Coupled Model of Heat and Power Flow in Unventilated PV/PCM Wall-Validation in a Component Scale

Abstract

The paper concerns the problem of the modeling of the thermal interaction between the phase change material (PCM) and photovoltaic (PV) panel, in the case of unventilated construction. The study aims to develop the numerical model of such a building element to support its proper future design under variable boundary conditions. The need for such a study comes from the realization of the research project which aims at developing a novel energy-activated thermal insulation composite system. Two different methods of PCM simulation using ESP-r software were compared. The model that was finally proposed was validated against experimental data, which proved its robustness. The MBE for the simulated and measured temperatures on the back of the PV panel did not exceed 2.0 °C and the maximum observed energy production difference was 4 Wh/m².

1. Introduction

In many studies, photovoltaic panel overheating was identified as a factor influencing the PV conversion process [1]. The effect of temperature on energy conversion performance is mainly visible under high solar irradiation, when the panels produce power close to the maximum nominal one. There are many studies on how to improve thermal performance and reduce the overheating effect, such as passive [2] and active ones [3,4]. One of the passive techniques for thermal stabilization of PV panels is to integrate the backside surface with phase change materials [5]. Such solutions were investigated in different configurations and the results are presented in the following papers, e.g., [6,7]. All the authors mentioned above consider PCM applications (in the form of composite plates or containers) in free-standing PV installations. However, the PCM is still effective in the case of ventilated BIPV [8,9]. The idea of façade-integrated PV presented and studied here seems to be more problematic because the PCM layer is limited to releasing stored energy during the day and is mainly cooled down during the night [10]. Nevertheless, experimental investigations proved that the application of inorganic PCM for a semi-transparent PV [11] and nanoparticle distributed PCM [12] can effectively decrease PV module temperature and increase its efficiency.

The system named En-ActivETICS (Energy Activated External Thermal Insulation Composite System), which was originally developed and further investigated, is presented in Figure 1. The concept of En-ActivETICS was investigated within the framework of the research project [13]. As can be seen, the PV panels are tightly glued to the polystyrene with a cement mortar, which considerably decreases the heat transfer on the backside of the panel. The PCM layer placed between the PV and the polystyrene plays the role of a thermal buffer with high latent heat capacity. The general idea is to substitute traditional cement plaster in the external thermal insulation composite system (ETICS) with flexible PV panels. Initial experimental analyses [14] revealed periodic overheating above the maximum exploitation temperature of 85 °C. This led to an improvement in the thermal inertia of the external layer by application of a PCM-cement composite. Finally, the developed En-ActivETICS is a multifunctional component characterized by power generation and latent heat storage. For further optimization of the system and performance prediction, it was necessary to analyze the system numerically. The main challenge was to investigate both phenomena (power generation and latent heat storage) in one coupled domain. The numerical simulations were considered to be one of the best techniques for investigating the En-ActivETICS in practice. The proposed model was initially calibrated based on short-term experiments. Finally, the results were compared with a double-repeated single-day experiment under sunny weather conditions.

The numerical tools needed for addressing the solution of the heat transfer with phase change can generally be subdivided into the following three different types [15]: fixed grid method [16], deformed grid method [17] and hybrid fixed/deformed method [18]. In building performance simulation programs, e.g., ESP-r, TRNSYS, or EnergyPlus, the most adequate and the easiest applicable solution/approach are fixed grid methods: enthalpy-based (EB), apparent heat capacity (AHC), or heat source (HS). The first implementation of a PCM model in TRNSYS using the EB method was done by [19] which was further developed and refined by [20,21,22]. The same approach was used in EnergyPlus by [23]. The apparent heat capacity method was compared with the heat source method [22,24], giving much better convergent results, and therefore it was originally implemented into ESP-r [25] and numerically validated [26]. The last integration of a latent heat storage model for Modelica using both EB and AHC methods was done by [27]. The comprehensive empirical validation and comparison of PCM modeling algorithms (mainly the EB method compared to the AHC method), commonly used in COMSOL, ESP-r, EnergyPlus and WUFI, were performed by [28]. In the EB method, the heat capacity is presented in terms of its integral form, H(T). The effective heat capacity (cp) is obtained as the derivative (dh/dT) of the enthalpy curves. The AHC method deals with heat capacity as a function of temperature within the temperature range of the phase transition. The RMSE values obtained for all PCM models by Wijesurija et al. were similar. Considering different photovoltaic and power flow models, from the simplest one to WATSUN-PV available in ESP-r, the authors decided to further develop a combined model in ESP-r.

