2.1. Dataset
To study the impact of solar PV implementation and ToU tariffs on religious and educational buildings in the central region of Saudi Arabia, we analyzed the power consumption for several mosques and schools over a complete year.
Load profiles for summer and winter days in the central region of Saudi Arabia were drawn based on the analogy used in [
10] and applied to the 2018 country’s load, as shown in
Figure 1. The ratio of power consumption in the central region of Saudi Arabia to the entire country is 0.32 in the summer and 0.27 in the winter. This difference highlights the impact of weather on power consumption, particularly due to the heavy use of air conditioning during the summer months. The central region of Saudi Arabia is the focal point of this analysis due to its significant population density, favorable climatic conditions, and its high potential for solar PV energy generation.
Figure 2 shows the average hourly loads in a mosque with a capacity of 1500 persons. The difference between the Friday load and other days of the week is related to the congregational prayer (Jummah), which lasts for an average of 40 min and encounters the maximum number of attendees for a prayer. As a result, the day of the week and time of day have a strong influence on the load of a mosque. For example, the load during weekdays is much lower than on weekends since many people are at their offices or schools during the day and will not be able to pray at mosques located in residential areas. In addition, power usage varies across different months due to seasonal factors, such as changes in weather conditions and fluctuations in mosque schedules. For instance, during hotter months, there may be an increased usage of air conditioning systems, while school schedules also influence the number of attendees and thus the power consumption in mosques. These variations contribute to the annual fluctuations in power consumption patterns [
29].
Figure 3 presents the monthly load profile for a school in Riyadh. The pattern of the school’s load is consistent during academic terms. On weekdays, the load starts at 5 am, reaches its peak at 10 am, and falls off at 1 pm. On weekends (Fridays and Saturdays), the load is negligible for most of the time. A similar behavior is observed during holidays.
To provide accurate data for analysis, we also considered the academic term and holiday periods as well as the typical school hours, which span from 7 am to 2 pm. The weekend days are Friday and Saturday. For mosques, prayer schedules and additional activities such as religious lectures were considered. These distinctions between school and mosque activity are crucial for understanding energy consumption patterns. While schools and mosques generally exhibit similar energy consumption patterns influenced by weather throughout the year, notable differences emerge between May and August due to their differing operational schedules. During this period, schools experience a significant reduction in energy use due to summer holidays, whereas mosques remain fully operational and even see an increase in energy consumption during Ramadan, when nightly prayers and religious activities draw larger congregations. Additionally, while the intense summer heat in Riyadh leads to increased air conditioning demand for both types of buildings, the reduced occupancy of schools during this time results in substantially lower energy consumption compared to mosques, which continue to require energy for cooling systems. These operational and seasonal variations account for the distinct differences in their load profiles during these months.
To determine the rooftop spaces in mosques and schools, surveys were conducted on these types of buildings in the central region. Schools have an average area of 1610 m
2. The situation for mosques is different as areas vary greatly. Five models of mosques were created based on capacity, which is defined as the maximum number of worshippers they can accommodate at a single prayer. According to the Ministry of Islamic Affairs statistics book [
30], the central region in Saudi Arabia has 24,931 mosques. However, the statistics book did not categorize mosques based on their capacity. Therefore, there is a need to categorize mosques based on capacity and area.
Power consumption data for several mosques and schools were collected for a complete year to use for forecasting and analysis. Forecasting of school loads was straightforward since it has a direct relation with weather and time. An Artificial Neural Network (ANN) with five hidden layers, Adam optimization, and an adaptive learning rate was used. The ANN was fed by the following features: 2 m temperature (T2M), total cloud cover (TCC), wind speed, partial aerosol optical depth at 550 nm for dust (DUAOD550), previous week demand, day of the year, hour, and holiday features. Weather features were extracted from the Copernicus Atmosphere Monitoring Service (CAMS) at the European Centre for Medium-Range Weather Forecasts (ECMWF) [
31].
For mosques, multiple records were missing. Pre-processing was required to predict the missing values and make the dataset useful. The pre-processing consisted of three phases: dataset preparation, mosque types, and activity modeling.
