Determine the Profiles of Power Consumption in Commercial Buildings in a Very Hot Humid Climate Using a Temporary Series

Abstract

With the growth of the nations, the commercial and public services sectors have recently seen an increase in their electricity usage. This demonstrates how crucial it is to understand a building’s behavior in order to lower its usage. This requires on-site data collection by qualified professionals and specialized equipment, which represents high costs. However, multiple studies have demonstrated that it is possible to find electricity-saving strategies from the study of electricity usage, recorded in an hourly period or less, captured by smart meters. In this context, the present study applies a methodology to determine useful information on the operation and characteristics of public buildings on the Ecuadorian coast based on the data gathered over a period of five consecutive months from smart meters. The methodology consists of four steps: (1) data cleaning and filling, (2) time-series decomposition, (3) the generation of consumption profile and (4) the identification of the temperature influence. According to the results, the pre-cooling of spaces accounts for 5% of all electricity used in the commercial buildings, while prolonged shutdown uses 10%. Approximately USD 1100 per month would be spent on the main building and USD 78 on the agency as a result.

1. Introduction

The appropriate management of energy consumption provides great support for the sustainable development of buildings and even the whole cities. The building sector is a massive energy consumer where there is significant opportunity to reduce energy waste [1]. Occupants and owners face the challenge of improving operational energy performance aimed at minimizing greenhouse gas emissions [2]. In Ecuador, during 2019, electricity consumption data for the commercial sector, services and public administration showed about 28.1% of the total national consumption, occupying the third place behind the industrial and residential sectors [1]. These data have been considered since the years 2020 and 2021 were periods characterized by confinement measures due to the COVID-19 pandemic, and the energy balance of the buildings is highly influenced by human behavior [3].

As part of the infrastructure implemented to provide public services, there are buildings intended for their operation, i.e., office use, technological facilities, collection area, among others. In order to specifically evaluate the energy consumption of these buildings, energy audits are carried out, for which it is necessary to use energy consumption submetering equipment, sensors and other devices. Acquiring these devices implies the availability of a considerable budget [4,5]. Conventional audits involve a physical walk-through of the building that may include leak testing, infrared imaging, door and window tightness testing, among others. In addition, audits require a team of trained personnel to inspect an entire building, involving high costs and considerable time [6].

On the other hand, the real consumption data provide accurate and reliable information about the real energy use behaviors of buildings. By using actual consumption data, it is possible to discover useful information related to electricity use in buildings, including typical daily electricity use patterns and their periodic variation. This information can be used to help improve the energy performance of buildings [7].

Data analytics for assessing the energy performance of buildings has the potential to provide a new solution for assessing energy efficiency, with a renewed approach that leverages analysis of multiple time-series data sets at high resolution, including building energy consumption and climate [8]. An example is the use of a clustering-based strategy to identify consumption patterns that characterize the operation of different types of buildings.

Hossain et al. [9] determined several energy indicators to identify specific operational behaviors and select characteristics of six commercial buildings located in the Köppen–Geiger climatic zones As, Cfa and Csc in the United States. For the analysis of energy consumption, recorded every 15 min, various statistical and machine learning techniques were used, such as clustering, regression analysis and principal component analysis, using the Energy-CRADLE platform. The daily operating pattern, HVAC schedules and base-to-peak load ratio were obtained. Li et al. [7] proposed a clustering-based strategy to identify typical daily electricity usage profiles of 40 university buildings in Australia, from two-year hourly electricity consumption data collected. The first step was to segment the raw data into 24 h segments to form daily electricity usage (DEU) profiles. The second step was to cluster the DEU profiles using a modified k-medoids clustering algorithm. The results showed that the proposed strategy allowed us to identify useful information related to the electricity use behaviors of several buildings, reducing the computational cost up to 97% compared to other methodologies such as Partitioning-Around-Medoids-based clustering strategy.

Another example of data analysis to evaluate the energy performance of buildings is the use of classical time-series decomposition to develop consumption forecasting models, but this approach does not analyze building systems or identify efficiency measures [10]. The time-series decomposition method can identify more specific operational characteristics of buildings and point out opportunities for energy savings. Classical time-series decomposition techniques have been used in a variety of applications including studies of economics, climate, energy and other time-varying phenomena but with limited application to buildings despite the benefits they represent for energy management [4].

Pickering et al. [4] conducted research of electrical energy consumption in six buildings located in the United States where the analysis of electrical energy consumption data at 15 min intervals showed that temperature has a linear correlation with consumption of 0.94 and that enabling quick and inexpensive energy audits can inform economic and energy-saving strategies. The research conducted by Allouhi et al. [11] shows that the end use of energy in commercial buildings depends on the region. It is observed that, in China, the highest growth occurs in the demand for lighting and other applications, such as office equipment, elevators and other electrical equipment. In addition, they found that the continuous monitoring and the complete comprehension of the key factors impacting the buildings’ energy use are required. Wu et al. [12] developed a study on building energy consumption based on data obtained from 50 multi- and single-function buildings. This applied to office buildings and the office sector in comprehensive buildings, excluding heat pumps and cooling systems. On the other hand, in the United States, the most notable growth in electricity consumption is in HVAC and water pumps, the deviations of energy intensity of other sub-items ranged from 3.9% to 16.7%. Also, in the United States, Xiao et al. [13] proposed a method to identify mislabeled commercial buildings based on the analysis of the energy time series collected by electric meters. This focused label adopted a widely used categorization metric, primary space usage (PSU). The method enabled the comparison of buildings with different PSU labels by comparing the temporal features extracted from the energy time series.

