comparing the Accuracy of Energy Prediction Models Based on Hourly and Daily Mean Outdoor Temperature

*Merve Kuru and Gülben Çalış*

### **Abstract**

It is well known that outdoor temperature highly effects energy consumption in buildings. Accordingly, outdoor temperature is an important parameter for constructing energy prediction models, however; the effect of using data with different time-intervals on the accuracy of models needs to be investigated. This chapter aims at investigating the impact of hourly and daily disaggregated data on the performance of energy models. Data were collected between January and December, 2015 from a commercial building located in Saint-Quentin-en Yveline, France. The daily and hourly HVAC electricity consumption were modeled based on daily mean and hourly outdoor temperature, respectively. The results show that the correlation between daily mean outdoor temperature and daily HVAC electricity consumption is stronger compared to the model based on hourly disaggregated data. Moreover, the correlation coefficient between daily HVAC electricity consumption and daily mean outdoor temperature was obtained as 0.82, whereas it was 0.70 between hourly HVAC electricity consumption and hourly outdoor temperature. The results indicate that hourly disaggregated data does not necessarily improve the accuracy of the energy prediction models.

**Keywords:** energy prediction models, outdoor temperature, disaggregated data, commercial buildings, regression analysis

#### **1. Introduction**

Electrical energy used for heating and cooling in buildings, businesses, and industry consume around half of the energy used in the European Union [1]. Therefore, understanding and predicting the energy consumption of heating, ventilating, and air-conditioning (HVAC) systems are beneficial for energy engineers, electricity providers, end-users, and policy makers in addressing energy sustainability challenges, the expansion of distribution networks, energy pricing, and policy development. In order to have accurate prediction models, the most influencing factors have to be included in the models [2]. Many researchers state that the outdoor temperature is an important factor that effects the HVAC energy consumption in buildings. Wu et al. [3] indicated that the outdoor temperature has a significant effect (R value = 0.905), whereas solar radiation has little somewhat

effect (R value = 0.32) on the building's energy consumption. In another study [4], it is indicated that the outdoor temperature has a significant effect on building's energy consumption (R value = 0.691), whereas the effect of relative humidity is statistically insignificant. Neto et al. [5] stated that the outdoor temperature is more important than solar radiation and relative humidity for predicting energy consumption. Li [6] found that the outdoor temperature was the most important factor that influences the residential electricity consumption (R value = 0.68).

 Accordingly, many researchers [7–17] constructed energy prediction models based on the outdoor temperature. KC and Ruth [18] investigated the relationship between outdoor temperature and institutional building electricity consumption by using data with 15 min intervals. The authors aggregated the data to calculate daily electricity use. Moreover, they aggregated outdoor temperature data, which was obtained from the local weather station with hourly intervals, to calculate daily mean outdoor temperature. Braun et al. [19] investigated the relationship between weather conditions and energy consumption via multiple regression (MR) analysis. The outdoor temperature and relative humidity data with 15 min intervals were obtained from a sensor whereas the gas and electricity data with hourly intervals were collected from the energy website of the company. The models were constructed for predicting weekly energy consumption. Li [6] also performed a MR analysis to establish the link between outdoor climate and residential electricity consumption. The study was conducted in Singapore between 2005 and 2016. The monthly average electricity consumption data of residential houses was obtained from Energy Market Authority. In addition, the outdoor climatic data were obtained from Meteorological Service Singapore. Amber et al. [20] developed several electricity consumption forecasting models for buildings in the UK. Moreover, climatic data including outdoor temperature, relative humidity, and wind speed were extracted in the form of daily mean values. Lai et al. [21] developed a prediction model for electricity consumption of a residential building by using the hourly energy consumption data as well as daily climate data including outdoor temperature and relative humidity. To unify the time interval of data, the authors aggregated the hourly energy consumption data to daily consumption data. On the other hand, Mathieu et al. [22] presented methods to analyze the electricity load data of a commercial and industrial (C and I) facility. The energy consumption data with 15 min intervals were obtained from the Pacific Gas and Electric Company, whereas the hourly outdoor temperature data was obtained from the nearest weather station. In order to construct an electricity model with 15 min interval, the authors interpolated the outdoor temperature data that matches to every 15 min interval. Yezioro et al. [23] constructed an hourly heating and cooling electricity consumption prediction model by using hourly weather data including the outdoor temperature, relative humidity, and set-point temperature, which were obtained from the Pennsylvania State Climate Office. Kwok and Lee [24] constructed an ANN model for simulating the hourly cooling consumption of an office building in Hong Kong. The authors obtained hourly climatic data from the Hong Kong Observatory and the actual data were collected from the air conditioning system of the building. Yuan et al. [25] used hourly electricity consumption and hourly weather data including outdoor temperature, relative humidity, and global radiation to develop ANN models for forecasting the hourly electricity consumption. The literature review shows that the models are generally constructed by using hourly and daily data. In other words, there is no consensus on the time interval of data that is used in the models. However, the effect of using hourly and daily disaggregated data on the performance of the prediction models has to be investigated.

