A Solution to Prevent a Blackout Crisis: Determining the Behavioral Potential and Capacity of Solar Power

Increasing the power grid peak in the summer time causes power outages in industries and residential areas in Iran. The most obvious example of this issue is the power outages in the summer of 2018. Management of the demand-side is the most important strategy to reduce the grid peak due to the high cost of the development of the power plant capacity (500$ per kilowatt). In the present study, the effect of behavioral parameters in decreasing the power grid peak was identified. The behavioral simulation was done as an agent-based model using the raw data of the time-use survey (TUS) of the Statistics Center of Iran. 4228 urban households were surveyed, and the quality of people’s behavior was determined in each time step of 15 minutes during the day and night with 2 deterministic and stochastic approaches. In the stochastic approach, the Markov chain method was used. It showed that the power grid peak can only be reduced by 10% with behavioral flexibility and up to 25% by upgrading technology. In addition, based on the power deficit in 2018, 2000 megawatts of solar power capacity must be added to the network at peak times to meet grid demand.


Introduction
Air conditioning) AC) is capable of saving lives during warm weather and has a major contribution to peak electricity demand during summer time. Throughout exceedingly hot days or heat waves, such an elevation in energy demand results in brownouts and dimouts [1]. The electric energy and electricity industry are also key factors for the economic system's propulsion in order not to affect the economic system and public security setting [2]. In many countries with significantly demanding seasonal cooling, the role of AC in peak electricity needs is remarkably greater than overall year-round demands. For instance, AC demand in Madrid, Spain, encompassed one-third of overall peak consumption in June 2008 [3]. In such countries as Singapore or most of those in the Middle East, which have completely yearround cooling demands, the AC contribution to peak loads can be as large as 50% or higher [3]. In the plethora of countries, a sharp elevation is predicted in contribution of space cooling to peak electricity loading, and the elevations are uppermost in hot countries, including India, in which the contribution rises from only 10% currently to 45% in 2050 [4]. As many cooling demands are fulfilled with electricitypowered fans or ACs, power systems are greatly influenced by the growing need for cooling. Elevated AC loadings particularly increase not only total electricity requirement but also peak electricity loadings. Application of ACs and electric fans for staying cool comprises approximately 20% of overall electricity, which is currently utilized in buildings worldwide [4,5]. Such a tendency starts to develop as the focus of global economic and demographic development is toward hotter countries. Oftentimes, demand-side management (DSM) programs are primarily aimed at lowering space-cooling loadings via demand response at periods of peak electricity demands [6]. The overall energy requirement of a building results from both its thermic setting and its inhabitants, which have a greater complication in the assessment and quantification than the building envelope and its thermic setting [7]. Therefore, the management of energy demands in buildings requires critical consideration of the behavior of occupants [8,9]. In this research, the amount of cooling load in the power grid peak and its reduction potential by observing behavioral issues in the form of codified scenarios are investigated by studying the behavioral details of household energy consumption using the summertimeuse survey of the Statistics Center of Iran in 2015 and by agent-based modeling of the residential sector in the Tehran. The bottlenecks and important goals pursued in this study are as follows: (1) development of bottom-up modeling tools in terms of behavioral functions; (2) accuracy of estimating the effective cooling load in the peak of Tehran electricity network by different building groups; (3) investigating the effect of increasing technology efficiency, comfort temperature, and a combination of both in the peak of the electricity network; (4) determining the behavioral potentials of reducing cooling energy consumption and its impact on the peak of the electricity network; and (5) determining the share of solar electricity to manage the power grid peak. Behavioral modeling methods in the field of energy with 2 stochastic and deterministic approaches and agent-based and bottom-up modeling methods are reviewed in the literature. The following organization is presented in this study. In Section 2, the background of blackouts in Iran is reported. In Section 3, the study methodological procedure is explained. In Section 4, the results and discussion is represented. And finally, in Section 5, the main research conclusions and discussions are synthesized.