In Ecuador, energy management in public buildings is limited due to the high costs of energy audits, the implementation of energy-saving measures, the implementation of energy-management systems, among others. However, according to data provided by the Agency for Regulation and Control of Energy and Non-Renewable Natural Resources [14] (ARC from the Spanish “Agencia de Regulación y Control de Energía y Recursos Naturales no Renovables”), since 2020, 144,911 smart meters have been installed in Ecuador, of which about 20% are in commercial buildings. This equipment collects a large amount of detailed information on electricity consumption from which it is feasible to determine the load profiles [15].

These aspects have motivated this research that proposes to analyze the energy consumption of three buildings, located in the city of Guayaquil, using the methodology of time-series decomposition and to determine its validity to obtain useful information on the operation and characteristics of public buildings on the Ecuadorian coast. The research is carried out through an algorithm developed by Garzón R. [16], for the collection and processing of electricity consumption data (recorded every 15 min), and identifying its correlation with climatic data simultaneously, based on the methodology established in Pickering et al. [4]. National Electricity Corporation (CNEL from Spanish Corporación Nacional de Electricidad) provided the data by downloading information from the smart meters used for electricity billing. This with the objective of obtaining several profiles of electricity consumption and specific behaviors of each building against the outside temperature. To meet this objective, the free software “R” is used to process the databases, then the decomposition of electricity consumption is performed and the Pearson correlation coefficient is calculated. Climate data are collected on site by a meteorological station of the Geological and Energy Research Institute (IIGE from Spanish Instituto de Investigación Geológico y Energético), during 2018, and it was identified that the temperature in Guayaquil varies between 26 °C and 35 °C during the hours of 8:00 to 17:00 [16]. The results show the pattern of electricity consumption during the operation of each building on weekdays and weekends. The methodology of time-series decomposition allowed us to interpret the main characteristics of the buildings that affect electricity consumption and that through proper energy management can reduce consumption, mainly affecting the economic expenditure and reducing CO₂ emissions. Their method was applied to a public data set that comes from the Department of General Services from Washington, D.C., as a case study, and 1000 cases were designed to evaluate the identification accuracy and correction accuracy. The results of the case study showed that 22.4% of the buildings were mislabeled, and there were high mislabel rates in the office buildings.

This study is structured from the definition of the case study, which considers three buildings of commercial and service use corresponding to the public sector located in the city of Guayaquil, Ecuador. This section details the energy-consumption characteristics of each building and the type of use and also considers meteorological data corresponding to the area in which they are located. Then, the study methodology applied for the respective analysis is detailed. Data cleaning and filling, the decomposition of the time series, the generation of consumption profiles and the identification of influential climatic parameters are performed. The results obtained from the consumption profiles that relate electricity consumption as a function of elapsed time in 24 h periods are shown below. Subsequently, in the discussion, the graphs found are analyzed considering the existing correlation with the monitored climatic data and finally the respective conclusions are generated.

2. Case Study

Three public buildings with energy-use indexes (EUI) higher than the average annual consumption value per square meter determined in the study by Vallejo et al. [17] were selected for this study: the Matriz Garzota Integrated Center of CNEL (E1), the 25 de Julio Integrated Center of CNEL (E2) and the Las Orquídeas agency of CNT (E3); see Figure 1a–c. All of them are located in the city of Guayaquil, Ecuador, which belongs to the coastal region. It has a very hot humid climate according to the local climatic zoning with more than 5000 Cooling Degree Days (CDDs 10 °C), and a classification 1A according to ASHRAE 90.1 [18], and belongs to the Aw group (tropical savannah climate), according to the Köppen–Gaige climate classification. During the year, the climate is characterized by two well-defined seasons, humid from January to April and dry the rest of the year. The average monthly temperature variations vary between 23.4 °C and 26.5 °C, and the maximum monthly value reached is greater than 30 °C. It is a humid area because the average monthly relative humidity oscillates between 63% and 76% [19].

Between 2016 and 2019, buildings E1 and E2 consumed on average 263 and 82 kWh/m², respectively, and building E3 consumed 845 kWh/m^2, in the same period. The EUI of the three buildings exceeds the average, 73 kWh/m² for commercial buildings and 342 kWh/m² for telecommunication buildings [17].

The first floor of the three buildings serves as a collection and customer service agency, while the upper floors have different uses. E1 has three floors with a construction area of 6390 m², 82% of which is air-conditioned. The two upper floors are administrative offices. E2 has eight floors with a construction area of 1779 m², 95% of which is air-conditioned. The upper six levels are used to store documents. E3 has two floors with a construction area of 699 m², 95% of which is air-conditioned. The upper floor is used as an equipment room. E1 and E2 are open from Monday to Friday from 8:00 am to 5:00 pm and Saturdays from 8:00 am to 1:00 pm, and E3 is open from Monday to Friday from 8:00 am to 4:30 pm.