This chapter aims at investigating the impact of using hourly and daily disaggregated data on the performance of energy prediction models. Data were collected between 01 January and 01 December, 2015 from a commercial building located in Saint-Quentin-en Yveline, France. The daily and hourly HVAC electricity

*Comparing the Accuracy of Energy Prediction Models Based on Hourly and Daily Mean Outdoor… DOI: http://dx.doi.org/10.5772/intechopen.87836* 

consumption models were constructed based on daily mean and hourly outdoor temperature, respectively. The following sections of the chapter describe datasets and methodology. Then, findings and conclusions are presented.

#### **2. Dataset and methodology**

#### **2.1 Dataset**

 The case study was conducted in an office building with 68,000 m<sup>2</sup> located in Saint-Quentin-en Yveline, France. The hourly and daily HVAC electricity consumption between 01 January and 01 December, 2015 was collected from the building management system. Moreover, the outdoor temperature was obtained from the nearest weather station. The hourly as well as daily energy consumption data was modeled based on using the hourly outdoor temperature data. It should be noted that weekends and public holidays were not included in the models since the building is not occupied during these days and the actual HVAC electricity consumption is observed as zero. In summary, a total of 223 daily mean and 3122 hourly outdoor temperature, as well as 223 daily HVAC electricity consumption and 3122 hourly HVAC electricity consumption data were used in the analysis.

#### **2.2 Methodology**

Statistical analyses were conducted to investigate the difference between the accuracy of the models constructed by using hourly and daily disaggregated data. Within this context, the correlation coefficient between variables and how much of the change in dependent variable (HVAC electricity consumption) can be associated to the change in independent variable (outdoor temperature) was investigated.

 The Pearson correlation coefficient is an indicator of the strength of the relationship between the variables when the variables are normally distributed and there is a linear relationship between them. On the other hand, if the variables are normally distributed, there is no linear relationship between them (i.e., there is a quadratic relationship) and there is a cause-effect relationship between the variables, regression analysis is carried out and the correlation coefficient is calculated to measure the strength of the relationship. First step in the statistical analyses is creating the scatter plot to understand the relationship between the variables. Then, the goodness of fit tests are conducted to check the normality of the variables. If there is quadratic and cause-effect relationship between the variables, the regression analysis is conducted. The regression parabola that best fits the data is drawn via a statistics program like SPSS. It should be noted that IBM SPSS Statistics V22.0 is used in this study. In addition to drawing the parabola, the statistics programs also output the correlation coefficient and a formula which is a prediction model.

The statistical significance of this model and the coefficient is checked with F test at significance level 0.05. However, this is not adequate to say that the model and the coefficient are appropriate. The appropriateness of the model should be assessed by defining residuals. For quadratic regression, residuals must be normally distributed.

In this study, the following steps were conducted in the analyses:


#### **3. Findings**

 **Figure 1** shows the scatter plots of daily HVAC electricity consumption versus daily mean outdoor temperature and hourly HVAC electricity consumption versus hourly outdoor temperature. The scatter plots show that there are quadratic relationships between HVAC electricity consumption and outdoor temperature. It should be noted that there is a cause-effect relationship between the HVAC electricity consumption and the outdoor temperature, where the HVAC electricity consumption (HVAC) is a dependent variable and the outdoor temperature (T) is an independent variable. Based on these facts, quadratic regression analyses were conducted to obtain the degree of relationships between daily independentdependent and hourly independent-dependent variables.

