1. Introduction
Refrigeration cycles were developed in the latter part of the nineteenth century. Since then, engineering systems employing these thermodynamic cycles have proliferated, serving a variety of applications in food refrigeration and freezing, ice production, gas liquefaction, and air conditioning (A-C). In the first part of the twenty-first century, A-C systems have become required fixtures in the buildings of most developed countries and are quickly making inroads in the rest of the world. As a result, heating, ventilation, and air conditioning (HVAC) systems globally consume an increasing fraction of the total primary energy sources (TPES). Currently, in the USA, HVAC systems consume more than 35% of the country’s TPES and are expected to reach high fractions in several developing countries, particularly those in lower geographic latitudes, such as the Peoples Republic of China, India, Indonesia, the Philippines, and Brazil [
1,
2]. While the global TPES increased by 1.9% annually, the global electricity generation increased by 3.3%. The increased demand for A-C in both developed and developing countries is considered one of the primary contributors to this difference [
3]. In the USA, the average demand for electricity for residential space cooling has surpassed the demand for heating and all other domestic uses and averages more than 16% of the total annual residential electricity consumption in the country [
4]. The corresponding figure for the southern part of the USA is close to 30% [
5].
A glance at the global map proves that most of the earth’s population lives in tropical, subtropical, and temperate regions, where the high temperatures make A-C usage necessary for domestic comfort during the hot seasons and continuously drive the local electricity demand to higher levels [
3,
5]. The higher A-C use in residential, public, and commercial buildings has two significant effects on electric power demand [
2]:
High power demand peaks are undesirable for the electricity-generating industry because:
Less efficient generation units are brought in line, and electricity generation is more costly.
Grid instabilities may follow.
The companies that generate electricity (utilities in the USA) must maintain spare capacity to satisfy the peak power demand.
It must be noted that the impending higher temperatures caused by Global Climate Change (GCC) and the increasing reliance of our society on A-C for summertime comfort are expected to accelerate A-C usage both in the USA and globally and to create additional challenges for the electricity-generation industry [
6].
The electricity-voracious A-C systems account for a high fraction of the electric energy demand in buildings during the summertime when temperatures are high [
7]. At the same time, the solar irradiance also peaks (typically with a short time lag). Hence, a solution to the peak diurnal and seasonal electricity demand is to generate more electricity from solar energy. Generating more electric power locally from the abundant energy of the sun would also alleviate the strain on the central electricity generation and distribution systems in the regions where the A-C usage is growing. Solar power generated with photovoltaic (PV) systems is the most suitable method to locally generate electricity for commercial, public and residential buildings. The decreasing cost of PV systems in combination with manufacturing improvements indicates that, in the future, we will see significantly more electric energy generation from solar irradiance [
2,
8,
9]. The other abundant renewable energy source, wind energy, has already proven to be commercially viable in several states. Wind turbines are increasingly used to generate renewable power for small communities/towns as well as for larger electricity grids [
10,
11,
12,
13].
Several national and regional governments have promulgated regulations and directives for the reduction of CO
2 emissions in order to mitigate the impending Global Climate Change (GCC). These regulations call for the substitution of coal power plants with renewables, and some go as far as the substitution of all fossil fuel power plants. However, solar irradiance is periodically variable, and the wind velocity is intermittent. As a result, substituting fossil fuel power plants with renewable power generation units makes it necessary to develop significant energy storage infrastructure, which tends to be costly [
14,
15,
16].
The higher penetration of renewables in electricity grids causes a commensurate decrease in the power demand for the non-renewable electricity generating units during the early morning hours—a time period when the A-C energy consumption is low, and the irradiance is very close to its (flat) peak.