The air conditioning system in all the buildings is controlled automatically using thermostats to regulate the interior temperature. Building E2 is an exception, since the ground floor does not have automatic control of the air conditioning system’s start-up temperature; in this case, it is the users who control the start-up manually.

3. Methodology

This section presents the methodology to clean and fill in the available databases, as well as the steps to follow to obtain the components that are part of the fifteen-minute electricity consumption of buildings. This is based on the study carried out by Pickering et al. [4]. Based on the components, the calculation methodology is described to determine the daily characteristic consumption profiles and the influence of climate on them. For this, an algorithm was developed in the R software 4.4.1, using the libraries “lubridate” for date management, “reshape2” for data frame organization; “padr” for filling empty data that meet the criterion every 15 min, “dplyr” for data management such as grouping, adding rows, etc.; “imputeTS” for filling data in time series; “forecast” for the move average function with which it is calculated; and libraries for graphing.

The information on electricity consumption used for the development of this work was provided by CNEL, an electricity distribution company. The data correspond to the total energy registered (every fifteen minutes) by electronic meters for remote metering used for electric service billings. Buildings E1 and E3 have Elster meter models A1052 and Alpha 3, respectively. E2 has an Itron model C1S meter. For the analysis, the same time interval is considered, from August to December 2018. On the other hand, ambient temperature data (°C) collected, during the same period, by a weather station, VAISALA model HMP155, meticulously equipped with a solar radiation shield for optimal precision and installed in the area, owned by the Geological and energy research institute (IIGE from Instituto de investigación Geologico y Energético in Spanish), was used.

3.1. Debugging and Data Filling

Debugging consists of extracting outliers or erroneous and unusual data from all the data. However, there are data that are not necessarily incorrect such as high energy consumption. This is due to situations within the building. In this sense, it is important to distinguish extreme outliers that are defined as values of a magnitude considerably larger than the average [4]. In order to perform the debugging, Equation (1) was used.

(1)$Outlier\ge {\displaystyle \frac{10}{n}}\times \sum _{i=1}^n{E}_i$

where ${\mathit{E}}_{\mathit{i}}$ is the electricity consumption in kWh at any time, and n is the number of observations in the data set. Once these values are detected, they are removed from the data set. Additionally, public holidays during a work week were eliminated due to the unusual occupancy and activities taking place in the building.

Then, the data filling is performed considering each occupancy schedule. In non-working hours, it was performed considering the last consumption recorded in the previous day, since the base load does not vary considerably in consecutive days [20]. In working hours, days with four or more consecutive missing data were eliminated because the filling in of missing data generates errors in subsequent analyses [8]. Linear interpolation was used to fill in working hours [21] using the “na_seadec” function, which uses seasonal interpolation ensuring that seasonal patterns are considered when filling in missing data.

3.2. Time-Series Decomposition

The decomposition of the time series was performed considering the methodology defined by Pickering et al. [4]. An additive model was used because the magnitude of seasonal fluctuations in electricity consumption does not vary with the trend. This model proposes that the sum of the components of a time series results in the original time series, as shown in Equation (2).

(2)$X_t=T_t+S_t+Z_t$

where X_t is the time series with the observed data, T_t is the trend of the time series, S_t is the seasonal component and Z_t is the irregular component.

Smoothed curves through moving averages were used to calculate the trend of the time series. In this work, we used k = 96, which corresponds to the number of observations during one day with a 15 min interval. The trend is obtained by calculating the mean between two days with complete data according to Equation (3).

(3)$T_t={\displaystyle \frac{{\sum }_{j=-k}^k{X}_{t+j}}{2k+1}}$

To calculate the seasonal component, first the trend is subtracted from the original time series (trendless series). Then, the average of data in each time interval is calculated. For this reason, the seasonal component represents 24 h of the day.

To calculate the irregular component, the trend and the seasonal component of the original series are subtracted. The Equation (4) is used to analyze the irregular component.

(4)$Z_t=X_t-T_t-S_t$

The irregular component Z_t, of the time series of the buildings has a normal distribution [4]. The values of this component present a variation that does not influence the final results, so calculating its variance allows us to understand how much energy is missing when using the time-series decomposition. This energy is calculated by Equation (5) and uses a 95% confidence interval.

(5)${\mu }_Z=1.96\times {\displaystyle \frac{{\sigma }_Z}{\sqrt{n}}}$

where 1.96 is the coefficient of the 95% confidence interval of a normal distribution, n is the number of days analyzed, μ_z is the computed uncertainty and σ_z is the standard deviation of the irregular component of the energy consumption.

3.3. Generation of Consumption Profiles

The operation of buildings depends on various factors such as occupancy and equipment, as well as their associated consumption. It is, therefore, important to make subsets of data based on these particular criteria and compare their behavior. Working and non-working days were established as subsets.