In ESP-r, the heat capacity as a linear function of temperature is defined within subroutine special materials [29]. This approach was implemented for the first time to model power generation from building-integrated PV systems [30], evaporative surfaces, latent heat storage in phase change materials and finally smart insulation materials [31]. From a technical point of view, there are some limitations in the analysis of the results for multiple special materials interacting with each other. It means that the case of multi-special material structures such as PV-PCM components [32] cannot be directly investigated in the existing version of ESP-r. A possible alternative approach is to simulate latent heat storage by a definition of the effective heat capacity function as changeable heat capacity (CHC). In both the AHC and the CHC approaches, the heat capacity function is defined in the same form (direct solution method), including latent and sensible heat, and the change in these parameters affects the next time step of simulation (explicit scheme). The main goal of the present study was to investigate both AHC and CHC methods to analyze heat transfer with latent heat storage in building construction. Then, for the numerically validated CHC model, the complex PV-PCM structure was defined and numerically analyzed for specific conditions of the experiment to validate the proposed model.

The paper presents the first experimental validation of the coupled model of heat and power flow in an unventilated PV/PCM wall. The concept of such a specifically constructed wall was developed by the authors under a wide research grant. The novelty of the present work results from a new approach to coupled modeling of the thermal interactions of PCM and PV in the ESP-r software. To confirm the accuracy of the model calculations, a component prototype was built that allowed the validation of the proposed model.

2. Materials and Methods

In order to verify the technical concept and validate the numerical model of the described above En-ActivETICS, pilot tests were conducted. For this purpose, a small-scale wall component was made using the oriented strand board (OSB) supporting construction. The test panel consisted of thermal insulation covered with the 3 cm layer of PCM mortar and the flexible PV panel (Figure 1).

For the mock-up development, the thin-film CIGS (copper indium gallium selenide) flexible panel with 30 W peak was selected.

Based on preliminary analyses conducted previously, three types of paraffins were selected to effectively absorb excess heat from the PV panel. The selection was made in accordance with the weather data for the location of the experiment. It was concluded that due to high temperature fluctuations on the backside of the PV panel, three materials characterized by overlapping phase transition range should be applied: RT25HC, RT28HC and RT35HC [33]. The thermal conductivity of all three PCMs is at the level of 0.2 [W/mK]. The partial enthalpy at specific temperatures for all three materials are presented in Figure 2. Selected materials are pure organic paraffins that require further treatment to be applied in building construction. Thus, paraffin was initially encapsulated using high-conductivity material as a core-shell and then hand-mixed with the pre-prepared mortar. The paraffin mass content in the prepared granules was approximately 40%, and these were also added to mortar in equal mass proportions (1:1). This means that the weight of the pure paraffin in the PCM-mortar was approximately at the level of 20%.

3. Results and Discussions

3.1. Measurements

Measurements used for the numerical model validation were planned and conducted in such a way as to be adequate for future real-scale application of test panels as façade-mounted components. Thus, the mock-up was mounted vertically, south-oriented. To comprehensively analyze the performance of components, local climatic data was recorded during the tests. As the most important parameter influencing power generation is solar irradiance, it was measured directly on the surface of the PV panel, using a second class pyranometer LP02 Hukseflux. In addition, air temperature, wind direction and velocity were also monitored with a 1-min time step. Measurements were carried out for two selected days characterized by clear sky conditions between 9 a.m. and 6 p.m. The measured values of solar irradiance, air temperature, and wind velocity are presented in Figure 3.

In order to ensure the optimal work of PV panels, MPPT (maximum power point tracking) technology was applied to the charge controller, which served two purposes. It optimized the current parameters for battery charging but also transferred the current to the receiver—LED lamps. Moreover, for the panel performance assessment and its comparison with the simulation results a Nemo D4-DC power meter for monitoring DC power supply with the accuracy of class 1 was used. The last parameter measured that was used for model validation was the temperature on the back side of the PV panel (between PV and PCM). It was measured by three PT-1000 sensors located in the central part of the panel. The accuracy of the sensor was ±0.5 °C. The schematic representation of the experimental system is presented in Figure 4.