In the first phase, a forecasting model of mosques was used to predict the power consumption for the missing days [
32]. Prior to this step, power consumption per m
2 was compared between new and old mosques for available days to ensure the suitability of the model. The model predicts loads that include prayers and other events, such as lectures and speeches. Thus, there is a need to subtract those loads from the total load. To do this, a daily load model was created by finding the ratio between the load in each hour and the load during the Maghrib prayer, which is the peak hour most of the time. After that, loads related to lectures and speeches can be identified and subtracted from the total load. In the second phase, the assumption of mosque types was performed by dividing them into five categories similar to the ranking of mosque Imams provided by the ministry. The proposed mosque categories are shown in
Table 1.
In the third phase, events other than prayers were modeled using a random process to predict their occurrence. A Poisson process was chosen to model the inter-activity time. The Poisson process can be defined as a renewal process in which the inter-arrival intervals have an exponential distribution function with a rate of occurrence
[
33]. In this process, the time interval [0, t] is divided into
n subintervals of very short duration
= t/n, with the following conditions holding: (i) the probability of more than one event occurrence in a subinterval is negligible; (ii) event occurrence in a particular interval is independent of the history of outcomes outside this interval.
Figure 4 illustrates the Poisson process chosen to model the inter-activity time.
The probability of an event occurrence
is approximately the binomial probability of
k occurrences in
independent Bernoulli trials with probability
at each trial. In addition, the expected number of event occurrences in the interval
is equal to
. Similarly, the average number of events in the interval
is
, which equals
. While keeping the length
t of the interval fixed, let the period length
reach zero, which implies that the number of periods
n goes to infinity while
remains fixed. Then, the binomial distribution approaches a Poisson distribution with parameter
. Thus, the number of event occurrences
in the interval
has a Poisson distribution with mean
:
Since most of the events occur in the mosque after the Isha prayer at night, it is safe to assume that all events will be held at that time and last for one hour.
Regarding the religious educational sessions, the situation is quite simple. These sessions have clear schedules, starting after the Asr prayer in the afternoon and lasting for two hours. These courses are provided twice per year: from September till November and from January till March. Since many mosques do not provide these kinds of courses, a Bernoulli random distribution was used to determine the number of mosques that will have courses to adjust their load profile.
After the completion of the pre-processing phase, a prediction model for consumed power and generated solar PV power was created. Measurements of power consumption for a mosque and a school were joined with the ERA5 dataset from ECMWF. ERA5 provides hourly estimates of a number of atmospheric, land, and oceanic climate variables [
34]. The features used for this work are listed in
Table 2.
To select features that feed the machine learning model, the Pearson correlation coefficient was used with respect to the consumed power and generated solar PV power.
where
is the correlation coefficient, n is the sample size, and X and Y are random variables. The correlation matrix between all the features is shown in
Figure 5.
As illustrated in
Figure 5, generated solar PV power has a strong correlation with net thermal radiation, TOA solar radiation, solar radiation, and T2M. On the other hand, consumed power is heavily dependent on T2M, TOA solar radiation, solar radiation, Hijri month, day of the week, holidays, and Dhuhr and Maghrib prayers.
Prior to feature selection, the dataset was integrated and cleaned of null and outlier records. Then, the dataset was divided into three subsets: training, validation, and testing, with proportions of 60/20/20. The validation subset was helpful in tuning the model’s hyper-parameters.
To predict power values, K-Nearest Neighbor (KNN) was used. The idea of KNN is based on the similarity of attributes to predict the values of new inputs. In other words, a new point is assigned a value based on a similarity measure and proximity with the points in the training set. The Euclidean distance, defined as the straight-line distance between two points in Euclidean space, was used to calculate the distance between the new point and the points in the training set.
where
n is the number of variables, and
and
are the variables of vectors
x and
y, respectively. To determine the number of neighbors, several values were tested. A
k of five neighbors and a Radial Basis Function (RBF) were found to be the best combination.