To ensure the continuity of the selected data when performing subsets, the following steps were followed according to Pickering et al. [4]: (a) calculation of the trend of the general time series obtained through the methodology described in Section 3.2; (b) the trend was subtracted from the general time series and a trendless time series was obtained; and (c) the new time series was grouped into subsets.

Once all the components of the time series were obtained, the seasonal component plus the mean of the trend value of the time series was used; this takes into account any variation in night time loads, and, in this way, the characteristic consumption profile of the subset analyzed is obtained. The entire procedure described is carried out using a function developed in R, which uses the functions “filter”, “weekdays” to filter specific days, “colMeans” and “mean”, which calculates the means of the decomposed components (seasonality and trend).

3.4. Identification of the Influence of Ambient Temperature on Consumption

To assess the hourly linear correlation between the ambient temperature and energy consumption of each building, it is necessary to identify data distribution. The Kolmogorov–Smirnov test was used to determine the normality of each variable hourly during the study period. The function “ks.test” was used in the R software to obtain the Kolmogorov–Smirnov statistic (D) and p-value. D measures the maximum distance between the empirical distribution of the data and the theoretical normal distribution. The p-value indicates the probability of observing the data under the null hypothesis (data follow a normal distribution). A significance level of 0.05 was used [22].

In order to identify the influence of climatic conditions on building electricity consumption, Pearson’s linear correlation coefficient was calculated, by Equation (6), to measure the strength of the relationship between ambient temperature and electricity consumption. The coefficients can vary from −1, for negative correlations, to +1, which represents a perfect linear correlation. Absolute values of Pearson’s coefficient greater than 0.41, and between 0.26 and 0.40, represent a strong and medium linear correlation, respectively. Values less than 0.25 mean that the linear correlation between the variables analyzed is small or null [23]. According to Tian et al. [24], several researchers have used this method to evaluate the correlation between the energy consumption and different parameters of the building and its environment.

(6)${\mathit{\rho }}_{\mathit{x},\mathit{y}}={\displaystyle \frac{\mathit{c}\mathit{o}\mathit{v}\left(\mathit{X},\mathit{Y}\right)}{{\mathit{\sigma }}_{\mathit{X}}{\mathit{\sigma }}_{\mathit{Y}}}}$

where

• $cov\left(X,Y\right)$ is the covariance of two variable X and Y.

• ${\sigma }_X$ is the standard derivation of X.

• ${\sigma }_Y$ is the standard derivation of Y.

4. Results

The results presented in this section are the product of the methodology applied to the data from the three case studies described, during the period from 1 August–30 December 2018 (152 days).

4.1. Decomposition of the Time Series

The decomposition of the data series allows a general understanding of global energy demand dynamics of the building [25]. Figure 2 shows the decomposition performed on the ambient temperature and electricity consumption data set of the three buildings. For better visualization in the figures, the results of one working week, from 3–8 September 2018, are presented. The four basic components of a classical time-series decomposition are shown: observed, seasonal, trend and irregular. The observed data can be obtained by summing the values of the trend, seasonal and irregular components.

In the first instance, the temperature data are decomposed to highlight the seasonal, trend and irregular characteristics. The seasonal component captures the diurnal temperature oscillation throughout the day and repeats on subsequent days. The trend component shows the overall magnitude and increase or decrease in temperature, while the irregular component shows any deviation in the observed trend component data and the seasonal component data as a whole [4]. The average temperature identified by the trend is 25.4 °C. A maximum decrease of 1 °C is observed on Tuesday and an increase of approximately 1 °C on Wednesday. With respect to the electricity consumption data, a similar decomposition applies.

The representation of the energy performance of building E1 is shown in Figure 3. In building E1, the energy power represents 55 kWh on weekdays. At its extremes, where the weekend begins and ends, a decrease in consumption is observed. Before the beginning of the week, there is a minimum value of 35 kWh, and, at the beginning of the weekend, this value increases to 45 kWh.

The time-series decomposition for E2 is shown in the Figure 4. According to the trend, building E2 has an overall consumption of 4 kWh on weekdays. This building only shows a decrease in consumption before the beginning of the week, reaching an overall consumption of 2 kWh. At the beginning of the weekend, electricity use maintains the same trend as on weekdays. Graphically, the trend component seems to oscillate significantly on weekdays but has a variability of less than 13%. The irregular component shows events due to daily periodicity. These events are probably due to random human interactions during working hours like E1. Outside working hours, they are practically zero and during working hours they can reach up to 4 kWh. Like E1 the seasonal component is repeated five times, due to the daily periodicity caused by usage pattern office equipment and HVAC [26], and its peak load is recorded at 7h00.

Figure 5 shows the time-series decomposition for E3. Building E3 presents a general consumption of 19 kWh. Graphically, at the beginning and end of the weekend, there is a decrease in consumption, 18.25 and 18.75 kWh, respectively. However, the variability is 2%, so it is considered as an almost constant consumption. The irregular component shows events that cannot be explained by daily periodicity and reaches values of up to 2 kWh. This means that, during working hours, the random consumption events are low with respect to the general load of the building. Prolonged time lapses with values close to 0 kWh are also observed. The seasonal component is repeated during the five working days with a variability of 2 kWh. In addition, it is important to note that the overall consumption of the building is never less than 17 kWh, as shown in the observed data.