Measured values of the power generated by PV and temperature on its backside were presented in Figure 5. It can be observed that, despite slightly higher irradiance recorded during the second day of the measurements, the power generation was higher during the first day. It should also be noted, based on the data presented in Figure 3b, that due to higher wind velocity, the temperature on the back side of the PV panel decreased, which resulted in an increase in the efficiency of the PV panel. Observation of such phenomena, the positive influence of temperature on power generation, confirmed the need for the development of the temperature control.

3.2. Numerical Model

The challenge of the numerical simulation of the system under investigation is the simultaneous consideration of mutually affected temperature dependence of PV and PCM, and its additional heat transfer due to power generation and phase transition, respectively. Moreover, the proper numerical model of such a system should include in the calculation procedure the influence of rapidly changing external environmental conditions affecting convective and radiation heat transfer coefficients.

The selected PV model, among the three available in the ESP-r, was the WATSUN-PV model that allows the most advanced consideration of the influence of the temperature on the power generation. The PV cell temperature is involved in the calculation of the short-circuit current (Equation (1)) and open-circuit voltage (Equation (2)). Finally, the power generated by PV is calculated using these two calculated electrical characteristics (Equation (3)) [34].

$$I_{sc}=I_{sc,ref}\frac{E_{T,eff}}{E_{T,ref}}[1+\alpha (T_{cell}-T_{cell,ref})]$$

(1)

$$V_{oc}=V_{oc,ref}\left[1-\gamma \left(T_{cell}-T_{cell,ref}\right)\right]·max\left\{\begin{array}{c}0\\ 1+\beta ·ln\left(\frac{E_{T,eff}}{E_{T,ref}}\right)\end{array}\right\}$$

(2)

$$P_{mp}=I_{mp,ref}·V_{mp,ref}\left(\frac{I_{sc}·V_{oc}}{I_{sc,ref}·V_{oc,ref}}\right)$$

(3)

The most important electrical and thermal parameters of the tested PV panel that are also used in simulation are given in

Table 1. Main electrical parameters of the tested PV panel.

Parameter	Unit	Value
Nominal power	[W]	30
Voltage at nominal power	[V]	34
Current at nominal power	[A]	0.88
Open circuit voltage	[V]	46
Short circuit current	[A]	0.97

and

Table 2. Thermal characteristics of the PV panel.

Parameter	Unit	Value
Temperature coefficient Voc	[%/°C]	−0.3
Temperature coefficient Isc	[%/°C]	0.01
Temperature coefficient Pmpp	[%/°C]	−0.35

, respectively.

Due to the fact that PV panel temperature is strongly affected by external environmental conditions, heat exchange processes on its outer surface were defined including time-dependent convection, short- and long-wave radiation (Equation (4)) [35].

$${\epsilon }_n\sigma \left[F_{s-g}\left(T{\left(x_L,t\right)}^4-T_g^4\right)+F_{s-sky}\left(T{\left(x_L,t\right)}^4-T_{sky}^4\right)\right]+h_{ce}\left[T\left(x_L,t\right)-T_e\right]+q_{sol}{=-\lambda \frac{\partial T\left(x,t\right)}{\partial x}|}_{x=x_L}$$

(4)

Furthermore, the influence of the additional heat accumulation in the PCM layer was investigated in two ways, by:

• apparent heat capacity (AHC) method using special material subroutine;
• changeable heat capacity (CHC) method using non-linear thermal properties subroutine.

The one-dimensional transient heat conduction using the AHC method is defined as (Equation (5)):

$$\frac{{\partial }^{2}T}{\partial x^2}=\frac{1}{\alpha }\frac{\partial T}{\partial t}+\frac{1}{\lambda }\rho \frac{\partial L}{\partial t}$$

(5)

Here, latent heat is defined as an integral from effective heat capacity Equation (6)):

$$L=\underset{C_s}{\overset{C_l}{{\displaystyle \int }}}{C}_{eff}\left(T\right)dT.$$

(6)

On the other hand, using the CHC method, heat conduction transfer in the PCM layer is described as (Equation (7)):

$$\frac{{\partial }^{2}T}{\partial x^2}=\frac{1}{\alpha }\frac{\partial T}{\partial t}$$

(7)

Where variation of heat capacity with temperature is included in thermal diffusivity of the material:

$$\alpha =\frac{\lambda }{\rho c\left(T\right)}$$

(8)

It has to be underlined that the heat capacity value used in the CHC method is the sum of the estimated value of effective heat capacity and specific heat of the material.

