1. Introduction
The Concentrator Photovoltaic (CPV) systems adopt an optics to focus solar radiation onto Triple-Junction (TJ) cells with a consequent increase in the electrical performances of the CPV system and the TJ cell temperatures. The Concentrator Photovoltaic and Thermal (CPV/T) systems allow instead to produce both electrical and thermal energy [
1]. Hence, the CPV/T systems have a high potential both in residential and industrial applications. For example, the thermal and electrical performances of a CPV/T cogeneration system applied to a textile industry, are analyzed in [
2]. A CPV/T system is used for a residential user in [
3].
In the literature, there is not a standard configuration of a CPV/T system capable to obtain both electrical and thermal energy, but there are several solutions, also depending on the optics [
4]. The performances of a parabolic concentrator are studied in [
5] in electrical and thermal terms. A CPV/T system which uses a Fresnel optics is studied in [
6].
The electrical and thermal performances of a CPV/T system depend above all on the TJ cell temperatures. A review of the different methodologies adopted to calculate the TJ cell temperature in high-concentration systems is reported in [
7]. There are methods that use direct measurements on the module and indirect methods based on atmospheric parameters. The study shows which the methods that adopt direct measurements are the best, but the methods based on atmospheric parameters are useful when direct measurements are not feasible. A Random Forest model capable to calculate the TJ cells temperature in a CPV system, is presented in [
8]. The TJ cell temperature has been evaluated for two typologies of TJ cells, referring to different concentration factor values and environmental conditions. Hence, in the literature, many studies show that the solar concentration causes an increase in the electrical performances of the CPV system and of the TJ cell temperatures [
9]. The temperature of TJ cells under concentration affects the cooling fluid temperature of a CPV/T system. Hence, by varying the mass flow-rate of the cooling fluid, it is possible to obtain different fluid temperatures, and consequently the thermal energy can be supplied in many thermal processes [
10]. A line-focus CPV/T system that adopts an active cooling is presented in [
11]. A concentration factor optimized value capable to give a fluid outlet temperature that matches the thermal and cooling requirements, decreasing the CPV/T system size, is determined in [
12] in different working conditions. The dynamic model of a CPV/T system is studied in [
13] to calculate the cooling fluid temperature.
There are not papers in the literature that determine, in each operation condition, all levels of temperature of a CPV/T system when it is adopted to supply thermal energy to a user during the year. Hence, it is first of all fundamental to define the temperature levels reached by the CPV/T systems to understand if this typology of system is able to meet, totally or partially, the residential user thermal needs during the year. Therefore, the main purpose in this paper is the accurate determination of the temperature levels reached in a line-focus CPV/T system, when it is used to satisfy the thermal energy demands of a residential user (heating, cooling, domestic hot water). For this purpose, in this paper a further in-depth of the model studied in [
14] is presented, determining an accurate tool capable to calculate the cooling fluid temperatures of the CPV/T system, the temperature stratification of the thermal tank and the temperatures of the user for different temporal scenarios. First, an experimental apparatus, built in the Laboratory of Applied Thermodynamics of the University of Salerno (Italy), can determine the cooling fluid temperature at the CPV/T system outlet according to same operation conditions of the theoretical model in terms of TJ cell temperature, Direct Normal Irradiation (DNI), environmental temperature, water mass flow-rate and temporal period. The good theoretical–experimental comparison in terms of the temperature of the working fluid at the CPV/T system outlet, is a basic aspect to calculate theoretically, by means of the TRNSYS 16 software [
15], the other levels of temperature of the CPV/T system for different temporal scenarios (hourly, weekly, monthly and yearly), such as the temperature stratification in the thermal tank and the temperatures of the user. Hence, it is possible to establish if a CPV/T system is able to satisfy the thermal loads of a residential user, or a thermal energy integration is necessary in some periods of the year.
2. Description of the Linear Focus CPV/T System
The experimental CPV/T system, realized in the Laboratory of Applied Thermodynamics of the University of Salerno (Italy), presents a linear optics that focuses the solar radiation on a tube where the Triple-Junction (TJ) cells are arranged in series and the cooling fluid flows (
Figure 1); the TJ cells are oriented downwards in the direction of the reflective surface. The number of cells depends on the electrical load. The optics is reflective and is realized by parabolic trough concentrator. The solar cells consist of InGaP/InGaAs/Ge and have an area of 1.0 cm
2 (
Table 1).
The experimental system also adopts a tracker capable of focusing the maximum solar radiation on the TJ cells. The freedom degrees of the system allow its movement in the north-south and east-west directions, and to modify the focal length in order to always have the maximum concentration. The first two freedom degrees allow the solar tracking by means of a rotation both in the horizontal plane to follow the sun in the azimuth direction and in the vertical plane to follow the sun in the zenithal direction. Moreover, the TJ solar cells are located at a variable distance from the primary optics, and then the focal length is considered as a further degree of freedom in the experimental tests. Hence, the parabolic optics is moved on a vertical axis and its distance is modified compared to the cells; the solar radiation that reaches the TJ cells and the concentration factor (C) can be then varied. A C value of about 100 is obtainable by the experimental CPV/T system corresponding to an optimum focal length.