4.2. Generation of Consumption Profiles

Figure 6 shows the daily consumption profiles, every 15 min, of buildings E1 (Figure 6a), E2 (Figure 6b) and E3 (Figure 6c) in kWh. These figures were displaced taking as a reference the consumption value at 0h00 on each day, so that the analyses start from zero consumption. These three figures show a marked difference between the behavior of weekends and weekdays, as well as the particularity of Monday among weekdays. The negative values of the consumption gradient (∆kWh) at a given time represent a consumption lower than the value identified at 00h00 of the same day. All buildings show different behavior on Saturday, which can be attributed to lower occupancy and different working hours. The first working hours of Monday morning show a decreasing energy consumption, a characteristic that is observed in the last hours of Sunday. This reduction in consumption in the morning shifts the entire Monday curve downward for the rest of the day, but that does not mean that less energy is consumed on Monday than on other workdays. If the time point for the 0 kWh benchmark was moved to approximately 7h00 for all buildings, one would see very similar usage between Monday and the other days of the week. Additionally, this difference can be attributed to many night time systems, such as large equipment, or desktop computers, that are not yet fully operational after being shut down over the weekend or lower employee occupancy.

Building E1 has a time lag of approximately 4 h between working hours (8:00 am to 5:00 pm) and the building’s energy consumption hours (6:00 am to 7:00 pm). Buildings E2 and E3 present a time lag of 2.5 to 3 h compared to the working hours, from 8:00 to 17:00 vs. 7:00 to 18:30 and from 08:00 to 16:30 vs. 7:00 to 18:30, respectively.

From Monday to Friday, building E1 presents a peak consumption gradient of 45 kWh at 7h00, with a duration of 1 h. Then, a steady increase is observed until reaching a maximum value at approximately 17h00. On weekdays, the building consumes between 45 and 90 kWh more electricity (every 15 min) compared to 0h00 each day, while on Sunday consumption remains above 15 kWh. In E2, from Monday to Friday, there is a gradient of maximum consumption at 08h00, and an almost constant consumption from 11h00 to 17h00 with an increase of 8 kWh, compared to midnight. On Sunday, consumption is constant from 0h00 and decreases from 19h00 onwards. Building E3 has two consumption peaks at 8:00 am and 5:00 pm from Monday to Friday, with an increase of 3 kWh compared to 0:00 am. Unlike E1 and E2, on Saturday and Sunday, a similar electricity use is observed with an approximate variation of 0.5 kWh between these days and a higher peak consumption at 18h00.

4.3. Identification of Influential Climatic Parameters

Previous to identifying lineal correlations between energy consumption and outdoor temperature, the Kolmogorov–Smirnov test was performed to determine the normality of data. The results are presented in Table 1.

In building E1, at 21:00 and 22:00, the Kolmogorov–Smirnov test suggests that the data do not follow a normal distribution, while the rest of the hours present low D values and p-values greater than the significance level, so the null hypothesis is not rejected, and it is determined that the data follow a normal distribution. Regarding building E2, at 20:00, the data do not follow a normal distribution. In all other hours, p-values are greater than 0.05, so the data are considered as normally distributed in those time slots. Electrical consumption presents p-values greater than 0.05, which indicates that the data follow a distribution compatible with normality. Finally, at 0h00, 8h00, 21h00, 22h00 and 23h00, the temperature data do not follow a normal distribution, since p-values are less than 0.05. At other times, normality is not rejected, suggesting that the temperature follows a normal distribution.

Taking into account that more than 90% of the data analyzed present a normal distribution, Pearson’s linear correlation coefficient analysis was performed between energy and the corresponding temperature, with the respective confidence intervals and p-values, from Monday to Friday. For each Pearson coefficient, a 95% confidence level was used. This means that p-values less than 0.05 represent a significant correlation between the variables. This result was obtained in order to observe the periods in which electricity consumption is influenced or not by the ambient temperature. Figure 7 shows the Pearson correlation between ambient temperature and power consumption for E1 (a), E2 (b) and E3 (c).

Figure 7a shows that, at night and in the early morning, the Pearson coefficients tend to be low (less than 0.4), with values close to zero, and the confidence intervals include the value 0, meaning that the compression is not significant. From 8:00 am to 5:00 pm, the Pearson coefficients increase and reach values above 0.75. This means that as the temperature increases, the use of electricity increases at that time. The confidence interval does not include 0, and the p-values are less than 0.05, which shows a strong and significant specification. This behavior evidences the use of air conditioning systems for space cooling. On the other hand, a null correlation is observed outside the aforementioned hours because the main electrical loads are not related to space air conditioning.