Blackouts and Brownouts in Iran.
The power supply system includes the generation, transmission, and distribution sections, and if any of these sections are disrupted, blackouts will occur [10]. The trend of demand and production capacity at the peak moment from 2007 to 2020 was increasing (from about 35000 MW in 2007 to about 58000 MW in 2020) (Figure 1). During these years, except for 2019 and 2020, the amount of power demand exceeded the production amount at the peak moment. Table 1 shows the hours of the power grid peak in the last 10 years. It is noteworthy that in 2020, the grid peak occurred at night, which indicates that the behavior of the energy consumption is changed and also the peak hours are changed from day to night.
In 2018, the capacity to generate electricity during peak hours was about 8000 MW less than the demand due to reduced rainfall and a sharp decline in the capacity of hydropower plants. If hydropower plants are taken out of operation, the lack of capacity of the country's thermal power plants is about 8000 MW. The plan of the development of the capacity of thermal power plants in 2019 and 2020 was about 7000 MW (Table 2) of which only 1500 MW of new capacity was built.
The share of different power plants in electricity generation and different sectors in electricity consumption is as shown in Figures 2 and 3. To increase energy security, Iran must diversify its energy supply [11] and power plants. The highest electricity generation in Iran is in combined cycle power plants (36%) and the highest electricity consumption is in the industrial (36%) and residential (32%) sectors.
According to the power plant construction process in the country from 1997 to 2020 (Figure 4), the capacity of power   International Journal of Photoenergy plants can be increased by an average of 2000 MW per year, which cannot compensate for the lack of capacity of thermal power plants, especially in years of water shortage. There-fore, to solve the blackout crisis, the solution must be sought along with increasing the capacity of power plants on the demand side [12]. As shown in Figure 5, the industry's electricity consumption in the peak hours of summer 2019 and 2020 is about 5000 MW, which is more than the storage power plants at this time (about 3000 MW). The high consumption of industrial electricity at the power grid peak shows the lack of a specific program in the field of the management of the load in this sector.
The peak of the power grid in most countries of the world, including Iran, is affected by the cooling load. As shown in Figure 6, the share of the cooling load from the grid peak in the United States of America is nearly 30% and in China and South Korea is more than 15% [4].

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The temperature in the hot summer months in Tehran averages about 36 degrees Celsius, which indicates the high potential of cooling electricity consumption in this city (Figures 7 and 8).

Importance of Solar Power in Meeting the Energy
Demands. The demand for solar electricity in the world is increasing, so that by 2050, the cheapest type of electricity is projected to be solar electricity. The installed capacity of solar power plants in the world by 2019 is equal to 627 thousand MW. More than 29 countries had more than a thousand megawatts of solar electricity by 2019 [13]. The price of solar panels is falling with a significant slope [14]. Solar electricity has the largest share of renewable energy types connected to the electricity grid. Some countries, such as Algeria, have paid special attention to solar power to meet the demand of the people [15]. The growth rate of the capacity of solar power plants in the world compared to last year was 28%. Iran has a high potential in the field of solar energy with 1,648,000 km 2 and 300 sunny days and 2200 kW/m 2 of radiation capacity. The distribution of solar radiation capacity in Iran is as shown in Figure 9.

Method: Stochastic and Agent-Based Modeling
The process of stochastic and agent-based modeling of this study is shown in Figure 10. In this research, the variable     3.1. Agent-Based Models. In agent-based simulations that consider behavioral issues, two deterministic and stochastic approaches are used. Deterministic agent-based models follow certain schedules. Schedules include load profiles that are numerically represented between zero and 1 [16]. Stochastic agent-based models use statistical distributions for determining residents' conditions and behavior [17]. Most stochastic models are developed based on the first-order Markov chain techniques [18,19]. Data from stochastic models are extracted from time-use surveys that describe consumer behavior [20]. The number of stochastic agentbased studies is four times more than deterministic approaches [21]. In this research, a stochastic agent-based model is used.

Behavioral Parameters.
Density, presence of residents, and their desired comfort temperature are considered as behavioral parameters of the model. An agent-based cooling simulation that takes into account the presence of individuals differs by approximately 10% from the actual state [22]. This issue shows the high performance of behavioral models to correctly detect the presence of people in the building. It should be noted that most of the behavioral     Figure 11). For instance, Hoyt et al. [23] report that the comfort temperature of cooling and heating reflects the behavioral parameters of the household. The behavioral parameters of the research are presented in Tables 3 and 4. 3.3. Determining the Presence of People in the Building Using Time-Use Survey: A Stochastic Approach. A behavioral data-base of people with the appropriate resolution, which is created by the government in different countries in the form of a time-use survey, is required for stochastic behavioral modeling [24]. The model of Walker and Pokoski [25] is one of the first time-use-based stochastic models. The Richardson model, developed in the United Kingdom based on the 2000 time-use survey, was the inspiration for stochastic behavioral research in this field [18]. The census of the time-use survey conducted by the Statistics Center of Iran    International Journal of Photoenergy in 2014 and 2015 is according to Table 5. Since our study is related to the power grid peak and this peak occurs in the summer, the census data of summer 2015 was used. 15 activity codes and their classification into 9 groups were performed according to Table 6.
The process of extracting the presence/absence statistics of individuals from the raw data of the time-use survey is shown in Figure 12.