#### **Figure 1.**

*Scatter plots daily HVAC electricity consumption versus daily mean outdoor temperature and hourly HVAC electricity consumption versus hourly outdoor temperature.* 

*Comparing the Accuracy of Energy Prediction Models Based on Hourly and Daily Mean Outdoor… DOI: http://dx.doi.org/10.5772/intechopen.87836* 

 The prerequisite for regression analysis is the normality of variables. Therefore, the Kolmogorov-Smirnov normality tests were conducted to check whether or not the data set is normally distributed, and the results are shown in **Table 1**. The *p*-values seen in the table are the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. Therefore, the results shown in **Table 1** indicate that daily mean outdoor temperatures are normally distributed at significance level 0.05, since the *p* value is higher than 0.05 whereas other variables are not normally distributed since their *p* values are lower than 0.05. However, it should be noted that if the skewness and kurtosis values of variables are between −2 and +2, then the distribution of variables can be assumed as normal distribution [26]. Therefore, it can be concluded that all variables distribute normally since their skewness and kurtosis values are within the range of −2 to +2 (**Table 1**).

 Next, the quadratic regression analyses were carried out via the SPSS program and the correlation coefficients (R) were calculated as 0.82 and 0.70 for daily and hourly relationships between HVAC electricity consumption and outdoor temperature, respectively. It should be noted that *p* values of F tests were obtained as 0.000 at the 0.005 significance level, which indicate that the coefficients are statistically significant. Moreover, the coefficients of prediction models are statistically significant at 0.05 since their *p* values are lower than 0.05 (**Table 2**).

The prediction models for HVAC electricity consumption according to the daily mean and hourly outdoor temperature were obtained as follows:

$$\text{dailyHVAC} = 0.528 \times T\_d^2 - 13.133 \times T\_d + 108.218, \text{R}^2 = 0.678 \tag{1}$$

$$\text{A boundaryHVAC} = \text{0.028} \times T\_h^2 - \text{0.796} \times T\_h + \text{7.363}, \text{R}^2 = \text{0.489} \tag{2}$$

The results indicate that approximately 68% of the change in the daily HVAC electricity consumption can be associated to the change in the daily mean outdoor temperature [Eq. (1)], whereas approximately 49% of the change in the hourly HVAC electricity consumption can be associated to the change in the hourly outdoor temperature [Eq. (2)].

**Figure 2** presents the actual HVAC electricity consumption datasets against the predicted HVAC electricity consumption dataset obtained from these models.

 It should be noted that residuals must be normally distributed to assure the significance of the correlation coefficients and appropriateness of these prediction models. The results of residuals' Kolmogorov-Smirnov normality tests shown in **Table 3** indicate that the residuals are not normally distributed at significance level 0.05, since their *p* values are lower than 0.05. However, it can be assumed that the residuals are normally distributed because their skewness and kurtosis values are within the range of −2 to +2 [26].


#### **Table 1.**

*The normality tests' results and skewness and kurtosis values of variables.* 


#### **Table 2.**

*The coefficients of prediction models.* 

**Figure 2.**  *Scatter plots of the actual and predicted HVAC electricity consumption vs. outdoor temperature.* 

*Comparing the Accuracy of Energy Prediction Models Based on Hourly and Daily Mean Outdoor… DOI: http://dx.doi.org/10.5772/intechopen.87836* 


**Table 3.** 

*The normality tests' results and skewness and kurtosis values of residuals.* 

### **4. Conclusion**

In this study, the quadratic regression analyses were carried out to understand the relationship between (1) daily HVAC electricity consumption and daily mean outdoor temperature and (2) hourly HVAC electricity consumption and hourly outdoor temperature. For the analyses, the datasets between 01 January and 01 December, 2015 were obtained from a commercial building located in Saint-Quentin-en Yveline, France. The main findings can be listed as follows:


The results show that the correlation between daily mean outdoor temperature and daily HVAC electricity consumption is stronger compared to the model based on hourly HVAC electricity consumption and hourly outdoor temperature. The findings of this study indicate that high temporal resolution of outdoor temperature and HVAC electricity consumption do not necessarily improve the accuracy of the energy consumption modeling.

#### **Acknowledgements**

This work has received funding from HIT2GAP "Highly Innovative building control Tools Tackling the energy performance gap" project of the European Union's Horizon 2020 research and innovation programme under grant agreement number No. 680708.

*ISBS 2019 - 4th International Sustainable Buildings Symposium* 

#### **Author details**

Merve Kuru and Gülben Çalış\* Civil Engineering Department, Ege University, İzmir, Turkey

\*Address all correspondence to: gulben.calis@ege.edu.tr

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Comparing the Accuracy of Energy Prediction Models Based on Hourly and Daily Mean Outdoor… DOI: http://dx.doi.org/10.5772/intechopen.87836* 

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#### Chapter 52