Building E2 shows a high correlation from 8:00 am to 10:00 am (Figure 7b). Subsequently, a decrease in correlation is observed until 5:00 pm. In this period, the p-values are low so the correlation is statistically significant. This reflects the use of air conditioning systems with a predominant electrical load from 8h00 to 10h00. However, until 17h00, the electrical demand of the air conditioning system is low in relation to the overall consumption of the building. Outside these hours, the behavior is similar to building E1, with negative coefficients being observed during the switching on and off of the buildings.

Figure 7c shows a strong linear correlation from 10h00 to 19h00, identifying the use of air conditioning systems. However, high variability of the coefficients is observed, unlike buildings E1 and E2. In addition, confidence intervals and p-values show statistical significance of the coefficients. This also occurs in the additional hours, where the Pearson coefficient ranges between 0.1 and 0.38. In addition, no negative values are observed in the on and off hours of the building.

5. Discussion

The research helps to determine electricity consumption profiles in commercial buildings in very hot humid climates using a time series. The buildings analyzed in this study were selected because they have a higher EUI than the average value of similar buildings located in the same climate zone. They are also characterized for being buildings in which customer service, administrative and technical activities related to a public service are carried out. For this reason, electricity consumption from Monday to Friday represents more than 80% of the overall consumption of each building.

During the analysis period (1 August to 30 December 2018), building E1 presented an average monthly consumption of 122,342 kWh (19.15 kWh/m²), representing USD 7585.21, considering the electricity tariff corresponding to USD 0.062/kWh [27]. Buildings E2 and E3 consumed on average 9670 kWh (5.43 kWh/m²) and 51,646 kWh (73.88 kWh/m²) per month, respectively. This represents an expense of USD 599 and USD 3202 for electricity use, not including the demand charge, which is considered in the electric service billing.

Despite the similarities in the activities carried out in the three buildings, the intensity of electricity use in the E3 building is four times higher than in E1, which has 6390 m² of construction (nine times larger than E3). This is due to the fact that E3 houses technical equipment that provides telecommunications services to the area. Its consumption represents 94% of the total electricity use, while the remaining 6% is due to the occupation of the building during working hours.

In the decomposition of the time series, the proportion of energy use during the working day is represented by the variability of the seasonal component. In E3, this component varies in the range of −1 to 1, while the other buildings present a wider range with respect to the observed data. On the other hand, by means of the irregular component, it is determined that all electricity consumption that is not associated with an expected or programmed event in E3 occurs at any time. On the contrary, in E1 and E2, they are related to the daily periodicity due to occupancy. This result is due to the operation of the technical equipment in E3, whose electricity consumption depends on different factors associated with its operation. A similar behavior was observed in the studies carried out by [13,28] in which they identified that the occupancy schedule causes different consumption patterns in commercial buildings compared to educational, residential or entertainment buildings. Finally, the seasonal component of the three buildings shows fluctuations in daily consumption, repeating throughout the week.

To analyze the particular characteristics of these fluctuations, daily consumption profiles were obtained in which three stages were identified: On the one hand, one corresponds to the first moment of the day in which the electrical consumption exceeds the night load. Its duration is related to the stabilization of consumption. On the other hand, the occupancy stage corresponds to the working day. Finally, shutdown begins when there is a sudden decrease in consumption and ends when the reference value of electricity used during the night is reached.

Stage: Switch-on

The results obtained from building E1 show that, from Monday to Friday, there is a programmed start-up, at 6:00 a.m., of an air conditioning system for the pre-cooling of spaces. The correlation of electricity consumption associated with this event with the ambient temperature is null. This is because the thermal load evacuated by the system is caused by the accumulation of heat during the night and not by the environmental conditions at that time. The daily profiles show the use of 45 to 50 kWh, for the pre-cooling of the building from 6h00 to 7h30, from Monday to Friday. Similarly, in building E2, the pre-cooling of spaces is performed from 7h00 to 8h00 with a consumption of 6 to 9 kWh every 15 min. Unlike E1, this event also occurs on Saturday from 7:00 to 8:30 am. Unlike E1 and E2, in building E3, there is no pre-cooling; the air conditioning system is turned on at 8h00 and cools the space to the set temperature for 1 h.

The consumption peaks reached by the three buildings before or at the beginning of the working day show that, during the night, there is heat accumulation inside the buildings. The electricity used in E1 and E2 during cooling corresponds to 6% of the total consumption of each building and represents a monthly expense of USD 453 and USD 32, respectively.

Bhikhoo et al. [29] established that, in cities with very hot humid climates, it is beneficial to use passive strategies that allow for exploiting the particularities of the climate. Considering the thermal oscillations that occur in the city, night ventilation is an alternative to reduce the thermal load of buildings during the night.

Stage: Occupation

In the results obtained in [7,9], different typical daily electricity usages were observed for weekdays, weekends and holidays in commercial buildings in which the highest consumption corresponded to working hours. In addition, they identified events of switching on air conditioning systems due to a considerable increase in energy consumption in the morning. Similarly, in building E1, during the occupancy period, the consumption presents an increasing behavior until it reaches its maximum value at 5:00 p.m., two hours after the peak of the ambient temperature. From 7:30 a.m. to 5:30 p.m., additional air conditioning systems are turned on to counteract the thermal load caused by the activities carried out and the environmental conditions and the inertia of the building during this period.