Markov Chain.
In the present study, the Markov chain method was used to understand the stochastic presence of people in the house. Most studies with a stochastic approach use the Markov chain method [26]. A Markov chain is a model for displaying a sequence of random variables in which the probability of each event occurring depends only on the previous event. So, the probability of occurrence of events in such a model depends only on the previous time, and other events do not interfere with the probability.
The Markov chain matrix was displayed as a transition probability matrix. P ij indicates the probability of transition from point i to j. In this way, the transition matrix represents the values of the state space set. In the present study, the state space has 2 elements (Equation (2)). The transition probability matrix is also in accordance with Equation (3). The Markov chain matrix can be represented as a transition probability matrix. P ij indicates the probability of transition from point i to j. S = 1, 2 f g= Absence in the building, presence in the building f g , ð2Þ P ij = P 11 P 12 In this matrix, according to the principles of probability, it should be ∑ K J=1 P ij = 1, which is the sum of the probabilities of each row in the matrix must be equal to 1. In general, in the Markov chain, p ij ðnÞ indicates the probability of reaching from state i to j in step.
The transition time step in this study is 15 minutes, and the transition probability matrix for each time step should be determined using the Markov chain. An example of a Markov chain step with and without considering the household dimension (Table 4) is shown in Tables 7 and 8. Table 9 shows the specifications of the bottom-up model used to simulate cooling peak loads. According to the data of the Tehran Municipality website, there are more than 2,867,000 residential houses in eightbuilding groups in the capital of Iran, which in this respect has the largest share in the network peak [27]. In this simulation, the computational core of the EnergyPlus program is used through the user interface of the DesignBuilder software. The open-source and modular features of E+ facilitate the addition of new simulation modules for developers [28]. The computing core has been developed as open-source codes by the US Department of Energy [29]. The Ashrae 90.1 standard is used as the basic mode for simulating new versions of the EnergyPlus Computational Core [16]. The simulated cooling load was converted into electrical load by considering the common cooling equipment in the country according to data of the Statistics Center of Iran (Table 10). A 3-story apartment is simulated for all building groups ( Figure 13). The bottom-up model is extended to all building groups with the archetype method.

Bottom-Up Model.
3.6. Scenarios. In this section, seven scenarios about the comfort temperature and technology upgrade have been developed, and the effects of each on the electric cooling load of the power grid peak are investigated. The formulation of the scenarios is based on the main research model, namely, stochastic and agent-based model.

Lighting and others
Type of air conditioning Figure 11: Influence of different behavioral characteristics of cooling energy consumption from the presence of people and comfort temperature. 7 International Journal of Photoenergy

Data collection method
In this survey, the required household information is collected through face-to-face interviews with the most informed household member and the completion of a questionnaire. Personal information is also collected in a self-reported manner by completing a questionnaire by each person aged 15 years and older in the sample household.

Sample size
This study was conducted in urban areas of the country for 4 seasons. The sample size in the whole statistical year (autumn and winter 2014 and spring and summer 2015) was equal to 16912 households. In summer, 8248 people belonging to 4228 households were referred. 5 Time step Time-use of people every 15 minutes is questioned.   Work and job activities (codes 01 to 05) 02 Working for the family in basic productive activities 03 Working for the household in nonprimary productive activities 04 Working for the family in construction activities 05 Working for the family to provide services for income     [30] and 22% use split coolers [31], one of the ways to control the electricity peak is increasing the efficiency of these two types of widely used cooling equipment in buildings. In this scenario, the dominant grade of cooling equipment in Iran, namely, grade G, has been upgraded to grade A. Behavioral characteristics of people during the day and night are determined based on the results of TUS. Grid stability is considered the same during the day and night.
3.6.5. Combined Scenarios. A combination of the above three scenarios (idea, cold room, and refrigerator) and the technology upgrade scenario is examined. Behavioral characteristics of people during the day and night are determined based on the results of TUS. Grid stability is considered the same during the day and night. (ii) The use of behavioral modeling methods with emphasis on human identity to study the peak of the electricity network has been done for the first time in this research. Lack of data and its integration is one of the limitations of this research (iii) Some of the new concepts introduced in this study, such as behavioral flexibility, did not exist before. Therefore, its formulation was limited  Figure 15, the results of the basic state of the model showed that the electric load of the model on the peak day is 2 to 8% different from the real state, which is a good adaptation.  Figure 17 shows the stochastic and deterministic probabilities of the presence of people in the building. The maximum difference between the probabilities of at least one person at home in a stochastic state with a deterministic state is 5%, which occurs at 14:24. From 12 a.m. to 7:12 p.m., the difference between stochastic and deterministic probabilities is between 2 and 3%. Between 10 and 15 o'clock, the difference between the stochastic and deterministic probabilities is about 2%. From 16:48 to 24, the difference between the stochastic and deterministic probabilities of the presence of people decreases and goes to zero.