2.2. Setup
The main goal of this work is to explore the possibility of installing renewable resources in public buildings and to quantify the benefits of this integration environmentally and economically. Due to the weather conditions in the central region, solar PV was considered to provide clean energy. The main part of a solar PV system is PV cells, which convert solar irradiation into electric power. PV panels consist of several thin layers of semi-conducting material, such as silicon, that generate electrical charges when exposed to light. PV panels can be classified into four categories based on the material used: mono-crystalline, poly-crystalline silicon, amorphous silicon, and thin film. Thin film PV panels have the lowest cost among the four types but also the lowest efficiency [
35]. Similarly, amorphous silicon panels have low efficiency but can be considered a good option since they are less sensitive to high temperatures and shading and have a simple procedure for mass production. Mono-crystalline panels are ranked the best in terms of efficiency, longevity, and space utilization but have a more complicated fabrication process that results in higher costs [
36]. In some cases, poly-crystalline panels can be seen as a cost-effective option despite lower efficiency than mono-crystalline panels [
35].
A 270 W mono-crystalline solar PV panel with dimensions of 1640 × 992 × 40 mm was considered in this analysis. To determine the costs of the solar PV system, assumptions regarding capital costs (CAPEX) from [
36] were applied. A summary of costs associated with the solar PV system is presented in
Table 3.
Several scenarios for the impact on the load profile and monthly bills were studied when the solar PV panels were installed on the rooftops of buildings. Scenarios included PV penetration of 25%, 50%, and 75%. PV penetration refers to the percentage of rooftop space covered by PV panels, where 75% penetration indicates that 75% of the roof area is utilized. We also explored variations in the rooftop area utilization at levels of 25%, 40%, 50%, 60%, 75%, 90%, and 100%. This analysis was in addition to a baseline case where no PV panels were installed.
Net Present Cost (NPC) was used to study the financial impact of PV system integration. NPC is the present value of all the costs related to the installation and operation of the component. It is subtracted from the present value of all revenues that it earns over the project lifetime. Unlike Net Present Value (NPV), all cash flows in NPC are considered outflows compared to the in or out cash flows for NPV [
37]. In NPC calculation, an interest rate of 3% and an inflation rate of 2% were considered. These rates are applied to reflect the time value of money over the lifetime of the project. While interest and inflation rates are crucial in calculating NPC, they are also typically considered in NPV calculations for a comprehensive financial analysis. However, for simplicity, they are primarily discussed here in the context of NPC. Based on these assumptions, a school with 75% PV penetration will have a capacity of 99.6 kW and will cost USD 105,213. This installation will reduce the annual electricity bill to USD 4955. Mosques, for the same PV penetration, will cost between USD 21,163 and USD 120,143 depending on the mosque’s size. These costs reflect the varied installation needs based on the building’s capacity and energy consumption patterns.
Calculation of GHG emissions avoidance was used to highlight the environmental impact of the PV systems. Reference emissions (RE) are calculated based on the avoided emissions from grid electricity using Saudi Arabia’s average grid emission factor of 0.654 tCO
2/MWh [
38]. Since solar PV systems do not produce emissions during operation, project emissions (PE) are considered negligible in our analysis. The annual GHG savings are calculated as the difference between RE and PE. The equation for determining annual GHG savings is as follows:
where
is the energy generated from solar PV in a year in MWh, and
is the average grid emissions factor for a year in tCO
2/MWh.
To quantify the benefits of emission reduction, the social cost of carbon (SCC) was used. SCC is defined as “the monetized damages associated with an incremental increase in carbon emissions in a given year” [
39]. SCC includes several factors, such as human health, losses to agriculture due to global warming, and property damages from increased flood risk. In Saudi Arabia, SCC ranges between 27 and 86 USD/tCO
2, with an average of 47 USD/tCO
2, according to Ricke et al. (2018) [
40]. This range is used in the analysis to estimate the economic impact of the GHG emissions avoided through the use of solar PV systems.
This methodology was applied to evaluate the environmental and economic benefits of integrating solar PV systems into the energy infrastructure of public buildings in the central region of Saudi Arabia. The combination of accurate data collection, predictive modeling, and financial analysis allows for a comprehensive assessment of the potential impact of renewable energy adoption in this region.