On the other hand, in building E2, during the occupancy period (from 8:00 am to 5:00 pm), the air conditioning system used during pre-cooling is kept on, with a sustained consumption of approximately 7 kWh fifteen minutes. E3 shows an increasing consumption similar to E1; however, its maximum consumption has the same magnitude as the cooling period.

Although the three buildings maintain active air conditioning systems, during the period of occupancy, the influence of temperature on electricity consumption is different. For E1, the Pearson coefficient reaches values greater than 0.6, while for E2 it varies between 0.2 and 0.4. This is due to the fact that, in E1, all the air conditioning systems have automatic control for their operation, so they have a direct response to variations in ambient temperature. In contrast, the air conditioning system on the second floor of E2 has manual control, so its operation does not respond to climatic conditions but to the specific thermal requirements of the permanent occupants. On the other hand, the variation of the Pearson coefficient does not show a pattern related to consumption. This is due to the fact that the air conditioning equipment used in this period is not the predominant electrical load of the building. In no case are values higher than 0.8 obtained due to electrical loads such as office equipment, lighting, among others, whose consumption is not related to temperature.

Stage: Switch-off

From Monday to Friday, from 17h30 to 19h00 in E1, the building is gradually turned off to a nightly consumption of 20 kWh approximately every 15 min. On Saturdays, the air conditioning system is turned off around 13h30. However, night time consumption is reached at 19h00, similar to a weekday, despite the fact that the working day ends at 13h00. During several weekends of the analysis period, the building’s night consumption reached 43 kWh every 15 min. On the other hand, on weekdays, the E2 building decreases its consumption from 17h00 and reaches the night load (1.5 kWh every 15 min) at 18h30. On Saturdays, the shutdown takes place for one hour, from 13h00 to 14h00. In E3, the shutdown stage is shorter, from 17h00 to 18h00. This is evidence that electricity is used more efficiently outside working hours. In E1 and E2, the prolonged shutdown of the building from Monday to Saturday represents 10% and 7.5% of the total consumption, which represents an expense of USD 740 and USD 46 per month. From these events, the restructuring of schedules is identified as a savings opportunity for commercial buildings [30,31]. Hossain et al. [9] identified that this strategy would generate savings of up to 5.6% of electricity consumption in buildings that use HVAC.

On Sundays, no work activities take place in any building. E1 has higher consumption, compared to the night load, during the day and reaches its maximum value after 1:00 p.m. in response to the variation in weather conditions. On the other hand, E2 presents an almost constant consumption throughout the day, similar to the electricity used during the night, while at E3 consumption is similar during the weekend.

The buildings analyzed are in a very hot humid climate zone that does not have a demand for heating throughout the year. Given that the demand for cooling is constant, energy-saving strategies focus on improving the performance of cooling systems, with the management of thermal loads and the control of operational parameters being key aspects for this purpose. In this sense, the results obtained in this research show the potential savings through the restructuring of on and off schedules of air conditioning equipment in office buildings that provide customer service in similar climatic zones.

6. Conclusions

The time-series decomposition of electricity consumption, recorded by smart meters every fifteen minutes, is a valid methodology to obtain useful information on the operation and characteristics of public buildings on the Ecuadorian coast. From the variation of the trend component of the E3 building on Monday, from 0h00 to the beginning of the working day, and the range of variation of the seasonal component, it was possible to identify the constant electricity consumption, from Monday to Sunday, of the telecommunications equipment. While the trend of E1 and E2 presented variations of up to 50%, E3 presented a maximum variation of 2%. On the other hand, through the irregular component, it was identified that during the occupation of buildings E1 and E2, there are unscheduled events, such as the connection of equipment to outlets or equipment other than air conditioning, which cause random electricity consumption. In contrast, in E3, such consumption occurs 24 h a day and is not associated with occupancy.

By determining the daily profiles of the three case studies, it was possible to identify patterns of efficient use. Of the three buildings analyzed, only building E3 has an operation stage coinciding with the working day. For this reason, it does not have electricity expenses associated with the pre-cooling of spaces or the prolonged shutdown of equipment used for the development of activities. However, E1 and E2 use 16% and 13% of the building’s total energy, respectively, due to these events. This represents USD 1100 per month (42 kWh/m2yr) for E1 and USD 78 for E2 (10.66 kWh/m2yr).

During the weekend, it was observed that, on Saturday, there is no pre-cooling of spaces in E1. However, the building is turned off at 19h00, despite the fact that the working day ends at 13h00, using energy without being required. On the other hand, E3 on weekends shows a consumption of 19kWh every 15 min, which corresponds only to the operation of telecommunications equipment since the building is not occupied.

All the operating characteristics of the three case studies were validated through on-site visits and conversations with personnel at the facilities. For this reason, the established profiles serve as input to identify patterns of electricity misuse and identify strategies to achieve savings without affecting the activities carried out.