Model Validation. According to
The most excellent behavioral flexibility in reducing the peak is 12 to 14 ( Figure 18). Therefore, a strategy in peak shaving is to direct the peak time to these hours.
From 11 a.m. to 5 p.m., the behavioral flexibility potential of household cooling energy consumption is between 70 and 134 MW, which is approximately equal to 10% of the cooling peak of Tehran's electricity grid. Table 11 shows the potential for behavioral flexibility on the network peak day by building groups.
From 1:45 to 6 a.m., the behavioral flexibility potential of household cooling energy consumption is about 50 to 65 MW ( Figure 19 and Table 12), which is approximately equal to 5% of the cooling peak of the Tehran power grid.

4.3.
Results of the Scenario. The cooling load peaks in the refrigerator (1.48 GW) and combined (ideal temperature and technology upgrade) (0.97 GW) scenarios are the maximum and minimum cooling loads in Tehran, respectively. The distance of 500 MW of these two scenarios indicates the high potential of reducing the peak of Tehran's power

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International Journal of Photoenergy grid by adjusting the comfort temperature and technology upgrade. As the efficiency of cooling technologies increases, the average cooling load in all comfort temperature scenarios decreases between 250 and 400 MW, and up to 25% of the network peak is reduced compared to the base scenario. The maximum difference between stochastic and deterministic electric loads in the refrigerator and cold sce-narios is 154 MW and 139 MW, respectively. This shows the flexibility of cooling energy consumption based on the presence of people in the building, in different scenarios. As productivity decreases, the potential for behavioral flexibility in energy consumption increases. The same thing happened in night peak scenarios (Figures 20-33 and  Tables 13 and 14). 30      14 International Journal of Photoenergy

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Conclusions
This study has estimated the electric cooling load of Tehran at the peak moment by stochastic and agent-based modeling. Density, presence of residents, and comfort temperature separately sorted by all building groups are considered as behavioral parameters of the model. Stochastic and deterministic presence of people based on the raw census data of the time-use survey of the Statistics Center of Iran in the summer of 2015, which was performed among 4228 households, was modeled using the Markov chain method for each time step of 15 minutes. The EnergyPlus computing core (DesignBuilder user interface) was used to develop the bottom-up model. In this study, scenarios based on household comfort temperature were developed. The results of this study showed that the most behavioral flexibility in reducing the peak is related to the 12 to 14 o'clock. So, a strategy in peak shaving is to direct the peak time to these hours. From 11 a.m. to 5 p.m., the behavioral flexibility potential of household cooling energy consumption is between 70 and 134 MW, which is approximately equal to 10% of the cooling peak of Tehran's electricity grid. The cooling load peak in the refrigerator (1.48 GW) and combined (ideal temperature and technology upgrade) (0.97 GW) scenarios are the maximum and minimum cooling loads in Tehran, respectively. The distance of 500 MW of these two scenarios indicates the high potential of reducing the peak of Tehran's power grid by adjusting the comfort temperature and technology upgrade. The maximum difference between stochastic and deterministic electric loads in the refrigerator and cold scenarios is 154 MW and 139 MW, respectively. As productivity decreases, the potential for behavioral flexibility in energy consumption increases. As the efficiency of cooling technologies increases, the average cooling load in all comfort temperature scenarios decreases between 250 and 400 MW, and up to 25% of the network peak is reduced compared to the base scenario. The same thing happened in night peak scenarios. This study, we developed possible scenarios of household comfort temperature and technology upgrade that provide a powerful tool for policymakers to manage and control the grid peak, while estimating the behavioral flexibility of reducing the power grid peak (almost 10%) and modeling energy consumption based on behavioral parameters with a resolution of 15 minutes. Based on the power deficit in 2018, 2000 megawatts of solar power capacity must be added to the network at peak times to meet grid demand.

Data Availability
The data used to support the findings of this study are included in the article.