A pyrheliometer (accuracy of 2%) is used to measure the solar radiation. PT100 thermo-resistances (accuracy of ±0.2 K) are adopted to measure the TJ cell, working fluid and environmental temperatures. In particular, in addition to the environmental temperature, the temperature of five TJ cells in different points of the tube and of the cooling fluid at the inlet and outlet of the tube subjected to the solar radiation, have been measured. All measures have been monitored by a data logger (accuracy 2%).
In the modeling, a cooling circuit is considered to preserve the TJ cells’ electric efficiency [
16] and to produce thermal energy (
Figure 2); a water tank is necessary to store the thermal energy. A thermostat that controls an automatic valve is adopted, and the cooling fluid, once it has reached the set-point temperature, is sent to the tank, and the cold fluid enters again the circuit. A CPV/T system with modules of sixty cells has been used in the model to match the residential user energy needs.
3. Modeling of the CPV/T System
A linear focus CPV/T system can satisfy, totally or partially, the electrical and thermal loads of a residential user [
17]. The evaluation of the cooling fluid temperatures is fundamental to understanding if a CPV/T system is able to match the typical thermal demands of a residential user (heating, cooling and Domestic Hot Water (DHW)).
Hence, the dynamic behavior of a linear focus CPV/T system is modeled in this paper by means of TRNSYS software [
15]. It can simulate in transient regime a system that presents a modular structure linking different subprograms; each subprogram generates an input for the next module. Therefore, the CPV/T system is modeled in TRNSYS by a built-in components library, considering several components such as mixers, pumps, diverters and valves. [
15].
DNI and TJ cell temperature represent the model input data and have been included in TRNSYS as generated functions, respectively evaluated in [
18] and experimentally in [
3,
4,
5,
6,
7,
8], as well as the energy needs of the residential user. On the contrary, the operation of CPV/T system, water tank and control strategy are modelled by means of the TRNSYS modules [
15], as shown in
Figure 3 and
Figure 4.
The thermal model of the CPV/T system considers the link between the water tank and the residential user demands adopting a proper control. The cooling fluid flows by the CPV/T system (
Figure 2) to the thermal tank, when the set-point temperature is reached: 50 °C (DHW), 60 °C (heating) and 90 °C (solar cooling). The cold fluid returns to the CPV/T system, and the hot fluid in the upper part of the tank can be used to satisfy the thermal needs of the user; an auxiliary boiler is used, if necessary.
Corresponding to every time step, the fluid temperature values at inlet and at the tank bottom are fixed, while the temperature of the fluid that flows by the CPV/T module to the tank is evaluated by means of the model. The TRNSYS module [
15] evaluates, for every time step, the fluid temperature and, operating together with the tank module, sends it to the user once it has reached the temperature value able to satisfy, according to the control system, the thermal demands of the residential user. Hence, the thermal tank model by means of the Type 4 module of TRNSYS, is also considered. A multi-node model is adopted to study the tank stratification [
19]. The tank has been subdivided in twenty nodes, spaced from each other by 0.18 m, and the hypothesis of perfect diffusion is considered.
The integrated TRNSYS model also presents a diverter, a pump and a mixer that link all the components of the CPV/T system and ensure its operation according to the control system (
Figure 4). In the CPV/T system cooling circuit, the pump, which presents an efficiency equal to 0.7, allows to cool the TJ cells and to recover thermal energy. Moreover, a two-way valve is also used at the CPV/T system outlet. An Absorption Heat Pump (COP = 0.9) is considered to satisfy the cooling load. Other fundamental parameters of the model have been defined: global heat transfer coefficient (2.1 W/K), CPV/T system inlet temperature (15 °C), boiler temperature difference (6 K), heat loss coefficient of the tank (8.0 × 10
−3 W/m
2K), etc. The capacity of the tank considered is 4500 L; the height and diameter of the tank are respectively equal to 1.5 and 0.5 m. The internal and external diameters of the tube are respectively equal to 32 and 35 mm, the fluid speed is 0.38 m/s; the volumetric flow-rate in the circuit is 1100 L/h.
Hence, the integrated model evaluates, in all the operation conditions and what was once known the TJ cell temperature, the cooling fluid temperature of the CPV/T system, the temperatures stratification in the tank and the temperatures of the user. The thermal model in TRNSYS of the CPV/T system adopts as an input the TJ cell temperature values obtained experimentally in [
3,
4,
5,
6,
7,
8].