Figure 1 depicts the electric power demand in the San Antonio, Texas, area on a typical day in the summer. It is apparent that the demand exhibits a flat maximum in the afternoon hours when the temperature and A-C utilization are very high. The electric power demand in this area is currently satisfied by a combination of coal, natural gas, nuclear, solar, and wind power plants. The figure also depicts the power demand from the non-renewable energy sources if there was significant solar capacity addition in the area so that solar installations generated 10%, 20%, and 30% of the annual electric energy. In this case, the non-solar power units would have to reduce or altogether stop supplying power during the morning hours when the irradiance is high, and the A-C energy demand is still low, causing the total electric power demand to also be low. The higher penetration of the renewable PV-generated energy creates the so-called
duck curve [
17,
18]
, and places severe constraints on the base-load units, and, especially, on the nuclear power plants, which operate with Rankine cycles that are difficult to adjust in short timescales but do not emit CO
2, and are essential in the decarbonization of the electricity-generating sector [
2,
19,
20,
21].
The southern part of the USA, which is inhabited by more than 130 million people and has high A-C demand during the summer, is a prime example of the expected supply–demand mismatch. Zero Energy Buildings (ZEBs) are connected to the electricity grid and act as small, distributed, PV-generating units. The development of large numbers of ZEBs in a region has been proven to lead to a duck-curve-type electric power demand. The problems associated with such trends of demand are alleviated with the adoption and construction of Grid-Independent Buildings (GIBs). GIBs utilize distributed energy storage; they are not connected to the grid and do not affect the operation of the electric grid. A recent study on GIBs determined the solar panel area and the power rating that is needed as well as the energy storage (hydrogen) requirements for two buildings that are energy sufficient, located in Fort Worth TX and Duluth, MN [
22]. This and similar studies concluded that a high fraction of the electricity generated by the PV cells in the GIBs is dissipated during the storage-regeneration process. The study also concluded that the improvement of the efficiencies of the systems used for the generation and storage of energy has significant effects on the needed infrastructure.
A high fraction of the stored energy in GIBs is used for the operation of A-C systems during the evening and night-time hours. Mitigation of the high energy dissipation during these hours and significant improvements of the GIB operation may be achieved with the development of systems for thermal storage (in this case, it would be “coolness storage”). Essentially, these systems use the surplus of electricity during the morning hours to chill water, store the water in large, insulated tanks, and pump the chilled water in the GIBs to ensure domestic comfort. It must be noted that such thermal storage for cooling is common for large buildings and groups of buildings in the southern part of the USA and is primarily promoted to flatten the peak electric power demand during the late and hot afternoons in the summertime: several hotel clusters, universities, clusters of office buildings, and airports produce and store chilled water during the night and morning hours. The stored chilled water is made available to the buildings during the peak-demand hours [
2,
23]. While there is some exergy loss in these thermal (coolness) storage systems during the relatively short time of storage, this exergy loss is significantly lower than the alternative of using stored chemical (or electrochemical) energy for the continuous operation of the A-C systems. It must be noted that chilled water systems for air conditioning have been studied and developed for several years. Recent studies in this area include the use of [
24] and the application of nanofluids as the chilled coolant that would circulate in the buildings [
25]. The current study does not examine or advocate new chiller technology but determines the energy storage requirements for the use of such chillers in a cluster of two thousand buildings.
In order to facilitate the transition to renewable energy, it is very likely that GIB communities will be developed as clusters of smaller buildings that utilize larger and more efficient systems for energy generation and storage and take advantage of any economies of scale. In addition, larger communities of GIBs will be able to utilize wind turbines and PV arrays (a combination of solar and efficiently generated wind energy) and accordingly optimize their generation and storage facilities [
2,
14]. This paper aims at the introduction of a hybrid storage system (hydrogen and thermal) that fulfills the electric energy requirements of a community of two thousand (2000) homes in North Texas. This is a prime region for renewable energy source utilization because the annually averaged irradiance is approximately 230 W/m
2 and average wind velocities exceed 8.5 m/s. Electricity for this microgrid is generated by arrays of PV cells and a small number of wind turbines. Chilled water is produced when there is electric energy surplus; it is stored in insulated tanks and used to satisfy the cooling needs of the cluster of buildings. Hydrogen storage and fuel cells are utilized for all the other electricity needs of the buildings when the generated electric power is inadequate to satisfy the power demand of the 2000 buildings. The calculations reveal the characteristics of the two energy storage systems that would enable the cluster of the two thousand buildings to function independently of the electricity grid and only use renewable energy sources.