Time-series decomposition assumes regular patterns of seasonality and trend, which may not adequately capture these irregularities. Unexpected loads and the implementation of strategies to improve energy efficiency could be incorrectly interpreted as noise or outliers. Therefore, it is necessary to know the occurrence of such events in order to analyze the time series for separate time periods. For this reason, the energy consumption of buildings during holidays must be excluded because they altered the normal distribution of the data and modified the consumption profile obtained.

In the Pickering et al. [4] research, a time-series decomposition of electrical consumption of buildings in different climatic zones is performed. However, the type of correlation between energy consumption and ambient temperature was not identified; the buildings did, however, use active air conditioning systems. Through the present study, it was identified that the temperature and hourly energy consumption of a commercial building, which uses cooling systems and is located in a humid and hot climatic zone, present a normal distribution, so it is feasible to identify the linear correlation through straightforward parametric methods such as the Pearson coefficient.

In the present study, the additive model is used because the seasonal component has a relatively constant magnitude over time. However, for future work, a thorough comparison between the additive model and the multiplicative model will be considered as an option. This would include the evaluation of fit metrics such as the Root Mean Square Error (RMSE) to identify which of the two models most accurately describes the dynamics between ambient temperature and electricity consumption.

Author Contributions

Conceptualization, E.C.V.-C., R.G. and M.D.O.L.; Methodology, E.C.V.-C., R.G. and M.D.O.L.; Software, E.C.V.-C. and R.G.; Validation, E.C.V.-C., R.G. and J.M.-G.; Formal analysis, E.C.V.-C. and R.G.; Investigation, E.C.V.-C. and R.G.; Resources, E.C.V.-C.; Data curation, E.C.V.-C. and J.M.-G.; Writing—original draft, E.C.V.-C.; Writing—review & editing, M.D.O.L., J.M.-G. and M.M.; Visualization, E.C.V.-C., J.M.-G. and M.M.; Supervision, J.M.-G. and M.M.; Project administration, E.C.V.-C.; Funding acquisition, J.M.-G. and M.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author. The datasets presented in this article are not available because they are from government buildings. Requests to access the datasets should be addressed to the General Manager of CNEL.

Acknowledgments

The authors thank the National Electricity Corporation (CNEL EP) for providing primary data on the electricity consumption of the buildings analyzed in this research.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. Building images of E1 (a), E2 (b) and E3 (c).

Figure 2. Time-series decomposition of ambient temperature.

Figure 3. E1 time-series decomposition. Measurements are taken every 15 min.

Figure 4. E2 time-series decomposition. Measurements are taken every 15 min.

Figure 5. E3 time-series decomposition. Measurements are taken every 15 min.

Figure 6. Daily energy consumption profiles in E1 (a), E2 (b) and E3 (c) for days of the week. All data from the analyzed period have been used.

Figure 7. Pearson correlation between ambient temperature and power consumption for E1 (a), E2 (b) and E3 (c).

Table 1

Kolmogorov–Smirnov test.

Hour	E1		E2		E3		Air Temperature
	D	p-Value	D	p-Value	D	p-Value	D	p-Value
0h00	0.121	0.129	0.114	0.472	0.055	0.914	0.126	0.021
1h00	0.115	0.165	0.120	0.459	0.063	0.826	0.103	0.096
2h00	0.100	0.322	0.135	0.352	0.052	0.942	0.080	0.325
3h00	0.106	0.231	0.165	0.146	0.068	0.751	0.093	0.168
4h00	0.103	0.255	0.151	0.210	0.085	0.465	0.094	0.159
5h00	0.098	0.314	0.130	0.381	0.071	0.720	0.079	0.350
6h00	0.144	0.968	0.131	0.336	0.078	0.603	0.091	0.193
7h00	0.124	0.119	0.079	0.707	0.051	0.954	0.107	0.081
8h00	0.102	0.247	0.060	0.915	0.076	0.613	0.133	0.012
9h00	0.091	0.377	0.054	0.960	0.066	0.756	0.078	0.348
10h00	0.085	0.467	0.105	0.296	0.090	0.377	0.082	0.283
11h00	0.077	0.578	0.082	0.599	0.059	0.866	0.051	0.850
12h00	0.062	0.812	0.070	0.807	0.047	0.976	0.067	0.536
13h00	0.040	0.996	0.082	0.580	0.058	0.884	0.043	0.950
14h00	0.043	0.991	0.089	0.513	0.046	0.985	0.047	0.906
15h00	0.054	0.922	0.085	0.554	0.084	0.469	0.054	0.792
16h00	0.084	0.457	0.106	0.286	0.052	0.947	0.069	0.492
17h00	0.110	0.175	0.071	0.761	0.086	0.445	0.044	0.938
18h00	0.096	0.661	0.227	0.176	0.055	0.915	0.036	0.992
19h00	0.088	0.679	0.146	0.204	0.053	0.951	0.061	0.650
20h00	0.137	0.050	0.183	0.048	0.057	0.898	0.093	0.166
21h00	0.154	0.023	0.133	0.327	0.052	0.943	0.129	0.017
22h00	0.158	0.018	0.152	0.147	0.059	0.873	0.156	0.002
23h00	0.117	0.143	0.190	0.067	0.047	0.977	0.155	0.002

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