The thermal energy obtained corresponds to the solar radiation incident on the TJ cells not converted into electric energy. The electrical production of a CPV system depends on DNI, concentration factor, optical efficiency and TJ cell temperature. The optical performances significantly affect the energy efficiency of a CPV system. In fact, only a well-sized optical system can adequately concentrate the solar radiation on the TJ cells ensuring a high electric producibility [
20]. The geometrical concentration factor (C
geo) is equal to the ratio between solar concentrator area (
) and TJ cell area (
)
and results constant once fixed the optics dimensions. According to the typology of optics, not all the power incident on the concentrator reaches the TJ cell, due to several losses. Hence, a more accurate measurement is given by the optical concentration factor (C
opt), defined as the ratio between the solar radiation concentrated on the TJ cell (I
c) and the DNI that represents the incident power flow on the optical system:
C
opt depends only on the system optical performances and not on the TJ cell electrical performances. The relationship between the two different definitions of concentration factor is the following
where
is the system optical efficiency equal to the ratio between the incident powers, respectively, on receiver and concentrator. The possibility of the experimental CPV plant varying the distance between optics and the TJ cell allows one to experimentally evaluate the optimal distance and the performances in the not focused positions.
Once the temporal level (hourly, daily, monthly) of the DNI is defined, the TJ cell electric energy is equal to [
21].
where A
c is the cell area, η
opt the optical efficiency [
21] and η
c the cell efficiency equal to:
The values of σ
t (temperature coefficient), T
ref (reference temperature) and η
ref (reference efficiency) are reported in
Table 1 according to the TJ cell manufacturer indications [
22].
Therefore, referring to the CPV system constituted by a variable number of cells subdivided in several modules, the CPV system electrical energy is calculated in this way
where n
c is the number of cells considered, η
mod is the module efficiency that until 100 cells is equal to 0.95 [
4], and η
inv is the inverter efficiency.
As said above, the thermal energy obtained by the TJ cells corresponds to radiation incident on the cells not converted into electric energy:
The CPV/T system electric efficiency (η
e,CPVT) depends on the TJ cells and module efficiencies
where p
par is a loss factor depending on the solar radiation and linked to parasitic power consumption for tracking motors and coolant pump. It is assumed to be 2.3% of the intercepted radiation power [
23].
The solar radiation incident on the TJ cell causes its heating, but also thermal energy losses due to radiative and convective transfer heat.
where ε
c (0.85) is the cell emissivity [
23]. The actual thermal energy is equal to the difference between total thermal energy and radiative and convective losses. Hence, considering the global thermal power and the TJ cell temperature values, the cooling fluid temperature in the CPV/T system is determinable by the equation.
where the values of the mass flow-rate and specific heat of the fluid are fixed in the TRNSYS module.
5. Conclusions
In this paper, the performances of a line-focus CPV/T system applied to a residential user have been studied. An integrated model has been realized in TRNSYS, where DNI, TJ cell temperature and the thermal needs of a residential user are the input data. Different temporal scenarios have been considered (hourly, weekly, monthly, yearly) to study the thermal performances of the CPV/T system during the year. The model results have been obtained in terms of the cooling fluid temperatures of the CPV/T system, temperature stratification in the tank in winter and in summer, and the temperatures of user.
In order to verify the goodness of the theoretical results obtained by the model, first of all a comparison between the results of the model in terms of the outlet temperature of the working fluid that flows in the CPV/T system and the same temperature, experimentally obtained in in the same working condition, has been realized. For example, on a sunny day, related to an average value of DNI of about 900 W/m2, a deviation from the theoretical and experimental results in terms of the percentage relative error varies, in the same operation conditions, by between about 0.5% and 5%.
The goodness of the theoretical–experimental comparison has represented a fundamental point to calculate theoretically, by means of the TRNSYS software, the temperature stratification in the thermal tank and the temperatures of the user. The temperature stratification in the tank of the CPV/T system, as a function of the height of the tank, has been obtained. Related to the winter season, the cloudy days determine a low thermal level with fluid temperature values variable between 28 and 56 °C according to the height; hence, the energy demands are matched by the boiler. A good stratification has instead been noted for the summer season, with temperature values variable between about 40 and 90 °C, and a very low integration is necessary.
In the winter season, the average TJ cell temperature is about 40 °C, while in summer its value is about 80 °C. The difference between the average values of the TJ cell temperature during hours of light and not during hours of light, can increase by up to 20 K.
Moreover, the TJ cell temperature during the hours of light, the average temperature of the tank and the temperatures of the user, have been also compared. From April to October, the tank average temperature is about 10 K higher than the temperature required by the fluid sent to the residential user and, generally, integration is not necessary. The situation is different in winter, where thermal integration by means of an auxiliary boiler is often necessary, because there is not a continuous energy contribution by the CPV/T system.
Finally, the TJ cell, cooling fluid, user and tank temperatures have been compared hourly, weekly, monthly and yearly to verify if a CPV/T system is able to satisfy the thermal loads of a residential user, or, if necessary, a thermal energy integration in some periods of the year when the TJ cell temperature is lower than the set-points fixed to satisfy the thermal loads. It has been verified that the CPV/T system covers a large part of the thermal demands of the residential user during the year; the thermal energy coverage is limited only in the winter months.