2. System Description
Thermal storage systems are complex and costly. For this reason, thermal storage systems have not been developed for individual households but for large buildings (hotels and commercial buildings) as well as clusters of larger buildings. For this study, a community of 2000 homes (the size of a small town) has been chosen in the North Texas area, an area rich in solar and wind resources. For the energy storage that is converted to electricity, a hydrogen system has been chosen. This choice was made because the region does not have any suitable geological formations for Pumped-Hydro Storage or Compressed-Air Energy Storage [
26,
27] and because battery storage is not suitable for the seasonal storage of energy—e.g., from winter and spring, when the winds are stronger, and there is a great deal of irradiance to the summertime, when A-C energy is needed.
Figure 1 depicts the schematic diagram with the main equipment and systems that would make this community grid-independent: an array of PV cells and a small number of wind turbines supply all the energy needs for the community.
Power controllers and a series of
Maximum Power Point Trackers (MPPT) are installed to ensure maximum electric power generation by the solar arrays. Depending on the hourly supply and demand for power, the generated power is suitably directed to the community of the buildings, to the refrigeration system (for chilled water production), or to the electrolysis system, which produces the hydrogen and stores it in pressurized tanks. The demand of the cluster of buildings has first priority; the refrigeration system has second priority in the allocation of power. If there is any remainder, the energy is stored in a hydrogen storage system. It must be noted that actual systems to be developed may have a number of chilled water tanks and hydrogen tanks strategically placed among the buildings of the community to optimize the overall operation of the system.
When there is not sufficient energy supply from the PV arrays and the wind turbines, the community’s demand for power is satisfied by a system of fuel cells that convert hydrogen to electricity. It must be noted that there are several types of fuel cells that may be used, including the solid oxide fuel cells that operate at higher temperatures [
28]. Information about the types and operation of the available types of fuel cells may be found in [
29] and information on their applications in [
27].
The refrigerator/chiller system operates and charges the chilled water tank during the hours in the morning, when the PV cells generate close to their maximum daily power and the A-C demand is lower. The water tank and the chilled water distribution system are well-insulated to minimize heat losses (actually “coolness losses”) to the surroundings. With this arrangement and distribution priorities, the refrigeration system almost always operates directly using the generated power of renewable energy sources. Thus, a great deal of the energy dissipation in the generation–storage–regeneration processes is avoided, the duck-curve phenomenon is minimized, and the hybrid storage system (hydrogen, chilled water) operates more efficiently than a single (hydrogen) storage system.
3. Governing Equations of the System
The energy inputs to the overall system of
Figure 2 are solar and wind. At any time period (0,
t), the electric energy generation from the PV arrays is given by the expression:
where the symbol
denotes the total irradiance—the sum of direct and diffuse irradiance—on the PV systems;
A is the total area of the PV panels;
ηTi is the efficiency of the PV cells during the time period
i; Δ
t is one hour, the timescale of the computations; and
n is the time period of the PV array operation, in hours. Since the timescale is one hour, when the insolation is measured in W/m
2, the total generated electricity is calculated in Wh.
The efficiency of the PV cells is not constant and depends (rather weakly) on the ambient temperature. The efficiency of commercial PV cells drops with increasing temperatures, typically by one percentage point (0.01) for every 4–8 °C ambient temperature rise above 25 °C. Thus, the efficiency of the PV cells may be modeled by Equation [
30]:
Typical yearly averaged values for the efficiency,
η25, are in the range 15–22% and for the sensitivity coefficient,
ksc, are in the range 0.001–0.005 °C
−1 [
26,
31]. In this study, the values
η25 = 20% and
ksc = 0.0020 were adopted for two reasons: (a) the larger number of buildings implies bigger systems and higher availability of capital, which allows the purchase of more efficient PV cells; and (b) the recent technological advances and trends in photovoltaics [
31] show that there are several types of PV cells in the market with efficiencies and sensitivity coefficients in these ranges.