In both methods, there is a need to define the function of heat capacity vs. temperature in the phase transition range. For this purpose, values of partial enthalpy (Figure 2) were summed, taking into account the percentage of the specific paraffin per unit kg. Obtained values were approximated by the linear function of latent heat vs. temperature, as a best fit. Even though both methods (AHC and CHC) give the possibility to deploy higher-order functions, in this specific case the best approximation was obtained for the linear function. Furthermore, to obtain the effective heat capacity function, defined latent heat function was integrated over the temperature and the constant value was the result of those calculations (horizontal line in Figure 6).

Main assumptions for the simulation:

• one-dimensional heat transfer,
• convective heat transfer is wind induced,
• south orientation of the component,
• constant value of thermal conductivity and density,
• 1-min step of calculation,
• hourly average values of weather parameters (based on 1-min-step measurements),
• location: city of Lodz (51°46′ N, 19° 27′ E, Poland, Central Europe).

Analysis of the temperature on the back side of the PV panel, obtained using two methods of PCM definition, showed that the results are coherent (Figure 7). The biggest differences were observed at the beginning of the day, at the level of approximately 0.5 °C, which is at the level of the accuracy of the sensors. The correlation coefficient calculated for both models was equal to 0.99 for both days and the MBE (mean bias error) was 0.11 and 0.19 for the first and second days of the analysis, respectively.

3.3. Model Validation

In order to validate the proposed model of the PV/PCM component, two types of results were compared: measured and calculated values of temperature on the backside of the PV panel and values of the power generated by the PV. All the results presented in this section were obtained using the CHC method for latent heat accumulation.

First, good agreement was obtained in terms of temperature fluctuations during the two selected days (Figure 8). The largest observed differences between the temperatures obtained from calculations and measurement were: 2.7 °C and 4.6 °C for the first and second days of measurement, respectively. However, these values occurred mainly at the beginning and at the end of the analyzed periods of time, and the MBE does not exceed 1.3 °C and 2.0 °C for the first and second days of the measurements, respectively. The discrepancy in the results in the morning hours could be caused by an unprecise definition of solar irradiance before measurement started. The measurements of solar irradiance on the PV panel surface were started along with the start of the temperature measurements. Thermal calculations for the earlier hours were done for the values of diffuse and global solar radiation. Furthermore, at night, a sudden drop in solar irradiance can be observed at about 4 p.m. (Figure 3a) which resulted in a fast decrease in measured temperature. Due to hourlyaveraged values used in ESP-r, this sudden decrease in solar irradiance value was not reflected in the simulation results. However, the correlation coefficient for the measured and calculated data was at the level of 0.99 for both days.

Based on the results presented in Figure 9, it can be observed that the proposed model also allows for a good prediction of the power generation. Although the calculated temperatures were overestimated compared to the measured values, this phenomenon cannot be observed in terms of energy production (

Table 3. Energy produced by PV [Wh/m²].

Source of Data	Day 1	Day 2
Measurement	87	88
Simulation	85	92

). Calculated values of total energy production by PV are almost equal to the measured ones, but for the first day the simulated value is slightly lower while for the second day, it is slightly higher. Such phenomena can be the result of the occurrence of instantaneous peaks of solar irradiance during the measurements and hourly averaged values used in calculations.

4. Conclusions

In the paper, a numerical investigation of the novel active façade system was presented. The proposed model for the EnActiv-ETICS simulation included:

• temperature-dependent power generation by PV
• latent heat capacity and its thermal influence on the PV performance
• influence of the variable weather conditions affecting the thermal performance of the system (wind-dependent surface convection coefficient and radiation coefficients)

Moreover, two methods of PCM definition were analyzed—AHC and CHC, which revealed that those methods give comparable results and can be used interchangeably. Finally, the results obtained for the simulation of the whole system were validated against the measurement data, which proved the model is robust and can be used for further up-scaled investigation of the En-ActivETICS application. It has to be underlined that the model was validated only for clear-sky conditions. However, since the main practical application of such a model is support in the system design process to avoid excessive PV overheating, consideration of extreme sunny days is justified. The model was proposed and is going to be used for further development of En-ActivETICS in terms of adjustment of phase transition temperature, to customize the system to the local climatic conditions. As the main purpose of the PCM application on the backside of the PV panel is to limit overheating, simulations will be performed under clear sky conditions.