Detailed tables on the hourly insolation and hourly temperature data for several locations in the North Texas region are available from the
National Solar Radiation Database [
32]. The five-year average data were computed from these databases to be used in the study. The averaging avoids the effects of large and weather-related temperature and insolation fluctuations—e.g., summer storms, dry spells, etc. The system of PV panels is stationary (this is typical of all the existing PV farms in the area). The PV panels face the southern direction and are positioned at an angle with the horizontal plane, 32°, which is approximately equal to the geographic latitude of the North Texas region [
2]. Thus, the total hourly insolation, which is incident on the PV panels and is generated by both direct and diffuse radiation, is computed from the data in the national database [
32].
For the wind energy contribution and the determination of the electric energy generated by the wind, turbines that have characteristics similar to those of the Vestas V120-2.2 turbines are envisioned. The choice of this type of wind turbine was made because of the following reasons:
They are medium-sized turbines and more suitable to supply energy to communities of buildings, where the small number of turbines used (0, 1, 2, or 3) is a parameter in the calculations.
Their rated velocity and other design parameters are a good fit for the wind characteristics in the region.
These turbines have a diameter
D = 120 m. Among the available tower heights, a tower with
H = 92 m was chosen, and this becomes the nacelle height used in the calculations. The cut-in velocity for the turbines is 3 m/s, the cut-out velocity is 20 m/s, and the rated velocity is 12 m/s, which implies that when the wind velocity is in the range 12 <
V < 20 m/s, the turbines generate the rated power of 2.2 MW. When the wind velocity is between the cut-in and the rated velocity, the power produced by the wind turbine is determined by the expression [
8,
33]:
where
is the electric power generated by a single wind turbine at a given hour,
i;
is the diameter of the wind turbine,
is the efficiency of the turbine–generator system,
is the air density, and
is the average wind velocity at the nacelle/tower height during the hour
i. The local wind velocity,
V, was determined from hourly data obtained from the databases of the National Oceanic and Atmospheric Administration [
34].
The timescale of all the computations is 1 h. During every hour, the electric energy demand of the community of buildings, EDi, is met either directly by the hourly energy generation of the wind and solar units or by the fuel cell system, which utilizes hydrogen storage. The energy demand of the refrigeration system is typically satisfied by the excess power generated by the combination of the PV array and wind turbine(s) during the early morning hours, when the A-C power demand is still low and solar irradiance is high. Thus, the refrigeration system directly utilizes any excess power generated to chill the needed quantity of water that would cool the buildings during the remainder of the 24 h period. Since heat losses are expected from the chilled water tank and the distribution system, the quantity of the chilled water is 10% more than the required amount for the cooling of the buildings. Effectively, it is stipulated for the calculations that the thermal storage system has a 10% heat leakage from the surroundings.
During all the hours of operation, when the hourly electric power generation from both the solar and wind systems is higher than the demand (the latter includes the energy used by the refrigerating system), the difference/surplus is converted by electrolysis to hydrogen energy and a new quantity of hydrogen is added to the hydrogen storage tank. During all hours, when the generation is less than the demand, the fuel cells consume some of the stored hydrogen to generate the deficit in demand–supply:
where
EPi is the energy generation during the hour
I,
EDi is the energy demand by the entire community, and
δESi is the change (surplus or deficit) of the quantity of the stored energy. At the end of the
ith hourly time period, the hydrogen energy storage level,
ES, becomes:
where
ηel is the efficiency of the electrolysis and
ηfc is the efficiency of the fuel cells. The efficiencies are used as parameters in the computations and are responsible for the energy dissipation in the storage–regeneration process.
The cooling season, which consists of the days when chilled water is produced and utilized to cool the community of the buildings, runs from 1 May to 15 October. To ensure system reliability at all times of the year, it was stipulated that the hydrogen storage tank must contain, at every hour of the year, enough energy to power the cluster of buildings and supply refrigeration power for a minimum of the following 240 h (ten days). This implies that the stored hydrogen energy level does not reach zero but always maintains a minimum quantity of hydrogen (and energy) to ensure the smooth operation of the microgrid. If the power generation systems fail or malfunction—e.g., after an extreme weather event, such as a severe summer storm, a tornado, or a winter polar vortex—the managers would have sufficient time for repairs in the system and/or to purchase additional hydrogen in the marketplace to ensure sufficient energy supply for the cluster [
35]. Actually, this is an advantage of using energy storage: bad weather events that cause local or total electricity grid disruptions are significantly mitigated utilizing the stored energy.
Solution Procedure
With the timescale of calculations chosen as 1 h, the governing equations yield a system of 8760 algebraic equations of the type of Equation (5). The solution is achieved by iteration using periodic conditions with a time period of one year. Thus, at the end of the year (hour 8760), the entire system must revert to its original state. Therefore, at hour 8760, the hydrogen storage system contains the same mass of hydrogen it had at the beginning of the year (hour 1 of the calculations). With the number of wind turbines fixed, the iteration yields the nominal rated power of the PV system and the area of the solar cells. The steps of the iteration are as follows:
A number of wind turbines (0, 1, 2, or 3) is stipulated for the supply of wind power. Based on this, the hourly wind power supply is computed for all the hours of the year.
An amount of stored energy in hydrogen ES0 at the beginning of the first hour is assumed, and the first trial for area A for the PV system is assumed. The trial values are recorded in a spreadsheet that also includes the following: (a) the hourly A-C demand; (b) the total hourly electric energy demand; (c) the energy supply from wind and solar; (d) the level of energy storage in hydrogen.
The stored energy in hydrogen at the end of the year, ES8760, is calculated and compared to the originally assumed value ES0. If ES0 < ES8760, additional energy generation is needed, and Aj is increased. If ES0 > ES8760, the PV cell area A is decreased.
Step 2 is repeated with the new value of Ai until ES0 = ES8760. This determines the PV rating and the PV cell area required, A, for the annual electricity generation.
With the area, A, determined, the correct value for ES0 is calculated in a second iteration using the minimum storage condition: on the hour when the storage level is at its minimum value, the entire system must have sufficient energy stored to satisfy the entire demand of the next 240 h (ten days), even when the two renewable energy sources generate no power.
The second part of the calculations entails the determination of the size (volume) of the chilled water tank(s). The refrigeration system cools the water—typically in the early morning hours—and the chilled water is stored in the tank(s) and is pumped in the buildings to supply “coolness” until the time when excess power is generated to be used in the chiller. Currently, there are several chilled water systems currently in operation and serve the cooling needs of hotels, office buildings, hospitals, universities, and airport terminals [
23,
25]. Because of their large scale, these cooling systems operate with more efficient refrigerator cycles (higher COPs) than systems in small buildings. Such systems are designed to reduce the peak electric power demand, they have been proven to be reliable and cost-effective, and they are often subsidized by the electricity-generating industry [
36,
37,
38].
The volume of the chilled water needed is calculated by the following expression:
where
Qday is the amount of heat to be removed daily from the cluster of buildings and includes the 10% heat leakage into the storage tank(s);
c is the specific heat of water, 4.184 kJ/(kgK);
ρ is the density of liquid water, 1000 kg/m
3; and Δ
T is the temperature difference between the chilled water and the warmer water return from the cluster of buildings. The latter is a system parameter typically in the range 10–15 K. For the calculations, a 12 °C temperature difference was stipulated, and the required capacity of the tank was determined from the maximum value of the daily heat transfer,
Qday.